Moth-Flame Algorithm for TCSC- and SMES-Based Controller Design in Automatic Generation Control of a Two-Area Multi-unit Hydro-power System

Abstract

An analysis on automatic generation control (AGC) performance of an interconnected two-area hydro–hydro-power system model is presented in this paper subjected to dynamic control of damped oscillations in the presence of thyristor-controlled series compensation (TCSC) and the superconducting magnetic energy storage (SMES) unit. In real time, the load profile characteristics are un-deterministic in nature. Therefore, the current article studies a diverse prospective of area load profiles [such as step load perturbation (SLP), random SLP and sinusoidal load perturbation] in view of AGC performance analysis. The present work is to improve the dynamic responses and to pursue their significances in damping oscillation after the addition of a fast-acting TCSC (as a damping controller) in area-1, whereas SMES unit is installed in area-2 (to provide large values of energy instantaneously). In the present prospect, a new control strategy based on Taylor theorem is implemented to modify the TCSC controller as well as the two-stage phase-compensating blocks are cascaded to both the TCSC and the SMES to improve the phase lag of the system. In this paper, a nature-inspired optimization paradigm [called moth-flame optimization (MFO) algorithm] is utilized to design the controller gains. Additionally, the robustness of the designed controller is investigated in the event of loaded condition and model parameter uncertainties through sensitivity analysis. Analytically, eigenvalues, performance indices values and transient details are presented in support of the designed MFO–TCSC–SMES controller. The obtained simulation results are compared to genetic algorithm (GA)-based designed GA–TCSC–SMES controller to show the optimizing performance of the MFO algorithm in the controller design. The simulation results showed that after the addition of a TCSC–SMES unit in the studied power system model, in addition to eliminating damped oscillations, the settling times of frequency and tie-line power flow are considerably reduced.

Appendix

1.1 Nominal Data of the Studied Two-Area Hydro–Hydro-Power System Model (Kundur 2008)

$T_{gi} = 0.2$ s, $T_{ri} = 5.0\,{\text{s}}$, $R_{ti} = 0.38$, $H = 3.0$ s, $D_{i} = 1.0$, $T_{w} = 1.0$ s, $R_{i} = 0.05$ Hz/p.u. MW.

1.2 Data for TCSC Controller

GA–TCSC–SMES [Studied]: $K_{\text{TCSC}} = 0.1565$, $T_{\text{TCSC}} = 0.1782$ s, $T_{1} = 0.1464$ s, $T_{3} = 0.1782$ s.

MFO–TCSC–SMES [Proposed]: $K_{\text{TCSC}} = 0.0128$, $T_{\text{TCSC}} = 0.7186$ s, $T_{1} = 0.0254$ s, $T_{3} = 0.7688$ s.

1.3 Data for SMES Controller

GA–TCSC–SMES [Studied]: $K_{\text{SMES}} = 0.1433$, $T_{\text{SMES}} = 0.1534$ s, $T_{5} = 0.0305$ s, $T_{7} = 0.0438$ s.

MFO–TCSC–SMES [Proposed]: $K_{\text{SMES}} = 0.0436$, $T_{\text{SMES}} = 0.7689$ s, $T_{5} = 0.0039$ s, $T_{7} = 0.5144$ s.

1.4 Parameters of GA

Number of parameters depends on problem variables (AGC configuration), number of bits = (number of parameters)*8, population size = 50, maximum number of iteration cycles = 100, mutation rate = 0.04, crossover rate = 80%.