An Analytical Solution To The Voltage-Constrained Stability Problem Of Real Ac Systems

Abstract

It has been concluded for quite some time now that no algebraic equation has been derived for the steady-state stability limit (SSSL) of a transmission system with resistance and node voltage constraints. As a resul t, many a criterion has been advocated in the different literatures for systems with losses; with no definite conclusions being reached about certain unresolved operational limits. These include, e.g., exact knowledge of the ‘stability reserve mar gin’ which has evoked many speculations during the analysis of blackout events recently reported for stressed systems worldwide. The results of the analytical so lution to the boundary problem presented in this paper reveal operational limits t hat couldn’t have been observed through equations without the resistance parameter. The approach yields an equation for the necessary c onditions of instability referred to the receiving-end voltage V R with the sufficient conditions hence the complete solution being provided by an equation for the sending volta ge E. The receiving-end equation relating internal voltages and sectional impedance elements will describe potential bounds of events in waiting (for E) to happen and h ence a metric for the distance to blackout. The sending voltages that will verify the V R relationship roots which are embodied in higher-order polynomial expressions for the cases considered are easily verifiable.