L-Index-Based Technique for Voltage Collapse Prediction and Voltage Stability Enhancement in Electrical Power Systems
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Abstract
Recent years have witnessed a notable increase in the occurrence of blackouts, especially in developing nations, attributed to the continuously growing demand on modern power networks. Given that the demand shows no signs of abating and is projected to increase further in the coming years, additional research on power system stability is imperative. This study, therefore, investigates voltage stability assessment in power systems using the L-index methodology, focusing on the Nigerian 28-bus system and the IEEE system. The L-index offers a practical means of identifying weak buses and evaluating voltage stability margins. Calculating L-index values for load buses under diverse conditions identifies critical points, with higher values indicating vulnerability. The research investigates injecting reactive power at load buses to prevent collapse, comparing outcomes with and without compensation. Analyzing the L-index's performance across varied loading scenarios confirms its precision in predicting breakdown points and identifying critical buses. Load flow analysis of the Nigerian 28-Bus system reveals that only bus 16 exceeds voltage limits, while line analysis shows total power losses. Increasing loadability exposes bus 16 as the weakest, supported by its low voltage magnitude. The research confirms bus 16 as the system's weakest point, guiding corrective measures to enhance stability and prevent collapse. Utilizing Matlab for implementation, this study contributes valuable insights into system vulnerability and provides a framework for improving voltage stability in power systems.
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References
Alayande, A. S., Jimoh, A. A. G., & Yusuff, A. A., (2020), Identification of Critical Elements in Interconnected Power Networks, Iranian Journal of Science and Technology - Transactions of Electrical Engineering, 44(1), 197–211. https://doi.org/10.1007/s40998-019-00235-1 DOI: https://doi.org/10.1007/s40998-019-00235-1
Alayande, A., A.O, S., Somefun, T., Ademola, A., Awosope, C., Okoyeigbo, O., & Popoola, O., (2021), Transient Stability Enhancement of a Power System Considering Integration of FACT Controllers Through Network Structural Characteristics Theory, Advances in Science, Technology and Engineering Systems Journal, 6(1), 968–981. https://doi.org/10.25046/aj0601107 DOI: https://doi.org/10.25046/aj0601107
Zohre Alipour, M. A. S. M., (2013), Structural Properties and vulnerability of Iranian 400kv Power Transmission Grid: a Complex Systems Approach, Industrial Engineering & Management, 2(3), 1–7. https://doi.org/10.4172/2169-0316.1000112 DOI: https://doi.org/10.4172/2169-0316.1000112
Abedi, A., Gaudard, L., & Romerio, F., (2018), Review of major approaches to analyze vulnerability in power system, Reliability Engineering and System Safety, 153–172. https://doi.org/10.1016/j.ress.2018.11.019 DOI: https://doi.org/10.1016/j.ress.2018.11.019
Hailu, E. A., Nyakoe, G. N., & Muriithi, C. M., (2023), Techniques of power system static security assessment and improvement: A literature survey, Heliyon, 9(3), e14524. https://doi.org/10.1016/j.heliyon.2023.e14524 DOI: https://doi.org/10.1016/j.heliyon.2023.e14524
Asadi Majd, A., Farjah, E., Rastegar, M., & Bacha, S., (2021), Generation and transmission expansion planning for bulk renewable energy export considering transmission service cost allocation, Electric Power Systems Research, 196(October 2020), 107197. https://doi.org/10.1016/j.epsr.2021.107197 DOI: https://doi.org/10.1016/j.epsr.2021.107197
Power quality and stability improvement of more ‑ electronics power systems, (2018).
Velayati, M. H., Amjady, N., & Khajevandi, I., (2015), Prediction of dynamic voltage stability status based on Hopf and limit induced bifurcations using extreme learning machine, International Journal of Electrical Power and Energy Systems, 69, 150–159. https://doi.org/10.1016/j.ijepes.2015.01.005 DOI: https://doi.org/10.1016/j.ijepes.2015.01.005
Pinzón, J. D., & Colomé, D. G., (2019), Real-time multi-state classification of short-term voltage stability based on multivariate time series machine learning, International Journal of Electrical Power and Energy Systems, 108, 402–414. https://doi.org/10.1016/j.ijepes.2019.01.022 DOI: https://doi.org/10.1016/j.ijepes.2019.01.022
Malbasa, V., Zheng, C., Chen, P. C., Popovic, T., & Kezunovic, M., (2017), Voltage Stability Prediction Using Active Machine Learning, IEEE Transactions on Smart Grid, 8(6), 3117–3124. https://doi.org/10.1109/TSG.2017.2693394 DOI: https://doi.org/10.1109/TSG.2017.2693394
Wokoma, B. A., Osegi, E. N., & Idachaba, A. O., (2019), Predicting Voltage Stability Indices of Nigerian 330kV 30 Bus Power Network Using an Auditory Machine Intelligence Technique, IEEE AFRICON Conference, 2019-Septe. https://doi.org/10.1109/AFRICON46755.2019.9133915 DOI: https://doi.org/10.1109/AFRICON46755.2019.9133915
Krishnan, V., & McCalley, J. D., (2012), Contingency assessment under uncertainty for voltage collapse and its application in risk based contingency ranking, International Journal of Electrical Power and Energy Systems, 43(1), 1025–1033. https://doi.org/10.1016/j.ijepes.2012.05.065 DOI: https://doi.org/10.1016/j.ijepes.2012.05.065
Wang, G., Zhang, Z., Bian, Z., & Xu, Z., (2021), A short-term voltage stability online prediction method based on graph convolutional networks and long short-term memory networks, International Journal of Electrical Power and Energy Systems, 127. https://doi.org/10.1016/j.ijepes.2020.106647 DOI: https://doi.org/10.1016/j.ijepes.2020.106647
Ghaghishpour, A., & Koochaki, A., (2020), An intelligent method for online voltage stability margin assessment using optimized ANFIS and associated rules technique, ISA Transactions, 102, 91–104. https://doi.org/10.1016/j.isatra.2020.02.028 DOI: https://doi.org/10.1016/j.isatra.2020.02.028
Rahi, O. P., Yadav, A. K., Malik, H., Azeem, A., & Bhupesh, K., (2012), Power system voltage stability assessment through artificial neural network, Procedia Engineering, 30, 53–60. https://doi.org/10.1016/j.proeng.2012.01.833 DOI: https://doi.org/10.1016/j.proeng.2012.01.833
Salama, M. M., Saied, E. M., Abou-Elsaad, M. M., & Ghariany, E. F., (2001), Estimating the voltage collapse proximity indicator using artificial neural network, Energy Conversion and Management, 42(1), 69–79. https://doi.org/10.1016/S0196-8904(00)00023-6 DOI: https://doi.org/10.1016/S0196-8904(00)00023-6
Ibrahim, A. M., & El-Amary, N. H., (2018), Particle Swarm Optimization trained recurrent neural network for voltage instability prediction, Journal of Electrical Systems and Information Technology, 5(2), 216–228. https://doi.org/10.1016/j.jesit.2017.05.001 DOI: https://doi.org/10.1016/j.jesit.2017.05.001
Goh, H. H., Chua, Q. S., Lee, S. W., Kok, B. C., Goh, K. C., & Teo, K. T. K., (2015), Evaluation for Voltage Stability Indices in Power System Using Artificial Neural Network, Procedia Engineering, 118, 1127–1136. https://doi.org/10.1016/j.proeng.2015.08.454 DOI: https://doi.org/10.1016/j.proeng.2015.08.454
Cai, H., & Hill, D. J., (2022), A real-time continuous monitoring system for long-term voltage stability with sliding 3D convolutional neural network, International Journal of Electrical Power and Energy Systems, 134. https://doi.org/10.1016/j.ijepes.2021.107378 DOI: https://doi.org/10.1016/j.ijepes.2021.107378
Jeyasurya, B., (1994), Artificial neural networks for power system steady-state voltage instability evaluation, Electric Power Systems Research, 29(2), 85–90. https://doi.org/10.1016/0378-7796(94)90065-5 DOI: https://doi.org/10.1016/0378-7796(94)90065-5
Nizam, M., Mohamed, A., & Hussain, A., (2010), Dynamic voltage collapse prediction in power systems using support vector regression, Expert Systems with Applications, 37(5), 3730–3736. https://doi.org/10.1016/j.eswa.2009.11.052
Tiwari, R., Niazi, K. R., & Gupta, V., (2012), Line collapse proximity index for prediction of voltage collapse in power systems, International Journal of Electrical Power and Energy Systems, 41(1), 105–111. https://doi.org/10.1016/j.ijepes.2012.03.022 DOI: https://doi.org/10.1016/j.ijepes.2012.03.022
Pama, A., & Radman, G., (2009), A new approach for estimating voltage collapse point based on quadratic approximation of PV-curves, Electric Power Systems Research, 79(4), 653–659. https://doi.org/10.1016/j.epsr.2008.09.018 DOI: https://doi.org/10.1016/j.epsr.2008.09.018
Woldu, T. A., Ziegler, C., & Wolter, M., (2020), A new method for prediction of static and dynamic voltage collapse using node parameters in large power networks, IEEE PES Innovative Smart Grid Technologies Conference Europe, 2020-Octob, 344–348. https://doi.org/10.1109/ISGT-Europe47291.2020.9248887 DOI: https://doi.org/10.1109/ISGT-Europe47291.2020.9248887
Pourbagher, R., Derakhshandeh, S. Y., & Hamedani Golshan, M. E., (2022), An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems, International Journal of Electrical Power and Energy Systems, 134. https://doi.org/10.1016/j.ijepes.2021.107425 DOI: https://doi.org/10.1016/j.ijepes.2021.107425
Satpathy, P. K., Das, D., & Dutta Gupta, P. B., (2004), Critical switching of capacitors to prevent voltage collapse, Electric Power Systems Research, 71(1), 11–20. https://doi.org/10.1016/j.epsr.2003.12.016 DOI: https://doi.org/10.1016/j.epsr.2003.12.016
Vanfretti, L., & Arava, V. S. N., (2020), Decision tree-based classification of multiple operating conditions for power system voltage stability assessment, International Journal of Electrical Power and Energy Systems, 123, 1–9. https://doi.org/10.1016/j.ijepes.2020.106251 DOI: https://doi.org/10.1016/j.ijepes.2020.106251
Razmi, H., Shayanfar, H. A., & Teshnehlab, M., (2012), Steady state voltage stability with AVR voltage constraints, International Journal of Electrical Power and Energy Systems, 43(1), 650–659. https://doi.org/10.1016/j.ijepes.2012.06.051 DOI: https://doi.org/10.1016/j.ijepes.2012.06.051
Perninge, M., & Söder, L., (2011), Risk estimation of the distance to voltage instability using a second order approximation of the saddle-node bifurcation surface, Electric Power Systems Research, 81(2), 625–635. https://doi.org/10.1016/j.epsr.2010.10.021 DOI: https://doi.org/10.1016/j.epsr.2010.10.021
Dobson, I., & Chiang, H. D., (1989), Towards a theory of voltage collapse in electric power systems, Systems and Control Letters, 13(3), 253–262. https://doi.org/10.1016/0167-6911(89)90072-8 DOI: https://doi.org/10.1016/0167-6911(89)90072-8
Church, C., Morsi, W. G., Diduch, C. P., El-Hawary, M. E., & Chang, L., (2010), Voltage collapse detection using ant colony optimization for smart grid applications, EPEC 2010 - IEEE Electrical Power and Energy Conference: “Sustainable Energy for an Intelligent Grid.” https://doi.org/10.1109/EPEC.2010.5697185 DOI: https://doi.org/10.1109/EPEC.2010.5697185
Verbič, G., & Gubina, F., (2004), A novel scheme of local protection against voltage collapse based on the apparent-power losses, International Journal of Electrical Power and Energy System, 26(5), 341–347. https://doi.org/10.1016/j.ijepes.2003.11.001 DOI: https://doi.org/10.1016/j.ijepes.2003.11.001
Nizam, M., Mohamed, A., & Hussain, A., (2010), Dynamic voltage collapse prediction in power systems using support vector regression, Expert Systems with Applications, 37(5), 3730–3736. https://doi.org/10.1016/j.eswa.2009.11.052 DOI: https://doi.org/10.1016/j.eswa.2009.11.052
Sanz, F. A., Ramirez, J. M., & Posada, J., (2016), Statistical method for on-line voltage collapse proximity estimation, International Journal of Electrical Power and Energy Systems, 82, 392–399. https://doi.org/10.1016/j.ijepes.2016.03.035 DOI: https://doi.org/10.1016/j.ijepes.2016.03.035
Al-Hinai, A., & Choudhry, T. M. A. C., (2001), Voltage Collapse Prediction for Interconnected Power Systems, In Proc. of 33rd North American Power Symposium (NAPS), College Station, TX, October 2001. College Station, TX. Retrieved from https://www.researchgate.net/publication/266450683
Balamourougan, V., Sidhu, T. S., & Sachdev, M. S., (2004), A technique for real time detection of voltage collapse in power systems, IEE Conference Publication, 2, 639–642. https://doi.org/10.1049/cp:20040205 DOI: https://doi.org/10.1049/cp:20040205
Pourjafari, E., & Mojallali, H., (2011), Predictive control for voltage collapse avoidance using a modified discrete multi-valued PSO algorithm, ISA Transactions, 50(2), 195–200. https://doi.org/10.1016/j.isatra.2010.12.006 DOI: https://doi.org/10.1016/j.isatra.2010.12.006
Wang, Y., Xu, Q., & Zheng, J., (2020), The new steady state voltage stability analysis methods with computation loads separation technique in DC power systems, International Journal of Electrical Power and Energy Systems, 115, 1–8. https://doi.org/10.1016/j.ijepes.2019.105482 DOI: https://doi.org/10.1016/j.ijepes.2019.105482
Li, X., Zhang, L., Jiang, T., Li, F., Chen, H., & Jia, H., (2021), Relaxed decoupled direct calculation of voltage collapse points and its application in static voltage stability region boundary formation, International Journal of Electrical Power and Energy Systems, 125, 1–13. https://doi.org/10.1016/j.ijepes.2020.106452 DOI: https://doi.org/10.1016/j.ijepes.2020.106452
Šmon, I., Pantoš, M., & Gubina, F., (2008), An improved voltage-collapse protection algorithm based on local phasors, Electric Power Systems Research, 78(3), 434–440. https://doi.org/10.1016/j.epsr.2007.03.012 DOI: https://doi.org/10.1016/j.epsr.2007.03.012
Liu, S., Shi, R., Zhang, T., Tang, F., Zhang, L., Liu, L., … Zhang, M., (2021), An integrated scheme for static voltage stability assessment based on correlation detection and random bits forest, International Journal of Electrical Power and Energy Systems, 130, 1–10. https://doi.org/10.1016/j.ijepes.2021.106898 DOI: https://doi.org/10.1016/j.ijepes.2021.106898
Yang, F., Ling, Z., Wei, M., Mi, T., Yang, H., & Qiu, R. C., (2021), Real-time static voltage stability assessment in large-scale power systems based on spectrum estimation of phasor measurement unit data, International Journal of Electrical Power and Energy Systems, 124, 1–10. https://doi.org/10.1016/j.ijepes.2020.106196 DOI: https://doi.org/10.1016/j.ijepes.2020.106196
Ratra, S., Tiwari, R., & Niazi, K. R., (2018), Voltage stability assessment in power systems using line voltage stability index, Computers and Electrical Engineering, 70, 199–211. https://doi.org/10.1016/j.compeleceng.2017.12.046 DOI: https://doi.org/10.1016/j.compeleceng.2017.12.046
Chandra, A., & Pradhan, A. K., (2019), Online voltage stability and load margin assessment using wide area measurements, International Journal of Electrical Power and Energy Systems, 108, 392–401. https://doi.org/10.1016/j.ijepes.2019.01.021 DOI: https://doi.org/10.1016/j.ijepes.2019.01.021
Yang, H., Qiu, R. C., Shi, X., & He, X., (2020), Unsupervised feature learning for online voltage stability evaluation and monitoring based on variational autoencoder, Electric Power Systems Research, 182(4), 1–13. https://doi.org/10.1016/j.epsr.2020.106253 DOI: https://doi.org/10.1016/j.epsr.2020.106253
Alzaareer, K., Saad, M., Mehrjerdi, H., Ziad El-Bayeh, C., Asber, D., & Lefebvre, S., (2020), A new sensitivity approach for preventive control selection in real-time voltage stability assessment, International Journal of Electrical Power and Energy Systems, 122, 1–10. https://doi.org/10.1016/j.ijepes.2020.106212 DOI: https://doi.org/10.1016/j.ijepes.2020.106212
Rodriguez-Garcia, L., Perez-Londono, S., & Mora-Florez, J., (2019), An optimization-based approach for load modelling dependent voltage stability analysis, Electric Power Systems Research, 177. https://doi.org/10.1016/j.epsr.2019.105960 DOI: https://doi.org/10.1016/j.epsr.2019.105960
Painuli, S., Singh Rawat, M., Vadhera, S., & Tamta, R., (2018), Comparison of Line Voltage Stability Indices for Assessment of Voltage Instability in high Voltage Network, In 1st International Conference on New Frontiers in Engineering, Science & Technology (pp. 819–825). New Delhi, India. Retrieved from https://www.researchgate.net/publication/322569809
Ramírez Perdomo, S. L., & Lozano, C. A. M., (2014), Evaluation of indices for voltage stability monitoring using PMU measurements, Ingenieria e Investigacion, 34(3), 44–49. https://doi.org/10.15446/ing.investig.v34n3.43002 DOI: https://doi.org/10.15446/ing.investig.v34n3.43002