Probabilistic Load Flow Considering Wind Generation Uncertainty

M. Aien, R. Ramezani, S. Mohsen Ghavami


Renewable energy sources, such as wind, solar and hydro, are increasingly incorporated into power grids, as a direct consequence of energy and environmental issues. These types of energies are variable and intermittent by nature and their exploitation introduces uncertainties into the power grid. Therefore, probabilistic analysis of the system performance is of significant interest. This paper describes a new approach to Probabilistic Load Flow (PLF) by modifying the Two Point Estimation Method (2PEM) to cover some drawbacks of other currently used methods. The proposed method is examined using two case studies, the IEEE 9-bus and the IEEE 57-bus test systems. In order to justify the effectiveness of the method, numerical comparison with Monte Carlo Simulation (MCS) method is presented. Simulation results indicate that the proposed method significantly reduces the computational burden while maintaining a high level of accuracy. Moreover, that the unsymmetrical 2PEM has a higher level of accuracy than the symmetrical 2PEM with equal computing burden, when the Probability Density Function (PDF) of uncertain variables is asymmetric.


probabilistic load flow; two point estimation method; uncertainty; wind turbine generator (WTG).

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B. Borkowska, “Probabilistic Load Flow”, IEEE Trans. Power App. and Syst., Vol. PAS-93, No. 3, pp. 752–759, 1974

P. Jorgensen, J. Christensen, J. Tande, “Probabilistic Load Flow Calculation Using Monte Carlo Techniques for Distribution Network with Wind Turbines”, in Proc. 8th International Conf. Harmonics and Quality of Power, Vol. 2, pp. 1146–1151, Athens, Greece, 1998

P. Zhang, S. Lee, “Probabilistic Load Flow Computation Using the Method of Combined Cumulants and Gram-charlier Expansion”, IEEE Trans. Power Syst., Vol. 19, No. 1, pp. 676–682, 2004

D. Lei, Z. Chuan-cheng, Y. Yi-han, Z. Pei, “Improvement of Probabilistic Load Flow to Consider Network Configuration Uncertainties”, APPEEC Power and Energy Engineering. Conf., Asia-Pacific, pp. 1–5, Wuhan, 2009

L. Dong, W. Cheng, H. Bao, Y. Yang, “Probabilistic Load Flow Analysis for Power System Containing Wind Farms”, APPEEC Power and Energy Engineering Conf., Asia-Pacific, pp. 1–4, Chengdu, 2010.

R. Allan, A. Leite da Silva, R. Burchett, “Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions”, IEEE Trans. Power App. and Syst., Vol. PAS-100, No. 5, pp. 2539–2546, 1981

L. Hong, L. Shi, L. Yao, Y. Ni, M. Bazargan, “Study on Fuzzy Load Flow with Consideration of Wind Generation Uncertainties”, Transmission Distribution Conference Exposition: Asia and Pacific, 2009, pp. 1–4, 2009.

H. P. Hong, “Discussion on “An Optimal Point Estimate Method for Uncertainty Studies” by J. He and G. Sallfors”, App. Math. Modeling, Vol. 19, No. 8, pp. 508–509, 1995

H. P. Hong, “An Efficient Point Estimate Method for Probabilistic Analysis”, Reliability Engineering and System Safety, Vol. 59, No. 3, pp. 261–267, 1998

C. –L. Su, “Probabilistic Load Flow Computation Using Point Estimate Method”, IEEE Trans. Power Syst., Vol. 20, No. 4, pp. 1843–1851, 2005

M. Basil, A. Jamieson, “Uncertainty of Complex Systems by Monte Carlo Simulation”, 16th North Sea flow measurement workshop, Gleneagles, pp. 1-10, 1998

G. Verbic, C. A. Canizares, “Probabilistic Optimal Power Flow in Electricity Markets Based on a Two-Point Estimate Method”, IEEE Trans. Power Syst., Vol. 21, No. 4, pp. 1883–1893, 2006

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