Statistical Economies of Scale in Battery Sharing

TL;DR

This paper demonstrates that sharing storage among wind generators over large distances yields significant economies of scale, with shared batteries providing the same reliability as individual batteries when grid spacing exceeds 500 km.

Contribution

It introduces a mathematical model showing that statistical independence of generators' net processes leads to invariant economies of scale in shared batteries at large grid spacings.

Findings

Economies of scale grow with grid spacing, becoming dramatic beyond 500 km.

Shared batteries can match the reliability of individual batteries regardless of the number of generators.

Statistical independence of net generation processes underpins the observed economies.

Abstract

The goal of this paper is to shed light on the statistical economies of scale achievable from sharing of storage between renewable generators. We conduct an extensive study using real world wind data from a grid of equispaced wind generators sharing a common battery. We assume each generator is contracted to meet a certain demand profile to a prescribed level of reliability. We find that the statistical diversity in wind generation across different locations yields useful economies of scale once the grid spacing exceeds 200 km. When the grid spacing exceeds 500 km, we find that the economies grow dramatically: The shared battery size becomes insensitive to the number of participating generators. This means that the generators can access a common, shared battery and collectively achieve the same reliability they would have, had each of them had the entire battery to themselves. To provide a rigourous foundation for this remarkable observation, we propose a mathematical model that demonstrates this phenomenon, assuming that the net generation (generation minus demand) processes associated with the generators are statistically independent. The result is derived by characterizing the large deviations exponent of the loss of load probability with increasing battery size, and showing that this exponent is invariant with the number of generators.