Abstract
The nonlinear dynamics of an incommensurate fractional-order single-machine infinite-bus (SMIB) power system benchmark model are explored and studied by means of modern nonlinear analysis theories, such as bifurcation, chaos, power spectral density (PSD), and bicoherence methods. The effect of incommensurate order derivatives on power system dynamics is presented. The study reveals that the power system undergoes interesting dynamics such as periodic motion, chaotic oscillations, and multistability whenever the system parameter values fall into particular ranges. A new fractional-order linear augmentation-based control scheme is applied to damp out the power system’s chaotic oscillation, change the stability of the coexisting states, and drive the system from multistability to monostability. The stability of the proposed control system is derived using Lyapunov theory. Simulation results confirmed the effectiveness and robustness of the proposed control scheme in damping power system oscillations and achieving good overall performance. The results in this paper will give a better understanding of the nonlinear dynamic behaviors of the incommensurate fractional-order SMIB power system.
Highlights
Power system is a complex nonlinear dynamical system with many components strongly interconnected, such as generators, buses, transformers, and many other kinds of loads and devices. e continuing interconnections of bulk power systems, brought about by economic and environmental pressures, has led to an increasingly complex nonlinear grid that must operate closer to its stability limits. erefore, recent power systems have to deal with system stability and reliability control challenges in the current and near future
E power system may be subjected to the disturbances of operation, parameter variation, time delay, noise, and uncertainties involved in a system, which may result in chaotic oscillations that can lead to power system failure, such as voltage collapse, angle divergence, or catastrophic blackout like what happened in the US in 1966 [1] and many other countries [2,3,4]. e power system’s dynamical behavior with various parameters is usually associated with complex nonlinear electromechanical oscillations
Rajagopal et al [19] discussed the nonlinear behavior of commensurate fractional-order power system, and the results revealed the existence of chaos oscillation which is suppressed using an adaptive sliding mode controller
Summary
Power system is a complex nonlinear dynamical system with many components strongly interconnected, such as generators, buses, transformers, and many other kinds of loads and devices. e continuing interconnections of bulk power systems, brought about by economic and environmental pressures, has led to an increasingly complex nonlinear grid that must operate closer to its stability limits. erefore, recent power systems have to deal with system stability and reliability control challenges in the current and near future.e power system may be subjected to the disturbances of operation, parameter variation, time delay, noise, and uncertainties involved in a system, which may result in chaotic oscillations that can lead to power system failure, such as voltage collapse, angle divergence, or catastrophic blackout like what happened in the US in 1966 [1] and many other countries [2,3,4]. e power system’s dynamical behavior with various parameters is usually associated with complex nonlinear electromechanical oscillations. Rajagopal et al [19] discussed the nonlinear behavior of commensurate fractional-order power system, and the results revealed the existence of chaos oscillation which is suppressed using an adaptive sliding mode controller.
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