Particle Swarm Optimization for Power Dispatch with Pumped Hydro

Recently, a new evolutionary computation technique, known as particle swarm optimization (PSO), has become a candidate for many optimization applications due to its high-performance and flexibility. The PSO technique was developed based on the social behavior of flocking birds and schooling fish when searching for food (Kennedy & Eberhart, 1995). The PSO technique simulates the behavior of individuals in a group to maximize the species survival. Each particle “flies” in a direction that is based on its experience and that of the whole group. Individual particles move stochastically toward the position affected by the present velocity, previous best performance, and the best previous performance of the group. The PSO approach is simple in concept and easily implemented with few coding lines, meaning that many can take advantage of it. Compared with other evolutionary algorithms, the main advantages of PSO are its robustness in controlling parameters and its high computational efficiency (Kennedy & Eberhart, 2001). The PSO technique has been successfully applied in areas such as distribution state estimation (Naka et al., 2003), reactive power dispatch (Zhao et al., 2005), and electromagnetic devices design (Ho et al., 2006). In the previous effort, a PSO approach was developed to solve the capacitor allocation and dispatching problem (Kuo et al., 2005). This chapter introduces a PSO approach for solving the power dispatch with pumped hydro (PDWPH) problem. The PDWPH has been reckoned as a difficult task within the operation planning of a power system. It aims to minimize total fuel costs for a power system while satisfying hydro and thermal constraints (Wood & Wollenberg, 1996). The optimal solution to a PDWPH problem can be obtained via exhaustive enumeration of all pumped hydro and thermal unit combinations at each time period. However, due to the computational burden, the exhaustive enumeration approach is infeasible in real applications. Conventional methods (El-Hawary & Ravindranath, 1992; Jeng et al., 1996; Allan & Roman, 1991; AlAgtash, 2001) for solving such a non-linear, mix-integer, combinatorial optimization problem are generally based on decomposition methods that involve a hydro and a thermal sub-problem. These two sub-problems are usually coordinated by LaGrange multipliers. The optimal generation schedules for pumped hydro and thermal units are then sequentially obtained via repetitive hydro-thermal iterations. A well-recognized difficulty is that solutions to these two sub-problems can oscillate between maximum and minimum generations with slight changes of multipliers (Guan et al., 1994; Chen, 1989). Consequently,