# three phase load flow analysis

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First Edition 2008 MOHAMMAD YUSRI HASSAN 2008

Hak cipta terpelihara. Tiada dibenarkan mengeluar ulang mana-mana bahagian artikel, ilustrasi, dan isi kandungan buku ini dalam apa juga bentuk dan cara apa jua sama ada dengan cara elektronik, fotokopi, mekanik, atau cara lain sebelum mendapat izin bertulis daripada Timbalan Naib Canselor (Penyelidikan dan Inovasi), Universiti Teknologi Malaysia, 81310 Skudai, Johor Darul Tazim, Malaysia. Perundingan tertakluk kepada perkiraan royalti atau honorarium. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopy, recording, or any information storage and retrieval system, without permission in writing from Universiti Teknologi Malaysia, 81310 Skudai, Johor Darul Tazim, Malaysia.

Perpustakaan Negara Malaysia Cataloguing-in-Publication Data

Recent developments in three phase load flow analysis / edited by: Mohammad Yusri Hassan. Includes index ISBN 978-983-52-0680-1 I. Electric power system--Load dispatching. I. Mohammad Yusri Hassan. 621.317

Editor: Mohammad Yusri Hassan Pereka Kulit: Mohd Nazir Md. Basri & Mohd Asmawidin Bidin

Diatur huruf oleh / Typeset by Fakulti Kejuruteraan Elektrik

Diterbitkan di Malaysia oleh / Published in Malaysia by PENERBIT

UNIVERSITI TEKNOLOGI MALAYSIA 34 38, Jln. Kebudayaan 1, Taman Universiti,

81300 Skudai, Johor Darul Tazim, MALAYSIA.

(PENERBIT UTM anggota PERSATUAN PENERBIT BUKU MALAYSIA/ MALAYSIAN BOOK PUBLISHERS ASSOCIATION dengan no. keahlian 9101)

Dicetak di Malaysia oleh / Printed in Malaysia by

UNIVISION PRESS SDN. BHD. Lot. 47 & 48, Jalan SR 1/9, Seksyen 9,

Jalan Serdang Raya, Taman Serdang Raya, 43300 Seri Kembangan,

Selangor Darul Ehsan, MALAYSIA.

Contents

v

CONTENTS

Preface ix

Chapter 1 Review of Load Flow Analysis Khalid Mohamed Nor

1

Chapter 2 Single-Phase Load Flow Analysis Khalid Mohamed Nor Hazli Mokhlis Taufiq A Gani

23

Chapter 3 Three-Phase Power-Flow Methods using Sequence Components Mamdouh Abdel-Akher Khalid Mohamed Nor

49

Chapter 4 Unbalanced Distribution Power Flow Analysis using Sequence and Phase Components Mamdouh Abdel-Akher Khalid Mohamed Nor

81

Contents vi

Chapter 5 Representing Single-Phase and Two-Phase Lines with Dummy Lines and Dummy Nodes Mamdouh Abdel-Akher Khalid Mohamed Nor

107

Chapter 6 Unbalanced Three Phase Power Flow with Dummy Lines and Nodes Mamdouh Abdel-Akher Khalid Mohamed Nor

113

Chapter 7 Three Phase Load Flow Analysis with Distributed Generation Syafii Ghazali Khalid M Nor M. Abdel-Akher

137

Chapter 8 Future Potentials and Works Syafii Ghazali and Khalid Mohamed Nor

153

Index

161

Preface

ix

PREFACE

Load Flow is the most used analysis in power system. It is required in virtually all aspect of engineering and technical activity in electrical power engineering. Due to its importance and significance, it was amongst the early area that power system researchers worked on especially with the advent of digital computers. Since its long history many can be forgiven for perceiving that all its well and not much need to be studied anymore about load flow.

In its early stage load flow was formulated as a balanced problem. It does simplify the problem in the sense the size of the variables to be solved is drastically reduced. The balanced problem was solved with many mathematical methods that exploit the intrinsic nature of the load flow problem. Over the years as the load flow algorithms increased in complexities, in terms of control variables and development of HVDC and FACTS, the original problem has to be modified and consequently, the programming code need to updated constantly from time to time. From another aspect, computer and computing technology has developed so fast and so much, that most of the original programs that implemented the load flow algorithm have been ported, from the main-frame, to minicomputer to UNIX workstation and now to the ubiquitous Microsoft windows based personal computer or personal workstation. How do we developed the algorithm and what computing technique that we need to employ that minimized the disruption in program maintenance as well ensure minimum computing resources is expended to achieve this objective?

Preface x

While transmission system may still remain a well balanced three phase networks, the distribution system is not necessarily so. This is because transposition used in transmission lines may not be available at all parts of a distribution system. Furthermore the advent of switching mode supplies that power the dominant portion of consumer loads in single phase, means the load are no longer balanced while the networks is lightly unbalanced. From a restricted point of view, but nonetheless quite significant, many networks in North America and some other parts of the world, use single phase and two phase networks to minimize the cost of transmission lines to supply remote loads over long distances. The load flow problem for this kind of network requires special considerations.

Many developments in load flow analysis is being reported in this monograph. Most materials have been published in refereed journals. They have been updated and edited for additional clarity and of course continuity of presentation. This monograph was conceived earlier as the number of work that was done students working under my supervision increased. The works developed towards a better understanding of the load flow analysis. It is not so much the formulation but rather the modeling and the application of previous works to solve a wider type of problems. This publication is hoped to add values to an already voluminous amount of information about load flow in the literature.

Mohammad Yusri Hassan Facuty of Electrical Engineering Universiti Teknologi Malaysia 2008

Literature Review of Load-Flow Analysis

1

1 LITERATURE REVIEW OF LOAD-

FLOW ANALYSIS

Khalid Mohamed Nor

1.1. Introduction

Power-flow studies is an essential tool in planning and designing the future expansion of power systems as well as determining the best operation of existing power systems. The main objective of an unbalanced three-phase power-flow study is to obtain the individual phase voltages at each bus corresponding to the network specified conditions. The balanced three-phase power-flow studies assume that the system unbalances may be neglected. However, there are many cases in which the unbalances of loads, untransposed transmission lines etc. cannot be ignored. Besides, in distribution systems, there are several examples in which the balanced conditions hypothesis cannot be applied. A typical case would be mixed single-phase, two-phase, and three-phase systems in which it is obviously impossible to use a balanced model hypothesis. These cases must be handled with a complete three-phase power system model, as has been proposed by several authors in the literature.

This chapter presents a survey of the basic formulation and the

various unbalanced power-flow algorithms used for solving and analyzing unbalanced electrical networks. The unbalanced three-

Recent Trends in Power System Operation

2

phase power-flow methods can be categorized into three main groups. Firstly, methods are developed for solving general network structure; therefore, these methods can be applied for solving meshed transmission as well as radial distribution power systems. The second group is particularly intended for radial distribution systems since they consider primarily the radial structure of the network. Most of the methods, in both first and second categories, are developed using power system models established in phase coordinates frame of reference.

Finally, the third category includes few methods that are

established based on symmetrical components frame of reference. These methods cannot solve power systems that contain single-phase and two-phase line segments which is the case in distribution power systems. Therefore, the application of these methods is limited to pure three-phase systems and they are normally used for power quality studies since voltage sag analysis is usually studied based on the concept of symmetrical components.

1.2. Discussion of the frame of reference

Power systems have been traditionally analyzed using symmetrical components matrix transformations [1]. This technique has been widely used in unbalanced electric power systems in steady-state analysis. Symmetrical components transformation decouples symmetrical three-phase power systems into positive-, negative-, and zero-sequence networks. Symmetrical power systems include components such as transposed transmission lines, transformers, and generators which can be decoupled using the symmetrical components transformation. The advantage of the sequence networks is that the problem size is greatly reduced and the formulation of the problem is simplified. In addition, many power system analyses can be integrated such as balanced and unbalanced power-flow.

Literature Review of Load-Flow Analysis

3

Unfortunately, if a power system includes components such as salient-pole synchronous machines, unbalanced loads, and untransposed lines, the network cannot be uncoupled by the mean of symmetrical components. Besides, the phase shifts introduced