Fokker--Planck analysis of photovoltaic systems

Journal Article · Wed Feb 01 04:00:00 EST 1978 · Energy (Stamford, Conn.); (United States)

DOI:https://doi.org/10.1016/0360-5442(78)90056-7· OSTI ID:5178281

Goldstein, L H

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 ..-->.. infinity are obtained, and their asymptotic values are compared. Finally, a simple system is analyzed to provide insight into the meaning of the equations developed.

• Research Organization: Sandia Labs., Albuquerque, NM
• OSTI ID: 5178281
• Journal Information: Energy (Stamford, Conn.); (United States), Journal Name: Energy (Stamford, Conn.); (United States) Vol. 3:1; ISSN ENGYD
• Country of Publication: United States
• Language: English

Related Subjects

14 SOLAR ENERGY
140501* -- Solar Energy Conversion-- Photovoltaic Conversion
DIFFERENTIAL EQUATIONS
EQUATIONS
FOKKER-PLANCK EQUATION
INSOLATION
MARKOV PROCESS
PERFORMANCE
PHOTOVOLTAIC POWER PLANTS
POWER PLANTS
PROBABILITY
SIMULATION
SOLAR CELL ARRAYS
SOLAR POWER PLANTS
STOCHASTIC PROCESSES
SYSTEMS ANALYSIS