A simple method for power system stability analysis with multiple time delays

There exist significant time delays in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS). To properly evaluate the impact of time delay is very important for power system online stability assessment and controller design. In this paper, the maximum delayed time that power system can sustain without losing its stability is denoted as its delay margin. From the viewpoint of Lyapunov stability, when a dynamic system is critical stable at a given equilibrium point, there must exist critical eigenvalue on the imaginary axis. This paper presents a simple method to determine such critical eigenvalue by tracing eigenvalue loci of a transformation matrix. Then the critical eigenvalue is used to determine the delay margin of power system. Comparing with previous approaches, such as Lyapunov function/functional method, LMI method, root clustering paradigm method, the presented method can locate the exact delay margin with no conservativeness and with less computation burden. Moreover, it can be easily applied to the stability analysis of bulk power system with multiple time delays. Finally, single machine and infinite bus system (SMIB) and WSCC 3-generator-9-bus system are employed to validate its effectiveness.