Statistical economies of scale in battery sharing

The goal of this paper is to shed light on the statistical economies of scale achievable from the sharing of storage between multiple renewable generators. To demonstrate these economies in practice, we present an extensive study using real-world wind data from a grid of equispaced wind generators sharing a common battery. Each of these generators is in turn contracted to meet a certain demand profile to a prescribed level of reliability. Interestingly, the statistical diversity in wind generation across different locations yields useful economies of scale once the grid spacing exceeds 200 km. However, 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 rigorous 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.

Automated summary

By sharing energy storage, multiple renewable generators can achieve economies of scale, with significant growth in economic benefits when grid spacing exceeds 500 km. The study shows that the shared battery size is insensitive to the number of participating generators, allowing them to collectively achieve the desired level of reliability.