Analysing load shedding to increase stability in the swing equation.

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Premnath, Bhairavi and Sofroniou, Anastasia (2025) Analysing load shedding to increase stability in the swing equation. Mathematics, 13 (8). pp. 1-25. ISSN 2227-7390

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Abstract

It is vital to study the stability of power systems under small perturbations to prevent blackouts. This study presents a load-shedding strategy that has been incorporated within the swing equation to reduce instability and delay the onset of chaotic dynamics. The objective of this study was to identify the minimal load reductions required after disturbances to maintain the frequency above a critical value. Analytical techniques such as eigenvalue analysis and perturbation methods can also be supported with numerical simulations using bifurcation diagrams, Lyapunov exponents, and the Simulink model. When compared to the conventional stepwise load-shedding method, the proposed approach allows for dynamic adjustments and presents a 49% increase in stable regions and a 45% reduction in recovery time. Performance was also analysed under different damping, inertia, and load scenarios. These results suggest that the strategy demonstrated in this research provides a robust and computationally practical solution for modern power system applications.

Item Type:	Article
Identifier:	10.3390/math13081314
Keywords:	Control; load shedding ; nonlinear dynamics; power system; swing equation
Subjects:	Mathematics
Depositing User:	Anastasia Sofroniou
Date Deposited:	30 May 2025 09:19
Last Modified:	30 May 2025 09:30
URI:	https://repository.uwl.ac.uk/id/eprint/13731

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References

Nayfeh, M.A. Nonlinear Dynamics in Power Systems. Ph.D. Thesis, Virginia Tech University, Blacksburg, VA, USA, 1990.

Nayfeh, M.A.; Hamdan, A.M.A.; Nayfeh, A.H. Chaos and instability in a power system—Primary resonant case. Nonlinear Dyn. 1990, 1, 313–339.

Kundur, P. Power system stability. In Power System Stability and Control; CRC Press: Boca Raton, FL, USA, 2007; Volume 10, p. 7-1.

Anastasia, S.; Bhairavi, P.; Kevin, M.J. An Insight into the Dynamical Behaviour of the Swing Equation. WSEAS Trans. Math. 2023, 22, 70–78.

HyungSeon, O. Analytic solution to swing equations in power grids with ZIP load models. PLoS ONE 2023, 18, e0286600.

Sofroniou, A.; Premnath, B. An Investigation into the Primary and Subharmonic Resonances of the Swing Equation. WSEAS Trans. Syst. Control 2023, 18, 218–230.

Sofroniou, A.; Premnath, B. Addressing the Primary and Subharmonic Resonances of the Swing Equation. WSEAS Trans. Appl. Theor. Mech. 2023, 18, 199–215.

Laghari, J.A.; Mokhlis, H.; Bakar, A.H.A.; Mohamad, H. Application of computational intelligence techniques for load shedding in power systems: A review. Energy Convers. Manag. 2013, 75, 130–140.

Urban, R.; Mihalic, R. WAMS-based underfrequency load shedding with short-term frequency prediction. IEEE Trans. Power Deliv. 2015, 31, 1912–1920.

Abbas, K.; Fini, M.H. An underfrequency load shedding scheme for hybrid and multiarea power systems. IEEE Trans. Smart Grid 2014, 6, 82–91.

Tofis, Y.; Timotheou, S.; Kyriakides, E. Minimal load shedding using the swing equation. IEEE Trans. Power Syst. 2016, 32, 2466–2467.

Mortaji, H.; Ow, S.H.; Moghavvemi, M.; Almurib, H.A.F. Load shedding and smart-direct load control using internet of things in smart grid demand response management. IEEE Trans. Ind. Appl. 2017, 53, 5155–5163. Mathematics 2025, 13, 1314 25 of 25

Mammoli, A.; Robinson, M.; Ayon, V.; Martínez-Ramón, M.; Chen, C.F.; Abreu, J.M. A behavior-centered framework for real-time control and load-shedding using aggregated residential energy resources in distribution microgrids. Energy Build. 2019, 198, 275–290.

Talwariya, A.; Singh, P.; Kolhe, M.L. Stackelberg game theory based energy management systems in the presence of renewable energy sources. IETE J. Res. 2021, 67, 611–619.

Dedovi´c, M.M.; Avdakovi´c, S.; Musi´c, M.; Kuzle, I. Enhancing power system stability with adaptive under frequency load shedding using synchrophasor measurements and empirical mode decomposition. Int. J. Electr. Power Energy Syst. 2024, 160, 110133.

Sofroniou, A.; Premnath, B. A Comprehensive Analysis into the Effects of Quasiperiodicity on the Swing Equation. WSEAS Trans. Appl. Theor. Mech. 2023, 18, 299–309.

Sofroniou, A.; Premnath, B. Analysing the Swing Equation using MATLAB Simulink for Primary Resonance, Subharmonic Resonance and for the case of Quasiperiodicity. WSEAS Trans. Circuits Syst. 2024, 23, 202–211.

Paganini, F.; Mallada, E. Global analysis of synchronization performance for power systems: Bridging the theory-practice gap. IEEE Trans. Autom. Control 2019, 65, 3007–3022.

Shariati, O.; Zin, A.M.; Khairuddin, A.; Pesaran, M.H.A.; Aghamohammadi, M.R. An integrated method for under frequency load shedding based on hybrid intelligent system-part II: UFLS design. In Proceedings of the 2012 Asia-Pacific Power and Energy Engineering Conference, Shanghai, China, 27–29 March 2012; pp. 1–9.

Jereminov, M.; Pandey, A.; Song, H.A.; Hooi, B.; Faloutsos, C.; Pileggi, L. Linear load model for robust power system analysis. In

Proceedings of the 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), Torino, Italy, 26–29 September 2017; pp. 1–6.

Lu, M.; ZainalAbidin, W.A.W.; Masri, T.; Lee, D.H.A.; Chen, S. Under-frequency load shedding (UFLS) schemes—A survey. Int. J.Appl. Eng. Res. 2016, 11, 456–472.

Larik, R.M.; Mustafa, M.W.; Aman, M.N. A critical review of the state-of-art schemes for under voltage load shedding. Int. Trans. Electr. Energy Syst. 2019, 29, e2828.

Crawford, J.D. Introduction to bifurcation theory. Rev. Mod. Phys. 1991, 63, 991.

Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A. Determining Lyapunov Exponents from a Time Series. Phys. D 1984, 16, 285–317.

Hao, H.; Li, F. Sensitivity analysis of load-damping characteristic in power system frequency regulation. IEEE Trans. Power Syst.2012, 28, 1324–1335.

Sofroniou, A.; Bishop, S. Dynamics of a Parametrically Excited System with Two Forcing Terms. Mathematics 2014, 2, 172–195.

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Analysing load shedding to increase stability in the swing equation.

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