Optimal Battery Placement in Power Grid

TL;DR

This paper investigates the optimal placement of batteries in power grids to minimize costs, revealing that network topology, especially the weighted degree, primarily influences placement decisions, and introduces a fast, accurate algorithm for practical use.

Contribution

It provides analytical insights linking topology to optimal battery placement and develops a scalable, efficient algorithm validated by numerical experiments.

Findings

Optimal placement depends mainly on the weighted degree in certain network conditions.

The proposed algorithm is approximately 100 times faster than commercial solvers.

The algorithm maintains high accuracy even when theoretical assumptions are relaxed.

Abstract

We study the optimal placement of an unlimited-capacity battery in power grids under a centralized market model, where the independent system operator (ISO) aims to minimize total generation costs through load shifting. The optimal battery placement is not well understood by the existing literature, especially regarding the influence of network topology on minimizing generation costs. Our work starts with decomposing the Mixed-Integer Linear Programming (MILP) problem into a series of Linear Programming (LP) formulations. For power grids with sufficiently large generation capacity or tree topologies, we derive analytical cost expressions demonstrating that, under reasonable assumptions, the weighted degree is the only topological factor for optimal battery placement. We also discuss the minor impact of higher-order topological conditions on tree-topology networks. To find the localized nature of a single battery's impact, we establish that the relative cost-saving benefit of a single battery decreases as the network scales. Furthermore, we design a low-complexity algorithm for weakly-cyclic networks. Numerical experiments show that our algorithm is not only approximately 100 times faster than commercial solvers but also maintains high accuracy even when some theoretical assumptions are relaxed.