Theoretical Foundation of the BCU Method for Direct Stability Analysis of Network-Reduction Power System Models with Small Transfer Conductances

The controlling unstable equilibrium point (u.e.p.) method is considered to be the most viable for direct stability analysis of practical power systems. The success of the controlling u.e.p. method, however, hinges upon its ability to find the (correct) controlling u.e.p. Recently, a systematic method, called boundary of stability region based controlling unstable equilibrium point method (BCU method), to find the controlling u.e.p. was developed. The BCU method has been evaluated in a large-scale power system and it compared favorably with other methods in terms of its reliability and the required computational efforts. In this paper, a theoretical foundation of the BCU method for the network-reduction classical machine stability model is developed. Sufficient conditions for the BCU method to find the correct controlling u.e.p. relative to a given fault are derived.