Matrix-Based Generalization for Power-Mismatch Newton-Raphson Load Flow Computations With Arbitrary Number of Phases

Henrique P Correa,Flavio H T Vieira

doi:10.1109/access.2020.2976770

Abstract

The standard power-mismatch Newton method is still frequently used for computing load flow due to its simplicity and generality. In this paper, a matrix-based generalization for the usual power flow equations to an arbitrary number of phases is derived. The proposed equations enable computing power injections and the Jacobian matrix in terms of submatrices that compose the network admittance matrix. Besides the more compact representation, another advantage of the proposed generalization is execution time reduction compared to the standard scalar formulation. Simulations are carried out to demonstrate the time reduction achieved via the proposed equations.

Highlights

Load flow algorithms are widely used in the analysis of power systems via simulation [1]–[5]
We review representative algorithms that have been considered for solving load flow problems
The power-based approach corresponds to the traditional Newton-Raphson load flow, whereas the current-based formulation has been more recently proposed as the current injection method [10], [11]

Summary

INTRODUCTION

Load flow algorithms are widely used in the analysis of power systems via simulation [1]–[5]. We present a generalized formulation of the power-mismatch equations that can reduce processing time for multi-phase systems. Scalar equations for power injection and Jacobian elements have been derived for three-phase systems [9] This fact represents a further motivation for achieving a matrix representation of power-mismatch load flow, since it will permit abstracting from the number of phases when handling the power injection and Jacobian matrix computations. Be previously computed from the specified network elements via their primitive admittance matrices; Provides a concise, matrix-based representation of power and Jacobian equations for multi-phase systems, independently of the number of system phases; Reduces execution time due to the multithreaded processing of matrix operations [28]

PRELIMINARIES

DERIVATION OF JACOBIAN EQUATIONS

PROCESSING TIME REDUCTION

Findings

VIII. CONCLUSION