Analytic Loss Minimization: A Proof

Abstract

Loss minimizing generator dispatch profiles for power systems are usually derived using optimization techniques. However, by partitioning and manipulating the \(Y_{bus}\) matrix, it is possible to derive the \(K_{GL}\) matrix, which can be used to analytically determine a loss minimizing dispatch for generators. This letter draws on recent research on the characterization of transmission system losses to demonstrate how the \(K_{GL}\) matrix achieves this impressive function. A new proof of the observed zero row summation property of the \(Y_{GGM}\) matrix is provided to this end.