The formulation of the optimal strategies for the electricity producers based on the particle swarm optimization algorithm

In competitive electricity markets, the producer as a market participant strives to find the optimal supply function with the objective of maximizing his/her producer surplus in the market clearing. The model of the producer surplus maximization is a bilevel mathematical programming problem within which the market clearing is taken into account. By using the deterministic approaches, it is difficult to obtain the global solution of the bilevel optimization problem, even for a single hourly market clearing. This is due to the fact that the objective function of such a problem is not concave, and there are nonlinear complementarity terms introduced by using the KKT conditions to represent the market clearing. When the bilevel optimization problem is modified to consider multiple hourly market clearings, such as to maximize the total producer surplus in one day, solving such a problem is almost intractable. A heuristic approach should be another option. For its simplicity and immunity to the local optimum, the particle swarm optimization (PSO) algorithm is employed in this paper to find the optimal supply function of the electricity producer. Based on the IEEE 30-bus test system, different simulation cases with respect to a single hourly market clearing and a daily market clearing are tested to show the efficiency and robustness of the PSO algorithm. In addition, the parameterization techniques used in formulating the optimal supply function are analyzed based on the simulation results.