Voltage stability assessment through measurement of a reduced state vector

The use of a real-time measurement system for the monitoring and control of voltage stability in power systems calls for the investigation of the possibility of reducing the number of the measurements. A clustering algorithm based on graph theory and an arbitrary coherency function is presented, and its applicability is tested for two proposed coherency criteria. The objective of the measurements was the monitoring of the proximity of the system state to voltage instability. The proximity indicators selected are the minimum singular values of the system Jacobian matrix. In the case of the reduced number of measurements, the approximate Jacobian was determined by assuming that all the elements of the state vector from one cluster have the same values as the one representative measurement taken from that cluster. The proximity indicator was then calculated from such an approximated matrix and compared with the values obtained by simulation when the acquisition of the complete state vector was assumed. The results show that reduced measurements are adequate for predicting voltage instability