Fast computational methods for locating fold points for the power flow equations

Authors:
Anwar Hussein;Ke Chen
Affiliations:
Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, UK;Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, UK
Venue:
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Year:
2004

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Abstract

Voltage collapse in a power system can occur following a progressive decline in voltage magnitude at the system buses and, mathematically, this phenomenon is associated with a fold bifurcation point occurring in the nonlinear algebraic equations used to model the power system. In this paper, we first discuss some of the methods used to speed up the process of detecting a fold bifurcation, focussing on designing test function methods to predict a performance index. We then discuss some iterative methods that can be used to improve the Newton iterations. In particular, we present new and efficient preconditioners of the two-level type for the Jacobian matrix. Numerical results are given using standard IEEE test bus systems.