This paper describes a modified Particle Swarm Optimization (PSO) method called Fitness Distance Ratio (FDR) PSO to solve the Optimal Power Flow (OPF) problem with ramp rate limits of the generators. To avoid premature convergence of the conventional PSO, a velocity updation has been carried out to improve its convergence performance. The proposed method is tested on 5-unit, 10-bus test system and 39 bus New England system. To validate the effectiveness of the proposed method, the OPF results are compared with other optimization methods. Transient stability limit of the generators are also incorporated in the formulation of OPF problem. Wheeling transactions and contingency analysis are also carried out on the New England test system and the system stability is checked. A 24-hour load curve is considered for the same system and transient stability constrained OPF solution is obtained through FDR PSO method and the results are presented.

Nowadays, power system planners and operators often use Optimal Power Flow (OPF) as a powerful assistant tool in both planning and operating stages. So, researchers have formulated the OPF problem considering some practical constraints. OPF problem is aimed at optimizing the operating cost of the power system while satisfying various system operating constraints. Practically, the objective function of the OPF problem is non-convex in nature. Hence, the artificial intelligence methods have been recently proposed to solve the OPF problem.

Abido (2002a) applied the Tabu Search (TS) algorithm to solve the OPF problem and demonstrated it on IEEE 30-bus system. The TS algorithm is a derivative free optimization technique used to solve the non-convex fuel cost functions. Roa-Sepulveda and Pavez-Lazo (2003) presented Simulated Annealing (SA) optimization algorithm to solve the OPF problem and the convergence characteristics have been demonstrated for different number of generations. Gnanadass et al. (2005) proposed improved Evolutionary Programming (EP) method to solve the OPF problem with ramp rate limits and non-smooth fuel cost functions. They proposed an EP algorithm in which the mutation is changing non-linearly with respect to the number of generations to avoid premature convergence. Recently, Ongsakul and Tantimaporn (2006) proposed an Improved Evolutionary Programming (IEP) algorithm to solve the OPF problem with non-convex fuel cost curves. In the IEP, two different types of mutations are used to generate the subpopulation and is tested on IEEE 30-bus system.

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