Hopf bifurcations in a SMIB power system with SSR

Abstract

This paper presents a Hopf bifurcation analysis for a Single-Machine Infinite-Bus (SMIB) power system experiencing SSR by applying a Hopf bifurcation theorem combined with numerically solving for the Monodromy matrices. A Hopf bifurcation in the system is predicted, together with stable periodic orbits.

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

“…The operating point loses stability at a Hopf bifurcation point where ȝ=H 1 . It regains stability at a reverse Hopf bifurcation for ȝ=H 2 . In this case a pair of complex conjugate eigenvalues will transversally cross from left half and right half of the complex plane, and then back to left half.…”

“…In case of no saturation, we set d 0 , d 1 , d 2 , d 3 , q 0 , q 1 , q 2 , and q 3 equal to zero in equations (1) and (2). In this case we have 23 ordinary nonlinear differential equations.…”

“…The bifurcation theorem was used by Zhu et al [2] 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. Tomim et al [3] proposed an index that identifies Hopf bifurcation points in power systems susceptible to subsynchronous resonance.…”

Application of Modern Optimal Control in Power System: Damping Detrimental Sub-Synchronous Oscillations

“…For the linear system, the control signal U which minimizes the performance index (Zhu et al, 1996;Patel & Munro, 1982;Khaki Sedigh, 2003;Ogata, 1990;Friedland, 1989;Kwakernaak, 1972):…”

Interior point based optimal voltage stability, oscillatory stability and ATC margin boundary tracing

“…Improper tuning of generation control parameters may lead to Hopf bifurcation [88][89][90]. Nonlinear load may also lead to Hopf bifurcation [91].…”