Probabilistic Study of Voltage in Distribution Network Considering Wind Turbine and Static Load Model with Gamma Distribution

Authors

Abstract

Uncertainty analysis of voltage in distribution system is the main feature of current study. This paper presents a probabilistic analysis of radial distribution networks considering wind power resources. The wind turbines are modeled as probability distribution functions. Also, the loads are modeled with Gaussian and gamma distributions. Monte Carlo simulation is used for the probabilistic load flow process. The proposed method is applied to the IEEE 33-bus distribution test system and the results are analyzed. The results validate the correctness and efficiency of the proposed technique.

Keywords


[1] Chen, P. C., Salcedo, R., et al., "Analysis of Voltage Profile Problems due to the Penetration of Distributed Generation in Low-Voltage Secondary Distribution Networks", IEEE Trans. on Power Delivery, Vol. 27, No. 4, 2012. [2] Su, C. L., "Stochastic Evaluation of Voltages in Distribution Networks with Distributed Generation using Detailed Distribution Operation Models", IEEE Trans. Power Syst., Vol. 25, No. 2, pp. 786-795, 2010. [3] Rodrigues, A. B., Prada, R. B., da Silva, M. D. G., "Voltage Stability Probabilistic Assessment in Composite Systems: Modeling Unsolvability and Controllability Loss", IEEE Trans. Power Syst., Vol. 25, No. 3, 2010. [4] Borkowska, B., "Probabilistic Load Flow", IEEE Trans. Power Appl. Syst., PAS-93, pp. 752–759, 1974. [5] Carpinelli, G., Caramia, P., Varilone, P., "Multi-Linear Monte Carlo Simulation Method for Probabilistic Load Flow of Distribution Systems with Wind and Photovoltaic Generation Systems", Renewable Energy, Vol. 76, pp. 283-295, 2015. [6] Allan, R., da Silva, A. L., Burchett, R., "Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions", IEEE Trans. Power App. Syst., No. 5, pp. 2539–2546, 1981. [7] Zhang, P., Lee, S. T., "Probabilistic Load Flow Computation using the Method of Combined Cumulants and Gram-Charlier Expansion", IEEE Trans. Power Systems, Vol. 19, No. 1, pp. 676-682, 2004. [8] Williams, T., Crawford, C., "Probabilistic Load Flow Modeling Comparing Maximum Entropy and Gram-Charlier Probability Density Function Reconstructions", IEEE Trans. Power Syst., Vol. 28, No. 1, 2013. [9] Usaola, J., "Probabilistic Load Flow in Systems with Wind Generation", IET Gener. Transm. Distrib., Vol.3, No. 12, pp. 1031–1041, 2009. [10] Pourahmadi-Nakhli, M., Seifi, A. R., Taghavi, R., "A Nonlinear-Hybrid Fuzzy/Probabilistic Load Flow for Radial Distribution Systems", Int. J. Electr. Power Energy Syst., Vol. 47, pp. 69–77, 2013. [11] Long, C., Farrag, M. E. A., Chengke, Z., Donald, M. H., "Statistical Quantification of Voltage Violations in Distribution Networks Penetrated by Small Wind Turbines and Battery Electric Vehicles", IEEE Trans. Power Syst., Vol. 28, No. 3, 2013. [12] Nikmehr, N., Ravadanegh, S. N., "Heuristic Probabilistic Power Flow Algorithm for Microgrids Operation and Planning", IET Gener. Transm. Distrib., Vol. 9, No. 11, pp. 985–995, 2015. [13] Aien, M., Rashidinejad, M., Fotuhi-Firuzabad, M., "On Possibilistic and Probabilistic Uncertainty Assessment of Power Flow Problem: A Review and a New Approach", Renewable and Sustainable Energy Reviews, Vol. 37, pp. 883–895, 2014. [14] Chen, C., Wu, W., Boming, Z., Sun, H., "Correlated Probabilistic Load Flow using a Point Estimate Method with Nataf Transformation", Electrical Power and Energy Systems, Vol. 65, pp. 325–333, 2015. [15] Villanueva, D., Feijóo, A. E., Pazos, J. L., "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. [16] 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. [17] Ran, X., Miao, S., "Three-Phase Probabilistic Load Flow for Power System with Correlated Wind, Photovoltaic and Load", IET Generation, Transmission & Distribution, Vol. 10, No. 12, pp. 3093–3101, 2016. [18] 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. [19] Wua, C., Wenb, F., Lou, Y., Xin, F., "Probabilistic Load Flow Analysis of Photovoltaic Generation System with Plug-in Electric Vehicles", Electrical Power and Energy Systems, Vol. 64, pp. 1221–1228, 2015. [20] Ruiz-Rodriguez, F. J., Hernandez, J. C., Jurado, F., "Probabilistic Load Flow for Photovoltaic Distributed Generation using the Cornish- Fisher Expansion", Elect. Power Syst. Res., Vol. 89, pp. 129–138, 2012. [21] Mahmoud, G. A., "Voltage Stability Analysis of Radial Distribution Networks using Catastrophe Theory", IET Gener. Trans. Distrib., Vol. 6, No. 7, pp. 612–618, 2012. [22] Janecek, E., Georgiev, D., "Probabilistic Extension of the Backward/Forward Load Flow Analysis Method", IEEE Trans. Power Syst., Vol. 27, No. 2, pp. 695-704, 2012. [23] Kersting, W. H., Distribution System Modeling and Analysis, 3rd ed. Boca Raton, FL: CRC, 2012. [24] Haque, M. H., "A General Load Flow Method for Distribution Systems", Electric Power Systems Research, Vol. 54, pp.47-54, 2000. [25] Dragoslav, R., Taleski, R., "Two Novel Methods for Radial and Weakly Meshed Network Analysis", Electric Power Systems Research, Vol. 48, pp. 79-87, 1998. [26] Tsai-Hsiang, C., Mo-Shing, C., et al., "Distribution System Power Flow Analysis –a Rigid Approach", IEEE Trans. Power Del., Vol. 6, No. 3, pp. 1146-1152, 1991. [27] Masoum, A. S., Moses, P. S., Masoum, M. A. S., "Real-Time Coordination of Plug-in Electric Vehicle Charging in Smart Grids to Minimize Power Losses and Improve Voltage Profile", IEEE Trans. Smart Grid, Vol. 2, No. 3, pp. 456–467, 2011. [28] Augugliaro, A., Dusonchet, et al., "A Compensation-Based Method to Model PV Nodes in Backward/Forward Distribution Network Analysis", COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 26, No. 2, pp. 481–493, 2007. [29] Tsai-Hsiang, C., Nien-Che, Y., "Loop Frame of Reference Based Three-Phase Power Flow for Unbalanced Radial Distribution Systems", Electric power systems research, Vol. 80, pp. 799-806, 2010. [30] Teng, J. H., "Modelling Distributed Generations in Three-Phase Distribution Load Flow", IET Gen., Transm., Distrib., Vol. 2, No. 3, pp. 330–340, 2008. [31] Papadopoulos, P., Skarvelis-Kazakos, S., et al., "Electric Vehicles’ Impact on British Distribution Networks", IET Electr. Syst. Transp., Vol. 2, No. 3, pp. 91–102, 2012. [32] Siano, P., Mokryani, G., "Probabilistic Assessment of the Impact of Wind Energy Integration into Distribution Networks", IEEE Trans. Power Syst., Vol. 28, No. 4, 2013. [33] Taylor, H. M., Karlin, S., An Introduction to Stochastic Modeling, 3rd edition, Academic Press, 1998. [34] Divya, K. C., Rao, P. S. N., "Models for Wind Turbine Generating Systems and Their Application in Load Flow Studies", Electr. Power Syst. Res., Vol. 76, pp. 844–856, 2006. [35] Tourandaz Kenari, M., Sepasian, M. S., Setayesh Nazar, M., "Probabilistic Load Flow Computation using Saddle-Point Approximation", COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 36, No. 1, pp. 48-61, 2017. [36] Blair, N., Dobos, A. P., Freeman, J., Neises, T., Wagner, M., Ferguson, T., Gilman P, Janzou, S., System Advisor Model, sam 2014.1. 14: General description, National Renewable Energy Laboratory, Golden, CO., 2014. [37] Ruiz-Rodriguez, F. J., Hernandez, J. C., Jurado, F., "Probabilistic Load Flow for Radial Distribution Networks with Photovoltaic Generators", IET Renew. Power Gener., Vol. 6, No. 2, pp. 110-121, 2012. [38] Ettehadi, M., Ghasemi, H., Vaezzadeh, S., "Voltage Stability Based DG Placement in Distribution Network", IEEE Trans. Power Deliv., Vol. 28, No. 1, pp. 171-178, 2013. [39] Vicente, W. C. B., Caire, R., Hadjsaid, N., "Probabilistic Load Flow for Voltage Assessment in Radial Systems with Wind Power", Int. J. Electr. Power Energy Syst., Vol. 41, pp. 27–33, 2012.