Multi-verse Optimization Algorithm for LFC of Power System with Imposed Nonlinearities Using Three-Degree-of-Freedom PID Controller

Abstract

The dynamic controller design problem for the load frequency control (LFC) of a realistic interconnected power system model is being studied in this paper. In view of this, the design and LFC performance analysis of three-degree-of-freedom proportional–integral–derivative (3DOF-PID) controller, intended by the proposed multi-verse optimization (MVO) algorithm, is presented. The simplicity of the structure and acceptability of the responses of the well-known proportional–integral–derivative controller, inherently, forces the higher DOF to be employed. The proposed MVO algorithm efficiently balances exploration and exploitation of the search space that yields promising solutions over the course of iteration. In response to this, it offers superior results as constrained optimization task. The investigated test system is a four-area configuration having each area composed of identical reheated thermal unit. The considered system is also installed with interline power flow controller in one of the areas. In the aforesaid system, the important physical constraints like time delay, governor deadband, boiler dynamics and generation rate constraint are also imposed. The performance of MVO-based design controller is compared to genetic algorithm-based one. The presented simulation results reveal the dominance of MVO-based 3DOF-PID controller in terms of settling time, peak deviation and magnitude of oscillations with the other investigated controller types. Additionally, sensitivity of the MVO-based designed 3DOF-PID controller from nominal condition to under loading and model parametric uncertainties is studied. This study reveals that the designed controller produces almost similar responses.

Appendix

Nominal data of the studied four-area test system (Sahu et al. 2015; Chandrakala and Balamurugan 2016).

System configuration:

$f = 60$ Hz, $P_{r1} = P_{r2} = P_{r3} = P_{r4} = 2000$ MW, total area load = 1000 MW, base rating = 2000 MW, initial loading = 50%.

System parameters:

$a_{ij} = - 1$, $B_{i} = 0.425$ p.u.MW/Hz, $K_{ri} = 0.5$, $K_{pi} = 120$ Hz/p.u.MW, $R_{ti} = 2.4$ Hz/p.u.MW, $T_{ij} = 0.086$, $T_{gi} = 0.08$ s, $T_{pi} = 20.0$ s, $T_{ri} = 10$ s, $T_{ti} = 0.3$ s.