Probabilistic power flow studies for transmission systems with photovoltaic generation using cumulants

Miao Fan, Vijay Vittal, Gerald Thomas Heydt, Raja Ayyanar

Research output: Contribution to journalArticlepeer-review

324 Scopus citations


This paper applies a probabilistic power flow (PPF) algorithm to evaluate the influence of photovoltaic (PV) generation uncertainty on transmission system performance. PV generation has the potential to cause a significant impact on power system reliability in the near future. A cumulant-based PPF algorithm suitable for large systems is used to avoid convolution calculations. Correlation among input random variables is considered. Specifically correlation between adjacent PV resources are considered. Three types of approximation expansions based on cumulants, namely the Gram-Charlier expansion, the Edgeworth expansion, and the Cornish-Fisher expansion, are compared, and their properties, advantages, and deficiencies are discussed. Additionally, a novel probabilistic model of PV generation is developed to obtain the probability density function (PDF) of the PV generation production based on the environmental conditions. The proposed approaches with the three expansions are compared with Monte Carlo simulations (MCS) with results for a 2497-bus representation of the Arizona area of the Western Electricity Coordinating Council (WECC) system.

Original languageEnglish (US)
Article number6185718
Pages (from-to)2251-2261
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number4
StatePublished - 2012


  • Cornish-Fisher expansion
  • Edgeworth expansion
  • Gram-Charlier expansion
  • correlation
  • cumulant
  • photovoltaic generation
  • probabilistic power flow study
  • renewable resources
  • stochastic power flow study

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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