A fuzzy-based non-dominated sorting genetic algorithm-II for joint energy and reserves market clearing

In this paper, market clearing of joint energy and reserves auctions is framed as a multi-objective mathematical programming (MMP) to simultaneously consider the economic and security objectives. Social welfare maximization, the minimization of lines overload and voltage deviation as well as loadability limit maximization are competitive objectives of the proposed market clearing framework. Traditional MMP methods such as direction scalarization and $$\varepsilon $$ε-constraint methods scalarize the objective vector into a single objective. Those cases are time-consuming and require a number of runs equal to the number of desired efficient solutions. In this paper, a fuzzy-based non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to find the optimal schedule of the units energy and reserves. In the proposed method, to improve the performance of NSGA-II, a fuzzy inference system is employed to dynamically set the parameters of NSGA-II ($$P_\mathrm{c}$$Pc and $$P_\mathrm{m})$$Pm). Results of testing the proposed multi-objective market clearing method on the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS) are presented and compared with the direction scalarization, the $$\varepsilon $$ε-constraint and weighted sum methods from efficiency, diversity and computational burden requirement points of view. These comparisons confirm the efficiency of the developed method.