With the development of the national unified electricity market, the market scale has gradually increased. Take inter-provincial medium- and long-term power transaction as an example, the number of market participants is over a thousand. The similarity of the bid prices of numerous market participants is likely to lead to multiple purchasing and selling pairs having the same social welfare. As a result, the market clearing problem that maximizes social welfare may have multiple optimal solutions. To ensure the effectiveness and fairness of market clearing, the multi-level objective sequential optimization should be implemented under multiple-solution scenarios. However, the existing methods based on multi-objective optimization cannot balance effectiveness and efficiency. To address this issue, take inter-provincial medium- and long-term power transaction that may have multiple solutions as a research objective, an efficient multi-level objective sequential optimization method is proposed in this paper. The main contributions are illustrated as follows:

First, the market clearing model with multi-level objective sequential optimization is established. Four objective functions are considered according to the industrial practices, including maximizing social welfare, maximizing transaction volume of renewable energy, maximizing total transaction volume, and equally distributing tradable power among purchasing and selling pairs with the same social welfare. Market clearing models considering the aforementioned four objective functions are separately established. The optimal objective functions of the preorder model are used as the operating constraints of the subsequent model to ensure the optimality of the objective functions with high priorities. By sequential solving these four market clearing models, the market clearing effectiveness and fairness can be guaranteed even under multiple-solution scenarios.

Second, the multiple-solution judgment auxiliary optimization model for the market clearing problem is established based on the bound constraints of the optimal solution, according to which the multiple-solution characteristics of market clearing problems can be recognized. The recognized multiple-solution characteristics can provide support for market operators to design the measure for handling multiple-solution scenarios. For instance, more objective functions can be introduced if multiple-solution scenarios cannot be effectively avoided after the sequential optimization of four objective functions. Besides, regarding the computational burden caused by the solution to four market clearing models, the multiple-solution judgment auxiliary optimization model is embedded into the sequential optimization process to simplify the clearing process by avoiding unnecessary optimization.

Third, to meet the calculation efficiency demand, the lossless acceleration method for market clearing based on solution information of the preorder model is proposed. For the market clearing models with multi-level objective functions, the optimal solution of the preorder model is used as the high-quality initial feasible solution of the subsequent model, which can guide the warm-start accelerating process of the subsequent model without the loss of accuracy. For the multiple-solution judgment auxiliary optimization model, the optimal solution of the preorder model is used as the initial feasible solution. Based on this, the termination criterion for the calculation process is established according to the comparison between the initial objective function and the current objective function. In this way, the judgment process can be accelerated without affecting judgment accuracy.

Finally, case studies based on practical inter-provincial medium- and long-term transaction data in China demonstrate that the proposed method can greatly improve the market clearing effect for the subordinate objectives while ensuring the optimality of the primary objective. In addition, benefiting from the proposed model solution acceleration strategy and the sequential optimization process simplification strategy, the market clearing efficiency can be improved by 37 times without the loss of accuracy under the typical scenario.