Load frequency control with moth-flame optimizer algorithm tuned 2-DOF-PID controller of the interconnected unequal three area power system with and without non-linearity

Abstract

This study proposes a two-degree-of-freedom PID controller based on the moth flame optimizer (MFO) algorithm for the load frequency management issue in a three-area unequal linked power system. Load frequency control is use to control the frequency of the grid to its scheduled value in the power system. A objective function is formulated in the LFC which will be utilized by the optimization techniques for the tuning of the parameter of the controller. The proposed controller’s efficiency is tested by contrasting it’s response with outcome of PID and fractional order PID (FOPID) for various scenario. The suggested controller’s parameters were concurrently tuned using a meta-heuristic approach called moth flam optimizer (MFO). The simulation result with MFO appraised with other optimizer like SCA (Sine–cosine algorithm), SSA (Slap swarm algorithm), PSO (Particle swarm optimization algorithm), ALO (Ant-lion optimization algorithm) for the various scenarios. The superiority of proposed techniques is further examine by including system non-linearity like governor Dead Band, generation Rate Constraint, and communication delay. Furthermore, to validate the supremacy of the suggested method, the statistical analysis with the help of Wilcoxon Sign Rank Test has been performed on 20 independent runs. The result gained through broad simulation states that the proposed tactic undoubtedly intensify the system performance compare to prevailing controllers and optimization technique in the existing literature.

Appendices

Appendix A

Three area unequal power system

$$\begin{aligned} {\text{K}}_{{{\text{p1}}}} = & {1}0{5};{\text{ K}}_{{{\text{p2}}}} = {1}00;{\text{ K}}_{{{\text{p3}}}} = {12}0;{\text{T}}_{{{\text{ps1}}}} = {2}0;_{ } {\text{T}}_{{{\text{PS2}}}} = {22};{\text{ T}}_{{{\text{ps3}}}} = {2}0;{\text{T}}_{{{\text{g1}}}} = 0.{4};{\text{ T}}_{{{\text{g2}}}} = 0.{3};_{{}} {\text{T}}_{{{\text{g3}}}} = 0.{3}; \\ {\text{B}}_{{2}} = & 0.{326};{\text{ B}}_{{1}} = 0.{326};{\text{ B}}_{{3}} = 0.{425};{\text{ Tt1}} = 0.{\text{6 Tt2}} = 0.{5};{\text{ Tt3}} = 0.{5};{\text{R}}_{{1}} = {2}.{5};{\text{ R}}_{{2}} = {3};{\text{ R}}_{{3}} = {2}.{5}; \\ {\text{T}}_{{{12}}} = & {\text{T}}_{{{23}}} = {\text{T}}_{{{31}}} = 0.0{8};{\text{f }} = {5}0{\text{ Hz}} \\ \end{aligned}$$