Voltage stability assessment using modal analysis based on power systems state estimation

Modal analysis has been widely used for voltage stability assessment based on the sensitivities of reactive powers with respect to voltage magnitudes obtained from the traditional power flow Jacobian. It provides a relative measure of proximity to voltage instability and determines participation factors to find the critical areas of the system. However, in practice, the most probable state of the system is determined by state estimation techniques. In this case, the number of measurements gathered from the network is greater than state variables to be estimated, resulting in a non-square Jacobian matrix. In the estimation process, a gain matrix is formed based on the non-square Jacobian and the covariances of the measurements. In this paper, a novel methodology is presented for voltage stability assessment. The properties of the eigenvalues and eigenvectors of a reduced gain matrix are exploited to evaluate the sensitivities of voltage magnitudes with respect to measurements obtained from phasor measurement units, proving that the proposed method is capable of determining the weakest buses related to voltage instability. Tests are conducted using IEEE 14 and 30 bus test systems to show the applicability and efficiency of the proposed methodology.