Probabilistic Static Voltage Stability Analysis Considering Load Variation

In power system operation, there are many random disturbances or uncertain factors, such as the variation of nodal injections, the change in network configuration and the measuring or forecasting errors. Probabilistic static voltage stability analysis can consider more uncertain factors in computation and offer more information in the critical point. Based on the present weighted least squares state estimate algorithm, the variation of loads is considered to form the probabilistic state estimate computation. Then the direct approach for the voltage stability analysis is introduced into the probabilistic environment to compute the probabilistic distribution of the stability critical point.In the on-line application, data in the next time period are obtained from load forecasting and disposed by the state estimate program, and then can be used as the original data for further advanced application functions. In the probabilistic state estimate algorithm, the stochastic property of forecasting load powers can be described by the statistic numerical characteristics, and more system operating states can be considered in one numerical calculation procedure. The probabilistic state estimate provides the initial value for the probabilistic static voltage stability analysis.In the direct approach of static voltage stability analysis, the expanded power flow equation is formulated according to the property of the singularity of Jacobian matrix at the critical point. This approach can figure out the critical point directly. The use of parameter transformation about load level λ overcomes the difficulty in numerical calculation caused by the singularity of Jacobian matrix near the critical point. In this thesis, from the bifurcation theory, the sufficient condition of static bifurcation and the necessary condition of saddle node bifurcation are analyzed, and the equations of direct approach are determined. The adoption of parameter transformation avoids the singularity of the Jacobian matrix. Based on the theory of optimal multiplier and multiple load flow solutions, the initialization for the right eigenvector is processed. At last the critical point is achieved by using the Newton method.In probabilistic static voltage stability analysis, the operation state in a period of...