An optimal frequency regulation in interconnected power system through differential evolution and firefly algorithm

Abstract

Automatic generation control is extensively used to regulate power plants in a modern area of the power system network. In this paper, automatic generation and frequency control in interconnected power system is presented. A multisource such as thermal, hydro, and gas-based power plant is considered in this study, which is carried out by incorporating nonlinearity like generation rate constants, HVDC link, and the conventional PID controller design. Further, an optimal setting of the PID controller is performed by employing evolutionary, and metaheuristic algorithm-based approaches such as differential evolution and firefly algorithm, respectively. With these algorithms, the proposed model has been tested with their performance evaluation and comparison characteristics are discoursed. The robustness of the proposed controllers is assessed based on comparative analyses to regulate the interconnected power network’s frequency profile under different loading conditions. The stability analysis is performed using the Eigen and Nyquist plots to assess the proposed controllers’ efficacy. Besides, the frequency control study is summarized with comparative assessment through various performance indices such as settling time, peak overshoot and undershoots under different operating conditions. Finally, the proposed control scheme, in the interconnected power system, is validated through a real-time digital simulation platform, i.e., OPAL-RT 5142. The comparison of simulation and real-time results demonstrates the effectiveness of the FA-optimized PID controller in comparison with that of the DE-optimized PID controller.

Appendices

Appendix-I

Area-I: R_t1 = 2.4; T_g1 = 0.08; T_t1 = 0.3; K_r1 = 0.3; T_r1 = 10; K_t1 = 0.60; K_p1 = 120; T_p1 = 20; β₁ = 0.425;

Area-II: R_t2 = 2.4; T_g2 = 0.08; T_t2 = 0.3; K_r2 = 0.3; T_r2 = 10; K_t2 = 0.60; K_p2 = 120; T_p2 = 20; β₂ = 0.42; α₁₂ =  − 1.0;

AC-link: T₁₂ = 0.0433 DC-link: K_dc = 1; T_dc = 0.2

Appendix-II: Parameters of system matrix A

A_1,1 = $- \frac{1}{{T_{{{\text{P}}1}} }};$ A₁,₂ = $- \frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_1,4 = $\frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_1,7 = $\frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_1,10 = $\frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_1,26 = $\frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_2,1 = $2\pi T{}_{12};$ A_2,3 = $- 2\pi T{}_{12};$ A_3,2 = $- \frac{{\alpha_{12} K_{{{\text{P}}2}} }}{{T_{{{\text{P}}1}} }};$ A_3,3=$- \frac{1}{{T_{{{\text{P}}2}} }};$ A_3,14=$\frac{{K_{{{\text{P}}2}} }}{{T_{{{\text{P}}2}} }};$ A_3,17 = $\frac{{K_{{{\text{P}}2}} }}{{T_{{{\text{P}}2}} }};$ A_3,20 = $\frac{{K_{{{\text{P}}2}} }}{{T_{{{\text{P}}2}} }};$ A_3,26 = $- \frac{{K_{{{\text{P}}1}} }}{{T_{{{\text{P}}1}} }};$ A_4,4 = $- \frac{1}{{T_{r1} }};$ A_4,4 = $\left( {\frac{{K_{{{\text{t}}1}} }}{{T_{r1} }} + \frac{{K_{r1} K_{{{\text{t}}1}} }}{{T_{{{\text{t}}1}} }}} \right);$ A_4,6 = $\frac{{K_{r1} K_{{{\text{t}}1}} }}{{T_{{{\text{t}}1}} }};$ A_5,5 = $- \frac{1}{{T_{{{\text{t}}1}} }};$ A_5,6 = $\frac{1}{{T_{t1} }};$ A_6,1 = $- \frac{1}{{R_{1} T_{{{\text{g}}1}} }};$ A_6,6 = $- \frac{1}{{T_{{{\text{g}}1}} }};$ A_7,1 = $\left( { - \frac{{2K_{{{\text{h1}}}} T_{{{\text{R}}1}} }}{{T_{{{\text{GH}}1}} R_{1} T_{{{\text{RH}}1}} }}} \right);$ A_7,7 = $- \frac{2}{{T_{W1} }};$ A_7,8 = $\left( {\frac{{2K_{h1} }}{{T_{w1} }} + \frac{{2K_{h1} }}{{T_{Gt1} }}} \right);$ A_7,9 = $\left( {\frac{{2K_{h1} T_{R1} }}{{T_{GH1} T_{RH1} }} + \frac{{2K_{h1} }}{{T_{GH1} }}} \right);$ A_8,1 = $\frac{{T_{{{\text{R}}1}} }}{{T_{{{\text{GH}}1}} R_{1} T_{{{\text{RH}}1}} }};$ A_8,8 = $- \frac{1}{{T_{{{\text{GH}}1}} }}$ A_8,9 = $\left( {\frac{1}{{T_{{{\text{GH}}1}} }} - \frac{{T_{{{\text{R}}1}} }}{{T_{{{\text{RH}}!}} T_{{{\text{GH}}1}} }}} \right);$ A_9,1 = $- \frac{1}{{R_{1} T_{{{\text{RH}}1}} }};$ A_9,9 = $- \frac{1}{{T_{{{\text{RH}}1}} }};$ A_10,10 = $- \frac{1}{{T_{{{\text{CD}}1}} }};$ A_10,11 = $\frac{{K_{{{\text{g}}1}} }}{{T_{{{\text{CD}}1}} }};$ A_10,12 = $- \left( {\frac{{K_{{{\text{g}}1}} T_{{{\text{CR}}1}} }}{{T_{F1} T_{{{\text{CD}}1}} }}} \right);$ A_11,11 = $- \frac{1}{{T_{F1} }};$ A_11,12 = $\left( {\frac{1}{{T_{F1} }} + \frac{{T_{{{\text{CR}}1}} }}{{T^{2}_{F1} }}} \right);$ A_12,1 = $- \frac{{X_{1} }}{{b_{1} R_{1} Y_{1} }};$ A_12,12 = $- \frac{{c_{1} }}{{b_{1} }};$ A_12,13 = $\frac{1}{{b_{1} }};$ A_13,1 = $\left( {\frac{{X_{1} }}{{R_{1} Y_{1}^{2} }} - \frac{1}{{R{}_{1}Y_{1} }}} \right);$ A_13,13 = $- \frac{1}{{Y_{1} }};$ A_14,14 = $- \frac{1}{{T_{{{\text{r}}2}} }};$ A_14,15 = $\left( {\frac{{K_{{{\text{t}}2}} }}{{T_{{{\text{R}}2}} }}x_{2} - \frac{{K_{{{\text{r}}2}} K_{{{\text{t}}2}} }}{{T_{{{\text{t}}2}} }}} \right);$ A_14,16 = $\frac{{K_{{{\text{r}}2}} K_{{{\text{t}}2}} }}{{T_{{{\text{t}}2}} }};$ A_15,15 = $- \frac{1}{{T_{{{\text{t}}2}} }};$