Analytic Loss Minimization: Theoretical Framework of a Second Order Optimization Method

Ioannis Dassios

doi:10.3390/sym11020136

Abstract

In power engineering, the Y b u s 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 G L and Y G G M 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 b u s . We define an appropriate matrix functional of several variables with complex elements and aim to obtain the minimum values of generator voltages.

Highlights

Electrical power system calculations rely heavily on Ybus, a symmetric square N × N matrix, which describes a power system network with N buses
By using a second order optimization method, an approximate solution of (10) in respect of VG ∈ Cm is given by the solution of the linear system: (0)
We defined the function of several variables with complex coefficients that describes this optimization problem and obtained the minimum values of generator voltages, so that the active power losses reduce the irreducible component, which arises from serving load currents

Summary

Introduction

Electrical power system calculations rely heavily on Ybus , a symmetric square N × N matrix, which describes a power system network with N buses. By taking advantage of its symmetry properties, it is useful to split the Ybus into sub-matrices and separately quantify the connectivity between load and generation nodes in the network; see [3]. This idea has been further applied to several power engineering problems [4,5,6,7]. In a case like that, it would not be clear whether the proposed solution would minimize losses when constant-power loads are present For this reason, in this article, we focus on and apply the results to the case of constant-current loads

Mathematical Background

Conclusions