Two-Stage Bi-Level Multi-Objective Optimization Model for Equilibrium Analysis of Electricity and Carbon Markets

Under the influence of the carbon market, the coupling between the medium- and long-term (MLT) market and the spot market becomes increasingly complex. Generation companies (Gencos) face high-dimensional decision-making problems, leading to diverse market equilibrium outcomes. To address this issue, a two-stage bi-level modeling framework is established. In the upper level, the bidding strategies of Gencos are modeled. In the lower level, the electricity and carbon markets clearing are modeled in two stages. The MLT market is cleared first, and its clearing results are passed to the spot market and carbon market clearing models. To solve the model, the diagonalization method (DM) algorithm is employed. Finally, based on the cases of physical delivery and financial delivery, different carbon reduction targets and new energy output scenarios are analyzed. The results show that, compared to financial delivery, transitional delivery can lower market electricity prices and reduce the impact of new energy output fluctuations on the market. However, it also reduces the revenue of Gencos. The carbon reduction cost is on average 25.34% higher than under financial delivery.