Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems

Abstract

A bifurcation analysis is used to investigate the complex dynamics of a heavily loaded single-machine-infinite-busbar power system modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System. The system has five mechanical and two electrical modes. The results show that, as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability in a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. The results show that adding damper windings may induce subsynchronous resonance.

The Effects of Machine Components on Bifurcation and Chaos as Applied to Multimachine System

“…Although damper windings have some benefits in transient stability, such as damping off speed oscillations, they may induce subsynchronous resonance. 2 We will show that damper windings reduce the compensation level at which subsynchronous resonance occurs.…”

“…In this case we have 24 ordinary nonlinear differential equations, (1)(2)(3)(4)(5)(6)(7)(8)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). As in the previous section, the stability of the equilibrium solution is studied by examination of the eigenvalues of the Jacobian matrix evaluated at the operating point.…”

“…The bifurcation theorem was used by Zhu et al [1] to demonstrate the existence of a Hopf bifurcation in a single machine infinite busbar (SMIB) power system, in which the dynamics of the damper windings and the AVR are neglected. Nayfeh et al [2] applied the bifurcation theory to a practical series capacitor compensated single machine power system, the BOARD-MAN turbine-generator system. Harb et al [3] applied a bifurcation analysis together with the method of multiple scales and Floquet theory to the CHOLLA #4 turbine-generator system.…”

Investigation of the influence of the level of longitudinal compensation on the occurrence and development of subsynchronous resonance

“…Согласно правилам устройства установок, существуют 3 категории потребителей: I, II и III [4]. Для электроприемников I категории перерыв электроснабжения может повлечь за собой опасность для жизни людей или серьезный ущерб для производства, поэтому они должны обеспечиваться электроэнергией от двух независимых источников питания с допустимым перерывом их электроснабжения только на время автоматического восстановления питания.…”

The Influence of Machine Saturation on Bifurcation and Chaos in Multimachine Power Systems

“…Tomim et al [3] proposed an index that identifies Hopf bifurcation points in power systems susceptible to subsynchronous resonance. Nayfeh et al [4] applied the bifurcation theory to a practical series capacitor compensated single machine power system, the BOARDMAN turbine-generator system. To make the analysis simple and manageable, the effect of stator and rotor iron saturation in synchronous machines was neglected in all of the bifurcation analysis given in the literature.…”