Probabilistic power flow analysis with generation dispatch including photovoltaic resources

Miao Fan, Vijay Vittal, Gerald T. Heydt, Raja Ayyanar

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


This paper proposes a novel probabilistic power flow (PPF) algorithm considering generation dispatch. The intent is to examine the influence of uncertainty due to photovoltaic (PV) generation resources and loads. PV generation uncertainty may have a significant impact on transmission systems since this resource is easily influenced by changing environmental conditions. However, it is prudent to include generation dispatch in the PPF algorithm since the dispatching strategy compensates for PV generation injections and influences the uncertainty in the results. The proposed PPF algorithm is based on the cumulant method. The Gram-Charlier expansion is applied to approximate the distribution of probabilistic variables. Furthermore, this paper also proposes a probabilistic optimal power dispatching strategy which considers uncertainty problems in the economic dispatch and optimizes the expected value of the total cost with the overload probability as a constraint. The Arizona area of the Western Electricity Coordinating Council (WECC) system is used to test the proposed PPF algorithm and compare results with Monte Carlo simulation (MCS).

Original languageEnglish (US)
Pages (from-to)1797-1805
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number2
StatePublished - 2013


  • Cumulant
  • Cumulative distribution function
  • Economic generation dispatch
  • Gram-Charlier expansion
  • Photovoltaic generation
  • Probabilistic optimal power dispatching strategy
  • Probabilistic power flow
  • Probability density function

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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