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A Fokker-Planck analysis of photovoltaic systems

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  • Goldstein, Lawrence H.

Abstract

The battery state-of-charge, S(t), of an arbitrary photovoltaic system is analyzed as a Markov process driven by random white Gaussian perturbations of periodic insolation and load-demand profiles. A Fokker-Planck equation for the probability density function of S(t) is derived, and S(t) minus its mean is recognized as a nonhomogeneous Wiener-Levy process. The Fokker-Planck equation is solved under conditions of no barriers, one absorbing barrier, and two absorbing barriers, and the resulting probability density functions are used to obtain bounds on the complementary cumulative distribution function for the first passage time, x(t)=P{T>t}, to the completely discharged or totally charged state. Limiting expressions for these bounds as t → 0 and t → ∞ are obtained, and their asymptotic values are compared. Finally, a simple system is analyzed to provide insight into the meaning of the equations developed.

Suggested Citation

  • Goldstein, Lawrence H., 1978. "A Fokker-Planck analysis of photovoltaic systems," Energy, Elsevier, vol. 3(1), pages 51-62.
    • Handle: RePEc:eee:energy:v:3:y:1978:i:1:p:51-62
    DOI: 10.1016/0360-5442(78)90056-7
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