Preface

This book is devoted to the issue of modeling and simulation of turbomachines, namely gas turbines and wind turbines. Gas turbines are the main engines for power generation and transportation, and wind turbines present an increasingly growing sector of renewable energy production. The design of these complex machines and, in particular, the development of control and diagnostic systems rely on mathematical modeling.

The book consists of three sections that include five chapters. Section 1 consists of the introductory chapter (Chapter 1), which introduces the area of modeling of gas and wind turbines and explains the demand for further model development.

Section 2 unites three chapters that offer particular improvements in gas turbine modeling. A novel methodology for the modeling of engine starting is presented in Chapter 2. Chapter 3 performs a thorough theoretical comparative analysis of models for the simulation of gas capacities between engine components, and offers practical recommendations on model applications, in particular for engine control purposes. In Chapter 4, the reader interested in gas turbine diagnostics can find the answer to how to compute important unmeasured parameters. Multiple algorithms for calculating these parameters are proposed and compared. The best algorithms allow accurate prognostics of engine lifetime.

In section 3, the field of wind turbine modeling is presented in Chapter 5. It introduces a general-purpose model that describes both aerodynamic and electric parts of a wind power plant. Such a detailed physics-based model helps with the development of more accurate control and diagnostic systems that will result in more effective electricity production.

In this way, the book includes four new studies in the area of gas and wind turbine modeling. These studies are interesting and useful for specialists in turbine engine control and diagnostics.

> **Igor Loboda** Instituto Politécnico Nacional, Ciudad de México, México

**Sergiy Yepifanov** National Aerospace University – Kharkiv Aviation Institute, Kharkiv, Ukraine

Section 1

Introduction

**1**

Section 1 Introduction

**Chapter 1**

*Igor Loboda*

**1. Introduction**

tation, and many other industries.

monitoring systems [2–4].

laws.

**3**

aviation industry [2] and so far have no alternatives.

Introductory Chapter: Gas and

Wind Turbines and Their Models

Turbomachines, in particular, a gas turbine (GT) and a wind turbine that are considered in the present book, are indispensable for power generation, transpor-

In the last decades, a GT industry has exposed a considerable growth [1]. A gas turbine combines high power and efficiency with relatively low weight and compactness. A turboshaft engine presents a principal driver for electricity production. It is also widely used in offshore oil platforms, petrochemical plants, refineries, gas stations, and so on. Many marine and other kinds of transport are equipped by gas turbine engines as well. Depending on a particular application and the range of produced power, the types of GTs embrace heavy-duty, aircraft-derivative, industrial, vehicular, small, and micro gas turbines [1]. Another large area of GT application is air transport. Different aircraft gas turbine engines, which can generally be divided into turbofans, turboprops, and turboshafts, have revolutionized the

Following a general development of the industry of gas turbines, the use of their mathematical models becomes more intensive. Modeling and simulation of GTs have been an effective way of design and manufacture. For example, the use of engine models enables to evaluate and optimize the engine performance before the engine fabrication. In addition to the design of the gas turbine engine itself, engine modeling and simulation are widely used in the development of control and

To have high power and efficiency performances, a gas turbine must operate near its functional and structural limits at different steady-state and dynamic modes. For doing so, an engine control system should be accurate enough. In the beginning of the gas turbine technology development, much experimentation was done to design this system. However, since the engine and its control system are more and more complex and expensive, physical experimenting to tailor, test, and validate the system is expensive and therefore limited. For this reason, mathematical modeling and simulation of GTs have been increasingly useful and effective methodology of the control system development. As a result of investigations, better understanding of engine dynamic behavior was gained, and more complex and exact engine dynamic models were developed. These models allow accurate predicting and analyzing engine dynamics. They also help a lot with decreasing fuel consumption and the development and optimization of multiple engine control

The abovementioned complexity and expensiveness of GTs and high demands to engine reliability and safety at low maintenance costs make it unavoidable to use advanced monitoring systems. Through diagnostic processing of engine measured parameters, these systems allow us to gain the knowledge about the health

## **Chapter 1**

## Introductory Chapter: Gas and Wind Turbines and Their Models

*Igor Loboda*

### **1. Introduction**

Turbomachines, in particular, a gas turbine (GT) and a wind turbine that are considered in the present book, are indispensable for power generation, transportation, and many other industries.

In the last decades, a GT industry has exposed a considerable growth [1]. A gas turbine combines high power and efficiency with relatively low weight and compactness. A turboshaft engine presents a principal driver for electricity production. It is also widely used in offshore oil platforms, petrochemical plants, refineries, gas stations, and so on. Many marine and other kinds of transport are equipped by gas turbine engines as well. Depending on a particular application and the range of produced power, the types of GTs embrace heavy-duty, aircraft-derivative, industrial, vehicular, small, and micro gas turbines [1]. Another large area of GT application is air transport. Different aircraft gas turbine engines, which can generally be divided into turbofans, turboprops, and turboshafts, have revolutionized the aviation industry [2] and so far have no alternatives.

Following a general development of the industry of gas turbines, the use of their mathematical models becomes more intensive. Modeling and simulation of GTs have been an effective way of design and manufacture. For example, the use of engine models enables to evaluate and optimize the engine performance before the engine fabrication. In addition to the design of the gas turbine engine itself, engine modeling and simulation are widely used in the development of control and monitoring systems [2–4].

To have high power and efficiency performances, a gas turbine must operate near its functional and structural limits at different steady-state and dynamic modes. For doing so, an engine control system should be accurate enough. In the beginning of the gas turbine technology development, much experimentation was done to design this system. However, since the engine and its control system are more and more complex and expensive, physical experimenting to tailor, test, and validate the system is expensive and therefore limited. For this reason, mathematical modeling and simulation of GTs have been increasingly useful and effective methodology of the control system development. As a result of investigations, better understanding of engine dynamic behavior was gained, and more complex and exact engine dynamic models were developed. These models allow accurate predicting and analyzing engine dynamics. They also help a lot with decreasing fuel consumption and the development and optimization of multiple engine control laws.

The abovementioned complexity and expensiveness of GTs and high demands to engine reliability and safety at low maintenance costs make it unavoidable to use advanced monitoring systems. Through diagnostic processing of engine measured parameters, these systems allow us to gain the knowledge about the health

conditions of main engine components and subsystems. Ideally, it is possible to have the necessary information about the influence of engine faults on the measured parameters by physical embedding the faults in real engines. However, it is a too risky and expensive way, and the assessment of engine technical state is usually based on different mathematical models. Since the diagnostic quality strongly depends on the accuracy of the models used, the issue of the diagnostic models development is important [4]. Although, many diagnostic GT models have been proposed and constructed so far, the existing demand for optimized models for different objectives and engine applications motivates the investigators to continue their efforts to further enhance gas turbine modeling.

*Y* !

*Introductory Chapter: Gas and Wind Turbines and Their Models*

*Y* ! <sup>¼</sup> *F U*!

number of equations reaches 15–20.

*DOI: http://dx.doi.org/10.5772/intechopen.92094*

tion at transients can be expressed by

program complex of the thermodynamic model.

<sup>0</sup> ¼ *F*ð*U* !

simplified data-driven models are determined on its basis.

Unknown coefficients *a*<sup>j</sup> for all the variables *Y*

*U* !

(baseline model *Y*

*Y*0ð*U* !

and *δ*Θ !

**5**

!

linear static model presented by

For a fixed operating mode (*U*

The required values *Yi* Θ

*Hij* <sup>¼</sup> *<sup>δ</sup>Yi δ*Θ *<sup>j</sup>* ¼

> ! 0 � � and *Yi* <sup>Θ</sup>

variation *δ*Θ *<sup>j</sup>* introduced by turn in health parameters.

<sup>¼</sup> *F U*!

, Θ � � !

The health parameters can shift a little the components' maps that allow considering a varying technical state of the engine. Mathematically, expression (1) is a result of solving a system of nonlinear algebraic equations that reflect the balance of mass, heat, and mechanical energy. For the engines of complex structure, the

The development of control algorithms and some diagnostic methods (see, e.g., [7]) relies on dynamic simulation. Within the thermodynamic model, the simula-

> ð Þ*t* , Θ ! , *t*

In contrast to the static simulation according to Eq. (1), the operating conditions

are now time functions. Time *t* is also separately added to the arguments to take into consideration inertia factors, namely, inertia moments of engine rotors, mass and energy accumulation in gas capacities, and warming-up of massive metal elements. Expression (2) is determined by the solution of differential equations that reflect combined operation of the engine components under dynamic conditions. The dynamic model is usually developed on the basis of the static model and uses approximately 70% of its software. In this way, these models constitute a common

As the thermodynamic model is complex and relatively slow, a number of

polynomial function provides accurate approximation of an engine baseline. For one

gas path variable *Y* and three operating conditions *u*i, this function looks like

Þ ¼ *<sup>a</sup>*<sup>0</sup> <sup>þ</sup> *<sup>a</sup>*1*u*<sup>1</sup> <sup>þ</sup> *<sup>a</sup>*2*u*<sup>2</sup> <sup>þ</sup> *<sup>a</sup>*3*u*<sup>3</sup> <sup>þ</sup> *<sup>a</sup>*4*u*1*u*<sup>2</sup> <sup>þ</sup> *<sup>a</sup>*5*u*1*u*<sup>3</sup> <sup>þ</sup> *<sup>a</sup>*6*u*2*u*<sup>3</sup> <sup>þ</sup> *<sup>a</sup>*7*u*<sup>2</sup>

squares method using the data generated by the static nonlinear model as input information. Real data collected under test bed or field conditions can also be used. Another simplified model obtained in the basis of the thermodynamic model is a

> *δY* !

influence coefficients of a matrix *H* are computed according an expression

*Yi* Θ ! 0

> ! *j*

model which runs one time for a healthy engine state and then one time for each

*Yi* Θ ! *j* � � � *Yi* <sup>Θ</sup>

!

¼ *HδΘ* !

of the gas path variables and operating conditions, respectively. The necessary

! 0 � �

� � ,<sup>Θ</sup> *<sup>j</sup>* � <sup>Θ</sup>0*<sup>j</sup>*

To quantify fault influence in gas turbine diagnostics, a healthy engine performance

Þ) is required. As mentioned in [8], a simple second-order

!

<sup>1</sup> <sup>þ</sup> *<sup>a</sup>*8*u*<sup>2</sup>

*:* (5)

are determined by the least


Θ0*<sup>j</sup>*

� �are calculated by the nonlinear static

<sup>2</sup> <sup>þ</sup> *<sup>a</sup>*9*u*<sup>2</sup> 3 (3)

(4)

!

*:* (1)

� �*:* (2)

Let us now come back to wind turbines. They present the principal source of renewable energy. Although wind turbines now generate only about 1% of the total energy, their development rate is by far higher than the rates of traditional energy sources, and the total power production is already about two times greater than the production of solar plants [5]. Being a megastructure, a wind turbine must meet strict requirements of reliability and safety. On the other hand, massive electricity production should be cost-effective. Due to these contradictory demands, as with gas turbines, the turbine itself and its control and monitoring systems need thorough optimization. To this end, a wide use of accurate mathematical modeling and simulation is a very effective strategy. For specific purposes, many different wind turbine models, e.g., aerodynamic, mechanical, economical, and environmental, have been proposed so far. For the needs of control and diagnostics, the generalpurpose model that describes both aerodynamic and electric parts of the power plant is mainly used.

### **2. Gas turbine modeling**

As with the models of other technical systems, the gas turbine models fall into two general categories: physics-based models and data-driven models. The physics-based models rely on the theory of gas turbines and therefore perform accurate simulation of various steady-state and transient modes. Being more complex than the datadriven models, physics-based models have however extended capabilities and offer the knowledge that can hardly be obtained from real data, for example, the information about the influence of the faults on engine performances. The data-driven models (aka black box models) do not require the information about internal structure and operation of the simulated engine. To build these models, optimization methods or, in the case of neural networks, machine learning techniques are employed using available real information as input data. These models are widespread because of their simplicity. The variety of such models is described in detail in the book [3].

#### **2.1 Thermodynamic model and its derivations**

Among physics-based gas turbine models, a nonlinear component-based model also called a thermodynamic model is primarily used for development of control and diagnostic systems. The model relies on the gas turbine theory [6]. The model involves aerothermal relations to compute gas path variables, and engine components such as compressors, combustion chamber, and turbines are given by their performance maps. The most of diagnostic methods are applied to engine at steady states. In this case, model output variables *Y* ! are computed employing operational conditions *U* ! and health parameters Θ ! as input data. In this way, the static model structure is given by

*Introductory Chapter: Gas and Wind Turbines and Their Models DOI: http://dx.doi.org/10.5772/intechopen.92094*

conditions of main engine components and subsystems. Ideally, it is possible to have the necessary information about the influence of engine faults on the measured parameters by physical embedding the faults in real engines. However, it is a too risky and expensive way, and the assessment of engine technical state is usually based on different mathematical models. Since the diagnostic quality strongly depends on the accuracy of the models used, the issue of the diagnostic models development is important [4]. Although, many diagnostic GT models have been proposed and constructed so far, the existing demand for optimized models for different objectives and engine applications motivates the investigators to continue

Let us now come back to wind turbines. They present the principal source of renewable energy. Although wind turbines now generate only about 1% of the total energy, their development rate is by far higher than the rates of traditional energy sources, and the total power production is already about two times greater than the production of solar plants [5]. Being a megastructure, a wind turbine must meet strict requirements of reliability and safety. On the other hand, massive electricity production should be cost-effective. Due to these contradictory demands, as with gas turbines, the turbine itself and its control and monitoring systems need thorough optimization. To this end, a wide use of accurate mathematical modeling and simulation is a very effective strategy. For specific purposes, many different wind turbine models, e.g., aerodynamic, mechanical, economical, and environmental, have been proposed so far. For the needs of control and diagnostics, the generalpurpose model that describes both aerodynamic and electric parts of the power

As with the models of other technical systems, the gas turbine models fall into two general categories: physics-based models and data-driven models. The physics-based models rely on the theory of gas turbines and therefore perform accurate simulation of various steady-state and transient modes. Being more complex than the datadriven models, physics-based models have however extended capabilities and offer the knowledge that can hardly be obtained from real data, for example, the information about the influence of the faults on engine performances. The data-driven models (aka black box models) do not require the information about internal structure and operation of the simulated engine. To build these models, optimization methods or, in the case of neural networks, machine learning techniques are employed using available real information as input data. These models are widespread because of their simplicity. The variety of such models is described in detail in the book [3].

Among physics-based gas turbine models, a nonlinear component-based model also called a thermodynamic model is primarily used for development of control and diagnostic systems. The model relies on the gas turbine theory [6]. The model involves aerothermal relations to compute gas path variables, and engine components such as compressors, combustion chamber, and turbines are given by their performance maps. The most of diagnostic methods are applied to engine at steady

!

!

are computed employing operational

as input data. In this way, the static model

their efforts to further enhance gas turbine modeling.

*Modeling of Turbomachines for Control and Diagnostic Applications*

plant is mainly used.

**2. Gas turbine modeling**

**2.1 Thermodynamic model and its derivations**

states. In this case, model output variables *Y*

and health parameters Θ

conditions *U*

**4**

!

structure is given by

$$
\vec{Y} = F\left(\vec{U}, \vec{\Theta}\right). \tag{1}
$$

The health parameters can shift a little the components' maps that allow considering a varying technical state of the engine. Mathematically, expression (1) is a result of solving a system of nonlinear algebraic equations that reflect the balance of mass, heat, and mechanical energy. For the engines of complex structure, the number of equations reaches 15–20.

The development of control algorithms and some diagnostic methods (see, e.g., [7]) relies on dynamic simulation. Within the thermodynamic model, the simulation at transients can be expressed by

$$
\overrightarrow{Y} = F\left(\overrightarrow{U}(t), \overrightarrow{\Theta}, t\right). \tag{2}
$$

In contrast to the static simulation according to Eq. (1), the operating conditions

*U* ! are now time functions. Time *t* is also separately added to the arguments to take into consideration inertia factors, namely, inertia moments of engine rotors, mass and energy accumulation in gas capacities, and warming-up of massive metal elements. Expression (2) is determined by the solution of differential equations that reflect combined operation of the engine components under dynamic conditions. The dynamic model is usually developed on the basis of the static model and uses approximately 70% of its software. In this way, these models constitute a common program complex of the thermodynamic model.

As the thermodynamic model is complex and relatively slow, a number of simplified data-driven models are determined on its basis.

To quantify fault influence in gas turbine diagnostics, a healthy engine performance (baseline model *Y* ! <sup>0</sup> ¼ *F*ð*U* ! Þ) is required. As mentioned in [8], a simple second-order polynomial function provides accurate approximation of an engine baseline. For one gas path variable *Y* and three operating conditions *u*i, this function looks like

$$Y\_0(\overrightarrow{U}) = a\_0 + a\_1u\_1 + a\_2u\_2 + a\_3u\_3 + a\_4u\_1u\_2 + a\_5u\_1u\_3 + a\_6u\_2u\_3 + a\_7u\_1^2 + a\_8u\_2^2 + a\_9u\_3^2 \tag{3}$$

Unknown coefficients *a*<sup>j</sup> for all the variables *Y* ! are determined by the least squares method using the data generated by the static nonlinear model as input information. Real data collected under test bed or field conditions can also be used.

Another simplified model obtained in the basis of the thermodynamic model is a linear static model presented by

$$
\delta \overrightarrow{Y} = H \delta \overrightarrow{\Theta} \tag{4}
$$

For a fixed operating mode (*U* ! -const), this model relates small relative changes *δY* ! and *δ*Θ ! of the gas path variables and operating conditions, respectively. The necessary influence coefficients of a matrix *H* are computed according an expression

$$H\_{\vec{\eta}} = \frac{\delta Y\_i}{\delta \Theta\_j} = \frac{Y\_i \left(\overrightarrow{\Theta}\_j\right) - Y\_i \left(\overrightarrow{\Theta}\_0\right)}{Y\_i \left(\overrightarrow{\Theta}\_0\right)} \bigg/ \frac{\Theta\_j - \Theta\_{0\vec{\eta}}}{\Theta\_{0\vec{\eta}}}.\tag{5}$$

The required values *Yi* Θ ! 0 � � and *Yi* <sup>Θ</sup> ! *j* � �are calculated by the nonlinear static model which runs one time for a healthy engine state and then one time for each variation *δ*Θ *<sup>j</sup>* introduced by turn in health parameters.

One more model based on the thermodynamic model is called a linear dynamic state space model and is presented by the two following equations:

$$\begin{aligned} \overrightarrow{\dot{X}}(t) &= A\overrightarrow{\Delta X}(t) + B\overrightarrow{\Delta U}(t) \\ \overrightarrow{\Delta Y} &= \overrightarrow{\bf C}\overrightarrow{\Delta X}(t) + D\overrightarrow{\Delta U}(t) \end{aligned} \tag{6}$$

Examples of such estimation include engine power [18] or thrust [19], compressor and turbine efficiencies [20, 21], and compressor air mass flow [21]. These variables help with monitoring of the mission of gas turbines, their integrity, and overall efficiency. They allow a more profound diagnosis of engine components as well. The issue of unmeasured variable estimation is challenging because it must allow

for an engine technical state. A reasonable solution for an offline monitoring is using a thermodynamic model. However, this model has intrinsic inaccuracy, is critical to computer resources, and is not always available. A Kalman filter-based dynamic model affords a faster estimation [19], but it has additional linearization and approximation errors, and its development still needs a thermodynamic model. For online monitoring, a good choice is using simple thermodynamic relations that allow computing some important unmeasured variables, for example, component efficiencies [20] and airflows [21], through measured quantities. Nevertheless,

In contrast, paper [22] offers a universal data-driven method to estimate any necessary unmeasured gas path variable. Additionally, to draw diagnostic information for online monitoring, it is proposed to extend traditional computing the

Chapter 4 of the present book presents new models of unmeasured variables to monitor engine lifetime. To evaluate the lifetime, the temperatures of gas and air around a critical element, turbine blade, should be known. Various variations of data-driven and physics-based models for these unmeasured variables are formed. By model comparison, the optimal ones are chosen and recommended for real

The type and configuration of a GT control system is an important factor. They are closely related with the complexity of engine dynamics and control tasks. An improper control system can cause severe damages to engine health. Control programs depend on engine operation modes such as start-up, dynamic operation, steady-state operation, and shutdown. In addition to a specific program for each mode, the control system has various protection programs to avoid overspeed,

Gas turbine control systems are usually of a closed-loop type. The system elaborates a correction to a control variable (e.g., fuel consumption) on the basis of a discrepancy between actual and necessary values of a controlled variable (e.g., rotor speed). To be effective, the closed-loop controller should "know" accurate relations between engine parameters. A conventional approach to controller development relies on generalized engine performances and average operating conditions. How-

As advanced gas turbines have several control variables, more flexible control laws can be developed to take into consideration actual engine operating conditions and technical state. Modem digital controllers are capable to realize such complex control and, as a result, minimize fuel consumption, extend engine life, and reduce

As with gas turbines, wind turbines are an important energy source. However, in contrast to the formers, they have the lowest greenhouse gas emissions and water

this choice is available only for few variables.

applications.

**3. Gas turbine control**

overheat, flameout, and so on.

maintenance costs.

**4. Wind turbines**

**7**

measured quantity deviations on the unmeasured variables.

*Introductory Chapter: Gas and Wind Turbines and Their Models*

*DOI: http://dx.doi.org/10.5772/intechopen.92094*

ever, engine operating and health conditions vary along time.

where *X* ! stands for a vector of state space variables and Δ denotes a difference between dynamic and static values of variables. Unknown matrices *A*, *B*, *C*, and *D* are computed through the static nonlinear model in the same way as the matrix *H*.

#### **2.2 Thermodynamic model improvements**

The development and diagnostic use of thermodynamic models began in the 1970s inspired by the works of Saravanamuttoo (for instance, [9]). Since then, many enhancements have been introduced in this model.

Stamatis et al. [10] proposed an adaptive simulation by an identified thermodynamic model, and then they used such simulation in gas turbine diagnostics [11].

Paper [12] introduces ellipsoid functions that more accurately describe components performance maps in a thermodynamic model. As a result, better model identification at steady states and transients is gained.

In the well-known universal software GasTurb [13] developed since the 1990s, there are special tools that help to verify and correct the compressor and turbine maps.

A more radical way to enhance compressor description is described in [14]. It is proposed to replace a compressor map by a stage-based compressor model. It is shown that the thermodynamic model after such a modification allows to identify faulty stages and recognize compressor fouling, tip wear, and erosion, thus making the diagnosis more profound.

Volponi et al. [15] propose to compliment a traditional thermodynamic model by a neural network-based data-driven model that compensates systematic measurement errors. The authors show that the new hybrid model considerably enhances simulation accuracy.

The above described enhancements contribute to a whole thermodynamic model or its static part. Nevertheless, simulation of transients has specific issues to address, and fast and accurate dynamic models are in demand [16]. Following this demand, paper [17] describes the model of turbine clearance dynamics intended to complement a traditional physics-based dynamic model. Such an extension of the traditional model does not practically change computation time but allows to consider a dynamic turbine performance and significantly enhance the accuracy of engine dynamic simulation.

The present book meets the mentioned demand for improved dynamic models addressing two related problems. The first problem presents the extension of dynamic model operation on engine starting (see Chapter 2). It is proposed to simulate the starting by a linear dynamic model supplemented with a simplified static model. The second problem presents accurate simulation of gas capacities in a nonlinear dynamic physics-based model (Chapter 3). A lot of different variations of capacity models are considered and compared, and the recommendations of application are given.

#### **2.3 Estimation of unmeasured variables**

In addition to traditional diagnostic functions, estimation of important unmeasured engine variables can be included into a gas turbine monitoring system.

#### *Introductory Chapter: Gas and Wind Turbines and Their Models DOI: http://dx.doi.org/10.5772/intechopen.92094*

Examples of such estimation include engine power [18] or thrust [19], compressor and turbine efficiencies [20, 21], and compressor air mass flow [21]. These variables help with monitoring of the mission of gas turbines, their integrity, and overall efficiency. They allow a more profound diagnosis of engine components as well.

The issue of unmeasured variable estimation is challenging because it must allow for an engine technical state. A reasonable solution for an offline monitoring is using a thermodynamic model. However, this model has intrinsic inaccuracy, is critical to computer resources, and is not always available. A Kalman filter-based dynamic model affords a faster estimation [19], but it has additional linearization and approximation errors, and its development still needs a thermodynamic model.

For online monitoring, a good choice is using simple thermodynamic relations that allow computing some important unmeasured variables, for example, component efficiencies [20] and airflows [21], through measured quantities. Nevertheless, this choice is available only for few variables.

In contrast, paper [22] offers a universal data-driven method to estimate any necessary unmeasured gas path variable. Additionally, to draw diagnostic information for online monitoring, it is proposed to extend traditional computing the measured quantity deviations on the unmeasured variables.

Chapter 4 of the present book presents new models of unmeasured variables to monitor engine lifetime. To evaluate the lifetime, the temperatures of gas and air around a critical element, turbine blade, should be known. Various variations of data-driven and physics-based models for these unmeasured variables are formed. By model comparison, the optimal ones are chosen and recommended for real applications.

## **3. Gas turbine control**

One more model based on the thermodynamic model is called a linear dynamic

!ð*<sup>t</sup>*<sup>Þ</sup>

(6)

!ð*<sup>t</sup>*<sup>Þ</sup>

stands for a vector of state space variables and Δ denotes a difference

!ð*<sup>t</sup>*Þ ¼ *<sup>A</sup>Δ<sup>X</sup>*!ð*<sup>t</sup>*Þ þ *<sup>B</sup>Δ<sup>U</sup>*

*<sup>Δ</sup><sup>Y</sup>*! <sup>¼</sup> *<sup>C</sup>Δ<sup>X</sup>*!ð*<sup>t</sup>*Þ þ *<sup>D</sup>Δ<sup>U</sup>*

between dynamic and static values of variables. Unknown matrices *A*, *B*, *C*, and *D* are computed through the static nonlinear model in the same way as the matrix *H*.

The development and diagnostic use of thermodynamic models began in the 1970s inspired by the works of Saravanamuttoo (for instance, [9]). Since then,

Stamatis et al. [10] proposed an adaptive simulation by an identified thermodynamic model, and then they used such simulation in gas turbine diagnostics [11]. Paper [12] introduces ellipsoid functions that more accurately describe components performance maps in a thermodynamic model. As a result, better model

In the well-known universal software GasTurb [13] developed since the 1990s, there are special tools that help to verify and correct the compressor and turbine maps. A more radical way to enhance compressor description is described in [14]. It is proposed to replace a compressor map by a stage-based compressor model. It is shown that the thermodynamic model after such a modification allows to identify faulty stages and recognize compressor fouling, tip wear, and erosion, thus making

Volponi et al. [15] propose to compliment a traditional thermodynamic model by a neural network-based data-driven model that compensates systematic measurement errors. The authors show that the new hybrid model considerably enhances

The above described enhancements contribute to a whole thermodynamic model or its static part. Nevertheless, simulation of transients has specific issues to address, and fast and accurate dynamic models are in demand [16]. Following this demand, paper [17] describes the model of turbine clearance dynamics intended to complement a traditional physics-based dynamic model. Such an extension of the traditional model does not practically change computation time but allows to consider a dynamic turbine performance and significantly enhance the accuracy of

The present book meets the mentioned demand for improved dynamic models addressing two related problems. The first problem presents the extension of dynamic model operation on engine starting (see Chapter 2). It is proposed to simulate the starting by a linear dynamic model supplemented with a simplified static model. The second problem presents accurate simulation of gas capacities in a nonlinear dynamic physics-based model (Chapter 3). A lot of different variations of capacity models are considered and compared, and the recommendations of application are given.

In addition to traditional diagnostic functions, estimation of important unmeasured engine variables can be included into a gas turbine monitoring system.

state space model and is presented by the two following equations:

*X*\_

*Modeling of Turbomachines for Control and Diagnostic Applications*

many enhancements have been introduced in this model.

identification at steady states and transients is gained.

the diagnosis more profound.

engine dynamic simulation.

**6**

**2.3 Estimation of unmeasured variables**

simulation accuracy.

**2.2 Thermodynamic model improvements**

where *X* !

> The type and configuration of a GT control system is an important factor. They are closely related with the complexity of engine dynamics and control tasks. An improper control system can cause severe damages to engine health. Control programs depend on engine operation modes such as start-up, dynamic operation, steady-state operation, and shutdown. In addition to a specific program for each mode, the control system has various protection programs to avoid overspeed, overheat, flameout, and so on.

> Gas turbine control systems are usually of a closed-loop type. The system elaborates a correction to a control variable (e.g., fuel consumption) on the basis of a discrepancy between actual and necessary values of a controlled variable (e.g., rotor speed). To be effective, the closed-loop controller should "know" accurate relations between engine parameters. A conventional approach to controller development relies on generalized engine performances and average operating conditions. However, engine operating and health conditions vary along time.

> As advanced gas turbines have several control variables, more flexible control laws can be developed to take into consideration actual engine operating conditions and technical state. Modem digital controllers are capable to realize such complex control and, as a result, minimize fuel consumption, extend engine life, and reduce maintenance costs.

### **4. Wind turbines**

As with gas turbines, wind turbines are an important energy source. However, in contrast to the formers, they have the lowest greenhouse gas emissions and water

consumption. Large turbines constitute wind farms to generate electricity for domestic consumption and for the electrical grid. Typically, they have a three-blade horizontal axis construction. The power limit of such a wind turbine is 16/27 times the kinetic energy of the passing air. The power losses include friction of rotor blades, mechanical losses in bearings and gearbox, and losses in a generator and converter. In commercial turbines, these losses can be lessen up to 20–25%. A general trend to increase efficiency and reduce maintenance costs is increasing power and size of a turbine unit. The large wind turbine has a capacity of 9.5 MW, overall height of 220 m, and diameter of 164 m [23].

**References**

12-383842-1

1-85233-784-2

[1] Boyce MP, editor. Gas Turbine Engineering Handbook. 4th ed. Oxford: Elsevier Inc; 2012. 956p. ISBN: 978-0-

[2] Kulikov GG, Thompson HA, editors. Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring, and Optimal Control. London: Springer; 2004. 309p. ISBN:

*DOI: http://dx.doi.org/10.5772/intechopen.92094*

*Introductory Chapter: Gas and Wind Turbines and Their Models*

turbine diagnostics. ASME Journal of Engineering for Power. 1983;**105**:

[10] Stamatis A, Mathioudakis K, Papailiou KD. Adaptive simulation of gas turbine performance. Journal of Engineering for Gas Turbines and

[11] Kamboukos P, Mathioudakis K. Multipoint non-linear method for enhanced component and sensor malfunction diagnosis. In: Proceedings of IGTI/ASME Turbo Expo 2006, 8–11 May 2006. USA: ASME; 2006. p. 9. ASME Paper GT2006-90451

Power. 1990;**112**:168-175

[12] Tsoutsanis E, Meskin N,

GT2014-25753

Benammar M, Khorasani K. An efficient component map generation method for prediction of gas turbine performance. In: Proceedings of ASME Turbo Expo 2014, 16–20 June 2014. USA: ASME; 2014. p. 12. ASME Paper

[13] GasTurb 12. Manual. Germany: GasTurb GmbH; 2015. 294p

[15] Volponi A, Brotherton T, Luppold R. Empirical tuning of on-board gas turbine engine model for real-time module performance estimation. Journal of Engineering for Gas Turbines and

[16] Jaw LC, Mattingly JD. Aircraft Engines Controls: Design, System Analysis, and Health Monitoring. Reston, Virginia: American Institute of Aeronautics and Astronautics, Inc; 2009

[17] Yepifanov S, Zelenskyi R, Loboda I. Modeling the gas turbine engine under

[14] Aretakis N, Roumeliotis I, Mathioudakis K. Performance model "zooming" for in-depth component fault diagnosis. Journal of Engineering for Gas Turbines and Power. 2011;**133**(3):1-11

Power. 2008;**130**(3)

875-884

[3] Asgari H, Chen XQ. Gas Turbines Modeling, Simulation and Control Using Artificial Neural Networks. London: CRC Press/Tailor & Francis Group; 2016. 176p. ISBN 13: 978-1-4987-2661-0

[4] Yunusov S, Labendik V, Guseynov S. Monitoring and Diagnostics of Aircraft Gas Turbine Engines. Germany:

LAMBERT Academic Publishing GmbH& Co; 2014. 196p. ISBN: 978-3-659-58272-1

[5] Available from: https://ourworldindata. org/energy [Accessed: 01 March 2020]

[6] HIH S, Rogers GFC, Cohen H, editors. Gas Turbine Theory. 5th ed. Edinburg: Person Education Limited; 2001. 491p.

[7] Ogaji SOT, Li YG, Sampath S et al. Gas path fault diagnosis of a turbofan engine from transient data using artificial neural networks. In: Proceedings of IGTI/ASME Turbo Expo 2003, 16–19 June 2003; Atlanta, Georgia, USA: ASME; 2003. p. 10. ASME Paper GT2003-38365

[8] Loboda I. Gas turbine condition monitoring and diagnostics. In: Injeti G, editor. Gas Turbines. Croatia: Sciyo; 2010. pp. 119-144. ISBN: 978-953- 307-146-6. Available from: http://www. intechopen.com/articles/show/title/ gas-turbine-condition-monitoring-and-

[9] Saravanamuttoo HIH, MacIsaac BD. Thermodynamic models for pipeline gas

diagnostics

**9**

ISBN 13: 978-0-13-015847-5

The efficiency can decrease because of the dust and insects in the air and possible ice accretion resulting in the altered aerodynamic profiles and efficiency losses of 1.2% per year. To monitor turbine performance and structure, accelerometers and strain sensors are usually installed in the nacelle. To assess the dynamics of turbine blades, digital image correlation and stereophotogrammetry are currently applied [24].

As with gas turbines, the design of such large structures as wind turbines needs mathematical modeling. In particular, for developing more accurate control and diagnostic systems, the general-purpose model that describes both aerodynamic and electric parts of the wind power plant is on demand. Chapter 5 of the present book introduces such a model.

## **Acknowledgements**

This work has been carried out with the support of the National Polytechnic Institute of Mexico (research project 20201738).

### **Author details**

Igor Loboda Instituto Politécnico Nacional, Ciudad de México, México

\*Address all correspondence to: igloboda@gmail.com

© 2020 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.

*Introductory Chapter: Gas and Wind Turbines and Their Models DOI: http://dx.doi.org/10.5772/intechopen.92094*

## **References**

consumption. Large turbines constitute wind farms to generate electricity for domestic consumption and for the electrical grid. Typically, they have a three-blade horizontal axis construction. The power limit of such a wind turbine is 16/27 times the kinetic energy of the passing air. The power losses include friction of rotor blades, mechanical losses in bearings and gearbox, and losses in a generator and converter. In commercial turbines, these losses can be lessen up to 20–25%. A general trend to increase efficiency and reduce maintenance costs is increasing power and size of a turbine unit. The large wind turbine has a capacity of 9.5 MW,

The efficiency can decrease because of the dust and insects in the air and possible ice accretion resulting in the altered aerodynamic profiles and efficiency losses of 1.2% per year. To monitor turbine performance and structure, accelerometers and strain sensors are usually installed in the nacelle. To assess the dynamics of turbine blades, digital image correlation and stereophotogrammetry are currently

As with gas turbines, the design of such large structures as wind turbines needs mathematical modeling. In particular, for developing more accurate control and diagnostic systems, the general-purpose model that describes both aerodynamic and electric parts of the wind power plant is on demand. Chapter 5 of the present

This work has been carried out with the support of the National Polytechnic

© 2020 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,

overall height of 220 m, and diameter of 164 m [23].

*Modeling of Turbomachines for Control and Diagnostic Applications*

Institute of Mexico (research project 20201738).

Instituto Politécnico Nacional, Ciudad de México, México

\*Address all correspondence to: igloboda@gmail.com

provided the original work is properly cited.

applied [24].

book introduces such a model.

**Acknowledgements**

**Author details**

Igor Loboda

**8**

[1] Boyce MP, editor. Gas Turbine Engineering Handbook. 4th ed. Oxford: Elsevier Inc; 2012. 956p. ISBN: 978-0- 12-383842-1

[2] Kulikov GG, Thompson HA, editors. Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring, and Optimal Control. London: Springer; 2004. 309p. ISBN: 1-85233-784-2

[3] Asgari H, Chen XQ. Gas Turbines Modeling, Simulation and Control Using Artificial Neural Networks. London: CRC Press/Tailor & Francis Group; 2016. 176p. ISBN 13: 978-1-4987-2661-0

[4] Yunusov S, Labendik V, Guseynov S. Monitoring and Diagnostics of Aircraft Gas Turbine Engines. Germany: LAMBERT Academic Publishing GmbH& Co; 2014. 196p. ISBN: 978-3-659-58272-1

[5] Available from: https://ourworldindata. org/energy [Accessed: 01 March 2020]

[6] HIH S, Rogers GFC, Cohen H, editors. Gas Turbine Theory. 5th ed. Edinburg: Person Education Limited; 2001. 491p. ISBN 13: 978-0-13-015847-5

[7] Ogaji SOT, Li YG, Sampath S et al. Gas path fault diagnosis of a turbofan engine from transient data using artificial neural networks. In: Proceedings of IGTI/ASME Turbo Expo 2003, 16–19 June 2003; Atlanta, Georgia, USA: ASME; 2003. p. 10. ASME Paper GT2003-38365

[8] Loboda I. Gas turbine condition monitoring and diagnostics. In: Injeti G, editor. Gas Turbines. Croatia: Sciyo; 2010. pp. 119-144. ISBN: 978-953- 307-146-6. Available from: http://www. intechopen.com/articles/show/title/ gas-turbine-condition-monitoring-anddiagnostics

[9] Saravanamuttoo HIH, MacIsaac BD. Thermodynamic models for pipeline gas turbine diagnostics. ASME Journal of Engineering for Power. 1983;**105**: 875-884

[10] Stamatis A, Mathioudakis K, Papailiou KD. Adaptive simulation of gas turbine performance. Journal of Engineering for Gas Turbines and Power. 1990;**112**:168-175

[11] Kamboukos P, Mathioudakis K. Multipoint non-linear method for enhanced component and sensor malfunction diagnosis. In: Proceedings of IGTI/ASME Turbo Expo 2006, 8–11 May 2006. USA: ASME; 2006. p. 9. ASME Paper GT2006-90451

[12] Tsoutsanis E, Meskin N, Benammar M, Khorasani K. An efficient component map generation method for prediction of gas turbine performance. In: Proceedings of ASME Turbo Expo 2014, 16–20 June 2014. USA: ASME; 2014. p. 12. ASME Paper GT2014-25753

[13] GasTurb 12. Manual. Germany: GasTurb GmbH; 2015. 294p

[14] Aretakis N, Roumeliotis I, Mathioudakis K. Performance model "zooming" for in-depth component fault diagnosis. Journal of Engineering for Gas Turbines and Power. 2011;**133**(3):1-11

[15] Volponi A, Brotherton T, Luppold R. Empirical tuning of on-board gas turbine engine model for real-time module performance estimation. Journal of Engineering for Gas Turbines and Power. 2008;**130**(3)

[16] Jaw LC, Mattingly JD. Aircraft Engines Controls: Design, System Analysis, and Health Monitoring. Reston, Virginia: American Institute of Aeronautics and Astronautics, Inc; 2009

[17] Yepifanov S, Zelenskyi R, Loboda I. Modeling the gas turbine engine under

its dynamic heating conditions. Journal of Engineering for Gas Turbines and Power - Transactions of ASME. 2015; **137**(3):1-10

[18] Jiang X, Mendoza E, Lin TP. Bayesian calibration for power splitting in single shaft combined cycle plant diagnostics. In: Proceedings of ASME Turbo Expo 2015, 15–19 June 2015. USA: ASME; 2015. p. 11. ASME Paper GT2015-43878

[19] Palmer C, Hettler E. Thrust measurement model-based correction system for turbine engine test cell dynamic data. In: Proceedings of ASME Turbo Expo 2015, 15–19 June 2015. USA: ASME; 2015. p. 8. ASME Paper GT2015-43720

[20] Kacprzynski GJ, Gumina M, Roemer MJ, Caguiat DE, Galie TR, McGroarty JJ. A prognostic modelling approach for predicting recurring maintenance for shipboard propulsion system. In: Proceedings of ASME Turbo Expo 2015, 15-19 June 2015. USA: ASME; 2015 ASME Paper No.2001-GT-0218

[21] Cortés O, Urquiza G, Hernández JA. Optimization of operating conditions for compressor performance by means of neural network inverse. Applied Energy. 2009;**86**:2487-2493

[22] Loboda I, Zárate M, Yepifanov S, Maravilla Herrera C, Ruiz P. Estimation of gas turbine unmeasured variables for an online monitoring system. International Journal of Turbo & Jet Engines. 2018. pp. 1-16. e-ISSN: 2191-0332 (e-publication)

[23] The World's Most Powerful Available Wind Turbine Gets Major Power Boost. UK: MHI Vestas Offshore; 2018. Available from: www.mhivesta soffshore.com [Accessed: 09 March 2020]

[24] Baqersad J, Niezrecki C, Avitabile P. Full-field dynamic strain prediction on a wind turbine using displacements of optical targets measured by stereophotogrammetry. Mechanical Systems and Signal Processing. 2015; **62–63**:284-295. DOI: 10.1016/j.ymssp. 2015.03.021

Section 2

Gas Turbines

**11**
