Applying Point Estimation and Monte Carlo Simulation Methods in Solving Probabilistic Optimal Power Flow Considering Renewable Energy Uncertainties

Authors

Abstract

The increasing penetration of renewable energy results in the change of the traditional power system planning and operation tools. As the generated power by the renewable energy resources are probabilistically changed, the certain power system analysis toll cannot be applied in this case. The probabilistic optimal power flow is one of the most useful tools regarding the power system analysis in the presence of uncertainties. In this paper, Monte Carlo simulation and point estimation methods are used to solve the POPF in the presence of wind and solar sources uncertainties. These methods are simulated on the PEGASE 89–bus European system. The most important novelty of this paper is arising from the comparison of detailed studies of point estimation methods with the Monte Carlo simulation method. As the obtained results confirm, the point estimation methods lead to an increase in the computing time efficiency in comparison to the Monte Carlo simulation method. Also, an increase in the number of sampling points in PEMs will result in an increase in the accuracy of the obtained results, while the computing time is still lower than the Monte Carlo simulation method.

Keywords


[1] Shargh, S., Khorshid Ghazani, B., Mohammadi–ivatloo, B., "Probabilistic Multi – Objective Optimal Power Flow Considering Correlated Wind Power and Load Uncertainties", Renewable Energy, Vol. 49, pp. 10-21, 2016. [2] Aien, M., Rashidinejad, M., Fotuhi-Firuzabad, M., "Probabilistic Optimal Power Flow in Correlated Hybrid Wind – PV Power System: A Review and A New Approach", Renewable and Sustainable Energy Reviews, Vol. 41, pp. 1437-1446, 2015. [3] Bie, P., Zhang, B., Li, H., "Probabilistic Power Flow Using Improved Monte Carlo Simulation Method with Correlated with Sources", 7th International Conference on Electronics and Information Engineering, Vol. 10322, 2017. [4] Villanueva, D., Feijoo, A. E., Pazos, J. I., "An Analytical Method to Solve the Probabilistic Load Flow Considering Load Demand Correlation Using the Dc Load Flow", Electric Power Systems Research, Vol. 110, pp. 1-8, 2014. [5] Verbic, G., Canizares, C. A., "Probabilistic Optimal Power Flow in Electricity Markets Based on Two – Point Estimate", IEEE Transaction on Power Systems, Vol. 21, No. 4, pp. 1883-1893, 2006. [6] Rosenblueth, E., "Point Estimate for Probability Moments", Proc. Natl. Acad. Sci., Vol. 72, No. 10, pp. 3812-3814, 1975. [7] Hong, H., "An Efficient Point Estimate Method for Probabilistic Analysis", Reliability Engineering & Systems Safety, Vol. 59, No. 3, pp. 261-267, 1998. [8] Yuan, Y., Zhou, J., Ju, P., Feuchtwang, J., "Probabilistic Load Flow Computation of a Power System Containing Wind Farms Using the Method of Combined Cumulants and Gram–Charlier Expansion", IET Renewable Power Generation, Vol. 5, No. 6, pp. 448-454, 2011. [9] Chen, C., Wu, W., Zhang, B., Sun, H., "Correlated Probabilistic Load Flow Using a Point Estimate Method with Nataf Transformation", International Journal of Electrical Power & Energy Systems, Vol. 65, pp. 325-333, 2015. [10] Ai, X., Wen, J., Wu, T., Lee, W., "A Discrete Point Estimate Method for Probabilistic Load Flow Based on The Measured Data of Wind Power", IEEE Transaction on Industry Applications, Vol. 49, No. 5, pp. 2244-2252, 2013. [11] Villanueva, D., Pazos, J., Feijoo, A., "Probabilistic Load Flow Including Wind Power Generation", IEEE Transactions on Power Systems, Vol. 26, No. 3, pp. 1659-1667, 2011. [12] Usaola, J., "Probabilistic Load Flow in Systems with Wind Generation", IET Generation, Transmission & Distribution, Vol. 3, No. 12, pp. 1031-1041, 2009. [13] Usaola, J., "Probabilistic Load Flow with Correlated Wind Power Injections", Electric Power Systems Research, Vol. 80, No. 5, pp. 528-536, 2010. [14] Morales, J., Baringo, L., Conejo, A., Minguez, R., "Probabilistic Power Flow with Correlated Wind Sources", IET Generation, Transmission & Distribution, Vol. 4, No. 5, pp. 641-651, 2010. [15] Gupta, N., "Probabilistic Load Flow with Detailed Wind Generator Models Considering Correlated Wind Generation and Correlated Loads", Renewable Energy, Vol. 94, pp. 96-105, 2016. [16] Kabir, M. N., Mishra, Y., Bansal, R. C., "Probabilistic Load Flow for Distribution Systems with Uncertain PV Generation", Applied Energy, Vol. 163, pp. 343-351, 2016 [17] Carpinelli, G., Caramia, P., Varilone, P., "Multi – Linear Monte Carlo Simulation Method for Probabilistic Load Flow of Distribution System with Wind and Photovoltaic Generation Systems", Renewable Energy, Vol. 76, pp. 283-295, 2015. [18] Tourandaz Kenari, M., Sepasian, M. S., Setayesh Nazari, M., "Study of Voltage in Distribution Network Considering Wind Turbine and Static Load Model with Gamma Distribution", JEM, Vol. 7, No. 4, pp. 28-41, 2018. [19] Morales, J., Conejo, A., Perez – Ruiz, J., "Simulating The Impact of Wind Production on Locational Marginal Prices", IEEE Transaction on Power Systems, Vol. 26, No. 2, pp. 820-828, 2011. [20] Dopazo, J. M., Klitin, O. A., Sasson, A. M., "Stochastic Load Flows", IEEE Transaction on Power Apparatus and Systems, Vol. 94, pp. 299-309, 1975. [21] Allan, R. N., Silva, A. M. L., "Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions", IEEE Transaction on Power Apparatus Systems, Vol. PAS-100, No. 5, pp. 2539-2546, 1981. [22] Li, X., Cao, J., Du, D., "Probabilistic Optimal Power Flow for Power Systems Considering Wind Uncertainty and Load Correlation", Neurocomputing, Vol. 148, No. 19, pp. 240-247, 2014. [23] Aien, M., Fotuhi Firuzabad, M., Rashidinejad, M., "Probabilistic Optimal Power Flow in Correlated Hybrid Wind Photovoltaic Power System", IEEE Transaction on Smart Grid, Vol. 5, No. 1, pp. 130-138, 2014. [24] Xiao, Q., "Comparing Three Methods for Solving Probabilistic Optimal Power Flow", Electric Power Systems Research, Vol. 124, pp. 92-99, 2015. [25] Rabiee, A., Mohammadi, M., "Transient Stability Constrained Probabilistic Optimal Power Flow in The Electricity Market Environment", Tabriz Journal of Electrical Engineering, Vol. 46, No. 1, pp. 169-183, 2016. [26] Morales, J., Perez – Ruiz, J., "Point Estimate Schemes to Solve the Probabilistic Power Flow", IEEE Transaction on Power Systems, Vol. 22, No. 4, pp. 1594-1601, 2007. [27] Aien, M., Rashidinejad, M., Fotuhi Firuzabad, M., "Probabilistic Optimal Power Flow in Correlated Hybrid Wind – PV Power Systems: A Review and A New Approach", Renewable and Sustainable Energy Reviews, Vol. 41, pp. 1437-1446, 2015. [28] Rajanarayan Prusty, B., Jena, D., "A Critical Review on Probabilistic Load Flow Studies in Uncertainty Constrained Power Systems with Photovoltaic Generation and A New Approach", Renewable and Sustainable Energy Review, Vol. 69, pp. 1286-1302, 2016. [29] Aien, M., Hajebrahimi, A., Fotuhi Firuzabad, M., "A Comprehensive Review on Uncertainty Modeling Techniques in Power System Studies", Renewable and Sustainable Energy Reviews, Vol. 57, pp. 1077-1089, 2016. [30] Miller, A. C., Rice, T. R., "Discrete Approximations of Probability Distributions", Management Science, Vol. 29, No. 3, pp. 352-362, 1983. [31] Tian, S., Wang, H., Xie, X., "Probabilistic Load Flow Analysis Considering the Correlation for Microgrid with Wind Photovoltaic System", 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, November, China, 2015. [32] Li, H., Zhang, A., "Three – Phase Power Flow Solution for Weakly Meshed Distribution System Including PV Type, Distribution Generation", Asia-Pacific Power and Energy Engineering Conference, pp. 1-7, 2009. [33] Nikmehr, N., Ravadanegh, N. S., "Heuristic Probabilistic Power Flow Alghorithm for Microgrids Operation and Planning", IET Generation, Transmission & Distribution, Vol. 9, No. 11, pp. 985-995, 2015. [34] Josz, C., Fliscounakis, S., Maeght, J., Panciatici, P., "AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE", http://arxiv.org/abs/1603.01533. [35] Fliscounakis, S., Panciatici, P., Capitanescu, F., Wehenkel, L., "Contingency Ranking with Respect to Overloads in Very Large Power Systems Taking into Account Uncertainty, Preventive and Corrective Actions", IEEE Transaction on Power Systems, Vol. 28, No. 4, pp. 4909-4917, 2013. [36] Allan, R. N., Al-Shakarchi, M. R. G., "Probabilistic Techniques in A.C. Load Flow Analysis", Proceedings of the Institution of Electrical Engineers, Vol. 124, No. 2, pp. 154-160, 1977. [37] Madrigal, M., Ponnambalam, K., "Probabilistic Optimal Power Flow", IEEE Canadian Conference on Electrical and Computer Engineering, Vol. 1, pp. 385–388, 1998. [38] Harr, M. E., "Probabilistic Estimates for Multivariate Analysis", Applied Mathematical Modeling, Vol. 13, No. 5, pp. 313–318, 1989. [39] Hong, H. P., "An Efficient Point Estimate Method for Probabilistic Analysis", Reliability Engineering and System Safety, Vol. 59, No. 3, pp. 261-267, 1998.