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

Until now, the estimation of transient stability transfer limits by means o f signal energy analysis has been limited to stable time-domain simulations . The present paper adapts this analysis to unstable simulations, and exten ds the method to long-term voltage stability limit estimation as well, ther eby 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 tim e-varying RMS voltage response at appropriate system buses and iii) averagi ng to obtain a "system" signal energy, In radial power systems, a more loca lized average is found to provide slightly better limit-estimating performa nce (i.e. "corridor" signal energy). However, both "system" and "corridor') signal energies are shown to rise asymptotically and predictably to the li mit with increasing power for stable cases, and decreasing power for unstab le cases. A simple theory explains this behaviour near the limit as being i nversely proportional to power transfer, and test cases performed on a vali dated model of the 1991 Hydro-Quebec system demonstrate the value of the ap proach.