Out-of-Step Detection on Transmission Lines Using Apparent Impedance Differential Method

In this paper a new method to detect power swing instability on transmission lines has been proposed that is insensitive to operating conditions and system changes. Changes in system conditions, network topology or in generator statuses effectively reflects as variations in Thevenin's (source) impedances as seen from either ends of a transmission line. Thevenin's (source) impedances can also vary during a power swing. The proposed method to detect power swing instability is based on the apparent impedance differential as measured at the sending and receiving end substations of a transmission line. In this method, a transmission line is considered a part of a two-machine equivalent with associated Thevenin (source) impedances. Using the two-machine equivalent model and the impedance differential, critical variables - the rotor angle difference between the two machines, the swing-center location and swing-center voltage – that are necessary to detect power swing instability can be determined taking into considerations the uncertainty in source impedances. Necessary and sufficient conditions based on the above critical variables have been proposed to aid in the detection of power swing instability. Necessary conditions are based on the rate-of-change of real power flow in the transmission line, the rate-of-change of the real part of the impedance differential, swing-center voltage and its rate-of-change. Sufficient condition is based on a Lyapunov function that considers the rate-of-change of the rotor angle. The proposed method has been tested on a single-machine infinite bus system, multi-machine power system using PSCAD-EMTDC software, and on a large-scale power system using the Power System Simulator Software (PSS/E) to demonstrate its effectiveness.