Planning Models for Single Wire Earth Return Power Distribution Networks GEOFREY BAKKABULINDI Licentiate Thesis Royal Institute of Technology School of Electrical Engineering Electric Power Systems Stockholm, Sweden 2012 TRITA-EE 2012:052 KTH School of Electrical Engineering ISSN 1653-5146 SE-100 44 Stockholm ISBN 978-91-7501-553-8 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licenti- atexamen i elektrotekniska system den 10 December 2012 klockan 09.00 i sal H1, Kungl Tekniska högskolan, Teknikringen 33, Stockholm. © Geofrey Bakkabulindi, December 2012 Tryck: Universitetsservice US AB iii Abstract The high cost of grid extension to rural areas, which are of- ten characterized by scattered communities with low load den- sities, requires the use of low cost electrification technologies to ensure economic viability. In Single Wire Earth Return (SWER) power distribution networks, the earth itself forms the current return path of the single phase system leading to sig- nificant cost savings on conductors, poles and poletop hardware compared to conventional systems. However, challenges exist in SWER with regard to earthing and safety as well as the depen- dence on earth conductivity to supply consumer loads. This work presents models for the optimal planning of SWER power distribution networks. The earth return path is mod- eled as a conductor based on the Carson line model taking into consideration specific ground properties of the considered loca- tion. A load flow algorithm for radial SWER networks is subse- quently formulated whereby the overhead line and ground volt- ages and currents are determined using the backward/forward sweep method. First, heuristic planning models are developed based on the SWER load flow model. The objective of the heuristic mod- els is to determine the optimum feeder configuration and over- head conductor subject to SWER load flow constraints and load growth over several time periods. Whereas the resulting solu- tions are good, they may not necessarily be globally optimum. Optimization models are then developed using mixed integer non-linear programming (MINLP) with the aim of obtaining global solutions to the SWER network planning problem. Since the MINLP formulations are limited to the accurate analysis of limited size networks, considerations and approximations for the analysis of larger networks are presented. The developed models are applied to a case study in Uganda to test their practical application. In addition, comparative studies are done to determine how the proposed optimization models compare with previous distribution planning models. The numerical analysis includes the impact of deterministic dis- tributed generation on the SWER planning problem. iv Results showed consistent performance of the proposed heuris- tic and optimization models, which also compared well with conventional models. The optimization models gave more cost- effective solutions to the SWER planning problem than the heuristic models. However, the former models had higher com- putational cost than the latter. The inclusion of distributed generation allowed for cheaper network solutions to be obtained. The models are applicable to the planning of Single Wire Earth Return networks for isolated mini-grids, grid-extension to previously un-electrified rural areas as well as the upgrade of SWER feeders in existing installations. Acknowledgments This work was part of a research cooperation between the Royal In- stitute of Technology (KTH), Stockholm, Sweden and Makerere Uni- versity, Kampala, Uganda. I thank the Swedish International Develop- ment Agency (SIDA) whose financial support under the Department of Research Cooperation (SAREC) has made this research possible. I am deeply grateful to my supervisors at KTH, Asst. Prof. Mikael Amelin and Prof. Lennart Söder, and Makerere University, Assoc. Prof. Izael P. Da Silva and Prof. E. Lugujjo, for the considerable advice, support and guidance they have provided throughout this re- search. The outstanding guidance of Asst. Prof. Mohammad R. Hesamzadeh later in the project is gratefully acknowledged. Special thanks to Prof. Amelin for the exhaustive review of this thesis and, together with Annika, making my visits to Stockholm more enjoyable. The continued advice and academically stimulating environment provided by my colleagues, friends and fellow PhD students at KTH and Makerere University are gratefully acknowledged. Special grati- tude to Dr. Al-Mas Sendegeya whose constant encouragement, ideas and critique of my work have been invaluable. Jochen Roeber is grate- fully acknowledged for providing practical information on the topic and facilitating field visits to SWER sites in Namibia. Finally, my utmost gratitude goes to my family, especially George William and Teopista Kawooya, for their love, faith and moral support both during this research and throughout my academic career. Stockholm November 2012 Geofrey Bakkabulindi v Contents Acknowledgments v List of Figures viii List of Tables x 1 Introduction 1 1.1 Background . 1 1.2 Scientific Objective . 3 1.3 Scope and Assumptions . 4 1.4 Contributions of Thesis . 4 1.5 List of Publications . 6 1.6 Division of Work between the Authors . 7 1.7 Outline of Thesis . 7 2 Overview of SWER Power Distribution 9 2.1 Technical concept . 9 2.2 Earthing and Safety . 13 2.3 Power Quality . 17 2.4 Comparison with Conventional Distribution . 19 2.5 Upgradability . 21 3 Mathematical Modeling of SWER 25 3.1 Line Impedance Model . 25 3.2 Line Shunt Admittance . 28 3.3 SWER Load Flow Model . 29 vi CONTENTS vii 4 Overview of Power Distribution Planning Models 31 4.1 Introduction . 31 4.2 Network Optimization . 33 4.3 Heuristic Models . 36 4.4 Optimal Feeder Configuration . 37 5 Proposed Heuristic Model for SWER Network Planning 39 5.1 Introduction . 39 5.2 Feeder Routing using the MST Algorithm . 41 5.3 Conductor Selection . 43 6 Application of Heuristic Model to a Case Study in Uganda 49 6.1 The Ntenjeru Case Study . 49 6.2 Case Study Network Data . 50 6.3 Simulation Results . 53 6.4 Discussion of Results . 58 6.5 Possible Improvements to Proposed Heuristic Model . 60 7 Proposed Optimization Models for SWER Network Planning 63 7.1 Introduction . 63 7.2 Feeder Routing Problem Formulation . 64 7.3 Conductor Selection Problem Formulation . 67 7.4 Approximations for Larger Networks . 71 8 Practical Application of Proposed Optimization Models 73 8.1 Comparative Studies . 74 8.2 Application to Case Study . 78 9 Closure 85 9.1 Conclusion . 85 9.2 Future Work . 87 Bibliography 89 List of Figures 2.1 Typical configuration of SWER distribution system [1] . 10 2.2 Two phase T-off from three-phase MV network to SWER isolating transformer (Gerus substation, Namibia) . 11 2.3 A SWER isolating transformer with two phase input (L) and single phase output (R) (Gerus substation, Namibia) . 11 2.4 A SWER customer connection transformer [2] . 12 2.5 Wenner four pin method for measuring soil resistivity [3] . 16 2.6 Cost comparison of two SWER configurations and conven- tional distribution . 21 2.7 A Single Wire Earth Return line supplying power to house- holds and commercial loads (Oshakati, Namibia) . 22 3.1 Model of Carson’s line with earth return [4] . 27 5.1 Flow diagram of heuristic conductor selection algorithm . 48 6.1 Demand point locations in case study area . 51 6.2 Optimum feeder route configuration . 54 6.3 Graphical presentation of heuristic conductor size selections for different scenarios . 58 8.1 Small scale feeder routing test network . 75 8.2 Optimum feeder route of 5 node test network . 75 8.3 Graphical comparison of heuristic and optimization model conductor selections for different scenarios . 78 8.4 Clustering and routing of case study area demand points . 81 viii List of Figures ix 8.5 Line-to-ground nodal voltage variations of clustered case study network with and without DG for selected conduc- tors . 83 8.6 Ground voltage variations of clustered case study network with and without DG for selected conductors . 83 List of Tables 2.1 Typical Soil Resistivity Values . 17 2.2 Minimum Separation of SWER Lines from Open Wire Com- munications . 18 6.1 Location and Demand data for case study network . 52 6.2 Electrical characteristics of selected conductors . 53 6.3 Relabeled demand points of optimum route for case study network . 55 6.4 Overall index results for conductor selection at 5% annual load growth over 10 years . 56 6.5 Index values for conductor selection in different scenarios . 57 8.1 Data for small scale 5 node test network [5] . 74 8.2 Conductor selection results using the heuristic and opti- mization models . 77 8.3 Location and Demand data for case study network . 79 8.4 Cluster leading node data . 80 8.5 Optimum branch conductor selections with and without DG 82 x List of Acronyms ACSR Aluminium Conductor Steel Reinforced DFC Distribution Feeder Configuration DG Distributed Generation GA Genetic Algorithm GAMS General Algebraic Modeling System GIS Geographic Information System GMR Geometric Mean Radius HA Heuristic Algorithm hp horse power KCL Kirchoff’s Current Law KTH Kungliga Tekniska Högskolan (Royal Institute of Technology) MILP Mixed Integer Linear Programming MINLP Mixed Integer Non-Linear Programming MST Minimum Spanning Tree MV Medium Voltage OM Optimization Model RDN Radial Distribution Network SIDA Swedish International Development Agency SWER Single Wire Earth Return TSP Traveling Salesman Problem UEDCL Uganda Electricity Distribution Company Limited xi Chapter 1 Introduction This chapter introduces the background of the research, the scientific objectives, scope and assumptions as well as the contributions and achievements. 1.1 Background The levels of electrification in most of sub-Saharan Africa are gener- ally low with large percentages of the population, especially in rural areas, going without modern forms of energy. In Uganda, for exam- ple, the electrification rate is currently about 9% countrywide and 3% in rural areas [6].