The Welfare Gap of Strategic Storage: Universal Bounds and Price Non-Linearity

TL;DR

This paper analyzes the efficiency loss in electricity storage markets, establishing bounds on welfare gains for linear and monomial price functions, and highlighting potential inefficiencies with convex prices.

Contribution

It provides universal bounds on welfare efficiency loss for storage under linear and monomial prices, and shows unbounded loss with convex prices.

Findings

Efficiency ratio bounded by 4/3 for linear prices

Efficiency ratio bounded by 2 for monomial prices

Unbounded efficiency loss for convex price functions

Abstract

This paper studies the efficiency of battery storage operations in electricity markets by comparing the social welfare gain achieved by a central planner to that of a decentralized profit-maximizing operator. The problem is formulated in a generalized continuous-time stochastic setting, where the battery follows an adaptive, non-anticipating policy subject to periodicity and other constraints. We quantify the efficiency loss by bounding the ratio of the optimal welfare gain to the gain under profit maximization. First, for linear price functions, we prove that this ratio is tightly bounded by $4/3$. We show that this bound is a structural invariant: it is robust to arbitrary stochastic demand processes and accommodates general convex operational constraints. Second, we demonstrate that the efficiency loss can be unbounded for general convex price functions, implying that convexity alone is insufficient to guarantee market efficiency. Finally, to bridge these regimes, we analyze monomial price functions, where the degree controls the curvature. For specific discrete demand scenarios, we demonstrate that the ratio is bounded by $2$, independent of the degree.