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This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.
Alidoust et al. (Tue,) studied this question.