Impact of local PMU-based equivalent methods on real-time voltage stability assessment

This study promotes a critical discussion about the phasor measurement unit (PMU)-based equivalent methods in order to investigate the impact of the Thevenin equivalent (TE) parameters on real-time power system voltage stability assessment. Although several articles indicate good performance at impedance magnitude matching theory, they neglect the influence of TE impedance angle and voltage source magnitude, introducing inaccuracies or mathematical inconsistencies in stability evaluation. The former three parameters are highlighted in this study due to being directly used to compute active power margins and indexes, according to the maximum power transfer theorem. The approach identifies the methods' robustness and weaknesses by the use of generic expressions. The main contribution of this study is presenting equations for directly calculating the parameters that may lead to inconsistent interpretations, particularly when measurement noise is considered. Disregarding these inconsistencies may result in an incorrect determination of the system's critical limit, increasing the risk of voltage instability. The conception of the new formulation relies on network equivalents based on the least-squares method, Tellegen's theorem and adaptive method. Following the simulations carried out in Nordic Test System, and 9, 14 and 39 Bus Test Cases available in MATPOWER, analyses substantiated in the derived expressions are given.