TY - JOUR
T1 - Probabilistic power flow studies for transmission systems with photovoltaic generation using cumulants
AU - Fan, Miao
AU - Vittal, Vijay
AU - Heydt, Gerald Thomas
AU - Ayyanar, Raja
N1 - Funding Information:
Manuscript received November 09, 2011; revised February 13, 2012; accepted March 06, 2012. Date of publication April 17, 2012; date of current version October 17, 2012. This work was supported by the Science Foundation of Arizona under the project Arizona’s Solar Market Analysis and Research Tool (AzSMART). Paper no. TPWRS-01071-2011.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Cornish-Fisher expansion
KW - Edgeworth expansion
KW - Gram-Charlier expansion
KW - correlation
KW - cumulant
KW - photovoltaic generation
KW - probabilistic power flow study
KW - renewable resources
KW - stochastic power flow study
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U2 - 10.1109/TPWRS.2012.2190533
DO - 10.1109/TPWRS.2012.2190533
M3 - Article
AN - SCOPUS:84867995366
SN - 0885-8950
VL - 27
SP - 2251
EP - 2261
JO - IEEE Transactions on Power Systems
JF - IEEE Transactions on Power Systems
IS - 4
M1 - 6185718
ER -