Solving OPF Problems using Biogeography Based and Grey Wolf Optimization Techniques

Introduction

The purpose of an optimal power flow (OPF) function is to schedule the power system control parameters which optimize a certain objective function while satisfying its equality and inequality constraints, power flow equations, system security and equivalent operating limits. The equality constraints are the nodal power balance equations, while the inequality constraints are the limits of all control or state variables. Optimal power flow (OPF) has been widely used for both the operation and planning of a power system (Wang, Murillo-Sanchez & Thomas, 2007). Introduced by Dommel and Tinney (1968) and discussed by Carpentier (1962), the control variables include generator active powers, generator bus voltages, transformer tap ratios and the reactive power generation of shunt compensators. In general, the total production cost is the main objective for optimal power flow problems. However, the other objectives, such as reduction of net-work loss, improvement of the voltage profile and enhancement of the voltage stability can also be included, as it has been progressively becoming easy to formulate and solve complex large-scaled problems with the advancement in computing technologies. OPF is a large scale, non-linear, non-convex and multimodal optimization problem with continuous and discrete control variables. The existence of non-linear power flow constraints makes the problem non-convex even in the absence of discrete control variables.

A wide variety of classical optimization techniques have been applied in solving the OPF problems considering a single objective function, such as nonlinear programming, quadratic programming, linear programming, Newton-based techniques (Huneault & Galiana 1991; Momoh & El-Hawary, 1999) sequential unconstrained minimization technique, interior point methods and the parametric method but unfortunately these methods are infeasible in practical systems because of non-linear characteristics like valve point effects. Hence, it becomes essential to develop optimization techniques which are capable of overcoming these drawbacks and handling such difficulties. Optimization problems have been solved by many population-based optimization techniques in the recent past. These techniques have been successfully applied to non-convex, non-smooth and non-differentiable optimization problems. Some of the population-based optimization methods are genetic algorithms (Gaing & Huang, 2004; Lai, Ma & Zhao, 1997; Paranjothi & Anburaja, 2002; Vennila & Sumi, 2013), simulated annealing (Rao & Pavez, 2001), particle swarm optimization (PSO) (Abido, 2002; Gaing & Huang, 2004; Zhao & Cao, 2004), evolutionary programming (Yuryevich & Wong, 1999), hybrid evolutionary programming (HEP) (Swain & Morris, 2000), chaotic ant swarm optimization (CASO) (Swain & Morris, 2000), Bacteria foraging optimization (BFO) (Ghosal, Chatterjee & Mukherjee, 2009), BAT Search Algorithm (Rao & Kumar, 2015), Quasi-Oppositional Biogeography-Based Optimization (Roy & Mandal, 2012), Hybridization of Biogeography Based Optimization (HBBO) (Roy & Mandal, 2013), artificial bee colony optimization (Dutta, Roy & Nandi, 2014), Soft Switch in technique (Aiswariya & Dhanasekaran, 2014) and other novel approaches (Arya, Mathur & Gupta, 2012).