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

Citation Formats

Wang, Peng, Barajas-Solano, David A., Constantinescu, Emil, Abhyankar, S., Ghosh, Donetta L., Smith, Barry, Huang, Zhenyu, and Tartakovsky, Alexandre M. Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input. United States: N. p., 2015. Web. doi:10.1137/130940050.
Wang, Peng, Barajas-Solano, David A., Constantinescu, Emil, Abhyankar, S., Ghosh, Donetta L., Smith, Barry, Huang, Zhenyu, & Tartakovsky, Alexandre M. Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input. United States. doi:10.1137/130940050.
Wang, Peng, Barajas-Solano, David A., Constantinescu, Emil, Abhyankar, S., Ghosh, Donetta L., Smith, Barry, Huang, Zhenyu, and Tartakovsky, Alexandre M. Tue . "Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input". United States. doi:10.1137/130940050.
@article{osti_1233777,
title = {Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input},
author = {Wang, Peng and Barajas-Solano, David A. and Constantinescu, Emil and Abhyankar, S. and Ghosh, Donetta L. and Smith, Barry and Huang, Zhenyu and Tartakovsky, Alexandre M.},
abstractNote = {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.},
doi = {10.1137/130940050},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
issn = {2166-2525},
number = 1,
volume = 3,
place = {United States},
year = {2015},
month = {9}
}