skip to main content

Probabilistic Assessment of Power Systems with Renewable Energy Sources based on an Improved Analytical Approach

1Faculty of Electrical Engineering, The University of Danang - University of Science and Technology, 54 Nguyen Luong Bang, Danang, Viet Nam

2The University of Danang, 41 Le Duan, Danang, Viet Nam

Received: 3 May 2021; Revised: 5 Jun 2021; Accepted: 25 Jun 2021; Available online: 30 Jun 2021; Published: 1 Nov 2021.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2021 The Authors. Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:

The increasing penetration of renewable energy sources has introduced great uncertainties and challenges into computation and analysis of electric power systems. To deal with uncertainties, probabilistic approaches need to be used. In this paper, we propose a new framework for probabilistic assessment of power systems taking into account uncertainties from input random variables such as load demands and renewable energy sources. It is based on the cumulant-based Probabilistic Power Flow (PPF) in combination with an improved clustering technique. The improved clustering technique is also developed in this study by making use of Principal Component Analysis (PCA) and Particle Swarm Optimization (PSO) to reduce the range of variation in the input data, thus increasing the accuracy of the traditional cumulant-based PPF (TCPPF) method. In addition, thanks to adopting PCA for dimensionality reduction, the improved clustering technique can be effectively dealt with a large number of input random variables so that the proposed framework for probabilistic assessment can be applied for large power systems. The IEEE-118 bus test system is modified by adding five wind and eight solar photovoltaic power plants to examine the proposed method. Uncertainties from input random variables are represented by appropriate probabilistic models. Extensive testing on the test system indicates good performance of the proposed approach in comparison to the traditional cumulant-based PPF and Monte Carlo simulation. The IEEE-118 bus test system is modified by adding five wind and eight solar photovoltaic power plants to examine the proposed method. Extensive testing on the test system, using Matlab (R2015a) on an Intel Core i5 CPU 2.53 GHz/4.00 GB RAM PC, indicates good performance of the proposed approach (PPPF) in comparison to the TCPPF and Monte Carlo simulation (MCS): In terms of computation time, PPPF needs 4.54 seconds, while TCPPF and MCS require 2.63 and 251 seconds, respectively; ARMS errors are calculated for methods using benchmark MCS and their values clearly demonstrate the higher accuracy of PPPF in estimating probability distributions compared to TCPPF, i.e., the maximum (Max) and mean (Mean) values of ARMS errors of all output random variables are: ARMSPPPFmax = 0.11%, ARMSTCPPFmax = 0.55%, and ARMSPPPFmean = 0.06%, ARMSTCPPFmean  = 0.35%.

Fulltext View|Download
Keywords: Renewable energy; uncertainty; Probabilistic Power Flow; clustering technique; power system

Article Metrics:

  1. Aien, M., Khajeh, M.G., Rashidinejad, M., & Fotuhi-Firuzabad, M. (2014). Probabilistic power flow of correlated hybrid wind-photovoltaic power systems. IET Renew Power Gen., 8, 649-658;
  2. Allan, R.N., & Al-Shakarchi, M.R.G. (1997). Probabilistic techniques in A.C. load-flow analysis. Proc. Inst. Elect. Eng., 124, 154-160;
  3. Bandyopadhyay S., & Maulik U. (2002). Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognit, 35(6), 1197-1208;
  4. Borkowska, B. (1974). Probabilistic load flow. IEEE Trans. Power App. Syst., PAS-93, 752-759;
  5. Bosisio, A., Berizzia, A.. Le, D.D., Bassic, F., & Giannuzzi, G. (2019). Improving DTR assessment by means of PCA applied to wind data. Electric Power Systems Research, 172, 193-200;
  6. Cai, D., Chen, J., Shi, D., Duan, X., Li, H., & Yao, M. (2012). Enhancements to the cumulant method for probabilistic load flow studies. Proceedings of 2012 IEEE power and energy society general meeting, San Diego, USA, pp. 1-8;
  7. Carpinelli, G., Caramia, P., & Varilone, P. (2015). Multi-linear Monte Carlo simulation method for probabilistic load flow of distribution systems with wind and photovoltaic generation systems. Renew. Energ., 76, 283-295;
  8. Christie, R., Power System Test Case Archive. (1993). Available online: (accessed on 21 April 2021)
  9. Deng, X., He, J., Zhang, P., & Sciubba, E. (2017). A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables. Energies, 10(10), 1623;
  10. Deng, X., Zhang, P., Jin, K., He, J., Wang, X., & Wang, Y. (2019). Probabilistic load flow method considering large-scale wind power integration. Journal of Modern Power Systems and Clean Energy, 7(4), 813-825;
  11. Falkenauer, E. (1998) Genetic Algorithms and Grouping Problems. John Wiley & Sons, Inc.: New York, NY, USA
  12. Fan, M., Vittal, V., Heydt, G.T., & Ayyanar, R. (2012). Probabilistic Power Flow Studies for Transmission Systems with Photovoltaic Generation Using Cumulants. IEEE Trans. Power Syst., 27(4), 2251-2261;
  13. Gan G., Ma C., & Wu, J. (2007) Data Clustering: Theory, Algorithms, and Applications. SIAM: Philadelphia, PA, USA
  14. Hajian, M., Rosehart, W.D., & Zareipour, H. (2013). Probabilistic power flow by Monte Carlo simulation with Latin Supercube sampling. IEEE Trans. Power Syst., 28(2), 1550-1559;
  15. Jackson, J.E. (1991) A Users Guide to Principal Component Analysis. Hoboken, Wiley: NJ, USA
  16. Jolliffe, I.T. (2002) Principal Component Analysis. Springer: New York, NY, USA
  17. Kuo, R., & Zulvia, F. (2013). Automatic clustering using an improved particle swarm optimization. J. Ind. Intell. Inf., 1, 46-51; doi: 10.12720/jiii.1.1.46-51
  18. Le, D.D., Gross, G., & Berizzi, A. (2015). Probabilistic Modeling of Multisite Wind Farm Production for Scenario-based Applications. IEEE Transactions on Sustainable Energy, 6(3), 748-758;
  19. Le, D.D., Berizzi, A., & Bovo, C. (2016). A probabilistic security assessment approach to power systems with integrated wind resources. Renewable Energy, 85, 114-123;
  20. Leite da Silva, A.M., & Milhorance de Castro, A. (2018). Risk Assessment in Probabilistic Load Flow via Monte Carlo Simulation and Cross-Entropy Method. IEEE Trans. Power Syst., 34(2), 1193 - 1202;
  21. Mohammadi, M., Shayegani, A., & Adaminejad, H. (2013). A new approach of point estimate method for probabilistic load flow. Int J Elec Power, 51, 54-60;
  22. Morales, J.M., & Perez-Ruiz, J. (2007). Point estimate schemes to solve the probabilistic power flow. IEEE Trans Power Syst, 22(4), 1594-1601;
  23. Nguyen, N.T.A., Le, D.D., Moshi, G.G., Bovo, C., & Berizzi, A. (2016). Sensitivity analysis on locations of Energy Storage in power systems with wind integration. IEEE Trans. Ind. Appl., 52, 5185-5193;
  24. Ruiz-Rodriguez, F.J., Hernandez, J.C., & Jurado, F. (2012). Probabilistic load flow for photovoltaic distributed generation using the Cornish-Fisher expansion. Electr. Power Syst. Res., 89, 129-138;
  25. Su, C.L. (2005). Probabilistic load-flow computation using point estimate method. IEEE Trans. Power Syst., 20, 1843-1851;
  26. Tao, C., & Franchetti, F. (2013). A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow. In Proceedings of the IEEE PES Innovative Smart Grid Technologies (ISGT), Washington, DC, USA, pp. 1-6;
  27. Van der Merwe, D.W., & Engelbrecht, A.P. (2003). Data clustering using particle swarm optimization. Proc. 2003 Congress on Evolutionary Computation, 1, 215-220;
  28. Xiao X., Dow E., Eberhart R., Ben Miled Z., & Oppelt. R.J. (2003). Gene Clustering using Self-Organizing Maps and Particle Swarm Optimization. Proceeding of Second IEEE International Workshop on High Performance Computational Biology, Nice, France;
  29. Zhang, P., & Lee, S.T. (2004). Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion. IEEE Trans. Power Syst., 19(1), 676-682;
  30. Zhou, Z., Tang, F., Liu, D., Wang, C., & Gao, X. (2020). Probabilistic Assessment of Distribution Network with High Penetration of Distributed Generator. Sustainability, 12, 1709;

Last update:

No citation recorded.

Last update:

No citation recorded.