Connections between Different Criteria of Small-signal Stability Analy sis of Power Systems

The small-signal stability analysis is of great significance for the secure operation of power systems. The most widely used tool for small-signal stability analysis is Lyapunov's first method which requires the detailed modeling of the system and the calculation of eigenvalues. In order to avoid the time-consuming calculation of eigenvalues, some other stability criteria have been proposed such as the Routh's criteria, root locus, Bode plot and Nyquist plot. And in order to avoid the detailed system modeling which is difficult or even impossible to obtain due to the increasing penetration of renewable energy, the impedance-based analysis method becomes more attractive for the stability assessment since it only requires the out-of-port characteristics of the system. Each of the above-mentioned methods may have a complete theoretical framework, but there are few studies to clearly reveal the connections between the different stability criteria and methods. To this end, this paper firstly conducts a universal investigation of different criteria in small-signal stability analysis, from the conventional eigenvalue-based methods to the recent impedance-based methods. Then, on this basis, their internal connections are analyzed and discussed. Finally, a case study is carried out to further validate all the criteria and their connections.