Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction Generator

*Imane Idrissi, Houcine Chafouk, Rachid El Bachtiri and Maha Khanfara*

## **Abstract**

This chapter presents the modeling and simulation results of variable speed wind turbine driven by doubly fed induction generator (DFIG). The feeding of the generator is ensured through its stator directly connected to the electrical grid and by its rotor connected to the grid through two power converters, which are controlled by the pulse width modulation (PWM) technique. This configuration is the most used in the wind power generation systems. For the variable speed operation of the studied system, the maximum power point tracking strategy is applied for the turbine, and the stator flux-oriented vector control is used for the generator. The MATLAB/Simulink software is used for the system modeling and simulation. For the wind velocity model, a random wind profile is simulated, and the turbine and the generator parameters are extracted from an existing wind turbine system in the literature. The obtained results are addressed in this chapter.

**Keywords:** wind turbine, variable speed operation, DFIG, PWM, MATLAB/Simulink, MPPT

## **1. Introduction**

With the global warming issues and the climate changes, there is a serious need for the use of the renewable energy resources in the electricity generation industry. Currently, the wind represents one of the most important renewable energy resources, used for generating electrical energy in the world. In terms of the total installed wind capacity, it becomes up to 539 GW across the globe in 2017 [1]. The rapid rate of the wind energy industry growth is caused by the cost-effectiveness of electricity production from wind farms, compared to electricity production cost from fossil fuel energy [2], the stability of electricity cost [3], the short commissioning time of wind farms [4], and the ingenuity of skillful engineers.

According to a wind market survey, the doubly fed induction generator (DFIG) is the most popular generator used in the speed variable wind turbines (SVWT) [5]. It is a wound rotor asynchronous machine which has the stator windings directly

connected to the electrical grid, and its rotor is linked to the constant frequency grid by means of two bidirectional power converters.

mechanical structural modeling of the wind turbine connected to the grid and based on DFIG has been developed, and it has been validated using NREL's simulation tool, FAST v7; for analysis of the dynamic behavior of the wind power plant with DFIG under the grid fault conditions, modeling of the whole system has been established in [16]. Furthermore, with the use of an electromagnetic transient simulation software, the wind turbine driven by DFIG model is elaborated in [17]. The organization of this chapter is as follows: the wind turbine structure is described in Section 2; the wind modeling turbine is presented in Section 3. In Section 4, the simulation results in MATLAB/Simulink environment are shown.

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

The wind turbine is a complex system containing different components, which involved different domains: electrical, mechanical, and electronic areas and others. The complete model of the studied wind turbine system is represented by a set of blocks each representing a functional entity of the system. The general structure of

As it is shown in the **Figure 2**, the wind velocity and the fixed-pitch angle represent the input of the wind turbine system. The aerodynamic conversion entity is formed of three blades which capture and convert the kinetic energy of the wind into mechanical energy, recovered on the slow rotating shaft. Then, the gearbox device increases the turbine low speed and makes it suitable with the generator rotational speed, which is about 1500 rpm. The generator receives mechanical energy and transforms it into electrical energy. The two power converters used are insulated gate bipolar transistor (IGBT) type and controlled by pulse width modulation (PWM) technique; they allow the independent control of the active and reactive powers and also the transfer of the slip power in two directions: from the

In this section, the mathematical model of each wind turbine block is presented.

The wind resource is an important element in a wind energy system, and it represents a determining factor in the calculation of electricity production because, under optimal conditions, the power captured by the wind turbine is a cubic

generator to the network and from the network to the generator.

Finally, the conclusion is presented in Section 5.

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

**2. The wind turbine structure**

a wind system is given by **Figure 2**.

**3. The wind turbine modeling**

**3.1 Wind speed model**

*Wind turbine system structure.*

**Figure 2.**

**81**

This configuration, known as "Scherbius structure" and shown in **Figure 1**, has several advantages of controlling independently active and reactive power [6, 7]. Moreover, the power converters used are sized to transfer only a fraction, equal to at most 30% of the turbine rated power [8, 9], which results in small-size, low-cost, less acoustic noise and reduced loss rate in the power converters [10]. Moreover, The DFIG-based wind turbine allows the rotor speed to be varied with the wind speed, and the speed variation range is around 30% around the synchronism speed [11]. As a result, the wind generation system could operate in hyposynchronous and hypersynchronous mode, which would extract the maximum aerodynamic power for each wind speed value.

In order to design fault diagnosis and control approaches based on models for wind turbines, the development of a mathematical model, which represents as much details as technically possible and gives an accurate idea of the dynamic behavior of the system, seems to be an important step. For several purposes, different wind turbine models have been developed. In literature, we find for wind systems the aerodynamic model, which aims to verify and optimize the blade design, depending on predefined specifications, while the mechanical model is used by engineers for establishing a safe and economical dimensioning of the whole wind turbine system. Moreover, the economic model is used in the case of manufacturing and installing wind turbines with the purpose to evaluate the cost-effectiveness. In addition, there are models which predict the weather conditions and the power output of wind farms. Furthermore, there are models, which have the objective of evaluating the impact of wind turbines on the environment such as the evaluation of noise produced by the wind turbine operation. Finally, the general-purpose models concerned with the electrical properties of wind turbines are widely used.

The speed variable wind turbine (SVWT) model, developed and simulated in this work, is concerned with providing time simulation signals that can be exploited for designing fault diagnosis approaches based on models; the software tool used for simulation is the MATLAB/Simulink environment. In [12], a wind turbine model of a fixed-speed, stall-regulated system has been developed with the aim of measuring and evaluating the power quality impact of wind turbines on the grid. In addition, a model for a wind turbine generation system based on a DFIG, including the mechanical dynamics, the wind turbine electrical system, the converter, and the electrical grid has been presented in [13]. Luis et al. [14] presented the most commonly used wind turbine model meeting objectives as production energy, safety of turbine, grid connection, and others. Moreover, in [15], the detailed

**Figure 1.** *Architecture Scherbius of DFIG-based wind turbine.*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

mechanical structural modeling of the wind turbine connected to the grid and based on DFIG has been developed, and it has been validated using NREL's simulation tool, FAST v7; for analysis of the dynamic behavior of the wind power plant with DFIG under the grid fault conditions, modeling of the whole system has been established in [16]. Furthermore, with the use of an electromagnetic transient simulation software, the wind turbine driven by DFIG model is elaborated in [17].

The organization of this chapter is as follows: the wind turbine structure is described in Section 2; the wind modeling turbine is presented in Section 3. In Section 4, the simulation results in MATLAB/Simulink environment are shown. Finally, the conclusion is presented in Section 5.

### **2. The wind turbine structure**

connected to the electrical grid, and its rotor is linked to the constant frequency grid

hyposynchronous and hypersynchronous mode, which would extract the maximum

In order to design fault diagnosis and control approaches based on models for wind turbines, the development of a mathematical model, which represents as much details as technically possible and gives an accurate idea of the dynamic behavior of the system, seems to be an important step. For several purposes, different wind turbine models have been developed. In literature, we find for wind systems the aerodynamic model, which aims to verify and optimize the blade design, depending on predefined specifications, while the mechanical model is used by engineers for establishing a safe and economical dimensioning of the whole wind turbine system. Moreover, the economic model is used in the case of manufacturing and installing wind turbines with the purpose to evaluate the cost-effectiveness. In addition, there are models which predict the weather conditions and the power output of wind farms. Furthermore, there are models, which have the objective of evaluating the impact of wind turbines on the environment such as the evaluation of noise produced by the wind turbine operation. Finally, the general-purpose models concerned with the electrical properties of wind turbines are widely used. The speed variable wind turbine (SVWT) model, developed and simulated in this work, is concerned with providing time simulation signals that can be exploited for designing fault diagnosis approaches based on models; the software tool used for simulation is the MATLAB/Simulink environment. In [12], a wind turbine model of a fixed-speed, stall-regulated system has been developed with the aim of measuring and evaluating the power quality impact of wind turbines on the grid. In addition, a

model for a wind turbine generation system based on a DFIG, including the mechanical dynamics, the wind turbine electrical system, the converter, and the electrical grid has been presented in [13]. Luis et al. [14] presented the most commonly used wind turbine model meeting objectives as production energy, safety of turbine, grid connection, and others. Moreover, in [15], the detailed

speed [11]. As a result, the wind generation system could operate in

This configuration, known as "Scherbius structure" and shown in **Figure 1**, has several advantages of controlling independently active and reactive power [6, 7]. Moreover, the power converters used are sized to transfer only a fraction, equal to at most 30% of the turbine rated power [8, 9], which results in small-size, low-cost, less acoustic noise and reduced loss rate in the power converters [10]. Moreover, The DFIG-based wind turbine allows the rotor speed to be varied with the wind speed, and the speed variation range is around 30% around the synchronism

by means of two bidirectional power converters.

*Modeling of Turbomachines for Control and Diagnostic Applications*

aerodynamic power for each wind speed value.

**Figure 1.**

**80**

*Architecture Scherbius of DFIG-based wind turbine.*

The wind turbine is a complex system containing different components, which involved different domains: electrical, mechanical, and electronic areas and others. The complete model of the studied wind turbine system is represented by a set of blocks each representing a functional entity of the system. The general structure of a wind system is given by **Figure 2**.

As it is shown in the **Figure 2**, the wind velocity and the fixed-pitch angle represent the input of the wind turbine system. The aerodynamic conversion entity is formed of three blades which capture and convert the kinetic energy of the wind into mechanical energy, recovered on the slow rotating shaft. Then, the gearbox device increases the turbine low speed and makes it suitable with the generator rotational speed, which is about 1500 rpm. The generator receives mechanical energy and transforms it into electrical energy. The two power converters used are insulated gate bipolar transistor (IGBT) type and controlled by pulse width modulation (PWM) technique; they allow the independent control of the active and reactive powers and also the transfer of the slip power in two directions: from the generator to the network and from the network to the generator.

**Figure 2.** *Wind turbine system structure.*

#### **3. The wind turbine modeling**

In this section, the mathematical model of each wind turbine block is presented.

#### **3.1 Wind speed model**

The wind resource is an important element in a wind energy system, and it represents a determining factor in the calculation of electricity production because, under optimal conditions, the power captured by the wind turbine is a cubic

function of the wind speed. The wind is a moving air mass, and the wind kinetic energy is given by:

$$E = \frac{1}{2} \cdot m \cdot v^2 \tag{1}$$

the variation of the mean wind speed [19, 20]. The variation of the wind speed

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

*ak* � sin ð Þ *ω<sup>k</sup>* � *t* (5)

*Vv*ðÞ¼ *t* 1 þ *ξv*ðÞ�*t ξ<sup>v</sup>* ð Þ � *Vv* (6)

*kv*

<sup>2</sup> (8)

<sup>2</sup> (9)

<sup>3</sup> (10)

(7)

*i*¼1

where A is the wind speed average value; *ak* is the amplitude of k-order harmonic; ω*<sup>k</sup>* is the pulsation of k-order harmonic; and i is the last harmonic rank

• The third method is the Weibull distribution in which a given site wind potential is obtained by measuring the average wind speed in regular time intervals. Then, the data obtained are then divided into numbers by wind speed classes using histogram [21]. The wind profile over a desired time period,

where Vv is the wind speed average value and ξ<sup>v</sup> is the disturbance mean value

where rand(t) is a function generating, in a uniform distribution, random numbers between 0 and 1 and (Cv, kv) is a parameter pair, determined by analysis of the wind class histogram. Cv is a scale factor generally greater than 5. The shape factor kv is greater than 3 if the histogram shape is like that of a normal distribution,

In this work, we adopted the second method to generate the random profile of

The aerodynamic conversion system is the wind turbine part, which is facing the wind; it generally comprises three blades of length R. Three-bladed wind turbines are much more common than two-bladed wind turbines. The turbine captures the kinetic energy of the wind and transforms it into mechanical energy recovered on

*Pwind* <sup>¼</sup> *<sup>ρ</sup>* � *<sup>S</sup>* � *vwind*<sup>3</sup>

*Paero* <sup>¼</sup> *Cp*ð Þ� *<sup>λ</sup>*, *<sup>β</sup> Pwind* <sup>¼</sup> *Cp*ð Þ� *<sup>λ</sup>*, *<sup>β</sup> <sup>ρ</sup>* � *<sup>S</sup>* � *vwind*<sup>3</sup>

� *Cp*ð Þ� *λ*, *β ρ* � *S* � *vwind*

The aerodynamic torque Taer is given by the following expression:

<sup>¼</sup> <sup>1</sup> 2 � Ω*<sup>t</sup>*

*ln rand t* ð Þ ð Þ *cv* � � <sup>1</sup>

v(t) is thus written in the form of the harmonic sum:

respecting the Weibull distribution, is given by:

*ξv*ðÞ¼ � *t*

characterized by an uniform distribution around a mean value.

the wind speed applied in the studied wind system input.

The kinetic power of the wind is given by:

The aerodynamic power is expressed as follows:

*Taer* <sup>¼</sup> *Paero* Ω*t*

**3.2 Aerodynamic conversion model**

the slow rotating shaft.

**83**

retained in the wind profile calculation.

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

expressed by:

*Vv*ðÞ¼ *<sup>t</sup> <sup>A</sup>* <sup>þ</sup>X*<sup>n</sup>*

where m is the moving air mass [g] and v is the air moving speed [m/s]. The wind power during is expressed as:

$$P\_{wind} = \frac{E}{\Delta t} \tag{2}$$

The wind speed v is generally represented by a scalar function evolving over time, given by V = f(t). It can also be divided into two components: a slowly varying part denoted as V0 and a random varying part denoted as Vt; it represents the wind fluctuations. Therefore, the wind velocity can be written as:

$$V(t) = V\_0 + V\_t(t) \tag{3}$$

To mathematically model the wind speed profile, the literature offers three techniques:

• The first method is white noise filtering technique, in which the turbulence impact is corrected by the use of a low-pass filter having the following transfer function [18]:

$$F(s) = \frac{1}{1 + \pi \cdot s} \tag{4}$$

where τ is the filter time constant. It depends on the rotor diameter and the wind turbulence intensity and the average wind speed. **Figure 3** shows the method of reconstruction of the wind profile using this technique.

• The second method of generating the wind speed profile is that which describes wind variations using the spectral density established by meteorologist I. Van der Hoven. In this model, the turbulence part is considered as a stationary random process, and therefore it does not depend on

**Figure 3.** *Wind profile construction scheme by white noise filtering.*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

the variation of the mean wind speed [19, 20]. The variation of the wind speed v(t) is thus written in the form of the harmonic sum:

$$V\_v(t) = A + \sum\_{i=1}^{n} a\_k \cdot \sin\left(a\_k \cdot t\right) \tag{5}$$

where A is the wind speed average value; *ak* is the amplitude of k-order harmonic; ω*<sup>k</sup>* is the pulsation of k-order harmonic; and i is the last harmonic rank retained in the wind profile calculation.

• The third method is the Weibull distribution in which a given site wind potential is obtained by measuring the average wind speed in regular time intervals. Then, the data obtained are then divided into numbers by wind speed classes using histogram [21]. The wind profile over a desired time period, respecting the Weibull distribution, is given by:

$$V\_v(t) = (1 + \xi\_v(t) - \xi\_v) \cdot V\_v \tag{6}$$

where Vv is the wind speed average value and ξ<sup>v</sup> is the disturbance mean value expressed by:

$$\xi\_v(t) = \left(-\frac{\ln\left(r\text{and}(t)\right)}{c\_v}\right)^{\frac{1}{k\_v}}\tag{7}$$

where rand(t) is a function generating, in a uniform distribution, random numbers between 0 and 1 and (Cv, kv) is a parameter pair, determined by analysis of the wind class histogram. Cv is a scale factor generally greater than 5. The shape factor kv is greater than 3 if the histogram shape is like that of a normal distribution, characterized by an uniform distribution around a mean value.

In this work, we adopted the second method to generate the random profile of the wind speed applied in the studied wind system input.

#### **3.2 Aerodynamic conversion model**

The aerodynamic conversion system is the wind turbine part, which is facing the wind; it generally comprises three blades of length R. Three-bladed wind turbines are much more common than two-bladed wind turbines. The turbine captures the kinetic energy of the wind and transforms it into mechanical energy recovered on the slow rotating shaft.

The kinetic power of the wind is given by:

$$P\_{wind} = \frac{\rho \cdot \mathbf{S} \cdot \upsilon\_{wind}{}^3}{2} \tag{8}$$

The aerodynamic power is expressed as follows:

$$P\_{\text{zero}} = \mathbf{C}\_p(\lambda, \beta) \cdot P\_{\text{wind}} = \mathbf{C}\_p(\lambda, \beta) \cdot \frac{\rho \cdot \mathbf{S} \cdot \boldsymbol{\nu}\_{\text{wind}}\boldsymbol{\beta}}{2} \tag{9}$$

The aerodynamic torque Taer is given by the following expression:

$$T\_{aer} = \frac{P\_{aero}}{\Omega\_{\text{f}}} = \frac{\mathbf{1}}{\mathbf{2} \cdot \Omega\_{\text{f}}} \cdot \mathbf{C}\_{p}(\lambda, \beta) \cdot \rho \cdot \mathbf{S} \cdot v\_{wind} \,^3 \tag{10}$$

function of the wind speed. The wind is a moving air mass, and the wind kinetic

<sup>2</sup> � *<sup>m</sup>* � *<sup>v</sup>*<sup>2</sup> (1)

*<sup>Δ</sup><sup>t</sup>* (2)

(4)

*V t*ðÞ¼ *V*<sup>0</sup> þ *Vt*ð Þ*t* (3)

*<sup>E</sup>* <sup>¼</sup> <sup>1</sup>

where m is the moving air mass [g] and v is the air moving speed [m/s].

*Pwind* <sup>¼</sup> *<sup>E</sup>*

The wind speed v is generally represented by a scalar function evolving over time, given by V = f(t). It can also be divided into two components: a slowly varying part denoted as V0 and a random varying part denoted as Vt; it represents the wind

To mathematically model the wind speed profile, the literature offers three

• The first method is white noise filtering technique, in which the turbulence impact is corrected by the use of a low-pass filter having the following transfer

*F s*ðÞ¼ <sup>1</sup>

• The second method of generating the wind speed profile is that which describes wind variations using the spectral density established by meteorologist I. Van der Hoven. In this model, the turbulence part is

1 þ *τ* � *s*

where τ is the filter time constant. It depends on the rotor diameter and the wind turbulence intensity and the average wind speed. **Figure 3** shows the method of

considered as a stationary random process, and therefore it does not depend on

energy is given by:

techniques:

**Figure 3.**

**82**

*Wind profile construction scheme by white noise filtering.*

function [18]:

The wind power during is expressed as:

fluctuations. Therefore, the wind velocity can be written as:

*Modeling of Turbomachines for Control and Diagnostic Applications*

reconstruction of the wind profile using this technique.

#### *Modeling of Turbomachines for Control and Diagnostic Applications*

where Ωt is the turbine speed [rad/s], ρ is the air density, ρ = 1.225 kg/m<sup>3</sup> ,S= π R2 is the rotor surface [m2 ], R is the blade length [m], and vwind is the wind speed upstream of the wind turbine rotor [m/s]. λ is the speed ratio. It is a unitless parameter, related to the design of each wind turbine, and it represents the ratio between the speed of the blade's end and that of the wind at the rotor axis or also called hub. λ is expressed as follows:

$$
\lambda = \frac{\Omega\_\text{f} \cdot R}{v} \tag{11}
$$

This parameter depends on the blade number of the wind turbine. If the blade number is reduced, the rotor speed is high, and a maximum of power is extracted from the wind. In the case of multiblade wind turbines (Western Wind Turbines), the speed ratio is equal to 1; for wind turbines with a single blade, λ is about 11. The three-bladed wind turbines, as in our study, have a speed ratio of 6 to 7. The speed ratio of Savonius wind turbines is less than 1 [22].

Cp is the power coefficient or aerodynamic transfer efficiency that varies with the wind speed. This coefficient has no unit, and it depends mainly on the blade aerodynamics, the speed ratio λ, and the blade orientation angle β. Betz has determined a theoretical maximum limit of the power coefficient Cpmax = 16/27 ∽ 0.59. Taking into account losses, wind turbines never operate at this maximum limit, and the best-performing wind turbines have a Cp between 0.35 and 0.45. Cp is specific to each wind turbine, and its expression is given by the wind turbine manufacturer or using nonlinear formulas. To calculate the coefficient Cp, different numerical approximations have been proposed in the literature. The Cp expressions frequently encountered in the literature are presented in **Table 1**.

Since we had as an objective the modeling and simulation of a three-bladed wind turbine with a nominal power of 3 kW; the parameters of both: the wind turbine and the generator have been used from [30]. For this reason, the analytical expression of the power coefficient Cp is given by:

$$\mathbf{C\_p} = \mathbf{6} \cdot \mathbf{10^{-7}} \cdot \boldsymbol{\lambda^5} + \mathbf{10^{-5}} \cdot \boldsymbol{\lambda^4} - \mathbf{65} \cdot \mathbf{10^{-5}} \cdot \boldsymbol{\lambda^3} + \mathbf{2} \cdot \mathbf{10^{-5}} \cdot \boldsymbol{\lambda^2} + \mathbf{76} \cdot \mathbf{10^{-3}} \cdot \boldsymbol{\lambda} + \mathbf{0.007} \tag{12}$$

This coefficient has a maximum value equal to 0,35 (Cpmax = 0,35 ) and an optimal value of relative speed equal to 7 (λ = 7).

The block diagram presenting the aerodynamic part is shown in **Figure 4**.

#### **3.3 Gearbox model**

The mechanical part of the wind turbine consists of the turbine shaft rotating slowly at speed Ωt, the gearbox having the multiplication gain G and driving the generator at a speed Ωg, by means of a fast secondary shaft.

The gearbox is a device that allows to multiply the turbine speed of Ω<sup>t</sup> by a multiplication gain G to make it adapt to the rapid speed of the generator Ωg. This device is considered ideal, because the gearbox elasticity, friction, and energy losses are considered negligible. The two equations mathematically modeling the operation of this device are given as follows:

$$\begin{cases} \mathbf{T\_g} = \frac{\mathbf{T\_{aer}}}{\mathbf{G}} \\\\ \mathbf{\Omega\_t} = \frac{\mathbf{\Omega\_g}}{\mathbf{G}} \end{cases} \tag{13}$$

**Power coefficient**

**85**

**Formula**

0*:*22 � 116

0*:*5 � 116

h

 i

� e

�

λ<sup>i</sup> þ 0*:*068 � λ [8, 24, 25]

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

21

λ<sup>i</sup> � 0, 4 � β � 5

Avec: 1

*λ<sup>i</sup>* ¼ 1

0*:*5176 � 116

Avec: 1

*λ<sup>i</sup>* ¼ 1

0*:*5109 � 116

Avec: 1

*λ<sup>i</sup>* ¼ 1

0*:*44 � 125

h

 i

� *e*

�

*λ<sup>i</sup>* [21]

16*:*5

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

*λ<sup>i</sup>* � 6*:*94

Avec: *λ<sup>i</sup>* ¼ 1 1

0*:*5 � 0*:*167 � *β* � 2 ð Þ� sin

0*:*3 �

6 � 10�7 � *λ*<sup>5</sup> þ 10�5 � *λ*<sup>4</sup> � 65 � 10�5 � *λ*<sup>3</sup> þ 2 � 10�5 � *λ*<sup>2</sup> þ 76 � 10�3 � *λ* þ 0*:*007 [30] 79*:*5633*:*10�5 � *λ*�5 � 17*:*375 � 10�4 � *λ*<sup>4</sup> þ 9*:*86 � 10�3 � *λ*<sup>3</sup> � 9*:*4 � 10�3 � *λ*<sup>2</sup> þ 6*:*38 � 10�2 � *λ* þ 0*:*001

[31]

0*:*00167 � *β* � 2 ð Þ� *sin π*� *λ*þ0, 1 ð Þ 10�0*:*3� *β*�2 ð Þ

h

 i

�

0*:*00184 � *λ* � 3 ð Þ� *β* [29]

*π*� *λ*�3 ð Þ 18*:*9�0*:*3� *β*�2 ð Þ

 i

�

0*:*00184 � *λ* � 3 ð Þ� *β* � 2 ð Þ [28]

h

Sinusoidal Polynomial

**Table 1.** *Different numerical formulas of the power coefficient Cp.*

þ*λ* 0, 002

*λ*þ0*:*08�*β* � 0*:*035

*β*3þ1

*λ<sup>i</sup>* � 0*:*4 � *β* � 5

h

*λ*þ0*:*08�*β* � 0*:*035

*β*3þ1

 i

� *e*

�

*λ<sup>i</sup>* þ 0*:*0068 � *λ* [27]

21

*λ<sup>i</sup>* � 0*:*4 � *β* � 5

h

*λ*þ0*:*08�*β* � 0*:*035

*β*3þ1

 i

� *e*

�

*λ<sup>i</sup>* þ 0*:*0068 � *λ* [26]

21

h

 i

12*:*5

� *e*

*λ<sup>i</sup>* avec 1

*λ<sup>i</sup>* ¼ 1 *λ*þ0*:*08�*β* � 0*:*035

*β*3þ1 [23]

*λ<sup>i</sup>* � 0*:*4 � *β* � 5

**type, Cp** Exponential


*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

> **Table 1.** *Different numerical*

*formulas of*

 *the power coefficient Cp.*

where Ωt is the turbine speed [rad/s], ρ is the air density, ρ = 1.225 kg/m<sup>3</sup>

*<sup>λ</sup>* <sup>¼</sup> <sup>Ω</sup>*<sup>t</sup>* � *<sup>R</sup> v*

This parameter depends on the blade number of the wind turbine. If the blade number is reduced, the rotor speed is high, and a maximum of power is extracted from the wind. In the case of multiblade wind turbines (Western Wind Turbines), the speed ratio is equal to 1; for wind turbines with a single blade, λ is about 11. The three-bladed wind turbines, as in our study, have a speed ratio of 6 to 7. The speed

Cp is the power coefficient or aerodynamic transfer efficiency that varies with the wind speed. This coefficient has no unit, and it depends mainly on the blade aerodynamics, the speed ratio λ, and the blade orientation angle β. Betz has determined a theoretical maximum limit of the power coefficient Cpmax = 16/27 ∽ 0.59. Taking into account losses, wind turbines never operate at this maximum limit, and the best-performing wind turbines have a Cp between 0.35 and 0.45. Cp is specific to each wind turbine, and its expression is given by the wind turbine manufacturer or using nonlinear formulas. To calculate the coefficient Cp, different numerical approximations have been proposed in the literature. The Cp expressions frequently

Since we had as an objective the modeling and simulation of a three-bladed wind turbine with a nominal power of 3 kW; the parameters of both: the wind turbine and the generator have been used from [30]. For this reason, the analytical expres-

Cp <sup>¼</sup> <sup>6</sup> � <sup>10</sup>�<sup>7</sup> � *<sup>λ</sup>*<sup>5</sup> <sup>þ</sup> <sup>10</sup>�<sup>5</sup> � *<sup>λ</sup>*<sup>4</sup> � <sup>65</sup> � <sup>10</sup>�<sup>5</sup> � *<sup>λ</sup>*<sup>3</sup> <sup>þ</sup> <sup>2</sup> � <sup>10</sup>�<sup>5</sup> � *<sup>λ</sup>*<sup>2</sup> <sup>þ</sup> <sup>76</sup> � <sup>10</sup>�<sup>3</sup> � *<sup>λ</sup>* <sup>þ</sup> <sup>0</sup>*:*<sup>007</sup> (12)

This coefficient has a maximum value equal to 0,35 (Cpmax = 0,35 ) and an

The block diagram presenting the aerodynamic part is shown in **Figure 4**.

The mechanical part of the wind turbine consists of the turbine shaft rotating slowly at speed Ωt, the gearbox having the multiplication gain G and driving the

The gearbox is a device that allows to multiply the turbine speed of Ω<sup>t</sup> by a multiplication gain G to make it adapt to the rapid speed of the generator Ωg. This device is considered ideal, because the gearbox elasticity, friction, and energy losses are considered negligible. The two equations mathematically modeling the opera-

> Tg <sup>¼</sup> Taer G

8 >><

>>:

<sup>Ω</sup><sup>t</sup> <sup>¼</sup> <sup>Ω</sup><sup>g</sup> G

upstream of the wind turbine rotor [m/s]. λ is the speed ratio. It is a unitless parameter, related to the design of each wind turbine, and it represents the ratio between the speed of the blade's end and that of the wind at the rotor axis or also

*Modeling of Turbomachines for Control and Diagnostic Applications*

], R is the blade length [m], and vwind is the wind speed

R2 is the rotor surface [m2

called hub. λ is expressed as follows:

ratio of Savonius wind turbines is less than 1 [22].

encountered in the literature are presented in **Table 1**.

sion of the power coefficient Cp is given by:

optimal value of relative speed equal to 7 (λ = 7).

tion of this device are given as follows:

generator at a speed Ωg, by means of a fast secondary shaft.

**3.3 Gearbox model**

**84**

,S= π

(11)

(13)

where Tg is torque on the generator shaft (N�m), Taer is the aerodynamic torque of the wind turbine (N � m), Ω<sup>g</sup> is the speed generator shaft (rad � s �1 ), Ω<sup>t</sup> is the turbine speed shaft (rad � s �1 ), and G is the multiplication gain; it is given by G = N1/N2.

**Figure 5** shows the gearbox model for determining the multiplication gain G, and **Figure 6** shows the gearbox block diagram.

The total inertia J consists of the turbine inertia Jt and the generator inertia Jg; it can be written according to the following equation [28]:

$$J = \frac{J\_t}{G^2} + J\_g \tag{14}$$

The total viscous friction coefficient fv consists of the generator friction coefficient fg and the turbine friction coefficient ft. The coefficient fv can be expressed as follows:

$$f\_v = \frac{f\_t}{G^2} + f\_g \tag{15}$$

The generator speed Ω<sup>g</sup> depends on the total mechanical torque Tmec. This torque is the result of the electromagnetic torque of the generator Tem, the viscous

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

*Tmec* ¼ *J* �

*dΩ<sup>g</sup>*

Therefore, from these previously established equations, the differential equation

The block diagram of the wind turbine mechanical part is presented in **Figure 8**. The diagram block of the whole wind turbine system is given in **Figure 9**.

*dt* (16)

*Tmec* ¼ *Tg* � *Tem* � *Tv* (17)

*Tv* ¼ *f* � *Ω<sup>g</sup>* (18)

*dt* <sup>¼</sup> *Tg* � *Tem* � *Tvis* (19)

friction torque Tv, and the torque applied on the generator shaft Tg.

of the mechanical system dynamics is expressed by:

*The several coefficients of the wind turbine mechanical part.*

**Figure 7.**

**87**

**Figure 6.**

*Block diagram of the gearbox.*

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

*J* � *dΩ<sup>g</sup>*

Therefore, the mechanical part can be modeled according to the diagram shown in **Figure 7**.

**Figure 4.** *Block diagram of the aerodynamic part.*

**Figure 5.** *The gearbox model.*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 6.** *Block diagram of the gearbox.*

where Tg is torque on the generator shaft (N�m), Taer is the aerodynamic torque of

**Figure 5** shows the gearbox model for determining the multiplication gain G,

*<sup>J</sup>* <sup>¼</sup> *Jt*

*<sup>f</sup> <sup>v</sup>* <sup>¼</sup> *ft*

The total inertia J consists of the turbine inertia Jt and the generator inertia Jg; it

The total viscous friction coefficient fv consists of the generator friction coefficient fg and the turbine friction coefficient ft. The coefficient fv can be expressed as follows:

Therefore, the mechanical part can be modeled according to the diagram shown

), and G is the multiplication gain; it is given by G = N1/N2.

�1

*<sup>G</sup>*<sup>2</sup> <sup>þ</sup> *Jg* (14)

*<sup>G</sup>*<sup>2</sup> <sup>þ</sup> *<sup>f</sup> <sup>g</sup>* (15)

), Ω<sup>t</sup> is the turbine

the wind turbine (N � m), Ω<sup>g</sup> is the speed generator shaft (rad � s

*Modeling of Turbomachines for Control and Diagnostic Applications*

speed shaft (rad � s

in **Figure 7**.

**Figure 4.**

**Figure 5.** *The gearbox model.*

**86**

*Block diagram of the aerodynamic part.*

�1

and **Figure 6** shows the gearbox block diagram.

can be written according to the following equation [28]:

**Figure 7.** *The several coefficients of the wind turbine mechanical part.*

The generator speed Ω<sup>g</sup> depends on the total mechanical torque Tmec. This torque is the result of the electromagnetic torque of the generator Tem, the viscous friction torque Tv, and the torque applied on the generator shaft Tg.

$$T\_{mcc} = f \cdot \frac{d\Omega\_{\rm g}}{dt} \tag{16}$$

$$T\_{\rm mec} = T\_{\rm g} - T\_{\rm em} - T\_{\rm v} \tag{17}$$

$$T\_v = f \cdot \mathcal{Q}\_{\mathfrak{g}} \tag{18}$$

Therefore, from these previously established equations, the differential equation of the mechanical system dynamics is expressed by:

$$J \cdot \frac{d\Omega\_{\rm g}}{dt} = T\_{\rm g} - T\_{em} - T\_{vis} \tag{19}$$

The block diagram of the wind turbine mechanical part is presented in **Figure 8**. The diagram block of the whole wind turbine system is given in **Figure 9**.

**Figure 8.**

*Block diagram of the wind turbine mechanical part.*

**Figure 9.** *Block diagram of the whole wind turbine system.*

In order to continuously reach the maximum power point provided by a wind turbine, operating over a wide range of wind speed, the maximum power point tracking (MPPT) control technique is used. In this chapter, the MPPT control without controlling the mechanical speed is presented [32]. This control strategy is based on the assumption that the wind speed little varies in steady state compared to the electrical constants of the wind turbine system. Therefore, at the maximum power point, the relative speed ʎ is equal to its optimum value λopt, and the power coefficient Cp is equal to its maximum value Cp-max, while the reference electromagnetic torque *C*<sup>∗</sup> *em* is given by:

$$\mathbf{C}\_{em}^{\*} = \frac{\mathbf{C}\_{aer-et}}{G} \tag{20}$$

The reference electromagnetic torque is proportional to the square of the generator speed Ωg. The block diagram which presents the MPPT control strategy

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

The doubly fed induction generator (DFIG) is a three-phase asynchronous machine, powered by two sources: by its stator and its rotor at the same time. Its main advantage is that it offers the possibility of controlling the power flows for the hypo- and hypersynchronous modes, either in the motor or generator operation. It also allows the variable speed operation of the system where it is integrated.

The DFIG model in the stationary reference frame, noted (α, β), is given in the

*isα isβ irα irβ*

where is<sup>α</sup> and is<sup>β</sup> are the stator currents in the stationary reference frame (α, β); ir<sup>α</sup> and ir<sup>β</sup> are the rotor currents in the reference frame (α, β); vs<sup>α</sup> and vs<sup>β</sup> are the stator stresses in the stationary reference frame (α, β); vr<sup>α</sup> and vr<sup>β</sup> are the rotor

matrix, the input or control matrix, and the output or observation matrix. They are,

<sup>σ</sup> � <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>s</sup> � � <sup>M</sup> � Rr

σ � Ls

M � Rs σ � Ls � Lr

� <sup>M</sup> σ � Lr

ð Þ 1 � σ

þ ½ �� *B*

*vsα vsβ vr<sup>α</sup> vr<sup>β</sup>*

σ � Ls � Lr

σ � Lr

� <sup>ω</sup><sup>s</sup> � <sup>ω</sup> σ � � �Rr

� <sup>M</sup> σ � Ls � ω

� <sup>ω</sup> �Rr

M σ � Ls � ω

M � Rr σ � Ls � Lr

<sup>ω</sup><sup>s</sup> � <sup>ω</sup> σ � �

σ � Lr

(24)

, B ∈ ℝn�m, and C ∈ ℝp�<sup>n</sup> are, respectively, the state

without the measurement of the generator speed is shown in **Figure 10**.

**3.4 DFIG model**

**Figure 10.**

state representation [33] as follows:

The matrices A ∈ ℝn�<sup>n</sup>

� ð Þ <sup>1</sup> � <sup>σ</sup>

respectively, given by:

A ¼

**89**

*d dt*

*Block diagram of the MPPT control without mechanical speed.*

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

voltages in the stationary reference frame (α, β).

�Rs σ � Ls

M � Rs σ � Ls � Lr

M σ � Lr � ω

<sup>σ</sup> � <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>s</sup>

� � �Rs

*isα isβ irα irβ*

3 7 7 7 <sup>5</sup> <sup>¼</sup> ½ �� *<sup>A</sup>*

$$\mathbf{C}\_{em}^\* = \mathbf{C}\_{p-\max} \cdot \frac{\rho \cdot \pi \cdot \mathbf{R}^5 \cdot \mathbf{\Omega}\_{\mathbf{g}}^2}{\mathbf{2} \cdot \boldsymbol{\lambda}\_{opt}^3 \cdot \mathbf{G}^3} \tag{21}$$

For simplification, the parameter K is expressed as:

$$K = \mathbf{C}\_{p-\max} \cdot \frac{\rho \cdot \boldsymbol{\pi} \cdot \mathbf{R}^{\\$}}{\mathbf{2} \cdot \boldsymbol{\lambda}\_{opt}^{3} \cdot \mathbf{G}^{3}} \tag{22}$$

Therefore:

$$\mathbf{C}\_{em}^\* = \mathbf{K} \cdot \mathbf{\Omega}\_{\mathbf{g}}^2 \tag{23}$$

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 10.** *Block diagram of the MPPT control without mechanical speed.*

The reference electromagnetic torque is proportional to the square of the generator speed Ωg. The block diagram which presents the MPPT control strategy without the measurement of the generator speed is shown in **Figure 10**.

#### **3.4 DFIG model**

In order to continuously reach the maximum power point provided by a wind turbine, operating over a wide range of wind speed, the maximum power point tracking (MPPT) control technique is used. In this chapter, the MPPT control without controlling the mechanical speed is presented [32]. This control strategy is based on the assumption that the wind speed little varies in steady state compared to the electrical constants of the wind turbine system. Therefore, at the maximum power point, the relative speed ʎ is equal to its optimum value λopt, and the power coefficient Cp is equal to its maximum value Cp-max, while the reference electro-

*em* <sup>¼</sup> *Caer*�*est*

*<sup>K</sup>* <sup>¼</sup> *Cp*� *max* � *<sup>ρ</sup>* � *<sup>π</sup>* � *<sup>R</sup>*<sup>5</sup>

*em* <sup>¼</sup> *<sup>K</sup>* � <sup>Ω</sup><sup>2</sup>

*<sup>ρ</sup>* � *<sup>π</sup>* � *<sup>R</sup>*<sup>5</sup> � <sup>Ω</sup><sup>2</sup>

<sup>2</sup> � *<sup>λ</sup>*<sup>3</sup>

<sup>2</sup> � *<sup>λ</sup>*<sup>3</sup>

*g*

*<sup>G</sup>* (20)

*opt* � *<sup>G</sup>*<sup>3</sup> (21)

*opt* � *<sup>G</sup>*<sup>3</sup> (22)

*<sup>g</sup>* (23)

*C*∗

*em* ¼ *Cp*� *max* �

*C*∗

magnetic torque *C*<sup>∗</sup>

**Figure 8.**

**Figure 9.**

*Block diagram of the wind turbine mechanical part.*

*Modeling of Turbomachines for Control and Diagnostic Applications*

*Block diagram of the whole wind turbine system.*

Therefore:

**88**

*em* is given by:

*C*∗

For simplification, the parameter K is expressed as:

The doubly fed induction generator (DFIG) is a three-phase asynchronous machine, powered by two sources: by its stator and its rotor at the same time. Its main advantage is that it offers the possibility of controlling the power flows for the hypo- and hypersynchronous modes, either in the motor or generator operation. It also allows the variable speed operation of the system where it is integrated.

The DFIG model in the stationary reference frame, noted (α, β), is given in the state representation [33] as follows:

$$\frac{d}{dt}\begin{bmatrix}\dot{i}\_{s\alpha} \\ \dot{i}\_{s\beta} \\ \dot{i}\_{ra} \\ \dot{i}\_{r\beta}\end{bmatrix} = [A] \cdot \begin{bmatrix} \dot{i}\_{s\alpha} \\ \dot{i}\_{s\beta} \\ \dot{i}\_{ra} \\ \dot{i}\_{r\beta} \end{bmatrix} + [B] \cdot \begin{bmatrix} \upsilon\_{s\alpha} \\ \upsilon\_{s\beta} \\ \upsilon\_{ra} \\ \upsilon\_{r\beta} \end{bmatrix} \tag{24}$$

where is<sup>α</sup> and is<sup>β</sup> are the stator currents in the stationary reference frame (α, β); ir<sup>α</sup> and ir<sup>β</sup> are the rotor currents in the reference frame (α, β); vs<sup>α</sup> and vs<sup>β</sup> are the stator stresses in the stationary reference frame (α, β); vr<sup>α</sup> and vr<sup>β</sup> are the rotor voltages in the stationary reference frame (α, β).

The matrices A ∈ ℝn�<sup>n</sup> , B ∈ ℝn�m, and C ∈ ℝp�<sup>n</sup> are, respectively, the state matrix, the input or control matrix, and the output or observation matrix. They are, respectively, given by:

$$\mathbf{A} = \begin{bmatrix} \frac{-\mathbf{R}\_{\mathrm{s}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}}} & \left(\frac{(\mathbf{1}-\sigma)}{\sigma} \cdot \boldsymbol{\alpha} + \boldsymbol{\alpha}\_{\mathrm{s}}\right) & \frac{\mathbf{M} \cdot \mathbf{R}\_{\mathrm{r}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}} \cdot \mathbf{L}\_{\mathrm{r}}} & \frac{\mathbf{M}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}}} \cdot \boldsymbol{\alpha} \\ -\left(\frac{(\mathbf{1}-\sigma)}{\sigma} \cdot \boldsymbol{\alpha} + \boldsymbol{\alpha}\_{\mathrm{s}}\right) & \frac{-\mathbf{R}\_{\mathrm{s}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}}} & -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}}} \cdot \boldsymbol{\alpha} & \frac{\mathbf{M} \cdot \mathbf{R}\_{\mathrm{r}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}} \cdot \mathbf{L}\_{\mathrm{r}}} \\ \frac{\mathbf{M} \cdot \mathbf{R}\_{\mathrm{s}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}} \cdot \mathbf{L}\_{\mathrm{r}}} & -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L}\_{\mathrm{r}}} \cdot \boldsymbol{\alpha} & \frac{-\mathbf{R}\_{\mathrm{r}}}{\sigma \cdot \mathbf{L}\_{\mathrm{r}}} & \left(\boldsymbol{\alpha}\_{\mathrm{s}} - \frac{\boldsymbol{\alpha}}{\sigma}\right) \\ \frac{\mathbf{M}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}}} \cdot \boldsymbol{\alpha} & \frac{\mathbf{M} \cdot \mathbf{R}\_{\mathrm{s}}}{\sigma \cdot \mathbf{L}\_{\mathrm{s}} \cdot \mathbf{L}\_{\mathrm{r}}} & -\left(\boldsymbol{\alpha}\_{\mathrm{s}} - \frac{\boldsymbol{\alpha}$$

$$\mathbf{B} = \begin{bmatrix} 1 & \mathbf{M} & \mathbf{M} & \mathbf{0} \\ \hline \sigma \cdot \mathbf{L\_s} & \mathbf{0} & -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L\_s} \cdot \mathbf{L\_r}} & \mathbf{0} \\ \mathbf{0} & \frac{1}{\sigma \cdot \mathbf{L\_s}} & \mathbf{0} & -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L\_s} \cdot \mathbf{L\_r}} \\ -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L\_s} \cdot \mathbf{L\_r}} & \mathbf{0} & \frac{1}{\sigma \cdot \mathbf{L\_r}} & \mathbf{0} \\ \mathbf{0} & -\frac{\mathbf{M}}{\sigma \cdot \mathbf{L\_s} \cdot \mathbf{L\_r}} & \mathbf{0} & \frac{1}{\sigma \cdot \mathbf{L\_r}} \end{bmatrix}.$$

$$\mathbf{C} = \begin{bmatrix} 1 & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{1} \end{bmatrix}$$

The input voltages of single phases of the rotor side converter (RSC) are

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

*VSa* <sup>¼</sup> <sup>2</sup> � *Sa* � *Sb* � *Sc*

8 >>>>>>><

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

>>>>>>>:

*VSb* <sup>¼</sup> <sup>2</sup> � *Sb* � *Sa* � *Sc*

*VSc* <sup>¼</sup> <sup>2</sup> � *Sc* � *Sa* � *Sb*

*Si* <sup>¼</sup> 1, *Si* <sup>¼</sup> <sup>0</sup>

(

*Vrabc* ½ �¼ *Rr* � *irabc* ½ �þ *Lr* �

*C* � *dVdc* 0, *Si* ¼ 1

The rotor voltage equations and the DC capacitor equation are given,

where Si represents the switch states, supposedly ideal to facilitate the rectifier

<sup>3</sup> � *Vdc*

<sup>3</sup> � *Vdc*

(25)

<sup>3</sup> � *Vdc*

*d*

*dt* <sup>¼</sup> *Sa* � *iSa* <sup>þ</sup> *Sb* � *iSb* <sup>þ</sup> *Sc* <sup>ð</sup> � *iSc*Þ � *idc* (28)

; i ¼ a, b, c (26)

*dt irabc* ½ �þ *VSabc* ½ � (27)

described as follows:

modeling, defined by:

respectively:

**Figure 12.**

**91**

*The block diagram of the RSC.*

where Rs and Ls are, respectively, the single-phase resistance and the cyclic single-phase inductance of the stator winding; Rr and Lr are, respectively, the single-phase resistance and the cyclic single-phase inductance of the rotor winding; M is the mutual inductance between the stator phase and the rotor phase; *<sup>σ</sup>* <sup>¼</sup> <sup>1</sup> � *<sup>M</sup>*<sup>2</sup> *Ls:Lr* is the leakage coefficient or the Blondel coefficient; ω<sup>s</sup> is the synchronism angular speed [rad/s]; and ω is the mechanical angular speed [rad/s].

In order to generate the reference rotor voltages which will be the input of the machine side converter, the stator flux-oriented vector control is applied to DFIG system [34].

#### **3.5 Power converter models**

The power electronic converters used consist of a rectifier made using semiconductors controlled at the opening and closing, and a three-phase voltage inverter consists of three reversible current switch arms, controlled at the opening and closing in the same time. Each arm consists of two switches, which contain each one insulated gate bipolar transistor (IGBT) and an antiparallel diode. The voltage capacitor DC allows the storage of the output rectifier energy. The passive filter type (L, R) is used to connect the inverter to the grid. Both converters used are controlled using pulse width modulation (PWM), and the power converter structure is given in **Figure 11**.

**Figure 11.** *Structure of the power converters (IGBT).*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

The input voltages of single phases of the rotor side converter (RSC) are described as follows:

$$\begin{cases} V\_{Sa} = \frac{\mathbf{2} \cdot \mathbf{S}\_a - \mathbf{S}\_b - \mathbf{S}\_c}{\mathbf{3}} \cdot V\_{dc} \\\\ V\_{Sb} = \frac{\mathbf{2} \cdot \mathbf{S}\_b - \mathbf{S}\_a - \mathbf{S}\_c}{\mathbf{3}} \cdot V\_{dc} \\\\ V\_{Sc} = \frac{\mathbf{2} \cdot \mathbf{S}\_c - \mathbf{S}\_a - \mathbf{S}\_b}{\mathbf{3}} \cdot V\_{dc} \end{cases} \tag{25}$$

where Si represents the switch states, supposedly ideal to facilitate the rectifier modeling, defined by:

$$\mathbf{S}\_{i} = \begin{cases} \mathbf{1}, \overline{\mathbf{S}\_{i}} = \mathbf{0} \\ \mathbf{0}, \overline{\mathbf{S}\_{i}} = \mathbf{1} \end{cases}; \mathbf{i} = \mathbf{a}, \mathbf{b}, \mathbf{c} \tag{26}$$

The rotor voltage equations and the DC capacitor equation are given, respectively:

$$\left[\left[V\_{rabc}\right] = R\_r \cdot \left[i\_{rabc}\right] + L\_r \cdot \frac{d}{dt}\left[i\_{rabc}\right] + \left[V\_{Sabc}\right] \tag{27}$$

$$\mathbf{C} \cdot \frac{d\mathbf{V}\_{dc}}{dt} = (\mathbf{S}\_a \cdot \dot{\mathbf{i}}\_{\rm Sa} + \mathbf{S}\_b \cdot \dot{\mathbf{i}}\_{\rm Sb} + \mathbf{S}\_c \cdot \dot{\mathbf{i}}\_{\rm Sc}) - \dot{\mathbf{i}}\_{dc} \tag{28}$$

**Figure 12.** *The block diagram of the RSC.*

B ¼

phase; *<sup>σ</sup>* <sup>¼</sup> <sup>1</sup> � *<sup>M</sup>*<sup>2</sup>

**3.5 Power converter models**

ture is given in **Figure 11**.

**Figure 11.**

**90**

*Structure of the power converters (IGBT).*

system [34].

1 σ � Ls

*Modeling of Turbomachines for Control and Diagnostic Applications*

0

� <sup>M</sup> σ � Ls � Lr <sup>0</sup> � <sup>M</sup>

*Ls:Lr* is the leakage coefficient or the Blondel coefficient; ω<sup>s</sup> is the

where Rs and Ls are, respectively, the single-phase resistance and the cyclic single-phase inductance of the stator winding; Rr and Lr are, respectively, the single-phase resistance and the cyclic single-phase inductance of the rotor winding; M is the mutual inductance between the stator phase and the rotor

synchronism angular speed [rad/s]; and ω is the mechanical angular speed [rad/s]. In order to generate the reference rotor voltages which will be the input of the machine side converter, the stator flux-oriented vector control is applied to DFIG

The power electronic converters used consist of a rectifier made using semiconductors controlled at the opening and closing, and a three-phase voltage inverter consists of three reversible current switch arms, controlled at the opening and closing in the same time. Each arm consists of two switches, which contain each one insulated gate bipolar transistor (IGBT) and an antiparallel diode. The voltage capacitor DC allows the storage of the output rectifier energy. The passive filter type (L, R) is used to connect the inverter to the grid. Both converters used are controlled using pulse width modulation (PWM), and the power converter struc-

1 σ � Ls

0

σ � Ls � Lr

<sup>0</sup> � <sup>M</sup>

C ¼

σ � Ls � Lr

1 σ � Lr

0

0

σ � Ls � Lr

0

1 σ � Lr

<sup>0</sup> � <sup>M</sup>

turbine and DFIG parameters are extracted from [30]. Some simulation results of

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

the wind system modeled in this study are presented in the figures below. **Figure 14** shows the random wind speed profile applied to the turbine.

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 15.**

**Figure 16.**

**Figure 17.** *Turbine speed [rpm].*

**93**

*Mechanical speed of DFIG [rpm].*

*Aerodynamic power [W].*

**Figure 13.** *The block diagram of the GSC.*

where Vrabc is the three-phase rotor voltage of DFIG [V]; irabc is the three-phase rotor current of DFIG [A]; C is the capacitor constant [F]; Vdc is the DC bus voltage [V]; idc is the DC output current [A].

The block diagrams of the rotor side converter (RSC) and the grid side converter (GSC) are given, respectively, in **Figures 12** and **13**.

## **4. Simulation results**

The variable speed wind turbine model based on DFIG with a power of 3 Kw has been developed and simulated using MATLAB/Simulink software. The

**Figure 14.** *Wind speed profile [m/s].*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

turbine and DFIG parameters are extracted from [30]. Some simulation results of the wind system modeled in this study are presented in the figures below. **Figure 14** shows the random wind speed profile applied to the turbine.

**Figure 15.** *Aerodynamic power [W].*

where Vrabc is the three-phase rotor voltage of DFIG [V]; irabc is the three-phase rotor current of DFIG [A]; C is the capacitor constant [F]; Vdc is the DC bus voltage

The block diagrams of the rotor side converter (RSC) and the grid side converter

The variable speed wind turbine model based on DFIG with a power of 3 Kw

has been developed and simulated using MATLAB/Simulink software. The

[V]; idc is the DC output current [A].

**4. Simulation results**

*The block diagram of the GSC.*

**Figure 13.**

**Figure 14.**

**92**

*Wind speed profile [m/s].*

(GSC) are given, respectively, in **Figures 12** and **13**.

*Modeling of Turbomachines for Control and Diagnostic Applications*

**Figure 16.** *Mechanical speed of DFIG [rpm].*

**Figure 17.** *Turbine speed [rpm].*

**Figure 21.**

**Figure 22.**

**Figure 23.**

**95**

*Zoom on the rotor currents [A].*

*Three-phase rotor current of DFIG [A].*

*Zoom on the stator currents [A].*

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

**Figure 18.** *Power coefficient Cp.*

**Figure 19.** *Speed ratio ʎ.*

**Figure 20.** *Three-phase stator current [A].*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 21.** *Zoom on the stator currents [A].*

**Figure 18.** *Power coefficient Cp.*

*Modeling of Turbomachines for Control and Diagnostic Applications*

**Figure 19.** *Speed ratio ʎ.*

**Figure 20.**

**94**

*Three-phase stator current [A].*

**Figure 22.** *Three-phase rotor current of DFIG [A].*

**Figure 23.** *Zoom on the rotor currents [A].*

*Modeling of Turbomachines for Control and Diagnostic Applications*

**Figure 24.** *The stator currents in the (α, β) reference [A].*

**Figure 25.** *The rotor currents in the (α, β) reference [A].*

The wind speed varies between [6 m/s] and [11 m/s]. **Figure 15** presents the aerodynamic power delivered by the wind turbine and it reached 3kw when the wind speed is up to 11 [m/s]. **Figures 16** and **17** illustrate respectively the mechanical speed of the generator shaft and the speed of the turbine shaft. It can be noticed from the **Figure 16** that during the simulation time (150 seconds), the generator

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

The **Figures 18** and **19** show respectively the variation of the power coefficient Cp and the variation of the speed ratio λ, which coincide with the maximum power

The simulation results of the wind system electrical part, including the electrical

characteristics of the DFIG, the power converters, and the capacitive bus, are

operates in both hypo and hyper synchronous operating modes.

coefficient and with the optimal speed ratio.

*The output voltages of the rotor side converter [V].*

presented in **Figures 20**–**27**.

**Figure 27.**

**Figure 28.**

**97**

*Voltage of the DC capacitor [V].*

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 26.** *Three-phase stator voltage [V].*

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

**Figure 27.** *Voltage of the DC capacitor [V].*

**Figure 24.**

**Figure 25.**

**Figure 26.**

**96**

*Three-phase stator voltage [V].*

*The stator currents in the (α, β) reference [A].*

*Modeling of Turbomachines for Control and Diagnostic Applications*

*The rotor currents in the (α, β) reference [A].*

**Figure 28.**

*The output voltages of the rotor side converter [V].*

The wind speed varies between [6 m/s] and [11 m/s]. **Figure 15** presents the aerodynamic power delivered by the wind turbine and it reached 3kw when the wind speed is up to 11 [m/s]. **Figures 16** and **17** illustrate respectively the mechanical speed of the generator shaft and the speed of the turbine shaft. It can be noticed from the **Figure 16** that during the simulation time (150 seconds), the generator operates in both hypo and hyper synchronous operating modes.

The **Figures 18** and **19** show respectively the variation of the power coefficient Cp and the variation of the speed ratio λ, which coincide with the maximum power coefficient and with the optimal speed ratio.

The simulation results of the wind system electrical part, including the electrical characteristics of the DFIG, the power converters, and the capacitive bus, are presented in **Figures 20**–**27**.

**References**

Update 2017; 2018

[1] Global Wind Energy Council, Global Wind Energy Report: Annual Market

*DOI: http://dx.doi.org/10.5772/intechopen.83690*

électrique. In: Quatrième Conférence

[10] Burton T, Jenkins N, Sharpe D, et al. Wind Energy Handbook. Chicester, United Kingdom: John Wiley & Sons;

[11] Kerboua A, Abid M. Hybrid fuzzy sliding mode control of a doubly-fed induction generator speed in wind turbines. Journal of Power Technologies.

[12] Petru T, Thiringer T. Modeling of wind turbines for power system studies. IEEE Transactions on Power Systems.

[13] Junyent-Ferré A, Gomis-Bellmunt O, Sumper A, et al. Modeling and control of the doubly fed induction generator wind turbine. Simulation Modeling Practice and Theory. 2010;

[14] Luis AS, Wen Y, de Jesus RJ. Modeling and control of wind turbine. Mathematical Problems in Engineering.

[15] Prajapat GP, Senroy N, Kar IN. Wind turbine structural modeling consideration for dynamic studies of DFIG based system. IEEE Transactions on Sustainable Energy. 2017;**8**(4):

[16] Syahputra R, Soesanti I. Modeling of wind power plant with doubly-fed induction generator. Journal of Electrical

Technology. 2017;**1**(3):126-134

[17] Widanagama A, Lidula N, Rajapakse AD, Muthumuni D. Implementation, comparison and application of an average simulation model of a wind turbine driven doubly fed induction generator. Energies. 2017;

Internationale sur le Génie Electrique CIGE. 2010. pp. 03-04

2011

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction…*

2015;**95**(2):126-133

2002;**17**(4):1132-1139

**18**(9):1365-1381

2013;**2013**:1-13

1463-1472

**10**(11):1726

[2] Energy Information Administration. Cost and performance characteristics of new generating technologies. Annual Energy Outlook 2018. 2018. pp. 1-3

[3] Local Government Association and The Energy Saving Trust. How much do wind turbines cost and where can I get funding? 2009. Available at: http:// www.local.gov.uk/home//journal\_ content/56/10180/3510194/ARTICLE

[4] http://www.ewea.org/wind-energy-

[5] Li H, Chen Z. Overview of different wind generator systems and their comparisons. IET Renewable Power Generation. 2008;**2**(2):123-138

[6] Orabi M, El-Sousy F, Godah H, et al. High-performance induction generatorwind turbine connected to utility grid.

[7] Muller S, Deicke M, De Doncker RW. Doubly fed induction generator systems for wind turbines. IEEE Industry Applications Magazine. 2002;**8**(3):26-33

[8] Davigny A. Participation aux services système de fermes d'éoliennes à vitesse variable intégrant du stockage inertiel d'énergie [doctoral thesis]. Doctoral School Sciences for the Engineer, University of Sciences and Technology

[9] Belmokhtar K, Doumbia ML,

Agbossou K. Modélisation et commande d'un système éolien à base de machine asynchrone à double alimentation pour la fourniture de puissances au réseau

In: 26th Annual International Telecommunications Energy Conference, INTELEC 2004. IEEE.

2004. pp. 697-704

of Lille; 2007

**99**

[Accessed: 11 February 2015]

basics/faq/

#### **Figure 29.**

*Three-phase rotor voltage [V].*

By applying the first-order passive filter (R, L) to the square-wave signals, given in **Figure 28**, the rotor voltages in sinusoidal form are obtained and shown in **Figure 29**.

## **5. Conclusion**

This chapter presents the modeling and simulation results of the most commonly used speed variable wind turbine driven by a doubly fed induction generator. In order to generate efficient and quick electrical power, the control techniques are applied, such as the MPPT control for wind turbine and the stator flux-oriented vector control are used for the generator. The wind turbine system and its control methods are established in the MATLAB/Simulink environment. The obtained signals are used for the design of fault diagnostic methods in future works.

## **Author details**

Imane Idrissi1,2\*, Houcine Chafouk2 , Rachid El Bachtiri<sup>3</sup> and Maha Khanfara<sup>1</sup>

1 CED: STI, FST, REEPER GROUP, PERE Laboratory, EST, USMBA University, Fez, Morocco

2 IRSEEM, ESIGELEC, Normandy University/UNIRouen, Rouen, France

3 REEPER GROUP, PERE Laboratory, EST, USMBA University, Fez, Morocco

\*Address all correspondence to: imane.idrissi@usmba.ac.ma

© 2019 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.

*Modeling and Simulation of the Variable Speed Wind Turbine Based on a Doubly Fed Induction… DOI: http://dx.doi.org/10.5772/intechopen.83690*

## **References**

By applying the first-order passive filter (R, L) to the square-wave signals, given

This chapter presents the modeling and simulation results of the most commonly used speed variable wind turbine driven by a doubly fed induction generator. In order to generate efficient and quick electrical power, the control techniques are applied, such as the MPPT control for wind turbine and the stator flux-oriented vector control are used for the generator. The wind turbine system and its control methods are established in the MATLAB/Simulink environment. The obtained sig-

, Rachid El Bachtiri<sup>3</sup> and Maha Khanfara<sup>1</sup>

in **Figure 28**, the rotor voltages in sinusoidal form are obtained and shown in

*Modeling of Turbomachines for Control and Diagnostic Applications*

nals are used for the design of fault diagnostic methods in future works.

1 CED: STI, FST, REEPER GROUP, PERE Laboratory, EST, USMBA University,

3 REEPER GROUP, PERE Laboratory, EST, USMBA University, Fez, Morocco

© 2019 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,

2 IRSEEM, ESIGELEC, Normandy University/UNIRouen, Rouen, France

\*Address all correspondence to: imane.idrissi@usmba.ac.ma

**Figure 29**.

**Figure 29.**

**5. Conclusion**

*Three-phase rotor voltage [V].*

**Author details**

Fez, Morocco

**98**

Imane Idrissi1,2\*, Houcine Chafouk2

provided the original work is properly cited.

[1] Global Wind Energy Council, Global Wind Energy Report: Annual Market Update 2017; 2018

[2] Energy Information Administration. Cost and performance characteristics of new generating technologies. Annual Energy Outlook 2018. 2018. pp. 1-3

[3] Local Government Association and The Energy Saving Trust. How much do wind turbines cost and where can I get funding? 2009. Available at: http:// www.local.gov.uk/home//journal\_ content/56/10180/3510194/ARTICLE [Accessed: 11 February 2015]

[4] http://www.ewea.org/wind-energybasics/faq/

[5] Li H, Chen Z. Overview of different wind generator systems and their comparisons. IET Renewable Power Generation. 2008;**2**(2):123-138

[6] Orabi M, El-Sousy F, Godah H, et al. High-performance induction generatorwind turbine connected to utility grid. In: 26th Annual International Telecommunications Energy Conference, INTELEC 2004. IEEE. 2004. pp. 697-704

[7] Muller S, Deicke M, De Doncker RW. Doubly fed induction generator systems for wind turbines. IEEE Industry Applications Magazine. 2002;**8**(3):26-33

[8] Davigny A. Participation aux services système de fermes d'éoliennes à vitesse variable intégrant du stockage inertiel d'énergie [doctoral thesis]. Doctoral School Sciences for the Engineer, University of Sciences and Technology of Lille; 2007

[9] Belmokhtar K, Doumbia ML, Agbossou K. Modélisation et commande d'un système éolien à base de machine asynchrone à double alimentation pour la fourniture de puissances au réseau

électrique. In: Quatrième Conférence Internationale sur le Génie Electrique CIGE. 2010. pp. 03-04

[10] Burton T, Jenkins N, Sharpe D, et al. Wind Energy Handbook. Chicester, United Kingdom: John Wiley & Sons; 2011

[11] Kerboua A, Abid M. Hybrid fuzzy sliding mode control of a doubly-fed induction generator speed in wind turbines. Journal of Power Technologies. 2015;**95**(2):126-133

[12] Petru T, Thiringer T. Modeling of wind turbines for power system studies. IEEE Transactions on Power Systems. 2002;**17**(4):1132-1139

[13] Junyent-Ferré A, Gomis-Bellmunt O, Sumper A, et al. Modeling and control of the doubly fed induction generator wind turbine. Simulation Modeling Practice and Theory. 2010; **18**(9):1365-1381

[14] Luis AS, Wen Y, de Jesus RJ. Modeling and control of wind turbine. Mathematical Problems in Engineering. 2013;**2013**:1-13

[15] Prajapat GP, Senroy N, Kar IN. Wind turbine structural modeling consideration for dynamic studies of DFIG based system. IEEE Transactions on Sustainable Energy. 2017;**8**(4): 1463-1472

[16] Syahputra R, Soesanti I. Modeling of wind power plant with doubly-fed induction generator. Journal of Electrical Technology. 2017;**1**(3):126-134

[17] Widanagama A, Lidula N, Rajapakse AD, Muthumuni D. Implementation, comparison and application of an average simulation model of a wind turbine driven doubly fed induction generator. Energies. 2017; **10**(11):1726

[18] Boukhamkham H. Diagnostique des défaillances dans une machine asynchrone utilisée dans une chaine éolienne [doctoral thesis]. University of Mohamed Khider Biskra; 2011

[19] Toual B. Modélisation et commande floue optimisée d'une génératrice à double alimentation, application à un système éolien à vitesse variable [doctoral thesis]. University of Batna 2; 2010

[20] Azzouz T. Modélisation et commande d'un système de conversion d'énergie éolienne à base d'une MADA [doctoral thesis]. Mohamed Khider-Biskra University; 2015

[21] Tameghe T, Andy T. Modélisation et simulation d'un système de jumelage éolien-diesel alimentant une charge locale [doctoral thesis]. University of Quebec in Abitibi-Témiscamingue; 2012

[22] Report ReGrid: Basics of wind energy. Renewables Academy (RENAC) AG, Schönhauser Allee 10-11, 10119 Berlin (Germany)

[23] Aguglia D, Viarouge P, Wamkeue R, et al. Determination of fault operation dynamical constraints for the design of wind turbine DFIG drives. Mathematics and Computers in Simulation. 2010; **81**(2):252-262

[24] Ackermann T. Wind Power in Power Systems. John Wiley & Sons; 2005

[25] Bechouche A. Utilisation des techniques avancées pour l'observation et la commande d'une machine asynchrone: application à une éolienne [doctoral thesis]. Mouloud Mammeri University; 2013

[26] Atoui I. Contribution Au Diagnostic De Defauts D'une Generatrice Asynchrone Dans Une Chaine De Conversion D'energie Eolienne [doctoral thesis]. Badji Mokhtar University of Annaba; 2015

[27] Sylla AM. Modélisation d'un émulateur éolien à base de machine asynchrone à double alimentation [doctoral thesis]. University of Quebec at Trois-Rivières; 2013

[28] El Aimani S. Modélisation des différentes technologies d'éoliennes intégrées dans un réseau de moyenne tension [doctoral thesis]. Central School of Lille; 2004

[29] Hacil M. Amélioration des performances des énergies éoliennes; 2012

[30] Pascal K. Modélisation et mise en œuvre d'une chaine de production éolienne à base de la MADA. Autre. 2013

[31] Poitiers F. Etude et commande de génératrices asynchrones pour l'utilisation de l'énergie éoliennemachine asynchrone a cage autonomemachine asynchrone à double alimentation reliée au réseau [doctoral thesis]. University of Nantes; 2003

[32] Bossoufi B, Karim M, Lagrioui A, et al. Observer backstepping control of DFIG-generators for wind turbines variable-speed: FPGA-based implementation. Renewable Energy. 2015;**81**:903-917

[33] Idrissi I, Chafouk H, et al. A bank of Kalman filters for current sensors faults detection and isolation of DFIG for wind turbine. In: 2017 International Renewable and Sustainable Energy Conference (IRSEC). IEEE. 2017. pp. 1-6

[34] Shao S, Abdi E, Barati F, et al. Stator-flux-oriented vector control for brushless doubly fed induction generator. IEEE Transactions on Industrial Electronics. 2009;**56**(10): 4220-4228

[18] Boukhamkham H. Diagnostique des

*Modeling of Turbomachines for Control and Diagnostic Applications*

[27] Sylla AM. Modélisation d'un émulateur éolien à base de machine asynchrone à double alimentation [doctoral thesis]. University of Quebec

[28] El Aimani S. Modélisation des différentes technologies d'éoliennes intégrées dans un réseau de moyenne tension [doctoral thesis]. Central School

[29] Hacil M. Amélioration des performances des énergies éoliennes;

[30] Pascal K. Modélisation et mise en œuvre d'une chaine de production éolienne à base de la MADA. Autre. 2013

[31] Poitiers F. Etude et commande de génératrices asynchrones pour l'utilisation de l'énergie éoliennemachine asynchrone a cage autonome-

alimentation reliée au réseau [doctoral thesis]. University of Nantes; 2003

[32] Bossoufi B, Karim M, Lagrioui A, et al. Observer backstepping control of DFIG-generators for wind turbines variable-speed: FPGA-based

implementation. Renewable Energy.

turbine. In: 2017 International Renewable and Sustainable Energy Conference (IRSEC). IEEE. 2017.

[34] Shao S, Abdi E, Barati F, et al. Stator-flux-oriented vector control for

brushless doubly fed induction generator. IEEE Transactions on Industrial Electronics. 2009;**56**(10):

[33] Idrissi I, Chafouk H, et al. A bank of Kalman filters for current sensors faults detection and isolation of DFIG for wind

2015;**81**:903-917

pp. 1-6

4220-4228

machine asynchrone à double

at Trois-Rivières; 2013

of Lille; 2004

2012

[19] Toual B. Modélisation et commande floue optimisée d'une génératrice à double alimentation, application à un système éolien à vitesse variable [doctoral thesis]. University of Batna 2; 2010

commande d'un système de conversion d'énergie éolienne à base d'une MADA [doctoral thesis]. Mohamed Khider-

[21] Tameghe T, Andy T. Modélisation et simulation d'un système de jumelage éolien-diesel alimentant une charge locale [doctoral thesis]. University of Quebec in Abitibi-Témiscamingue; 2012

[22] Report ReGrid: Basics of wind energy. Renewables Academy (RENAC) AG, Schönhauser Allee 10-11, 10119

[23] Aguglia D, Viarouge P, Wamkeue R, et al. Determination of fault operation dynamical constraints for the design of wind turbine DFIG drives. Mathematics and Computers in Simulation. 2010;

[24] Ackermann T. Wind Power in Power Systems. John Wiley & Sons; 2005

asynchrone: application à une éolienne [doctoral thesis]. Mouloud Mammeri

[26] Atoui I. Contribution Au Diagnostic

[25] Bechouche A. Utilisation des techniques avancées pour l'observation

et la commande d'une machine

De Defauts D'une Generatrice Asynchrone Dans Une Chaine De Conversion D'energie Eolienne [doctoral thesis]. Badji Mokhtar University of Annaba; 2015

défaillances dans une machine asynchrone utilisée dans une chaine éolienne [doctoral thesis]. University of

Mohamed Khider Biskra; 2011

[20] Azzouz T. Modélisation et

Biskra University; 2015

Berlin (Germany)

**81**(2):252-262

University; 2013

**100**

## *Edited by Igor Loboda and Sergiy Yepifanov*

This book presents new studies in the area of turbomachine mathematical modeling with a focus on models applied to developing engine control and diagnostic systems. The book contains one introductory and four main chapters. The introductory chapter describes the area of modeling of gas and wind turbines and shows the demand for further improvement of the models. The first three main chapters offer particular improvements in gas turbine modeling. First, a novel methodology for the modeling of engine starting is presented. Second, a thorough theoretical comparative analysis is performed for the models of engine internal gas capacities, and practical recommendations are given on model applications, in particular for engine control purposes. Third, multiple algorithms for calculating important unmeasured parameters for engine diagnostics are proposed and compared. It is proven that the best algorithms allow accurate prognosis of engine remaining lifetime.The field of wind turbine modeling is presented in the last main chapter. It introduces a generalpurpose model that describes both aerodynamic and electric parts of a wind power plant. Such a detailed physics-based model will help with the development of more accurate control and diagnostic systems.In this way, this book includes four new studies in the area of gas and wind turbine modeling. These studies will be interesting and useful for specialists in turbine engine control and diagnostics.

Published in London, UK © 2020 IntechOpen © FooTToo / iStock

Modeling of Turbomachines for Control and Diagnostic Applications

Modeling of Turbomachines

for Control and Diagnostic

Applications

*Edited by Igor Loboda and Sergiy Yepifanov*