ANN controller for heavy duty gas turbine plant.

Balamurugan, S. ; Xavier, R. Joseph ; Jeyakumar, A. Ebenezer 等

Introduction

Gas turbine plants are used for isolated and standalone operations. They are mainly used in oil fields, desert areas, off shore installations and bio gas plants. An effective control strategy is required to keep the system stable under disturbance.

The Transfer function model of heavy duty gas turbine has been developed by Rowen [1] based upon his field experience and the tests he conducted in the gas turbine plants. This model has been used in many works such as, the dynamic analysis of combined cycle plant [2], twin shaft gas turbine model [3], combustion turbine model [4] and even in micro turbine power generation [5]. The transfer function simplification has been validated [6]. The droop governor is found to be an appropriate one [7]. The droop setting value and rotor time constant have been optimized [8]. After tuning the parameters, the response of the gas turbine plant shows steady state error.

To improve the transient and steady state response, PID controller is required. The parameters of PID controller have been tuned using ZN method and the steady state error is removed. In this paper, Artificial Neural Network is used for control which uses backpropagation algorithm for training. The trained ANN brings back the system to steady state. It is found that ANN controller yields a better response than the conventional PID controller.

Mathematical Model of Gas Turbine Plant

The Transfer function model developed by Rowen [1] with the following simplifications is considered for the simulation of the response of an isolated gas turbine plant.

i. If the frequency variation is not greater than [+ or -]1%, the acceleration control will become inactive. It can be eliminated.

ii. The turbine output is predominantly controlled by the set point so the need for temperature control is significantly diminished, thereby allowing elimination of temperature control.

iii. The multiplier used in the transfer function can be neglected for small speed variations.

The simulation proof for these simplifications is developed by Balamurugan et al [6]. The simplified block diagram of gas turbine plant is shown in Figure 1.

[FIGURE 1 OMITTED]

The speed governor is the primary means of gas turbine control. The droop governor operates on the speed error. The droop governor is a straight proportional controller in which output is proportional to speed error. The gas turbine requires significant percentage of rated fuel to support self sustaining no load conditions and this percentage is approximately 23%. The fuel system consists of two time constants in which one is associated with the gas valve positioning system,

[e.sub.1] = a/bs + c [F.sub.d] (1)

and the other is the volumetric time constant associated with the downstream piping and fuel gas distribution manifold,

[W.sub.f] = [K.sub.f]/[[tau].sub.f] s + 1 [e.sub.1] (2)

The torque characteristics of gas turbine are essentially linear with respect to fuel flow and turbine speed, expressed by the relation

[f.sub.1] = 1.3 ([W.sub.f] - 0.23) + 0.5 (1 -N) (3)

The rotor time constant is the time necessary for the rotor to double its speed if the initial rate of speed change is maintained after removal of rated load torque. The rotor speed is compared with the reference speed and the error is given to the speed governor.

A unit step load disturbance has been given to the gas turbine using MATLAB Simulink [9] and the response is obtained as shown in Figure 2. The response shows that there is a steady state error. An appropriate secondary controller has to be included to improve both the steady state and transient response.

[FIGURE 2 OMITTED]

PID Controller

Proportional--Integral--Derivative (PID) controllers are widely used in many control applications because of their simplicity and robustness [10]. It is well known that if the control law employs integral control, the system has no steady state error. However, it increases the type of the system by one. Therefore the response with integral control is slow during the transient period. In the absence of the integral control, the gain of the closed loop system can be increased significantly thereby improving the transient response. Similarly the closed loop system stability can be improved by the differential control, and therefore PID controller will improve the static and dynamic accuracy. Let the PID controller be implemented as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

error, e = [y.sub.r] - y (5)

Where, u, [y.sub.r] and y are the controller output, the set point and the plant output respectively. The transfer function of the controller is

[G.sub.c] (s) = [k.sub.p] + [k.sub.i]/s + [k.sub.d] s (6)

The three parameters in the PID controller proportional gain ([k.sub.p]), integral gain ([k.sub.i]) and derivative gain ([k.sub.d]) are to be tuned. In this paper, Ziegler Nichols' method has been used for the tuning.

PID Controller Tuning Using ZN Method

Though there are many methods [11]-[14] to tune PID and PI control for plants, Ziegler Nichols' method [15] still has its importance in tuning the PID controller because of its simplicity. In this method the plant is kept under closed loop proportional controller and the gain of the controller is increased in steps to bring the system to marginally stable condition. The gain at which the system reaches marginal stable condition is called ultimate gain ([K.sub.cu]). The time period of the sustained oscillation is called ultimate period ([T.sub.u]). These two parameters are used for finding the unknown parameters [k.sub.p], [k.sub.i] and [k.sub.d]

For the heavy duty gas turbine plant the ultimate gain and ultimate period are found to be 5.5665 and 1.262 respectively. Using these values the unknown values of PID controller are tuned. The values are shown in Table 1.

The response of the gas turbine plant with the PID controller compared with the open loop response is shown in Figure 3.It shows that the PID controller is providing a improved steady state and transient response.

[FIGURE 3 OMITTED]

Neural Network Controller

The ANN can be used for controlling the gas turbine plant [16]. Fuzzy logic and ANN controller can be used to provide the control input to meet zero steady state error and better dynamic performance [17]. For the learning of ANN, Backpropogation algorithm is used [16]. Input--output patterns are collected from the conventional PID controller. Out of 126 data, 100 have been chosen randomly for training and remaining 26 for testing. The network has been trained using gradient decent method until the absolute value of the error is below 0.005. The learning rate has been taken as 0.5.

The ANN trained for the control is a three layer network with one neuron in the input and output layer. 12 and 9 are the neurons taken in first and second hidden layers respectively. Tansig is the activation function taken for the hidden layers and purelin for the output layer. The architecture is shown in Figure 4.

[FIGURE 4 OMITTED]

A program written in MATLAB [18] has been implemented to perform the training. The convergence plot is shown in Figure 5.

[FIGURE 5 OMITTED]

The response of the gas turbine plant with the above mentioned ANN controller is simulated with a step load disturbance. The comparison plot shown in Figure 6 indicates that the time domain response of ANN controller is well damped.

[FIGURE 6 OMITTED]

Conclusion

In this paper, the simplified mathematical model of gas turbine plant is taken and it is controlled by PID and ANN controller. The PID controller parameters are tuned using ZN method. The ZN tuned PID controller yields satisfactory transient and steady state response of gas turbine plant. ANN allows the integration of expert knowledge into control system very easily. ANN has been trained using backpropogation algorithm. Simulation results shows that the use of ANN in controlling the gas turbine plant gives better results than the PID controller.

APPENDIX

[f.sub.1] = Turbine torque

[W.sub.f] = Per unit fuel flow

[K.sub.f] = Fuel System gain constant = 1

[[tau].sub.f] = Fuel system time constant = 0.4

N = per unit turbine rotor speed

s = Laplace operator

[e.sub.1] = Valve position

[F.sub.d] = Per unit fuel demand signal

a,b,c = Fuel system transfer function coefficients a = 1; b = 0.05; c = 1

W,X,Y,Z = Governor transfer function coefficients

W = [K.sub.d]; X = 0; Y = 0.05; Z = 1

[K.sub.d] = Droop gain = 2 to 10%

[[tau].sub.1] = Rotor time constant = 12.2

[k.sub.p], [k.sub.I], [k.sub.D] = PID parameters

t = time

u(t) = control signal

e(t) = error signal

References

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[4] L.N. Hannett, Afzal Khan, "Combustion Turbine Dynamic Model Vlidation Tests," IEEE Transactions on Power Systems, 8 (1993) 152-158.

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[6] S.Balamurugan, R.Joseph Xavier, A.Ebinezer Jeyakumar, "Simulation of Response of Gas Turbine Plant with Controllers," Procedings of National System Conference, Manipal, India 2007, ref no. P105.

[7] S.Balamurugan, R.Joseph Xavier, "Selection of Governor for Heavy Duty Gas Turbine Power Plant," National Conference on Modern trends in Electrical and Instrumentation systems, Coimbatore, India 2005, 365-371.

[8] S.Balamurugan, R.Joseph Xavier, A.Ebinezer Jeyakumar, "Selection of Governor and Optimization of its Droop Setting and Rotor Time Constant for Heavy Duty Gas Turbine Plants," Indian Journal of Power and River Valley Development, 57 (2007) 35-37.

[9] MATLAB User Manuals, Mathworks Inc., USA, 2000.

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[14] G.H. Cohen and G.A. Coon, "Theoretical consideration of retarded control," Trans. Amer. Soc. Mech. Eng., Vol. 75, 827-834, 1953.

[15] J.G.Ziegler, N.B.Nichols, "Optimum Setting for Automatic Controllers," Transactions of ASME, 64 (1942) 759-768.

[16] Lauren Fausett, "Fundamentals of neural networks architectures, algorithms and application," Prentice Hall Publication, 1994.

[17] Kawakita Y, Ohsawa Y, Arai K, "Power system stabilizing control by SMES using fuzzy techniques and neural networks," Elect. Engg. Jpn., vol. 114, 9-17, 1994.

[18] MATLAB Neural Networks Tool Box User Manuals, Mathworks Inc., USA, 2000.

S. Balamurugan (1), R. Joseph Xavier (2) and A. Ebenezer Jeyakumar (3)

(1) Senior Lecturer, Dept. of Electrical Engineering Amrita School of Engineering, Coimbatore, India

(2) Principal, Sri Ramakrishna Institute of Technology, Coimbatore, India

(3) Principal (Retd.), Government College of Engineering, Salem, India

Table 1. Tuned values of PID controller using ZN method.

Control   [k.sub.p]   [k.sub.j]   [k.sub.d]

PID         3.3399      5.2917      0.5267