**Meet the editor**

Ricardo Albarracín Sánchez received his BSc, MSc and PhD degrees in Electrical Engineering, respectively, in 2008, 2010 and 2014 from the Universidad Carlos III de Madrid (UC3M), Spain. Currently, he is an assistant professor at the Senior Technical School of Engineering and Industrial Design (ETSIDI) at the Universidad Politécnica de Madrid (UPM). He is a member of the re-

search group Networks and Installations at Low Voltage and High Voltage (RIBAT) and an assistant to the Director for International Mobility (Erasmus+ School coordinator). His main research interest areas are electrical insulation, partial discharges, condition monitoring, UHF sensors, nanodielectrics, power transformers and renewable energy.

Contents

**Preface VII**

**Section 1 Insulation Systems Modelling for Power Transformers 1**

Carrascal, Carlos Renedo and Fernando Delgado

Chapter 2 **Thermal Modelling of Electrical Insulation System in Power**

Chapter 3 **Modeling and Simulation of Rotating Machine Windings Fed**

**Section 2 Environmentally Friendly Insulation Gases as Alternatives to**

Chapter 5 **Typical Internal Defects of Gas-Insulated Switchgear and Partial**

Fuping Zeng, Ju Tang, Xiaoxing Zhang, Siyuan Zhou and Cheng Pan

**by High-Power Frequency Converters for**

Cristina Fernández-Diego, Inmaculada Fernández, Felix Ortiz, Isidro

Agustín Santisteban, Fernando Delgado, Alfredo Ortiz, Carlos J.

Fermin P. Espino Cortes, Pablo Gomez and Mohammed Khalil

Chapter 1 **Assessment of Dielectric Paper Degradation through**

**Mechanical Characterisation 3**

**Transformers 31**

Renedo and Felix Ortiz

**Insulation Design 51**

**Sulfur Hexafluoride Gas 77**

**Environmental Protection 79**

**Discharge Characteristics 103**

Chapter 4 **Development Prospect of Gas Insulation Based on**

Hussain

Dengming Xiao

## Contents

#### **Preface XI**


Fuping Zeng, Ju Tang, Xiaoxing Zhang, Siyuan Zhou and Cheng Pan


Preface

DPI2015-71219-C2-2-R).

The reliability of power grids and their electrical assets is crucial to avoid discontinuity of the electrical supply and breakdowns. To prevent those non-desirable scenarios, it is neces‐ sary to carry out a proper maintenance of electrical insulation systems. The advances in computing are allowing the implementation of models that behave as real systems. This book provides the reader with models for electrical insulation evaluation of power trans‐ formers, power electronics, voltage sensors and power generators and proposes environ‐

The editor would like to acknowledge the authors for their contributions. In addition, the editor would like to thank the Spanish Ministry of Economy and Competitiveness (project

Dept. of Electrical, Electronic and Automation Engineering and Applied Physics

**Prof. Ricardo Albarracín Sánchez**

Madrid, Spain

E.T.S. Ingeniería y Diseño Industrial (ETSIDI) Universidad Politécnica de Madrid (UPM)

mentally friendly insulation gases as alternatives to sulphur hexafluoride gas.


## Preface

**Section 3 Insulation Weaknessess Modelling for Electrical Devices Used**

Chapter 7 **Simulation and Optimization of Electrical Insulation in Power Quality Monitoring Sensors Applied in the**

Rezende Cano and Joao Batista Rosolem

**Section 4 Insulation Aging Modelling of Power Generators 173**

Chapter 8 **Generator Insulation-Aging On-Line Monitoring Technique Based on Fiber Optic Detecting Technology 175**

Sender Rocha dos Santos, Rodrigo Peres, Wagner Francisco

**in Smart Grids 127**

**Medium-Voltage 151**

Mona Ghassemi

**VI** Contents

Peter Kung

Chapter 6 **Electrical Insulation Weaknesses in Wide Bandgap Devices 129**

> The reliability of power grids and their electrical assets is crucial to avoid discontinuity of the electrical supply and breakdowns. To prevent those non-desirable scenarios, it is neces‐ sary to carry out a proper maintenance of electrical insulation systems. The advances in computing are allowing the implementation of models that behave as real systems. This book provides the reader with models for electrical insulation evaluation of power trans‐ formers, power electronics, voltage sensors and power generators and proposes environ‐ mentally friendly insulation gases as alternatives to sulphur hexafluoride gas.

> The editor would like to acknowledge the authors for their contributions. In addition, the editor would like to thank the Spanish Ministry of Economy and Competitiveness (project DPI2015-71219-C2-2-R).

> > **Prof. Ricardo Albarracín Sánchez** Dept. of Electrical, Electronic and Automation Engineering and Applied Physics E.T.S. Ingeniería y Diseño Industrial (ETSIDI) Universidad Politécnica de Madrid (UPM) Madrid, Spain

**Section 1**

**Insulation Systems Modelling for Power**

**Transformers**

**Insulation Systems Modelling for Power Transformers**

**Chapter 1**

Provisional chapter

**Assessment of Dielectric Paper Degradation through**

DOI: 10.5772/intechopen.77972

Power transformers life is limited fundamentally by the insulation paper state, which can be analysed through different techniques such as furanic compound concentration, dissolved gases, methanol concentration, Fourier transform infrared spectroscopy, X-ray diffraction, scanning electron microscope, refractive index of cellulose fibres, degree of polymerisation or tensile strength. The two last techniques provide the best way to evaluate mechanical resistance of insulation paper. This chapter describes briefly the most remarkable studies about post-mortem assessment and thermal ageing tests in which mechanical properties are some of the characteristics evaluated to determine paper degradation. This work also gathers the main relationships developed until now to relate different by-products generated during transformer operation with loss of paper mechanical properties. Finally, this chapter defines the future approaches, which could be used to

Keywords: dielectric paper, insulation oil, tensile strength, post-mortem, thermal ageing

Since the nineteenth century, the use of alternating current (AC) against direct current (DC) was imposed. The machine used for increasing or reducing of AC voltage is the transformer, which has allowed the development of the power market, making possible the electricity transport over long distances thanks the reduction of Joule losses during high-voltage (HV)

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Assessment of Dielectric Paper Degradation through

**Mechanical Characterisation**

Mechanical Characterisation

Fernando Delgado

Fernando Delgado

Abstract

test

1. Introduction

Cristina Fernández-Diego, Inmaculada Fernández, Felix Ortiz, Isidro Carrascal, Carlos Renedo and

Cristina Fernández-Diego, Inmaculada Fernández, Felix Ortiz, Isidro Carrascal, Carlos Renedo and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77972

study paper degradation.

#### **Assessment of Dielectric Paper Degradation through Mechanical Characterisation** Assessment of Dielectric Paper Degradation through Mechanical Characterisation

DOI: 10.5772/intechopen.77972

Cristina Fernández-Diego, Inmaculada Fernández, Felix Ortiz, Isidro Carrascal, Carlos Renedo and Fernando Delgado Cristina Fernández-Diego, Inmaculada Fernández, Felix Ortiz, Isidro Carrascal, Carlos Renedo and Fernando Delgado

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.77972

#### Abstract

Power transformers life is limited fundamentally by the insulation paper state, which can be analysed through different techniques such as furanic compound concentration, dissolved gases, methanol concentration, Fourier transform infrared spectroscopy, X-ray diffraction, scanning electron microscope, refractive index of cellulose fibres, degree of polymerisation or tensile strength. The two last techniques provide the best way to evaluate mechanical resistance of insulation paper. This chapter describes briefly the most remarkable studies about post-mortem assessment and thermal ageing tests in which mechanical properties are some of the characteristics evaluated to determine paper degradation. This work also gathers the main relationships developed until now to relate different by-products generated during transformer operation with loss of paper mechanical properties. Finally, this chapter defines the future approaches, which could be used to study paper degradation.

Keywords: dielectric paper, insulation oil, tensile strength, post-mortem, thermal ageing test

#### 1. Introduction

Since the nineteenth century, the use of alternating current (AC) against direct current (DC) was imposed. The machine used for increasing or reducing of AC voltage is the transformer, which has allowed the development of the power market, making possible the electricity transport over long distances thanks the reduction of Joule losses during high-voltage (HV)

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

transport. Electrical insulation and cooling systems are critical parts of electric power transformers during their operation [1].

Transformer losses generate heat, which produces an increase in temperature and an efficiency decrease. Once a power transformer starts its operation, heat begins to be produced, which origins a progressive increase of the temperature. This increase continues until permanent regime conditions are reached. The temperature rise above the service conditions results in an accelerated degradation of the insulating materials. Additionally, insulation systems of oilfilled transformers are subjected to repeated lightning impulses, which brings potential risk to the insulation system, being the liquid/solid interface the weak link. Assessment of insulation condition can be obtained by partial discharge (PD) monitoring [2]. For instance, some authors [3–8] have analysed the effect of oil and pressboard ageing (electrical and/or thermal) on the characteristic of PD from inception to flashover, surface discharge inception voltage (SDIV) variation, creepage discharge inception voltage (CDIV) or creepage discharge flashover voltage (CDFV) of oil/solid insulation specimens with different ageing degrees. Other authors have studied the effect of polarity on the accumulation of charges at the oil-solid interface [9], the accumulative effect of repeated lightning impulses and its damage mechanism [10], the electrical deterioration caused by PD under long-term AC voltage [11] or the performance of alternative liquids in comparison with mineral oil [12].

On the other hand, thermal ageing of insulation system in power transformers can favour the initiation of short-circuit forces, which can end up in a permanent deformation or failure [13].

> insulation would imply re-manufacturing the transformer almost completely, which is not practical. Consequently, it can be concluded that the life of a power transformer is limited fundamentally by the insulation paper state, which highlights the enormous importance of

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

5

Not only solid insulation components suffer continuous ageing, but also the dielectric oil. During transformers operation, the insulation system degrades generating a wide range of by-products such as furanic compounds, water, CO2, CO, low and high molecular weight acids, and so on [16]. These by-products can influence the normal operation of the transformers causing a raise of failure probability. Therefore, it is important to determine the ageing state of the transformers through the monitoring of the condition of their electrical insulation. The state of degradation of the oil can be determined through various parameters such as interfacial tension, oxidation stability, acidity, dissolved gases analysis (DGA), breakdown voltage, dissipation factor, and so on [16, 17]. In the case of insulation paper, the study of its degradation can be done through the determination of the degree of polymerisation (DP) or through the tensile index. The purpose of these two procedures is to determine the mechanical strength of the paper. While the first method does a representative strength measure, the second one determines the true measurement [18]. However, both tests can only be carried out through scrapping transformers, since in both cases it is necessary to take a sample of the

knowing its behaviour and its degradation rate over time.

Figure 1. Transformer failures and their causes.

solid component, which requires drain the oil.

The type of cooling system in power transformers depends on different factors, mainly associated with the machine power. The two main groups in which this kind of systems can be divided are: dry and liquid cooling. For small transformers (100–50,000 kVA) [14], the external surface of the transformer is sufficient to evacuate by convection and/or radiation the generated heat to the environment. In such cases, the transformer is air-cooled, being called dry transformer. These transformers depend on air to enter at the bottom, flow upward over the core and coil surfaces and exit through the openings near to the top. In medium-large powers, the cooling system is generally of liquid type, so that the core and the windings are immersed in oil and contained in a steel tank. This kind of transformers is named oil-filled and in them, the oil absorbs the heat generated, transports it and dissipates it to the environment through an exchange boundary. In some cases, this boundary is the outer surface of the tank, often flapped, which evacuates heat by natural convection and radiation. As the power of the transformer increases, external radiators are added to increase the exchange surface as well as fans to force the convection. In high-power transformers, the cooling of the oil can be also carried out by means of an oil–water exchanger.

In power systems, most of power transformers are oil-filled [15], and their insulation system is mainly composed of cellulose [16]. The oil provides electrical insulation together with cellulosic materials, as well as cooling. Once a transformer starts its operation, the insulation system degrades over time through different physical–chemical mechanisms. In the case of oil, it is quite simple to maintain it in suitable conditions, and it is even feasible to replace if it would be required. However, this is not possible with solid insulation because this cover wires which constitute the windings of the transformer. Under a practical point of view, replacing the solid


Figure 1. Transformer failures and their causes.

transport. Electrical insulation and cooling systems are critical parts of electric power trans-

4 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Transformer losses generate heat, which produces an increase in temperature and an efficiency decrease. Once a power transformer starts its operation, heat begins to be produced, which origins a progressive increase of the temperature. This increase continues until permanent regime conditions are reached. The temperature rise above the service conditions results in an accelerated degradation of the insulating materials. Additionally, insulation systems of oilfilled transformers are subjected to repeated lightning impulses, which brings potential risk to the insulation system, being the liquid/solid interface the weak link. Assessment of insulation condition can be obtained by partial discharge (PD) monitoring [2]. For instance, some authors [3–8] have analysed the effect of oil and pressboard ageing (electrical and/or thermal) on the characteristic of PD from inception to flashover, surface discharge inception voltage (SDIV) variation, creepage discharge inception voltage (CDIV) or creepage discharge flashover voltage (CDFV) of oil/solid insulation specimens with different ageing degrees. Other authors have studied the effect of polarity on the accumulation of charges at the oil-solid interface [9], the accumulative effect of repeated lightning impulses and its damage mechanism [10], the electrical deterioration caused by PD under long-term AC voltage [11] or the performance of

On the other hand, thermal ageing of insulation system in power transformers can favour the initiation of short-circuit forces, which can end up in a permanent deformation or failure [13]. The type of cooling system in power transformers depends on different factors, mainly associated with the machine power. The two main groups in which this kind of systems can be divided are: dry and liquid cooling. For small transformers (100–50,000 kVA) [14], the external surface of the transformer is sufficient to evacuate by convection and/or radiation the generated heat to the environment. In such cases, the transformer is air-cooled, being called dry transformer. These transformers depend on air to enter at the bottom, flow upward over the core and coil surfaces and exit through the openings near to the top. In medium-large powers, the cooling system is generally of liquid type, so that the core and the windings are immersed in oil and contained in a steel tank. This kind of transformers is named oil-filled and in them, the oil absorbs the heat generated, transports it and dissipates it to the environment through an exchange boundary. In some cases, this boundary is the outer surface of the tank, often flapped, which evacuates heat by natural convection and radiation. As the power of the transformer increases, external radiators are added to increase the exchange surface as well as fans to force the convection. In high-power transformers, the cooling of the oil can be also

In power systems, most of power transformers are oil-filled [15], and their insulation system is mainly composed of cellulose [16]. The oil provides electrical insulation together with cellulosic materials, as well as cooling. Once a transformer starts its operation, the insulation system degrades over time through different physical–chemical mechanisms. In the case of oil, it is quite simple to maintain it in suitable conditions, and it is even feasible to replace if it would be required. However, this is not possible with solid insulation because this cover wires which constitute the windings of the transformer. Under a practical point of view, replacing the solid

formers during their operation [1].

alternative liquids in comparison with mineral oil [12].

carried out by means of an oil–water exchanger.

insulation would imply re-manufacturing the transformer almost completely, which is not practical. Consequently, it can be concluded that the life of a power transformer is limited fundamentally by the insulation paper state, which highlights the enormous importance of knowing its behaviour and its degradation rate over time.

Not only solid insulation components suffer continuous ageing, but also the dielectric oil. During transformers operation, the insulation system degrades generating a wide range of by-products such as furanic compounds, water, CO2, CO, low and high molecular weight acids, and so on [16].

These by-products can influence the normal operation of the transformers causing a raise of failure probability. Therefore, it is important to determine the ageing state of the transformers through the monitoring of the condition of their electrical insulation. The state of degradation of the oil can be determined through various parameters such as interfacial tension, oxidation stability, acidity, dissolved gases analysis (DGA), breakdown voltage, dissipation factor, and so on [16, 17]. In the case of insulation paper, the study of its degradation can be done through the determination of the degree of polymerisation (DP) or through the tensile index. The purpose of these two procedures is to determine the mechanical strength of the paper. While the first method does a representative strength measure, the second one determines the true measurement [18]. However, both tests can only be carried out through scrapping transformers, since in both cases it is necessary to take a sample of the solid component, which requires drain the oil.

The knowledge of the oil and paper ageing processes through the measure of the real state of degradation of the machine is essential to predict the failure of a transformer in service [19, 20], which can be due to different causes as was gathered by Murugan and Ramasamy [21], Figure 1.

The main aim of this chapter is to describe the opportunities offered by the variables obtained through stress–strain curve in post-mortem studies as well as accelerated thermal ageing tests carried out in laboratory, describing some of its advantages and challenges. This chapter is structured as follows: Section 2 explains some of the most used methods to evaluate paper ageing. Section 3 exposes the main post-mortem studies carried out until now, as well as the methods and a mathematical model based on DP and tensile index used to analyse paper degradation. The following section describes accelerated thermal ageing tests in which mechanical properties have been used to determine paper degradation. Additionally, this section describes a mathematical model defined by the authors of this chapter, which can be used to determine the paper ageing through mechanical properties, obtained from tensile test. Finally, the conclusions are presented.

#### 2. Paper degradation assessment

The study of paper ageing in power transformers is critical to maximise the operation period, and it can be carried out through different methods, some of the most used are:

#### 2.1. Furanic compounds concentration

This is a non-intrusive technique, which can be used to estimate the ageing of the dielectric paper. It has been concluded by different authors [22–32] that there is a relation between furanic compounds and degree of polymerisation. This relation has been defined through mathematical models such as gathered in Table 1.

2.2. Dissolved gas analysis

Table 1. Furans and DP correlations.

2FAL: mg of furfural/kg of oil.

Total furans: mg of total concentration of furans/kg of oil. Cfur: mg of total concentration of furans/kg of oil.

2.3. Methanol concentration

electron impact mode [36].

is like HPLC.

DP <sup>¼</sup> <sup>325</sup> � <sup>19</sup>

DP <sup>¼</sup> <sup>1</sup>

DP <sup>¼</sup> <sup>1850</sup>

DP <sup>¼</sup> <sup>1</sup>

DP <sup>¼</sup> <sup>800</sup>

DP <sup>¼</sup> <sup>1</sup>:4�log10 ð Þ <sup>2</sup>FAL

DP <sup>¼</sup> <sup>2</sup>:6�log10 ð Þ <sup>2</sup>FAL

It is a technique used to identify faults during transformer operation. This analysis can be also utilised to describe the paper ageing through CO and CO2 dissolved in the oil. Different works have showed that there is a relationship between the concentration of these gases and the DP (CO2/CO ≤ 7.4, DP > 600; 7.4 < CO2/CO < 8.0, 400 < DP < 600; 8 ≤ CO2/CO < 8.7, 250 < DP < 400; CO2/CO ≥ 8.7, DP < 250) [34, 35]. The gases, which can be extracted from the oil using different methods [18], are detected using the gas chromatography technique whose operating principle

Mathematical model Reference

<sup>0</sup>:<sup>0035</sup> � <sup>1</sup>:<sup>51</sup> � log10ð Þ <sup>2</sup>FAL ; <sup>150</sup> <sup>≤</sup> DP <sup>≤</sup> <sup>1000</sup> (2) [23]

<sup>2</sup>:3þ2FAL<sup>0</sup> ; <sup>150</sup> <sup>≤</sup> DP <sup>≤</sup> <sup>600</sup> (3) [24]

½ �þ <sup>0</sup>:186�2FAL <sup>1</sup> (5) [27]

DP ¼ 356:1 � 343:8 � log10½ � TotalFurans (6) [28]

DP <sup>¼</sup> <sup>402</sup>:<sup>47</sup> � <sup>220</sup>:<sup>87</sup> � log10 Cfur (9) [30] DP ¼ �<sup>121</sup> � ln Cfur <sup>þ</sup> <sup>458</sup> (10) [31] DP ¼ 405:25 � 347:22 � log10ð Þ 2FAL (11) [32]

DPav: average degree of polymerisation of the cellulosic paper in the windings of a scrapped transformer.

DP: degree of polymerisation of the cellulosic paper in the windings of a transformer.

�0:<sup>0035</sup> � log10ð Þ� <sup>2</sup>FAL � <sup>0</sup>:<sup>88</sup> <sup>4</sup>:<sup>51</sup> (4) [25, 26]

<sup>0</sup>:<sup>003</sup> ; <sup>200</sup> <sup>≤</sup> DPav <sup>≤</sup> <sup>800</sup> (7) [29]

<sup>0</sup>:<sup>0049</sup> ; (8) [30]

<sup>13</sup> � log10ð Þ <sup>2</sup>FAL ; <sup>100</sup> <sup>≤</sup> DP <sup>≤</sup> <sup>900</sup> (1) [22]

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7

The determination of the amount of this alcohol can be used to monitor the depolymerisation of the paper under normal operating conditions of the transformer. Methanol offers a faster indication of the early stages of paper degradation than furans [18]. This volatile product can be measured through a gas chromatograph equipped with a mass selective detector in the

These models are empirical, obtained through experimental data, so when they are applied to a 2-FAL concentration of for example 0.25 ppm, the value of DP ranges from 764.45 to 535.45 Therefore, there is a huge difference between the results.

These compounds can be determined through high performance liquid chromatography (HPLC) or extraction with methanol [32, 33]. The first step of the furanic compounds measure is to extract them from the oil, which can be done through solid–liquid extraction or liquid– liquid extraction. After that, it is analysed by the HPLC in which it is eluted in the specified column and detected through an ultra violet (UV) detector [18].

A varied range of factors could affect the analysis of furanic compounds: high moisture (furfuryl alcohol, FA), overheating or normal ageing (2-furfuraldehyde, 2FAL), high temperature (5metyl-2furfural, 5MEF).


DP: degree of polymerisation of the cellulosic paper in the windings of a transformer. 2FAL: mg of furfural/kg of oil.

DPav: average degree of polymerisation of the cellulosic paper in the windings of a scrapped transformer. Total furans: mg of total concentration of furans/kg of oil.

Cfur: mg of total concentration of furans/kg of oil.

Table 1. Furans and DP correlations.

The knowledge of the oil and paper ageing processes through the measure of the real state of degradation of the machine is essential to predict the failure of a transformer in service [19, 20], which can be due to different causes as was gathered by Murugan and Ramasamy [21],

6 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

The main aim of this chapter is to describe the opportunities offered by the variables obtained through stress–strain curve in post-mortem studies as well as accelerated thermal ageing tests carried out in laboratory, describing some of its advantages and challenges. This chapter is structured as follows: Section 2 explains some of the most used methods to evaluate paper ageing. Section 3 exposes the main post-mortem studies carried out until now, as well as the methods and a mathematical model based on DP and tensile index used to analyse paper degradation. The following section describes accelerated thermal ageing tests in which mechanical properties have been used to determine paper degradation. Additionally, this section describes a mathematical model defined by the authors of this chapter, which can be used to determine the paper ageing through mechanical properties, obtained from tensile test.

The study of paper ageing in power transformers is critical to maximise the operation period,

This is a non-intrusive technique, which can be used to estimate the ageing of the dielectric paper. It has been concluded by different authors [22–32] that there is a relation between furanic compounds and degree of polymerisation. This relation has been defined through

These models are empirical, obtained through experimental data, so when they are applied to a 2-FAL concentration of for example 0.25 ppm, the value of DP ranges from 764.45 to 535.45

These compounds can be determined through high performance liquid chromatography (HPLC) or extraction with methanol [32, 33]. The first step of the furanic compounds measure is to extract them from the oil, which can be done through solid–liquid extraction or liquid– liquid extraction. After that, it is analysed by the HPLC in which it is eluted in the specified

A varied range of factors could affect the analysis of furanic compounds: high moisture (furfuryl alcohol, FA), overheating or normal ageing (2-furfuraldehyde, 2FAL), high tempera-

and it can be carried out through different methods, some of the most used are:

Figure 1.

Finally, the conclusions are presented.

2. Paper degradation assessment

2.1. Furanic compounds concentration

ture (5metyl-2furfural, 5MEF).

mathematical models such as gathered in Table 1.

Therefore, there is a huge difference between the results.

column and detected through an ultra violet (UV) detector [18].

#### 2.2. Dissolved gas analysis

It is a technique used to identify faults during transformer operation. This analysis can be also utilised to describe the paper ageing through CO and CO2 dissolved in the oil. Different works have showed that there is a relationship between the concentration of these gases and the DP (CO2/CO ≤ 7.4, DP > 600; 7.4 < CO2/CO < 8.0, 400 < DP < 600; 8 ≤ CO2/CO < 8.7, 250 < DP < 400; CO2/CO ≥ 8.7, DP < 250) [34, 35]. The gases, which can be extracted from the oil using different methods [18], are detected using the gas chromatography technique whose operating principle is like HPLC.

#### 2.3. Methanol concentration

The determination of the amount of this alcohol can be used to monitor the depolymerisation of the paper under normal operating conditions of the transformer. Methanol offers a faster indication of the early stages of paper degradation than furans [18]. This volatile product can be measured through a gas chromatograph equipped with a mass selective detector in the electron impact mode [36].

#### 2.4. Fourier transform infrared spectroscopy

Infrared spectroscopy is a technique used for materials analysis, which uses the infrared region of the electromagnetic (EM) spectrum [37]. It is based on the specific vibration frequencies, which have the chemical bonds of the substances. These frequencies correspond to the energy levels of the molecule and depend on the shape of the potential energy surface of the molecule, the molecular geometry, the atomic mass and the vibrational coupling. If a sample receives light with the same energy from that vibration and the molecules suffer a change in their bipolar moment during vibration, then this will appear in the infrared spectrum. To make measurements on a sample, a monochrome ray of infrared light is passed through the sample, and some of this radiation is absorbed by the sample and some of it is transmitted. By repeating this operation in a range of wavelengths, an infrared spectrum can be obtained. This spectrum represents the molecular absorption and transmission, generating a fingerprint of a sample with absorption peaks, which correspond to the frequencies of vibrations between the bonds of the atoms that constitute the material. The size of the peaks in the spectrum is a direct indication of the amount of material [37, 38]. This technique provides precise information about functional groups (O-H, CH, C=O, C-O) changes [37, 38].

2.7. Refractive index of cellulose fibres

Figure 2. SEM result of Kraft paper.

2.8. Degree of polymerisation

2.9. Stress: strain curve

and length L0 (mm).

spectrum by observing dispersion colour through DSM [41].

accepted that this failure occurs when DP = 150 to 200 [34].

viscosity has been obtained the DP can be estimated.

The refractive index (RI) of cellulose fibres can be determined using the dispersion staining method (DSM) whose principle is as follows: when cellulose fibres are immersed in liquid, white light will be dispersed at the boundary of the two substances. At this point, there is a spectrum that does not refract (it passes straight through). This particular spectrum has the condition: "RI of cellulose fibre = RI of immersion-liquid." When this particular spectrum is intercepted by an optical mask and condenses the spectra that are not intercepted, the cellulose fibre appears to be coloured. It is possible to know the RI of cellulose fibres at a particular

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The degree of polymerisation can be defined as the average number of glucose rings in each cellulose chain and it is dimensionless [19]. These chains of cellulose break up during transformer operation by exposure to oxygen, moisture and heat, which produce a decrease of mechanical strength of paper. This weakening end up in transformer fail and it is commonly

The DP of dielectric paper can be measured using an Ubbelohde viscometer tube [42]. The first step of the procedure is to measure the viscosity of paper, deionised water and cupriethylenediamine (Cuen) mixture and the next step is to calculate the specific viscosity. Once the specific

The paper strength is due to fibre strength and inter-fibre bonding strength [18]. Tensile strength (TS) can be described by stress and strain curve (Figure 3), which is obtained through tensile test. This test is used to determine the behaviour of a material when a specimen is clamped in an axial loading frame (Figure 4). The data obtained from this test (load and displacement) are used to determine stress and strain using the original specimen cross-sectional area A0 (m2)

#### 2.5. X-ray diffraction

This is a rapid analytical technique based on the dispersion of the X-ray beam by matter and on the constructive interference of waves that are in phase and that are dispersed in certain directions of space. X-rays are generated in a cathode ray tube by heating a filament to produce electrons, which are accelerated toward the sample applying a voltage. When the electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic Xray spectrum is obtained which allows the identification of crystalline phases qualitatively and quantitatively. The crystal structure and crystallinity are the key properties of the crystalline polymer material for deciding its electrical performance. By analysing the length, width, height and diffraction angle, crystal structure identification and chemical phase analysis could be implemented. Therefore, X-RD analysis is very helpful in the investigation of the crystal structure of the cellulose fibres in the transformer paper [39].

#### 2.6. Scanning electron microscope

Scanning electron microscope (SEM) can obtain the electronic image of sample's surface to show its microstructure [40]. The SEM is capable of producing high-resolution images of a sample surface (Figure 2). A heated electron emission produces an electron beam, which is focused by one or two condenser lenses to a fine focal spot. The beam passes through a pair of scanning coils in the objective lens, which deflect the beam both horizontally and vertically. Consequently, the beam scans in a raster fashion over a rectangular area of the sample surface [39]. It allows knowing in detail the state of the surface of a material, which can provide important information about the microstructure, impurities, degree and origin of alteration of the material.

Assessment of Dielectric Paper Degradation through Mechanical Characterisation http://dx.doi.org/10.5772/intechopen.77972 9

2.4. Fourier transform infrared spectroscopy

8 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

about functional groups (O-H, CH, C=O, C-O) changes [37, 38].

structure of the cellulose fibres in the transformer paper [39].

2.6. Scanning electron microscope

the material.

2.5. X-ray diffraction

Infrared spectroscopy is a technique used for materials analysis, which uses the infrared region of the electromagnetic (EM) spectrum [37]. It is based on the specific vibration frequencies, which have the chemical bonds of the substances. These frequencies correspond to the energy levels of the molecule and depend on the shape of the potential energy surface of the molecule, the molecular geometry, the atomic mass and the vibrational coupling. If a sample receives light with the same energy from that vibration and the molecules suffer a change in their bipolar moment during vibration, then this will appear in the infrared spectrum. To make measurements on a sample, a monochrome ray of infrared light is passed through the sample, and some of this radiation is absorbed by the sample and some of it is transmitted. By repeating this operation in a range of wavelengths, an infrared spectrum can be obtained. This spectrum represents the molecular absorption and transmission, generating a fingerprint of a sample with absorption peaks, which correspond to the frequencies of vibrations between the bonds of the atoms that constitute the material. The size of the peaks in the spectrum is a direct indication of the amount of material [37, 38]. This technique provides precise information

This is a rapid analytical technique based on the dispersion of the X-ray beam by matter and on the constructive interference of waves that are in phase and that are dispersed in certain directions of space. X-rays are generated in a cathode ray tube by heating a filament to produce electrons, which are accelerated toward the sample applying a voltage. When the electrons have sufficient energy to dislodge inner shell electrons of the target material, characteristic Xray spectrum is obtained which allows the identification of crystalline phases qualitatively and quantitatively. The crystal structure and crystallinity are the key properties of the crystalline polymer material for deciding its electrical performance. By analysing the length, width, height and diffraction angle, crystal structure identification and chemical phase analysis could be implemented. Therefore, X-RD analysis is very helpful in the investigation of the crystal

Scanning electron microscope (SEM) can obtain the electronic image of sample's surface to show its microstructure [40]. The SEM is capable of producing high-resolution images of a sample surface (Figure 2). A heated electron emission produces an electron beam, which is focused by one or two condenser lenses to a fine focal spot. The beam passes through a pair of scanning coils in the objective lens, which deflect the beam both horizontally and vertically. Consequently, the beam scans in a raster fashion over a rectangular area of the sample surface [39]. It allows knowing in detail the state of the surface of a material, which can provide important information about the microstructure, impurities, degree and origin of alteration of

#### 2.7. Refractive index of cellulose fibres

The refractive index (RI) of cellulose fibres can be determined using the dispersion staining method (DSM) whose principle is as follows: when cellulose fibres are immersed in liquid, white light will be dispersed at the boundary of the two substances. At this point, there is a spectrum that does not refract (it passes straight through). This particular spectrum has the condition: "RI of cellulose fibre = RI of immersion-liquid." When this particular spectrum is intercepted by an optical mask and condenses the spectra that are not intercepted, the cellulose fibre appears to be coloured. It is possible to know the RI of cellulose fibres at a particular spectrum by observing dispersion colour through DSM [41].

#### 2.8. Degree of polymerisation

The degree of polymerisation can be defined as the average number of glucose rings in each cellulose chain and it is dimensionless [19]. These chains of cellulose break up during transformer operation by exposure to oxygen, moisture and heat, which produce a decrease of mechanical strength of paper. This weakening end up in transformer fail and it is commonly accepted that this failure occurs when DP = 150 to 200 [34].

The DP of dielectric paper can be measured using an Ubbelohde viscometer tube [42]. The first step of the procedure is to measure the viscosity of paper, deionised water and cupriethylenediamine (Cuen) mixture and the next step is to calculate the specific viscosity. Once the specific viscosity has been obtained the DP can be estimated.

#### 2.9. Stress: strain curve

The paper strength is due to fibre strength and inter-fibre bonding strength [18]. Tensile strength (TS) can be described by stress and strain curve (Figure 3), which is obtained through tensile test.

This test is used to determine the behaviour of a material when a specimen is clamped in an axial loading frame (Figure 4). The data obtained from this test (load and displacement) are used to determine stress and strain using the original specimen cross-sectional area A0 (m2) and length L0 (mm).

Figure 3. Stress–strain curve.

Figure 4. An universal servo hydraulic test machine (model ME-405-1, SERVOSIS) with an axial load cell of �1 kN capacity, an actuator of �50 mm of dynamic stroke and equipped with pneumatic flat grips.

Stress (σ) is the internal load applied to a specific surface; it is usually expressed in Pa or MPa when the value is high.

$$
\sigma = \frac{F}{A\_0} = \frac{F}{b \cdot a} \tag{1}
$$

<sup>ε</sup> <sup>¼</sup> <sup>l</sup> � <sup>l</sup><sup>0</sup> l0

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

At the beginning of stress–strain curve (Figure 3), many materials follow Hooke's law, so that stress is proportional to strain being the modulus of elasticity or Young's modulus (Y, Pa) the constant of proportionality. As strain increases, many materials end up deviating from this linear proportionality, the point in which this happens is named the proportional limit. This behaviour is associated with plastic strain. This plasticity requires molecular mobility and not all materials have it. The microstructural rearrangements associated with plastic strain are usually not reversed when the load is removed, so the proportional limit is often the same as or close to the materials' elastic limit, which is the stress needed to produce a permanent residual strain on a specimen once this is unloaded. A parameter related with this behaviour is the yield stress (σy, Pa), which is the stress required to generate plastic strain in a specimen and it is often considered to be the stress needed to generate a permanent strain of 0.2%. In the stress–strain curve appears a point of Maximum Tensile Strength (σmax, Pa), beyond this point the material appears to strain soften. The area under the stress–strain curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material to get that strain [43]. An additional param-

TI <sup>¼</sup> <sup>F</sup>=<sup>a</sup>

). Dielectric papers used in the isolation system of oil-filled transformers have different values of

As dielectric paper ages, the risk of transformer failure will rise. According to the study carried out by Murugan and Ramasamy [21], approximately 41% of the faults produced in a fleet of transformers (196 transformers ranging from 33 to 400 kV and from 5 to 315 MVA) were due to failures in the insulation system. Thus, it is critical to monitor the condition of the insulating

presspaper

σmax (MPa) MD 110 91 110 91 ≥ 70

ε (%) MD 2.4 2.8 2.4 2.8 ≥ 6

Grade K diamond dotted

> 0.2 > 0.2 > 0.2 > 0.2 0.7

XD 50 40 39 40 ≥

XD 7.6 7.8 7.5 7.8 ≥ 8

<sup>G</sup> (3)

Grade 3 diamond dotted

PSP 3050

50

presspaper

); F is the load (kN); a is the original width of the

eter, which can be obtained through stress–strain curve, is the tensile index.

Grade 3 presspaper

where TI is the tensile index (kN m�<sup>1</sup> kg�<sup>1</sup>

the mechanical properties (Table 2).

Property Grade K

Typical thickness (mm)

specimen (m) and G is the grammage (kg m�<sup>2</sup>

presspaper

MD: machine direction of paper; and XD: cross direction of paper.

Table 2. Typical mechanical properties of dielectric papers.

(2)

11

where σ is the stress (Pa); F is the load (N); A0 is the original specimen cross-sectional area (m2 ); a is the original width of the specimen (m) and b is de original thickness of the specimen (m).

Strain (ε) is the change in the size or shape of a specimen due to internal stress produced by one or more loads applied to it or by thermal expansion.

Assessment of Dielectric Paper Degradation through Mechanical Characterisation http://dx.doi.org/10.5772/intechopen.77972 11

$$
\varepsilon = \frac{l - l\_0}{l\_0} \tag{2}
$$

At the beginning of stress–strain curve (Figure 3), many materials follow Hooke's law, so that stress is proportional to strain being the modulus of elasticity or Young's modulus (Y, Pa) the constant of proportionality. As strain increases, many materials end up deviating from this linear proportionality, the point in which this happens is named the proportional limit. This behaviour is associated with plastic strain. This plasticity requires molecular mobility and not all materials have it. The microstructural rearrangements associated with plastic strain are usually not reversed when the load is removed, so the proportional limit is often the same as or close to the materials' elastic limit, which is the stress needed to produce a permanent residual strain on a specimen once this is unloaded. A parameter related with this behaviour is the yield stress (σy, Pa), which is the stress required to generate plastic strain in a specimen and it is often considered to be the stress needed to generate a permanent strain of 0.2%. In the stress–strain curve appears a point of Maximum Tensile Strength (σmax, Pa), beyond this point the material appears to strain soften. The area under the stress–strain curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material to get that strain [43]. An additional parameter, which can be obtained through stress–strain curve, is the tensile index.

$$\text{TI} = \frac{\text{F}\_{\text{a}}}{\text{G}} \tag{3}$$

where TI is the tensile index (kN m�<sup>1</sup> kg�<sup>1</sup> ); F is the load (kN); a is the original width of the specimen (m) and G is the grammage (kg m�<sup>2</sup> ).

Dielectric papers used in the isolation system of oil-filled transformers have different values of the mechanical properties (Table 2).

As dielectric paper ages, the risk of transformer failure will rise. According to the study carried out by Murugan and Ramasamy [21], approximately 41% of the faults produced in a fleet of transformers (196 transformers ranging from 33 to 400 kV and from 5 to 315 MVA) were due to failures in the insulation system. Thus, it is critical to monitor the condition of the insulating


MD: machine direction of paper; and XD: cross direction of paper.

Table 2. Typical mechanical properties of dielectric papers.

Stress (σ) is the internal load applied to a specific surface; it is usually expressed in Pa or MPa

Figure 4. An universal servo hydraulic test machine (model ME-405-1, SERVOSIS) with an axial load cell of �1 kN

where σ is the stress (Pa); F is the load (N); A0 is the original specimen cross-sectional area (m2

a is the original width of the specimen (m) and b is de original thickness of the specimen (m). Strain (ε) is the change in the size or shape of a specimen due to internal stress produced by

<sup>¼</sup> <sup>F</sup>

<sup>b</sup> � <sup>a</sup> (1)

);

<sup>σ</sup> <sup>¼</sup> <sup>F</sup> A0

capacity, an actuator of �50 mm of dynamic stroke and equipped with pneumatic flat grips.

10 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

one or more loads applied to it or by thermal expansion.

when the value is high.

Figure 3. Stress–strain curve.

solid, which can be carried out through techniques based on paper ageing by-products (furanic compounds, methanol, dissolved gases…), DP or stress–strain curve. The last technique is the best way to analyse paper degradation [18]. However, the implementation of the two last techniques is only possible through post-mortem studies (scrapping transformers). Another possibility to paper assessment is through correlations based on thermal ageing tests carried out in laboratory. The following sections describe the possibilities that stress–strain offer in order to obtain useful information not only in post-mortem studies, but also in accelerated thermal ageing tests.

the winding. Additionally, these authors obtained that there is a good correlation between DP and the content of furanes in the oil and that the CO2/CO ratio can be used to detect the degree of carbonisation of the insulation paper. Martins et al. [47] also evaluated the condition of a single power transformer, specifically a 63-MVA, 150/63/10-kV, shell-type unit to make a decision regarding its transfer to a new substation. They measured the DP from selected points in the transformer connections insulation to get a paper-ageing diagnostic and compare it with the predicted diagnostic based on the previous oil analysis [dissolved gas analysis (DGA), colour, appearance, breakdown voltage, water content, acidity, dielectric dissipation factor, sediment and sludge, interfacial tension, flash point and furanic compounds]. Their evaluation showed that the calculation of DP using correlations based on 2-FAL require care because DP values depend on variables such as temperature, oxygen, water content, oil type and degradation oil. These authors also estimated DP values using the calculated thermal profiles. However, their results concluded that loading data included the daily peaks are insufficient to obtain an accurate temperature distribution. Finally, they concluded that more post-mortem studies with detailed operational data would improve the knowledge of the correlation between 2-FAL in oil and the DP of insulating paper. DP was also used to estimate paper ageing in the post-mortem assessment carried out by other authors [28, 48]. Leibfried et al. [28] proposed a systematical method for taking paper samples from scrapped power transformers and a methodology for the evaluation of DP values suggesting a grouping into different types of transformers, at least in Germany, which the operation mode and consequently the ageing rate inside transformers is substantially different. Using the data obtained in their study, Leibried et al. derived a formula to estimate average DP through the 2-FAL concentration, although they obtained that this equation does not provide 100% reliable evaluation of transformer condition. In the case of Jalbert and Lessard [48], insulating paper from six power transformers (open-breathing core-type power transformers built in 1958, initially cooled with OFWF systems and since 1990s modified to OFAF cooling systems) as well as representative oil samples needed to evaluate the oil quality and its content of chemical markers (furans and alcohols) were tested. These authors concluded that it is critical to obtain a complete DP profile of the transformer in order to apply any model. They also focused on the need to establish concentration thresholds to define more accurately the insulation paper condition. The experimental results of these post-mortem assessments give a variation of DP values ranged from less than 5% to more than 40%, which indicates the results variability of this technique.

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

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13

It was not until 2014, that post-mortem studies were carried out considering not only DP, but also tensile index, despite the fact that some authors like Emsley et al. [49] have developed an expression, which correlated DP and tensile strength with temperature and time. The approach applied by Carcedo et al. [50] showed a case study, which used, the model proposed by Emsley et al. to predict the values of tensile index and degree of polymerisation [49], in an alternative way for post-mortem assessment. These authors estimated temperature distributions considering the machine life-span and the DP and TI values of new and aged Kraft paper. Carcedo et al. [50] took paper samples from a failed distribution transformer (three-phase transformer with a rated power of 800 kVA at 50 Hz and manufactured in 1986 with an ONAN cooling system) to measure DP and TI. Later, the temperature distributions were obtained

based on DP and TI test results and Emsley et al. model [49]:

However, the implementation of the two last techniques is impossible during transformer operation because it is not possible obtain paper samples from in-service transformers and the only opportunity is through post-mortem studies (scrapping transformers). Another possibility to paper assessment is through correlations based on thermal ageing tests carried out in laboratory. The following sections describe the possibilities that stress–strain offer in order to obtain useful information not only in post-mortem studies, but also in accelerated thermal ageing tests.

#### 3. Post-mortem studies

Although power transformers are tested machines whose life-span pass 20 years even in many cases 40 years [44, 45], their failure diagnostics are becoming increasingly important due to the high cost of these devices.

The aim of power transformers post-mortem studies is to understand the failure mechanisms, so it is essential to collect information about the fault, sequence of events previous the fault, protective operation and protective devices performance. This information requires to be collected immediately after the failure occurs, to reproduce it accurately. Therefore, if there is no an efficient diagnostic methodology included in maintenance program, test results will not be useful to prevent future failures. There are cases in which failures do not manifest in a protective device operation, so routine monitoring can help to detect abnormal operation conditions. Though end-of-life assessments can provide useful information, they are not always conclusive enough to make the decision about the appropriate time to remove a transformer from service. This is the reason why the availability of the history of test results from a power transformer may help to have a better evaluation about the most suitable moment to replace this kind of machines [46].

There are some examples of post-mortem studies that have used the DP as technique to determine the paper ageing. For instance, Koch et al. [17] through a research project in which worked together the IEH Karlsruhe, power stations, utilities and a manufacturer. One of its aims was the definition of a correlation between DP and furanes in the oil, the other aim was to obtain data about the ageing process of transformers populations. This project carried out the post-mortem analysis of two generator transformers. The result tests showed that the lowest DP value occurs at about 75% of the winding length and not at the top in the LV and the HV windings. This allowed to conclude that the hot spot temperature does not occur at the top of the winding. Additionally, these authors obtained that there is a good correlation between DP and the content of furanes in the oil and that the CO2/CO ratio can be used to detect the degree of carbonisation of the insulation paper. Martins et al. [47] also evaluated the condition of a single power transformer, specifically a 63-MVA, 150/63/10-kV, shell-type unit to make a decision regarding its transfer to a new substation. They measured the DP from selected points in the transformer connections insulation to get a paper-ageing diagnostic and compare it with the predicted diagnostic based on the previous oil analysis [dissolved gas analysis (DGA), colour, appearance, breakdown voltage, water content, acidity, dielectric dissipation factor, sediment and sludge, interfacial tension, flash point and furanic compounds]. Their evaluation showed that the calculation of DP using correlations based on 2-FAL require care because DP values depend on variables such as temperature, oxygen, water content, oil type and degradation oil. These authors also estimated DP values using the calculated thermal profiles. However, their results concluded that loading data included the daily peaks are insufficient to obtain an accurate temperature distribution. Finally, they concluded that more post-mortem studies with detailed operational data would improve the knowledge of the correlation between 2-FAL in oil and the DP of insulating paper. DP was also used to estimate paper ageing in the post-mortem assessment carried out by other authors [28, 48]. Leibfried et al. [28] proposed a systematical method for taking paper samples from scrapped power transformers and a methodology for the evaluation of DP values suggesting a grouping into different types of transformers, at least in Germany, which the operation mode and consequently the ageing rate inside transformers is substantially different. Using the data obtained in their study, Leibried et al. derived a formula to estimate average DP through the 2-FAL concentration, although they obtained that this equation does not provide 100% reliable evaluation of transformer condition. In the case of Jalbert and Lessard [48], insulating paper from six power transformers (open-breathing core-type power transformers built in 1958, initially cooled with OFWF systems and since 1990s modified to OFAF cooling systems) as well as representative oil samples needed to evaluate the oil quality and its content of chemical markers (furans and alcohols) were tested. These authors concluded that it is critical to obtain a complete DP profile of the transformer in order to apply any model. They also focused on the need to establish concentration thresholds to define more accurately the insulation paper condition. The experimental results of these post-mortem assessments give a variation of DP values ranged from less than 5% to more than 40%, which indicates the results variability of this technique.

solid, which can be carried out through techniques based on paper ageing by-products (furanic compounds, methanol, dissolved gases…), DP or stress–strain curve. The last technique is the best way to analyse paper degradation [18]. However, the implementation of the two last techniques is only possible through post-mortem studies (scrapping transformers). Another possibility to paper assessment is through correlations based on thermal ageing tests carried out in laboratory. The following sections describe the possibilities that stress–strain offer in order to obtain useful information not only in post-mortem studies, but also in accelerated

12 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

However, the implementation of the two last techniques is impossible during transformer operation because it is not possible obtain paper samples from in-service transformers and the only opportunity is through post-mortem studies (scrapping transformers). Another possibility to paper assessment is through correlations based on thermal ageing tests carried out in laboratory. The following sections describe the possibilities that stress–strain offer in order to obtain useful information not only in post-mortem studies, but also in accelerated thermal

Although power transformers are tested machines whose life-span pass 20 years even in many cases 40 years [44, 45], their failure diagnostics are becoming increasingly important due to the

The aim of power transformers post-mortem studies is to understand the failure mechanisms, so it is essential to collect information about the fault, sequence of events previous the fault, protective operation and protective devices performance. This information requires to be collected immediately after the failure occurs, to reproduce it accurately. Therefore, if there is no an efficient diagnostic methodology included in maintenance program, test results will not be useful to prevent future failures. There are cases in which failures do not manifest in a protective device operation, so routine monitoring can help to detect abnormal operation conditions. Though end-of-life assessments can provide useful information, they are not always conclusive enough to make the decision about the appropriate time to remove a transformer from service. This is the reason why the availability of the history of test results from a power transformer may help to have a better evaluation about the most suitable

There are some examples of post-mortem studies that have used the DP as technique to determine the paper ageing. For instance, Koch et al. [17] through a research project in which worked together the IEH Karlsruhe, power stations, utilities and a manufacturer. One of its aims was the definition of a correlation between DP and furanes in the oil, the other aim was to obtain data about the ageing process of transformers populations. This project carried out the post-mortem analysis of two generator transformers. The result tests showed that the lowest DP value occurs at about 75% of the winding length and not at the top in the LV and the HV windings. This allowed to conclude that the hot spot temperature does not occur at the top of

thermal ageing tests.

ageing tests.

3. Post-mortem studies

high cost of these devices.

moment to replace this kind of machines [46].

It was not until 2014, that post-mortem studies were carried out considering not only DP, but also tensile index, despite the fact that some authors like Emsley et al. [49] have developed an expression, which correlated DP and tensile strength with temperature and time. The approach applied by Carcedo et al. [50] showed a case study, which used, the model proposed by Emsley et al. to predict the values of tensile index and degree of polymerisation [49], in an alternative way for post-mortem assessment. These authors estimated temperature distributions considering the machine life-span and the DP and TI values of new and aged Kraft paper. Carcedo et al. [50] took paper samples from a failed distribution transformer (three-phase transformer with a rated power of 800 kVA at 50 Hz and manufactured in 1986 with an ONAN cooling system) to measure DP and TI. Later, the temperature distributions were obtained based on DP and TI test results and Emsley et al. model [49]:

$$DP\_t = \frac{k\_2 \cdot DP\_0 \cdot e^{k\_2 t}}{e^{k\_2 t} \cdot (DP\_0 \cdot k\_{1\_0} + k\_2) - DP\_0 \cdot k\_{1\_0}} \tag{4}$$

$$T\Pi\_t - T\Pi\_0 = \mathbf{K}\_1 \cdot e^{-k\_2 t} + \mathbf{K}\_2 \cdot \ln\left(e^{k\_2 t} - \mathbf{K}\_3\right) - \mathbf{K}\_4\tag{5}$$

$$k\_{1\_0} = A\_{1\_0} \cdot \mathcal{e}^{\frac{-\mathcal{E}\_{\rm r10}}{R^\*T}} \tag{6}$$

$$k\_2 = A\_2 \cdot \sigma^{\frac{-\mathcal{E}\_{\rm r2}}{\rm F^{\rm T}}} \tag{7}$$

$$K\_1 = \frac{k\_2 \cdot k\_{1\_0}}{k\_2} \tag{8}$$

$$K\_2 = k\_4 \cdot K \tag{9}$$

$$K\_3 = k\_{1\_0} \cdot K'\tag{10}$$

$$K\_4 = K\_2 \cdot (\ln(1 - K\_3)) + K\_1 \tag{11}$$

$$K^{'} = \frac{DP\_0}{DP\_0 \cdot k\_{1\_0} + k\_2} \tag{12}$$

where DPt is the insulation DP value at time t; DP0 is the initial insulation DP value; t is the time (s); k10 is the initial rate at which bonds break; k2 is the rate at which k10 changes; TIt is the insulation tensile strength index value at time t; TI0 is the initial insulation tensile strength index value; k10, k2, k3 and k4 constants can be obtained assuming that Arrhenius equation is valid from normal temperature of power transformers up to the temperatures used in ageing experiments:

$$k = A \cdot e^{\frac{-\mathbb{E}\_q}{kT}} \tag{13}$$

3 transformers of 254 MVA, 420/13.8 kV; 3 transformers of 250 MVA, 400/121 kV; 15 transformers of 250 MVA, 420/15.75 kV; 1 transformer of 200 MVA, 231/121 kV; 1 transformer of 200 MVA, 230/121 kV). These machines were studied through post-mortem analysis carried out for several years. The study of these devices analysed the values of DP, tensile strength, as well as, information from running history of the transformers (DGA and 2-FAL). They observed that transformers with similar level of ageing are defined rather by manufacturer and construction than by the loading regime, which has less influence. Moreover, they found that the correlation of DP and tensile strength corresponds with specific transformers groups. Nevertheless, there are some transformers whose DP values range far less in comparison with tensile strength, which might indicate a higher accuracy of this variable to distinguish paper degradation. On the other hand, the DGA tests showed that they are essential for ageing evaluation because they can provide information about running problems (ineffective cooling, leaking, higher

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15

Even though the number of post-mortem studies has increased during the last years, there is not enough data to develop an accurate end-of-life failure model [53]. For this reason, it is essential to go on with the study of scrapped transformers to obtain more information about the most representative variables of the transformer ageing. Initially, the state of insulating

gases development).

Figure 5. Temperature distribution using different test results.

where k is a rate constant; A is the pre-exponential factor (s�1); Ea is the activation energy (J mol�1); R is the molar gas constant (8.314 JK�1 mol�1) and T is the temperature (K).

Finally, these temperature distributions obtained by Carcedo et al. [50] and represented by authors of this chapter (Figure 5) were compared in order to show the suitability of tensile analysis for post-mortem studies. These authors concluded that the maximum difference for the same point was less than 3.3 K; therefore, both methods were suitable for post-mortem evaluations, being the TI more reliable and repeatable indicator.

Azis et al. also used stress–strain curve to investigate the mechanical strength of paper from 10 scrapped power transformers [51]. These authors not only used TI to carried out the transformers assessment, but also the low molecular weight acid (LMA). They concluded that there is a relationship between LMA in oil and TI of paper, which tends to be generic for both laboratory tests and in-service ageing data.

In the paper written by Müllerová et al. [52], was described the methodology followed to create and utilise as a making decision tool a database which gathers data about the condition of the insulation system of a group of 24 transformers (1 transformer of 330 MVA, 400/121 kV; Assessment of Dielectric Paper Degradation through Mechanical Characterisation http://dx.doi.org/10.5772/intechopen.77972 15

Figure 5. Temperature distribution using different test results.

DPt <sup>¼</sup> <sup>k</sup><sup>2</sup> � DP<sup>0</sup> � <sup>e</sup><sup>k</sup>2<sup>t</sup>

TIt � TI<sup>0</sup> ¼ K<sup>1</sup> � e

14 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

ek2<sup>t</sup> � ðDP<sup>0</sup> � k<sup>10</sup> þ k2Þ � DP<sup>0</sup> � k<sup>10</sup>

�Ea10

�Ea2

<sup>k</sup>2<sup>t</sup> � <sup>K</sup><sup>3</sup>

K<sup>4</sup> ¼ K<sup>2</sup> � ð Þþ ln 1ð Þ � K<sup>3</sup> K<sup>1</sup> (11)

� <sup>K</sup><sup>4</sup> (5)

<sup>R</sup>∗<sup>T</sup> (6)

<sup>R</sup>∗<sup>T</sup> (7)

�Ea RT (13)

�k2<sup>t</sup> <sup>þ</sup> <sup>K</sup><sup>2</sup> � ln <sup>e</sup>

k<sup>10</sup> ¼ A<sup>10</sup> � e

k<sup>2</sup> ¼ A<sup>2</sup> � e

<sup>K</sup><sup>1</sup> <sup>¼</sup> <sup>k</sup><sup>2</sup> � <sup>k</sup><sup>10</sup> k2

<sup>K</sup><sup>2</sup> <sup>¼</sup> <sup>k</sup><sup>4</sup> � <sup>K</sup><sup>0</sup>

<sup>K</sup><sup>3</sup> <sup>¼</sup> <sup>k</sup><sup>10</sup> � <sup>K</sup><sup>0</sup>

<sup>¼</sup> DP<sup>0</sup> DP<sup>0</sup> � k<sup>10</sup> þ k<sup>2</sup>

where DPt is the insulation DP value at time t; DP0 is the initial insulation DP value; t is the time (s); k10 is the initial rate at which bonds break; k2 is the rate at which k10 changes; TIt is the insulation tensile strength index value at time t; TI0 is the initial insulation tensile strength index value; k10, k2, k3 and k4 constants can be obtained assuming that Arrhenius equation is valid from normal temperature of power transformers up to the temperatures used in ageing experiments:

k ¼ A � e

where k is a rate constant; A is the pre-exponential factor (s�1); Ea is the activation energy (J mol�1); R is the molar gas constant (8.314 JK�1 mol�1) and T is the temperature (K).

Finally, these temperature distributions obtained by Carcedo et al. [50] and represented by authors of this chapter (Figure 5) were compared in order to show the suitability of tensile analysis for post-mortem studies. These authors concluded that the maximum difference for the same point was less than 3.3 K; therefore, both methods were suitable for post-mortem

Azis et al. also used stress–strain curve to investigate the mechanical strength of paper from 10 scrapped power transformers [51]. These authors not only used TI to carried out the transformers assessment, but also the low molecular weight acid (LMA). They concluded that there is a relationship between LMA in oil and TI of paper, which tends to be generic for both

In the paper written by Müllerová et al. [52], was described the methodology followed to create and utilise as a making decision tool a database which gathers data about the condition of the insulation system of a group of 24 transformers (1 transformer of 330 MVA, 400/121 kV;

K0

evaluations, being the TI more reliable and repeatable indicator.

laboratory tests and in-service ageing data.

(4)

(8)

(9)

(10)

(12)

3 transformers of 254 MVA, 420/13.8 kV; 3 transformers of 250 MVA, 400/121 kV; 15 transformers of 250 MVA, 420/15.75 kV; 1 transformer of 200 MVA, 231/121 kV; 1 transformer of 200 MVA, 230/121 kV). These machines were studied through post-mortem analysis carried out for several years. The study of these devices analysed the values of DP, tensile strength, as well as, information from running history of the transformers (DGA and 2-FAL). They observed that transformers with similar level of ageing are defined rather by manufacturer and construction than by the loading regime, which has less influence. Moreover, they found that the correlation of DP and tensile strength corresponds with specific transformers groups. Nevertheless, there are some transformers whose DP values range far less in comparison with tensile strength, which might indicate a higher accuracy of this variable to distinguish paper degradation. On the other hand, the DGA tests showed that they are essential for ageing evaluation because they can provide information about running problems (ineffective cooling, leaking, higher gases development).

Even though the number of post-mortem studies has increased during the last years, there is not enough data to develop an accurate end-of-life failure model [53]. For this reason, it is essential to go on with the study of scrapped transformers to obtain more information about the most representative variables of the transformer ageing. Initially, the state of insulating solid was measured through DP; however, later assessments have demonstrated that in some cases the tensile or index strength can be more sensitive to differentiate the level of paper ageing.

paper in mineral oil at four temperatures. The results of their study showed that there is a direct relationship between the DP and the moisture in paper and the concentration of furanic compounds. These authors also proposed as paper end-of-life criteria a DP = 200 and a tensile strength equal to 50% of its original value. Other authors such as Yoshida et al. [70] also implemented ageing tests using mineral oil as dielectric liquid at different temperatures (120, 140 and 160C). In this case, they analysed the behaviour of Kraft and pressboard paper, obtaining as main conclusions the existence of a relationship between the concentration of CO/CO2 and the evolution of the DP and the tensile strength. On the other hand, Hill et al. [71] studied the tensile strength of the paper, the DP and the concentration of furans in ageing tests of Kraft paper in mineral oil at different temperatures, obtaining as a result the existence of a relationship between furans, DP and tensile strength. In addition, these authors proposed a paper degradation model based on the tensile strength. Emsley et al. [49, 72, 73] also proposed a degradation model, although this was based on the relationship between tensile strength and DP for Kraft paper and cotton paper aged in mineral oil. Since last decade, ageing studies have begun to take into account alternative oils. For example, Mcshane et al. [74–77] evaluated DP, tensile strength, moisture in oil and paper, as well as furan content when Kraft and thermal upgraded paper were aged in a mineral oil and in a natural ester. The results of their tests showed that the degradation rate experienced by the paper during thermal ageing at different temperatures was lower in the natural ester. These authors proposed the protective mechanisms developed by the ester that might explain the minor degradation suffered by the paper in the alternative oil. Other authors such as Shim et al. [78] also obtained greater thermal stability in the natural ester compared to mineral oil by the measure of the tensile strength for Kraft and diamond dotted paper. Similar results were presented by Azis [18], who analysed paper degradation using tensile strength, breakdown voltage, dynamic viscosity, acidity and concentration of low and high molecular weight acids in the oil. The measure of the concentration of low molecular weight acids (LMA) allowed observing that these tend to remain in the natural ester, which might explain the best behaviour of the Kraft paper during the ageing, in addition to the hydrolytic protection made by the oil. The behaviour of thermal upgraded and Kraft paper in mineral oil and in natural ester was also evaluated by Abdelmalik et al. [79], who studied the tensile and dielectric strength of the paper. Their results also showed that oils based on natural esters protect better against the degradation than mineral oil. Saruhashi et al. [80] studied for aramid paper tensile index, as well as breakdown voltage, acidity, colour and kinematic viscosity of the oil. In their study, they carry out ageing tests at two temperatures in three different oils (silicone, natural ester and synthetic ester). They found a slight variation of the tensile index in the three oils. The degradation of Kraft paper aged in a natural ester was also evaluated through the tensile strength by Widyanugraha et al. [35], who also measured the gases generated during ageing at two different temperatures. The tensile strength suffered initially a decrease and subsequently an increase during thermal ageing. It was assumed that this behaviour was due to the transesterification process. The tensile strength of the paper, besides other characteristic properties of the oil degradation, was analysed by Madavan and Balaraman [81], who obtained that the paper aged in oils based on natural esters had a lower degradation compared to Kraft paper immersed in mineral oil. In recent years, different authors have tried to find additional methods to study paper degradation when this is aged thermally in laboratory. For example, Arroyo et al. [16, 82, 83] related the paper's tensile index

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

17

#### 4. Accelerated thermal ageing in laboratory

Currently, most of oil-filled power transformers use as dielectric liquid, mineral oil, which is obtained from the middle range of petroleum-derived distillates. This fluid has shown suitable thermal and dielectric properties to carry out its functions as cooling and insulation. Nevertheless, it possess two important drawbacks, the first one is its low flash point and the second one is its low biodegradability, which can represent a high risk if spills or leaks would take place. This situation has led to the development of alternative transformer oils such as silicones, synthetic and natural esters. In particular, vegetal oils have drawn most attention and research [54].

During last two decades, the study of transformer oil-based nanofluids has become of great interest due to their prospective properties as cooling and dielectric liquids [55]. For example, Li et al. [56] prepared a nanofluid dispersing Fe3O4 nanoparticles in a vegetal oil and using oleic acid as surfactant. These authors compared the behaviour of this nanofluid with the pure oil measuring power frequency breakdown voltage and relative permittivity. The breakdown voltage of nanofluids has also been measured by Thabet et al. [57], nevertheless, in that work the insulation liquid was based on mineral oil and different nanoparticles (ZnO, MgO, Al2O3, TiO2, SiO2, LiTaO3, Fe3O4, graphite), as well as multi-nanoparticles collections, which were combination of two of the nanoparticles studied previously. These dielectric properties and other such as dissipation factor, dielectric constant or electrical resistivity have been studied by many authors [58, 59], analysing the effect of different nanoparticles (CaCu3Ti4O12, TiO2, Al2O3). The streamers in transformer oils under lightning impulse voltage have been observed, too by authors such as et al. [60, 61], Cavallini et al. [62], Sima et al. [63] and Liu et al. [64] or simulated as Velasco et al. [65]. The last ones not only evaluated dielectric properties, but also thermal conductivity of nanofluids obtained through the dispersion of AlN nanoparticles. The effect of nanoparticles on heat transfer characteristics was also studied by Guan et al. [64] and Morega et al. [66]. The last ones additionally evaluated the specific magnetisation of other nanofluid to open new venues in optimising conventional electrotechnic constructions or to design novel devices [67]. Creeping discharge and flashover characteristics of the oil/pressboard interface under AC and impulse voltages was studied by Lv et al. for a nanofluid based on TiO2 nanoparticles [68], obtaining an increase of the shallow trap density and a lower shallow trap energy level of oil-impregnated pressboard which can improve the creeping flashover strength of oil/pressboard interface.

When it is desired, the replacement of one usual component of the insulation system, as in the case of alternative dielectric oils, it is important to study the stability of the new system and compare it with the system widely used in power transformers (mineral oil/Kraft paper). For this reason, many accelerated thermal ageing studies have been carried out in the laboratory.

The first laboratory tests of accelerated thermal ageing focused on the behaviour of paper in mineral oil. For instance, Shroff and Stannett [69] aged Kraft paper and thermal upgraded paper in mineral oil at four temperatures. The results of their study showed that there is a direct relationship between the DP and the moisture in paper and the concentration of furanic compounds. These authors also proposed as paper end-of-life criteria a DP = 200 and a tensile strength equal to 50% of its original value. Other authors such as Yoshida et al. [70] also implemented ageing tests using mineral oil as dielectric liquid at different temperatures (120, 140 and 160C). In this case, they analysed the behaviour of Kraft and pressboard paper, obtaining as main conclusions the existence of a relationship between the concentration of CO/CO2 and the evolution of the DP and the tensile strength. On the other hand, Hill et al. [71] studied the tensile strength of the paper, the DP and the concentration of furans in ageing tests of Kraft paper in mineral oil at different temperatures, obtaining as a result the existence of a relationship between furans, DP and tensile strength. In addition, these authors proposed a paper degradation model based on the tensile strength. Emsley et al. [49, 72, 73] also proposed a degradation model, although this was based on the relationship between tensile strength and DP for Kraft paper and cotton paper aged in mineral oil. Since last decade, ageing studies have begun to take into account alternative oils. For example, Mcshane et al. [74–77] evaluated DP, tensile strength, moisture in oil and paper, as well as furan content when Kraft and thermal upgraded paper were aged in a mineral oil and in a natural ester. The results of their tests showed that the degradation rate experienced by the paper during thermal ageing at different temperatures was lower in the natural ester. These authors proposed the protective mechanisms developed by the ester that might explain the minor degradation suffered by the paper in the alternative oil. Other authors such as Shim et al. [78] also obtained greater thermal stability in the natural ester compared to mineral oil by the measure of the tensile strength for Kraft and diamond dotted paper. Similar results were presented by Azis [18], who analysed paper degradation using tensile strength, breakdown voltage, dynamic viscosity, acidity and concentration of low and high molecular weight acids in the oil. The measure of the concentration of low molecular weight acids (LMA) allowed observing that these tend to remain in the natural ester, which might explain the best behaviour of the Kraft paper during the ageing, in addition to the hydrolytic protection made by the oil. The behaviour of thermal upgraded and Kraft paper in mineral oil and in natural ester was also evaluated by Abdelmalik et al. [79], who studied the tensile and dielectric strength of the paper. Their results also showed that oils based on natural esters protect better against the degradation than mineral oil. Saruhashi et al. [80] studied for aramid paper tensile index, as well as breakdown voltage, acidity, colour and kinematic viscosity of the oil. In their study, they carry out ageing tests at two temperatures in three different oils (silicone, natural ester and synthetic ester). They found a slight variation of the tensile index in the three oils. The degradation of Kraft paper aged in a natural ester was also evaluated through the tensile strength by Widyanugraha et al. [35], who also measured the gases generated during ageing at two different temperatures. The tensile strength suffered initially a decrease and subsequently an increase during thermal ageing. It was assumed that this behaviour was due to the transesterification process. The tensile strength of the paper, besides other characteristic properties of the oil degradation, was analysed by Madavan and Balaraman [81], who obtained that the paper aged in oils based on natural esters had a lower degradation compared to Kraft paper immersed in mineral oil. In recent years, different authors have tried to find additional methods to study paper degradation when this is aged thermally in laboratory. For example, Arroyo et al. [16, 82, 83] related the paper's tensile index

solid was measured through DP; however, later assessments have demonstrated that in some cases the tensile or index strength can be more sensitive to differentiate the level of paper ageing.

Currently, most of oil-filled power transformers use as dielectric liquid, mineral oil, which is obtained from the middle range of petroleum-derived distillates. This fluid has shown suitable thermal and dielectric properties to carry out its functions as cooling and insulation. Nevertheless, it possess two important drawbacks, the first one is its low flash point and the second one is its low biodegradability, which can represent a high risk if spills or leaks would take place. This situation has led to the development of alternative transformer oils such as silicones, synthetic and natural esters. In particular, vegetal oils have drawn most attention and research [54].

During last two decades, the study of transformer oil-based nanofluids has become of great interest due to their prospective properties as cooling and dielectric liquids [55]. For example, Li et al. [56] prepared a nanofluid dispersing Fe3O4 nanoparticles in a vegetal oil and using oleic acid as surfactant. These authors compared the behaviour of this nanofluid with the pure oil measuring power frequency breakdown voltage and relative permittivity. The breakdown voltage of nanofluids has also been measured by Thabet et al. [57], nevertheless, in that work the insulation liquid was based on mineral oil and different nanoparticles (ZnO, MgO, Al2O3, TiO2, SiO2, LiTaO3, Fe3O4, graphite), as well as multi-nanoparticles collections, which were combination of two of the nanoparticles studied previously. These dielectric properties and other such as dissipation factor, dielectric constant or electrical resistivity have been studied by many authors [58, 59], analysing the effect of different nanoparticles (CaCu3Ti4O12, TiO2, Al2O3). The streamers in transformer oils under lightning impulse voltage have been observed, too by authors such as et al. [60, 61], Cavallini et al. [62], Sima et al. [63] and Liu et al. [64] or simulated as Velasco et al. [65]. The last ones not only evaluated dielectric properties, but also thermal conductivity of nanofluids obtained through the dispersion of AlN nanoparticles. The effect of nanoparticles on heat transfer characteristics was also studied by Guan et al. [64] and Morega et al. [66]. The last ones additionally evaluated the specific magnetisation of other nanofluid to open new venues in optimising conventional electrotechnic constructions or to design novel devices [67]. Creeping discharge and flashover characteristics of the oil/pressboard interface under AC and impulse voltages was studied by Lv et al. for a nanofluid based on TiO2 nanoparticles [68], obtaining an increase of the shallow trap density and a lower shallow trap energy level of oil-impregnated pressboard which can improve the creeping

When it is desired, the replacement of one usual component of the insulation system, as in the case of alternative dielectric oils, it is important to study the stability of the new system and compare it with the system widely used in power transformers (mineral oil/Kraft paper). For this reason, many accelerated thermal ageing studies have been carried out in the laboratory. The first laboratory tests of accelerated thermal ageing focused on the behaviour of paper in mineral oil. For instance, Shroff and Stannett [69] aged Kraft paper and thermal upgraded

4. Accelerated thermal ageing in laboratory

16 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

flashover strength of oil/pressboard interface.

with an indirect measure of its degradation, such as the concentration of methanol and ethanol in the oil. They also proposed three degradation models for Kraft and thermal upgraded paper. Each model was based on a different property (tensile index, DP, methanol and ethanol concentration in oil). The proposed models were obtained from the ageing data of the paper in mineral oil at three temperatures. Finally, they evaluated the influence that the concentration of stabilisation additives can have on the thermal stability of thermal upgraded paper. The results showed that the higher this concentration is, the better the paper stability, although it changes whereas the degradation of the paper takes place. Another alternative model based on a damage parameter D to predict the remaining life of Kraft paper has been defined by the authors of this chapter. This parameter can be based on any mechanical property (strength, Young's modulus, yield stress, energy consumed, strain under ultimate strength, etc.) obtained of the tensile test (Annex). This damage parameter can be used to evaluate additional mechanical properties which have not been used previously in a new proposed mathematical model based on temperature and time. The damage parameter D is defined as:

$$D = 1 - \frac{\text{Property}\_i}{\text{Property}\_0} \tag{14}$$

All these works have found that the thermal degradation of the paper can be evaluated using mechanical parameters such as tensile strength or TI. However, until now, other parameters obtained from the tensile test have not been considered, such as Young's modulus, strain, elastic limit, and so on, which might offer a more accurate view of the loss of mechanical strength by the paper. On the other hand, the use of SEM for materials aged in mineral oil seems to provide additional information on the relationship between the shape of cellulose fibres and their mechanical strength. Regarding the behaviour of cellulosic material in alternative oils, although several ageing studies have been carried out, degradation models based on mechanical properties have not been proposed. These mathematical models will allow to estimate the remaining life of dielectric papers as a function of temperature and time. The development of these degradation models requires analyse which mechanical properties can offer a better description of the loss of mechanical resistance. Additionally, the utilisation of SEM can help to detect when the

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

19

behaviour of the solid insulation becomes fragile increasing the failure probability.

There are several techniques that can be used to evaluate insulation paper degradation; however, the two most used in post-mortem analysis have been the degree of polymerisation (DP) and tensile strength. One of these post-mortem studies obtained as conclusions that the experimental results give a variation of DP values ranged from less than 5% to more than 40%, which indicates the results variability of this technique. On the other hand, all these end-of-life studies have shown the necessity of complement DP profile of the transformer with chemical markers such as furans, methanol, dissolved gases, and so on. Because of these by-products derived from paper and oil degradation can detect running problems (ineffective cooling,

leaking, higher gases development), which might be useful to prevent future failures.

Data obtained from post-mortem analysis should be complemented with tests carried out in the laboratory. These tests have provided useful correlations between oil markers and paper degradation in a short period of time and make possible establish comparisons between mineral and alternative oils in accelerated thermal ageing tests. The measure of paper mechanical strength has been limited until now at the estimation of tensile strength and tensile index, in spite of the fact that additional parameters (Young's modulus, yield stress, energy consumed, etc.) obtained in the tensile test can provide more accurate analysis of the loss of mechanical properties. For instance, the energy consumed might be more convenient to follow the changes of mechanical properties of insulation paper since in its definition the other two parameters (strength and strain) are used. Data obtained from stress–strain curve should be complemented with the information provided by techniques as SEM, which could detect behaviour changes in the paper related with type of failure. This could be carried out using texture analysis, which might provide information about thermal degradation of paper using the information provided by the statistical variation of pixels grey level intensities in an image. The results obtained from PD measurements have shown that solid ageing has little influence; nonetheless, oil ageing has great influence on PD characteristics over liquid/solid interface.

5. Conclusions

where Propertyi is the value of a macroscopic property (strength, yield stress…) in any situation of time (t) and temperature (T) and Property0 is the value of the same property of the original paper not subject to ageing. It can be observed that the damage parameter D can only take values between 1 and 0. The value 1 represents an insulation paper which has lost all its mechanical resistance whereas the value 0 corresponds to new insulation solid.

The evolution of D with t for different ageing conditions can be obtained through the mathematical model:

$$D = D\_{\text{max}} \cdot \left(1 - \exp(-a \cdot t)\right) \tag{15}$$

where the parameter a is a rate constant that indicates the effect of oil temperature in which the paper is aged, on the increase of the damage, D, suffered by paper along the time; Dmax is the maximum value reached experimentally by the damage; t is the time (h). The parameter a can be expressed by means of Arrhenius equation as a function of the ageing temperature.

Finally, the analysed Property can be expressed as a function of the time and the temperature:

$$\text{Property}\_i = \text{Property}\_0 \cdot \left(1 - D\_{\text{max}} \left(1 - \exp(-a \cdot t) \right) \right) \tag{16}$$

This mathematical model, which determines the damage suffered by paper aged in an oil, is a simplified macroscopic model that takes into account the general damage experienced by the paper.

On the other hand, Pei et al. [40] tried to relate the degradation suffered by pressboard aged at 130�C in mineral oil, through the tensile strength, with the microscopic appearance of its surface, using for this analysis the scanning electron microscope (SEM). The results of his study showed that the pressboard degradation is accompanied by changes in the superficial structure.

All these works have found that the thermal degradation of the paper can be evaluated using mechanical parameters such as tensile strength or TI. However, until now, other parameters obtained from the tensile test have not been considered, such as Young's modulus, strain, elastic limit, and so on, which might offer a more accurate view of the loss of mechanical strength by the paper. On the other hand, the use of SEM for materials aged in mineral oil seems to provide additional information on the relationship between the shape of cellulose fibres and their mechanical strength. Regarding the behaviour of cellulosic material in alternative oils, although several ageing studies have been carried out, degradation models based on mechanical properties have not been proposed. These mathematical models will allow to estimate the remaining life of dielectric papers as a function of temperature and time. The development of these degradation models requires analyse which mechanical properties can offer a better description of the loss of mechanical resistance. Additionally, the utilisation of SEM can help to detect when the behaviour of the solid insulation becomes fragile increasing the failure probability.

#### 5. Conclusions

(14)

with an indirect measure of its degradation, such as the concentration of methanol and ethanol in the oil. They also proposed three degradation models for Kraft and thermal upgraded paper. Each model was based on a different property (tensile index, DP, methanol and ethanol concentration in oil). The proposed models were obtained from the ageing data of the paper in mineral oil at three temperatures. Finally, they evaluated the influence that the concentration of stabilisation additives can have on the thermal stability of thermal upgraded paper. The results showed that the higher this concentration is, the better the paper stability, although it changes whereas the degradation of the paper takes place. Another alternative model based on a damage parameter D to predict the remaining life of Kraft paper has been defined by the authors of this chapter. This parameter can be based on any mechanical property (strength, Young's modulus, yield stress, energy consumed, strain under ultimate strength, etc.) obtained of the tensile test (Annex). This damage parameter can be used to evaluate additional mechanical properties which have not been used previously in a new proposed mathematical model

<sup>D</sup> <sup>¼</sup> <sup>1</sup> � Propertyi

where Propertyi is the value of a macroscopic property (strength, yield stress…) in any situation of time (t) and temperature (T) and Property0 is the value of the same property of the original paper not subject to ageing. It can be observed that the damage parameter D can only take values between 1 and 0. The value 1 represents an insulation paper which has lost all its

The evolution of D with t for different ageing conditions can be obtained through the mathe-

where the parameter a is a rate constant that indicates the effect of oil temperature in which the paper is aged, on the increase of the damage, D, suffered by paper along the time; Dmax is the maximum value reached experimentally by the damage; t is the time (h). The parameter a can

Finally, the analysed Property can be expressed as a function of the time and the temperature:

This mathematical model, which determines the damage suffered by paper aged in an oil, is a simplified macroscopic model that takes into account the general damage experienced by the

On the other hand, Pei et al. [40] tried to relate the degradation suffered by pressboard aged at 130�C in mineral oil, through the tensile strength, with the microscopic appearance of its surface, using for this analysis the scanning electron microscope (SEM). The results of his study showed

that the pressboard degradation is accompanied by changes in the superficial structure.

be expressed by means of Arrhenius equation as a function of the ageing temperature.

<sup>D</sup> <sup>¼</sup> <sup>D</sup>max � <sup>1</sup> � expð Þ �<sup>a</sup> � <sup>t</sup> (15)

Propertyi <sup>¼</sup> Property<sup>0</sup> � <sup>1</sup> � <sup>D</sup>max <sup>1</sup> � expð Þ �<sup>a</sup> � <sup>t</sup> (16)

Property<sup>0</sup>

based on temperature and time. The damage parameter D is defined as:

18 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

mechanical resistance whereas the value 0 corresponds to new insulation solid.

matical model:

paper.

There are several techniques that can be used to evaluate insulation paper degradation; however, the two most used in post-mortem analysis have been the degree of polymerisation (DP) and tensile strength. One of these post-mortem studies obtained as conclusions that the experimental results give a variation of DP values ranged from less than 5% to more than 40%, which indicates the results variability of this technique. On the other hand, all these end-of-life studies have shown the necessity of complement DP profile of the transformer with chemical markers such as furans, methanol, dissolved gases, and so on. Because of these by-products derived from paper and oil degradation can detect running problems (ineffective cooling, leaking, higher gases development), which might be useful to prevent future failures.

Data obtained from post-mortem analysis should be complemented with tests carried out in the laboratory. These tests have provided useful correlations between oil markers and paper degradation in a short period of time and make possible establish comparisons between mineral and alternative oils in accelerated thermal ageing tests. The measure of paper mechanical strength has been limited until now at the estimation of tensile strength and tensile index, in spite of the fact that additional parameters (Young's modulus, yield stress, energy consumed, etc.) obtained in the tensile test can provide more accurate analysis of the loss of mechanical properties. For instance, the energy consumed might be more convenient to follow the changes of mechanical properties of insulation paper since in its definition the other two parameters (strength and strain) are used. Data obtained from stress–strain curve should be complemented with the information provided by techniques as SEM, which could detect behaviour changes in the paper related with type of failure. This could be carried out using texture analysis, which might provide information about thermal degradation of paper using the information provided by the statistical variation of pixels grey level intensities in an image.

The results obtained from PD measurements have shown that solid ageing has little influence; nonetheless, oil ageing has great influence on PD characteristics over liquid/solid interface. Additionally, it has been observed by different authors that thermal ageing has significant impacts on surface morphology of insulation solid, which influences the developing process of PD. Therefore, it is necessary to analyse the effect of increasing the ageing time on the reduction in partial discharge magnitude for application in on-field practical tests. This analysis needs to take into account not only mineral oil, but also new insulating oils (natural and synthetic esters) which have proved to be a viable substitute. Moreover, there is an incomplete understanding of the oil/solid interface yet, as well as a lack of standardisation in PD measurements for diagnostic purposes of the HV components in which insulating liquids are employed.

D = textscan(fileID,'%f %f');

F = zeros((length(F\_data)-1)/nm,1); pos = zeros((length(F\_data)-1)/nm,1);

for i = 1:((length(F\_data)-1)/nm).

1) + 4) + pos\_data(nm\*(i-1) + 5));

pdte1 = (sigma(n + 1)-sigma(n))/(eps(n + 1)-eps(n));

pdte2 = (sigma(n + 2)-sigma(n + 1))/(eps(n + 2)-eps(n + 1)); pdte3 = (sigma(n + 3)-sigma(n + 2))/(eps(n + 3)-eps(n + 2));

if (abs((pdte1-pdte2)/pdte1) < 3e-2) && (abs((pdte2-pdte3)/pdte1) < 3e-2).

pos0 = pos\_data(1); eps = (pos-pos0)./l;

sigma = F./a0; % Calculate.

F(i) = 0.25\*(F\_data(nm\*(i-1) + 2) + F\_data(nm\*(i-1) + 3) + F\_data(nm\*(i-1) + 4) + F\_data(nm\*(i-

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

21

pos(i) = 0.25\*(pos\_data(nm\*(i-1) + 2) + pos\_data(nm\*(i-1) + 3) + pos\_data(nm\*(i-

fclose(fileID);

F\_data = D{1}; pos\_data = D{2};

1) + 5));

end

n = 0;

while true. n = n + 1;

pdte = pdte1;

if n + 3==length(sigma).

break.

break.

end

end

% Preparate Data.

Finally, the use of nanoparticles in power transformers has opened new ways in optimising their design because different studies have obtained an enhancement in dielectric properties (breakdown strength, partial discharge inception voltage, creeping flashover strength of oilimpregnated papers…) and thermal conductivity without significant change in the viscosity.

#### Acknowledgements

The authors are grateful for the funding received to carry out this work from the State Scientific and Technical Research and Innovation Plan under the DPI2013-43897-P grant agreement, financed by the Government of Spain.

### A. Annex

Having the data of Force (kN) and Displacement (mm), the following sequence of MATLAB, allows to obtain the different mechanical parameters of the material, which will be used in the mathematical model based on damage parameter defined by the authors of this chapter.

1-Define the constants: Initial length, Gramage, A0, a…

2-Load from a file with the results of Force (kN), Position (mm).

3-Matlab performs the calculations, represents the stress–strain graph and shows a summary table with the mechanical parameters.

clc

clear.

% Define constants.

a0 = 3;g = 0.15783222;a = 0.015;l = 180;

nm = 4;

% Open files Data.

fileID = fopen('data.txt');

```
D = textscan(fileID,'%f %f');
fclose(fileID);
% Preparate Data.
F_data = D{1};
pos_data = D{2};
F = zeros((length(F_data)-1)/nm,1);
pos = zeros((length(F_data)-1)/nm,1);
for i = 1:((length(F_data)-1)/nm).
F(i) = 0.25*(F_data(nm*(i-1) + 2) + F_data(nm*(i-1) + 3) + F_data(nm*(i-1) + 4) + F_data(nm*(i-
1) + 5));
pos(i) = 0.25*(pos_data(nm*(i-1) + 2) + pos_data(nm*(i-1) + 3) + pos_data(nm*(i-
1) + 4) + pos_data(nm*(i-1) + 5));
end
pos0 = pos_data(1);
eps = (pos-pos0)./l;
sigma = F./a0;
% Calculate.
n = 0;
while true.
n = n + 1;
pdte1 = (sigma(n + 1)-sigma(n))/(eps(n + 1)-eps(n));
pdte2 = (sigma(n + 2)-sigma(n + 1))/(eps(n + 2)-eps(n + 1));
pdte3 = (sigma(n + 3)-sigma(n + 2))/(eps(n + 3)-eps(n + 2));
if (abs((pdte1-pdte2)/pdte1) < 3e-2) && (abs((pdte2-pdte3)/pdte1) < 3e-2).
pdte = pdte1;
break.
end
if n + 3==length(sigma).
break.
end
```
Additionally, it has been observed by different authors that thermal ageing has significant impacts on surface morphology of insulation solid, which influences the developing process of PD. Therefore, it is necessary to analyse the effect of increasing the ageing time on the reduction in partial discharge magnitude for application in on-field practical tests. This analysis needs to take into account not only mineral oil, but also new insulating oils (natural and synthetic esters) which have proved to be a viable substitute. Moreover, there is an incomplete understanding of the oil/solid interface yet, as well as a lack of standardisation in PD measurements for diagnostic

Finally, the use of nanoparticles in power transformers has opened new ways in optimising their design because different studies have obtained an enhancement in dielectric properties (breakdown strength, partial discharge inception voltage, creeping flashover strength of oilimpregnated papers…) and thermal conductivity without significant change in the viscosity.

The authors are grateful for the funding received to carry out this work from the State Scientific and Technical Research and Innovation Plan under the DPI2013-43897-P grant agreement,

Having the data of Force (kN) and Displacement (mm), the following sequence of MATLAB, allows to obtain the different mechanical parameters of the material, which will be used in the mathematical model based on damage parameter defined by the authors of this chapter.

3-Matlab performs the calculations, represents the stress–strain graph and shows a summary

purposes of the HV components in which insulating liquids are employed.

20 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Acknowledgements

A. Annex

clc

clear.

nm = 4;

% Define constants.

% Open files Data.

fileID = fopen('data.txt');

financed by the Government of Spain.

table with the mechanical parameters.

a0 = 3;g = 0.15783222;a = 0.015;l = 180;

1-Define the constants: Initial length, Gramage, A0, a…

2-Load from a file with the results of Force (kN), Position (mm).

hold on.

axis([0 epsd 0 max(sigma)]).

plot([eps(1) eps(i\_corte)],[sigmay sigmay],':k'). plot([eps(i\_corte) eps(i\_corte)],[0 sigmay],':k').

maximum tension','Absorbed Energy','Tensile Index'};

\*Address all correspondence to: fdezdiegoc@unican.es

University of Cantabria, Santander, Cantabria, Spain

9780444995117 0444417133 9780444417138

Engineering, University of Cantabria, Santander, Cantabria, Spain

t.Position = [vert/2 vert-50 t.Extent(3) t.Extent(4)];

t.ColumnName = {'Elasticity Modulus','Elastic limit','Maximun Tension','Deformation under

1 Electrical and Energy Engineering Department, School of Industrial and Telecomunications

2 LADICIM (Laboratory of Materials Science and Engineering), School of Civil Engineering,

[1] Karsai K, Kerényi D, Kiss LL. Large Power Transformers. Amsterdam; New York: Elsevier; New York, NY, U.S.A.: Distribution for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987. Studies in electrical and electronic engineering, 25. 614 p. ISBN: 0444995110

[2] Siada AA. Power Transformer Condition Monitoring and Diagnosis. Chapter 2: Power Transformer Condition Monitoring and Diagnosis: concepts and Challeges. Albarracin R, Robles G, Ardila-Rey JA, Cavallini A, Passaglia Pagination R: c. 300pp. 2018. ISBN: 978-1-

, Felix Ortiz<sup>1</sup>

Assessment of Dielectric Paper Degradation through Mechanical Characterisation

http://dx.doi.org/10.5772/intechopen.77972

23

, Isidro Carrascal<sup>2</sup>

,

\*, Inmaculada Fernández<sup>1</sup>

dat = {pdte,sigmay,sigmar,epsd,Am,ts};

plot(eps,rect1,'–r'). plot(eps,rect2,'–m').

% Resumen Data.

t = uitable(f);

t.Data = dat;

Author details

References

78561-254-1

Cristina Fernández-Diego<sup>1</sup>

Carlos Renedo<sup>1</sup> and Fernando Delgado<sup>1</sup>

```
end
rect1 = pdte.*eps;
sigmar = sigma(length(sigma));
epsd = eps(length(sigma));
rect2 = pdte.*(eps-0.002);
sigmay = 0;
for i = 1:length(sigma).
if abs((sigma(i)-rect2(i))/sigma(i)) < 1e-2.
sigmay = sigma(i);
i_corte = i;
break.
end
end
Am = 0;
tem = zeros(length(sigma)-1,1);
for i = 1:length(sigma)-1.
tem(i) = (sigma(i + 1) + sigma(i))*0.5*(eps(i + 1)-eps(i));
Am = Am+tem(i);
end
ts = max(F)/a/g/1000;
% Screen size.
ss = get(0,'screensize');
width = ss(3);
height = ss(4);
% Graphic.
f = figure;
vert = ss(4)/1.5;
horz = ss(3)/1.5;
set(f,'Position',[(width/2)-horz/2, (height/2)-vert/2, horz, vert]);
plot(eps,sigma,'b').
```

```
hold on.
axis([0 epsd 0 max(sigma)]).
plot(eps,rect1,'–r').
plot(eps,rect2,'–m').
plot([eps(1) eps(i_corte)],[sigmay sigmay],':k').
plot([eps(i_corte) eps(i_corte)],[0 sigmay],':k').
% Resumen Data.
dat = {pdte,sigmay,sigmar,epsd,Am,ts};
t = uitable(f);
t.ColumnName = {'Elasticity Modulus','Elastic limit','Maximun Tension','Deformation under
maximum tension','Absorbed Energy','Tensile Index'};
t.Data = dat;
```
t.Position = [vert/2 vert-50 t.Extent(3) t.Extent(4)];

## Author details

end

rect1 = pdte.\*eps;

sigmay = 0;

i\_corte = i;

break.

Am = 0;

end end

end

sigmar = sigma(length(sigma));

22 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

if abs((sigma(i)-rect2(i))/sigma(i)) < 1e-2.

tem = zeros(length(sigma)-1,1);

tem(i) = (sigma(i + 1) + sigma(i))\*0.5\*(eps(i + 1)-eps(i));

set(f,'Position',[(width/2)-horz/2, (height/2)-vert/2, horz, vert]);

for i = 1:length(sigma)-1.

Am = Am+tem(i);

ts = max(F)/a/g/1000;

ss = get(0,'screensize');

% Screen size.

width = ss(3); height = ss(4);

% Graphic. f = figure;

vert = ss(4)/1.5; horz = ss(3)/1.5;

plot(eps,sigma,'b').

epsd = eps(length(sigma)); rect2 = pdte.\*(eps-0.002);

for i = 1:length(sigma).

sigmay = sigma(i);

Cristina Fernández-Diego<sup>1</sup> \*, Inmaculada Fernández<sup>1</sup> , Felix Ortiz<sup>1</sup> , Isidro Carrascal<sup>2</sup> , Carlos Renedo<sup>1</sup> and Fernando Delgado<sup>1</sup>

\*Address all correspondence to: fdezdiegoc@unican.es

1 Electrical and Energy Engineering Department, School of Industrial and Telecomunications Engineering, University of Cantabria, Santander, Cantabria, Spain

2 LADICIM (Laboratory of Materials Science and Engineering), School of Civil Engineering, University of Cantabria, Santander, Cantabria, Spain

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TDEI.2014.004277

mission & Distribution. 2018;12(5):1171-1176. DOI: 10.1049/iet-gtd.2017.1183


[81] Madavan R, Balaraman S. Failure analysis of transformer liquid - solid insulation system under selective environmental conditions using weibull statistics method. Engineering Failure Analysis. 2016;65:26-38. DOI: 10.1016/j.engfailanal.2016.03.017

**Chapter 2**

Provisional chapter

**Thermal Modelling of Electrical Insulation System in**

DOI: 10.5772/intechopen.78070

Temperature is one of the limiting factors in the application of power transformers. According to IEC 60076-7 standard, a temperature increase of 6C doubles the insulation ageing rate, reducing the expected lifetime of the device. Power losses of the transformer behave as a heating source, and the insulating liquids act as a coolant circulating through the windings and dissipating heat. For these reasons, thermal modelling becomes an important fact of transformer design, and both manufacturers and utilities consider it. Different techniques for thermal modelling have been developed and used for determining the hot-spot temperature, which is the highest temperature in the winding, and it is related with the degradation rate of the solid insulation. First models were developed as a first estimation for modelling the hot-spot temperature and the top-oil temperature. These models were based on thermal-electric analogy and are known as dynamic models. Other two different kinds of models are widely used for thermal modelling, known as Computational Fluid Dynamics (CFD) and Thermal Hydraulic Network Models (THNMs). These two techniques determine the temperature and velocity fields in the winding and in the insulating fluid. In this chapter, the different techniques for transformer thermal modelling will be introduced

Keywords: thermal modelling, power transformer, electrical insulation system, CFD,

Power transformers are key devices in the electrical grids, and this is a main reason for utilities and manufacturers to improve its performance and lifetime expectancy. Although its performance

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Thermal Modelling of Electrical Insulation System in

**Power Transformers**

Power Transformers

Agustín Santisteban, Fernando Delgado,

Agustín Santisteban, Fernando Delgado, Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz

Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78070

Abstract

and described.

THNM

1. Introduction


#### **Thermal Modelling of Electrical Insulation System in Power Transformers** Thermal Modelling of Electrical Insulation System in Power Transformers

DOI: 10.5772/intechopen.78070

Agustín Santisteban, Fernando Delgado, Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz Agustín Santisteban, Fernando Delgado, Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78070

#### Abstract

[81] Madavan R, Balaraman S. Failure analysis of transformer liquid - solid insulation system under selective environmental conditions using weibull statistics method. Engineering

[82] Arroyo OH, Jalbert J, Fofana I, Ryadi M. Temperature dependence of methanol and the tensile strength of insulation paper: Kinetics of the changes of mechanical properties

[83] Arroyo OH, Fofana I, Jalbert J, Rodriguez E, Rodriguez IB, Ryadi M. Assessing changes in thermally upgraded papers with different nitrogen contents under accelerated aging. IEEE Transactions on Dielectrics and Electrical Insulation. 2017;24(3):1829-1839. DOI:

during ageing. Cellulose. 2017;24(2):1031-1039. DOI: 10.1007/s10570-016-1123-7

Failure Analysis. 2016;65:26-38. DOI: 10.1016/j.engfailanal.2016.03.017

30 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

10.1109/TDEI.2017.006449

Temperature is one of the limiting factors in the application of power transformers. According to IEC 60076-7 standard, a temperature increase of 6C doubles the insulation ageing rate, reducing the expected lifetime of the device. Power losses of the transformer behave as a heating source, and the insulating liquids act as a coolant circulating through the windings and dissipating heat. For these reasons, thermal modelling becomes an important fact of transformer design, and both manufacturers and utilities consider it. Different techniques for thermal modelling have been developed and used for determining the hot-spot temperature, which is the highest temperature in the winding, and it is related with the degradation rate of the solid insulation. First models were developed as a first estimation for modelling the hot-spot temperature and the top-oil temperature. These models were based on thermal-electric analogy and are known as dynamic models. Other two different kinds of models are widely used for thermal modelling, known as Computational Fluid Dynamics (CFD) and Thermal Hydraulic Network Models (THNMs). These two techniques determine the temperature and velocity fields in the winding and in the insulating fluid. In this chapter, the different techniques for transformer thermal modelling will be introduced and described.

Keywords: thermal modelling, power transformer, electrical insulation system, CFD, THNM

#### 1. Introduction

Power transformers are key devices in the electrical grids, and this is a main reason for utilities and manufacturers to improve its performance and lifetime expectancy. Although its performance

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Table 1. Relative ageing rate for different hot-spot temperatures [1].

is over 99%, heat generation becomes a key factor for power limitation and expected lifetime. Transformer insulation ageing is sensible to temperature, doubling the ageing rate with a 6�C increase over the designed temperature according to IEC Standard 60076-7 [1]. High temperatures are caused by losses in the device, mainly due to Joule losses and eddy losses in the windings. The transformer insulation system that consists of a dielectric fluid and a solid insulation is the most critical part, and its degradation is related with the expected lifetime of the device [1]. The standard previously cited proposes a formulation to determine the ageing acceleration with the temperature

$$\mathcal{U} = \mathcal{2}^{((\theta\_h - 98)/6)} \tag{1}$$

thermal capacitance of the transformer [2]. The circuit is modelled by a partial differential equation whose solution gives the evolution of the hot-spot temperature over time. Normally, to simplify the solution, an intermediate circuit often comes with the hot-spot temperature

pu � τoil,rated �

where the terms are as follows: R, ratio of rated load losses to no-load losses; K, the load factor; μpu, oil viscosity (per-unit value); θamb, ambient temperature (�C); θhs, hot-spot temperature (�C); θoil, top-oil temperature (�C); Δθoil,rated, rated top-oil temperature rise over ambient (�C); Δθhs,rated, rated hot-spot temperature rise over top-oil temperature (�C); τoil,rated, rated oil time constant (s); τwdg,rated, rated winding time constant (s); n is a constant obtained from tables; and Pcu,pu(θhs) load loss's dependence on temperature (per-unit

In addition, the IEC 60076-7 standard proposes their own method with Eqs. (5) and (6):

1 þ R � �<sup>x</sup>

ent power rates and contrasted its accuracy with experimental measurements.

Figure 1. Dynamic models presented in [2]. (a) Top-oil model and (b) hot-spot model.

1 þ R � �<sup>x</sup> pu � τwdg,rated �

∂θoil

� <sup>Δ</sup>θoi ( ) � <sup>f</sup> <sup>1</sup>ð Þþ <sup>t</sup> <sup>Δ</sup>θhi <sup>þ</sup> <sup>H</sup> � gr � <sup>K</sup><sup>y</sup> � <sup>Δ</sup>θhi � � (5)

1 þ R

<sup>þ</sup> <sup>Δ</sup>θoi � <sup>Δ</sup>θor � <sup>1</sup> <sup>þ</sup> <sup>R</sup> � <sup>K</sup><sup>2</sup>

where Eq. (5) is applied for increasing the load factor and Eq. (6) is applied for decreasing the load factor. The functions f1, f2 and f3 can be calculated as explained in [1]. With these two models, the hot-spot temperature of a power transformer can be predicted over time, under different load conditions. In [2], both methods are tested with different transformers of differ-

� �<sup>x</sup> ( )

∂θhs

<sup>∂</sup><sup>t</sup> <sup>þ</sup> ð Þ <sup>θ</sup>oil � <sup>θ</sup>amb

Thermal Modelling of Electrical Insulation System in Power Transformers

Δθ<sup>n</sup> oil,rated

<sup>∂</sup><sup>t</sup> <sup>þ</sup> ð Þ <sup>θ</sup>hs � <sup>θ</sup>oil <sup>n</sup>þ<sup>1</sup> Δθ<sup>n</sup> hs,rated

1þn

http://dx.doi.org/10.5772/intechopen.78070

� <sup>f</sup> <sup>3</sup>ð Þþ <sup>t</sup> <sup>H</sup> � gr � <sup>K</sup><sup>y</sup> (6)

(3)

33

(4)

These models are associated with the differential equations, Eqs. (3) and (4) [2].

pu � <sup>Δ</sup>θhs,rated <sup>¼</sup> <sup>μ</sup><sup>n</sup>

pu � <sup>Δ</sup>θoil,rated <sup>¼</sup> <sup>μ</sup><sup>n</sup>

model to obtain the top-oil temperature, Figure 1.

<sup>1</sup> <sup>þ</sup> <sup>R</sup> � <sup>K</sup><sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>R</sup> � <sup>μ</sup><sup>n</sup>

<sup>K</sup> � Pcu, puð Þ <sup>θ</sup>hs � �un

<sup>θ</sup>hðÞ¼ <sup>t</sup> <sup>θ</sup><sup>a</sup> <sup>þ</sup> <sup>Δ</sup>θoi <sup>þ</sup> <sup>Δ</sup>θor � <sup>1</sup> <sup>þ</sup> <sup>R</sup> � <sup>K</sup><sup>2</sup>

<sup>θ</sup>hðÞ¼ <sup>t</sup> <sup>θ</sup><sup>a</sup> <sup>þ</sup> <sup>Δ</sup>θor � <sup>1</sup> <sup>þ</sup> <sup>R</sup> � <sup>K</sup><sup>2</sup>

value).

$$\mathcal{U}I = e^{\left(\frac{15000}{110+273} - \frac{15000}{6\_h+273}\right)}\tag{2}$$

where V is the relative ageing rate of the insulation, which is calculated by Eq. (1) for normal insulation paper and by Eq. (2) for thermally upgraded insulation paper, and θ<sup>h</sup> refers to the hot-spot temperature (�C). Both equations indicate that the relative ageing rate is sensible to hot-spot temperature variations as shown in Table 1.

For this reason, the estimation of the hot-spot temperature becomes an important task for manufacturers and utilities. Different models have been developed for the study of hot-spot temperature in oil-immersed power transformers that will be introduced in the following sections.

#### 2. Dynamic models

The first thermal modelling technique described is the dynamic thermal model. These models are based on the thermoelectric analogy to design a circuit based on the thermal resistance and thermal capacitance of the transformer [2]. The circuit is modelled by a partial differential equation whose solution gives the evolution of the hot-spot temperature over time. Normally, to simplify the solution, an intermediate circuit often comes with the hot-spot temperature model to obtain the top-oil temperature, Figure 1.

These models are associated with the differential equations, Eqs. (3) and (4) [2].

$$\frac{1+R\cdot K^2}{1+R}\cdot\mu\_{pu}^n\cdot\Delta\theta\_{oil,rated} = \mu\_{pu}^n\cdot\tau\_{oil,rated}\cdot\frac{\partial\theta\_{oil}}{\partial t} + \frac{(\theta\_{oil}-\theta\_{amb})^{1+n}}{\Delta\theta\_{oil,rated}^n} \tag{3}$$

$$\left\{\mathbf{K} \cdot \mathbf{P}\_{cu,pu}(\Theta\_{\mathrm{hs}})\right\} u\_{pu}^{n} \cdot \Delta \Theta\_{\mathrm{hs},ntted} = \mu\_{pu}^{n} \cdot \pi\_{\mathrm{wdg},ntted} \cdot \frac{\partial \Theta\_{\mathrm{hs}}}{\partial t} + \frac{(\Theta\_{\mathrm{hs}} - \Theta\_{\mathrm{oil}})^{n+1}}{\Delta \Theta\_{\mathrm{hs},ntted}^{n}} \tag{4}$$

where the terms are as follows: R, ratio of rated load losses to no-load losses; K, the load factor; μpu, oil viscosity (per-unit value); θamb, ambient temperature (�C); θhs, hot-spot temperature (�C); θoil, top-oil temperature (�C); Δθoil,rated, rated top-oil temperature rise over ambient (�C); Δθhs,rated, rated hot-spot temperature rise over top-oil temperature (�C); τoil,rated, rated oil time constant (s); τwdg,rated, rated winding time constant (s); n is a constant obtained from tables; and Pcu,pu(θhs) load loss's dependence on temperature (per-unit value).

In addition, the IEC 60076-7 standard proposes their own method with Eqs. (5) and (6):

is over 99%, heat generation becomes a key factor for power limitation and expected lifetime. Transformer insulation ageing is sensible to temperature, doubling the ageing rate with a 6�C increase over the designed temperature according to IEC Standard 60076-7 [1]. High temperatures are caused by losses in the device, mainly due to Joule losses and eddy losses in the windings. The transformer insulation system that consists of a dielectric fluid and a solid insulation is the most critical part, and its degradation is related with the expected lifetime of the device [1]. The standard previously cited proposes a formulation to determine the ageing acceleration

�C) Normal paper Thermally upgraded paper

 0.125 0.036 0.25 0.073 0.5 0.145 1.0 0.282 2.0 0.536 110 4.0 1.0 116 8.0 1.83 16.0 3.29 128 32.0 5.8 64.0 10.1 128.0 17.2

32 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

15000 <sup>110</sup>þ273� <sup>15000</sup> θhþ273 

where V is the relative ageing rate of the insulation, which is calculated by Eq. (1) for normal insulation paper and by Eq. (2) for thermally upgraded insulation paper, and θ<sup>h</sup> refers to the hot-spot temperature (�C). Both equations indicate that the relative ageing rate is sensible to

For this reason, the estimation of the hot-spot temperature becomes an important task for manufacturers and utilities. Different models have been developed for the study of hot-spot temperature in oil-immersed power transformers that will be introduced in the following sections.

The first thermal modelling technique described is the dynamic thermal model. These models are based on the thermoelectric analogy to design a circuit based on the thermal resistance and

U ¼ e

hot-spot temperature variations as shown in Table 1.

Table 1. Relative ageing rate for different hot-spot temperatures [1].

<sup>U</sup> <sup>¼</sup> <sup>2</sup>ð Þ ð Þ <sup>θ</sup>h�<sup>98</sup> <sup>=</sup><sup>6</sup> (1)

(2)

with the temperature

θ<sup>h</sup> (

2. Dynamic models

$$\Theta\_{\hbar}(t) = \Theta\_{\hbar} + \Delta\Theta\_{\vec{n}} + \left\{\Delta\Theta\_{\partial\vec{r}} \cdot \left[\frac{1 + \mathcal{R} \cdot \mathcal{K}^2}{1 + \mathcal{R}}\right]^\times - \Delta\Theta\_{\vec{n}}\right\} \cdot f\_1(t) + \Delta\Theta\_{\vec{n}} + \left(\mathcal{H} \cdot \mathcal{g}\_r \cdot \mathcal{K}^\mathcal{Y} - \Delta\Theta\_{\mathcal{U}}\right) \tag{5}$$

$$\Theta\_h(t) = \Theta\_a + \Delta\Theta\_{or} \cdot \left[\frac{1 + R \cdot K^2}{1 + R}\right]^\chi + \left\{\Delta\Theta\_{oi} - \Delta\Theta\_{or} \cdot \left[\frac{1 + R \cdot K^2}{1 + R}\right]^\chi\right\} \cdot f\_3(t) + H \cdot g\_r \cdot K^\psi \tag{6}$$

where Eq. (5) is applied for increasing the load factor and Eq. (6) is applied for decreasing the load factor. The functions f1, f2 and f3 can be calculated as explained in [1]. With these two models, the hot-spot temperature of a power transformer can be predicted over time, under different load conditions. In [2], both methods are tested with different transformers of different power rates and contrasted its accuracy with experimental measurements.

Figure 1. Dynamic models presented in [2]. (a) Top-oil model and (b) hot-spot model.

These temperature rises are caused by the combination of voltage-related losses (no-load losses) and current-related losses (load losses). The loss distribution is a scalar function P(r,φ,

netic (EM) losses is usually made using the Finite Element Method (FEM). Windings are divided into many rectangular sections with a uniform ampere-turn distribution. The eddy

> <sup>P</sup> <sup>¼</sup> <sup>ω</sup><sup>2</sup> � <sup>B</sup><sup>2</sup> � <sup>T</sup><sup>2</sup> 24 � r

where B is the peak leakage flux density (T), ω = 2πf, where f is the frequency (Hz), T is the conductor dimension perpendicular to the direction of the leakage flux density (m) and r is the

The axial and radial flux densities are assumed to be constant over a single conductor and equal to the value at its centre. The total eddy losses for each winding are calculated by

The boundary conditions can influence the results. A transformer is a 3D construction, in which the windings usually are symmetric, but the surrounding steel parts (core and tank)

The temperature rise over ambient temperature has to be calculated based on this loss distribution taken into account thermal conductivity of the metal, the thermal conductivity of the electrical insulation and convective cooling due to oil flow (viscosity of oil is important, which

The temperature rise of a transformer winding above the ambient temperature is built up from three component temperature rises: (1) the temperature rise of the inlet oil, (2) the temperature rise of the cooling oil as it passes through the transformer and (3) the temperature rise of the

Figure 3. Three-phase transformer with five-legged core and LV winding with a large pitch (front, top and side views,

losses are calculated for each conductor using Eq. (7)

).

integrating the losses of all its conductors.

makes the oil temperature also an important parameter).

] over the volume of these transformer metal parts. The determination of electromag-

Thermal Modelling of Electrical Insulation System in Power Transformers

http://dx.doi.org/10.5772/intechopen.78070

(7)

35

z) [W/m<sup>3</sup>

resistivity (Ω�m/mm<sup>2</sup>

are not, Figure 3.

and cross sections).

Figure 2. Complex top-oil thermal circuit [3].

For both models, a large number of parameters obtained from heat-run tests are necessary for calculations. However, the model proposed in [2] requires less input data than the model proposed by the standards.

Other complex models have been developed for top-oil and hot-spot temperature prediction. These models take into account the different thermal resistances that appear from the different heating sources in power transformer as shown in Figure 2 [3]. In addition, models for bottomoil temperature and bottom-winding temperature have been developed in [4].

In conclusion, dynamic thermal models are useful and can be implemented in computer software without hardly computational cost, requiring less than 5 min in a normal PC. However, the input data necessary to run the model come from the results of heat-run tests, which made this method dependent on the knowledge of these results.

#### 3. Steady-state models

An alternative to dynamic models is steady-state model. Steady-state models attempt to predict the temperature field in the transformer winding, determining the hot-spot temperature and its location. In these modelling techniques, the geometrical parameters of the transformer winding gain importance. Among the former, the one that is based on heat-run test is shown in the next section. Then, between the second ones, models based on Computational Fluid Dynamics (CFD) and those based on Thermal-Hydraulic Network Modelling (THNM) are developed.

#### 3.1. Hot-spot temperature rise from normal heat-run test data

The fundamental objective of a transformer thermal modelling is to be able to accurately predict winding and component temperature rises above ambient temperature. For the industry and transformer users, the determination of the location of the hot-spot and the hot-spot temperature rise is especially interesting. In [1], the limit temperature for top oil and hot spot is established at 105 and 120C for normal operation.

These temperature rises are caused by the combination of voltage-related losses (no-load losses) and current-related losses (load losses). The loss distribution is a scalar function P(r,φ, z) [W/m<sup>3</sup> ] over the volume of these transformer metal parts. The determination of electromagnetic (EM) losses is usually made using the Finite Element Method (FEM). Windings are divided into many rectangular sections with a uniform ampere-turn distribution. The eddy losses are calculated for each conductor using Eq. (7)

$$P = \frac{\omega^2 \cdot \mathcal{B}^2 \cdot T^2}{24 \cdot \rho} \tag{7}$$

where B is the peak leakage flux density (T), ω = 2πf, where f is the frequency (Hz), T is the conductor dimension perpendicular to the direction of the leakage flux density (m) and r is the resistivity (Ω�m/mm<sup>2</sup> ).

For both models, a large number of parameters obtained from heat-run tests are necessary for calculations. However, the model proposed in [2] requires less input data than the model

Other complex models have been developed for top-oil and hot-spot temperature prediction. These models take into account the different thermal resistances that appear from the different heating sources in power transformer as shown in Figure 2 [3]. In addition, models for bottom-

In conclusion, dynamic thermal models are useful and can be implemented in computer software without hardly computational cost, requiring less than 5 min in a normal PC. However, the input data necessary to run the model come from the results of heat-run tests, which

An alternative to dynamic models is steady-state model. Steady-state models attempt to predict the temperature field in the transformer winding, determining the hot-spot temperature and its location. In these modelling techniques, the geometrical parameters of the transformer winding gain importance. Among the former, the one that is based on heat-run test is shown in the next section. Then, between the second ones, models based on Computational Fluid Dynamics (CFD) and those based on Thermal-Hydraulic Network Modelling (THNM)

The fundamental objective of a transformer thermal modelling is to be able to accurately predict winding and component temperature rises above ambient temperature. For the industry and transformer users, the determination of the location of the hot-spot and the hot-spot temperature rise is especially interesting. In [1], the limit temperature for top oil and hot spot is

oil temperature and bottom-winding temperature have been developed in [4].

made this method dependent on the knowledge of these results.

34 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

3.1. Hot-spot temperature rise from normal heat-run test data

established at 105 and 120C for normal operation.

proposed by the standards.

Figure 2. Complex top-oil thermal circuit [3].

3. Steady-state models

are developed.

The axial and radial flux densities are assumed to be constant over a single conductor and equal to the value at its centre. The total eddy losses for each winding are calculated by integrating the losses of all its conductors.

The boundary conditions can influence the results. A transformer is a 3D construction, in which the windings usually are symmetric, but the surrounding steel parts (core and tank) are not, Figure 3.

The temperature rise over ambient temperature has to be calculated based on this loss distribution taken into account thermal conductivity of the metal, the thermal conductivity of the electrical insulation and convective cooling due to oil flow (viscosity of oil is important, which makes the oil temperature also an important parameter).

The temperature rise of a transformer winding above the ambient temperature is built up from three component temperature rises: (1) the temperature rise of the inlet oil, (2) the temperature rise of the cooling oil as it passes through the transformer and (3) the temperature rise of the

Figure 3. Three-phase transformer with five-legged core and LV winding with a large pitch (front, top and side views, and cross sections).

winding above the cooling oil. These temperatures can be measured in the surrounding of the transformer and in three points of it: inlet and outlet oil temperatures and mean winding temperature.

The temperature increase of the oil on passing through the transformer is the difference between the inlet and the outlet oil temperatures, but in a transformer, usually there are more than one parallel oil paths, and each one could have their own temperature rise. It is accepted that this increase is approximately the difference between the top-oil temperature and the cooled oil inlet temperature [1].

The temperature rise of the winding above the oil is referred to as the "gradient," g. A mean value for this is obtained from the difference between the mean winding temperature, usually determined by resistance measurements, and the mean oil temperature. The gradient can vary with position because of local variations in winding losses and cooling effectiveness.

The temperature rise at the hot spot, Δθ<sup>h</sup> ( �C), top-oil temperature, Δθ<sup>o</sup> ( �C), is expected to be greater than the mean winding gradient, g, as expressed by a hot-spot factor, H, Eq. (8):

$$
\Delta\theta\_h = \Delta\theta\_0 + (H \cdot \text{g}) \tag{8}
$$

where H could be expressed as the product of two dimensionless factors, Qfac, related to additional loss, and Sfac, related to the efficiency of cooling, Eq. (9):

$$H = \mathbb{Q}\_{\text{fuc}} \cdot \mathbb{S}\_{\text{fuc}} \tag{9}$$

For transformer manufacturers, a good thermal design is a very important issue. Aspects as material, winding geometry, oil paths through the windings, or oil velocity are very relevant.

Figure 4. Transformer thermal diagram with the measured quantities highlighted. A—Top-oil temperature derived as the average of the tank outlet oil temperature and the tank oil pocket temperature. B—Mixed oil temperature in the tank at the top of the winding (often assumed to be the same temperature as A). C—Temperature of the average oil in the tank. D—Oil temperature at the bottom of the winding. E—Bottom of the tank. gr—Average winding to average oil (in tank) temperature gradient at rated current. H—Hot-spot factor. P—Hot-spot temperature. Q—Average winding temperature

Thermal Modelling of Electrical Insulation System in Power Transformers

http://dx.doi.org/10.5772/intechopen.78070

37

Mathematical models allow predicting transformer temperatures and winding hot-spot temperatures with good accuracy. Transformer manufacturers use these models to make their designs and any significant design variants. However, simulating the loss distribution in the structural metal parts of a transformer requires a very large number of small mesh elements. Nevertheless, calculating the temperature rise distribution in the structural metal parts

Tackling numerically, a complex physical problem using computational resources has only been able since few years ago. In fact, the current powerful computing resources allow us to discretize complex geometries. Then, the underlying governing equations, for example, differential equations (DEs), can be solved assuming small simplifications. The discretization process converts these DEs in a set of algebraic equations that can be solved using numerical algorithms. Regarding our topic, in which heat transfer and fluid dynamics physics are involved, the numerical method that carries out this process is named Computational Fluid

This design determines the cost and the insulation ageing (transformer life).

requires a much higher resolution mesh density.

determined by resistance measurement.

3.2. Computational fluid dynamics modelling

Dynamics (CFD).

The H factor can be derived from Figure 4 and can be expressed according to Eq. (10):

$$H = \frac{\Theta\_h - \Theta\_0}{\Theta\_w - \frac{\Theta\_0 - \Theta\_b}{2}} \tag{10}$$

where θ<sup>w</sup> and θ<sup>b</sup> are, respectively, the average winding and bottom-oil temperatures (�C).

The Q-factor is a dimensionless factor as a ratio of two losses, and in cylindrical coordinates is defined according to Eq. (11)

$$Q\_{\rm fac} = \frac{q(r, z, \varphi, \mathbf{T})}{q\_{\rm ave}} \tag{11}$$

where q (r, z, φ, T) is the local loss density at a location (W/m<sup>3</sup> ), r is the radial position, φ is the angle in circumferential position, z is the axial position, T is the local temperature at (r, z, φ) (K) and qave is the average loss of the winding at an average temperature (W/m<sup>3</sup> ).

Heat transfer can be propagated in different directions, the overall heat transfer being a series and parallel parts of (1) the insulation between the neighbouring conductors that are in direct contact with each other. This is in a radial direction. (2) The insulation paper and oil boundary layer between the conductor and the oil flow. This is in an axial direction. (3) The winding copper. This is located in the tangential direction and usually can be neglected.

Thermal Modelling of Electrical Insulation System in Power Transformers http://dx.doi.org/10.5772/intechopen.78070 37

Figure 4. Transformer thermal diagram with the measured quantities highlighted. A—Top-oil temperature derived as the average of the tank outlet oil temperature and the tank oil pocket temperature. B—Mixed oil temperature in the tank at the top of the winding (often assumed to be the same temperature as A). C—Temperature of the average oil in the tank. D—Oil temperature at the bottom of the winding. E—Bottom of the tank. gr—Average winding to average oil (in tank) temperature gradient at rated current. H—Hot-spot factor. P—Hot-spot temperature. Q—Average winding temperature determined by resistance measurement.

For transformer manufacturers, a good thermal design is a very important issue. Aspects as material, winding geometry, oil paths through the windings, or oil velocity are very relevant. This design determines the cost and the insulation ageing (transformer life).

Mathematical models allow predicting transformer temperatures and winding hot-spot temperatures with good accuracy. Transformer manufacturers use these models to make their designs and any significant design variants. However, simulating the loss distribution in the structural metal parts of a transformer requires a very large number of small mesh elements. Nevertheless, calculating the temperature rise distribution in the structural metal parts requires a much higher resolution mesh density.

#### 3.2. Computational fluid dynamics modelling

winding above the cooling oil. These temperatures can be measured in the surrounding of the transformer and in three points of it: inlet and outlet oil temperatures and mean winding

The temperature increase of the oil on passing through the transformer is the difference between the inlet and the outlet oil temperatures, but in a transformer, usually there are more than one parallel oil paths, and each one could have their own temperature rise. It is accepted that this increase is approximately the difference between the top-oil temperature and the

The temperature rise of the winding above the oil is referred to as the "gradient," g. A mean value for this is obtained from the difference between the mean winding temperature, usually determined by resistance measurements, and the mean oil temperature. The gradient can vary

�C), top-oil temperature, Δθ<sup>o</sup> (

Δθ<sup>h</sup> ¼ Δθ<sup>0</sup> þ ð Þ H � g (8)

H ¼ Qfac � Sfac (9)

�C), is expected to be

(10)

(11)

), r is the radial position, φ is the

).

with position because of local variations in winding losses and cooling effectiveness.

additional loss, and Sfac, related to the efficiency of cooling, Eq. (9):

36 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

where q (r, z, φ, T) is the local loss density at a location (W/m<sup>3</sup>

and qave is the average loss of the winding at an average temperature (W/m<sup>3</sup>

copper. This is located in the tangential direction and usually can be neglected.

greater than the mean winding gradient, g, as expressed by a hot-spot factor, H, Eq. (8):

The H factor can be derived from Figure 4 and can be expressed according to Eq. (10):

<sup>H</sup> <sup>¼</sup> <sup>θ</sup><sup>h</sup> � <sup>θ</sup><sup>0</sup> <sup>θ</sup><sup>w</sup> � <sup>θ</sup>0�θ<sup>b</sup> 2

where θ<sup>w</sup> and θ<sup>b</sup> are, respectively, the average winding and bottom-oil temperatures (�C).

The Q-factor is a dimensionless factor as a ratio of two losses, and in cylindrical coordinates is

Qfac <sup>¼</sup> q rð Þ ; <sup>z</sup>; <sup>φ</sup>; <sup>T</sup> qave

angle in circumferential position, z is the axial position, T is the local temperature at (r, z, φ) (K)

Heat transfer can be propagated in different directions, the overall heat transfer being a series and parallel parts of (1) the insulation between the neighbouring conductors that are in direct contact with each other. This is in a radial direction. (2) The insulation paper and oil boundary layer between the conductor and the oil flow. This is in an axial direction. (3) The winding

where H could be expressed as the product of two dimensionless factors, Qfac, related to

temperature.

cooled oil inlet temperature [1].

defined according to Eq. (11)

The temperature rise at the hot spot, Δθ<sup>h</sup> (

Tackling numerically, a complex physical problem using computational resources has only been able since few years ago. In fact, the current powerful computing resources allow us to discretize complex geometries. Then, the underlying governing equations, for example, differential equations (DEs), can be solved assuming small simplifications. The discretization process converts these DEs in a set of algebraic equations that can be solved using numerical algorithms. Regarding our topic, in which heat transfer and fluid dynamics physics are involved, the numerical method that carries out this process is named Computational Fluid Dynamics (CFD).

#### 3.2.1. CFD basic concepts

CFD is based on the solution of the Navier-Stokes equations. These are a set of Partial Differential Equations (PDE) that state the mass, momentum and energy conservations, Eqs. (15)– (17). However, it is not possible to solve them in an exact way (except some scarce and special cases). CFD allows solving these PDE by means of the geometrical model discretization. The latter converts the PDE in a set of algebraic equations that can be solved using specialised numerical algorithms, such as Gauss elimination algorithm, on a computer. These algorithms obtain the solution (velocity, pressure, temperature, in the case of power transformers) at discrete points of the studied domain [5]

$$\nabla \cdot (\rho u) = 0 \tag{12}$$

three indexes (i,j,k). The deformation grade (mesh quality) of the elements of this meshing type is generally smaller than in the other case. In addition, the cells can be oriented in the main

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By contrast, unstructured meshing can be used in very complex geometries. The cells may have any shape (quadrilateral or triangular shapes in 2D, tetrahedral or hexahedral shapes in 3D), thus a better adaption to the geometry is obtained. However, this type of mesh generates a set of algebraic equations whose solution time is habitually higher. Finally, the mesh refinement grade affects the solution accuracy. Generally, the finer the mesh, the more accurate the

The solution of the set of algebraic equations resulting from the discretization of the geometric model is the last step. This can be done using direct or iterative methods. The latter are habitually used to solve the Conjugate Heat Transfer (CHT) problems since the computational requirements are smaller than that required by the former methods. For instance, CHT problems are commonly solved using iterative methods such as Conjugate gradient, Gauss-Seidel

In addition, to solve the algebraic equations, a convergence criterion is needed to be considered. This is often implied to assume a maximum error in the residuals of the governing equations. That is, the solution obtained is not exact. In other words, another error appears in

In comparison with other numerical tools (for instance, THNM), a lot of computing time and a great amount of computational resources are needed by CFD. However, this technique allows

flow direction, thus capturing the flow phenomena in a better way.

knowing the fluid flow and heat transfer phenomena in fine detail.

solution is.

Figure 5. Geometry definition.

and Multigrid.

the numerical model solution.

$$\rho(\boldsymbol{\mu}\cdot\nabla)\mathbf{u} = \nabla\left[pI + \mu\left(\nabla\boldsymbol{u} + (\nabla\boldsymbol{u})^T\right) - \frac{2}{3}\mu(\nabla\cdot\boldsymbol{u})I\right] + F \tag{13}$$

$$
\rho \mathbf{C}\_p \boldsymbol{\mu} \cdot \nabla T = \nabla \cdot (k \nabla T) + \mathbf{q} \tag{14}
$$

where r, u, p, I, μ, F, Cp T and q of Eqs. (12)–(14) are, respectively, density (kg/m<sup>3</sup> ), velocity vector (m/s), pressure (Pa), identity matrix, dynamic viscosity (Pa�s), body force vector (N/m<sup>3</sup> ), specific heat capacity (J/kg�K), temperature (K) and unitary heat transfer (W/m<sup>3</sup> ).

The first step in this kind of modelling is usually to determine the dimensions number of the geometrical model: 2D or 3D, generally. This is very important since the geometrical model is the first source of errors. For instance, if 2D models were considered in CFD, important edge effects that contribute to heat transfer and flow phenomena could be obviated.

Generally, CAD tools are used to draw the geometry (Solidworks, Inventor, etc.). These tools allow defining the geometry with a high-detail level. The latter is an essential aspect to be considered since a very detailed geometry can excessively complicate the numerical model without significant improvement in the problem definition. For instance, in the case of the power transformer shown in Figure 5, it was decided to simplify the phase using angular and plane symmetries since these simplifications did not affect the solution accuracy.

The physics involved in the problem analysed must be described. In CFD, many mathematical models can be used to define the heat transfer and flow phenomena. In fact, an adequate selection of the model and a correct setting of the boundary conditions supported by this model are a crucial task to avoid errors in the numerical solution obtained.

This task consists in the division of the geometric model in smaller parts (cells). This is the socalled discretization. There are mainly three discretization techniques: finite element, finite volume and finite difference. At the same time, these techniques generate structured and/or unstructured meshes.

Structured meshing is habitually used in simple geometries such as the one shown in Figure 5. This geometry consists in volumetric cells of six faces that can uniquely be identified using

Figure 5. Geometry definition.

3.2.1. CFD basic concepts

obviated.

unstructured meshes.

discrete points of the studied domain [5]

CFD is based on the solution of the Navier-Stokes equations. These are a set of Partial Differential Equations (PDE) that state the mass, momentum and energy conservations, Eqs. (15)– (17). However, it is not possible to solve them in an exact way (except some scarce and special cases). CFD allows solving these PDE by means of the geometrical model discretization. The latter converts the PDE in a set of algebraic equations that can be solved using specialised numerical algorithms, such as Gauss elimination algorithm, on a computer. These algorithms obtain the solution (velocity, pressure, temperature, in the case of power transformers) at

<sup>T</sup>

� 2 3

rð Þ u � ∇ u ¼ ∇ pI þ μ ∇u þ ð Þ ∇u

38 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

where r, u, p, I, μ, F, Cp T and q of Eqs. (12)–(14) are, respectively, density (kg/m<sup>3</sup>

specific heat capacity (J/kg�K), temperature (K) and unitary heat transfer (W/m<sup>3</sup>

plane symmetries since these simplifications did not affect the solution accuracy.

model are a crucial task to avoid errors in the numerical solution obtained.

vector (m/s), pressure (Pa), identity matrix, dynamic viscosity (Pa�s), body force vector (N/m<sup>3</sup>

The first step in this kind of modelling is usually to determine the dimensions number of the geometrical model: 2D or 3D, generally. This is very important since the geometrical model is the first source of errors. For instance, if 2D models were considered in CFD, important edge effects that contribute to heat transfer and flow phenomena could be

Generally, CAD tools are used to draw the geometry (Solidworks, Inventor, etc.). These tools allow defining the geometry with a high-detail level. The latter is an essential aspect to be considered since a very detailed geometry can excessively complicate the numerical model without significant improvement in the problem definition. For instance, in the case of the power transformer shown in Figure 5, it was decided to simplify the phase using angular and

The physics involved in the problem analysed must be described. In CFD, many mathematical models can be used to define the heat transfer and flow phenomena. In fact, an adequate selection of the model and a correct setting of the boundary conditions supported by this

This task consists in the division of the geometric model in smaller parts (cells). This is the socalled discretization. There are mainly three discretization techniques: finite element, finite volume and finite difference. At the same time, these techniques generate structured and/or

Structured meshing is habitually used in simple geometries such as the one shown in Figure 5. This geometry consists in volumetric cells of six faces that can uniquely be identified using

∇ � ð Þ¼ ru 0 (12)

þ F (13)

).

), velocity

),

μð Þ ∇ � u I

rCpu � ∇T ¼ ∇ � ð Þþ k∇T q (14)

three indexes (i,j,k). The deformation grade (mesh quality) of the elements of this meshing type is generally smaller than in the other case. In addition, the cells can be oriented in the main flow direction, thus capturing the flow phenomena in a better way.

By contrast, unstructured meshing can be used in very complex geometries. The cells may have any shape (quadrilateral or triangular shapes in 2D, tetrahedral or hexahedral shapes in 3D), thus a better adaption to the geometry is obtained. However, this type of mesh generates a set of algebraic equations whose solution time is habitually higher. Finally, the mesh refinement grade affects the solution accuracy. Generally, the finer the mesh, the more accurate the solution is.

The solution of the set of algebraic equations resulting from the discretization of the geometric model is the last step. This can be done using direct or iterative methods. The latter are habitually used to solve the Conjugate Heat Transfer (CHT) problems since the computational requirements are smaller than that required by the former methods. For instance, CHT problems are commonly solved using iterative methods such as Conjugate gradient, Gauss-Seidel and Multigrid.

In addition, to solve the algebraic equations, a convergence criterion is needed to be considered. This is often implied to assume a maximum error in the residuals of the governing equations. That is, the solution obtained is not exact. In other words, another error appears in the numerical model solution.

In comparison with other numerical tools (for instance, THNM), a lot of computing time and a great amount of computational resources are needed by CFD. However, this technique allows knowing the fluid flow and heat transfer phenomena in fine detail.

#### 3.2.2. Main research lines of CFD applied to transformer thermal modelling

As can be seen in Figure 6, the cooling system of a power transformer is a closed loop that consists mainly of a heat source (windings), a heat sink (radiators) and a tank. Most CFD studies are focused on the thermal-fluid behaviour of the cooling system inside the windings. Nonetheless, some efforts have been put into the thermal modelling of the radiators too. The next subsections present a brief review of these topics.

cooling [12]. In 2014, Yatsevsky carried out a 2D-axisymmetric simulation of a CHT model of a transformer, including the core, the tank and the radiator, in order to predict hot spots in an oil-immersed transformer with natural convection. The developed model has shown a good adequacy verified by experiments [13]. Recently, Torriano et al. have developed a 3D CHT model of an Oil Natural (ON) disc-type power transformer-winding scale model. An underestimation of the average and hot-spot temperatures was obtained in this model in comparison with the experimental setup when the entire cooling loop was considered. This is the reason why the authors chose to reduce the computational domain to the winding, setting the inlet

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boundary conditions. This way, the model accuracy was improved significantly [14].

lower for the vegetable oils in the initial design than that of mineral oil [17].

mineral oil.

3.2.4. Radiator modelling

The substitution of mineral oil by new biodegradable dielectric liquids is another research line in which CFD is used as an analysis tool. However, few experimental and theoretical works can be found in the study related with the cooling capacity of these new liquids. In 2015, Park et al. employed a 2D-CFD model to obtain temperature and velocity profiles of some alternative liquids used in a distribution transformer of 2.3 MVA and a power transformer of 16.5 MVA [15]. In the same year, Lecuna et al. carried out a 3D-CFD simulation of an ONAN distribution transformer comparing a natural ester, a synthetic ester, a high kinematic viscosity silicone oil and a low kinematic viscosity silicone oil with a mineral oil [16]. These works conclude that alternative liquids produce higher temperatures in the transformer windings designed for mineral oil. More recently, Santisteban et al. evaluated the cooling performance of two alternative vegetal liquids with that of a typical mineral oil. This task was carried out using a 2D-axisymmetric model of an LVW with zigzag cooling in which temperature distributions, hot-spot temperatures and their locations, and hot-spot factors were determined. In contrast to the results of the previous works, this work shows that the hot-spot temperature is

Finally, CFD is also used to analyse the advantage of using natural esters in the transformer insulation system. For instance, in 2016, Fernandez et al. published a work in which laboratory experiments and CFD simulations are combined to study the influence of vegetable oils in the life span of the winding insulation paper [18]. It was concluded that, even though the chapter suffers worse thermal conditions when it is immersed in vegetable oils, the physical properties of these oils extend the life span of this chapter, Figure 7. That is, in the long term, both effects tend to the balance and the degradation is similar to the one obtained in windings cooled by

Most of the power transformers have fan-cooled radiators. CFD can be used to improve the cooling capability of these components. Few works can be found with this subject. In fact, this topic has mainly begun to be treated in this decade. For instance, Kim et al. presented in 2013, a predictive and experimental study about the cooling performance of the radiators used in oil-filled power transformers with two different cooling methods, ONAN and Oil-Directed Air Natural (ODAN) [19]. The aim was to experimentally evaluate the cooling capacity of the radiator and compare the results with those obtained with two different predictive methods. CFD was one of these methods. The authors stated that the radiator optimization could be

#### 3.2.3. Winding modelling

As mentioned previously, the main goal of the winding CFD modelling is to numerically predict the hot-spot temperature and temperature distributions in oil-immersed transformers since their life span depends on it. First works were developed at the beginning of this century. For instance, Mufuta et al. and El Wakil et al. modelled two windings using this technique. The former characterises the oil flow through an array of discs with different spaces between discs and different inlet conditions [7]. The latter employed a 2D axisymmetric model of a power transformer with six different geometries and six different inlet velocities in order to study the heat transfer and oil flow through the windings [8]. In the same decade, other authors have contributed to this labour. For instance, Torriano performed 2D and 3D simulations of an LV winding (LVW) of a power transformer with zigzag cooling to determine the effects of several elements, such as sticks and inter-sticks, in the temperature distribution [6, 9]. In 2011, Gastelurrutia et al. carried out a study where they developed a 3D and a 2D model of an Oil Natural-Air Natural (ONAN) distribution transformer. They demonstrated the good capacity of the simplified 2D model to represent the thermal behaviour of the whole transformer [10]. In 2012, Tsili et al. established a methodology to develop a 3D model to predict hot-spot temperature [11]. In this year, Skillen et al. carried out a CFD simulation of a 2D non-isothermal flow axisymmetric model in order to characterise the oil flow in transformer winding with zigzag

Figure 6. Schematic of oil circulation in a power transformer [6].

cooling [12]. In 2014, Yatsevsky carried out a 2D-axisymmetric simulation of a CHT model of a transformer, including the core, the tank and the radiator, in order to predict hot spots in an oil-immersed transformer with natural convection. The developed model has shown a good adequacy verified by experiments [13]. Recently, Torriano et al. have developed a 3D CHT model of an Oil Natural (ON) disc-type power transformer-winding scale model. An underestimation of the average and hot-spot temperatures was obtained in this model in comparison with the experimental setup when the entire cooling loop was considered. This is the reason why the authors chose to reduce the computational domain to the winding, setting the inlet boundary conditions. This way, the model accuracy was improved significantly [14].

The substitution of mineral oil by new biodegradable dielectric liquids is another research line in which CFD is used as an analysis tool. However, few experimental and theoretical works can be found in the study related with the cooling capacity of these new liquids. In 2015, Park et al. employed a 2D-CFD model to obtain temperature and velocity profiles of some alternative liquids used in a distribution transformer of 2.3 MVA and a power transformer of 16.5 MVA [15]. In the same year, Lecuna et al. carried out a 3D-CFD simulation of an ONAN distribution transformer comparing a natural ester, a synthetic ester, a high kinematic viscosity silicone oil and a low kinematic viscosity silicone oil with a mineral oil [16]. These works conclude that alternative liquids produce higher temperatures in the transformer windings designed for mineral oil. More recently, Santisteban et al. evaluated the cooling performance of two alternative vegetal liquids with that of a typical mineral oil. This task was carried out using a 2D-axisymmetric model of an LVW with zigzag cooling in which temperature distributions, hot-spot temperatures and their locations, and hot-spot factors were determined. In contrast to the results of the previous works, this work shows that the hot-spot temperature is lower for the vegetable oils in the initial design than that of mineral oil [17].

Finally, CFD is also used to analyse the advantage of using natural esters in the transformer insulation system. For instance, in 2016, Fernandez et al. published a work in which laboratory experiments and CFD simulations are combined to study the influence of vegetable oils in the life span of the winding insulation paper [18]. It was concluded that, even though the chapter suffers worse thermal conditions when it is immersed in vegetable oils, the physical properties of these oils extend the life span of this chapter, Figure 7. That is, in the long term, both effects tend to the balance and the degradation is similar to the one obtained in windings cooled by mineral oil.

#### 3.2.4. Radiator modelling

3.2.2. Main research lines of CFD applied to transformer thermal modelling

40 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

next subsections present a brief review of these topics.

Figure 6. Schematic of oil circulation in a power transformer [6].

3.2.3. Winding modelling

As can be seen in Figure 6, the cooling system of a power transformer is a closed loop that consists mainly of a heat source (windings), a heat sink (radiators) and a tank. Most CFD studies are focused on the thermal-fluid behaviour of the cooling system inside the windings. Nonetheless, some efforts have been put into the thermal modelling of the radiators too. The

As mentioned previously, the main goal of the winding CFD modelling is to numerically predict the hot-spot temperature and temperature distributions in oil-immersed transformers since their life span depends on it. First works were developed at the beginning of this century. For instance, Mufuta et al. and El Wakil et al. modelled two windings using this technique. The former characterises the oil flow through an array of discs with different spaces between discs and different inlet conditions [7]. The latter employed a 2D axisymmetric model of a power transformer with six different geometries and six different inlet velocities in order to study the heat transfer and oil flow through the windings [8]. In the same decade, other authors have contributed to this labour. For instance, Torriano performed 2D and 3D simulations of an LV winding (LVW) of a power transformer with zigzag cooling to determine the effects of several elements, such as sticks and inter-sticks, in the temperature distribution [6, 9]. In 2011, Gastelurrutia et al. carried out a study where they developed a 3D and a 2D model of an Oil Natural-Air Natural (ONAN) distribution transformer. They demonstrated the good capacity of the simplified 2D model to represent the thermal behaviour of the whole transformer [10]. In 2012, Tsili et al. established a methodology to develop a 3D model to predict hot-spot temperature [11]. In this year, Skillen et al. carried out a CFD simulation of a 2D non-isothermal flow axisymmetric model in order to characterise the oil flow in transformer winding with zigzag

> Most of the power transformers have fan-cooled radiators. CFD can be used to improve the cooling capability of these components. Few works can be found with this subject. In fact, this topic has mainly begun to be treated in this decade. For instance, Kim et al. presented in 2013, a predictive and experimental study about the cooling performance of the radiators used in oil-filled power transformers with two different cooling methods, ONAN and Oil-Directed Air Natural (ODAN) [19]. The aim was to experimentally evaluate the cooling capacity of the radiator and compare the results with those obtained with two different predictive methods. CFD was one of these methods. The authors stated that the radiator optimization could be

equations. These principles are applied to solve the temperature and oil flow fields in several parts of the transformer (windings, core, coolers). THNM applied on the windings can be useful

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THNM models are the coupling of two different networks: the hydraulic network and the thermal network. The hydraulic network comprises the oil flows through channels and nodes. The oil flow is modelled using the electric circuit analogy where the oil flow and pressure correspond to, respectively, electrical current and voltage. The thermal network models the heat transfer between the active parts and the cooling circuit of the transformer. Temperaturedependent properties of the materials and heat transfer coefficients make both networks to be

The hydraulic network corresponding to a disc winding with barriers is shown in Figure 8. The hydraulic network consists of eight nodes, four per axial side, where two of the nodes correspond to the entrance and exit of the coolant and the three remaining nodes per side are where the coolant branches or merges. The network is represented by its electrical circuit analogy where the physical quantity associated to each node corresponds to the sum of the static and dynamic pressures. In the circuit, resistances represent frictional pressure drops, and resistances in the nodes represent the local pressure drops as well. Buoyancy effect is represented by generators representing the gain of pressure due to gravitational effects. Since the hydraulic resistances depend on the flow, the hydraulic circuit proposed in Figure 8 is a

nonlinear circuit that has to be solved with an iterative procedure [24].

Figure 8. Analogy hydraulic circuit versus hydraulic network.

for predicting the hot-spot temperature.

coupled.

3.3.1. Hydraulic network

Figure 7. Velocities (mm/s) and temperatures (C) distributions.

done in this way. On the other hand, to improve the cooling capacity of the radiators, the fan's location in the radiators has to be studied. Paramane et al. conducted this in 2014 using both CFD and experimental studies [20]. They considered horizontal and vertical blowing directions. For the transformer studied, they found that the horizontal blowing direction had a higher performance due to the lesser air sideway leakages that those of the vertical blowing case. Two years later, in 2016, the same authors carried out the same type of study [21]. However, as a novelty, they provide the effect of the blowing direction on the temperature and velocity distributions of the oil inside the radiators.

Finally, in 2017, Ríos et al.? presented the result comparison of two models (a semi-analytical model and a CFD model) with the experimental results of a radiator of a 30-MVA power transformer working in ONAN mode. The objective was to validate both models in order to use them in the optimization of the current radiator design [22]. This aim was accomplished. An extension of this work was presented the same year with the goal of analysing the thermal-fluid dynamic behaviour of the radiator working in ONAF mode with vertical blowing of the fans [23]. The results obtained, which were validated with experimental and CFD results, showed that the semi-analytical model they proposed was a useful tool for radiator design processes.

#### 3.3. Thermal hydraulic network modelling, THNM

THNM is a technique for transformer thermal modelling that relies on three basic principles: mass conservation, momentum conservation and energy conservation. It implies a subdivision of the domain in multiple elements where the conservation principles are observed as a convergence condition.

This model describes the conservation principles by algebraic equation sets that makes the solving time shorter than CFD that describes the same principles into a set of partial differential equations. These principles are applied to solve the temperature and oil flow fields in several parts of the transformer (windings, core, coolers). THNM applied on the windings can be useful for predicting the hot-spot temperature.

THNM models are the coupling of two different networks: the hydraulic network and the thermal network. The hydraulic network comprises the oil flows through channels and nodes. The oil flow is modelled using the electric circuit analogy where the oil flow and pressure correspond to, respectively, electrical current and voltage. The thermal network models the heat transfer between the active parts and the cooling circuit of the transformer. Temperaturedependent properties of the materials and heat transfer coefficients make both networks to be coupled.

#### 3.3.1. Hydraulic network

done in this way. On the other hand, to improve the cooling capacity of the radiators, the fan's location in the radiators has to be studied. Paramane et al. conducted this in 2014 using both CFD and experimental studies [20]. They considered horizontal and vertical blowing directions. For the transformer studied, they found that the horizontal blowing direction had a higher performance due to the lesser air sideway leakages that those of the vertical blowing case. Two years later, in 2016, the same authors carried out the same type of study [21]. However, as a novelty, they provide the effect of the blowing direction on the temperature

Finally, in 2017, Ríos et al.? presented the result comparison of two models (a semi-analytical model and a CFD model) with the experimental results of a radiator of a 30-MVA power transformer working in ONAN mode. The objective was to validate both models in order to use them in the optimization of the current radiator design [22]. This aim was accomplished. An extension of this work was presented the same year with the goal of analysing the thermal-fluid dynamic behaviour of the radiator working in ONAF mode with vertical blowing of the fans [23]. The results obtained, which were validated with experimental and CFD results, showed that the semi-analytical model they proposed was a useful tool for radiator design processes.

THNM is a technique for transformer thermal modelling that relies on three basic principles: mass conservation, momentum conservation and energy conservation. It implies a subdivision of the domain in multiple elements where the conservation principles are observed as a conve-

This model describes the conservation principles by algebraic equation sets that makes the solving time shorter than CFD that describes the same principles into a set of partial differential

and velocity distributions of the oil inside the radiators.

Figure 7. Velocities (mm/s) and temperatures (C) distributions.

42 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

3.3. Thermal hydraulic network modelling, THNM

rgence condition.

The hydraulic network corresponding to a disc winding with barriers is shown in Figure 8. The hydraulic network consists of eight nodes, four per axial side, where two of the nodes correspond to the entrance and exit of the coolant and the three remaining nodes per side are where the coolant branches or merges. The network is represented by its electrical circuit analogy where the physical quantity associated to each node corresponds to the sum of the static and dynamic pressures. In the circuit, resistances represent frictional pressure drops, and resistances in the nodes represent the local pressure drops as well. Buoyancy effect is represented by generators representing the gain of pressure due to gravitational effects. Since the hydraulic resistances depend on the flow, the hydraulic circuit proposed in Figure 8 is a nonlinear circuit that has to be solved with an iterative procedure [24].

Figure 8. Analogy hydraulic circuit versus hydraulic network.

#### 3.3.2. Thermal network

Thermal network describes the heat transfer phenomena on the transformer and on the transformer elements. There are two main mechanisms of heat transfer in a transformer winding: heat conduction in the conductors and in the solid insulation, and convection from the active part to the cooling oil. The convection term highly depends on the oil flow distribution, which is given by the hydraulic network. In addition, hydraulic network depends on temperature buoyancy effect and temperature-dependent properties of the cooling oil. This coupling between networks enhances the necessity to apply iterative procedures to solve both networks. A simple way to imagine the oil loop of a transformer is described as follows: the oil is heated in the windings, then flows through a piping system reaching the radiator, where it is cooled and finally goes through another piping system to reach the starting point. Although there is heat exchange in the piping system, it is considered negligible compared to the heat exchanged

Thermal driving force is generated due to density variations along the loop and can be

coefficient of the oil (1/K), ΔθOl is the vertical temperature gradient (�C) and ΔH is the height difference between the centre point of the radiator and the centre point of the winding (m).

When the pump runs directly to the windings, the total driving pressure will be the sum of the thermal driving force and the pump driving force where the pump pressure is much higher

The pressure drop can be subdivided into two different groups: major and minor losses. Major losses involve the frictional pressure drops and minor losses involve the local pressure drops

¼ ∮ r � gcosφ � dl (15)

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), β is the volume expansion

! is the gravity vector, φ is the angle between velocity and gravity

pT ¼ r<sup>r</sup> � g � β � Δθol � ΔH (16)

⇀ � dl ⇀

in radiators and windings. It is represented in Figure 10.

is the path vector.

For simplicity, Eq. (16) can be expressed as follows:

where r<sup>r</sup> is the oil density at a reference temperature (kg/m3

due to accessories in the cooling circuit (valves, junctions, etc.).

pT ¼ ∮ r� g

expressed by Eq. (15)

vectors and l

where r is the oil density, g

than the thermal driving pressure.

Figure 10. Oil loop of a transformer.

!

An approach for the thermal part of a transformer winding is to build a thermal network. For the case of a disc winding, the analogy with electric circuits is useful to model the heat transfer in two directions, axial and radial. A resistive term is used for modelling heat conduction between conductor and solid insulation and a resistive term is used for the convective part, which depends on the oil flow distribution. A good approach consists in assuming that the thermal resistance of the conductor is negligible, considering only the resistance of the solid insulation. A voltage source represents the oil temperature and a current source represents the heat generation on each node. Figure 9 represents the thermal network previously described, where the Rλ<sup>i</sup> represents the thermal resistance for conductive terms, Rα<sup>i</sup> represents the thermal resistance for convective terms, θbi and θti represent the temperature on the channels and Pγ<sup>i</sup> represents the heat source in the conductors [24].

#### 3.3.3. Complete loop modelling

Other application of THNM is to model the complete oil loop of the transformer. It is based on the global pressure equilibrium of the oil loop, considering core, tank, winding and radiators, taking into account thermal driving forces, pump forces and pressure drops in the whole loop. Thermal driving forces appear due to density changes with temperature. Driving forces and pressure drop depend on the oil flow rate. The oil flow rate, Qo, represents the equilibrium between driving forces and pressure drops.

Figure 9. Thermal network of a transformer winding disc.

A simple way to imagine the oil loop of a transformer is described as follows: the oil is heated in the windings, then flows through a piping system reaching the radiator, where it is cooled and finally goes through another piping system to reach the starting point. Although there is heat exchange in the piping system, it is considered negligible compared to the heat exchanged in radiators and windings. It is represented in Figure 10.

Thermal driving force is generated due to density variations along the loop and can be expressed by Eq. (15)

$$p\_T = \oint \rho \cdot \vec{\g} \cdot \vec{dl} = \oint \rho \cdot \mathbf{g} \cos \phi \cdot dl \tag{15}$$

where r is the oil density, g ! is the gravity vector, φ is the angle between velocity and gravity vectors and l ! is the path vector.

For simplicity, Eq. (16) can be expressed as follows:

3.3.2. Thermal network

Pγ<sup>i</sup> represents the heat source in the conductors [24].

between driving forces and pressure drops.

Figure 9. Thermal network of a transformer winding disc.

3.3.3. Complete loop modelling

Thermal network describes the heat transfer phenomena on the transformer and on the transformer elements. There are two main mechanisms of heat transfer in a transformer winding: heat conduction in the conductors and in the solid insulation, and convection from the active part to the cooling oil. The convection term highly depends on the oil flow distribution, which is given by the hydraulic network. In addition, hydraulic network depends on temperature buoyancy effect and temperature-dependent properties of the cooling oil. This coupling between networks enhances the necessity to apply iterative procedures to solve both networks. An approach for the thermal part of a transformer winding is to build a thermal network. For the case of a disc winding, the analogy with electric circuits is useful to model the heat transfer in two directions, axial and radial. A resistive term is used for modelling heat conduction between conductor and solid insulation and a resistive term is used for the convective part, which depends on the oil flow distribution. A good approach consists in assuming that the thermal resistance of the conductor is negligible, considering only the resistance of the solid insulation. A voltage source represents the oil temperature and a current source represents the heat generation on each node. Figure 9 represents the thermal network previously described, where the Rλ<sup>i</sup> represents the thermal resistance for conductive terms, Rα<sup>i</sup> represents the thermal resistance for convective terms, θbi and θti represent the temperature on the channels and

44 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Other application of THNM is to model the complete oil loop of the transformer. It is based on the global pressure equilibrium of the oil loop, considering core, tank, winding and radiators, taking into account thermal driving forces, pump forces and pressure drops in the whole loop. Thermal driving forces appear due to density changes with temperature. Driving forces and pressure drop depend on the oil flow rate. The oil flow rate, Qo, represents the equilibrium

$$p\_T = \rho\_r \cdot \mathbf{g} \cdot \boldsymbol{\beta} \cdot \Delta\theta\_{cl} \cdot \Delta H \tag{16}$$

where r<sup>r</sup> is the oil density at a reference temperature (kg/m3 ), β is the volume expansion coefficient of the oil (1/K), ΔθOl is the vertical temperature gradient (�C) and ΔH is the height difference between the centre point of the radiator and the centre point of the winding (m).

When the pump runs directly to the windings, the total driving pressure will be the sum of the thermal driving force and the pump driving force where the pump pressure is much higher than the thermal driving pressure.

The pressure drop can be subdivided into two different groups: major and minor losses. Major losses involve the frictional pressure drops and minor losses involve the local pressure drops due to accessories in the cooling circuit (valves, junctions, etc.).

Figure 10. Oil loop of a transformer.

The driving pressure on the loop must be equal to the total pressure drop. Energy conservation is also applied to the loop. The energy balance of the winding is presented in Eq. (17)

$$p\_{\gamma} = \rho \cdot c\_p \cdot Q\_o \cdot \Delta \theta\_{ol} \tag{17}$$

Applying a special discretization and following THNM principles, there are some assumptions that are taken in this kind of models: perfect thermal mixing is considered at junctions, fully developed flows are assumed in oil channels and exterior walls are con-

Thermal Modelling of Electrical Insulation System in Power Transformers

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47

The accuracy of these models has been tested and resulted acceptable. In order to increase this accuracy, many authors have tried to focus into two different parameters that come from correlations from datasets that are local pressure drop coefficients and convective heat transfer

The knowledge of these two parameters is small in this application since there is not much experience to define them. However, some authors have defined these parameters based on datasets obtained from CFD results. Using CFD to accurately these two parameters has improved the performance of detailed THNMs. These kinds of models are known as CFD calibrated THNMs and integrate both main techniques of transformer

THNM modelling predicts temperature distribution and velocity in the channels of the windings of the transformer. Hot-spot and top-oil temperatures can be estimated using THNM in a fast calculation, taking less than 5 min in a normal computer. These results show small deviations with respect to the obtained CFD models that are below 5% of deviation in hot-

Other kinds of THNM modelling are the detailed radiator models. These models rely on the same principles than detailed winding models, but applied on the radiator part. Thermal modelling of radiators is complex, although radiators are mechanically simple, because of the following reasons: oil temperature varies in function of the height and per radiator panel, temperature variation is a function of the oil mass flow and the local heat flux, the local heat flux is dependent on the temperature difference between oil and ambient air and the local air

Especially, focus needs to be made on the air velocities distribution since there exist three possible configurations: air natural (AN), air forced (AF) with vertical air flow and air forced with horizontal flow. With AN configuration, the air flow through the panels is originated by buoyancy forces of the hot air. The buoyancy force will be in equilibrium with the pressure

In the case of AF, air flow distribution generated from the fans has to be previously defined in order to obtain the heat transfer coefficient in the radiator plates. In order to better understand and model the air distribution over the radiator panels, CFD simulations have been carried out. Determining that the air coming from a fan spread in a conic way, an effective air velocity can be calculated based on the volumetric air capacity of the fan and the cone surface. With

velocity and the local air velocity are variable along the position in the radiator [25].

these assumptions, thermal modelling of the radiator can be made.

sidered as adiabatic.

thermal modelling.

spot and top-oil temperature.

3.3.5. Detailed radiator model

drop of the air flow through the panels.

coefficient.

where Pγ are the power losses in the winding (W), cp is the specific heat of the oil at average oil temperature (J/kg�K), <sup>r</sup> is the density at bottom-oil temperature (kg/m<sup>3</sup> ) and Qo is the volume oil flow (m3 /s).

With these two equations, Eqs. (16) and (17), there are three variables that are volume oil flow Qo, bottom-oil temperature TOb and top-oil temperature TOt. Eq. (18) is added when considering the energy balance in the radiator

$$k\_p \cdot O \cdot (T\_0(\mathbf{x}) - T\_a)d\mathbf{x} = -\rho \cdot c\_p \cdot Q\_0 \cdot dT\_0(\mathbf{x}) \tag{18}$$

where kp is the total heat transfer coefficient (HTC) (W/m<sup>2</sup> K), O is the circumference of the outer radiator cross section (m), TO(x) is the oil temperature at position x (K) and QO is the oil flow through the radiator (m<sup>3</sup> /s).

Assuming that the HTC does not change along the radiator in a significant way, the solution of Eq. (19) is

$$T\_0(\mathbf{x}) = T\_a + (T\_{ot} - T\_a) \cdot e^{-\frac{k\_p U}{\rho \cdot c\_p \cdot Q\_p} x} \tag{19}$$

Then, integrating the cooling power in the radiator

$$P = \int\_{0}^{L\_{\text{R}}} (T\_o(\mathbf{x}) - T\_d) \cdot \mathbf{k}\_p \cdot \mathbf{O} \cdot d\mathbf{x} \tag{20}$$

result in the following equation:

$$P = \rho \cdot c\_p \cdot Q\_o \cdot (T\_{ot} - T\_d) \cdot \left(1 - e^{-\frac{k\_p \cdot O \cdot l\_p}{\rho \cdot c\_p \cdot Q\_o}}\right) \tag{21}$$

In this explanation, it is assumed that there is no heat exchange in the tank and there are no core losses. Consequently, from Eqs. (16), (17) and (21), two unknown temperatures and the oil flow can be determined [24].

#### 3.3.4. Detailed winding model

THNM can be developed for predicting the temperature and oil flow distribution in a transformer winding in detail. For this type of modelling, bottom-oil temperature and oil flow rate have to be taken as inputs for the model. There is also the possibility to introduce a nonuniform power source in the active part of the winding.

Applying a special discretization and following THNM principles, there are some assumptions that are taken in this kind of models: perfect thermal mixing is considered at junctions, fully developed flows are assumed in oil channels and exterior walls are considered as adiabatic.

The accuracy of these models has been tested and resulted acceptable. In order to increase this accuracy, many authors have tried to focus into two different parameters that come from correlations from datasets that are local pressure drop coefficients and convective heat transfer coefficient.

The knowledge of these two parameters is small in this application since there is not much experience to define them. However, some authors have defined these parameters based on datasets obtained from CFD results. Using CFD to accurately these two parameters has improved the performance of detailed THNMs. These kinds of models are known as CFD calibrated THNMs and integrate both main techniques of transformer thermal modelling.

THNM modelling predicts temperature distribution and velocity in the channels of the windings of the transformer. Hot-spot and top-oil temperatures can be estimated using THNM in a fast calculation, taking less than 5 min in a normal computer. These results show small deviations with respect to the obtained CFD models that are below 5% of deviation in hotspot and top-oil temperature.

#### 3.3.5. Detailed radiator model

The driving pressure on the loop must be equal to the total pressure drop. Energy conservation

where Pγ are the power losses in the winding (W), cp is the specific heat of the oil at average oil

With these two equations, Eqs. (16) and (17), there are three variables that are volume oil flow Qo, bottom-oil temperature TOb and top-oil temperature TOt. Eq. (18) is added when consider-

outer radiator cross section (m), TO(x) is the oil temperature at position x (K) and QO is the oil

Assuming that the HTC does not change along the radiator in a significant way, the solution of

T0ð Þ¼ x Ta þ ð Þ� Tot � Ta e

P ¼ r � cp � Qo � ð Þ� Tot � Ta 1 � e

In this explanation, it is assumed that there is no heat exchange in the tank and there are no core losses. Consequently, from Eqs. (16), (17) and (21), two unknown temperatures and the oil

THNM can be developed for predicting the temperature and oil flow distribution in a transformer winding in detail. For this type of modelling, bottom-oil temperature and oil flow rate have to be taken as inputs for the model. There is also the possibility to introduce a non-

p<sup>γ</sup> ¼ r � cp � Qo � Δθol (17)

kp � O � ð Þ T0ð Þ� x Ta dx ¼ �r � cp � Q<sup>0</sup> � dT0ð Þx (18)

� kp�<sup>O</sup> r�cp�Qo

ð Þ� Toð Þ� x Ta k<sup>p</sup> � O � dx (20)

�kp�O�LR r�cp�Qo � � ) and Qo is the volume

K), O is the circumference of the

�<sup>x</sup> (19)

(21)

is also applied to the loop. The energy balance of the winding is presented in Eq. (17)

temperature (J/kg�K), <sup>r</sup> is the density at bottom-oil temperature (kg/m<sup>3</sup>

46 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

where kp is the total heat transfer coefficient (HTC) (W/m<sup>2</sup>

/s).

P ¼

L ðR

0

Then, integrating the cooling power in the radiator

uniform power source in the active part of the winding.

oil flow (m3

Eq. (19) is

/s).

flow through the radiator (m<sup>3</sup>

result in the following equation:

flow can be determined [24].

3.3.4. Detailed winding model

ing the energy balance in the radiator

Other kinds of THNM modelling are the detailed radiator models. These models rely on the same principles than detailed winding models, but applied on the radiator part. Thermal modelling of radiators is complex, although radiators are mechanically simple, because of the following reasons: oil temperature varies in function of the height and per radiator panel, temperature variation is a function of the oil mass flow and the local heat flux, the local heat flux is dependent on the temperature difference between oil and ambient air and the local air velocity and the local air velocity are variable along the position in the radiator [25].

Especially, focus needs to be made on the air velocities distribution since there exist three possible configurations: air natural (AN), air forced (AF) with vertical air flow and air forced with horizontal flow. With AN configuration, the air flow through the panels is originated by buoyancy forces of the hot air. The buoyancy force will be in equilibrium with the pressure drop of the air flow through the panels.

In the case of AF, air flow distribution generated from the fans has to be previously defined in order to obtain the heat transfer coefficient in the radiator plates. In order to better understand and model the air distribution over the radiator panels, CFD simulations have been carried out. Determining that the air coming from a fan spread in a conic way, an effective air velocity can be calculated based on the volumetric air capacity of the fan and the cone surface. With these assumptions, thermal modelling of the radiator can be made.

#### 4. Summary

In this chapter, different techniques for transformer thermal modelling have been introduced. The main goal of all of them is to predict the hot-spot temperature in the transformer windings with good accuracy. Due to the complex phenomena involved in transformer thermal modelling, the models have to be previously validated with experimental data. The first models are the dynamic models, which take into account different load factors to predict hot-spot and topoil temperatures over time. These models are useful to predict hot-spot temperatures in scenarios of emergency load. The steady-state models predict the temperature and velocity profiles in the windings of the transformer for a selected load rate. These models, CFD and THNM, are useful for design steps to predict the thermal behaviour of the transformer. CFD is a more accurate method, whereas THNM is faster and requires less computational resources. Both are used for design steps of transformer windings. Steady-state models are also used to test the cooling performance of alternative dielectric liquids, such as natural esters, in power transformers by comparing hot-spot temperature and pressure drop over the windings.

[7] Mufuta J, van den Bulck E. Modelling of the mixed convection in the windings of a disctype power transformer. Applied Thermal Engineering. 2000;20(5):417-437. ISSN: 1359-

Thermal Modelling of Electrical Insulation System in Power Transformers

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49

[8] Wakil NE, Chereches N, Padet J. Numerical study of heat transfer and fluid flow in a power Transformer. International Journal of Thermal Sciences. Jun 1, 2006;45(6):615. ISSN:

[9] Torriano F, Picher P, Chaaban M. Numerical investigation of 3D flow and thermal effects in a disc-type transformer winding. Applied Thermal Engineering. Jul, 2012;40:121-131. ISSN:

[10] Gastelurrutia J. et al. Numerical modelling of natural convection of oil inside distribution transformers. Applied Thermal Engineering. 2011;31:493-505. ISSN 1359-4311. DOI: 10.1016/

[11] Tsili MA, Amoiralis EI, Kladas AG, Souflaris AT. Power transformer thermal analysis by using an advanced coupled 3D heat transfer and fluid flow FEM model. International Journal of Thermal Sciences. Mar, 2012;53:188-201. CrossRef. ISSN: 1290-0729. DOI:

[12] Skillen A, Revell A, Iacovides H, Wu W. Numerical prediction of local hot-spot phenomena in transformer windings. Applied Thermal Engineering. Apr, 2012;36:96-105. ISSN: 1359-

[13] Yatsevsky VA. Hydrodynamics and heat transfer in cooling channels of oil-filled power transformers with multicoil windings. Applied Thermal Engineering. Feb, 2014;63(1):347-

[14] Torriano F. Numerical and experimental thermofluid investigation of different disc-type power transformer winding arrangements. The International Journal of Heat and Fluid

[15] Park T. Numerical analysis of local hot-spot temperatures in transformer windings by using alternative dielectric fluids. Electrical Engineering. 2015;97(4):261-268. ISSN: 0003-

[16] Lecuna R et al. Thermal-fluid characterization of alternative liquids of power transformers: A numerical approach. IEEE Transactions on Dielectrics and Electrical Insulation.

[17] Santisteban A et al. Numerical analysis of the hot-spot temperature of a power transformer with alternative dielectric liquids. IEEE Transactions on Dielectrics and Electrical Insulation.

[18] Fernández C et al. Thermal degradation assessment of kraft paper in power transformers insulated with natural esters. Applied Thermal Engineering. Jul 5, 2016;104:129-138. ISSN:

2015;22(5):2522-2529. ISSN: 1070-9878. DOI: 10.1109/TDEI.2015.004793

2017;24(5):3226-3235. ISSN: 1070-9878. DOI: 10.1109/TDEI.2017.006228

1359-4311. DOI: 10.1016/j.applthermaleng.2016.05.020

353. CrossRef. ISSN: 1359-4311. DOI: 10.1016/j.applthermaleng.2013.10.055

4311. DOI: 10.1016/S1359-4311(99)00034-4

j.applthermaleng.2010.10.004

10.1016/j.ijthermalsci.2011.10.010

Flow. 2018;69:62-72. ISSN: 0142-727X

9039

4311. DOI: 10.1016/j.applthermaleng.2011.11.054

1290-0729. DOI: 10.1016/j.ijthermalsci.2005.09.002

1359-4311. DOI: 10.1016/j.applthermaleng.2012.02.011

#### Author details

Agustín Santisteban\*, Fernando Delgado, Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz

\*Address all correspondence to: santistebana@unican.es

ETSIIT University of Cantabria, Santander, Spain

#### References


[7] Mufuta J, van den Bulck E. Modelling of the mixed convection in the windings of a disctype power transformer. Applied Thermal Engineering. 2000;20(5):417-437. ISSN: 1359- 4311. DOI: 10.1016/S1359-4311(99)00034-4

4. Summary

Author details

References

IEC 60076-60077, 2011

In this chapter, different techniques for transformer thermal modelling have been introduced. The main goal of all of them is to predict the hot-spot temperature in the transformer windings with good accuracy. Due to the complex phenomena involved in transformer thermal modelling, the models have to be previously validated with experimental data. The first models are the dynamic models, which take into account different load factors to predict hot-spot and topoil temperatures over time. These models are useful to predict hot-spot temperatures in scenarios of emergency load. The steady-state models predict the temperature and velocity profiles in the windings of the transformer for a selected load rate. These models, CFD and THNM, are useful for design steps to predict the thermal behaviour of the transformer. CFD is a more accurate method, whereas THNM is faster and requires less computational resources. Both are used for design steps of transformer windings. Steady-state models are also used to test the cooling performance of alternative dielectric liquids, such as natural esters, in power transformers by comparing hot-spot temperature and pressure drop over the windings.

48 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Agustín Santisteban\*, Fernando Delgado, Alfredo Ortiz, Carlos J. Renedo and Felix Ortiz

[1] IEC Power transformers—Part 7: Loading guide for oil-immersed power transformers.

[2] Susa D. Dynamic thermal modelling of power transformers. IEEE Transactions on Power

[3] Susa D. Dynamic thermal modelling of power transformers: Further development—Part I. IEEE Transactions on Power Delivery, 10. Oct 2006;21(4):1961-1970. ISSN: 0885-8977

[4] Susa D. Dynamic thermal modelling of power transformers: Further development—Part II. IEEE Transactions on Power Delivery, 10. Oct 2006;21(4):1971-1980. ISSN: 0885-8977

[6] Torriano F, Chaaban M, Picher P. Numerical study of parameters affecting the temperature distribution in a disc-type transformer winding. Applied Thermal Engineering. 2010;30(14):

[5] COMSOL Multiphysics. COMSOL Multiphysics Reference Manual. 2013. pp. 1-1262

2034-2044. ISSN: 1359-4311. DOI 10.1016/j.applthermaleng.2010.05.004

\*Address all correspondence to: santistebana@unican.es

Delivery, 0, 1. Jan 2005;20(1):197-204. ISSN: 0885-8977

ETSIIT University of Cantabria, Santander, Spain


[19] Kim M, Cho SM, Kim J. Prediction and evaluation of the cooling performance of radiators used in oil-filled power transformer applications with non-direct and direct-oil-forced flow. Experimental Thermal and Fluid Science. Jan 1, 2013;44:392. ISSN: 0894-1777. DOI: 10.1016/j.expthermflusci.2012.07.011

**Chapter 3**

Provisional chapter

**Modeling and Simulation of Rotating Machine**

Modeling and Simulation of Rotating Machine

**Insulation Design**

Insulation Design

Mohammed Khalil Hussain

Mohammed Khalil Hussain

Abstract

1. Introduction

http://dx.doi.org/10.5772/intechopen.78064

Fermin P. Espino Cortes, Pablo Gomez and

Fermin P. Espino Cortes, Pablo Gomez and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Windings Fed by High-Power Frequency Converters for**

DOI: 10.5772/intechopen.78064

Modern power systems include a considerable amount of power electronic converters related to the introduction of renewable energy sources, high-voltage direct current (HVDC) systems, adjustable speed drives, and so on. These components introduce repetitive pulses generated by the commutation of semiconductor switches, resulting in overvoltages with very steep fronts and high dielectric stresses. This phenomenon is one of the main causes of accelerated insulation aging of motors in power electronic-based systems. This chapter presents state-of-the-art computational tools for the analysis of motor windings excited by fast-front pulses related to the use of frequency converters based on pulsewidth modulation (PWM). These tools can be applied for the accurate prediction of overvoltages and dielectric stresses required to propose insulation design improvements. In the case of the stress-grading system used in medium-voltage (MV) motors, transient finite-element method (FEM) is used to study the effect of fast pulses. It is shown how, by controlling the material properties and the design of the stress-grading systems, solutions to reduce the adverse effects of fast pulses from PWM-type inverters can be proposed. Keywords: dielectric stress, fast-front pulses, motor windings, pulse-width modulation

The detrimental effect of steep voltage surges propagating along the windings of power components such as transformers, reactors, motors, generators, and so on has been a topic of great interest for almost a century (see for instance [1–6]). In the case of motors, these surges

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Windings Fed by High-Power Frequency Converters for


#### **Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation Design** Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation Design

DOI: 10.5772/intechopen.78064

Fermin P. Espino Cortes, Pablo Gomez and Mohammed Khalil Hussain Fermin P. Espino Cortes, Pablo Gomez and Mohammed Khalil Hussain

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78064

#### Abstract

[19] Kim M, Cho SM, Kim J. Prediction and evaluation of the cooling performance of radiators used in oil-filled power transformer applications with non-direct and direct-oil-forced flow. Experimental Thermal and Fluid Science. Jan 1, 2013;44:392. ISSN: 0894-1777. DOI:

[20] Paramane SB. CFD study on thermal performance of radiators in a power transformer: Effect of blowing direction and offset of fans. IEEE Transactions on Power Delivery. 2014;

[21] Paramane SB. A coupled internal-external flow and conjugate heat transfer simulations and experiments on radiators of a transformer. Applied Thermal Engineering. 2016;103:

[22] Rodriguez GR. Numerical and experimental thermo-fluid dynamic analysis of a power transformer working in ONAN mode. Applied Thermal Engineering. 2017;112:1271-1280.

[23] Garelli L. Reduced model for the thermo-fluid dynamic analysis of a power transformer radiator working in ONAF mode. Applied Thermal Engineering. 2017;124:855-864. ISSN:

[24] Radakovic Z, Sorgic M. Basics of thermal-hydraulic model for thermal design of oil power transformers. IEEE Transactions on Power Delivery. 2010;25(2):790-802. ISSN: 0885-8977.

[25] van der Weken W, Paramane SB, Mertens M, Chandak V, Coddé J.. Increased efficiency of thermal calculations via the development of a full thermohydraulic radiator model. IEEE Transactions on Power Delivery. 2016;31(4):1473-1481. ISSN: 0885-8977. DOI: 10.1109/

10.1016/j.expthermflusci.2012.07.011

50 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

29(6):2596-2604. ISSN: 0885-8977

DOI: 10.1109/TPWRD.2009.2033076

TPWRD.2015.2501431

961-970. ISSN: 1359-4311

ISSN: 1359-4311

1359-4311

Modern power systems include a considerable amount of power electronic converters related to the introduction of renewable energy sources, high-voltage direct current (HVDC) systems, adjustable speed drives, and so on. These components introduce repetitive pulses generated by the commutation of semiconductor switches, resulting in overvoltages with very steep fronts and high dielectric stresses. This phenomenon is one of the main causes of accelerated insulation aging of motors in power electronic-based systems. This chapter presents state-of-the-art computational tools for the analysis of motor windings excited by fast-front pulses related to the use of frequency converters based on pulsewidth modulation (PWM). These tools can be applied for the accurate prediction of overvoltages and dielectric stresses required to propose insulation design improvements. In the case of the stress-grading system used in medium-voltage (MV) motors, transient finite-element method (FEM) is used to study the effect of fast pulses. It is shown how, by controlling the material properties and the design of the stress-grading systems, solutions to reduce the adverse effects of fast pulses from PWM-type inverters can be proposed.

Keywords: dielectric stress, fast-front pulses, motor windings, pulse-width modulation

#### 1. Introduction

The detrimental effect of steep voltage surges propagating along the windings of power components such as transformers, reactors, motors, generators, and so on has been a topic of great interest for almost a century (see for instance [1–6]). In the case of motors, these surges

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

have been traditionally associated with energization, re-energization, or incoming lightning pulses [7]. Over the last decades, this has become a larger issue with the increasing use of frequency converters for speed and torque control, which introduce repetitive steep-front voltage impulses and associated partial discharges into the machine windings (see Figure 1). The insulation of this type of devices is subjected to high and sustained electric and thermal stresses [8, 9]. This effect is further amplified by the use of long connection cables [10].

means of a topological connection between the corresponding nodes. This is called a zig-zag

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation…

http://dx.doi.org/10.5772/intechopen.78064

53

The distributed parameter model of an MTL is completely characterized by its electrical parameter matrices: series impedance matrix Z and shunt admittance matrix Y. For the case of machine windings, these matrices are obtained from the geometrical configuration of the machine. Considering the typical stator coil diagram depicted in Figure 3, the incident surge

Figure 2. Multi-conductor transmission line model of the coil with a zig-zag connection (three turns are considered for

connection and is shown in Figure 2.

the purpose of illustration) [21].

Figure 3. Coil sections in the stator frame [21].

Industrial surveys and other studies show that 20–40% of rotating machine failures are due to stator winding problems, and 70% of these are due to insulation failures [11–16]. Dielectric stress along motor's windings associated with the propagation of fast-front voltage surges is a major source of premature deterioration or failure of the insulation system of these devices [9, 17].

Early motor representations for fast-transient studies consisted of approximating the surge impedance of the motor as a simple lumped termination of the feeding cable [18]. This allowed understanding and predicting the transient overvoltages produced at the cable/motor connection. However, overvoltages can appear at several points inside the machine coils during the transient period. Models that are more detailed were later introduced to consider the transient potential distribution along windings. These models are known as white box models and can be classified in lumped and distributed parameter representations [7]. Although the former are easier to implement and less computationally expensive, the latter are more accurate since the wave propagation along the winding coils is introduced in a more precise manner.

Rudenberg first introduced the application of traveling wave theory to study the fast-transient behavior of windings [19]. A more rigorous approach based on a multi-conductor line model and applied to transformer windings was described by Rabins in 1960 [20]. Oraee [4] and Guardado [5] independently developed this approach for electrical machines in the 1980s. The main idea of their modeling approach is that a coil can be approximated by a multi-conductor transmission line (MTL): each conductor represents a turn (or group of turns) of the coil, and the continuity between the end of one turn and the beginning of the next one is preserved by

Figure 1. Typical voltage to ground of a medium-voltage winding fed by a three-level converter.

means of a topological connection between the corresponding nodes. This is called a zig-zag connection and is shown in Figure 2.

The distributed parameter model of an MTL is completely characterized by its electrical parameter matrices: series impedance matrix Z and shunt admittance matrix Y. For the case of machine windings, these matrices are obtained from the geometrical configuration of the machine. Considering the typical stator coil diagram depicted in Figure 3, the incident surge

Figure 2. Multi-conductor transmission line model of the coil with a zig-zag connection (three turns are considered for the purpose of illustration) [21].

Figure 3. Coil sections in the stator frame [21].

have been traditionally associated with energization, re-energization, or incoming lightning pulses [7]. Over the last decades, this has become a larger issue with the increasing use of frequency converters for speed and torque control, which introduce repetitive steep-front voltage impulses and associated partial discharges into the machine windings (see Figure 1). The insulation of this type of devices is subjected to high and sustained electric and thermal

Industrial surveys and other studies show that 20–40% of rotating machine failures are due to stator winding problems, and 70% of these are due to insulation failures [11–16]. Dielectric stress along motor's windings associated with the propagation of fast-front voltage surges is a major source of premature deterioration or failure of the insulation system of these devices

Early motor representations for fast-transient studies consisted of approximating the surge impedance of the motor as a simple lumped termination of the feeding cable [18]. This allowed understanding and predicting the transient overvoltages produced at the cable/motor connection. However, overvoltages can appear at several points inside the machine coils during the transient period. Models that are more detailed were later introduced to consider the transient potential distribution along windings. These models are known as white box models and can be classified in lumped and distributed parameter representations [7]. Although the former are easier to implement and less computationally expensive, the latter are more accurate since the

Rudenberg first introduced the application of traveling wave theory to study the fast-transient behavior of windings [19]. A more rigorous approach based on a multi-conductor line model and applied to transformer windings was described by Rabins in 1960 [20]. Oraee [4] and Guardado [5] independently developed this approach for electrical machines in the 1980s. The main idea of their modeling approach is that a coil can be approximated by a multi-conductor transmission line (MTL): each conductor represents a turn (or group of turns) of the coil, and the continuity between the end of one turn and the beginning of the next one is preserved by

wave propagation along the winding coils is introduced in a more precise manner.

Figure 1. Typical voltage to ground of a medium-voltage winding fed by a three-level converter.

stresses [8, 9]. This effect is further amplified by the use of long connection cables [10].

52 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

[9, 17].

will propagate along two different regions: slot and overhang. Due to the variation in the electromagnetic field distribution in these two regions, the corresponding parameter matrices will also be different [5].

Another challenging aspect of machine-winding modeling is the computation of electrical parameters. Common approaches followed for this task are (1) measuring the parameters, (2) applying analytical expressions, and (3) applying numerical methods. Analytical and numerical methods are the only possible choices for new designs. However, since machine windings have complex geometrical features, the available analytical expressions rely on numerous approximations and assumptions and are therefore restricted to particular geometries. Numerical methods are applicable in a more general sense as long as detailed geometrical and electrical data are available, which is the case at the design stage [22].

One of the first insulation problems stemming from the use of power frequency converters with medium-voltage (MV) motors was associated with the electric stresses on the surface of the coils. Partial discharge (PD) and heat can erode the coatings of the stress-grading (SG) system [23], aggravating the problem and, perhaps, eventually destroying the ground-wall insulation. This process can take a long time to produce a critical failure, but the ozone produced as a byproduct of surface PD [24] may accelerate the degradation and hence the need to rewind the motor [23].

The SG system in MV-rotating machines is composed of two coatings: the conductive armor coating and the semi-conductive stress-grading coating. The conductive armor coating is a relatively conductive layer that is usually applied in the form of a tape to the surface of the ground-wall insulation in form-wound coils that lies inside the stator slot of a rotating machine. The function of this coating is to limit the surface potential of the coil to a value equal or close to ground potential, thereby avoiding the possibility of discharges between the coil insulation and the slot wall. The length of the conductive armor coating extends beyond the end of the slot [25], as illustrated by part A in Figure 4. The semi-conductive-grading coating starts at the end of the conductive armor coating, part B, also in the form of a tape, and they are often overlapped by a couple of centimeters, shown as region E. The purpose of the semiconductive-grading coating is to produce a smooth transition from the potential in the conductive armor coating to the high voltage (HV) on the surface of the coil insulation outside of the slot, shown as part C in Figure 4. The graded voltage drop along the surface of the coil avoids harmful high electric field concentrations.

The conductive armor coating is commonly a composite of either varnish or polyester resin filled with graphite or carbon black. It is considered as a constant conductivity layer with values between 10 and 0.01 S/m. The semi-conductive-grading coating of coils is a composite of silicon carbide (SiC) and varnish or polyester resin, with a field-dependent conductivity. A profile of the voltage from the slot exit to the end of the semi-conductive-grading tape (SGT) measured using an alternating current (AC) electrostatic voltmeter is shown in Figure 5. The coil was energized with 8 kVrms at 60 Hz. The conductive armor tape (CAT) is at ground potential (first 10 cm in the plot of Figure 5) while along the SGT the voltage increases smoothly (after 10 cm), something that is accomplished by the generation of resistive heat as

seen in the inserted infrared image of Figure 5, where the section of the SG presents a hot spot. The slope of the voltage defines the tangential electric field on the surface of the stress-grading region. Overvoltages and pulses having steep fronts, like those from PWM-type inverters, considerable modify the stress relief in the SGT and in the portion of the CAT that is outside of the slot. The design of the stress grading and the conductive armor coatings has become difficult under this condition, and modeling had resulted in a useful tool in understanding the

Figure 5. Illustration showing conductive armor and stress-grading coatings on a form-wound coil under sinusoidal 60-

Figure 4. Illustration showing conductive armor and semi-conductive-grading coatings on a form-wound coil [26].

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation…

http://dx.doi.org/10.5772/intechopen.78064

55

influence of the various design parameters.

Hz voltage [26].

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation… http://dx.doi.org/10.5772/intechopen.78064 55

will propagate along two different regions: slot and overhang. Due to the variation in the electromagnetic field distribution in these two regions, the corresponding parameter matrices

Another challenging aspect of machine-winding modeling is the computation of electrical parameters. Common approaches followed for this task are (1) measuring the parameters, (2) applying analytical expressions, and (3) applying numerical methods. Analytical and numerical methods are the only possible choices for new designs. However, since machine windings have complex geometrical features, the available analytical expressions rely on numerous approximations and assumptions and are therefore restricted to particular geometries. Numerical methods are applicable in a more general sense as long as detailed geometrical and

One of the first insulation problems stemming from the use of power frequency converters with medium-voltage (MV) motors was associated with the electric stresses on the surface of the coils. Partial discharge (PD) and heat can erode the coatings of the stress-grading (SG) system [23], aggravating the problem and, perhaps, eventually destroying the ground-wall insulation. This process can take a long time to produce a critical failure, but the ozone produced as a byproduct of surface PD [24] may accelerate the degradation and hence the

The SG system in MV-rotating machines is composed of two coatings: the conductive armor coating and the semi-conductive stress-grading coating. The conductive armor coating is a relatively conductive layer that is usually applied in the form of a tape to the surface of the ground-wall insulation in form-wound coils that lies inside the stator slot of a rotating machine. The function of this coating is to limit the surface potential of the coil to a value equal or close to ground potential, thereby avoiding the possibility of discharges between the coil insulation and the slot wall. The length of the conductive armor coating extends beyond the end of the slot [25], as illustrated by part A in Figure 4. The semi-conductive-grading coating starts at the end of the conductive armor coating, part B, also in the form of a tape, and they are often overlapped by a couple of centimeters, shown as region E. The purpose of the semiconductive-grading coating is to produce a smooth transition from the potential in the conductive armor coating to the high voltage (HV) on the surface of the coil insulation outside of the slot, shown as part C in Figure 4. The graded voltage drop along the surface of the coil

The conductive armor coating is commonly a composite of either varnish or polyester resin filled with graphite or carbon black. It is considered as a constant conductivity layer with values between 10 and 0.01 S/m. The semi-conductive-grading coating of coils is a composite of silicon carbide (SiC) and varnish or polyester resin, with a field-dependent conductivity. A profile of the voltage from the slot exit to the end of the semi-conductive-grading tape (SGT) measured using an alternating current (AC) electrostatic voltmeter is shown in Figure 5. The coil was energized with 8 kVrms at 60 Hz. The conductive armor tape (CAT) is at ground potential (first 10 cm in the plot of Figure 5) while along the SGT the voltage increases smoothly (after 10 cm), something that is accomplished by the generation of resistive heat as

electrical data are available, which is the case at the design stage [22].

54 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

will also be different [5].

need to rewind the motor [23].

avoids harmful high electric field concentrations.

Figure 4. Illustration showing conductive armor and semi-conductive-grading coatings on a form-wound coil [26].

Figure 5. Illustration showing conductive armor and stress-grading coatings on a form-wound coil under sinusoidal 60- Hz voltage [26].

seen in the inserted infrared image of Figure 5, where the section of the SG presents a hot spot. The slope of the voltage defines the tangential electric field on the surface of the stress-grading region. Overvoltages and pulses having steep fronts, like those from PWM-type inverters, considerable modify the stress relief in the SGT and in the portion of the CAT that is outside of the slot. The design of the stress grading and the conductive armor coatings has become difficult under this condition, and modeling had resulted in a useful tool in understanding the influence of the various design parameters.

The remaining of this chapter is divided as follows: Section 2 describes the modeling and parameter determination of motor windings excited by the fast pulses produced by an inverter. Section 3 describes a finite-element method (FEM)-based approach to analyze the performance of stress-grading systems. Finally, Section 4 presents the conclusions and final remarks of this chapter.

2.1. Winding model

<sup>Y</sup><sup>0</sup> <sup>¼</sup> <sup>Z</sup>ð Þ <sup>x</sup>;<sup>s</sup> �<sup>1</sup>

related as follows:

d dx

boundary conditions at x and x + Δx [31]:

where the chain matrix of the segment is defined as

U<sup>R</sup> IR � �

ϕð Þ¼ Δx;s

Uð Þ x;s Ið Þ x;s � �

> Uð Þ x þ Δx;s Ið Þ x þ Δx;s � �

In Eq. (3), <sup>ψ</sup> is the propagation constant matrix of the line, given by <sup>ψ</sup> <sup>¼</sup> <sup>M</sup> ffiffiffi

model of the machine-winding coil, according to the following procedure [21]:

in order to obtain a single chain matrix representing the complete coil.

¼ ϕ1ϕ2ϕ3ϕ2ϕ<sup>1</sup>

1. The coil is divided into five segments, as shown in Figures 2 and 6.

Wave propagation along the non-uniform multi-conductor transmission system representing the winding is defined by the Telegrapher equations in the Laplace domain as follows [30, 31]:

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation…

<sup>¼</sup> <sup>0</sup> �Zð Þ <sup>x</sup>;<sup>s</sup> �Yð Þ x;s 0

In Eq. (1), U(x,s) and I(x,s) are the voltage and current vectors at point x along the line, Z(x,s) and Y(x,s) are the series impedance and shunt-admittance matrices of the line per unit length, respectively. According to Eq. (1), the winding electrical parameters are a function of both space and time. Voltages and currents at the terminals of the segment can be related using the chain matrix definition, assuming constant parameters over a segment Δx and applying

¼ ϕð Þ Δx;s

coshðÞ� <sup>ψ</sup>Δ<sup>x</sup> <sup>Y</sup>�<sup>1</sup>

and λ are the eigenvalue and eigenvector matrices of the Z(x,s)Y(x,s) product, respectively. In addition, Y<sup>0</sup> is the characteristic admittance matrix of the line segment, given by

2. Each of the five chain matrices is obtained from Eq. (3) as a function of parameters Z and Y,

3. The chain matrices are multiplied according to the cascaded connection shown in Figure 6

Voltages and currents at the sending (S) and receiving (R) nodes of the complete coil are

U<sup>S</sup> IS � �

In Eq. (4), Φ11, Φ12, Φ21, and Φ<sup>22</sup> are the elements of the complete chain matrix representation of the coil. This representation is transformed into an equivalent admittance matrix form to

<sup>¼</sup> <sup>Φ</sup><sup>11</sup> <sup>Φ</sup><sup>12</sup> <sup>Φ</sup><sup>21</sup> <sup>Φ</sup><sup>22</sup> � � <sup>U</sup><sup>S</sup>

IS

which are different in the geometrical regions identified as overhang and slot.

�Y0sinhð Þ <sup>ψ</sup> <sup>Δ</sup><sup>x</sup> <sup>Y</sup>0coshð Þ <sup>ψ</sup>Δ<sup>x</sup> <sup>Y</sup>�<sup>1</sup>

ψ. The two-port representation defined by Eq. (2) is the basis of the non-uniform

" #

Uð Þ x;s Ið Þ x;s

<sup>0</sup> sinhð Þ ψΔx

0

� � <sup>U</sup>ð Þ <sup>x</sup>;<sup>s</sup>

Ið Þ x;s

� � (1)

http://dx.doi.org/10.5772/intechopen.78064

� � (2)

λ <sup>p</sup> <sup>M</sup>�<sup>1</sup>

� � (4)

(3)

57

, where M

## 2. Fast-transient modeling of rotating machine windings for inverter excitation

The computer model described in this section for the prediction of the fast-transient response of the machine winding is a non-uniform, multi-conductor, distributed-parameter model defined in the frequency domain. This model is selected over other alternatives given its good balance between high accuracy and practicality, as explained below:


The winding electrical parameters (capacitance, inductance, and losses) in the overhang and slot regions of the coil are calculated using the finite-element method (FEM)-based software COMSOL Multiphysics [29], as described in Section 2.2.

Figure 6. Cascaded connection of chain matrices to model all coil regions [22].

#### 2.1. Winding model

The remaining of this chapter is divided as follows: Section 2 describes the modeling and parameter determination of motor windings excited by the fast pulses produced by an inverter. Section 3 describes a finite-element method (FEM)-based approach to analyze the performance of stress-grading systems. Finally, Section 4 presents the conclusions and final

2. Fast-transient modeling of rotating machine windings for inverter

balance between high accuracy and practicality, as explained below:

56 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

the inductive and capacitive coupling between turns [21].

manner than a lumped parameter model based on circuit theory [27].

form motor, as shown in Figures 3 and 6.

COMSOL Multiphysics [29], as described in Section 2.2.

Figure 6. Cascaded connection of chain matrices to model all coil regions [22].

in the time domain [28].

The computer model described in this section for the prediction of the fast-transient response of the machine winding is a non-uniform, multi-conductor, distributed-parameter model defined in the frequency domain. This model is selected over other alternatives given its good

1. Why non-uniform? The distribution of electric and magnetic fields is different in the slot and overhang regions, resulting in different electrical parameters for each region that should be considered to accurately reproduce the pulse propagation. In this case, the nonuniform model consists of five segments considering the typical geometry of a wound-

2. Why multi-conductor? This modeling approach of the winding allows natural inclusion of

3. Why based on distributed parameters? A distributed parameter model based on transmission line theory can represent the propagation of a fast pulse along windings in a more rigorous

4. Why defined in the frequency domain? The partial differential equations describing wave propagation in time domain become ordinary differential equations in the frequency domain, making the solution more straightforward. In addition, including frequency dependence of the system parameters is substantially easier in the frequency domain than

The winding electrical parameters (capacitance, inductance, and losses) in the overhang and slot regions of the coil are calculated using the finite-element method (FEM)-based software

remarks of this chapter.

excitation

Wave propagation along the non-uniform multi-conductor transmission system representing the winding is defined by the Telegrapher equations in the Laplace domain as follows [30, 31]:

$$
\frac{d}{d\mathbf{x}} \begin{bmatrix} \mathbf{U}(\mathbf{x},s) \\ \mathbf{I}(\mathbf{x},s) \end{bmatrix} = \begin{bmatrix} 0 & -\mathbf{Z}(\mathbf{x},s) \\ -\mathbf{Y}(\mathbf{x},s) & 0 \end{bmatrix} \begin{bmatrix} \mathbf{U}(\mathbf{x},s) \\ \mathbf{I}(\mathbf{x},s) \end{bmatrix} \tag{1}
$$

In Eq. (1), U(x,s) and I(x,s) are the voltage and current vectors at point x along the line, Z(x,s) and Y(x,s) are the series impedance and shunt-admittance matrices of the line per unit length, respectively. According to Eq. (1), the winding electrical parameters are a function of both space and time. Voltages and currents at the terminals of the segment can be related using the chain matrix definition, assuming constant parameters over a segment Δx and applying boundary conditions at x and x + Δx [31]:

$$
\begin{bmatrix}
\mathbf{U}(\mathbf{x} + \Delta \mathbf{x}, \mathbf{s}) \\
\mathbf{I}(\mathbf{x} + \Delta \mathbf{x}, \mathbf{s})
\end{bmatrix} = \boldsymbol{\Phi}(\Delta \mathbf{x}, \mathbf{s}) \begin{bmatrix}
\mathbf{U}(\mathbf{x}, \mathbf{s}) \\
\mathbf{I}(\mathbf{x}, \mathbf{s})
\end{bmatrix} \tag{2}
$$

where the chain matrix of the segment is defined as

$$\boldsymbol{\Phi}(\Delta \mathbf{x}, \mathbf{s}) = \begin{bmatrix} \cosh(\mathfrak{q}\Delta \mathbf{x}) & -\mathbf{Y}\_0^{-1} \sinh(\mathfrak{q}\Delta \mathbf{x}) \\ -\mathbf{Y}\_0 \sinh(\mathfrak{q}\Delta \mathbf{x}) & \mathbf{Y}\_0 \cosh(\mathfrak{q}\Delta \mathbf{x}) \mathbf{Y}\_0^{-1} \end{bmatrix} \tag{3}$$

In Eq. (3), <sup>ψ</sup> is the propagation constant matrix of the line, given by <sup>ψ</sup> <sup>¼</sup> <sup>M</sup> ffiffiffi λ <sup>p</sup> <sup>M</sup>�<sup>1</sup> , where M and λ are the eigenvalue and eigenvector matrices of the Z(x,s)Y(x,s) product, respectively. In addition, Y<sup>0</sup> is the characteristic admittance matrix of the line segment, given by <sup>Y</sup><sup>0</sup> <sup>¼</sup> <sup>Z</sup>ð Þ <sup>x</sup>;<sup>s</sup> �<sup>1</sup> ψ. The two-port representation defined by Eq. (2) is the basis of the non-uniform model of the machine-winding coil, according to the following procedure [21]:


Voltages and currents at the sending (S) and receiving (R) nodes of the complete coil are related as follows:

$$
\begin{bmatrix} \mathbf{U}\_{\mathcal{R}} \\ \mathbf{I}\_{\mathcal{R}} \end{bmatrix} = \boldsymbol{\Phi}\_{1} \boldsymbol{\Phi}\_{2} \boldsymbol{\Phi}\_{3} \boldsymbol{\Phi}\_{2} \boldsymbol{\Phi}\_{1} \begin{bmatrix} \mathbf{U}\_{\mathcal{S}} \\ \mathbf{I}\_{\mathcal{S}} \end{bmatrix} = \begin{bmatrix} \boldsymbol{\Phi}\_{11} & \boldsymbol{\Phi}\_{12} \\ \boldsymbol{\Phi}\_{21} & \boldsymbol{\Phi}\_{22} \end{bmatrix} \begin{bmatrix} \mathbf{U}\_{\mathcal{S}} \\ \mathbf{I}\_{\mathcal{S}} \end{bmatrix} \tag{4}
$$

In Eq. (4), Φ11, Φ12, Φ21, and Φ<sup>22</sup> are the elements of the complete chain matrix representation of the coil. This representation is transformed into an equivalent admittance matrix form to include the zig-zag connection in order to preserve continuity between turns as a pulse propagates along the coil (see Figure 2) [32, 33]. This yields

$$
\begin{bmatrix} \mathbf{U}\_{\\$} \\ \mathbf{U}\_{\\$} \end{bmatrix} = \begin{bmatrix} \mathbf{Y}\_{\\$\\$} + \mathbf{Y}\_{\text{com11}} & -(\mathbf{Y}\_{\\$R} + \mathbf{Y}\_{\text{com12}}) \\ -(\mathbf{Y}\_{\\$R} + \mathbf{Y}\_{\text{com21}}) & \mathbf{Y}\_{\\$R} + \mathbf{Y}\_{\text{com22}} \end{bmatrix}^{-1} \begin{bmatrix} \mathbf{I}\_{\\$} \\ \mathbf{U}\_{\\$} \end{bmatrix} \tag{5}
$$

geometry. Self-inductance Lii is obtained from the magnetic energy Wm,i due to the injection of

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation…

Lii <sup>¼</sup> <sup>2</sup>Wm,i I 2 i

Mutual inductance Lij is obtained from the magnetic energy Wm,ij due to the simultaneous

Ljj (9)

http://dx.doi.org/10.5772/intechopen.78064

� 1 2 Ii Ij Lii þ Ij Ii

When using this method, all self inductances must be computed first and then applied for the

The series losses matrix (R) of the winding is considered frequency-dependent and obtained from the concept of complex penetration depth [22]. The dielectric losses matrix (G) is computed using the "electric currents" module in COMSOL [29]. Finally, the series impedance and shunt admittance matrices required by the winding model are computed according to Z = R + sL

A schematic cross-section of the coil considered in this study is shown in Figure 7. The main parameters of the stator coil are summarized in Table 1. Figure 8 shows a schematic representation and a picture of the experimental setup. Besides the MV form-wound coil under test, it includes a waveform generator (Keysight 33500B), an oscilloscope (Agilent DSO-X 2014A), and a 100-Ω load connected at the end of the coil. Steel plates were included to emulate the EM field distribution in the slot region [34]. The experimental setup was placed in a laboratory

The capacitance and inductance matrices are computed from FEM simulations using COMSOL Multiphysics, as explained in Section 2.2. Sample simulations are shown in Figures 9

Figure 9 shows the distribution of electric potential when turn 1 (top turn) is excited with 1 V, while all other turns and the slot walls are grounded. This allows the calculation of the first column of the capacitance matrix of the coil using Eq. (7). Figure 10 shows the distribution of magnetic energy density when turn 1 is excited with 1 A, while all other turns are left unexcited. Integrating this magnetic energy density results in the magnetic energy required in

The winding model is validated considering a PWM-type excitation with different rise times between 100 and 500 ns connected to the first turn of the coil. The rest of winding is represented

facility free of EM interference. More details of this test case can be found in [35].

Lij <sup>¼</sup> Wm,ij IiIj

(8)

59

a current Ii to turn i:

2.2.3. Losses

and Y = G + sC.

2.3. Case study

and 10 for the first turn.

Eq. (8) to compute the self-inductance of turn 1.

injection of current to turns i and j:

computation of mutual inductances.

The admittance matrix and chain matrix elements are related according to the following expressions:

$$\mathbf{Y}\_{\rm ss} = -\boldsymbol{\Phi}\_{12}^{-1}\boldsymbol{\Phi}\_{11\prime}\mathbf{Y}\_{\rm SR} = -\boldsymbol{\Phi}\_{12}^{-1} = -\boldsymbol{\Phi}\_{22}\boldsymbol{\Phi}\_{12}^{-1}\boldsymbol{\Phi}\_{11} + \boldsymbol{\Phi}\_{21\prime}\mathbf{Y}\_{\rm RR} = -\boldsymbol{\Phi}\_{22}\boldsymbol{\Phi}\_{12}^{-1} \tag{6}$$

In Eq. (5), admittance submatrices Ycon11, Ycon12, Ycon21, and Ycon<sup>22</sup> are included to connect the end of each turn to the beginning of the next one (zig-zag connection), as well as the source and load admittances representing winding terminal connections.

The Laplace-domain voltages at each turn of the coil are obtained from Eq. (5). These voltages are finally transformed into transient voltage responses in the time domain by means of the application of the inverse numerical Laplace transform [28].

#### 2.2. Parameter computation

FEM-based simulation program COMSOL Multiphysics is used to compute the capacitance and inductance matrices in the overhang and slot regions of the machine winding [29]. For the calculation of inductance in the slot region, it is assumed that the slot walls behave as magnetic insulation due to eddy currents at the high frequencies related to the pulses produced by frequency converters, meaning that the flux is normal to the boundary and does not penetrate the core. In the overhang region, these walls are replaced by an open-boundary condition.

#### 2.2.1. Capacitance

Capacitance matrix C is calculated using the electrostatics module of COMSOL using the forced voltage method as follows [22]:

$$
\begin{bmatrix} Q\_1 \\ \vdots \\ Q\_n \end{bmatrix} = \begin{bmatrix} \mathbf{C}\_{11} & \cdots & \mathbf{C}\_{1n} \\ \vdots & \ddots & \vdots \\ \mathbf{C}\_{n1} & \cdots & \mathbf{C}\_{nn} \end{bmatrix} \begin{bmatrix} \boldsymbol{U}\_1 \\ \vdots \\ \boldsymbol{U}\_n \end{bmatrix} \tag{7}
$$

The charge in all n elements due to conductor i is obtained by exciting conductor i with a fixed voltage while defining all other conductors at zero potential, thus obtaining the i-th column of the capacitive matrix. This process is repeated for each conductor to obtain the complete matrix.

#### 2.2.2. Inductance

Inductance matrix L is computed from the magnetic energy method [22]. The current is nonzero in one or two terminals at a time and the energy density is integrated over the whole Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation… http://dx.doi.org/10.5772/intechopen.78064 59

geometry. Self-inductance Lii is obtained from the magnetic energy Wm,i due to the injection of a current Ii to turn i:

$$L\_{ii} = \frac{2\mathcal{W}\_{m,i}}{I\_i^2} \tag{8}$$

Mutual inductance Lij is obtained from the magnetic energy Wm,ij due to the simultaneous injection of current to turns i and j:

$$L\_{i\dot{j}} = \frac{W\_{m,i\dot{j}}}{I\_i I\_{\dot{j}}} - \frac{1}{2} \left( \frac{I\_i}{I\_{\dot{j}}} L\_{i\dot{i}} + \frac{I\_{\dot{j}}}{I\_i} L\_{\dddot{j}} \right) \tag{9}$$

When using this method, all self inductances must be computed first and then applied for the computation of mutual inductances.

#### 2.2.3. Losses

include the zig-zag connection in order to preserve continuity between turns as a pulse

� ��<sup>1</sup> I<sup>S</sup>

U<sup>R</sup> � �

<sup>12</sup> <sup>Φ</sup><sup>11</sup> <sup>þ</sup> <sup>Φ</sup>21, <sup>Y</sup>RR ¼ �Φ22Φ�<sup>1</sup>

(5)

(7)

<sup>12</sup> (6)

<sup>¼</sup> <sup>Y</sup>SS <sup>þ</sup> <sup>Y</sup>con<sup>11</sup> �ð Þ <sup>Y</sup>SR <sup>þ</sup> <sup>Y</sup>con<sup>12</sup> �ð Þ YSR þ Ycon<sup>21</sup> YRR þ Ycon<sup>22</sup>

The admittance matrix and chain matrix elements are related according to the following

<sup>12</sup> ¼ �Φ22Φ�<sup>1</sup>

In Eq. (5), admittance submatrices Ycon11, Ycon12, Ycon21, and Ycon<sup>22</sup> are included to connect the end of each turn to the beginning of the next one (zig-zag connection), as well as the source and

The Laplace-domain voltages at each turn of the coil are obtained from Eq. (5). These voltages are finally transformed into transient voltage responses in the time domain by means of the

FEM-based simulation program COMSOL Multiphysics is used to compute the capacitance and inductance matrices in the overhang and slot regions of the machine winding [29]. For the calculation of inductance in the slot region, it is assumed that the slot walls behave as magnetic insulation due to eddy currents at the high frequencies related to the pulses produced by frequency converters, meaning that the flux is normal to the boundary and does not penetrate the core. In the overhang region, these walls are replaced by an open-boundary condition.

Capacitance matrix C is calculated using the electrostatics module of COMSOL using the

C<sup>11</sup> ⋯ C1<sup>n</sup> ⋮⋱⋮ Cn<sup>1</sup> ⋯ Cnn

The charge in all n elements due to conductor i is obtained by exciting conductor i with a fixed voltage while defining all other conductors at zero potential, thus obtaining the i-th column of the capacitive matrix. This process is repeated for each conductor to obtain the complete matrix.

Inductance matrix L is computed from the magnetic energy method [22]. The current is nonzero in one or two terminals at a time and the energy density is integrated over the whole

3 7 5

U<sup>1</sup>

⋮ Un

propagates along the coil (see Figure 2) [32, 33]. This yields

58 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

<sup>12</sup> <sup>Φ</sup>11, <sup>Y</sup>SR ¼ �Φ�<sup>1</sup>

load admittances representing winding terminal connections.

application of the inverse numerical Laplace transform [28].

Q1 ⋮ Qn

2 6 4

2 6 4

U<sup>S</sup> U<sup>R</sup> � �

<sup>Y</sup>ss ¼ �Φ�<sup>1</sup>

2.2. Parameter computation

forced voltage method as follows [22]:

2.2.1. Capacitance

2.2.2. Inductance

expressions:

The series losses matrix (R) of the winding is considered frequency-dependent and obtained from the concept of complex penetration depth [22]. The dielectric losses matrix (G) is computed using the "electric currents" module in COMSOL [29]. Finally, the series impedance and shunt admittance matrices required by the winding model are computed according to Z = R + sL and Y = G + sC.

#### 2.3. Case study

A schematic cross-section of the coil considered in this study is shown in Figure 7. The main parameters of the stator coil are summarized in Table 1. Figure 8 shows a schematic representation and a picture of the experimental setup. Besides the MV form-wound coil under test, it includes a waveform generator (Keysight 33500B), an oscilloscope (Agilent DSO-X 2014A), and a 100-Ω load connected at the end of the coil. Steel plates were included to emulate the EM field distribution in the slot region [34]. The experimental setup was placed in a laboratory facility free of EM interference. More details of this test case can be found in [35].

The capacitance and inductance matrices are computed from FEM simulations using COMSOL Multiphysics, as explained in Section 2.2. Sample simulations are shown in Figures 9 and 10 for the first turn.

Figure 9 shows the distribution of electric potential when turn 1 (top turn) is excited with 1 V, while all other turns and the slot walls are grounded. This allows the calculation of the first column of the capacitance matrix of the coil using Eq. (7). Figure 10 shows the distribution of magnetic energy density when turn 1 is excited with 1 A, while all other turns are left unexcited. Integrating this magnetic energy density results in the magnetic energy required in Eq. (8) to compute the self-inductance of turn 1.

The winding model is validated considering a PWM-type excitation with different rise times between 100 and 500 ns connected to the first turn of the coil. The rest of winding is represented

Figure 7. Cross section of the coil with three insulation layers [35].


Figure 8. Experimental setup for validation of the inverter-coil setup: (a) schematic diagram showing main parts and (b)

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photography of laboratory components [35].

Figure 9. Capacitance calculation using forced voltage method in FEM [35].

Table 1. Rotating machine parameters [35].

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Figure 8. Experimental setup for validation of the inverter-coil setup: (a) schematic diagram showing main parts and (b) photography of laboratory components [35].

Figure 9. Capacitance calculation using forced voltage method in FEM [35].

Figure 7. Cross section of the coil with three insulation layers [35].

60 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Table 1. Rotating machine parameters [35].

Turns per stator coil 7 Length of overhang region 0.33 m Conductor width (w) 5.35 mm Conductor height (h) 2.85 mm Resistivity of stator bar conductor 1.7 <sup>10</sup><sup>8</sup> <sup>Ω</sup><sup>m</sup> Thickness of interturn insulation (δ1) 0.2 mm Thickness of main insulation (δ2) 1.41 mm Thickness of ground-wall insulation (δ3) 0.36 mm Relative permittivity of the interturn insulation 2.5 Relative permittivity of the main insulation 2 Relative permittivity of the ground-wall ins 2.8 Slot width (W) 8.9 mm Slot height (H) 24.2 mm Slot length 0.45 m

Figure 10. Inductance calculation using magnetic energy method in FEM [35].

by a 100-Ω load. This type of excitation is obtained from the waveform generator emulating the phase-to-ground voltage from a voltage source inverter.

Figure 11 shows the comparison of the simulated and measured transient voltage at the first winding turn for excitations with different rise times. It can be noticed that the magnitude of the overshoot produced depends on the rise time of the excitation. A second assessment of the winding corresponds to a similar setup, but with an open-ended condition of the coil. This results in noticeable oscillations, which are reproduced in a very accurate manner by the winding model, as shown in Figure 12, which illustrates the transient response at the far end

of the winding. As in the previous case, the maximum overvoltages are related to the highest

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The effect of the excitation rise time is analyzed in a more general manner in Figure 13, which shows the potential difference between turns for different rise times. According to this figure,

Modeling of stress-grading systems of MV rotating machines is an essential tool for their design

the potential difference is inversely proportional to the rise time of the excitation.

Figure 13. Potential difference between turns considering different rise times of the excitation [35].

Figure 12. Transient overvoltage at the last turn of the coil for open-ended case [35].

3. Modeling of stress-grading systems from rotating machines

and optimization. An accurate model can serve several purposes, such as [36]: 1. describing how the system is likely to behave under certain conditions;

rise time of the excitation.

Figure 11. Transient overvoltage at the first turn of the coil terminated in 100-Ω load [35].

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Figure 12. Transient overvoltage at the last turn of the coil for open-ended case [35].

by a 100-Ω load. This type of excitation is obtained from the waveform generator emulating the

Figure 11 shows the comparison of the simulated and measured transient voltage at the first winding turn for excitations with different rise times. It can be noticed that the magnitude of the overshoot produced depends on the rise time of the excitation. A second assessment of the winding corresponds to a similar setup, but with an open-ended condition of the coil. This results in noticeable oscillations, which are reproduced in a very accurate manner by the winding model, as shown in Figure 12, which illustrates the transient response at the far end

phase-to-ground voltage from a voltage source inverter.

Figure 10. Inductance calculation using magnetic energy method in FEM [35].

62 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

Figure 11. Transient overvoltage at the first turn of the coil terminated in 100-Ω load [35].

Figure 13. Potential difference between turns considering different rise times of the excitation [35].

of the winding. As in the previous case, the maximum overvoltages are related to the highest rise time of the excitation.

The effect of the excitation rise time is analyzed in a more general manner in Figure 13, which shows the potential difference between turns for different rise times. According to this figure, the potential difference is inversely proportional to the rise time of the excitation.

#### 3. Modeling of stress-grading systems from rotating machines

Modeling of stress-grading systems of MV rotating machines is an essential tool for their design and optimization. An accurate model can serve several purposes, such as [36]:

1. describing how the system is likely to behave under certain conditions;


FEM has become one of the most commonly used techniques for modeling stress-grading systems [37–39]. With FEM, the geometry can be considered including most of the details that influence the electric field distribution. To determine how the electric field stress is distributed during PWM voltage excitation, the problem must be solved in the time domain with considerably small time steps. This, together with the high nonlinearity of the semi-conductive stress-grading coating, makes modeling of SG systems a complicated task [40, 41].

#### 3.1. Modeling of stress-grading systems

In the general case, problems with stress-grading systems can be represented with subdomains of conductors, subdomains of perfect dielectrics (air or another surrounding medium and main insulation), and subdomains of stress-grading materials [42]. Conductors can be considered perfect conducting regions of known potential. Neglecting the dielectric loss component of the materials, the equation to be solved is of the form [43]

$$\nabla \cdot [-\sigma(\mathbf{E}) \nabla \mathcal{U}] + \frac{\partial [\nabla \cdot (\varepsilon\_r \varepsilon\_0 (-\nabla \mathcal{U}))]}{\partial t} = 0 \tag{10}$$

field distribution and resistive heat produced in the CAT and SGT of form-wound coils under

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With the aid of an infrared camera, it is possible to observe the heat generated because of the electric stress grading under fast pulses. In order to show this condition, a 4.2-kV form wound coil was energized with 4-kV squared pulses with a repetition rate of 2000 pulses per second, and the temperature was registered using an infrared camera model Flir-SC500. As it can be seen in Figure 14, the heat distribution is different in comparison to that presented in Figure 5 for power frequency (60 Hz); under this condition, the high electric stress moves from the SGT to the CAT at slot exit. Something important to notice in the infrared image is the presence of hot spots that follow the patterns of the CAT tapping; this will be discussed in Section 3.4.

Usually, modeling of the conductive armor coating and the semi-conductive-grading coatings is done separately; however, under fast pulses, it is important to understand the combined performance of both coatings. Therefore, the analysis of coil ends working with PWM voltages

A useful tool in FEM modeling is the ability of reducing the dimension of the elements used to discretize the stress-grading coating subdomain [29]. These coatings are applied in thin layers that require a very fine element discretization; otherwise, if a coarse discretization of the subdomains is used, numerical instability may result [47]. Assuming that the conductivity of the semi-conductive coating depends only on the tangential component of the electric field, the elements used in the SG coatings can be reduced to one dimension (1D) [48]. If the geometry of the problem is considered in two dimensions (2D), as shown in Figure 15(a), the subdomains

Figure 14. Temperature profile on a 4.2-kV coil end under 650-ns rise time pulses with a repetition rate of 2000 pulses per

3.2. FEM modeling of stress-grading coatings under PWM voltage waveforms

the application of fast rise time pulses.

requires the simultaneous simulation of both coatings.

second. Peak voltage: 4.0 kV [26].

3.2.1. Finite-element dimension reduction on the stress-grading coatings

where σ is the electrical conductivity, ε<sup>r</sup> is the relative permittivity, and ε<sup>0</sup> is the vacuum permittivity. The electric field dependency (σð Þ E ) of the semi-conductive-grading coating helps to limit the maximum electric field on the surface of the coil giving adaptability to different designs and voltage levels [44]. For proper FEM simulations, it is required to know the nonlinearity of the electrical conductivity at high electric stress for the semi-conductive-grading material. One of the most common expressions used to define the electric field dependency in S/m of this coating is given by [45, 46]

$$
\sigma(E\_t) = \sigma\_0 \exp(\alpha E\_t'') \tag{11}
$$

where σ<sup>0</sup> = 1.85 x 10�<sup>9</sup> S/m, α= 0.00112, and n = 0.67. Eq. (10) can be solved analytically or numerically. FEM or an Equivalent Electric Circuit Model [36] can be used for this purpose. FEM is widely used to model the SG coatings due to some advantages over, for example, equivalent circuit models. With circuit models, some geometric aspects of the SG systems, like overlapping of coatings or the sharp end of the slot exit, are difficult to be considered. In addition, with FEM, the thermal field problem can be solved using the same geometry, taking as a source of heat the ohmic losses from the electric solution.

Transient FEM with efficient algorithms needs to be used in order to solve the highly nonlinear problem associated with SG coatings. Nowadays, FEM software provides new capabilities that allow performing highly nonlinear simulations. The "electric currents" module of the FEMbased software COMSOL Multiphysics [29] is used in the next sections to compute the electric

field distribution and resistive heat produced in the CAT and SGT of form-wound coils under the application of fast rise time pulses.

#### 3.2. FEM modeling of stress-grading coatings under PWM voltage waveforms

2. modifying the material characteristics to match specific requirements;

64 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

a maintenance policy.

3.1. Modeling of stress-grading systems

in S/m of this coating is given by [45, 46]

materials, the equation to be solved is of the form [43]

as a source of heat the ohmic losses from the electric solution.

task [40, 41].

3. predicting the effects of aging and determining the material's life time in order to establish

FEM has become one of the most commonly used techniques for modeling stress-grading systems [37–39]. With FEM, the geometry can be considered including most of the details that influence the electric field distribution. To determine how the electric field stress is distributed during PWM voltage excitation, the problem must be solved in the time domain with considerably small time steps. This, together with the high nonlinearity of the semi-conductive stress-grading coating, makes modeling of SG systems a complicated

In the general case, problems with stress-grading systems can be represented with subdomains of conductors, subdomains of perfect dielectrics (air or another surrounding medium and main insulation), and subdomains of stress-grading materials [42]. Conductors can be considered perfect conducting regions of known potential. Neglecting the dielectric loss component of the

<sup>∇</sup>∙½ �þ �σð Þ <sup>E</sup> <sup>∇</sup><sup>U</sup> <sup>∂</sup>½ � <sup>∇</sup>∙ð Þ <sup>ε</sup>rε0ð Þ �∇<sup>U</sup>

where σ is the electrical conductivity, ε<sup>r</sup> is the relative permittivity, and ε<sup>0</sup> is the vacuum permittivity. The electric field dependency (σð Þ E ) of the semi-conductive-grading coating helps to limit the maximum electric field on the surface of the coil giving adaptability to different designs and voltage levels [44]. For proper FEM simulations, it is required to know the nonlinearity of the electrical conductivity at high electric stress for the semi-conductive-grading material. One of the most common expressions used to define the electric field dependency

σð Þ¼ Et σ0exp αEt

where σ<sup>0</sup> = 1.85 x 10�<sup>9</sup> S/m, α= 0.00112, and n = 0.67. Eq. (10) can be solved analytically or numerically. FEM or an Equivalent Electric Circuit Model [36] can be used for this purpose. FEM is widely used to model the SG coatings due to some advantages over, for example, equivalent circuit models. With circuit models, some geometric aspects of the SG systems, like overlapping of coatings or the sharp end of the slot exit, are difficult to be considered. In addition, with FEM, the thermal field problem can be solved using the same geometry, taking

Transient FEM with efficient algorithms needs to be used in order to solve the highly nonlinear problem associated with SG coatings. Nowadays, FEM software provides new capabilities that allow performing highly nonlinear simulations. The "electric currents" module of the FEMbased software COMSOL Multiphysics [29] is used in the next sections to compute the electric

<sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>0</sup> (10)

<sup>n</sup> ð Þ (11)

With the aid of an infrared camera, it is possible to observe the heat generated because of the electric stress grading under fast pulses. In order to show this condition, a 4.2-kV form wound coil was energized with 4-kV squared pulses with a repetition rate of 2000 pulses per second, and the temperature was registered using an infrared camera model Flir-SC500. As it can be seen in Figure 14, the heat distribution is different in comparison to that presented in Figure 5 for power frequency (60 Hz); under this condition, the high electric stress moves from the SGT to the CAT at slot exit. Something important to notice in the infrared image is the presence of hot spots that follow the patterns of the CAT tapping; this will be discussed in Section 3.4.

Usually, modeling of the conductive armor coating and the semi-conductive-grading coatings is done separately; however, under fast pulses, it is important to understand the combined performance of both coatings. Therefore, the analysis of coil ends working with PWM voltages requires the simultaneous simulation of both coatings.

#### 3.2.1. Finite-element dimension reduction on the stress-grading coatings

A useful tool in FEM modeling is the ability of reducing the dimension of the elements used to discretize the stress-grading coating subdomain [29]. These coatings are applied in thin layers that require a very fine element discretization; otherwise, if a coarse discretization of the subdomains is used, numerical instability may result [47]. Assuming that the conductivity of the semi-conductive coating depends only on the tangential component of the electric field, the elements used in the SG coatings can be reduced to one dimension (1D) [48]. If the geometry of the problem is considered in two dimensions (2D), as shown in Figure 15(a), the subdomains

Figure 14. Temperature profile on a 4.2-kV coil end under 650-ns rise time pulses with a repetition rate of 2000 pulses per second. Peak voltage: 4.0 kV [26].

for the CAT and SGT can be discretized using one-dimensional elements (electric shielding boundary in COMSOL), thereby considerably reducing the total number of elements and, in most cases, making it easier for the solution to converge.

However, simulations using discretization of the CAT and SGT with one dimension elements reduction can give a sufficiently good approximation when these details are not required in

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When the response of an SG system during a PWM waveform needs to be modeled, a large computing time is generally required, since the time step is defined by the fast rise time of the pulses (1 μs or less) and the simulation time is in the order of several milliseconds. Using reduced dimension elements in the CAT and SGT domains makes the simulation computationally more efficient. One example of the convenience of this dimension reduction is shown with the transient simulation of electric field and heat in a coil with 3-mm thickness of the ground-wall insulation, and 1 mm CAT and SGT thickness; the length of the CAT is 50 mm from the slot exit. The CAT conductivity is 0.01 S/m, and the relative permittivity is 100. The length of the SGT is 100 mm. The SGT has a relative permittivity of 20 and a nonlinear conductivity given by Eq. (11). Considering a phase-to-ground three-level PWM voltage [50], which waveform is shown in the inset of Figure 17(a), the magnitude of the tangential electric stress versus time is present along both coatings, as it can be observed in Figure 17(a). The magnitude of the resistive heat density along the CAT and SGT as a function of time and electric field is presented in Figure 17(b). According to this figure, the

The tangential component of the electric field in the CAT is well below the tangential electric field in the SGT (Figure 17(a)), but the heat generated in this coating is considerably higher (Figure 17(b)). Experimental work on form-wound coils stressed by fast pulses has shown that this condition can damage the CAT, allowing surface PD to appear right at the slot exit [51, 52]. The next section introduces the use of FEM modeling to investigate possible solu-

Figure 17. (a) Tangential electric field distribution along the surface from the slot end of the coil under a phase to ground

the simulations.

heat is concentrated mainly in the CAT.

tions to this problem.

PWM waveform and (b) resistive heat [53].

Consider for simulation the 2D geometry of the coil end shown in Figure 15(a) and the transient voltage of a leading edge of one PWM pulse, shown in Figure 15(b). The pulse has a rise time of 1 μs and an overshoot of around of 1.6 times the nominal phase to ground peak voltage for a 6.6-kV coil. The thickness of the ground-wall insulation is 3 mm, the CAT and SGT are 0.5 mm thick, and their lengths are 50 and 100 mm, respectively. The CAT conductivity is 0.01 S/m, and the conductivity of the SGT is given by Eq. (11). The relative permittivities (εr) of the CAT and the SGT are, respectively, 50 and 20. A comparison of the results for the electric field on the CAT and SGT using 1D and 2D elements is presented in Figure 16. As it can be seen in this figure, this 1D simplification does not modify the results when compared to the solution obtained considering 2D elements.

In addition, the simplification from a 2D to a 1D modeling can be indeed useful, especially when non-axial-symmetric geometries need to be modeled in three dimensions. For example, form-wound coils can be modeled in 3D, when considering 2D elements in the stressgrading subdomains [49]. One problem that occurs with this simplification is that geometrical details like overlapping in multilayer systems are sometimes difficult to implement.

Figure 15. (a) Cross-section illustration of the form-wound coil and (b) transient pulse voltage waveform considered in the transient FEM simulations [26].

Figure 16. Tangential electric field distribution along the stress-grading coatings computed using (a) 2D elements and (b) 1D elements.

However, simulations using discretization of the CAT and SGT with one dimension elements reduction can give a sufficiently good approximation when these details are not required in the simulations.

for the CAT and SGT can be discretized using one-dimensional elements (electric shielding boundary in COMSOL), thereby considerably reducing the total number of elements and, in

Consider for simulation the 2D geometry of the coil end shown in Figure 15(a) and the transient voltage of a leading edge of one PWM pulse, shown in Figure 15(b). The pulse has a rise time of 1 μs and an overshoot of around of 1.6 times the nominal phase to ground peak voltage for a 6.6-kV coil. The thickness of the ground-wall insulation is 3 mm, the CAT and SGT are 0.5 mm thick, and their lengths are 50 and 100 mm, respectively. The CAT conductivity is 0.01 S/m, and the conductivity of the SGT is given by Eq. (11). The relative permittivities (εr) of the CAT and the SGT are, respectively, 50 and 20. A comparison of the results for the electric field on the CAT and SGT using 1D and 2D elements is presented in Figure 16. As it can be seen in this figure, this 1D simplification does not modify the results when compared to the

In addition, the simplification from a 2D to a 1D modeling can be indeed useful, especially when non-axial-symmetric geometries need to be modeled in three dimensions. For example, form-wound coils can be modeled in 3D, when considering 2D elements in the stressgrading subdomains [49]. One problem that occurs with this simplification is that geometrical details like overlapping in multilayer systems are sometimes difficult to implement.

Figure 15. (a) Cross-section illustration of the form-wound coil and (b) transient pulse voltage waveform considered in

Figure 16. Tangential electric field distribution along the stress-grading coatings computed using (a) 2D elements and (b)

most cases, making it easier for the solution to converge.

66 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

solution obtained considering 2D elements.

the transient FEM simulations [26].

1D elements.

When the response of an SG system during a PWM waveform needs to be modeled, a large computing time is generally required, since the time step is defined by the fast rise time of the pulses (1 μs or less) and the simulation time is in the order of several milliseconds. Using reduced dimension elements in the CAT and SGT domains makes the simulation computationally more efficient. One example of the convenience of this dimension reduction is shown with the transient simulation of electric field and heat in a coil with 3-mm thickness of the ground-wall insulation, and 1 mm CAT and SGT thickness; the length of the CAT is 50 mm from the slot exit. The CAT conductivity is 0.01 S/m, and the relative permittivity is 100. The length of the SGT is 100 mm. The SGT has a relative permittivity of 20 and a nonlinear conductivity given by Eq. (11). Considering a phase-to-ground three-level PWM voltage [50], which waveform is shown in the inset of Figure 17(a), the magnitude of the tangential electric stress versus time is present along both coatings, as it can be observed in Figure 17(a). The magnitude of the resistive heat density along the CAT and SGT as a function of time and electric field is presented in Figure 17(b). According to this figure, the heat is concentrated mainly in the CAT.

The tangential component of the electric field in the CAT is well below the tangential electric field in the SGT (Figure 17(a)), but the heat generated in this coating is considerably higher (Figure 17(b)). Experimental work on form-wound coils stressed by fast pulses has shown that this condition can damage the CAT, allowing surface PD to appear right at the slot exit [51, 52]. The next section introduces the use of FEM modeling to investigate possible solutions to this problem.

Figure 17. (a) Tangential electric field distribution along the surface from the slot end of the coil under a phase to ground PWM waveform and (b) resistive heat [53].

#### 3.3. Modeling for the design of stress-grading coatings under PWM voltages

As mentioned before, the SG systems in motor coil ends can fail because of the excessive heat generated when they operate under fast rise time pulses like those produced by adjustable speed drives. The excessive heat produced in the CAT can be considered the first problem to be solved in order to improve the performance of these coatings under fast pulses. Figure 18 shows the resistive heat density for the same case presented in Figure 16. It can be noticed that the heat is produced mainly in the CAT. The heat and electric field in the CAT can be reduced by increasing the conductivity of this coating; however, the high stress will be now moved to the SGT. A possible solution consists of controlling both the material properties and the designs of stress-grading system [26]. For example, a sectionalized stress-grading system consisting of two coatings with different conductive properties can be used in the CAT in addition to the SGT in order to divide the electric field and ohmic losses at the coil end. The first part, starting from the slot end, is a highly conductive coating, and the second part is now referred to as stress-grading coating for high-frequency components (SGHF). The SGHF coating is designed to filter and relieve the fast rise front of the pulses, while a third coating (SGLF) is used to grade the lower frequency components of the PWM voltage waveform.

3.4. Simulation of the tapping of stress-grading systems under fast pulses

Figure 19. (a) Resistive heat and (b) electric field distribution along the sectionalized stress-grading system.

thickness between segments with two tape thickness [54].

Figure 20. Heat in the CAT and SGT coatings considering the tape overlappings.

As mentioned before, an important characteristic of FEM modeling of stress-grading systems is the possibility of taking into account some details of the geometry that can influence the stress distribution under fast rise time pulses. In tape-based SG systems, the SGT usually overlaps the CAT a couple of centimeters, with one or two full-lapped turns followed by halflapped turns until it reaches the desired length. During FEM modeling, the overlapping interfaces can be reproduced as in the real condition; however, it is not usual to consider the tape interfaces. Optical micrographs of the overlapping tape sections, obtained from formwound coils, have shown that there are transition sections of the coatings with only one tape

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Two-dimensional FEM simulations of the stress-grading system are performed considering the coatings configuration and the voltage waveform from Figure 15, but now the geometrical shape of the half overlapping between tape turns is included. For this case, the conductivity of the CAT was considered as 0.01 S/m, with a relative permittivity of 50,

As an example, consider a sectionalized stress-grading system where the thickness of the SGHF and SGLF layers is duplicated (1 mm), and the electric properties of the first layer are conductivity of 0.5 S/m, and ε<sup>r</sup> = 50, for the second conductive layer (SGHF): conductivity of 0.05 S/m, and ε<sup>r</sup> = 50. The third layer SGT is an with the same nonlinear characteristic given by Eq. (11), but with a value of <sup>σ</sup><sup>0</sup> = 1.85 <sup>10</sup><sup>8</sup> S/m.

The distribution of resistive heat and electric field is modified, as it can be seen in Figure 19. With the first conductive layer, the maximum heat is moved to the SGHF and SGLF layers and reduced in around 50%, see Figure 19(a). The electric field is not increased in the SGLF in comparison with the electric field in the original design presented in Figure 16, as shown in Figure 19(b). This is an example of how modeling allows modifying the properties and dimensions of the stress-grading coatings in order to obtain the desired stress grading.

Figure 18. Resistive heat distribution along the stress-grading coatings for the same case of the results presented in Figure 14.

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Figure 19. (a) Resistive heat and (b) electric field distribution along the sectionalized stress-grading system.

#### 3.4. Simulation of the tapping of stress-grading systems under fast pulses

3.3. Modeling for the design of stress-grading coatings under PWM voltages

68 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

components of the PWM voltage waveform.

but with a value of <sup>σ</sup><sup>0</sup> = 1.85 <sup>10</sup><sup>8</sup> S/m.

Figure 14.

As mentioned before, the SG systems in motor coil ends can fail because of the excessive heat generated when they operate under fast rise time pulses like those produced by adjustable speed drives. The excessive heat produced in the CAT can be considered the first problem to be solved in order to improve the performance of these coatings under fast pulses. Figure 18 shows the resistive heat density for the same case presented in Figure 16. It can be noticed that the heat is produced mainly in the CAT. The heat and electric field in the CAT can be reduced by increasing the conductivity of this coating; however, the high stress will be now moved to the SGT. A possible solution consists of controlling both the material properties and the designs of stress-grading system [26]. For example, a sectionalized stress-grading system consisting of two coatings with different conductive properties can be used in the CAT in addition to the SGT in order to divide the electric field and ohmic losses at the coil end. The first part, starting from the slot end, is a highly conductive coating, and the second part is now referred to as stress-grading coating for high-frequency components (SGHF). The SGHF coating is designed to filter and relieve the fast rise front of the pulses, while a third coating (SGLF) is used to grade the lower frequency

As an example, consider a sectionalized stress-grading system where the thickness of the SGHF and SGLF layers is duplicated (1 mm), and the electric properties of the first layer are conductivity of 0.5 S/m, and ε<sup>r</sup> = 50, for the second conductive layer (SGHF): conductivity of 0.05 S/m, and ε<sup>r</sup> = 50. The third layer SGT is an with the same nonlinear characteristic given by Eq. (11),

The distribution of resistive heat and electric field is modified, as it can be seen in Figure 19. With the first conductive layer, the maximum heat is moved to the SGHF and SGLF layers and reduced in around 50%, see Figure 19(a). The electric field is not increased in the SGLF in comparison with the electric field in the original design presented in Figure 16, as shown in Figure 19(b). This is an example of how modeling allows modifying the properties and

Figure 18. Resistive heat distribution along the stress-grading coatings for the same case of the results presented in

dimensions of the stress-grading coatings in order to obtain the desired stress grading.

As mentioned before, an important characteristic of FEM modeling of stress-grading systems is the possibility of taking into account some details of the geometry that can influence the stress distribution under fast rise time pulses. In tape-based SG systems, the SGT usually overlaps the CAT a couple of centimeters, with one or two full-lapped turns followed by halflapped turns until it reaches the desired length. During FEM modeling, the overlapping interfaces can be reproduced as in the real condition; however, it is not usual to consider the tape interfaces. Optical micrographs of the overlapping tape sections, obtained from formwound coils, have shown that there are transition sections of the coatings with only one tape thickness between segments with two tape thickness [54].

Two-dimensional FEM simulations of the stress-grading system are performed considering the coatings configuration and the voltage waveform from Figure 15, but now the geometrical shape of the half overlapping between tape turns is included. For this case, the conductivity of the CAT was considered as 0.01 S/m, with a relative permittivity of 50,

Figure 20. Heat in the CAT and SGT coatings considering the tape overlappings.

and the CAT-CAT overlappings occurring every centimeter. The conductivity of the SGT is given by Eq. (11). The shape considered for the tape overlappings is shown in the inset of Figure 20. In the same figure, the simulation results show how the CAT-CAT overlappings present high values of heat, behavior that is experimentally confirmed by the temperature distribution presented in Figure 14. These results demonstrate how the quality of the application of these tape-based coatings must be guaranteed to avoid early problems with the machines fed by PWM drives.

Author details

References

73(1):1-10

sion. 1997;12(1):24-31

ings. 1st ed. Hersey: IGI Global; 2013

Canada. US: IEEE; 2007. pp. 1-7

Fermin P. Espino Cortes<sup>1</sup>

, Pablo Gomez<sup>2</sup>

\*Address all correspondence to: pablo.gomez@wmich.edu

1 Instituto Politecnico Nacional, Mexico City, Mexico 2 Western Michigan University, Kalamazoo, MI, USA

Electrical Engineers. 1934;53(1):139-146

3 University of Baghdad, Baghdad, Iraq

\* and Mohammed Khalil Hussain2,3

http://dx.doi.org/10.5772/intechopen.78064

71

[1] Calvert JF. Protecting machines from line surges. Transactions of the American Institute of

Modeling and Simulation of Rotating Machine Windings Fed by High-Power Frequency Converters for Insulation…

[2] Abetti PA, Maginniss FJ. Fundamental oscillations of coils and windings. Transactions of American Institute of Electrical Engineers. Part III: Power Apparatus and Systems. 1954;

[3] Cornick KJ, Thompson TR. Steep-fronted switching voltage transients and their distribution in motor windings. Part 2: Distribution of steep-fronted switching voltage transients in motor windings. IEE Proceedings B – Electric Power Applications. 1982;129(2):56-63 [4] Oraee H, McLaren PG. Surge voltage distribution in line-end coils of induction motors. IEEE Transactions on Power Apparatus and Systems. 1985;PAS-104(7):1843-1848

[5] Guardado JL, Cornick KJ. A computer model for calculating steep-fronted surge distribution in machine windings. IEEE Transactions on Energy Conversion. 1989;4(1):95-101 [6] Guardado JL, Cornick KJ, Venegas V, Naredo JL, Melgoza E. A three-phase model for surge distribution studies in electrical machines. IEEE Transactions on Energy Conver-

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[9] Stone GC, Culbert I. Review of stator insulation problems in medium voltage motors fed from voltage source PWM drives. In: Proceedings of International Symposium on Electrical Insulating Materials (ISEIM'14); 1–5 June 2014; Niigata, Japan. US: IEEE; 2014. pp. 50-53

#### 4. Conclusions

Two crucial topics for the proper insulation design of MV motors excited by PWM drives have been reviewed in this chapter: modeling of the windings for pulse propagation analysis and modeling of the stress-grading system.

A frequency domain non-uniform multi-conductor transmission line approach has been used to study the fast-front transient response of a machine-winding coil when a PWM-type excitation from an inverter is applied. The parameters of the coil were calculated using the finiteelement method. The results when applying a PWM-type excitation to the coil show that the rise time of the source and the length of the cable has an important effect on the transient overvoltage produced at different turns of the coil, as well as in the potential difference between adjacent turns. The comparison between simulation and experimental results, in terms of oscillatory behavior and magnitude, demonstrates that both the winding model and the cable model selected result in a very accurate prediction of the fast-transient response related to the use of inverters in medium-voltage induction machines. Since the winding model is considered as linear for high frequencies, a frequency domain-modeling approach is a very good option to study the fast-transient response of machine windings.

On the other hand, the conductive armor and semi-conductive-grading coatings are important parts of the insulation system in rotating machines. The correct design of these coatings becomes difficult when PWM voltages feed the machine from adjustable speed drives. The stress-grading coatings often cannot effectively relieve the stress during repetitive surge voltages and, in the extreme case, hot spots and/or PDs will gradually destroy the coatings, making the problem worse. FEM modeling is a useful tool in understanding the influence of the various design parameters eliminating the trial and error methods that usually require more time and other resources. By reducing the dimension of the elements used to discretize the stress-grading coatings subdomains, it is possible to reduce the computational burden, but when a detailed geometry of the stress-grading system needs to be included in the simulation, this option cannot be considered. By using FEM modeling, it is possible to compute the maximum electric field, power loss, or voltage at the end of the SGT and use these variables in conjunction with optimization subroutines to obtain improved designs.

## Author details

and the CAT-CAT overlappings occurring every centimeter. The conductivity of the SGT is given by Eq. (11). The shape considered for the tape overlappings is shown in the inset of Figure 20. In the same figure, the simulation results show how the CAT-CAT overlappings present high values of heat, behavior that is experimentally confirmed by the temperature distribution presented in Figure 14. These results demonstrate how the quality of the application of these tape-based coatings must be guaranteed to avoid early problems

Two crucial topics for the proper insulation design of MV motors excited by PWM drives have been reviewed in this chapter: modeling of the windings for pulse propagation analysis and

A frequency domain non-uniform multi-conductor transmission line approach has been used to study the fast-front transient response of a machine-winding coil when a PWM-type excitation from an inverter is applied. The parameters of the coil were calculated using the finiteelement method. The results when applying a PWM-type excitation to the coil show that the rise time of the source and the length of the cable has an important effect on the transient overvoltage produced at different turns of the coil, as well as in the potential difference between adjacent turns. The comparison between simulation and experimental results, in terms of oscillatory behavior and magnitude, demonstrates that both the winding model and the cable model selected result in a very accurate prediction of the fast-transient response related to the use of inverters in medium-voltage induction machines. Since the winding model is considered as linear for high frequencies, a frequency domain-modeling approach is

On the other hand, the conductive armor and semi-conductive-grading coatings are important parts of the insulation system in rotating machines. The correct design of these coatings becomes difficult when PWM voltages feed the machine from adjustable speed drives. The stress-grading coatings often cannot effectively relieve the stress during repetitive surge voltages and, in the extreme case, hot spots and/or PDs will gradually destroy the coatings, making the problem worse. FEM modeling is a useful tool in understanding the influence of the various design parameters eliminating the trial and error methods that usually require more time and other resources. By reducing the dimension of the elements used to discretize the stress-grading coatings subdomains, it is possible to reduce the computational burden, but when a detailed geometry of the stress-grading system needs to be included in the simulation, this option cannot be considered. By using FEM modeling, it is possible to compute the maximum electric field, power loss, or voltage at the end of the SGT and use these variables in conjunction with optimization subroutines to obtain

a very good option to study the fast-transient response of machine windings.

with the machines fed by PWM drives.

70 Simulation and Modelling of Electrical Insulation Weaknesses in Electrical Equipment

modeling of the stress-grading system.

4. Conclusions

improved designs.

Fermin P. Espino Cortes<sup>1</sup> , Pablo Gomez<sup>2</sup> \* and Mohammed Khalil Hussain2,3

\*Address all correspondence to: pablo.gomez@wmich.edu


#### References


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**Section 2**

**Environmentally Friendly Insulation Gases as**

**Alternatives to Sulfur Hexafluoride Gas**
