A Fast Algorithm for Identification and Tracing of Voltage and Oscillatory Stability Margin Boundaries

• Published in: Proceedings of the IEEE Vol. 93; no. 5; pp. 934 - 946
• Main Authors: Yuan Zhou, Ajjarapu, V.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bifurcation; Boundaries; Control algorithms; differential and algebraic equations (DAE); Eigenvalues; Eigenvalues and eigenfunctions; Electric potential; Hopf bifurcation; load margin; manifold; margin boundary tracing; Mathematical analysis; Power system analysis computing; Power system dynamics; Power system interconnection; Power system measurements; Power system security; Power system stability; saddle node bifurcation (SNB); Saddles; Stability; Studies; time-domain simulation; Voltage; voltage stability; Voltage-controlled oscillators
• ISSN: 0018-9219; 1558-2256
• DOI: 10.1109/JPROC.2005.847254

This paper presents a framework based on a differential manifold approach that combines identification and tracing of both saddle node and Hopf bifurcation margin boundaries without calculating any eigenvalues. For a given base case, we first identify either the saddle node or Hopf bifurcation. The Hopf bifurcation is easily detected by observing the sign change of scalar index in the tangent vector without eigenvalue calculation. Based on manifold and bifurcation theory, a unified formulation for a variety of bifurcation related voltage and oscillatory stability margin boundary tracing in multiparameter space is proposed. The bifurcation-related margin boundary could be traced along any control scenario in multicontrol parameter space combined with any given loading scenario. This is achieved by moving from one boundary point to the next without retracing the entire PV curve. This paves the way for online voltage and oscillatory stability assessment. The unified boundary predictor-corrector-identifier tracing framework is originally employed to trace both voltage collapse and oscillatory stability margin boundaries, which are limited by the saddle node and Hopf bifurcation, respectively. The manifold-based methodologies presented in this paper facilitate the development of fast margin monitoring and control algorithms.