Premnath, Bhairavi (2025) Nonlinear dynamics and chaos with applications in power systems. Post-Doctoral thesis, University of West London.

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Abstract

This thesis investigates the rich and complex behaviour of nonlinear dynamical systems through the lens of the Swing Equation, a fundamental model in power system dynamics. The Swing Equation, characterised by its nonlinear properties, exhibits diverse dynamical phenomena including period-doubling bifurcations, quasiperiodicity, chaos, and intermittency. The primary aim of this study is to apply the principles of nonlinear dynamics and perturbation theory to uncover the intricate patterns of stability and instability that arise under varying system parameters and external excitations.
A comprehensive exploration of both analytical and numerical techniques is undertaken to examine the system’s response to primary and subharmonic resonances, including the transitions leading to chaos. Through methods such as the Floquet theory, method of strained parameters, and tangent instability analysis, the study evaluates the swing equation’s sensitivity to perturbations and external forcing.
The investigation further explores the effects of quasiperiodicity specifically, how quasiperiodic forcing influences the system’s route to chaos and alters its basins of attraction and Lyapunov exponents. These theoretical insights are supported by detailed graphical simulations, including bifurcation diagrams and Poincar´e maps, which visualise the transitions and loss of synchronism. Moreover, the study incorporates experimental modelling using Matlab Simulink, simulating the swing equation under various resonance conditions and comparing the results with the analytical predictions. Integrity diagrams are constructed to identify regions of stability and quantify chaotic transitions. An additional focus is placed on the phenomenon of intermittency, exploring how the swing equation responds to small fluctuations in system parameters such as inertia and voltage, and how these contribute to erratic switching between ordered and chaotic states.
Finally, the thesis examines load shedding as a stabilisation strategy. Analytical derivations are presented for both conventional and modified schemes, and their impact on system behaviour is validated through numerical simulation. This multifaceted approach provides a deeper understanding of nonlinear behaviour in power systems and highlights the importance of robust analytical tools in predicting and mitigating chaotic responses. The findings have direct applications in improving resilience and control in modern electrical grids, particularly under conditions of high variability and complexity.

Item Type:	Thesis (Post-Doctoral)
Identifier:	10.36828/thesis/14029
Subjects:	Mathematics
Depositing User:	Mary Blomley
Date Deposited:	27 Aug 2025 10:04
Last Modified:	28 Aug 2025 10:15
URI:	https://repository.uwl.ac.uk/id/eprint/14029

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