Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power

ABSTRACT

In this paper a procedure is established for solving the Probabilistic Load Flow in an electrical power network, considering correlation between power generated by power plants, loads demanded on each bus and power injected by wind farms. The method proposed is based on the generation of correlated series of power values, which can be used in a MonteCarlo simulation, to obtain the probability density function of the power through branches of an electrical network.

In this paper a procedure is established for solving the Probabilistic Load Flow in an electrical power network, considering correlation between power generated by power plants, loads demanded on each bus and power injected by wind farms. The method proposed is based on the generation of correlated series of power values, which can be used in a MonteCarlo simulation, to obtain the probability density function of the power through branches of an electrical network.

Cite this paper

nullD. Villanueva, A. Feijóo and J. Pazos, "Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power,"*Smart Grid and Renewable Energy*, Vol. 2 No. 1, 2011, pp. 12-20. doi: 10.4236/sgre.2011.21002.

nullD. Villanueva, A. Feijóo and J. Pazos, "Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power,"

References

[1] B. Borkowska, “Probabilistic Load Flow,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-93, No. 3, May-June 1974, pp. 752-755.

[2] R. N. Allan, B. Borkowska and C. H. Grigg, “Probabilistic Analysis of Power Flows,” Proceedings of the Institution of Electrical Engineers, London, Vol. 121, No. 12, December 1974, pp. 1551-1556.

[3] A. M. Leite da Silva, S. M. P. Ribeiro, V. L. Arienti, R. N. Allan and M. B. Do Coutto Filho, “Probabilistic Load Flow Techniques Applied to Power System Expansion Planning,” IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990, pp. 1047-1053.

[4] R. N. Allan, C. H. Grigg and M. R. G. Al-Shakarchi, “Numerical Techniques in Probabilistic Load Flow Problems,” International Journal for Numerical Methods in Engineering, Vol. 10, No. 4, March 1976, pp. 853-860.

[5] R. N. Allan, A. M. Leite da Silva and R. C. Burchett, “Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 5, May 1981, pp. 2539-2546.

[6] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic a. c. Load Flow,” Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 6, June 1976, pp. 531-536.

[7] R. N. Allan, A. M. Leite da Silva and R. C. Burchett, “Discrete Convolution in Power System Reliability,” IEEE Transactions on Reliability, Vol. R-30, No. 5, December 1981, pp. 452-456.

[8] R. N. Allan and A. M. Leite da Silva, “Probabilistic Load Flow Using Multilinearisations,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 128, No. 5, September 1981, pp. 280-287.

[9] A. M. Leite da Silva, R. N. Allan, S. M. Soares and V. L. Arienti, “Probabilistic Load Flow Considering Network Outages,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 132, No. 3, May 1985, pp. 139-145.

[10] A. M. Leite da Silva, V. L. Arienti and R. N. Allan, “Probabilistic Load Flow Considering Dependence between Input Nodal Powers,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, No. 6, June 1984, pp. 1524-1530.

[11] R. N. Allan, C. H. Grigg, D. A. Newey and R. F. Simmons, “Probabilistic Power-Flow Techniques Extended and Applied to Operational Decision Making,” Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 12, December 1976, pp. 1317-1324.

[12] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic Techniques in a. c. Load Flow Analysis,” Proceedings of the Institution of Electrical Engineers, Vol. 124, No. 2, February 1977, pp. 154-160.

[13] A. M. Leite da Silva and V. L. Arienti, “Probabilistic Load Flow by a Multilinear Simulation Algorithm,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 137, No. 4, July 1990, pp. 276-282.

[14] C. L. Su, “Probabilistic Load-Flow Computation Using Point Estimate Method,” IEEE Transactions on Power Systems, Vol. 20, No. 4, pp. November 2005, 1843-1851.

[15] M. Brucoli, F. Torelli and R. Napoli, “Quadratic Probabilistic Load Flow with Linearly Modelled Dispatch,” Electrical Power & Energy Systems, Vol. 7, No. 3, July 1985, pp. 138-146.

[16] X. Li, X. Chen, X. Yin, T. Xiang and H. Liu, “The Algorithm of Probabilistic Load Flow Retaining Nonlinearity,” Proceedings of 2002 PowerCon, International Conference on Power System Technology, Kunming, Vol. 4, 10 October 2002, pp. 2111-2115.

[17] P. Zhang and S. T. Lee, “Probabilistic Load Fow Computation Using the Method of Combined Cumulants and Gram-Charlier Expansion,” IEEE Transactions Power Systems, Vol. 19, No.1, February 2004, pp. 676-682.

[18] J. Usaola, “Probabilistic Load Flow with Wind Production Uncertainty Using Cumulants and Cornish-Fisher Expansion,” International Journal of Electrical Power and Energy Systems, Vol. 31, No. 9, 2009, pp. 474-481.

[19] P. Jorgensen, J. S. Christensen and J. O. Tande, “Probabilistic Load Flow Calculation Using Monte Carlo Techniques for Distribution Network with Wind Turbines,” 8th International Conference on Harmonics and Quality of Power, Athens, Vol. 2, 14-16 October 1998, pp. 1146-1151.

[20] C. L. Su, “Distribution Probabilistic Load Flow Solution Considering Network Reconfiguration and Voltage Control Devices,” 15th Power Systems Computation Conference, Liege, August 2005.

[21] Z. Hu and X. Wang, “A Probabilistic Load Flow Method Considering Branch Outages,” IEEE Transactions on Power Systems, Vol. 21, No. 2, May 2006, pp. 507-514.

[22] N. D. Hatziargyriou, T. S. Karakatsanis and M. Papadopoulos, “Probabilistic Load Flow in Distribution Systems Containing Dispersed Wind Power Generation,” IEEE Transactions on Power Systems, Vol. 8, No. 1, February 1993, pp. 159-165.

[23] N. D. Hatziargyriou, T. S. Karakatsanis and M. P. Papadopoulos, “The Effect of Wind Parks on the Operation of Voltage Control Devices,” 14th International Conference and Exhibition on Electricity Distribution. Part 1. Contributions, London, Vol. 5, June 1997, pp. 1-5.

[24] N. D. Hatziargyriou, T. S. Karakatsanis and M. I. Lorentzou, “Voltage Control Settings to Increase Wind Power Based on Probabilistic Load Flow,” International Journal of Electrical Power and Energy Systems, Vol. 27, No. 9-10, 2005, pp. 656-661.

[25] P. Caramia, G. Carpinelli, M. Pagano and P. Varilone, “Probabilistic Three-Phase Load Flow for Unbalanced Electrical Distribution Systems with Wind Farms,” IET Renewable Power Generation, Vol. 1, No. 2, June 2007, pp. 115-122.

[26] J. Usaola, “Probabilistic Load Flow with Correlated Wind Power Injections,” Electric Power Systems Research, Vol. 80, No. 5, 2010, pp. 528-536.

[27] L. Freris and D. Infield, “Renewable Energy in Power Systems,” John Wiley & Sons, Chichester, 2008.

[28] D. Villanueva, A. Feijoo and J. L. Pazos, “Correlation between Power Generated by Wind Turbines from Different Locations,” Scientific Proceedings of the European Wind Energy Conferences, Warsaw, 2010, pp 183-185.

[29] A. Feijóo, J. Cidrás and J. L. G. Dornelas, “Wind Speed Simulation in Wind Farms for Steady-State Security Assessment of Electrical Power Systems,” IEEE Transactions on Energy Conversion, Vol. 14, No. 4, December 1999, pp. 1582-1588.

[30] A. Feijóo and R. Sobolewsky, “Simulation of Correlated Wind Speeds,” International Journal of Integrated Energy Systems, Vol. 1, No. 2, 2009, pp. 99-106.

[31] D. Villanueva and A. Feijóo, “A Genetic Algorithm for the Simulation of Correlated Wind Speeds,” International Journal of Integrated Energy Systems, Vol. 1, No. 2, 2009, pp. 107-112.

[32] G. Papaefthymiou and P. Pinson, “Modeling of Spatial Dependence in Wind Power Forecast Uncertainty,” Proceedings of the 2008 PMAPS, Mayagüez, May 2008.

[33] X. Lu, M. McElroy and J. Kiviluoma, “Global Potential for Wind-Generated Electricity,” Proceedings of the National Academy of Sciences of the United States of America, Washington, 2009.

[34] F. Vallée, J. Lobry and O. Deblecker, “System Reliability Assessment Method for Wind Power Integration,” IEEE Transactions on Power Systems, Vol. 23, No. 3, 2008, pp 1288-1297.

[35] D. Villanueva, J. L. Pazos and A. Feijóo, “Probabilistic Load Flow Including Wind Power Generation,” IEEE Transactions on Power Systems, 2011. (Accepted)

[1] B. Borkowska, “Probabilistic Load Flow,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-93, No. 3, May-June 1974, pp. 752-755.

[2] R. N. Allan, B. Borkowska and C. H. Grigg, “Probabilistic Analysis of Power Flows,” Proceedings of the Institution of Electrical Engineers, London, Vol. 121, No. 12, December 1974, pp. 1551-1556.

[3] A. M. Leite da Silva, S. M. P. Ribeiro, V. L. Arienti, R. N. Allan and M. B. Do Coutto Filho, “Probabilistic Load Flow Techniques Applied to Power System Expansion Planning,” IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990, pp. 1047-1053.

[4] R. N. Allan, C. H. Grigg and M. R. G. Al-Shakarchi, “Numerical Techniques in Probabilistic Load Flow Problems,” International Journal for Numerical Methods in Engineering, Vol. 10, No. 4, March 1976, pp. 853-860.

[5] R. N. Allan, A. M. Leite da Silva and R. C. Burchett, “Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 5, May 1981, pp. 2539-2546.

[6] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic a. c. Load Flow,” Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 6, June 1976, pp. 531-536.

[7] R. N. Allan, A. M. Leite da Silva and R. C. Burchett, “Discrete Convolution in Power System Reliability,” IEEE Transactions on Reliability, Vol. R-30, No. 5, December 1981, pp. 452-456.

[8] R. N. Allan and A. M. Leite da Silva, “Probabilistic Load Flow Using Multilinearisations,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 128, No. 5, September 1981, pp. 280-287.

[9] A. M. Leite da Silva, R. N. Allan, S. M. Soares and V. L. Arienti, “Probabilistic Load Flow Considering Network Outages,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 132, No. 3, May 1985, pp. 139-145.

[10] A. M. Leite da Silva, V. L. Arienti and R. N. Allan, “Probabilistic Load Flow Considering Dependence between Input Nodal Powers,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, No. 6, June 1984, pp. 1524-1530.

[11] R. N. Allan, C. H. Grigg, D. A. Newey and R. F. Simmons, “Probabilistic Power-Flow Techniques Extended and Applied to Operational Decision Making,” Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 12, December 1976, pp. 1317-1324.

[12] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic Techniques in a. c. Load Flow Analysis,” Proceedings of the Institution of Electrical Engineers, Vol. 124, No. 2, February 1977, pp. 154-160.

[13] A. M. Leite da Silva and V. L. Arienti, “Probabilistic Load Flow by a Multilinear Simulation Algorithm,” IEE Proceedings of Part C: Generation, Transmission and Distribution, Vol. 137, No. 4, July 1990, pp. 276-282.

[14] C. L. Su, “Probabilistic Load-Flow Computation Using Point Estimate Method,” IEEE Transactions on Power Systems, Vol. 20, No. 4, pp. November 2005, 1843-1851.

[15] M. Brucoli, F. Torelli and R. Napoli, “Quadratic Probabilistic Load Flow with Linearly Modelled Dispatch,” Electrical Power & Energy Systems, Vol. 7, No. 3, July 1985, pp. 138-146.

[16] X. Li, X. Chen, X. Yin, T. Xiang and H. Liu, “The Algorithm of Probabilistic Load Flow Retaining Nonlinearity,” Proceedings of 2002 PowerCon, International Conference on Power System Technology, Kunming, Vol. 4, 10 October 2002, pp. 2111-2115.

[17] P. Zhang and S. T. Lee, “Probabilistic Load Fow Computation Using the Method of Combined Cumulants and Gram-Charlier Expansion,” IEEE Transactions Power Systems, Vol. 19, No.1, February 2004, pp. 676-682.

[18] J. Usaola, “Probabilistic Load Flow with Wind Production Uncertainty Using Cumulants and Cornish-Fisher Expansion,” International Journal of Electrical Power and Energy Systems, Vol. 31, No. 9, 2009, pp. 474-481.

[19] P. Jorgensen, J. S. Christensen and J. O. Tande, “Probabilistic Load Flow Calculation Using Monte Carlo Techniques for Distribution Network with Wind Turbines,” 8th International Conference on Harmonics and Quality of Power, Athens, Vol. 2, 14-16 October 1998, pp. 1146-1151.

[20] C. L. Su, “Distribution Probabilistic Load Flow Solution Considering Network Reconfiguration and Voltage Control Devices,” 15th Power Systems Computation Conference, Liege, August 2005.

[21] Z. Hu and X. Wang, “A Probabilistic Load Flow Method Considering Branch Outages,” IEEE Transactions on Power Systems, Vol. 21, No. 2, May 2006, pp. 507-514.

[22] N. D. Hatziargyriou, T. S. Karakatsanis and M. Papadopoulos, “Probabilistic Load Flow in Distribution Systems Containing Dispersed Wind Power Generation,” IEEE Transactions on Power Systems, Vol. 8, No. 1, February 1993, pp. 159-165.

[23] N. D. Hatziargyriou, T. S. Karakatsanis and M. P. Papadopoulos, “The Effect of Wind Parks on the Operation of Voltage Control Devices,” 14th International Conference and Exhibition on Electricity Distribution. Part 1. Contributions, London, Vol. 5, June 1997, pp. 1-5.

[24] N. D. Hatziargyriou, T. S. Karakatsanis and M. I. Lorentzou, “Voltage Control Settings to Increase Wind Power Based on Probabilistic Load Flow,” International Journal of Electrical Power and Energy Systems, Vol. 27, No. 9-10, 2005, pp. 656-661.

[25] P. Caramia, G. Carpinelli, M. Pagano and P. Varilone, “Probabilistic Three-Phase Load Flow for Unbalanced Electrical Distribution Systems with Wind Farms,” IET Renewable Power Generation, Vol. 1, No. 2, June 2007, pp. 115-122.

[26] J. Usaola, “Probabilistic Load Flow with Correlated Wind Power Injections,” Electric Power Systems Research, Vol. 80, No. 5, 2010, pp. 528-536.

[27] L. Freris and D. Infield, “Renewable Energy in Power Systems,” John Wiley & Sons, Chichester, 2008.

[28] D. Villanueva, A. Feijoo and J. L. Pazos, “Correlation between Power Generated by Wind Turbines from Different Locations,” Scientific Proceedings of the European Wind Energy Conferences, Warsaw, 2010, pp 183-185.

[29] A. Feijóo, J. Cidrás and J. L. G. Dornelas, “Wind Speed Simulation in Wind Farms for Steady-State Security Assessment of Electrical Power Systems,” IEEE Transactions on Energy Conversion, Vol. 14, No. 4, December 1999, pp. 1582-1588.

[30] A. Feijóo and R. Sobolewsky, “Simulation of Correlated Wind Speeds,” International Journal of Integrated Energy Systems, Vol. 1, No. 2, 2009, pp. 99-106.

[31] D. Villanueva and A. Feijóo, “A Genetic Algorithm for the Simulation of Correlated Wind Speeds,” International Journal of Integrated Energy Systems, Vol. 1, No. 2, 2009, pp. 107-112.

[32] G. Papaefthymiou and P. Pinson, “Modeling of Spatial Dependence in Wind Power Forecast Uncertainty,” Proceedings of the 2008 PMAPS, Mayagüez, May 2008.

[33] X. Lu, M. McElroy and J. Kiviluoma, “Global Potential for Wind-Generated Electricity,” Proceedings of the National Academy of Sciences of the United States of America, Washington, 2009.

[34] F. Vallée, J. Lobry and O. Deblecker, “System Reliability Assessment Method for Wind Power Integration,” IEEE Transactions on Power Systems, Vol. 23, No. 3, 2008, pp 1288-1297.

[35] D. Villanueva, J. L. Pazos and A. Feijóo, “Probabilistic Load Flow Including Wind Power Generation,” IEEE Transactions on Power Systems, 2011. (Accepted)