An Efficient Affine Arithmetic-Based Optimal Dispatch Method for Active Distribution Networks With Uncertainties of Electric Vehicles

Affine Arithmetic (AA) is an effective interval analysis method for addressing uncertainties in power systems. However, previous research on AA-based optimization problems has struggled to accurately capture the uncertainties associated with electric vehicles (EVs) and the cumulative impact of uncertainties on energy storage systems (ESSs). Moreover, the reformulated AA model presents a significant computational challenge due to the high number of variables and constraints. This study proposes an efficient AA-based economic dispatch (AAED) method for active distribution networks incorporating EVs and ESSs while accounting for uncertainties. Specifically, an EV charging load-interval (CLI) model is developed to effectively capture the randomness of plug-in/plug-out times and initial/target energy. A confidence level is defined to prevent excessive conservatism in the CLI model. An ESS model is also formulated within the AA domain to address the cumulative impact of persistent uncertainty, ensuring an accurate state of charge monitoring. To enhance the computational efficiency of the AAED model without sacrificing accuracy, a fast-solving strategy is introduced. This strategy involves eliminating many state variables and constraints and replacing them with derived analytical partial deviation formulations that map the relationship between state and decision variables. Simulation results confirm the effectiveness of the proposed model and method.