A unified approach for estimating transient and long-term stability transfer limits

Until now, the estimation of transient stability transfer limits by means of signal energy analysis has been limited to stable time-domain simulations. The paper adapts this analysis to unstable simulations, and extends the method to long-term voltage stability limit estimation as well, thereby proposing a unified approach for both criteria. The method is based on (i) performing transient or long-term time-domain simulations (depending on the type of limit to be found), (ii) extracting the signal energy of the time-varying RMS voltage response at appropriate system buses, and (iii) averaging to obtain a "system" signal energy. In radial power systems, a more localized average is found to provide slightly better limit-estimating performance (i.e. "corridor" signal energy). However, both "system" and "corridor" signal energies are shown to rise asymptotically and predictably to the limit with increasing power for stable cases, and decreasing power for unstable cases. A simple theory explains this behaviour near the limit as being inversely proportional to power transfer, and test cases performed on a validated model of the 1991 Hydro-Quebec system demonstrate the value of the approach.