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Title: Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

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.
Authors:
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Publication Date:
OSTI Identifier:
1233777
Report Number(s):
PNNL-SA-100191
Journal ID: ISSN 2166-2525; KJ0401000
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM/ASA Journal on Uncertainty Quantification; Journal Volume: 3; Journal Issue: 1
Publisher:
SIAM
Research Org:
Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
PDF method, stochastic differential equations, power grid, uncertainty quantification