A restriction on the power system by theoretical requisitions of the BCU method

In power system transient stability analysis, the boundary of stability region based controlling unstable equilibrium point method (BCU method) has gained much interest due to its sound theoretical foundations. Among the requirements of the theory of the BCU method, the one-parameter-transversality condition is difficult or even impossible to check directly. Under these requirements, it is proved that, if the corresponding lossless system is not completely stable, a gradient system should not be completely stable either. This suggests an indirect approach in verifying the abstract conditions. A sufficient condition for not-complete stability of the gradient system is also proposed.