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

TL;DR

This paper introduces a regularized MIP model for energy storage system optimization that ensures realistic solutions and efficiently solves complex trilevel interdiction problems in power systems.

Contribution

It develops a regularized MIP model with zero integrality gap, enabling accurate and efficient solutions for ESS optimization and complex network interdiction problems.

Findings

Regularized MIP model admits zero integrality gap.

Model provides near-optimal solutions for ESS OPF.

Enables solving intractable trilevel interdiction problems.

Abstract

Incorporating energy storage systems (ESS) into power systems has been studied in many recent works, where binary variables are often introduced to model the complementary nature of battery charging and discharging. A conventional approach for these ESS 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 ESS optimal power flow (OPF) problem. 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 ESS OPF problem, thereby providing a valid and tight upper bound for the ESS OPF problem. 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.