A New Design for Robust Control of Power System Stabilizer Based on Moth Search Algorithm

Abstract

This paper presents a new optimal design for the stability and control of the synchronous machine connected to an infinite bus. The model of the synchronous machine is 4th order linear Philips-Heffron synchronous machine. In this study, a PID controller is utilized for stability and its parameters have been achieved optimally by minimizing a fitness function to removes the unstable Eigen-values to the left-hand side of the imaginary axis. The considered parameters of the PID controller are optimized based on a new nature-inspired, called moth search algorithm. The proposed system is then compared with the particle swarm optimization as a high-performance and popular algorithm for different operating points. Final results show that using a moth search algorithm gives better efficiency toward the compared particle swarm optimization.

Appendixes

System data:

Machine (pu):

x_d = 1.6, x_d^′ = 0.32, x_q = 1.55.

v_t0 = 1.05, w₀ = 314(rad/s), Td0′ = 6.0 (s).

D = 0; M = 10.

P, Q = Electrical active and reactive power of output machine (pu).

Transmission Line (Pu):

r_e = 0; x_e = 0.4

Exciter:

K_e = 50; T_e = 0.05 (s).

Washout Filter:

T_w = 5 (s).

The function of k-parameters and other data are presented below:

i_q0 = (P * v_t0)/sqrt((P * x_q) ² + (v_t0² + Q * x_q) ²);

v_d0 = i_q0 * x_q;

v_q0 = ((v_t0²) − (v_d0²)) ^0.5;

i_d0 = (Q + xq*(i_q0²))/v_q0;

E_q0 = v_q0 + i_d0*x_q;

E₀ = sqrt((v_d0 + i_q0 * x_e)² + (v_q0-i_d0 * x_e)²);

delta = tan⁻¹((v_d0 + i_q0*x_e)/(v_q0 − i_d0*x_e));

K₁ = (((xq − x_d′)/(xe + x_d′))*(i_q0 * E₀ * sin(delta))) + ((E_q0 * E₀ * cos(delta))/(x_e + x_q));

K₂ = (E₀ * sin(delta))/(x_e + x_d);

K₃ = (x_e + x_d^’)/(x_e + x_d);

K₄ = ((x_d − x_d′)/(x_e + x_d^′)) * (E₀ * sin(delta));

 K₅ = ((x_q * v_d0 * E₀ * cos(delta))/((x_e + x_q) * v_t0)) − ((x_d^′ * v_d0 * E₀ * sin(delta))/((x_e + x_d^′) * v_t0));

K₆ = (x_e * v_q0)/((x_e + x_d^′) * v_t0);