# 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.