Abstract—This paper proposes a robust and strong algorithm to solve Optimal Power Flow (OPF) with valve-point effect in power systems involving a Unified Power Flow Controller (UPFC). In a power system, installing the UPFC can improve power transfer capability, transient stability, and system reliability, reduce loss in the transmission network and the fuel cost of generators. In order to apply UPFC in OPF problem, a mathematical model needs to be set for it. In this paper a new model based on the Injection Power Model (IPM) is presented. Due to the nonlinearity of OPF problem, it is essential to use an exact and strong method to solve it. In recent years, evolutionary and heuristic advantages of algorithms in terms of the modeling capability and search power lead to their higher application in the complicate problem like OPF. This paper presents a modified shuffle frog-leaping algorithm (MSLFA) to solve the OPF problem. The MSFLA has a flexible and well balanced mechanism in order to enhance and adapt to global and local exploration abilities. Simulation results on the modified IEEE 30-bus and 5-bus test systems indicate that the proposed MSLFA algorithm approach can obtain better solutions than other optimization algorithms. Index Terms—Evolutionary algorithm, FACTS devices, Optimal Power flow, SFLA , UPFC. I. INTRODUCTION Flexible AC transmission system (FACTS) devices are integrated in power systems to control power flow, increase transmission line capability to their thermal limit, and to improve the security of the transmission systems [1,2]. Power electronics were applied to FACTS controllers for rapid response and improved controllability [3,4]. FACTS devices could also be used to minimize the total generator fuel cost when the power flow controls are not needed. Along a variety of FACTS devices, UPFC is a one of the most versatile member of FACTS. In this paper, UPFC is applied in the OPF problem by a new model based on the IPM model. The UPFC offers a unique combination of fast shunt and series compensations and provides a flexible power system control. Therefore, it can be utilized in the power system to control line active and reactive power, achieve maximum power transfer capability, stabilize system, reduce total generation cost associated with out-of-merit order, significantly improve power system reliability, and help the system operate with more security[5,6]. A mathematical Manuscipt recived July 14, 2011; revised August 15, 2011. Authors are with the Shiraz University of Technology, Shiraz, Iran, (corresponding author to provide phone: +987117264103; fax: +987117353502; e-mail: nayeri@ sutech.ac.ir). model is required for investigating the effects of UPFC on power system operation. Several models have been suggested for UPFC device in steady-state power flow analysis [7-10]. Some authors modeled this device with modifications of Jacobian matrix [1, 11]. Mihalic [12] introduces a steady-state UPFC model based on a single, ideal, and series voltage source. They used a mathematical decomposition method and a linearized network model (DC load flow). Ge and Chung [13,14] proposed a method to include the power flow control need of UPFC in the OPF, based on linear programming. Kalyan proposed a steady state model suggested in [15] which is based on one ideal series voltage source and one ideal shunt current source. Ambriz-Perez [16, 17] utilizes two ideal voltage sources, one in series and one in parallel, to develop a UPFC steady state model. In the above methods, Jacobian matrix must be calculated in each iterate and it speeds down the calculation greatly. To solve this problem, in this paper a new way of modeling UPFC is presented. In this model Jacobian matrix is constant and needs to be calculated only once in the entire optimization process which speeds up the calculation to a great extent. OPF control is used to minimize the total generator fuel cost subject to power balance constraint, real and reactive power generation limits, voltage limits and transmission line limits. The development of evolutionary algorithms over the last decade has enabled researchers to consider these issues in a better fashion. The advantages of evolutionary algorithms in terms of the modeling capability and search power have encouraged their application to the OPF problem in power systems. Many classical techniques have been reported in the literature [18-20] to solve the OPF problem such as nonlinear programming (NLP), quadratic programming (QP) and linear programming (LP). The gradient based methods [4,20] and Newton methods[15] suffer from the difficulty in handling inequality constraints. Moreover, these NLP and QP methods rely on convexity to obtain the global optimum solution and are forced to simplify relationships in order to ensure convexity. To apply linear programming, input output function is to be expressed as a set of linear functions, which may lead to loss of accuracy. Moreover they do not guarantee converge to the global optimum of the general non convex OPF problem. These days evolutionary algorithms have been suggested to overcome the mentioned difficulties of classical methods. The SLFA algorithm is accurate and general to solve the complicated optimization problems. It can jump from the current searching point into the effective area directly by the Application of Modified Shuffled Frog Leaping Algorithm on Optimal Power Flow Incorporating Unified Power Flow Controller Majid Nayeripour, Mohammad Rasoul Narimani, and Taher Niknam International Journal of Modeling and Optimization, Vol. 1, No. 3, August 2011 191