Control Strategies of a Gas Turbine Generator: A Comparative Study

Received Jan 22, 2020 Revised Oct 2, 2020 Accepted Nov 6, 2020 Gas turbine generators are commonly used in oil and gas industries due to their robustness and association with other operating systems in the combined cycles. The electrical generators may become unstable under severe load fluctuations. For these reasons, maintaining the stability is paramount to ensure continuous functionality. This paper deals with the modeling and simulation of a single shaft gas turbine generator using the model developed by Rowen and incorporating different types of controllers, viz a ZeiglerNichols PID controller, a Fuzzy Logic Controller (FLC), FLC-PID and finally a hybrid PID/FLC/FLC-PID controller. The study was undertaken under Matlab / Simulink environment with data related to an in-service power plant owned by Sonatrach, Algiers, Algeria. The results show that FLC-PID and hybrid tuned controllers provide the best time domain performances.


INTRODUCTION
In most refineries, cogeneration is very often used to generate electricity and to provide steam for the processing units. Power generation plants, which are usually interconnected with utilities, have very complicated structures with some inherent problems associated with power and voltage oscillations caused by the different connected loads and particularly high power induction motors. These problems seriously affect power plant operations and may even lead to a blackout. To facilitate the design and analysis of such complex systems, modeling and simulation are required.
Rowen has developed a model based on the concept of the transfer function for a heavy duty gas turbine in 1983 [1]. This model was verified by simulation by [2], and subsequently used to study the dynamic analysis of combined cycle plants [3], twin shaft gas turbine plant [4] and even micro gas turbine plants [5]. From the control point of view, Rowen and Hannet et al. contributions used conventional fixed gain PI controllers for speed, temperature and acceleration controllers. Later Grosa et al. [6] and Camporeale et al. [7] introduced non-linear lumped parameter models to decouple the interaction between the speed and the exhaust temperature loops. To achieve this, a precise dynamic model and an accurate transfer function of the gas turbine are required, which are very difficult to achieve in practice without extensive tests and extensive expertise.

GAS TURBINE MODELLING
The schematic diagram of a simple-cycle single shaft gas turbine which is designed to operate at higher speeds, typically in the range of 50,000-120,000 rpm, is shown in Figure 1 [1]. It consists of an axial air compressor, so the entering air temperature is raised; and a combustion chamber where fuel and air are injected. This followed by the turbines, which develop a rotary mechanical torque to drive a synchronous generator [2].

Figure.1. A simple-cycle gas turbine
In 1983, Rowen [1] has developed a simplified model of a gas turbine, which may be considered as a reference and alsoreconsidered by many other researchers in their investigations [2][3][4][5][6][7]. It consists of a set of algebraic equations describing the steady state characteristics of a gas turbine [3,4]. This model is represented in Figure 2. This model was introduced by Rowen in [3] and completed in [8]. The main industrial gas turbine components are the compressor, the combustion chamber and the turbine operating under the Brayton cycle [9], that it can be divided into two interconnected subsystems [10]- [12]. Three important regulators are used, the first to control the (speed/ power) under partial load conditions, the second to control the temperature controller and the third to control the acceleration.

The fuel system
The fuel system consists of the fuel valve and the actuator, which can be modeled by the following equation [13], [14].
Where is the gas turbine fuel flow (per unit), fuel system gain constant, 1 valve position and fuel system time constant.

The valve positionner
The valve positionnerequation is given by: Where is the input variable to the fuel system (per unit) and (a, b, c) are the cofficients of the fuel system transfer function.

The turbine functions
The turbine torque, the exhaust temperature and the air flow rate denoted in Figure 2 respectively 1 , 2 and 3 are calculated using the following equations [15]: Where wris the per unit turbine rotor speed, is the rated exhaust temperature and ∆ is the diviation speed.

The rotor function
The rotor time constant of a gas turbine power plant varies in a wide range from 12.
During normal operating conditions, frequency and power are the two fundamental variables controlled by the main control loop [16][17][18][19]. When the operations of the system change, or become abnormal, the temperature and acceleration controllers are activated. However, under normal operating conditions, the Rowen model can be further simplified by neglecting the acceleration and the temperature controllers. The speed / power regulator becomesthenthe predominant. The transfer function of the simplified model under normal operating conditions is illustrated by Figure 3.

CONTROL DESIGN AND ANALYSIS
In industrial control systems, the classical regulator PID-ZN is often used. However, in this paper, a new design based on the fuzzy logic theory is introduced. In fact, a fuzzy logic controller, FLC-PID controller and ahybrid controller are used in order to improve the performances of the controlled system. The proposed regulators are shown in Figure 4.

Fuzzy logic Controller
The simulink block and the meshgrid function of the FLC controller is shown in Figure 5.

Figure 5. FLC Simulink block and meshgrid function
The designed FLC will determine the amount of fuel flow to the combustion chamber over its transient operation. The FLC and the available gas turbine constitute a closed loop. Figure 6 illustrates the process of the fuzzification and defuzzification for controller. Figure 6. Implementation of the fuzzy controller After fuzzifying of the input values, the controller uses the corresponding input linguistic terms and the rule base to determine the resulting linguistic terms of the output variables. Defuzzification is the process of converting the degrees of membership of the output linguistic variables within their linguistic terms into crisp numerical values [20]. The defined fuzzy function used in this paper for the first and the second input and the output of the fuzzy functions are given in Figure 7. Table 1 describes the fuzzy tuning rule for the FLC Controller.  Figure 8 shows the PID control system with a fuzzy gain scheduler. The approach taken here is to explore fuzzy rules and reasoning to generate the controller parameters. It is assumed that   S i i i I l ℎ * , * are generated and determined by a set of fuzzy rules and as a function ofthe error and the variation of the error of the set speed. The fuzzy tuning rules for the fuzzy gain scheduler controller are described in Tables 2, 3 and 4. The defined fuzzy functions used for the first and second input (

PID-Fuzzy Logic Controller
) and the output of the fuzzy function are defined in Figure 10.  Table 5 gives the parameters for the different used controllers: The PID controller is configured according to the method of Ziegler and Nichols; it allows a quick adjustment on the basis of the reading of the index response [22].

Gain values of the controllers
As a function of the error and the variation of the error generated between the reference and the measurement, the fuzzy controllerproduces a control signal, which is used to control the speed of the gas turbine. Multiplier coefficients can be added to amplify or attenuate the value of the inputs and the outputs within the limits of the operating ranges. The combination of FLC and PID allows to design other technical control systems. Depending on the error, the FLC readjusts and modifies the coefficients of the PID controller to improve the static and the dynamic performances.

Hybrid Controller
The hybrid controller is combined between three regulators (PID, FLC & FLC-PID), a multiport switch is designed to select a regulator according to the absolute error to improve the static and the dynamic performances. It should be noted that each controller can be activated over a period in order to give the best performances.
The simulating block of the controlled speed and the power of the gas turbine under Matlab/Simulink is given by Figure 12.    [25]. Figure 17 Dynamic response in the power demand and in the speed of a gas turbine controlled by Recurrent fuzzy-neural network controller [26].
As can be seen in Figures 14 and 15, a zero steady state error is achieved with all the controllers. However, for the dynamic responses, the fuzzy-PID logic controller and the hybrid controller responded faster as far as the speed time response is concerned with relatively a small overshoot resulting in a smooth speed response. The performances of a gas turbine are obtained using several controllers (PID-ZN, FLC, FLC-PID and Hybrid Controller). To validate our results, they are compared to those available in the literature [25][26] as seen in Figures 16 and 17. It is clear that the power and speed characteristics follow the same trend as those obtained in our paper.

CONCLUSION
In this paper, the model developed by Rowen for a gas turbine is reconsidered. Different controllers are used to control the speed and power of this turbine. In fact, four regulators PID ZN, FLC, FLC-PID and S i i i I l hybrid were tested by simulation. The results obtained showed clearly that the FLC-PID and the hybrid controllers have the best performances in terms of time response and steady state error. These controllers will be used in future works to study the behavior of a gas turbine connected to a grid. Amar Bousbaine was born in Bouira in 1960. He received his Bsc, MSc and PhD respectively at the University of Tizi Ouzou in 1985 and at the University of Strathclyde in 1990 and at the University of Sheffield in 1995. He is currently reader in Electronics in the college of Engineering and Technology at the university of Derby, UK. He is also an active researcher in the field of power system for electric vehicules, renewable energy sources, hydrogen fuel cells and autonomous control for drives. He published over 70 papers in referred journal.