Abstract: Aiming at the strategic bidding of power suppliers and clearing of markets with carbon and green certificate trading, a bi-level algorithm based on value function approximation is proposed. Firstly, a bi-level model is established, aiming to maximize the profit of power suppliers while considering pricing constraints, power flow constraints, and carbon quota constraints. Secondly, a response surface method-based value function approximation technique is proposed, which can transform the bi-level model into a single-layer model without introducing integer variables, enabling rapid computation. Furthermore, the response surface method-based value function approximation technique is improved from the perspective of compactly supported smooth weight functions, which assigns distinct weight factors to different sample points. This addresses the challenge of accurately fitting non-smooth value functions and enhances computational precision. Finally, simulation analysis is used to verify the effectiveness of the proposed algorithm. The simulation results show that the efficiency of the proposed method is more than 3 times that of the traditional bi-level algorithm without loss of calculation accuracy, which provides an effective tool for clearing of markets and the strategic bidding of power suppliers under coupled markets.