I- Introduction

II- Load Flow Formulation

III- Models

IV- The Newton’s Method and Wirtinger’s Calculus Applied to Load Flow Problem

V- Tracing QV Curves

References

Abstract

Load flow methods for distribution networks such as Backward Forward Sweep (BFS) have a good computational performance and can find solutions with accuracy. However, some studies may demand the determination of low voltage solutions, and this poses a problem for these methods since they cannot find these solutions due to convergence issues. This paper presents a load flow method based on a novel complex-valued formulation developed for distribution networks, which works well on radial topologies by using an incidence matrix to avoid complicated series element models, allow high-performance and low-voltage solution capability. The formulation is solved by Newton’s method via Wirtinger’s calculus. To prove the lowvoltage solution capability, both sides of QV curves, i.e., unstable and stable regions were traced on balanced and unbalanced networks. Performance tests in the IEEE test feeders show that the runtime is less than or equal to the runtime of the BFS method. Furthermore, the line R/X ratio and the number of controlled voltage node or volt-var functions do not affect the computational performance, yielding advantages over the classic Newton and BFS methods.

INTRODUCTION

THE QV and PV curves provide important information about voltage stability of a system. In transmission systems, these curves are traced by Continuation Power Flow (CPF) techniques [1], [2]. These techniques use Newton’s method to solve the real-valued load flow formulation, and its Jacobian matrix helps to predict the curves’ points and to detect bifurcation and unstable points. Voltage stability analyses for distribution networks were not necessary for the past, nevertheless, over the last decade, these networks are evolving from static overplanned networks to dynamic active systems which will require operation planning similar to transmission systems in some aspects. The main reason for this transformation is the increased penetration of distributed generators (DG) [3]. In this new reality, the existent tools to analyze distribution systems no longer support the information needs for the new decision-making process to operate this networks. One such area in need of new tools is voltage stability analyses. This is the reason why the feasibility of CPF in distribution networks should be revised; what it implies to have effective and efficient load flow methods available. One of the load flow methods most widely used in distribution networks is the Backward Forward Sweep (BFS) [4], developed by taking advantage of the radial topology, resulting in an efficient tool. However, the lack of a Jacobian matrix makes it impractical to use into CPF techniques. Furthermore, the BFS method can’t find points of the left side of QV curves or the low side of PV curves, due to convergence issues on low voltage solutions [5].