A small-population based parallel differential evolution algorithm for short-term hydrothermal scheduling problem considering power flow constraints

Short-term optimal hydrothermal scheduling plays one of the most important roles in the modern power system plan and operation. The problem aims at minimizing the total fuel cost of the thermal units while satisfying various constraints such as power balance, water balance and other constraints on thermal units as well as hydro units. Except for the above various constraints, transmission network topology and valve point effects are also introduced into the mathematical optimizing model of the short-term hydrothermal scheduling (STHS) problem. Then a small-population based parallel differential evolution approach is proposed to solve the STHS problem considering power flow constraints. In the proposed approach, a large population is divided into several subpopulations each with a small population size and several parallel running processes of one or more CPUs are performed synchronously each evolving a certain subpopulation and searching for the optimal solution independently. Two different methods are employed in the proposed parallel DE approach in order to avoid low diversity of the small population in each process. One is implemented through the small population itself and the other through the communication mechanism among different running processes. Four constraint handling rules as well as a lead operation are proposed to enhance the feasibility of solutions. Numerical results for two well-known sample test systems are presented to demonstrate the capabilities of the proposed parallel DE algorithm to generate optimal solutions of STHS problem. Two other test systems with transmission networks of standard IEEE 9-bus and IEEE 39-bus are also employed to test the effectiveness of the proposed parallel DE algorithm. The results demonstrate the superiority of the proposed algorithm.