Real-Time Voltage Stability Limits Assessment Using Thevenin Equivalent in Power Systems

Year 2021, , 1101 - 1112, 31.07.2021

Enes Talha Gümüş , Mehmet Ali Yalçın

https://doi.org/10.29130/dubited.890924

Abstract

In this study, voltage stability evaluation of an N-bus power system is made by using the Thevenin impedance observed from an any load bus and the impedance of the load in the bus. The Thevenin equivalent impedance seen from the bus is computed using an optimization-based approach. Only the current, voltage and power factor measurements of the related bus are used for the proposed approach. The impedance stability index of the bus is computed using the Thevenin equivalent impedance obtained with the proposed approach and the impedance of the load. The computed index provides an opportunity to evaluate the voltage stability status of the bus in real time. It is observed that the critical power values corresponding to the impedance stability index computed using Thevenin impedance obtained with the proposed approach and critical power values derived from power flow are very close to each other.

Keywords

Voltage stability, Optimization, Thevenin equivalent

Güç Sistemlerinde Thevenin Eşdeğer Devresi Kullanılarak Gerilim Kararlılığı Sınırlarının Gerçek Zamanlı Değerlendirmesi

Abstract

Bu çalışmada, çok baralı bir güç sisteminin herhangi bir yük barasından görülen Thevenin empedansı ve yük empedansı kullanılarak yük barasına gerilim kararlılığı değerlendirmesi yapılmıştır. Gerilim kararlılığı analilizi yapılacak baradan görülen Thevenin eşdeğer devre empedansı optimizasyon esaslı bir yaklaşımla hesaplanmıştır. Optimizasyon yaklaşımı için yerel baradan sadece akım, gerilim ve güç faktörü ölçümleri yapılmıştır. Hesaplanan Thevenin eşdeğer devre empedansı ve baradaki yükün empedansı ile baraya ait empedans kararlılık indeksi hesaplanmıştır. Hesaplanan empedans kararlılık indeksi, baranın gerilim kararlılığı durumunu gerçek zamanlı olarak takip etme imkanı sunmuştur. Önerilen yaklaşımla elde edilen Thevenin empedansı ile hesaplanan empedans kararlılık indeksine karşılık gelen kritik güç değeri ve güç akışından elde edilen kritik güç değerinin birbirine çok yakın olduğu görülmüştür.

Keywords

Gerilim Kararlılığı, Optimizasyon, Thevenin eşdeğer devresi

References

• [1] S. Ravındra, V. C. V. Reddy, and S. Sıvanagaraju, “Power system security analysis under transmission line outage condition,” Ijireeice, vol. 3, no. 1, pp. 46–50, 2015, doi: 10.17148/ijireeice.2015.3109.
• [2] I. Alhamrouni, M. A. Alif, B. Ismail, M. Salem, A. Jusoh, and T. Sutikno, “Load flow based voltage stability indices for voltage stability and contingency analysis for optimal location of STATCOM in distribution network with integrated distributed generation unit,” Telkomnika (Telecommunication Comput. Electron. Control., vol. 16, no. 5, pp. 2302–2315, 2018, doi: 10.12928/TELKOMNIKA.v16i5.10577.
• [3] K.Döşoğlu, “Gerilim-Reaktif Güç Kontrol Modelli Kademe Değiştirici Transformatörün Gerilim Kararlılığı Üzerindeki Etkisi,” Düzce Üniversitesi Bilim ve Teknol. Derg., vol. 9, no. 1, pp. 278–292, Jan. 2019, doi: 10.29130/dubited.521863.
• [4] M. S. S. Danish, T. Senjyu, S. M. S. Danish, N. R. Sabory, N. K, and P. Mandal, “A Recap of Voltage Stability Indices in the Past Three Decades,” Energies, vol. 12, no. 8, p. 1544, Apr. 2019, doi: 10.3390/en12081544.
• [5] S. L. Ramírez-P, C. A. Lozano-M, and N. G. Caicedo-D, “Review and classification of indices for voltage stability monitoring using PMU measurements,” J. Eng. Sci. Technol. Rev., vol. 11, no. 4, pp. 180–198, 2018, doi: 10.25103/jestr.114.23.
• [6] B. Bozali and A. Öztürk, “Türkiye 400 KV’luk Güç Sistemi İçin Optimal Fazör Ölçüm Birimlerinin Yerleşim Yerlerinin Belirlenmesi,” Düzce Üniversitesi Bilim ve Teknol. Derg., vol. 8, no. 2, pp. 1319–1336, Apr. 2020, doi: 10.29130/dubited.659075.
• [7] Y. Lee and S. Han, “Real-time voltage stability assessment method for the Korean power system based on estimation of Thévenin equivalent impedance,” Appl. Sci., vol. 9, no. 8, 2019, doi: 10.3390/app9081671.
• [8] B. Brusilowicz, W. Rebizant, and J. Szafran, “A new method of voltage stability margin estimation based on local measurements,” in 2011 International Conference on Advanced Power System Automation and Protection, Oct. 2011, pp. 2443–2447, doi: 10.1109/APAP.2011.6180655.
• [9] B. Shakerighadi, F. Aminifar, and S. Afsharnia, “A real-time voltage stability index based on local measurements,” in 2015 23rd Iranian Conference on Electrical Engineering, May 2015, pp. 1492–1497, doi: 10.1109/IranianCEE.2015.7146456.
• [10] K. Vu, M. M. Begovic, D. Novosel, and M. M. Saha, “Use of local measurements to estimate voltage-stability margin,” IEEE Trans. Power Syst., vol. 14, no. 3, pp. 1029–1035, 1999, doi: 10.1109/59.780916.
• [11] J. E. Tobón V., R. E. C. Gutiérrez, and J. M. Ramirez, “27-Voltage collapse detection based on local measurements,” Electr. Power Syst. Res., vol. 107, pp. 77–84, 2014, doi: 10.1016/j.epsr.2013.09.013.
• [12] Z. Yun, X. Cui, and K. Ma, “Online Thevenin Equivalent Parameter Identification Method of Large Power Grids Using LU Factorization,” IEEE Trans. Power Syst., vol. 34, no. 6, pp. 4464–4475, Nov. 2019, doi: 10.1109/TPWRS.2019.2920994.
• [13] I. Smon, G. Verbic, and F. Gubina, “Local Voltage-Stability Index Using Tellegen’s Theorem,” IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1267–1275, Aug. 2006, doi: 10.1109/TPWRS.2006.876702.
• [14] R. Maharjan and S. Kamalasadan, “Voltage stability index for online voltage stability assessment,” in 2015 North American Power Symposium (NAPS), Oct. 2015, pp. 1–6, doi: 10.1109/NAPS.2015.7335245.
• [15] Y. Wang, W. Li, and J. Lu, “A new node voltage stability index based on local voltage phasors,” Electr. Power Syst. Res., vol. 79, no. 1, pp. 265–271, 2009, doi: 10.1016/j.epsr.2008.06.010.
• [16] M.H.Haque, “25-On-line monitoring of maximum permissible loading of a power system within voltage stability limits,” IEE Proc. Gener. Transm. Distrib., vol. 150, no. 1, 2003, doi: 10.1093/oxfordjournals.ndt.a091183.
• [17] A. Birchfield et al., “A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids,” Energies, vol. 10, no. 8, p. 1233, Aug. 2017, doi: 10.3390/en10081233.
• [18] A. Wiszniewski, “45-New criteria of voltage stability margin for the purpose of load shedding,” IEEE Trans. Power Deliv., vol. 22, no. 3, pp. 1367–1371, 2007, doi: 10.1109/TPWRD.2006.886772.
• [19] D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math., vol. 11, no. 2, pp. 431–441, Jun. 1963, doi: 10.1137/0111030.
• [20] C. Kanzow, N. Yamashita, and M. Fukushima, “Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints,” J. Comput. Appl. Math., vol. 172, no. 2, pp. 375–397, 2004, doi: 10.1016/j.cam.2004.02.013.
• [21] S. Polster, H. Renner, D. T. Duong, and K. Uhlen, “Voltage stability monitoring using a modified thevenin impedance,” 2017 IEEE Manchester PowerTech, Powertech 2017, pp. 2–7, 2017, doi: 10.1109/PTC.2017.7980864.
• [22] R. Kaur and D. Kumar, “Transient Stability Improvement of IEEE 9 Bus System Using Power World Simulator,” MATEC Web Conf., vol. 57, 2016, doi: 10.1051/matecconf/20165701026.
• [23] N. A. M. Ismail, A. A. M. Zin, A. Khairuddin, and S. Khokhar, “A comparison of voltage stability indices,” Proc. 2014 IEEE 8th Int. Power Eng. Optim. Conf. PEOCO 2014, pp. 30–34, 2014, doi: 10.1109/PEOCO.2014.6814394.
• [24] Electronics Hub, Maximum Power Transfer Theorem (MPTT),(04 Mart 2021),[Çevrimiçi], Erişim: https://www.electronicshub.org/maximum-power-transfer-theorem/