Symmetric method for obtaining network-power-loss components induced by sources and loads at individual buses in ac power networks

Abstract

A symmetric method for obtaining network-power-loss components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established at first. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Expressing the network power loss in terms of source's and load's powers by this matrix expression, a symmetric algebraic calculation formula for obtaining the network-power-loss components is produced after manipulating by Shapley value theorem, by which the obtaining of network-power-loss components are achieved. The set of network-power-loss components provides a new efficient tool for economic operation of AC power networks.