BEYOND SADDLE-NODE BIFURCATION POINT OF ILL-CONDITIONED POWER SYSTEMS: A CASE STUDY OF NIGERIAN NATIONAL GRID
DOI:
https://doi.org/10.4314/njt.v44i1.10Keywords:
Fold point, Physical parameterization, local parameterization, latus rectum, directrix, voltage collapseAbstract
Estimating the margin for voltage collapse is a critical concern for power system utility companies and stakeholders in developing power systems. A common approach uses Euclidean distance in continuation power flow to address singularity-induced network constraints. However, this method fails to capture exact topological properties, leading to overly conservative stability margin predictions. To overcome these limitations, this study introduces the arc-length path to the existing model, leveraging numerical simulations with varying step sizes. The optimal step size value was determined through various simulations, including 19 incremental step size adjustments and 8-step size reductions. The results of these simulations validated the findings. Notably, combining arc length and Euclidean distance for margin estimation reveals that the latus rectum, corresponding to local parameterization, and the margin to voltage collapse are equidistant from the saddle-node bifurcation point.
References
[1] Yavdat, I., “A finding of the maximal saddle-node bifurcation for systems of differential equations”. Journal of Differential Equations No. 378, pp.610-625, 2024. doi.org/10.1016/ j.jde.2023.10.026
[2] Onah, J. N., Madueme, T. C., and Ukwueze, V. C. “Contingency Evaluation of a Peturbed Electric Network”, Journal of Electrical and Electronics Engineering. Vol.10, No.5, pp. 136-142, 20215. https://www.iosrjournals.org/ iosr-jeee/Papers/Vol10-issue5/Version-2/Q010 52136142.pdf
[3] Farid, K., Shahriar, A., and Hamid, R. S. “Voltage Stability in Electrical Power Systems: The Continuation Power Flow (CPF) Methods”. Wiley-IEEE Press, No1. pp.97 – 118, 2023. DOI: 10.1002/9781119830634.ch5
[4] Oludamilare, B. A., Komla, A. F., David, T. O., Oyedokun, E., and Idowu, O. “Power System Voltage Stability Margin Estimation Using Adaptive Neuro-Fuzzy Inference System Enhanced with Particle Swarm Optimization”. Sustainability. No.14, Vol.22, pp.1-17, 2022. doi.org/10.3390/su142215448
[5] Yanqin, X. “On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order", Journal of Differential Equations. No.380, pp.146-180, 2023. https://doi.org/10.1 016/j.jde.2023.10.037
[6] Peng, H. M., Cao, Y. J., Huang, X. Q., and Huang, C. “Continuous power flow for islanding microgrid without balance nodes”, Proceedings of the CSEE, No.6, pp.2057-2067, 2016. DOI:10.1109/PESGM41954.2020.92819 67
[7] Toro, M., Segundo, J., Visairo, N., Nuñez, C., Esparza, A., and Torres, U. “Pseudo Arc-Length Continuation Power Flow Method in a Real-Time Controller”, IEEE International Autumn Meeting on Power, Electronics, and Computing, No.7, pp.1-6, 2023. DOI: 10.1109 /ROPEC58757.2023.10409477
[8] Farid, K., Shahriar, A., and Hamid, R. S. “The continuation power flow methods”. Wiley IEEE-Press, No.1, pp.97 – 118, 2023. DOI: 10. 1002/9781119830634.
[9] Dan, W., Franz-Erich, W., Bin, W., and Le, X. “Searching for the shortest path to voltage instability boundary: From Euclidean space to algebraic manifold”, International Journal of Electrical Power and Energy Systems. Vol.131, pp.1-11, 2021. https://doi.org/10.1016/j.ijepes. 2021.107127
[10] Madhavi, G., Harika, V., and Kumar, C. “Voltage stability analysis using continuation power flow under contingency”, Journal of Theoretical and Applied Information Technology. No.8, Vol.2, pp.2373-2383. https: //www.ijareeie.com/upload/2013/august/53_voltage.pdf
[11] Tong, J., Kaiyao, W., and Zhuocheng, F. “A Boundary-derivative direct method for computing saddle-node bifurcation Points in voltage stability analysis”, Electrical Power and systems, No.112, Vol.9, pp.119-208, 2023. https://doi.org/10.1016/j.ijepes.2019.04.039
[12] Jagun, Z. O. O., and Onah, J. N. “Improving the transfer capability of poor transmission system”, EKSU Journal of Science and Technology. No.4, Vol.1, pp.63-69, 2018. https://www.researchgate.net/publication/358367901_Improving_the_Transfer_Capability_of_a_Poor_Transmission_System
[13] Onah, J. N., Onyishi, D. U., Eze, C. C., and Ogbahor, G. A. “Estimating the collapse point of a transmission line in developing power systems”, Arid Zone Journal of Engineering, Technology and Environment, No. 19, Vol.4, pp.807-814. https://azojete.com.ng/index.php/a zojete/article/view/815
[14] Onah, J. N., Jagun, Z. O. O., Madueme, T. C., and Oti, S. E. “Estimating the margin to voltage collapse in a dwindling electric power network”, Nigerian Journal of Technology, No.2, Vol.38, pp.470 – 475, 2019. DOI:10.43 14/njt.v38i2.25
[15] Chong, R., Xiao, W., Xi, W., Fang, G., Yepeng, Li., “Improved continuation power flow calculation method based on a coordinated combination of parameterization”. IEEE 2nd International Electrical and Energy Conference (CIEEC). Beijin Chaina. pp.207-211, 04-06th November, 2018. DOI: 10.1109/CIEEC.2018.8745861
[16] Aakash, J. U. “Steps to find vertex focus and directrix of the parabola”, 2024. Available online at: https://byjus.com/jee/how-to-find-the -vertex-focus-and-directrix-of-the-parabola-wi th-the-given-equation/. Accessed on 4th March, 2024
[17] Ding, H., and Zhou, J. “Global existence and blow-up for a parabolic problem of Kirchhoff type with logarithmic nonlinearity”, Applied Mathematical Optimization, No.83, pp.1651–1707, 2021. https://link.springer.com/article/ 10.1007/s00245-019-09603-z
[18] Onah, J. N., Omeje, C. O., Onyishi, D. U., and Oluwadurotimi, J. “Single Topology Neural Network-Based Voltage Collapse Prediction of Developing Power Systems”, Nigerian Journal of Technology, 2024; 43(2), pp. 309 –316; https://doi.org/10.4314/njt.v43i2.14
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Nigerian Journal of Technology
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The contents of the articles are the sole opinion of the author(s) and not of NIJOTECH.
NIJOTECH allows open access for distribution of the published articles in any media so long as whole (not part) of articles are distributed.
A copyright and statement of originality documents will need to be filled out clearly and signed prior to publication of an accepted article. The Copyright form can be downloaded from http://nijotech.com/downloads/COPYRIGHT%20FORM.pdf while the Statement of Originality is in http://nijotech.com/downloads/Statement%20of%20Originality.pdf
For articles that were developed from funded research, a clear acknowledgement of such support should be mentioned in the article with relevant references. Authors are expected to provide complete information on the sponsorship and intellectual property rights of the article together with all exceptions.
It is forbidden to publish the same research report in more than one journal.
How to Cite
