Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input
Abstract
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, while the uncertainties from renewable generation exhibit colored noises. Here we use the probability density function (PDF) method, together with a novel large-eddy-diffusivity (LED) closure, to derive a closed-form deterministic partial differential equation (PDE) for the joint PDF of the SODEs describing a power generator with correlated-in-time power input. The proposed LED accurately captures the effect of nonzero correlation time of the power input on systems described by a divergent stochastic drift velocity. The resulting PDE is solved numerically. The accuracy of the PDF method is verified by comparison with Monte Carlo simulations.
BibTeX entry
@article{wang-2015-probabilistic,
title = { { Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input } },
author = {Wang, P. and Barajas-Solano, D. A. and Constantinescu, E. and Abhyankar, S. and Ghosh, D. and Smith, B. F. and Huang, Z. and Tartakovsky, D. M.},
journal = {SIAM/ASA J. Uncert. Quantif.},
volume = {3},
issue = {1},
pages = {873-896},
year = {2015},
doi = {10.1137/130940050},
}