Frequency Regulation with Storage: On Losses and Profits

TL;DR

This paper develops an analytical model for storage operators providing frequency regulation, accounting for losses and profits, and reveals how efficiency and regulation duration impact profitability.

Contribution

It introduces a novel analytical solution for decision-making in frequency regulation storage, incorporating future uncertainties and energy losses.

Findings

Profitability decreases with longer regulation commitment periods.

Higher roundtrip efficiency reduces energy loss costs.

Expected energy loss cost increases with frequency deviation dispersion.

Abstract

Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future frequency deviation trajectories as functional uncertainties in a receding horizon robust optimization problem. We constrain the expected terminal state-of-charge to be equal to some target to allow storage operators to make good decisions not only for the present but also the future. Thanks to this constraint, the amount of electricity traded on day-ahead markets is an implicit function of the regulation power sold to grid operators. The implicit function quantifies the amount of power that needs to be purchased to cover the expected energy loss that results from providing frequency regulation. We show how the marginal cost associated with the expected energy loss decreases with roundtrip efficiency and increases with frequency deviation dispersion. We find that the profits from frequency regulation over the lifetime of energy-constrained storage devices are roughly inversely proportional to the length of time for which regulation power must be committed.