The optimal admittance matrix problem in DC networks

Abstract

This paper establishes a general framework for network optimization in DC systems, namely the optimal admittance matrix (OAM) problem, which finds the optimal admittance matrix that minimizes power loss given the power injection information. The OAM problem offers a complementary viewpoint to the optimal power flow which finds the optimal power injections given the admittance matrix. A solution algorithm based on successive linear programming is designed to solve the OAM problem efficiently. Two numerical rules are discovered from the optimal admittance matrix given by the OAM problem, which are of interest to both power system theory and practice. The sparsity rule says that the optimal admittance matrix is sparse. The proportionality rule says that the optimal nodal self-admittance is nearly directly proportional to its power injection in absolute value, i.e., power loss is reduced by those buses with heavier generation or load having greater self-admittances. These rules are still valid when a moderate stability constraint is adopted. Conversely, the proportionality rule also gives an intuitive guide to power injection management. The obtained results reveal how the network and power injections coordinate with each other for better system performance.