State estimation in unbalanced distribution networks by symmetrical components

Document Type : Article

Authors

1 Department of Electrical and Computer Engineering, University of Tehran, Tehran, P.O. Box 14395-515, Iran

2 Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, P.O. Box: V6T 1Z4, Canada

3 - Department of Electrical and Computer Engineering, University of Tehran, Tehran, P.O. Box 14395-515, Iran - Department of Electrical and Computer Engineering Illinois Institute of Technology, Chicago, IL, P.O. Box 60616-3793, USA

Abstract

State estimation (SE) of a power distribution network plays a vital role in the distribution management systems (DMSs). SE results can monitor and counteract grid technical challenges like tracking the unbalanced operation condition. In this paper, we propose a new approach for unbalanced distribution system SE which is based on the decomposition of the original problem into three subproblems by applying the symmetrical components. The subproblems are of lower dimensions and solved in parallel leading to much less computation time. The convex relaxation method is applied to address nonconvex ac power flow equations and formulate the distribution network SE problem as a semidefinite program (SDP). Furthermore, an algorithm is proposed to detect and attenuate bad data in measurements along with the SE solution. The proposed unbalanced distribution system SE approach is applied to the IEEE 37- and 123-bus distribution test systems with µPMU and pseudo measurement. The results are compared with those of three-phase SDP-based and linearized SE methods. The superiority of proposed approach is verified in terms of computation time and accuracy.

Keywords


References:
1. Madani, V., Das, R., Aminifar, F., et al. "Distribution automation strategies challenges and opportunities in a changing landscape", IEEE Trans. on Smart Grid, 6(4), pp. 2157-2165 (2015). DOI: 10.1109/TSG.2014.2368382.
2. Das, R., Madani, V., Aminifar, F., et al. "Distribution automation strategies: Evolution of technologies and the business case", IEEE Trans. on Smart Grid, 6(4), pp. 2166-2175 (2015). DOI: 10.1109/PESGM.2015.7286018.
3. Panteli, M. and Kirschen, D. "Situation awareness in power systems: Theory, challenges and applications", Electric Power Syst. Research, 122, pp. 140- 151 (2015). DOI: 10.1109/PESGM.2015.7286018.
4. Primadianto, A. and Lu, C.-N. "A review on distribution system state estimation", IEEE Trans. on Power Syst., 32(5), pp. 3875-3883 (2016). DOI: 10.1109/TPWRS. 2016.2632156.
5. Clements, K. "The impact of pseudo-measurements on state estimator accuracy", In 2011 IEEE Power and Energy Soc. Gen. Meet., 2011, pp. 1-4: IEEE (2011). DOI: 10.1109/PES.2011.6039370.
6. Teimourzadeh, S. Aminifar, F. and Shahidehpour, M. "Contingency-constrained optimal placement of micro- PMUs and smart meters in microgrids", IEEE Trans. on Smart Grid, 10(2), pp. 1889-1897 (2017). DOI: 10.1109/TSG.2017.2780078.
7. Wang, G., Giannakis, G., Chen, J., et al. "Distribution system state estimation: An overview of recent developments", Frontiers of Information Technology and Electronic Engineering. 20(1), pp. 4-17 (2019). DOI: 10.1631/FITEE.1800590.
8. Fotuhi-Friuzabad, M. Safdarian, A. Moeini-Aghtaie, et al. "Upcoming challenges of future electric power systems: sustainability and resiliency", Scientia Iranica. 23(4), pp. 1565-77 (2016). DOI: 10.24200/sci.2016.2229.
9. Alinejad Osbouei, B. and Kazemi Karegar, H. "Power system thevenin equivalent estimation based on phasor measurements", Scientia Iranica, 25(6), pp. 3559-68 (2018). DOI: 10.24200/sci.2017.4373.
10. Zhao, J., Netto, M., Huang, Zh., et al. "Roles of dynamic state estimation in power system modeling, monitoring and operation", IEEE Trans. on Power Syst., 36(3), pp. 2462-2472 (2020). DOI: 10.1109/TPWRS. 2020.3028047.
11. Muscas, C., Pegoraro, P.A. Sulis, S., et al. "New Kalman filter approach exploiting frequency knowledge for accurate PMU-based power system state estimation", IEEE Transactions on Instrumentation and Measurement, 69(9), pp. 6713-6722 (2020). DOI: 10.1109/TIM.2020.2977744.
12. Ajoudani, M., Shiekholeslami, A., and Zakariazadeh, A. "Improving state estimation accuracy in active distribution networks by coordinating real-time and pseudo-measurements considering load uncertainty", IET Generation, Transmission and Distribution, 16(8), pp. 1620{1638 (2022). DOI: 10.1049/gtd2.12388.
13. Lu, C.N., Teng, J.H., and Liu, W.-H.E "Distribution system state estimation", IEEE Trans. on Power syst., 10(1), pp. 229-240 (1995). DOI: 10.1109/59.373946.
14. Lin, W.-M. and Teng, J.-H. "Distribution fast decoupled state estimation by measurement pairing", IEEE Proc. Gen., Trans. and Dist., 143(1), pp. 43-48 (1996). DOI: 10.1049/ip-gtd:19960049.
15. Lin, W.-M., and Teng, J.-H. "State estimation for distribution systems with zero-injection constraints", In Proc. of Power Ind. Computer App. Conf., pp. 523- 529 (1995). DOI: 10.1109/59.486142.
16. Haughton, D. and Heydt, G.T. "A linear state estimation formulation for smart distribution systems", IEEE Trans. on Power Syst., 28(2), pp. 1187-1195 (2012). DOI: 10.1109/TPWRS.2012.2212921.
17. Weng, Y. Fardanesh, B., Ilic, M.D., et al. "Novel approaches using semidefinite programming method for power systems state estimation", In 2013 North Am. Power Symp. (NAPS), pp. 1-6: IEEE (2013). DOI: 10.1109/NAPS.2013.6666874.
18. Zhu, H. and Giannakis, G.B. "Power system nonlinear state estimation using distributed semidefinite programming", IEEE Journal of Selected Topics in Signal Processing, 8(6), pp. 1039-1050 (2014). DOI: 10.1109/JSTSP.2014.2331033.
19. Yao, Y. Liu, X. Zhao, D., et al. "Distribution system state estimation: A semidefinite programming approach", IEEE Trans. on Smart Grid, 10(4), pp. 4369-4378 (2018). DOI: 10.1109/TSG.2018.2858140.
20. Fernandes, T.R. Venkatesh, B., and Almeida, M.C. "Symmetrical components based state estimator for power distribution systems", In IEEE Transactions on Power Systems, 36(3), pp. 2035-2045 (2021). DOI: 10.1109/TPWRS.2020.3026639.
21. Gol, M. "Three-phase state estimation based on symmetrical components", In 2020 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe), pp. 186-190. IEEE (2020). DOI: 10.1109/ISGTEurope47291.2020.9248822.
22. Lin, C. Wu, W., and Guo, Y. "Decentralized robust state estimation of active distribution grids incorporating microgrids based on PMU measurements", IEEE Trans. on Smart Grid, 11(1), pp. 810-820 (2019). DOI: 10.1109/tsg.2019.2937162.
23. Baran, M.E. Kelley, A.W. "A branch-current-based state estimation method for distribution systems", In IEEE Transactions on Power Systems, 10(1), pp. 483- 91 (1995). DOI: 10.1109/59.373974.
24. Kron, G. "Tensorial analysis of integrated transmission systems part I. the six basic reference frames", Trans. of the Am. Inst. of Electrical Engineers, 70(2), pp. 1239-1248 (1951). DOI: 10.1109/T-AIEE.1951.5060553.
25. Lavaei, J. and Low, S.H. "Zero duality gap in optimal power  flow problem", IEEE Trans. on Power Syst., 27(1), pp. 92-107 (2011). DOI: 10.1109/TPWRS. 2011.2160974.
26. Glover, J., Sarma, M., and Overbye, T., Power system analysis and design, SI version, Cengage Learning, (2012).
27. Aspremont, A. Ghaoui, L. Jordan, E., et al. "A direct formulation for sparse PCA using semidefinite programming", In Advances in neural information processing systems, pp. 41-48 (2005). DOI. 10.1137/050645506.
28. Thompson, R. "Principal submatrices V: Some results concerning principal submatrices matrices", J. Res. Nat. Bur. Standards Sect. B., 72(2), pp. 115-125 (1968).
29. Fortescue, C. "Method of symmetrical co-ordinates applied to the solution of polyphase networks", Trans. of the Am. Ins. of Elec. Eng., 37(2), pp. 1027-1140 (1918). DOI: 10.1109/T-AIEE.1918.4765570.
30. Boyd, S. Vandenberghe, L., Convex optimization. Cambridge university press (2004). 
31. So, A., Ye, Y., and Zhang, J. "A unified theorem on SDP rank reduction", Math. of Operations Research, 33(4), pp. 910{920 (2008).
32. Shabalin, A. and Nobel, A. "Reconstruction of a lowrank matrix in the presence of Gaussian noise", Journal of Multivariate Analysis, 118, pp. 67-76 (2013). https://doi.org/10.1016/j.jmva.2013.03.005.
33. (2019-09-30). Available: http://sites.ieee.org/pestestfeeders/.
34. Stewart, E.M. and von Meier, A., Phasor Measurements for Distribution System Applications (2016). https://doi.org/10.1002/9781118755471.sgd087.
35. Gholami, M. Abbaspour, A. Fattaheian-Dehkordi, et al. "Optimal allocation of PMUs in active distribution network considering reliability of state estimation results", IET Generation, Transmission and Distribution, 14(18), pp. 3641-51 (2020). https://doi.org/10.1049/iet-gtd.2019.1946.
36. Almeida, D., Fernandes, T., Ugarte. L. "State estimation and active distribution networks", In Planning and Operation of Active Distribution Networks, pp. 377-402 Springer, Cham (2022).
37. Farkhondeh, J. Bahmanyar, A., and Shabanzadeh, M. "Optimal meter placement in distribution feeders using branch-current based three-phase state estimation: A quest for observability enhancement", In 2020 10th Smart Grid Conference (SGC), pp. 1-6. IEEE (2020). DOI: 10.1109/SGC52076.2020.9335754.
38. Aminifar, F., Safdarian, A., Fotuhi-Firuzabad, M., et al. "A multi-objective framework for enhancing the reliability and minimizing the cost of PMU deployment in power systems", Scientia Iranica, 23(6), pp. 2917- 2927 (2016). https://doi.org/10.24200/sci.2016.4001.
39. Kerns, B. "Optimal micro phasor measurement unit placement for complete observability of the distribution system", University of British Columbia (2018). DOI: 10.14288/1.0372012.
40. Dugan, R. "Opendss manual", EPRI,[Online] Available at: http://sourceforge. net/apps/mediawiki/ electricdss/index. php. 
41. Stewart, E. and von Meier, A. "Phasor measurements for distribution system applications", Smart Grid Handbook, pp. 1-10 (2016). DOI: 10.1002/9781118755471.sgd087.
42. Grant, M. Boyd, S. and Ye, Y. "CVX: Matlab software for disciplined convex programming", (2009). 
43. Mosek, A. "The MOSEK optimization software", Online at http://www. mosek. com, 54(2-1), pp. 5-10 (2010).
44. Vieira, J., Freitas, W., and Morelato, A. "Phasedecoupled method for three-phase power- flow analysis of unbalanced distribution systems", IEEE Proc. Gen., Trans. and Dist., 151(5), pp. 568-574 (2004). DOI: 10.1049/ip-gtd:20040831.
45. Gonen, T. Electric power distribution engineering. CRC press; Aug 18 (2015). 
46. Dadashzade, A., Aminifar, F., and Davarpanah, M. "Unbalanced source detection in power distribution networks by negative sequence apparent powers", in IEEE Transactions on Power Delivery, 36(1), pp. 481- 483 (Feb 2021). DOI: 10.1109/TPWRD.2020.3029437.
Volume 31, Issue 17
Transactions on Computer Science & Engineering and Electrical Engineering (D)
November and December 2024
Pages 1517-1529
  • Receive Date: 27 July 2021
  • Revise Date: 04 April 2022
  • Accept Date: 01 August 2022