Harris Hawks-Based Optimization Algorithm for Automatic LFC of the Interconnected Power System Using PD-PI Cascade Control

Abstract

This paper presents a new optimization tool-based population parameter called Harris hawks optimizer (HHO) and its application study to fine-tune the gains of well-designed proportional-derivative proportional-integral (PD-PI) cascade control to suppress the load frequency control (LFC) issues. The HHO based PID and PD-PI controllers are broadly implemented at two models with many circumstances for each model to ensure the effectiveness and the robustness of the proposed scheme at a high load disturbance, nonlinearity, and some critical parameters associated with the interconnected power system. First, a two-area non-reheat power plant is implemented, and the gains of PID and PD-PI controllers are adjusted using the proposed algorithm. In order to introduce extra realistic challenges, the governor-dead band is also modeled to ensure the robustness of the HHO/PD-PI in handling nonlinearity properties. Furthermore, to guarantee the suitability of the proposed HHO/PD-PI, a model with a mixture of power plants is carried out with and without the HVDC link, which is raised for the practical problems of LFC. Simulation results proved that; the proposed techniques HHO/PID and HHO/PD-PI provide superior performance compared to other reported strategies such as DE/PID, TLBO/PID, IGWO/PID, multi-objective/PID, and TLBO/2DOF-PID controllers. Finally, the dynamic investigation has also been completed using the random load pattern in system model-2, which shows the superior performance of HHO/PID and HHO/PD-PI schemes.

Appendices

Appendix 1: Two-area two-unit power plant [15, 17, 22]

$P_{R} = 2000{\text{ MW}};$ $P_{L} = 1000{\text{ MW}};$ $f = 60{\text{ H}}_{{\text{Z}}} ;$ $B_{1} = B_{2} = 0.425 {\text{p}}.{\text{u}}.{\text{ MW}}/{\text{H}}_{{\text{Z}}}$; $R_{1} = R_{2} = 2.4{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.$; $T_{g1} = T_{g2} = 0.08{\text{ s}}$; $T_{t1} = T_{t2} = 0.3 s$; $K_{PS1} = K_{PS2} = 120{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.$; $T_{PS1} = T_{PS2} = 20 {\text{ s}}$; $T_{12} = 0.545 {\text{p}}.{\text{u}}.;{ }a_{12} = - 1.$

Appendix 2: Two-area two-unit with governor dead band [22, 36, 37]

$B_{1} = B_{2} = 0.425 {\text{p}}.{\text{u}}.{\text{ MW}}/{\text{H}}_{{\text{Z}}}$; $R_{1} = R_{2} = 2.4{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.$; $T_{g1} = T_{g2} = 0.2{\text{ s}}$; $T_{t1} = T_{t2} = 0.3 s$;

$K_{PS1} = K_{PS2} = 120{\text{ H}}_{Z} /{\text{p}}.{\text{u}}$; $T_{PS1} = T_{PS2} = 20 {\text{ s}}$; $T_{12} = 0.0707 {\text{p}}.{\text{u}}.;{ }a_{12} = - 1.$

Appendix 3: Two-area six-unit power plant [14, 19, 22]

$B_{1} = B_{2} = 0.4312 {\text{p}}.{\text{u}}.{\text{ MW}}/{\text{H}}_{{\text{Z}}}$; $R_{1} = R_{2} = R_{3} = 2.4{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.$; $T_{sg1} = T_{sg2} = 0.08{\text{ s}}$; $T_{t1} = T_{t2} = 0.3 s$;

$K_{r1} = K_{r2} = 0.3;$ $T_{r1} = T_{r2} = 10 s;$ $K_{PS1} = K_{PS2} = 68.9566{\text{ H}}_{Z} /{\text{p}}.{\text{u}}$; $T_{PS1} = T_{PS2} = 11.49 {\text{ s}}$;

$T_{12} = 0.0433 {\text{p}}.{\text{u}}.;{ }a_{12} = - 1;$ $T_{w1} = T_{w2} = 1{\text{ s}};$ $T_{RS1} = T_{RS2} = 5 {\text{ s}}$; $T_{RH1} = T_{RH2} = 78.75 {\text{ s}}$;

$T_{GH1} = T_{GH2} = 0.2 {\text{ s}}$; $X_{C} = 0.6 s$; $Y_{C} = 1 {\text{s}};$ $c_{g} = 1 s;$ $b_{g} = 0.05 s;$ $T_{F1} = T_{F2} = 0.23 {\text{s}}$; $T_{CD1} = T_{CD2} = 0.2 {\text{s}}$;

$T_{CR1} = T_{CR2} = 0.01 {\text{s}}$; $K_{T} = 0.543478$; $K_{H} = 0.326084$; $K_{G} = 0.130438$; $K_{DC} = 1$; $T_{DC} = 0.2 s$;