The optimal control of storage for arbitrage and buffering, with energy applications

TL;DR

This paper develops a computationally efficient method for optimal control of energy storage systems used for arbitrage and buffering, employing stochastic dynamic programming and local decision-making, with practical applications demonstrated using UK electricity data.

Contribution

It introduces a novel approach combining stochastic dynamic programming with local, time-dependent control policies for energy storage management.

Findings

Optimal control decisions depend only on near-future costs and system evolution.

The method is computationally tractable for long-term energy system management.

Application to UK electricity data demonstrates practical effectiveness.

Abstract

We study the optimal control of storage which is used for both arbitrage and buffering against unexpected events, with particular applications to the control of energy systems in a stochastic and typically time-heterogeneous environment. Our philosophy is that of viewing the problem as being formally one of stochastic dynamic programming, but of using coupling arguments to provide good estimates of the costs of failing to provide necessary levels of buffering. The problem of control then reduces to that of the solution, dynamically in time, of a deterministic optimisation problem which must be periodically re-solved. We show that the optimal control then proceeds locally in time, in the sense that the optimal decision at each time $t$ depends only on a knowledge of the future costs and stochastic evolution of the system for a time horizon which typically extends only a little way beyond $t$. The approach is thus both computationally tractable and suitable for the management of systems over indefinitely extended periods of time. We develop also the associated strong Lagrangian theory (which may be used to assist in the optimal dimensioning of storage), and we provide characterisations of optimal control policies. We give examples based on Great Britain electricity price data.