A partial differential equation system for modelling stochastic storage in physical systems with applications to wind power generation

Howell, S. D. and Duck, P.W. and Hazel, A. and Johnson, P.V. and Pinto, Helena and Strbac, G. and Proudlove, N. and Black, Mary (2011) A partial differential equation system for modelling stochastic storage in physical systems with applications to wind power generation. IMA Journal of Management Mathematics, 22 (3). pp. 231-252. (https://doi.org/10.1093/imaman/dpp022)

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Abstract

Analytic solutions exist only for highly idealized simple problems in stochastic storage; while simulation is available for complex problems, it is generally impractically slow. In this paper, a system of partial differential equations (PDEs), based on a novel combination of the techniques used to value options in finance, is developed and shown to efficiently value stochastic storage. The PDE system requires somewhat non-standard (but well-defined) numerical solution methods, which are up to nine orders of magnitude faster than simulation (and yet yields the same results). These faster calculations should permit better analysis of system design and operating procedures (including optimization) for a large set of problems in physical and financial stochastic storage. The motivation for this work is in the management of significant amounts of wind-generated electricity into a power system, in particular by smoothing out random fluctuations in supply.

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