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

S. D. Howell, P.W. Duck, A. Hazel, P.V. Johnson, Helena Pinto, G. Strbac, N. Proudlove, Mary Black

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.
LanguageEnglish
Pages231-252
Number of pages22
JournalIMA Journal of Management Mathematics
Volume22
Issue number3
Early online date22 Nov 2009
DOIs
Publication statusPublished - Jul 2011

Fingerprint

Wind Power
Stochastic Modeling
Finance
Wind power
Partial differential equations
Power generation
Electricity
Partial differential equation
Systems analysis
Analytic Solution
Large Set
Power System
System of equations
System Design
Well-defined
Smoothing
Simulation
Numerical Solution
Fluctuations
Optimization

Keywords

  • finance
  • wind energy
  • storage value
  • stochastic processes
  • real options

Cite this

Howell, S. D. ; Duck, P.W. ; Hazel, A. ; Johnson, P.V. ; Pinto, Helena ; Strbac, G. ; Proudlove, N. ; Black, Mary. / A partial differential equation system for modelling stochastic storage in physical systems with applications to wind power generation. In: IMA Journal of Management Mathematics. 2011 ; Vol. 22, No. 3. pp. 231-252.
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A partial differential equation system for modelling stochastic storage in physical systems with applications to wind power generation. / Howell, S. D.; Duck, P.W.; Hazel, A.; Johnson, P.V.; Pinto, Helena; Strbac, G.; Proudlove, N.; Black, Mary.

In: IMA Journal of Management Mathematics, Vol. 22, No. 3, 07.2011, p. 231-252.

Research output: Contribution to journalArticle

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