A novel two-swarm based PSO search strategy for optimal short-term hydro-thermal generation scheduling

The optimal power generation of hydro-thermal systems to minimize total operating costs is one of the most important targets in short-term hydro-thermal scheduling (STHS) and its evaluation is complicated by several complex and interconnected equality and inequality constraints. To solve this type of problem, it is necessary to develop on one side a model of the system characterized by a fair and proper treatment of all the equality and inequality constraints and on the other a performing optimization algorithm simultaneously considering not only the minimization of the operating costs but also the feasibility of the proposed solution. The paper presents a novel two-swarm based PSO (Particle Swarm Optimization) search strategy developed for solving these kinds of STHS problems. To exclude constraint violations as far as possible during the optimization process, first a complete inequality and equality constraints treatment of the hydrothermal systems was developed, combined with a fair spillage modelling. Then, a recent evolution of the particle swarm optimization algorithm ASD-PSO (Adaptive Search Diversification-Particle Swarm Optimization) was modified, introducing a secondary swarm able to exploit the potential contribution of the infeasible solutions. Within the context of this new strategy, two different swarms were designed, each characterized by a different treatment of the infeasible solutions, and each interacting properly with the other at every iteration. The primary swarm dealt with feasible solutions, resulting from the manipulation of constraint repairing strategies, and with a limited number of infeasible solutions whose potential contribution in the search process was not wasted out but it was properly weighted on the basis of the violation degree. The secondary swarm involved less manipulated solutions that were subjected only to one repair strategy in order to foster the exploration capability of the swarm. At each iteration, the two swarms independently update their position and velocity but partially interact with each other to obtain mutual advantages from their different peculiarities. This novel two-swarm based strategy for solving short-term hydro-thermal scheduling (STHS) problems was validated by comparing the achieved performance in terms of accuracy with those of several algorithms proposed in literature. Six different test cases, widely analysed in the literature and characterized by increasing complexity, were considered. In all the considered Test Cases, the algorithm performed very well with minimum total fuel costs that were still lower than all the feasible solutions proposed in the literature, and that satisfied all the equality and inequality constraints of the system.