Exact relaxation of complementary constraints for optimal bidding strategy for electric vehicle aggregators

Abstract

Abstract This paper concentrates on the optimal bidding strategy of a plug‐in electric vehicle aggregator (PEVA) using indirect load control in the day‐ahead energy market, which is generally formulated as bilevel programming. However, this bilevel model is nonconvex and intractable due to the complementary constraints imposed to preclude plug‐in electric vehicles (PEVs) from simultaneously charging and discharging. To handle this problem, an exact relaxation method is first proposed to remove the complementary constraints of the PEVs' charging and discharging behaviours. To further reduce the complexity of the model, a method is proposed for the exact relaxation of the complementary slackness of Karush‐Kuhn‐Tucker (KKT) conditions in the reformulated mathematical program with equilibrium constraints. By removing the complementary constraints, the relaxation methods can effectively reduce the complexity of the model and improve the computational performance. The results of the case study demonstrate the exactness and efficiency of the proposed relaxation methods. Specifically, in the test case with 1000 PEVs and 20 scenarios, 220,000 constraints are removed by the two exact relaxation methods. Moreover, using the second exact relaxation method, in the test case with 400 PEVs and 60 scenarios and the case with 1000 PEVs and 60 scenarios, the computational time drops by 30.3% and 23.3%, respectively.