On existence of equilibria of multi-port linear AC networks with constant-power loads

Abstract : In this brief note we give an answer to the following question: Given a multi-port, linear AC network with instantaneous constant-power loads identify a set of active and reactive load powers for which there is no steady-state operating condition of the network-in this case we say that the power load is inadmissible. The identification is given in terms of feasibility of simple linear matrix inequalities, hence it can be easily verified with existing software. For one-or two-port networks the proposed feasibility test is necessary and sufficient for load power admissibility with the test for the former case depending only on the network data. Two benchmark numerical examples illustrate our results. Index Terms-Constant power loads, AC LTI circuits, existence of equilibria.