Quantitative Analysis of Steady State Stability in Power Networks

A quantitative analysis of the steady state stability of a general network with arbitrary PV, PQ and slack buses is presented. Steady state stability is that property of the power network defining the constraints on the bus injections under which a steady state equilibrium exists. Necessary and sufficient conditions for steady state stability as well as an algorithm to verify these conditions are derived. The degree of steady state stability of the injections (operating points) is quantified through a computable scalar stability margin. Such a stability margin serves as a design measure with which to compare the steady state stability of different operating points or networks. This result is extended to include the important case where the injections are restricted to certain subspaces. Another result is a simple-to-verify sufficient conditions for steady state stability-in the vicinity of a feasible injection vector