Direct Methods for Stability Analysis: An Introduction
The conventional time–domain approach numerically integrates both the fault-on system and the postfault system. The stability of the postfault system is assessed based on the simulated postfault trajectory. The typical simulation period for the postfault system is 10 s and can go beyond 15 s if multiswing instability is of concern, making this conventional approach rather time-consuming. This time-consuming nature makes the conventional time–domain approach infeasible for practical application in power system online stability assessments (Chiang, 1996, 1999; El-kady et al., 1986; Groom et al., 1996). By contrast, direct methods only integrate the fault-on system and determine, without integrating the postfault system, whether or not the postfault system will remain stable once the fault is cleared by comparing the system energy (when the fault is cleared) to a critical energy value. Direct methods not only avoid the time-consuming numerical integration of the postfault system but they also provide a quantitative measure of the degree of system stability/instability (Chiang, 1991; Chiang et al., 1995; Fouad and Vittal, 1988; Gibescu et al., 2005; Hiskens and Hill, 1989).
The fundamental problem of transient stability is the following: starting from the postfault initial state X(tcl), will the postfault system settle down to the steady state condition Xs? In other words, the purpose of power system stability ...