Modified sine cosine algorithm-based fuzzy-aided PID controller for automatic generation control of multiarea power systems

Abstract

The research paper presents implementation of a fuzzy rule and membership function-based fuzzy-aided PID controller for automatic generation control (AGC) in multiarea nonlinear power system. At the initial stage of this proposed work, a three-area nine-unit installed interconnected network is considered for developing different dynamic responses in response to AGC analysis. A modified approach named modified sine cosine algorithm (M-SCA) is proposed for tuning the gain parameters of the above-proposed fuzzy controller to produce close optimum gain values. The proposed modified algorithm is developed from its original sine cosine algorithm by improving and updating few equations which is capable of making the balance between exploration and exploitation levels of this algorithm and improving the updating quality of iteration. To impose supremacy of M-SCA technique, it is examined through convergence curves and its performance is compared with host sine cosine algorithm, genetic algorithm, and particle swarm optimization algorithm. For controller supremacy analysis, the performance of the proposed fuzzy-aided PID controller is compared with conventional I, PI, and PID controllers, and it has been revealed that proposed M-SCA-tuned fuzzy-aided PID controller exhibits better performances through different deviated responses for AGC analysis. To demonstrate most standard and supremacy of proposed approaches, finally these are tested through a five-area ten-unit system considering some physical nonlinear constraints like generation rate constraint, governor dead band, boiler dynamics and time delay. At the final observation level, the proposed fuzzy controller has gone through different sensitivity analyses with variation of different system parametric conditions and different load conditions.

Appendices

Appendix A

Power system parameters

$K_{{ps_{i} }}$ = Power system gain = 120 Hz/pu MW; $T_{{ps_{i} }}$ = Time constant of power system = 20 s; $B_{i}$ = Frequency bias parameter = 0.425 pu MW/Hz.

Thermal power station

$T_{{G_{i} }}$ = Time constant of governor = 0.08 s; $K_{{r_{i} }}$ = Coefficient of reheat turbine = 0.333; $T_{{r_{i} }}$ = Reheat time constant = 10 s; $T_{{T_{i} }}$ = Time constant of turbine = 0.3 s; $R_{i}$ = 2.4 Hz/pu MW.

Boiler dynamics parameters

$K_{1}$ = 0.85; $K_{2}$ = 0.095; $K_{3}$ = 0.92; $K_{1B}$ = 0.03; $T_{1B}$ = 26 s; $T_{RB}$ = 69; $C_{B}$ = 200; $T_{D}$ = 0; T_F= 10.

Hydropower station

$T_{{g_{i} }}$ = Governor time constant = 0.041 s; $T_{1}$ = Speed governor reset time = 0.5135; $T_{2}$ = Transient droop time constant = 10 s; $T_{W}$ = Water time constant = 1 s; $R_{i}$ = 2.4 Hz/pu MW.

Wind power station

$K_{2}$ = Coefficient of hydraulic pitch actuator = 1.25; $T_{{P_{2} }}$ = Time constant of hydraulic pitch actuator = 0.041 s; $T_{{P_{1} }}$ = 0.60 s; $K_{4}$ = Coefficient of data fit-pitch response = 1.40; $R_{i}$ = 2.4 Hz/pu MW.

Diesel power station

$K_{Diesei}$ = 16.5 = Coefficient of diesel power system; $R_{i}$ = = 2.4 Hz/pu MW (Regulation).

Gas power station

$b_{i}$ = Valve position constant = 0.05; $c_{i}$ = Valve position constant = 1; $X_{i}$ = Speed governor lead time = 0.6 s; $Y_{i}$ = Lag time constant = 1 s; $T_{{CR_{i} }}$ = Time delay of Combustion reaction = 0.3 s; $T_{{F_{i} }}$ = Time constant of fuel = 0.23 s; $T_{{CD_{i} }}$ = Time constant of compressor discharge = 0.2 s; R_i = 2.4 Hz/pu MW.(Regulation).

Appendix B

Thermal system: T_g = 0.08; T_t = 0.3; K_r = 0.333; T_r= 10. P_T = 0.5; hydro system: T_H = 48.7; T₁ = 0.513; T₂ = 10; T_W = 1; P_H= 0.5; wind system: T_P1 = 0.6; T_P2 = 0.041; K₄ = 1.4; P_W = 0.124. Gas system: c₁ = 0.049; b₁ = 1; X₁ = 0.06; Y₁ = 1.1; T_CR1 = 0.01; T_F1 = 0.239; T_CD1 = 0.2; P_G = 0.125; diesel plant: K_diesel = 16.5; P_D= 0.125; R = 2.4.