Static Voltage Stability Study Of Power Systems Based On Wu Elimination Method And Network Flow Theory

As the development of economy, power systems are characterized with large power grids, ultra high voltage, large capacity machine and long distance transmission. The security and stability of the power systems have great impact on the development of economy. In recent years, the black-out catastrophes led to huge economic losses and impact upon the whole society. As a result, it is meaningful to study voltage instability, voltage collapse and safety indicators of voltage stability, in order to avoid voltage collapse. In this paper, the main work and conclusions are as follows:(1) Introduction of Wu Elimination Method. The Method is applied to obtain analytical solutions of the power flow equations of a three-node system with neither extraneous roots nor missing roots. A minor group of solutions are obtained under low load other than the major group of solutions. The solutions obtained by Wu Elimination Method are the basis of study on the mechanism of voltage stability.(2) Based on computation, static analysis of voltage stability is presented. Analytical V-P, V-Q curves, VPQ three-dimension surfaces and the stable operation area are obtained as well as the steady state operation area. Properties of the power-flow Jacobian matrix, reduced Jacobian matrix and the power/angle submatrix are also analyzed.(3) Analysis on the properties of the equilibriums obtained by Wu Elimination is presented. It is found that the voltages of the four sets of equilibrium in the three-node system are with different amplitudes and angles. Discussion are made on the stability of the four sets of equilibrium based on the changing profiles of the active power flows in branches. (4) Based on the Network Flow theory, a potential method is proposed in this paper to predict the power system voltage collapse based on branch flows. The idea is as follow: in a connected power system, there is at least one branch in which the active power reaches the maximum value no later than the system reaches the capacity limit. Case studies of both 173-bus and IEEE 300-bus power systems are used to validate the proposed theory and method.