Probabilistic density function method for stochastic odes of power systems with uncertain power input

P. Wang, D. A. Barajas-Solano, E. Constantinescu, S. Abhyankar, D. Ghosh, B. F. Smith, Z. Huang, A. M. Tartakovsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)873-896
Number of pages24
JournalSIAM-ASA Journal on Uncertainty Quantification
Issue number1
StatePublished - 2015
Externally publishedYes


  • PDF method
  • Renewable energy
  • Swing equation
  • Uncertainty quantification

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Probabilistic density function method for stochastic odes of power systems with uncertain power input'. Together they form a unique fingerprint.

Cite this