Analytic loss minimization: Theoretical framework of a second order optimization method

In power engineering, the Y bus is a symmetric N × N square matrix describing a power system network with N buses. By partitioning, manipulating and using its symmetry properties, it is possible to derive the K GL and Y GGM matrices, which are useful to define a loss minimisation dispatch for generators. This article focuses on the case of constant-current loads and studies the theoretical framework of a second order optimization method for analytic loss minimization by taking into account the symmetry properties of Y bus . We define an appropriate matrix functional of several variables with complex elements and aim to obtain the minimum values of generator voltages.