Regularized MIP Model for Integrating Energy Storage Systems and Its Application for Solving a Trilevel Interdiction Problem

In modeling battery energy storage systems (BESS) in power systems, binary variables are used to represent the complementary nature of charging and discharging. A conventional approach for these BESS optimization problems is to relax binary variables and convert the problem into a linear program. However, such linear programming relaxation models can yield unrealistic fractional solutions, such as simultaneous charging and discharging. In this paper, we develop a regularized mixed-integer programming (MIP) model for the optimal power flow (OPF) problem with BESS. We prove that, under mild conditions, the proposed regularized model admits a zero integrality gap with its linear programming relaxation; hence, it can be solved efficiently. By studying the properties of the regularized MIP model, we show that its optimal solution is also near optimal to the original OPF problem with BESS, thereby providing a valid and tight upper bound for the OPF problem with BESS. The use of the regularized MIP model allows us to solve a trilevel min - max - min network contingency problem, which is otherwise intractable to solve.