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

Journal Article · Tue Sep 22 00:00:00 EDT 2015 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/130940050· OSTI ID:1233777

Wang, Peng; Barajas-Solano, David A.; Constantinescu, Emil; Abhyankar, S.; Ghosh, Donetta L.; Smith, Barry; Huang, Zhenyu; Tartakovsky, Alexandre M.

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.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1233777
• Report Number(s): PNNL-SA-100191; KJ0401000
• Journal Information: SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, Issue 1; ISSN 2166-2525
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

PDF method
stochastic differential equations
power grid
uncertainty quantification