Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.
Revised: December 30, 2015 |
Published: September 22, 2015
Citation
Wang P., D.A. Barajas-Solano, E. Constantinescu, S. Abhyankar, D.L. Ghosh, B. Smith, and Z. Huang, et al. 2015.Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input.SIAM/ASA Journal on Uncertainty Quantification 3, no. 1:873-896.PNNL-SA-100191.doi:10.1137/130940050