A method for power suppliers’ optimal cooperative bidding strategies considering network losses

The bidding strategies of power suppliers to maximize their interests is of great importance. The proposed bi-level optimization model with coalitions of power suppliers takes restraint factors into consideration, such as operating cost reduction, potential cooperation, other competitors’ bidding behavior, and network constraints. The upper model describes the coalition relationship between suppliers, and the lower model represents the independent system operator’s optimization without network loss (WNL) or considering network loss (CNL). Then, a novel algorithm, the evolutionary game theory algorithm (EGA) based on a hybrid particle swarm optimization and improved firefly algorithm (HPSOIFA), is proposed to solve the bi-level optimization model. The bidding behavior of the power suppliers in equilibrium with a dynamic power market is encoded as one species, with the EGA automatically predicting a plausible adaptation process for the others. Individual behavior changes are employed by the HPSOIFA to enhance the ability of global exploration and local exploitation. A novel improved firefly algorithm (IFA) is combined with a chaotic sequence theory to escape from the local optimum. In addition, the Shapley value is applied to the profit distribution of power suppliers’ cooperation. The simulation, adopting the standard IEEE-30 bus system, demonstrates the effectiveness of the proposed method for solving the bi-level optimization problem