Numerical study of optimized fractional-order controller for chaos control of nonlinear dynamical power system

Abstract

Summary Nonlinear dynamical system exhibit bifurcation, chaos, and instability due to initial conditions and parametric variation. The power system is also nonlinear dynamical system, which exhibits these behaviors due to different initial operating conditions and uncertain variation in parameter like reactive power load demand. The fractional‐order controller is introduced as the better choice for several control systems as compared to conventional proportional‐integral‐derivative controllers owing to its merits. This paper proposes a first ever numerical study of novel use of optimized fractional‐order controller for control of chaos in power system. This paper discusses the steps to optimize the order of fractional controller. The role of fractional‐order controller is to inject or withdraw the precise amount of reactive power to control chaotic nature of voltage. The proposed controller will perturb the dynamics of the nonlinear power system and push it to nonchaotic and bounded stable state because of precise state feedback control. Precise perturbation in reactive‐power value inhibits voltage bifurcation point, chaos, and instability thereafter. Fourth order benchmark model of the power system is used as a case study in the paper.

Local bifurcation analysis of brushless DC motor

“…We can now define the center manifold from Equation 17. When the center manifold W C is tangent to center subspace E C , the functions h 1 (u, δ) and h 2 (u, δ) deviating from the axis u axis to the axes v and w should be calculated at the neighborhood of the origin.…”

“…3,[8][9][10] Chaos control, chaos synchronization, and chaos stabilization on BLDCM or power system were implemented by various methods. [11][12][13][14][15][16][17][18] Besides chaos control, some mechanical analyses have been conducted in terms of force and energy cycling on the BLDCM. 19 In general, chaos control has been interesting since chaotic angular velocity is detrimental to the operation of the motor.…”

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

“…In recent years, fractional-order sliding mode control has been applied to other fields and has better control result. Reference [27] proposed a novel optimized fractional-order controller for control of chaos in power system and discussed the steps to optimize the order of fractional controller. e proposed controller perturbed the dynamics of the nonlinear power system and pushed it to nonchaotic and bounded stable state.…”

Dynamics and complexity analysis of the conformable fractional‐order two‐machine interconnected power system

“…Meanwhile, it is a complex system with a very high degree of nonlinearity, which makes it difficult to establish accurate mathematical models for the power systems. In a recent year, some progress has been made in studying chaotic oscillations of fractional‐order power systems by using the traditional fractional‐order definition of Riemann‐Liouville and Caputo 29,30 . However, as a new differential operator, the conformable fractional calculus is not studied in the chaotic oscillation of fractional‐order power system.…”

“…In a recent year, some progress has been made in studying chaotic oscillations of fractional-order power systems by using the traditional fractionalorder definition of Riemann-Liouville and Caputo. 29,30 However, as a new differential operator, the conformable fractional calculus is not studied in the chaotic oscillation of fractional-order power system. So, it is of great practical and theoretical significance to analyze the chaotic oscillation and complexity feature of power system with the conformable fractional calculus.…”