Two-stage coevolutionary constrained multi-objective optimization algorithm for solving optimal power flow problems with wind power and FACTS devices

As a large amount of wind energy is integrated into the grid, the randomness it brings poses a challenge to modern power systems. The application of Flexible AC Transmission Systems (FACTS) in the grid is becoming more and more common, and it is necessary to consider how to choose suitable equipment in the appropriate locations. In this paper, a multi-objective optimal power flow (MOOPF) model with wind farms and FACTS devices is established. The Weibull probability density function is used to establish the wind speed model, and the cost problem brought by wind power is considered. The locations and ratings of thyristor-controlled series compensators, thyristor-controlled phase shifters, and static VAR compensators are added to the system as control variables. In addition, the constraints on the prohibited operating areas of thermal power generators and the valve point effect are also considered. Coevolutionary constrained multi-objective optimization algorithm (CCMO) is an advanced technology, and this paper improves it and names it two-stage coevolutionary constrained multi-objective optimization algorithm (TSCCMO). The proposed algorithm uses the constraint violation value as an additional objective function in the sub-population environmental selection process, and integrates a neighborhood selection strategy into the mating selection process. The population evolution process is divided into two stages, in the first stage the two populations cooperate weakly, and in the second stage the two populations will have strong cooperation. TSCCMO is used to solve this complex constrained MOOPF problem, and its results are compared and analyzed with CCMO, NSGA–II–CDP, C3M, and PPS. The comprehensive performance of TSCCMO is the best among the 6 cases.