| Abstract: | In this study we formulate the power equations of power systems that are operating in their steady states into what we call the dtic and Hermitian power equations in terms of nodal active/reactive powers. These quadratic and Hermitian power equations are then generalized in terms of active/reactive power indices, based on which we complete three tasks: (i) deriving possible eigenvalue/singular‐value inequalities for nodal voltage stability evaluation with or without power flow computations; (ii) examining possible positive/negative definiteness, semi‐definiteness and indefiniteness of power systems that are useful in nodal voltage stability evaluation and convex/concave analysis; and (iii) scrutinizing possible convexity/concavity properties of power systems and their application. The static structure characteristics of power systems are reported here for the first time and theoretical results related to these static structural characteristics are significant in evaluating nodal voltage stability of the power systems quantitatively and qualitatively. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. |
