An application of the Fokker-Planck equation in stochastic reservoir theory

摘要

The distribution of the storage and of the outflow of a reservoir with a piecewise linear constant operating rule and Gaussian white-noise input is derived by analytically solving the Fokker-Planck equation. The proposed operating rule may approximate the well-known standard policy or, by increasing the number of intervals with constant outflow, may approximate the operating rule of existing reservoirs. The form of the solution renders possible the probabilistic analysis of the behavior of a water reservoir without numerical calculations.