A Distributionally Robust Bi-level Optimization Model for Power Market Considering Source–Load Interaction and Carbon Permit Allocation

To control the uncertain risk of source–load interaction, this paper proposes a distributionally robust equilinear model of the power market clearing considering the carbon permit allocation. Firstly, a novel bi-level market-clearing framework that considers the allocation of carbon emission rights is proposed to coordinate energy trading between system operators and load aggregators in the market trading mechanism. Then, based on the conditional value at risk (CVaR) and distributionally robust (DR) theories, a risk avoidance expression and its equivalent convex form for the power constraint under the load aggregators are designed to address the risk of load uncertainty in load aggregators, revealing the underlying mechanism of risk avoidance under the DR CVaR power constraint. By leveraging the characteristics of a normal distribution and the Karush–Kuhn–Tucker condition, the proposed nonlinear bi-level DR CVaR market-clearing model is transformed into an efficient single-level linear model, resulting in reduced model solving difficulty, computational time, and resource consumption. Finally, the simulation of the case shows that the DR CVaR market-clearing model and the equilinear model can realize efficient allocation and complementary optimization of flexible resources in the market environment and improve the operation economy and stability of the power system.