Research on the design and optimization model of capacity market clearing mechanism based on lagrange multiplier method

Abstract

The integration of renewable energy sources and unpredictable demand has increased the complexity of electricity markets, challenging traditional capacity market-clearing models that restrict bidding to non-decreasing curves. This study proposes that allowing both non-decreasing and non-increasing bidding strategies enhances market flexibility and efficiency. To validate this, a hybrid optimization algorithm Lagrange Multiplier-based Dynamic Beetle Antenna Swarm Optimization (LM-DBASO) is developed. The capacity market clearing problem is formulated as a nonlinear, large-scale, multi-objective optimization task incorporating efficiency, reliability, and fairness. A weighted-sum scalarization method enables tractability, with priorities embedded into a single objective function. LM method ensures constraint satisfaction, while the DBASO component provides adaptive global search. Unlike penalty-based methods, LM-DBASO maintains feasibility throughout the search process. The model is implemented in PyTorch for scalability and computational efficiency. A game-theoretic perspective approximates Nash equilibrium through iterative convergence, ensuring that no generator can unilaterally improve its outcome. Simulation results demonstrate the model's effectiveness, achieving an efficiency ratio of 98%, electricity conception ratio of 99%, and system security ratio of 95%. The proposed approach improves bidding rationality, accelerates market clearing, and enhances societal welfare, making LM-DBASO a robust solution for modern electricity market challenges.