Differential Evolution And Its Application On The Optimal Scheduling Of Electrical Power System

Similar to genetic algorithm, differential evolution algorithm is based on population iteration. The swarm intelligence, which is obtained by means of the cooperation and competition of the population's individuals, directs the process of the optimization. In essence, the next generation population is generated by the difference based mutation operator and one-to-one competitive strategy for survival and at last the population will include or be adjacent to the optimal solution. As a novel evolutionary computing technique, differential evolution is simple, effective and easy to implement. The differential evolution algorithm also has powerful ability to search for the optimal solution. Differential evolution algorithm has become a new research hot point in optimization computation now, while the theory of the algorithm is still in initial stages of research.The in-depth research of differential evolution and its application on the optimization scheduling of electrical power systems is made. During the process of mathematical modeling of differential evolution, a mathematical description of the basic conception of differential evolution algorithm is given. The concepts of the individual state, population state and population state space are defined. The process of the population state transition has been proved to be a Markov chain process and the Markov chain model of differential evolution is proposed. The theory analysis of the differential evolution has been completed, which demonstrates that the differential evolution algorithm is not able to guarantee the global convergence. The research of different variants and parameter setting, which can influence the performance of differential evolution, has been done.During the evolution process of differential evolution algorithm, good solutions are generated and the'survival of the fittest'theory of Darwin is employed to select the better solutions, which results in failures of the abandoned individual's effective component and the reduction of population diversity. Thus the differential evolution algorithm is not able to explore new space and traps in local optima. So weighting space exploration and exploitation is employed for improving the differential evolution algorithm to enhance the convergence speed and solution quality. In this paper, two novel improved differential evolution algorithms are proposed, in which the scale and crossover factors of the differential evolution are adaptively modified by the information process mechanism of the biological immune system, which can improve the performance of differential evolution algorithm. The first one is the self-adaptive differential evolution algorithm based on the gaussian disturbances and immune system theory. In the optimizing process gaussian disturbance is employed to increase the variety of the individual, which can make the algorithm avoid trapping into the local optima and improve its performance. The second one is the self-adaptive differential evolution algorithm based on the quadratic approximation operator and immune system theory. The quadratic approximation operator is employed for local search to improve the exploitation performance.Dynamic economic emission dispatch and short-term combined economic emission scheduling of hydrothermal power systems with cascaded reservoirs are of non-linear optimization problems. They represent the characteristics of multi-objective, high dimensions and constraints. So the traditional methods are no longer fit for solving these optimization problems. In this paper, a price penalty factor approach is utilized here to convert the bi-objective problems into single objective ones. In order to handle constraints effectively, heuristic rules are proposed to handle ramp rate constraints and water dynamic balance constraints, heuristic strategies based on priority list are employed to handle active power balance constraints, and the feasibility-based selection rules are developed to handle the reservoir storage volumes constraints. The heuristic strategies also can increase the variety of the individual and extend the search scope. The thermal unit with the lower average full-load cost will have the higher priority to dispatch more generation power in the heuristic strategies based on priority list, so that the even better scheduling solutions can be obtained. At last, the differential evolution algorithm is improved to enhance the search ability and improve the solution quality.In the end, the promising research and detail work are discussed, which mainly include the theory analysis of the population topology structure of the differential evolution, the way to employ the search space information available in the search process to adaptively search for optima and improve the differential evolution to solve the different electrical power dispatch problems to obtain the optimal scheduling solutions.