Study of dynamic voltage stability of power systems

International Journal of Electrical Engineering Education, Oct 2000 by Tripathy, S C

Abstract A model of a power system with load dynamics is studied to investigate the voltage collapse phenomenon. The reactive power demand at a load bus is slowly increased until the voltage magnitude sharply falls to a very low level. This is caused by saddle node bifurcation. This is also steady state voltage instability or collapse. However, as the reactive power load is increased slowly from a small value, initially the eigenvalues which were in the left half s-plane move to the right half s-plane and again return to the left half plane. This is called Hopf bifurcation which produces node voltage oscillations. This latter phenomenon happens in a dynamic state. If voltage regulator action at the generator bus is considered and hard limits on the exciter voltage are imposed, then this results in sustained oscillations of the bus voltage and chaotic transient response.

Keywords chaos, Hopf; saddle node bifurcation; voltage collapse

Inadequate reactive support is the main cause of voltage instability and collapse in power systems. During the past decade the utilities have reported serious problems in maintaining network stability, particularly voltage stability in their power systems.

Saddle-node1 and Hopf2 bifurcations have been recognised as some of the reasons, albeit not the only ones,3 for voltage stability problems in a variety of power system models. Local bifurcations are detected by monitoring the eigenvalues of the current operating state. As certain parameters in the system change slowly, allowing the system to quickly recover and maintain a stable operating point, the system eventually turns unstable, either due to one of the eigenvalues becoming zero (saddle-node, transcritical, pitchfork bifurcations), or due to a pair of complex conjugate eigenvalues crossing the imaginary axis of the complex s-plane (Hopf bifurcation). The instability of the system is reflected in the state variables (usually represented by angle, frequency and voltage magnitude) by a continuous change of bus voltage decrease leading to collapse, increase of frequency and angle leading to loss of synchronism or by an oscillatory behaviour of the variables. In some cases these bifurcations can be associated with the power transfer limit of the transmission lines. In other instances the bifurcations appear to be due to a voltage control problem, such as the fast-acting automatic voltage regulator (AVR2,4) of the generator. In all cases bifurcations occur in very stressed systems, i.e. the region of stability of the current operating point (stable equilibrium point) is small, hence the system is not able to withstand small perturbations and becomes unstable.

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S. C. Tripathy

Indian Institute of Technology, New Delhi, India E-mail. sct@iet.auc.dk