2015/09/18 by J. F. Cruise, Cruise, James, Stan Zachary +1
Economics, Econometrics and Finance · Engineering · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Smart Grid Energy Management #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1509.05788
openalex publication_date 2015/09/18 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We study the optimal control of storage which is used for both arbitrage and\nbuffering against unexpected events, with particular applications to the\ncontrol of energy systems in a stochastic and typically time-heterogeneous\nenvironment. Our philosophy is that of viewing the problem as being formally\none of stochastic dynamic programming, but of using coupling arguments to\nprovide good estimates of the costs of failing to provide necessary levels of\nbuffering. The problem of control then reduces to that of the solution,\ndynamically in time, of a deterministic optimisation problem which must be\nperiodically re-solved. We show that the optimal control then proceeds locally\nin time, in the sense that the optimal decision at each time t depends only\non a knowledge of the future costs and stochastic evolution of the system for a\ntime horizon which typically extends only a little way beyond t. The approach\nis thus both computationally tractable and suitable for the management of\nsystems over indefinitely extended periods of time. We develop also the\nassociated strong Lagrangian theory (which may be used to assist in the optimal\ndimensioning of storage), and we provide characterisations of optimal control\npolicies. We give examples based on Great Britain electricity price data.\n