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AVR placement Using Backtracking Technic

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AVR placement Using Backtracking Technic

  1. 1.     ្រកសួងអប់រំយុវជន និងកី វិទយ ថ នបេចចកវិទយកមពុជ េដប៉ តឺម៉ង់េទពយេកសលយ អគគិសនី និងថមពល គំេ ងសញញ ប័្រតវិស្វករ ្របធនបទ : ករគណន និងេ្រជើសេរើសទី ំងសំ ប់ ក់ AVR េនេលើប ្ត ញែចកចយតង់សយុងមធយម ២២ គីឡូវ៉ុល និស ិត : ែញ៉ត ៉ ឯកេទស : អគគិសនី និងថមពល ្រគូទទួលបនទុក : េ ក ឃុន ចនធ ឆន ំសិក : ២០១៣ - ២០១៤ MINISTERE DE L’EDUCATION, DE LA JEUNESSE ET DES SPORTS INSTITUT DE TECHNOLOGIE DU CAMBODGE DEPARTEMENT DE GENIE ELECTRIQUE ET ENERGETIQUE MEMOIRE DE FIN D’ETUDE Titre : Calcul de la taille et Optimum le placement d’AVR à la ligne de Moyenne Tension 22kV Etudiant : NHET Ra Spécialité : Electrique et Energétique Tuteur de stage : M. KHUN Chanthea Année Scolaire : 2013 – 2014
  2. 2.     MINISTERE DE L’EDUCATION, DE LA JEUNESSE ET DES SPORTS INSTITUT DE TECHNOLOGIE DU CAMBODGE DEPARTEMENT DE GENIE ELECTRIQUE ET ENERGETIQUE MEMOIRE DE FIN D’ETUDE INGENIEUR DE M. NHET Ra Date de soutenance : le 30 juin 2014 «Autorise la soutenance du mémoire » Directeur de l’Institut : ___________________ Phnom Penh, le 2014 Titre : Calcul de la taille et optimum le placement d’AVR à la ligne de Moyenne Tension 22kV Établissement du stage : Électricité du Cambodge Chef du département : M. CHY Cheapok Professeur d’encadrement : M. KHUN Chanthea Responsable de l’établissement : M. RANN Seihakkiry PHNOM PENH, 2014
  3. 3.     ្រកសួងអប់រំយុវជន និងកី វិទយ ថ នបេចចកវិទយកមពុជ េដប៉ តឺម៉ង់ េទពេកសលយអគគិសនី និងថមពល គំេ ងសញញ ប័្រតវិស្វករ របស់និស ិត: ែញ៉ត ៉ កលបរិេចឆទករពរនិេកខបបទ: ៣០ មិថុន ២០១៤ អនុញញ តឲយករពរគេ្រមង នយកវិទយ ថ ន _________________ ៃថងទី ែខ ឆន ំ២០១៤ ្របធនបទ: ករគណន និងេ្រជើសេរើសទី ំងសំ ប់ ក់ AVR េនេលើ ប ្ត ញែចកចយតង់សយុង មធយម ២២គីឡូវ៉ុល សហ្រគស : អគគិសនីកមពុជ ្របធនេដប៉ តឺម៉ង់ : េ ក ជី ជប៉ុក ្រ ្ត ចរយដឹកនំគំេ ង : េ ក ឃុន ចនធ អនកទទួលខុស្រតូវកនុងសហ្រគស : េ ក ៉ ន់ សីហៈគីរី ជធនីភនំេពញ ឆន ំ២០១៤
  4. 4. i ACKNOWLEDGEMENT I take this opportunity to express my profound gratitude and deep regards to my beloved persons for their exemplary guidance, monitoring and constant encouragement throughout this report without them this report could not have been written. I would like to express a deep sense of gratitude to Dr. OM Romny, General Director of Institute of Technology of Cambodia, for the authorization me for the defense studies to complete my academic program. I would like to express my sincere gratitude to Mr. NUTH Sothan, Deputy Director, for preparing and managing all ITC programs. The programs were well integrated with academic standards allow all teachers ITC to be effective in their educational missions. I would like to express my very great appreciation to Mr. PHOL Norith, Deputy Director, in charge of projects and schedules ITC. I am obliged to Mr. CHY Cheapok, Head of Electrical Engineering and Energy, who has devoted much time to help students Electrical and Energy department. A memorable thank you to Mr. Khun Chanthea, my advisor, who directed my research and consulted me long for my internship. I would like to say thank you to Mr. CHUN Piseth, Director of cooperate planning and project, who allows me to have an internship at EDC. In particular, I would like to deeply thank to Mr. TOUCH La, who constantly help me throughout my report. Finally, I would like to convey my heartfelt thanks to my parents for their constantly support and encourage me. I would like to thank to all my professors in GEE department and all people around me for their encouragement and help me enjoy along this painstaking work.
  5. 5. ii សេចក្តីេសខេប ក្នុខនិសក្េបបទសនេះបង្ហា ញអំពីក្ម្មេិក្ាដែលខ្ុំបានស្វើសៅអគ្គិេនីក្ម្ពុជា អេ់រយេះសពលបីដខ គ្ឺចាប់ពីថ្ងៃទី ១៧ ដខក្ុម្ភេះរហូតែល់ថ្ងៃ ១៥ ដខ ឧេភា ឆ្ន ំ ២០១៤។ សោលគ្ំនិតថ្នការស្វើនិសក្េបបបទសនេះស ើខគ្ឺសែើម្បីស្វើ ការដក្លំអរ តខ់េយុខម្្យម្សោយស្បើ្បាេ់ Automatic Voltage Regulator សោយសារដតមានការធ្លា ក្់តខ់ េយុខជាសរឿយៗ សៅសលើបណ្តត ញតខ់េយុខម្្យម្។ ជាក្់ដេតខ បណ្តត ញដចក្ចាយតខ់េយុខក្នុខសខតត ថ្្ពដែខ មាន ការធ្លា ក្់តខ់េយុខហួេពីេតខ់ោររបេ់ អគ្គិេនីក្ម្ពុជា សោយសារដតក្ំស ើនថ្នអនក្ស្បើ្បាេ់។ សៅក្នុខ និសក្េបបទសនេះ្តូែបានដបខដចក្ជា ៦ ជំពូក្េំខាន់ៗ។ ជំពូក្ទី ១ គ្ឺសតត តសៅសលើ បទបង្ហា ញទូសៅ និខ ្ក្ុម្ ហុន (អគ្គិេនីក្ម្ពុជា)។ ជំពូក្ទី ២ គ្ឺបង្ហា ញអំពី។ ជំពូក្ទី ៣ បក្្សាយអំពីែិ្ីសាស្រេតដែលយក្ម្ក្ស្បើ្បាេ់ េំរាប់ការស្វើនិសក្េបបទសនេះ។ ជំពូក្ទី ៤ គ្ឺសរៀបរាប់លំអិតអំពី បណ្តត ញ ២២ kV សៅសលើ្បព័នធដែលមាន្សាប់ រួម្បញ្ជូលំំខ Software ដែលយក្ម្ក្ស្បើ្បាេ់។ ជំពូក្ទី ៥ គ្ឺ បង្ហា ញអំពីការេននិោា នរួម្ និខ ជំពូក្ទី ៦ ផ្ត ល់ជា អនុសាស្រេតេំរាប់អនក្ដែលចខ់ស្វើការ្សាែ្ជាែបនតរ។
  6. 6. iii RESUME Ce rapport est le fruit de mon stage de fin d’études au sein d’Electricité du Cambodge. Pendant trois mois : du 17 février au 15 mai 2014. L’essentiel de ce rapport porte sur l’amélioration de chute de tension dans le réseau de la distribution en replaçant Régulateur Automatique de Tension (AVR) sur le système existant quand il y a le chute de tension sur le system Moyenne de Tension. En réalité, le réseau de distribution système sur la province de Prey Veng il y avait la chute de tension moins de limitation. Ce rapport se compose de six chapitres principaux. La première présente l’introduction générale sur l’état de lieu de l’entreprise. Deuxième concentre sur de l’étude bibliographique du calcul. Le troisième décrit la méthode de calcul. Le quantième indique le détail sur le système existence. Le cinquième présente les résultats de l’étude et de discussion. Le sixième se consacre à la conclusion générale du rapporte et certaines recommandations sont proposées dans ce dernier chapitre.
  7. 7. iv SUMMARY This report represents my internship for final year at Electricity of Cambodia during three months. It take place from 17, February until 15, June 2014. The importance point of this report is about the improvement of voltage drop in the radial distribution system by optimal Automatic Voltage Regulator (AVR) into the existing system. Voltage drop always happen in the distribution network due to the load increasing. EDC proposed a plan to improve voltage profile by Optimal AVR placement. Six chapters compose in this report. Chapter I focus on introduction and the details on the history of (EDC). Chapter II mainly deals with literature review. Chapter III presents the methodology of this report and also a brief description on the software tool used. Chapter IV details the Prey Veng province profile on power sector and presents the existing power system of study area. Chapter V details on results after placing AVR into an appropriate place by using Backtracking algorithm. Chapter VI presents the conclusions and recommendations drawn from this report with summary of the main findings.
  8. 8. v Table of Contents ACKNOWLEDGEMENT............................................................................................................... i សេចក្តីេសខេប.....................................................................................................................................ii RESUME .......................................................................................................................................iii SUMMARY................................................................................................................................... iv 1 INTRODUCTION................................................................................................................... 1 1.1 OVERVIEW..................................................................................................................... 1 1.1.1 RATIONAL.............................................................................................................. 1 1.1.2 OBJECTIVE ............................................................................................................. 2 1.1.3 SCOPE AND LIMITATION.................................................................................... 2 1.1.4 REPORT OUTLINE................................................................................................. 2 1.2 TRUCTURE OF ELECTRICITY OF CAMBODIA....................................................... 4 1.2.1 HISTORY OF EDC.................................................................................................. 4 1.2.2 ORGANISATION .................................................................................................... 4 1.2.3 STRUCTURE ........................................................................................................... 6 1.2.4 ENERGY POLICY................................................................................................... 7 2 LITERATURE REVIEW........................................................................................................ 8 2.1 Symmetrical spacing ........................................................................................................ 8 2.2 Asymmetrical spacing...................................................................................................... 9 2.3 GMR of Bundled conductors ......................................................................................... 11 2.4 INDUCTANCE FO THREE-PHASE DOUBLE-CIRCUIT LINES............................. 11 2.5 GAUSS-SEIDEL METHOD.......................................................................................... 13 2.5.1 Power Flow solution ............................................................................................... 14 2.5.2 Gauss-Seidel Power flow solution.......................................................................... 16 2.6 NEWTON-RAPHSON METHOD ................................................................................ 17 2.6.1 Newton-Raphson Power Flow solution .................................................................. 18 2.6.2 Line Flow and Losses ............................................................................................. 23 2.7 Approximate Methods of Analysis ................................................................................ 24
  9. 9. vi 2.7.1 Voltage Drop........................................................................................................... 24 2.8 INTRODUCTION OF ALGORITHM .......................................................................... 26 2.8.1 BACKTRACKING ALGORITHM........................................................................ 26 2.8.2 Depth-First Search .................................................................................................. 27 2.9 Backtracking Technique................................................................................................. 29 2.10 Game Trees .................................................................................................................... 29 3 METHODOLOGY................................................................................................................ 31 3.1 DESCRIPTION OF METHODOLOGY........................................................................ 31 3.2 Line Resistance .............................................................................................................. 31 3.3 TEMPERATURE EFFECT ........................................................................................... 32 3.4 SKIN EFFECT............................................................................................................... 32 3.5 Asymmetrical spacing.................................................................................................... 33 3.6 STUDY POWER FLOW ............................................................................................... 34 3.6.1 Power Flow solution ............................................................................................... 34 3.7 BACK TRACKING ALGORITHM.............................................................................. 36 3.8 STEPS FOR OPTIMAL VOLTAGE REGULATOR PLACEMENT IN RDS USING BACK TRACKING ALGORITHM:........................................................................................ 38 3.9 Flow chart for optimal auto-voltage regulator placement using back tracking algorithm: ………………………………………………………………………………………….39 3.10 BRIEF DESCRIPTION ABOUT SOFTWARE TOOL ................................................ 40 3.10.1 Calculating Load Flow............................................................................................ 40 4 CASE STUDY (PREY VENG)............................................................................................. 41 4.1 OVERVIEW................................................................................................................... 41 4.2 PROFILE OF PREY VENG .......................................................................................... 41 4.3 POWER LOSSES .......................................................................................................... 42 4.4 RELIABILITY INDICES .............................................................................................. 43 4.5 EXISTING DISTRIBUTION SYSTEM........................................................................ 43
  10. 10. vii 4.6 LINE PARAMETER COMPUTATION ....................................................................... 45 4.7 VOLTAGE PROFILE IN PREY VENG ....................................................................... 46 4.8 Voltage Profile On 70% Loads for the future extension................................................ 50 4.9 DETERMINING REQUIRE REGULATOR TYPE AND SIZE .................................. 55 5 RESULT OFTER AVR IMPLEMENTION.......................................................................... 56 6 Conclusion and Recommendation......................................................................................... 61 6.1 Conclusion...................................................................................................................... 61 6.2 Recommendations.......................................................................................................... 61 7 References ............................................................................................................................. 62 Appendix-A Single Line Diagram Before and After AVR is implemented................................. 64 Appendix-B Cable Specifications................................................................................................. 65 Appendix-C Crosse-Arm 22 kV ................................................................................................... 69 Appendix-D AVR specifications (Cooper Power Systems) ......................................................... 73 Appendix-E The report of Interruption......................................................................................... 75
  11. 11. viii LIST OF FIGURES Figure 1.1. Electricity of Cambodia Head Quarter ........................................................................ 4 Figure 1.2. Managerial infrastructure of EDC ............................................................................... 6 Figure 1.3. Energy policy of EDC ................................................................................................. 7 Figure 2.1.Three-phase line with symmetrical spacing ................................................................. 8 Figure 2.2. Three-phase line with asymmetrical spacing............................................................... 9 Figure 2.3. Example of bundled arrangements ............................................................................ 11 Figure 2.4. Transposed double-circuit ......................................................................................... 12 Figure 2.5. A typical bus of the power system............................................................................. 15 Figure 2.6. Transmission line model for calculating line flows................................................... 23 Figure 2.7. Line-to-neutral equivalent ......................................................................................... 25 Figure 2.8. Phasor diagram .......................................................................................................... 25 Figure 2.9. Backtracking enable a person to find his way through a maze ................................. 27 Figure 2.10. Depth tree search ..................................................................................................... 28 Figure 2.11. Backtracking algorithm technique........................................................................... 29 Figure 2.12. Gram tree problem example .................................................................................... 30 Figure 3.1. Three-phase line with asymmetrical spacing............................................................. 34 Figure 3.2. A typical bus of the power system............................................................................. 35 Figure 3.3. 19 bus RDS before shifting of auto-voltage regulators ............................................. 37 Figure 3.4. 19 bus RDS after shifting of auto-voltage regulators................................................ 37 Figure 3.5. Flow chart of Backtracking algorithm....................................................................... 39 Figure 3.6. View of analysis option of PSS/Adept ...................................................................... 40 Figure 4.1. map of Prey Veng province....................................................................................... 41 Figure 4.2. Distribution line configuration position 1 and 2........................................................ 45 Figure 4.3. Graphic of Voltage profile before AVR are implemented ........................................ 54 Figure 5.1. Voltage profile after AVR is implemented................................................................ 60
  12. 12. ix LIST OF TABLES Table 3.1. Cable resistivity and temperature coefficient.............................................................. 32 Table 3.2. Skin effect table........................................................................................................... 33 Table 4.1. Socio-economic indicator............................................................................................ 42 Table 4.2. Transmission line and distribution losses report......................................................... 43 Table 4.3. Reliability indices reported in October 2013 .............................................................. 43 Table 4.4. The summary of quantities for Prey Veng.................................................................. 44 Table 4.5. Line parameter calculation.......................................................................................... 45 Table 4.6. Line parameter calculation.......................................................................................... 46 Table 4.7. Line parameter calculation.......................................................................................... 46 Table 4.8. Result of power flow before AVR implemented (50% on load) ................................ 47 Table 4.9. Powers flow Details in Prey Veng province before AVR placement on (70% load) . 50 Table 5.1. Powers flow Details in Prey Veng province after AVR placement............................ 56
  13. 13. x LIST OF ABBREVIATION EDC : Electricité du Cambodge MV : Medium voltages AC : Alternative Current DC : Direct Current CEP : Cambodia Electricity Private Co., Ltd. EAC : Electricity Authority of Cambodia EDC : Electricité Du Cambodge IPP : Independent Power Producer KEP : Khmer Electrical Power Co., Ltd. PP : Phnom Penh S : Puissance d’apparence (MVA) V : Tension (v) I : Courant (A) P : Puissance active (kW) Q : Puissance réactive (kVAR) BT : Backtracking Algorithm
  14. 14. 1 1 INTRODUCTION 1.1 OVERVIEW Electricity is the principle of the development since every fields: economy, public health care, education, agriculture, infrastructure, and industrial are depend on it. In the name of the developing country, Cambodia is really need an electricity for the country development since all the infrastructures are almost destroyed by the civil war for three decades. So electricity play an important role to make those fields can be processed. However, the power system is constantly being faced with many significantly problems such as increasing load demand, lacking of power supply and losses that really affect the voltage profile (Voltage drop, Swell, Sage Harmonic etc.). Voltage drop in the radial distribution network is considered as a critical problems which is commonly occur due the length of the distribution line and the increasing of the electricity consumption. The long lengths of the distribution line; especially in rural area, is first causes that contribute to the voltage drop because the distance between source and consumer is far from each other. The tremendous increase of load demand also is a part that cause a voltage drop along the distribution line even we have planned for that. There are many solution have been proposed regarding to this problem such as creating a sub-transmission line, optimization AVR placement, optimization DG, and also, optimization Capacitor bank to maintain the voltage level. However, the problem is not end up yet since we do not know where to place it into an appropriate place and what size should be implemented. 1.1.1 RATIONAL Electricity consumption has been increased in the last recent years due to the country development. However, it is currently face with many problems which contribute a negative effect to the voltage quality, especially in the power distribution system network. In my report will study the existing electricity distribution system in Prey Veng province, presently, with too far distribution network in a various customer categories cause a voltage drop. Due to the fact that voltage is drop at the end of the distribution line, we cannot afford to connect with the MV load.
  15. 15. 2 This project never been done before so, it is really interesting me to do a research study on this topic and also the results of such a study provide valuable information needed to solve a certain problem with the results that open up possibilities for further research. 1.1.2 OBJECTIVE The main objective of this report is to maintain voltage level with in the desired limits and reduces power losses in the system in the following ways:  To maintain the voltage level within the limitation (±5%)  To maximize losses in the power distribution system,  To allow the MV load customer able to connect the EDC’s grid system  To provide a means document to further researcher 1.1.3 SCOPE AND LIMITATION Aspect of improving voltage profile of electricity distribution system demands vast coverage of study and a complex assessment. This report therefore has following scopes and limitations:  It focuses mainly on 22 kV distribution voltage levels, which are the primary distribution systems of study area.  PSS/Adept software tool, which is relevant to power distribution engineering, has been used for Load Flow.  Backtracking algorithm are used for optimal AVR placement after observing voltage drop. 1.1.4 REPORT OUTLINE Contents of this report are organized 6 different chapters. Following this chapter on introduction and a brief detail on the history of Electricity of Cambodia (EDC). Chapter 2 mainly deals with literature review. In this chapter a method for line data calculation and line configuration are presented. Moreover, it details about all every possible methods for optimal AVR placement. Chapter 3 presents the methodology of this report and also a brief description on the software tool used.
  16. 16. 3 Chapter 4 details the Prey Veng province profile on power sector and presents the existing power system of study area. This chapter presents a voltage profile of Prey Veng province in which its voltage is drop over the limitation. Chapter 5 details on results after placing AVR into an appropriate place by using Backtracking algorithm. Chapter 6 presents the conclusions and recommendations drawn from this report with summary of the main findings.
  17. 17. 4 1.2 TRUCTURE OF ELECTRICITY OF CAMBODIA 1.2.1 HISTORY OF EDC Electricity has been presented in Cambodia since 1906 by the Company of Electricity and Water (CEE), the Union of Electricity Indochina (UNEDI) and the Franco-Khmer Electricity Company (CFKE). In October 1958, Cambodian government has bought the rights from these companies and formed Electricité Du Cambodge (EDC) to produce, transport and distribute electricity in Phnom Penh city and other provinces also. During the Khmer Red regime, the electrical infrastructure of the EDC was destroyed. Figure 1.1. Electricity of Cambodia Head Quarter 1.2.2 ORGANISATION The main entities in the electricity sector are:
  18. 18. 5  The Ministry of Industry, Mines and Energy (MINE): established in 1993 and responsible for placing and administering government policies, strategies and development and investment plans for the sector owner. Its functions are surrounding the restructuring of power sector, the electricity trade with neighboring countries, major investment projects and the full management of rural electrification. Excluded from his command is the hydrocarbon sector, which is the Cambodian National Petroleum Authority. In partnership with the Ministry of Economy and Finance (MEF), the MINE is the owner of Electricity of Cambodia (EDC).  The Electricity Authority of Cambodia (EAC): regulate power sector, an independent body, established in 2001, responsible for the authorization, tariffs probation fixing and imposing standard performance and conflicts arrangement. The EAC consists of three members appointed by the Prime Minister and secretes headed by an Executive Director and behavior departments legislation, Financial, Regulation of electricity and personnel administration.  The Electricity of Cambodia (EDC) in 1996, it became a limited liability completely anonymous state has a responsibility to produce, transmit and distribute electricity throughout Cambodia. On a national level, its main functions are the creation of the main transmission grid and import or export electricity with neighboring countries. (Electricity of Cambodia, 2014)
  19. 19. 6 1.2.3 STRUCTURE Tariff, license, Financial Performence, Enforce the regulation, rule and Standard. Policy, Planning, Technical standard Ownership of EDC (J.Vitor, 2014) Figure 1.2. Managerial infrastructure of EDC Royal Government of Cambodia Electricity Authority Cambodia Ministry of Mines and Energy Ministry of Economic and Finance Electrical Entreprise PEU EDCPECIPP
  20. 20. 7 1.2.4 ENERGY POLICY (J.Vitor, 2014) To provide an adequate supply for energy throughout Cambodia at reasonable and affordable price To ensure a reliable and secure electricty supply at reasonalbe price, which facilitates investment in Cambodia and development of national economy To encourage exploration and environmentally and socially acceptable develpment of energy resources needed for supply to all sectors of Cambodia economy To encourage the efficient use of energy and to minimize detrimental environmental effects resulted from energy supply and consumption Figure 1.3. Energy policy of EDC
  21. 21. 8 2 LITERATURE REVIEW 2.1 Symmetrical spacing Consider one meter length of a three-phase line with three conductors each with radius r , symmetrically spaced in a triangular configuration as shown in Figure 2-1. Assuming balanced three-phase currents, we have 0 cba III (2.1) From (2.1) the total flux linkage of phase a conductors is                           D I D I r I cbaa 1 ln 1 ln ' 1 ln102 7  (2.2) Substituting for acb III  I                     D I r I aaa 1 ln ' 1 ln102 7  ' ln102 7 r D Ia   (2.3) Because for symmetry, acb   , and the three inductances are identical. Therefore, the inductance per phase per kilometer length is Figure 2.1.Three-phase line with symmetrical spacing CI bI aI DD D
  22. 22. 9 kmmH D D L s /ln2.0 (2.4) Where 'r is the geometric mean radius, GMR, and is shown by sD . For a solid round conductor, 4 1   reDs for stranded conductor sD can be evaluated from (3.1). Comparison of (2.3) with (2.4) shows that inductance per phase for a three-phase circuit with equilateral spacing is the same as for one conductor of a single-phase circuit. 2.2 Asymmetrical spacing Practical transmission lines cannot maintain symmetrical spacing of conductors because of construction considerations. With asymmetrical spacing, even with balanced currents, the voltage drop due to line inductance will be unbalanced. Consider one meter length of a three-phase line with three conductors, each with radiusr . The conductors are asymmetrically spaced with distances shown in Figure 2.2. The application of (2.4) will result in the following flux linkages.                             1312 7 1 ln 1 ln ' 1 ln102 D I D I r I cbaa Figure 2.2. Three-phase line with asymmetrical spacing c b a 13D 23D 12D
  23. 23. 10                             2312 7 1 ln 1 ln ' 1 ln102 D I D I r I cabb                             2313 7 1 ln 1 ln ' 1 ln102 D I D I r I bacc (2.5) Or in matrix form LI (2.6) Where the symmetrical inductance matrix L is given by                     ' 1 ln 1 ln 1 ln 1 ln ' 1 ln 1 ln 1 ln 1 ln ' 1 ln 102 2313 2312 1312 7 rDD DrD DDr L (2.7) For balanced three-phase currents with aI as reference, we have aab IaII 2 240   aac aIII   120 (2.8) Where the operator  1201a and  12012 a . Substituting in (2.4) result in                             1312 27 1 ln 1 ln ' 1 ln102 D a D a rI L a a a                              2312 27 1 ln 1 ln ' 1 ln102 D a D a rI L b b b                              2313 27 1 ln 1 ln ' 1 ln102 D a D a rI L c c c  (2.9)
  24. 24. 11 2.3 GMR of Bundled conductors Extra-high voltage transmission lines are usually constructed with bundled conductors. Bundling reduces the line reactance, which improves the line performance and increases the power capability of the line. Bundling also reduces the voltage surface gradient, which in turn reduces corona loss, radio interference, and surge impedance. Typically, bundled conductors consist of two, three, or four subconductors symmetrically arranged in configuration as shown in Figure 2.3. The subcondutors within a bundle are separated at frequent intervals by spacer-dampers. Spacer- dampers prevent clashing, provide damping, and connect the subconductors in parallel. The GMR of the equivalent single conductor is obtained by using (2.9). If sD is the GMR of each subconductor and d is the bundle spacing, we have For the two-subconductor bundle dDdDD ss b s  4 2 )( (2.10) For the three-subcondcutor bundle 3 28 3 )( dDddDD ss b s  (2.11) For the four-subcondutor bundle 4 316 42/1 09.1)2( dDdddDD ss b s  (2.12) 2.4 INDUCTANCE FO THREE-PHASE DOUBLE-CIRCUIT LINES A three-phase double-circuit line consists of two identical three-phase circuits. The circuits are operated with 212121 ,, ccbbaa  in parallel. Because of geometrical differences between Figure 2.3. Example of bundled arrangements d d d d d d d d
  25. 25. 12 conductors, voltage drop due to line inductance will be unbalanced. To achieve balance, each phase conductor must be transposed within its group and with respect to the parallel three-phase line. Consider a three-phase double-circuit line with relative phase position 222111 cbacba  , as shown in figure 2.4. The method of GMD can be used to find the inductance per phase. To do this, we group identical phases together and use (2.12) to find the GMD between each phase group 4 22122111 babababaAB DDDDD  4 22122111 cbcbcbcbBC DDDDD  4 22122111 cacacacaAC DDDDD  (2.13) The equivalent GMD per phase is then 3 ACBCAB DDDGMD  (2.14) Similarly, from (2.10), the GMR of each phase group is 2121 4 2 )( aa b Saa b SSA DDDDD  2121 4 2 )( bb b Sbb b SSB DDDDD  Figure 2.4. Transposed double-circuit 33S 22S 11S 2c 2b 2a1c 1b 1a
  26. 26. 13 2121 4 2 )( cc b Scc b SSB DDDDD  (2.15) Where b SD is the geometric mean radius of the bundled conductors given by (2.10) and (2.15). The equivalent geometric mean radius for calculating the per-phase inductance to neutral is 3 SCSBSAL DDDGMR  (2.16) The inductance per phase in millihenries per kilometer is kmmH GMR GMD L L /ln2.0 (2.17) (Power System Analysis, 1999) 2.5 GAUSS-SEIDEL METHOD The Gauss-Seidel method is also known as the method of successive displacements. To illustrate the technique, consider the solution of the nonlinear equation given by 0)( xf (2.18) The above function is rearranged and written as )(xgx  (2.19) If )(k x is an initial estimate of the variable x, the following iterative sequences is formed. )( )()1( kk xgx  (2.20) A solution is obtained when the difference between the absolute value of the successive iterative is less than a specified accuracy, i.e.,  )()1( kk xx Where  is the desired an accuracy. We now consider the system of n equations in nvariables 1211 ),...,,( cxxxf n 
  27. 27. 14 ............................. ),...,,( 2212 cxxxf n  (2.21) nnn cxxxf ),...,,( 21 Solving for one variable from each equation, the above functions are rearranged and written as ),...,,( 21111 nxxxgcx  ............................... ),...,,( 21222 nxxxgcx  (2.22) ),...,,( 21 nnnn xxxgcx  The iteration procedure is initiated by assuming an approximate solution for each of the independent variables ),...,,( )0()0( 2 )0( 1 nxxx . Equation (2.22) results in a new approximate solution ),...,,( )1()1( 2 )1( 1 nxxx . In the Gauss-Seidel method, the updated values of the variables calculated in the preceding equations are immediately used in the solution of the subsequent equations. At the end of each iteration, the calculated values of all variables are tested against the previous values. If all changes in the variables are within the specified accuracy, a solution has converged, otherwise another iteration must be performed. The rate of convergence can often be increased by using a suitable acceleration factor , and the iterative sequence becomes  )()1()()1( k i k i k i k i xxxx    (2.23) 2.5.1 Power Flow solution Consider a typical bus of a power system network as shown in Figure 2.5.transmission lines are represented by their equivalent  model where impedances have been converted to per unit admittances on a common MVA base. Application of KCL to this bus results in niniiiiniii niiniiiiiii VyVyVyVyyyy VVyVVyVVyVyI   ...)...( )(...)()( 2211210 22110 (2.24)
  28. 28. 15 Or    n j jij n j ijii ijVyyVI 00 (2.25) iV 1V 1iy 2V iI 2iy nV iny 0iy The real and reactive power at bus i is * iiii IVjQP  (2.26) Or * i ii i V jQP I   (2.27) Substituting for iI in 2.25 yields      n j n j jijiji i ii VyyV V jQP 0 1 * ij  (2.28) From the above relation, the mathematical formulation of the power flow problem results in a system of algebraic nonlinear equation which must be solved by iterative techniques. Figure 2.5. A typical bus of the power system
  29. 29. 16 2.5.2 Gauss-Seidel Power flow solution In the power flow study, it’s necessary to solve the set of nonlinear equations represented by (2.27) for two unknown variables at each node. In the Gauss-Seidel method (2.28) is solved for iV and the iterative sequence becomes ij y Vy V jQP V ij k jijk i sch i sch i k i        )( )(* )1( (2.29) Where ijy shown in lowercase letters is the actual admittance in per unit. sch iP and sch iQ are the net real and reactive powers expressed in per unit. In wiring the KCL, current entering bus i was assumed positive. Thus, for buses, where real and reactive powers are injected into the bus, such as generator buses, sch iP and sch iQ has positive values. For load buses where real and reactive powers are flowing away from the bus, sch iP and sch iQ have negative values. If (2.27) is solved for iP and iQ we have                   n j k jij n j ij k i k i k i VyyVVP 0 )( 0 )()(*)1( ij  (2.30)                   n j k jij n j ij k i k i k i VyyVVQ 0 )( 0 )()(*)1( ij  (2.30) The power flow equation is usually expressed in terms of the elements of the bus admittance matrix. Since the off-diagonal elements of the bus admittance matrix busY , shown by uppercase letters, are ijij yY  , and the diagonal elements are  ijij yY , (2.30) becomes ij y Vy V jQP V ij k jijk i sch i sch i k i        )( )(* )1( (2.31)
  30. 30. 17                          n j j k jijii k i k i k i VYYVVP 1 1 )()()(*)1( ij  (2.32)                          n j j k jijii k i k i k i VYYVVQ 1 1 )()()(*)1( ij  (2.33) 2.6 NEWTON-RAPHSON METHOD The most widely used method for solving simultaneous nonlinear algebraic equations is the Newton-Raphson method. Newton’s method is a successive approximation procedure based on an initial estimate of the unknown and the use of Taylor’s series expansion. Consider the solution of the one-dimensional equation given by cxf )( (2.34) If )0( x is an initial estimate of the solution, and )0( x is a small deviation from the correct solution, we must have cxxf  )( )0()0( Expanding the left-hand side of the above equation in Taylor’s series about )0( x yields cx dx fd i x dx df xf              ...)( 2 1 ( 2)0( )0( 2 2 )0( )0( )0( Assuming the error )0( x is very small, the higher-order terms can be neglected, with result in )0( )0( )0( x dx df c        Where )( )0()0( xfcc  Adding )0( x to the initial estimate will result in the second approximation
  31. 31. 18 )0( )0( )0()1(         dx df c xx Successive use of this procedure yields the Newton-Raphson algorithm )( )()( kk xfcc  (2.35) )( )( )( k k k dx df c x         (2.36) )()()1( kkk xxx  (3.74) (2.36) can be rearranged as )()()( kkk xjc  (2.37) Where )( )( k k dx df j        The relation in (2.37) demonstrates that the nonlinear equation 0)(  cxf is approximated by the tangent line on the curve at )(k x . Therefore, a linear equation is obtained in terms of the small changes in the variable. The intersection of the tangent line with the x-axis results in )1( k x . 2.6.1 Newton-Raphson Power Flow solution Because of its quadratic convergence, Newton’s method is mathematically superior to the Gauss-Seidel method and is less prone to divergence with ill-conducted problem. For large power systems, the Newton-Raphson method is found to be more efficient and practical. The number of iterations required to obtain a solution is independent of the system size, but more functional evaluations are required at each iteration. Since in the power flow problem and voltage magnitude are specified for the voltage-controlled buses, the power flow equation is formulated in polar form. We can get the equation of the bus admittance matrix as:
  32. 32. 19   n j jiji VYI 1 (2.38) In the above equation, j includes bus i . Expressing this equation in polar form, we have   n j jijjiji VYI 1  (2.39) The complex power at bus i is iiii IVjQP * (2.40) Substituting from (2.37) for iI in (2.38)   n j jijjijiii VYVjQP 1  (2.41) Separating the real and imaginary parts,   n j jiijijjii YVVP 1 )cos(  (2.42)   n j jiijijjii YVVQ 1 )sin(  (2.43) Equation …. and … constitute a set of nonlinear algebraic equations in terms of the independent variables, voltage magnitude in per unit, and phase angle in radians. We have two equation for each voltage-controlled bus, given by …. Expanding … and …. In Taylor’s series about the initial estimate and neglecting all higher order terms results in the following set of linear equations.
  33. 33. 20                         k n k k n k Q Q P P   2 2 =                                                                           )()( 2 )( 2 )( 2 2 )()( 2 )( 2 )( 2 2 )()( 2 )( 2 )( 2 2 )()( 2 )( 2 )( 2 2 k nV nQ k V nQ k nV Q k V Q k n nQ k nQ k n Q k Q k nV nP k V nP k nV P k V P k n nP k nP k n P k P                                           k n k k n k V V   2 2   In the above equation, bus 1 is assumed to be the slack bus. The Jacobian matrix gives the linearized relationship between small changes in voltage angle )(k i and voltage magnitude )(k iV with the small changes in real and reactive power )(k iP and )(k iQ . Elements of the Jacobian matrix are the partial derivatives of (3.80) and (3.81), evaluated at )(k i and )(k iV . In short form, it can be written as                       VJJ JJ Q P  43 21 (2.44) For voltage-controlled buses, the voltage magnitude are known. Therefore, if m buses of the system are voltage-controlled, m equations involving Q and V and the corresponding columns of the Jacobian matrix are eliminated. Accordingly, there are n-1 real power constraints and n-1- m reactive power constraints, and the Jacobian matrix is of order (2n-2-m) x (2n-2-m). 1J is of the order )1()1(  nn , 2J is of the order )1()1( mnn  , 3J is of the order )1()1(  nmn , and 4J is of the order )1()1( mnmn  . The diagonal and the off-diagonal elements of 1J are
  34. 34. 21 )sin( jiij ij ijji i i YVV P       (2.45) )sin( jiijijji i i YVV P      ij  (2.46) The diagonal and the off-diagonal elements of 2J are     ij jiijijjiiiii i i YVYV V P )cos(cos2  (2.47) )cos( jiijijji i i YVV V P     ij  (2.48) The diagonal and the off-diagonal elements of 3J are )cos( jiij ij ijji i i YVV Q       (2.49) )cos( jiijijji i i YVV Q      ij  (2.50) The diagonal and the off-diagonal elements of 2J are     ij jiijijjiiiii i i YVYV V Q )cos(sin2  (2.51) )sin( jiijiji i i YV V Q     ij  (2.52) The terms )(k iP and )(k iQ are the difference between the scheduled and calculated values, known as the power residuals, given by )()( k i sch i k i PPP  (2.53) )()( k i sch i k i QQQ  (2.54)
  35. 35. 22 The new estimates for bus voltages are )()()1( k i k i k i   (2.55) )()()1( k i k i k i VVV  (2.56) The procedure for power flow solution by the Newton-Raphson method is as follows: 1. For load buses, where sch iP and sch iQ are specified, voltage magnitudes and phase angles are set equal to the slack bus values, or 1.0 and 0.0, i.e., 0.1)0( iV and 0.0)0( i . For voltage- regulated buses, where iV and sch iP are specified, phase angles are set equal to the slack bus angle, or 0, i.e., )0( i =0. 2. For load buses, sch iP and sch iQ are calculated from (3.81)) and (3.82) and )(k iP and )(k iQ are calculated from (254) and (2.56) 3. For voltage-controlled buses, )(k iP and, are calculated from (2.54) and (2.56), respectively. 4. The elements of the Jacobian matrix ( 1J , 2J , 3J and 4J ) are calculated from (2.51)- (2.52). 5. The linear simultaneous equation (3.83) is solved directly by optimally ordered triangular factorization and Gaussian elimination. 6. The new voltage magnitudes and phase angles are computed from (2.54) and (2.56) 7. The process is continued until the residuals )(k iP and )(k iQ are less than the specified accuracy, i.e., eP k i  )( eQ k i  )(
  36. 36. 23 2.6.2 Line Flow and Losses After the iterative solution of bus voltages, the next step is the computation of line flows and line losses. Consider the line connecting the two buses i and j in Figure 16. The line current ijI , measured at bus i and defined positive in the direction. ji  is given by iijiijilij VyVVyIII 00 )(  (2.57) Similarly, the line current jiI measured at bus j and defined positive in the direction ij  is given by jiijijilji VyVVyIII 00 )(  (2.58) The complex power ijS from bus i to j and jiS from bus j to i be * ijiij IVS  (2.59) * jiiji IVS  (2.60) The power loss in line ji  is the algebraic sum of the power flows determined from (2.58) and (2.59), i.e., jiijijL SSS  (2.61) Figure 2.6. Transmission line model for calculating line flows 0jy0iy 0jI0iI jV lIiV ijI
  37. 37. 24 2.7 Approximate Methods of Analysis A distribution feeder provides service to unbalanced three-phase, two-phase, and single- phase loads over untransposed three-phase, two-phase, and single-phase line segments. This combination leads to three-phase line currents and line voltages being unbalanced. In order to analyze these conditions as precisely as possible, it will be necessary to model all three phases of the feederaccurately, however, many times only a “ballpark” answer is needed. When this is the case, some approximate methods of modeling and analysis can be employed. It is the purpose of this chapter to develop some of the approximate methods and leave for later chapters the exact models and analysis. All of the approximate methods of modeling and analysis will assume perfectly balanced three- phase systems. It will be assumed that all loads are balanced three-phase, and all line segments will be three-phase and perfectly transposed. With these assumptions, a single line-to-neutral equivalent circuit for the feeder will be used. (Power System Analysis, 1999) 2.7.1 Voltage Drop A line-to-neutral equivalent circuit of a three-phase line segment serving a balanced three- phase load is shown in Figure 2.7. Kirchhoff’s voltage law applied to the circuit of Figure 2.7 gives: ( ). . .s L LV V R jX I V R I jX I      (2.62) The phasor diagram for Equation 2.63 is shown in 2.8. In Figure 2.8 the phasor for the voltage drop through the line resistance (RI) is shown in phase with the current phasor, and the phasor for the voltage drop through the reactance is shown leading the current phasor by 90 degrees. The dashed lines represent the real and imaginary parts of the impedance (ZI) drop. The voltage drop down the line is defined as the difference between the magnitudes of the source and the load voltages. base s LV V V  (2.63)
  38. 38. 25 R jX VL I Vs Load Figure 2.7. Line-to-neutral equivalent I   ZI VL RI jXI Réel(ZI) Im(ZI) Figure 2.8. Phasor diagram The angle between the source voltage and the load voltage (δ) is very small. Because of that, the voltage drop between the source and load voltage is approximately equal to the real part of the impedance drop. ( . )base eV R Z I (2.64)
  39. 39. 26 2.8 INTRODUCTION OF ALGORITHM In many engineering disciplines, a large spectrum of optimization problem has grown in size and complexity. In some instances, the solution to complex multidimensional problems by using classical optimization techniques is sometimes difficult and/or expensive. This realization has led to an increased interest in a special class of searching algorithm, namely, evolutionary algorithms. In general, these are referred to as “stochastic” optimization techniques and their foundations lie in the evolutionary patterns observed in living things. 2.8.1 BACKTRACKING ALGORITHM As an algorithm-design technique, backtracking can be described as an organized exhaustive search which often avoids searching the whole search space. It is a variation of a brute- force generate-and-test approach where the test is incorporated into the generation phase so that only admissible (i.e., satisfying problem constraints) solutions are generated. Backtracking is a general algorithmic technique which must be customized for each individual problem. This search technique is named backtracking because it is akin to the process that a person uses to find his way out through a maze (see Figure 2.9). At a junction where the path forks into several directions, the person may simply follow one of the directions (say the leftmost) and if the current path ends at a dead end, the person would backtrack (i.e., go back by following the tracks made by his footsteps as if he was walking on sand) to the nearest junction and follow the next unexplored direction.
  40. 40. 27 Backtracking is applicable to both types of problems: decision and optimization. A decision problem seeks a solution that satisfies certain constraints. A decision problem normally calls for a Yes/No answer regarding the existence of a solution satisfying the problem’s constraints. On the other hand, an optimization problem seeks a solution that satisfies the problem’s constraints and, at the same time, maximizes (or minimizes) some objective function. The 0/1-knapsack problem, we saw earlier, is an example of an optimization problem, while the subset-sum problem is an example of a decision problem. Backtracking is capable of solving the optimization version of a problem because, as we shall see, it allows for the generation of all possible solutions that satisfy the problem’s constraints. 2.8.2 Depth-First Search Depth-First traversal is a type of backtracking in a graph. If we use an alpha-numeric order for node traversal we can define a unique ordering of the nodes encountered in a connected graph. Figure 2.9. Backtracking enable a person to find his way through a maze
  41. 41. 28 procedure depth_first_tree_search(v:node) u : node; begin for each child u of v loop depth_first_tree_search(u); end loop; end depth_first_tree_search; (Erickson, 2014) 2 11 3 10 12 4 5 6 7 8 9 13 14 1615 17 18 Figure 2.10. Depth tree search
  42. 42. 29 2.9 Backtracking Technique Backtracking is used to solve problems in which a feasible solution is needed rather than an optimal one, such as the solution to a maze or an arrangement of squares in the 15-puzzle. Backtracking problems are typically a sequence of items (or objects) chosen from a set of alternatives that satisfy some criterion. Figure 2.11. Backtracking algorithm technique 2.10 Game Trees The state-space tree showing all legal moves of both players starting from some valid game state is called the game tree. We can define a function that estimates the value of any game state relative to one of the players. For example, a large positive value can mean that this is a good move for Player 1, while a large negative value would represent a good move for Player 2. The computer plays the game by expanding the game tree to some arbitrary depth and then bringing back values to the current game state node.
  43. 43. 30 Figure 2.12. Gram tree problem example (Ericksion, 2014)
  44. 44. 31 3 METHODOLOGY 3.1 DESCRIPTION OF METHODOLOGY The foremost endeavor is to improve the voltage level in power distribution system using Backtracking algorithm and the process of case study of the existing system in Prey Veng province. Therefore, the methodology of this report has been devised with following algorithm.  Identification of the main objective  Data collection from the existing system of the study area  Voltage computation in each feeder of the existing system and compare with the standard values.  Backtracking algorithm are used for optimal AVR placement after observing voltage drop.  Voltage improvement assessment after reinforcement  Conclusion and recommendation 3.2 Line Resistance The resistance of the conductor is very important in transmission efficiency evaluation and economic studies. The dc resistance of a solid round conductor at a specified temperature is given by A l Rdc   (3.1) Where  = conductor resistivity l = conductor length A = conductor cross-sectional area The conductor resistance is affected by three factors: frequency, spiraling, and temperature. When ac flows in a conductor, the current distribution is not uniform over the conductor cross- sectional area and the current density is greatest the surface of the conductor. This causes the ac resistance to be somewhat higher than the dc resistance. This behavior is known as skin effect. At 60Hz, the ac resistance is about 2 percent higher than the dc resistance.
  45. 45. 32 3.3 TEMPERATURE EFFECT Since a stranded conductor is spiraled, each strand is longer than the finished conductor. These results in a slightly higher resistance than the value calculated from 4.1. The conductor resistance increases as temperature increase. This changed can be considered linear over the range of temperature normally encountered and may be calculated from 1 2 12 tT tT RR    (3.2) Where 2R : Conductor resistance in the temperature 2t 1R : Conductor resistance in the temperature 1t T : is a temperature constant that depends on the conductor material For Aluminum 228T . Because of the above effects, the conductor resistance is best determined from manufacturer’s data. Table 3.1. Cable resistivity and temperature coefficient Material Resistivity )(20 mC  Coefficient Temperature Ct 1 Silver 8 1059.1   243.0 Copper 8 1072.1   234.5 Hard Copper 8 1077.1   241.5 Aluminum 8 1083.1   228 Because of the above effects, the conductor resistance is best determined from manufacturers’ data. 3.4 SKIN EFFECT Describes the phenomena of alternating current flowing more densely near the surface of the conductor. The net effect is a reduction in effective area and an increase in the resistance.
  46. 46. 33 ( )ac dcR f x R  (3.3) _ 0.063598 1.6093 dc km x f R    1  (Optimal and Sizing , 2011-2012) Table 3.2. Skin effect table X K X K X K X K 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00000 1.00000 1.00001 1.00004 1.00013 1.00032 1.00067 1.00124 1.00212 1.00340 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.00519 1.00758 1.01071 1.01470 1.01069 1.02582 1.03323 1.04205 1.05240 1.06440 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 1.07816 1.00375 1.11126 1.13069 1.15207 1.17538 1.20056 1.22753 1.25620 1.28644 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 1.31800 1.35102 1.38504 1.41900 1.45570 1.49202 1.52879 1.56587 1.60314 1.64051 (PSS/ADEPT Training Course , 2010) 3.5 Asymmetrical spacing Practical transmission lines cannot maintain symmetrical spacing of conductors because of construction considerations. With asymmetrical spacing, even with balanced currents, the voltage drop due to line inductance will be unbalanced. Consider one meter length of a three-phase line c
  47. 47. 34 with three conductors, each with radius r. The conductors are asymmetrically spaced with distances shown in Figure 4.8. kmmH GMR GMD L L /ln2.0 (3.4) Where 3 132312 DDDGMD  3 SCSBSAL DDDGMR  3.6 STUDY POWER FLOW 3.6.1 Power Flow solution Power flow studies, commonly known as load flow, form an important part of power system analysis. They are necessary for planning, economic scheduling, and control of an existing system as well as planning for its future expansion. The problem consists of determining the magnitudes and phase angle of voltages at each bus and active and reactive power flow in each line. In solving power flow solution problem, the system is assumed to be operating underbalanced conditions and a single-phase model is used. Four qualities are associated with ach Figure 3.1. Three-phase line with asymmetrical spacing b a 13D 23D 12D
  48. 48. 35 bus. There are voltage magnitude V , phase angle , real power P, and reactive power Q. The system bus Consider a typical bus of a power system network as shown in Figure 1.transmission lines are represented by their equivalent  model where impedances have been converted to per unit admittances on a common MVA base. Application of KCL to this bus results in niniiiiniii niiniiiiiii VyVyVyVyyyy VVyVVyVVyVyI   ...)...( )(...)()( 2211210 22110 (3.5) Or    n j jij n j ijii ijVyyVI 00 (3.6) iV 1V 1iy 2V iI 2iy iny nV 0iy The real and reactive power at bus i is * iiii IVjQP  (3.7) Figure 3.2. A typical bus of the power system
  49. 49. 36 Or * i ii i V jQP I   (3.8) Substituting for iI in 6.24 yields      n j n j jijiji i ii VyyV V jQP 0 1 * ij  (3.9) From the above relation, the mathematical formulation of the power flow problem results in a system of algebraic nonlinear equation which must be solved by iterative techniques. (Saadat H. , 1999) 3.7 BACK TRACKING ALGORITHM In this section, the analytical method name back tracking Algorithm is explained to find the optimal number and location of auto-voltage regulators in radial distribution system using Back Tracking algorithm. Let the voltage regulators are initially located at branches 8, 11, 13, and 18 as shown in figure. It is proposed to reduce the number of AVR in a radial distribution system by shifting the AVR to junction of laterals (such as from buses 11 and 13 to bus 10) and observe the voltage profile. If it satisfies the voltage constraint, then this will be taken as optimal location for the single AVR at bus 10 instead of two AVR at buses 11 and 13 (shown in figure 3.3). This procedure is repeated starting from tail end buses to the source bus and find the optimal number and location of AVR.
  50. 50. 37 Figure 3.3. 19 bus RDS before shifting of auto-voltage regulators Figure 3.4. 19 bus RDS after shifting of auto-voltage regulators 6 9 13 1 2 3 4 5 7 8 10 11 12 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
  51. 51. 38 3.8 STEPS FOR OPTIMAL VOLTAGE REGULATOR PLACEMENT IN RDS USING BACK TRACKING ALGORITHM: Step 1: Read line and load data. Step 2: Conduct load flow analysis for the system and compute the voltages at each bus, real and reactive power losses of the system. Step 3: Identify the buses, which have violation of voltage limits. Step 4: Obtain optimal number and location of AVR by using back tracking algorithm. Step 5: Again run the load flows with AVR, then compute voltages at all buses, real and reactive power losses. Step 6: Determine the reduction in power loss and net saving objective function Eqn. Step 7: Print the results.
  52. 52. 39 3.9 Flow chart for optimal auto-voltage regulator placement using back tracking algorithm: Start 1. Using PSS/ADEPT study POWER FLOW 2. Find optimal point for placing AVR in radial power distribution systems END int?ref realV V Optimal po  Figure 3.5. Flow chart of Backtracking algorithm Yes No Read System line and load data, base kV and kVA, iteration count (IC) =1 and tolerance (e) = 0.0001 Perform load flow and calculate voltage at each bus, real and reactive power losses
  53. 53. 40 3.10 BRIEF DESCRIPTION ABOUT SOFTWARE TOOL The software tools; Power System Simulator/Advanced Distribution Engineering Productive Tool (PSS/ADEPT) has been used for this study. This tool is mainly used for; Load Flow, Short circuit analysis, Protection Coordination and Reliability analysis. PSS/ADEPT software has been basically developed for engineers and technical personal for designing/analyzing Electrical Distribution Systems. This software offers a wide spectrum of applications specifically, Load Flow Analysis, Short-Circuit Analysis, Harmonics Studies, Distribution Reliability Studies (DRA), etc. with multi node system. 3.10.1 Calculating Load Flow A load flow solution is a steady-state representation of node voltages, current and power flows. PSS/ADEPT can perform a load flow analysis on your network and display the results on the diagram. (PSS/ADEPT 5.2 Users Manual, June 2005) Figure 3.6. View of analysis option of PSS/Adept
  54. 54. 41 4 CASE STUDY (PREY VENG) 4.1 OVERVIEW Figure 4.1. map of Prey Veng province (La & Serm, 2014) 4.2 PROFILE OF PREY VENG Prey Veng is located in the Southeast of Cambodia. It borders Kampong Cham to the North, Svay Rieng to the East, Vietnam to South and the Mekong River and Kandal to the West. The area of the province is 4883 square kilometers. The topography is of most of the province is lowland paddy fields. Along the western border formed by the Mekong River there are floodplain areas. Its climate is tropical and consists of a rainy season from May to October and a dry season from November to April. Normally, at the beginning of the rainy season, the average temperature
  55. 55. 42 is about 28.36 °C and maximum 23.7 °C to 32.9 °C. The total population of Prey Veng province is 1,162,609 persons with population density of 238 inhabitants per 2 km . (MAFF www.maff.gov.kh) Table 4.1. Socio-economic indicator N0 Particulars Value Year 1 Population 1,162,609 persons 2007 2 Total Area 4,883 2 km 2007 3 Population density (person/ 2 km ) 238 persons/ 2 km 2007 4 GDP per capita $2,200 2011 5 Population age over 18years 2007 6 Temperature 23.70 C-32.90 C (Average: 28.360 C) 2007 7 Rainfall 1,350 mm/year 8 Adults with literacy 467,500 (93.30%) persons (Men: 226,161 (93.74%), Women: 241,339 (92.90%)) 2007 9 Provincial Border East: Svay Rieng Province and Vietnam West: Kandal Province North: Kampong Cham Province South: Vietnam 2007 (Prey Veng Province, 2014) 4.3 POWER LOSSES Losses in distribution system are normally higher than in transmission systems. According to the EDC’s report, power distribution losses in Prey Veng province high due to its transmission line length as shown in table:
  56. 56. 43 Table 4.2. Transmission line and distribution losses report N0 Transmission Loss (%) Distribution Loss (%) Year 1 8.8% 10% 2013 2 8.8% 10% 2014 4.4 RELIABILITY INDICES Prey Veng has started keeping track of reliability Indices and only two indices are being considered presently, i,e; SAIDI, and SAIFI. On the whole, SAIDI, and SAIFI figures of Prey Veng are the summation of the reliability indices of Transmission and Distribution System. For the year 2014, the calculate reliability indices are given Table 4.3. Reliability indices reported in October 2013 Reliability Indices Calculation Value for 2014 Unite SAIFI 14 Interruption/Customer/Year SAIDI 189 Minutes/Customer/Year (Sokun, October 2013) 4.5 EXISTING DISTRIBUTION SYSTEM In the existing system of Prey Veng distribution system, the conductors are constructed with AAC of either 150 mm2 or 70 mm2 . For operational security and safety the 22 kV supply will be solidly earthed at the generator transformers. The protection equipment such as MV ring main unit, MV overhead load break switch, and overhead air break switch are installed for maintenance and equipment outage. A spare circuit breaker is installed for future expansion along with provision for one additional feeder. Moreover, it exists 5 capacitors banks in which it capacities are shown in the table:
  57. 57. 44 Table 4.4. The summary of quantities for Prey Veng Item Unit Quantity Concrete poles 14 m concrete Each 64 12 m concrete Each 192 9 m concrete Each 908 MV switchgear MV Ring Main Unite 630A Each 1 MV overhead load break Switch 630A Each 1 MV Overhead Air break switch 400A Each 1 LV Capacitors 25 kVA Each 1 30 kVA Each 3 45 kVA Each 4 75 kVA Each 2 125 kVA Each 2 Customers C 1 residential Each 2,514 C 2 Commercial Each 9 C 3 Industrial Each 9 C 4 Public Each 52 (Design Report , November 2002)
  58. 58. 45 4.6 LINE PARAMETER COMPUTATION Figure 4.2. Distribution line configuration position 1 and 2 By using the Appendix-B, the cable resistance R at 20 0 C are used to calculate conductor reactance X Ω/km as indicated in table (7) by using equation (4.4). Table 4.5. Line parameter calculation Type Overhead Line AAC Section mm2 70 150 Position 1 GMD mm 1271.984415 Rayon mm 4.720348719 6.909882989 GMR mm 3.676211279 5.381422283 L mH/km 1.169290163 1.093076157 X Ω/km 0.367343339 0.343400003 Position 2 GMD mm 1327.614394 Rayon mm 4.720348719 5.381422283 GMR mm 3.676211279 5.381422283 B A CB A C 0.7m 1.4m 1.8 m Position1 Position 2
  59. 59. 46 L mH/km 1.177851249 1.101637244 X Ω/km 0.370032883 0.346089547 (Phelps Dodode International , 2014) Using equation (4.2) and (4.4) to obtain conductor resistance Rac(70o C) Ω/km. Table 4.6. Line parameter calculation Type Overhead Line (AAC) 70 150 Rdc(20o C) Rac(20o C) Ω/km 0.4172 0.1964 Rac(70o C) Ω/km 0.5011 0.2358 Line impedance Z [Ω/km] including resistance R and reactance X of the power system in Prey Veng province are shown in table 9. Those impedance are calculated due the line configuration and the conductor size. Table 4.7. Line parameter calculation Type Overhead Line AAC Section [mm2 ] 70 150 Z [Ω/km] Possition 1 0.5012+j0.3673 0.2358+j0.3434 Possition 2 0.5012+j0.3700 0.2358+j0.3460 4.7 VOLTAGE PROFILE IN PREY VENG As shown in the table normal operation in the existing system current ( , ,a b cI I I ), voltage , ,ab bc caV V V start to reduce lower than the limitation and power losses in each bus are shown in the table below.
  60. 60. 47 Power Flow Details Current: Amps 6/7/2014 Voltage: kVolts LL 2:20:12PM Power: kWatts, kvars System Base kVA: 100000.00 Table 4.8. Result of power flow before AVR implemented (50% on load) Name 1st Node 2nd Node Phase I(a) |V| Min V Total Branch Power Total Losses Regulation Total Dist a b c ab bc ca P Q P Q Line1 NODE1 NODE2 ABC 106.35 19.77 20 3,615 484 8 11 10.14 1 Line2 NODE3 NODE4 ABC 106.31 19.57 20 3,607 494 48 64 11.05 7 Line3 NODE4 NODE5 ABC 104.97 19.41 19 3,512 574 39 52 11.77 12 Line4 NODE5 NODE9 ABC 103.59 19.13 19 3,426 641 75 101 13.05 22 Tran1 NODE9 NODE10 ABC 93.23 21.28 21 3,351 742 8 56 3.27 22 Line5 NODE10 NODE11 ABC 93.10 21.02 21 3,343 798 73 92 4.45 34 Line6 NODE11 NODE12 ABC 93.08 20.97 21 3,270 889 12 15 4.68 36 Line8 NODE12 NODE14 ABC 81.96 20.95 21 2,783 1,061 9 11 4.77 38 Line9 NODE14 NODE16 ABC 81.39 20.92 21 2,750 1,080 9 11 4.91 40 Line10 NODE16 NODE18 ABC 80.83 20.90 21 2,717 1,099 9 11 5.00 42 Line11 NODE18 NODE20 ABC 75.68 20.88 21 2,470 1,187 8 9 5.09 44
  61. 61. 48 Line12 NODE20 NODE22 ABC 74.07 20.87 21 2,386 1,222 8 9 5.14 46 Line13 NODE22 NODE24 ABC 73.74 20.86 21 2,364 1,235 8 9 5.18 48 Line20 NODE24 NODE26 ABC 73.41 20.85 21 2,342 1,248 8 8 5.23 50 Line19 NODE26 NODE28 ABC 72.89 20.84 21 2,311 1,264 7 8 5.27 52 Line18 NODE28 NODE30 ABC 72.38 20.84 21 2,280 1,280 7 8 5.27 54 Line17 NODE30 NODE32 ABC 71.42 20.83 21 2,225 1,304 7 8 5.32 56 Line16 NODE32 NODE34 ABC 70.92 20.83 21 2,194 1,320 7 8 5.32 58 Line15 NODE34 NODE36 ABC 70.43 20.82 21 2,163 1,335 7 8 5.36 60 Line14 NODE36 NODE38 ABC 69.82 20.82 21 2,126 1,352 7 7 5.36 62 Line21 NODE38 NODE40 ABC 69.34 20.82 21 2,096 1,367 7 7 5.36 64 Line22 NODE40 NODE42 ABC 66.00 20.83 21 1,899 1,437 5 5 5.32 66 Line23 NODE42 NODE44 ABC 65.57 20.83 21 1,871 1,450 5 5 5.32 67 Line24 NODE44 NODE46 ABC 64.77 20.84 21 1,819 1,470 4 4 5.27 69 Line25 NODE46 NODE48 ABC 64.03 20.84 21 1,767 1,490 0 0 5.27 69 Line26 NODE48 NODE49 ABC 61.92 20.86 21 1,767 1,378 16 15 5.18 75 Line28 NODE50 NODE51 ABC 61.92 20.86 21 1,750 1,393 0 0 5.18 75 Line29 NODE51 NODE52 ABC 34.15 20.86 21 855 890 0 0 5.18 75 Line30 NODE53 NODE54 ABC 34.06 20.88 21 855 890 2 1 5.09 78 Line31 NODE54 NODE56 ABC 32.53 20.89 21 776 887 1 1 5.05 80 Line32 NODE56 NODE57 ABC 6.29 20.88 21 219 60 0 3 5.09 82 Line33 NODE57 NODE58 ABC 4.10 20.88 21 143 38 0 3 5.09 84 Line34 NODE58 NODE60 ABC 2.74 20.88 21 95 25 0 3 5.09 86
  62. 62. 49 Line35 NODE60 NODE62 ABC 1.38 20.87 21 48 13 0 3 5.14 88 Line36 NODE65 NODE66 ABC 30.33 20.89 21 556 946 0 0 5.05 80 Line37 NODE66 NODE68 ABC 21.05 20.89 21 480 592 0 1 5.05 80 Line38 NODE68 NODE69 ABC 20.18 20.89 21 480 551 0 1 5.05 81 Line41 NODE69 NODE71 ABC 10.05 20.89 21 361 42 0 1 5.05 82 Line42 NODE71 NODE72 ABC 0.00 20.89 21 0 2 0 2 5.05 83 Line45 NODE74 NODE75 ABC 10.06 20.89 21 361 45 0 0 5.05 82 Line61 NODE75 NODE104 ABC 4.75 20.89 21 171 16 0 0 5.05 82 Line62 NODE104 NODE106 ABC 2.63 20.89 21 95 0 0 2 5.05 83 Line63 NODE106 NODE108 ABC 1.38 20.89 21 48 13 0 2 5.05 85 Line46 NODE75 NODE76 ABC 5.53 20.88 21 190 61 0 1 5.09 83 Line50 NODE51 NODE84 ABC 28.43 20.86 21 896 503 0 0 5.18 75 Line51 NODE85 NODE86 ABC 27.48 20.86 21 848 519 1 1 5.18 77 Line52 NODE86 NODE89 ABC 25.32 20.86 21 728 557 1 2 5.18 79 Line53 NODE89 NODE91 ABC 23.54 20.86 21 609 594 0 0 5.18 79 Line54 NODE91 NODE92 ABC 2.17 20.86 21 76 21 0 3 5.18 81 Line55 NODE92 NODE93 ABC 2.15 20.86 21 76 18 0 3 5.18 83 Line58 NODE91 NODE95 ABC 21.58 20.87 21 533 573 1 2 5.14 81 Line60 NODE95 NODE100 ABC 5.54 20.86 21 190 60 0 3 5.18 83 Line56 NODE95 NODE73 ABC 0.00 20.87 21 0 0 0 0 5.14 81 Line57 NODE95 NODE96 ABC 16.59 20.87 21 152 580 0 0 5.14 81 Total System Losses: 407.48 502.96
  63. 63. 50 4.8 Voltage Profile On 70% Loads for the future extension According to Mr. Touch La, a staff at cooperate planning and project department, he said that he planned to increase load up to 70% for the new MV loads extension. Load flow solution (70%) for 42 bus practical RDS without voltage regulators is performed. Observing the voltage levels, it is found that all bus voltages violate since the voltage profile is lower than ±5 of the voltage limitation. The current ( , ,a b cI I I ), voltage , ,ab bc caV V V , and the reduction voltage in each branch are shown in the table below. Table 4.9. Powers flow Details in Prey Veng province before AVR placement on (70% load) Power Flow Details Current: Amps 6/7/2014 Voltage: kVolts LL 2:20:12PM Power: kWatts, kvars System Base kVA: 100000.00 Name 1st Node 2nd Node Phase I(a) |Va| Min V Total Branch Power Total Losses Regulation (%) Total Dist P Q P Q Line1 NODE1 NODE2 ABC 163.08 19.71 20 5,405 1,435 19 27 10.41 1 Line2 NODE3 NODE4 ABC 163.14 19.18 19 5,387 1,408 112 161 12.82 7 Line3 NODE4 NODE5 ABC 161.08 18.76 19 5,208 1,225 91 131 14.73 12 Line4 NODE5 NODE9 ABC 159.01 17.94 18 5,051 1,072 177 256 18.45 22
  64. 64. 51 Tran1 NODE9 NODE10 ABC 144.55 19.61 20 4,874 816 15 108 10.86 22 Line5 NODE10 NODE11 ABC 144.61 18.79 19 4,859 707 176 250 14.59 34 Line6 NODE11 NODE12 ABC 144.62 18.65 19 4,683 457 29 42 15.23 36 Line8 NODE12 NODE14 ABC 123.61 18.55 19 3,989 197 21 30 15.68 38 Line9 NODE14 NODE16 ABC 122.57 18.44 18 3,934 156 21 29 16.18 40 Line10 NODE16 NODE18 ABC 121.52 18.34 18 3,880 115 21 29 16.64 42 Line11 NODE18 NODE20 ABC 111.02 18.25 18 3,527 23 17 24 17.05 44 Line12 NODE20 NODE22 ABC 107.68 18.17 18 3,403 82 16 22 17.41 46 Line13 NODE22 NODE24 ABC 107.05 18.09 18 3,367 111 16 22 17.77 48 Line20 NODE24 NODE26 ABC 106.42 18.01 18 3,331 139 16 22 18.14 50 Line19 NODE26 NODE28 ABC 105.36 17.93 18 3,282 172 16 21 18.50 52 Line18 NODE28 NODE30 ABC 104.31 17.85 18 3,233 204 15 21 18.86 54 Line17 NODE30 NODE32 ABC 102.21 17.78 18 3,151 247 15 20 19.18 56 Line16 NODE32 NODE34 ABC 101.16 17.71 18 3,103 278 14 20 19.50 58 Line15 NODE34 NODE36 ABC 100.11 17.64 18 3,056 308 14 19 19.82 60 Line14 NODE36 NODE38 ABC 98.79 17.58 18 3,000 341 14 19 20.09 62 Line21 NODE38 NODE40 ABC 97.74 17.51 18 2,953 370 13 18 20.41 64 Line22 NODE40 NODE42 ABC 89.51 17.47 17 2,673 476 8 11 20.59 66 Line23 NODE42 NODE44 ABC 88.48 17.44 17 2,632 498 8 11 20.73 67
  65. 65. 52 Line24 NODE44 NODE46 ABC 86.45 17.40 17 2,557 531 8 10 20.91 69 Line25 NODE46 NODE48 ABC 84.45 17.40 17 2,483 563 0 0 20.91 69 Line26 NODE48 NODE49 ABC 83.88 17.26 17 2,482 485 30 38 21.55 75 Line28 NODE50 NODE51 ABC 83.88 17.26 17 2,453 523 0 0 21.55 75 Line29 NODE51 NODE52 ABC 42.19 17.26 17 1,197 398 0 0 21.55 75 Line30 NODE53 NODE54 ABC 42.16 17.24 17 1,197 398 4 3 21.64 78 Line31 NODE54 NODE56 ABC 38.97 17.23 17 1,087 417 2 1 21.68 80 Line32 NODE56 NODE57 ABC 10.74 17.21 17 306 93 0 2 21.77 82 Line33 NODE57 NODE58 ABC 7.01 17.21 17 200 60 0 2 21.77 84 Line34 NODE58 NODE60 ABC 4.68 17.20 17 133 40 0 2 21.82 86 Line35 NODE60 NODE62 ABC 2.35 17.20 17 67 20 0 2 21.82 88 Line36 NODE65 NODE66 ABC 31.21 17.23 17 779 511 0 0 21.68 80 Line37 NODE66 NODE68 ABC 24.51 17.23 17 672 288 0 0 21.68 80 Line38 NODE68 NODE69 ABC 24.15 17.22 17 672 260 0 0 21.73 81 Line41 NODE69 NODE71 ABC 17.39 17.21 17 506 115 0 1 21.77 82 Line42 NODE71 NODE72 ABC 0.00 17.21 17 0 1 0 1 21.77 83 Line45 NODE74 NODE75 ABC 17.40 17.21 17 506 116 0 0 21.77 82 Line61 NODE75 NODE104 ABC 8.09 17.21 17 239 30 0 0 21.77 82 Line62 NODE104 NODE106 ABC 4.53 17.21 17 133 22 0 2 21.77 83
  66. 66. 53 Line63 NODE106 NODE108 ABC 2.35 17.21 17 67 20 0 2 21.77 85 Line46 NODE75 NODE76 ABC 9.40 17.20 17 266 87 0 1 21.82 83 Line50 NODE51 NODE84 ABC 42.20 17.26 17 1,255 126 0 0 21.55 75 Line51 NODE85 NODE86 ABC 40.06 17.24 17 1,189 148 2 1 21.64 77 Line52 NODE86 NODE89 ABC 34.84 17.22 17 1,020 204 2 1 21.73 79 Line53 NODE89 NODE91 ABC 29.87 17.22 17 852 259 0 0 21.73 79 Line54 NODE91 NODE92 ABC 3.57 17.21 17 106 4 0 2 21.77 81 Line55 NODE92 NODE93 ABC 3.58 17.21 17 106 5 0 2 21.77 83 Line58 NODE91 NODE95 ABC 26.50 17.21 17 746 262 1 1 21.77 81 Line60 NODE95 NODE100 ABC 9.40 17.19 17 266 86 0 2 21.86 83 Line56 NODE95 NODE73 ABC 0.00 17.21 17 0 0 0 0 21.77 81 Line57 NODE95 NODE96 ABC 13.99 17.21 17 213 358 0 0 21.77 81 Total System Losses: 914.56 1,348.29 It is observed that from Table10, without voltage regulators in the system losses are 914.56kW with the reactive power losses 1,348.29kVAr.
  67. 67. 54 Voltage profile in the normal operation is useable because it is stay within the limitation. However, as shown in figure 32 voltage profile is lower than the limitation when the loads are increase up to 70% and recently, the power system confronts with many problem since the increasing an MV loads demand. (EDC’s report on December 2013). Responded to this issue, there many alternative solution are proposed such as distribution generation optimization, creating a sub-transmission 35 kV, implementation AVR into an appropriate location. Among those solution, Implementation AVR is approved to be done in other to maintain voltage profile. Figure 4.3. Graphic of Voltage profile before AVR are implemented
  68. 68. 55 4.9 DETERMINING REQUIRE REGULATOR TYPE AND SIZE The circuit determines the type of voltage regulator required. The circuit voltage and kVA- ratings and the required amount of voltage correction determines the regulator size. 1000 6753 1000 177.22 3 22000 3 three phasekVA kVA Rated load Amps Amps line to linevolts volts           According to the Annex-D the AVR specification, we choose only 150 Amps, Re 150 22 3300gulator inkVA Load amps rangeinkV kVA     (How step-Volatge regulators operate, February 1993)
  69. 69. 56 5 RESULT OFTER AVR IMPLEMENTION By applying the Backtracking algorithm for the 42 bus system, it is found that one voltage regulator at bus 4, between node 11and node 12, is sufficient to maintain the voltage profile at all buses. Table 5.1. Powers flow Details in Prey Veng province after AVR placement Power Flow Details Current: Amps 6/7/2014 Voltage: kVolts LL 2:20:12PM Power: kWatts, kvars System Base kVA: 100000.00 Name 1st Node 2nd Node Phase I(a) |V| Min V Total Branch Power Total Losses Regulation (%) Total Dist a b c ab bc ca P Q P Q Line1 NODE1 NODE2 ABC 153.80 19.73 20 5,249 514 17 24 10.32 1 Line2 NODE3 NODE4 ABC 153.82 19.31 19 5,233 490 99 142 12.23 7 Line3 NODE4 NODE5 ABC 151.80 18.98 19 5,067 326 81 116 13.73 12 Line4 NODE5 NODE9 ABC 149.76 18.36 18 4,920 188 157 226 16.55 22 Tran1 NODE9 NODE10 ABC 134.78 20.34 20 4,763 37 17 116 7.55 22 Line5 NODE10 NODE11 ABC 134.76 19.74 20 4,746 153 153 214 10.27 34
  70. 70. 57 Tran1~ NODE11 NODE12 ABC 121.28 21.91 22 4,593 368 13 94 0.41 34 Line8 NODE12 NODE14 ABC 104.68 21.85 22 3,915 680 15 20 0.68 36 Line9 NODE14 NODE16 ABC 103.85 21.79 22 3,866 711 15 20 0.95 38 Line10 NODE16 NODE18 ABC 103.02 21.74 22 3,818 742 15 19 1.18 40 Line11 NODE18 NODE20 ABC 95.02 21.69 22 3,471 870 13 16 1.41 42 Line12 NODE20 NODE22 ABC 92.50 21.65 22 3,352 921 12 15 1.59 44 Line13 NODE22 NODE24 ABC 92.01 21.61 22 3,320 942 12 15 1.77 46 Line20 NODE24 NODE26 ABC 91.52 21.57 22 3,288 964 12 15 1.95 48 Line19 NODE26 NODE28 ABC 90.73 21.53 22 3,243 989 12 14 2.14 50 Line18 NODE28 NODE30 ABC 89.94 21.49 21 3,198 1,014 11 14 2.32 52 Line17 NODE30 NODE32 ABC 88.40 21.46 21 3,120 1,050 11 13 2.45 54 Line16 NODE32 NODE34 ABC 87.62 21.43 21 3,076 1,074 11 13 2.59 56 Line15 NODE34 NODE36 ABC 86.85 21.40 21 3,032 1,098 11 13 2.73 58 Line14 NODE36 NODE38 ABC 85.89 21.37 21 2,980 1,125 10 12 2.86 60 Line21 NODE38 NODE40 ABC 85.13 21.35 21 2,936 1,148 10 12 2.95 62 Line22 NODE40 NODE42 ABC 79.43 21.34 21 2,660 1,248 7 8 3.00 64 Line23 NODE42 NODE44 ABC 78.72 21.32 21 2,620 1,267 7 7 3.09 65 Line24 NODE44 NODE46 ABC 77.34 21.31 21 2,547 1,296 6 7 3.14 67 Line25 NODE46 NODE48 ABC 76.02 21.31 21 2,474 1,325 0 0 3.14 67 Line26 NODE48 NODE49 ABC 74.46 21.27 21 2,474 1,208 23 26 3.32 73
  71. 71. 58 Line28 NODE50 NODE51 ABC 74.46 21.27 21 2,451 1,234 0 0 3.32 73 Line29 NODE51 NODE52 ABC 39.36 21.27 21 1,196 820 0 0 3.32 73 Line30 NODE53 NODE54 ABC 39.28 21.28 21 1,196 820 3 0 3.27 76 Line31 NODE54 NODE56 ABC 37.00 21.28 21 1,087 827 2 0 3.27 78 Line32 NODE56 NODE57 ABC 8.67 21.27 21 306 88 0 3 3.32 80 Line33 NODE57 NODE58 ABC 5.65 21.26 21 200 56 0 3 3.36 82 Line34 NODE58 NODE60 ABC 3.78 21.26 21 133 37 0 3 3.36 84 Line35 NODE60 NODE62 ABC 1.90 21.26 21 67 19 0 3 3.36 86 Line36 NODE65 NODE66 ABC 32.59 21.28 21 779 915 0 0 3.27 78 Line37 NODE66 NODE68 ABC 23.67 21.28 21 672 557 0 0 3.27 78 Line38 NODE68 NODE69 ABC 22.94 21.28 21 672 514 0 1 3.27 79 Line41 NODE69 NODE71 ABC 13.93 21.27 21 506 87 0 1 3.32 80 Line42 NODE71 NODE72 ABC 0.00 21.27 21 0 2 0 2 3.32 81 Line45 NODE74 NODE75 ABC 13.93 21.27 21 505 90 0 0 3.32 80 Line61 NODE75 NODE104 ABC 6.50 21.27 21 239 4 0 0 3.32 80 Line62 NODE10 4 NODE106 ABC 3.63 21.27 21 133 11 0 2 3.32 81 Line63 NODE10 6 NODE108 ABC 1.90 21.27 21 67 20 0 2 3.32 83 Line46 NODE75 NODE76 ABC 7.60 21.27 21 266 86 0 1 3.32 81
  72. 72. 59 Line50 NODE51 NODE84 ABC 35.85 21.27 21 1,254 414 0 0 3.32 73 Line51 NODE85 NODE86 ABC 34.31 21.26 21 1,188 436 2 1 3.36 75 Line52 NODE86 NODE89 ABC 30.68 21.26 21 1,020 490 1 1 3.36 77 Line53 NODE89 NODE91 ABC 27.45 21.26 21 852 543 0 0 3.36 77 Line54 NODE91 NODE92 ABC 2.90 21.25 21 106 13 0 3 3.41 79 Line55 NODE92 NODE93 ABC 2.90 21.25 21 106 10 0 3 3.41 81 Line58 NODE91 NODE95 ABC 24.81 21.26 21 746 530 1 2 3.36 79 Line60 NODE95 NODE100 ABC 7.61 21.24 21 266 85 0 3 3.45 81 Line56 NODE95 NODE73 ABC 0.00 21.26 21 0 0 0 0 3.36 79 Line57 NODE95 NODE96 ABC 16.88 21.26 21 213 584 0 0 3.36 79 Total System Losses: 758.57 1,156.17
  73. 73. 60 Figure 5.1. Voltage profile after AVR is implemented As shown in figure 32, after AVR are implemented in a radial distribution system voltage profile in the limitation under ±5%. However, it is not the desirable result in which the voltage is equal to 22 kV.
  74. 74. 61 6 Conclusion and Recommendation 6.1 Conclusion In radial distribution systems it is necessary to maintain voltage levels at various buses by placing AVR at suitable locations. In this project, Optimal AVR placement is discussed to maintain the voltage profile. The proposed Back tracking algorithm determines the optimal number, location of voltage regulators to maintain voltage profile within the desired limits and reduces the losses in the system. Voltage profile before AVR is implemented started to decrease lower than the limitation (±5%) when the load increase up to 50%. In addition, EDC want to increase MV loads up to 70% to respond the increasing electricity consumption. However, the voltage profile (Simulation result) plummeted to 18.77 kV at the end of the distribution line. After AVR is implemented, Voltage profile stay within the limitation even the power consumption shoot up to 70%. According to the simulation result, Voltage profile at the end of the distribution line is 22.17 kV. 6.2 Recommendations For further research, the decision makers may consider on:  Using Genetic Algorithm or Fuzzy Set to make the research study more accurate and precise.  Propose another alternative solution such as sub-transmission line, Optimal CAPO, or creating a new power Distribution Line.
  75. 75. 62 7 References (1999). In S. Hadi, Power System Analysis (pp. 113-121). Milwaukee, Wisconsin: International Editions. (1999). In H. Saadat, Power System Analysis (pp. 189-222). Milwaukee, Wisconsin: Internation Editions. (2014, June 16). Retrieved from PHELPS DODGE INTERNATIONAL: http://pdic.co.th/Home/Customer-Services/Brochures.aspx (2014, June 16). Retrieved from Phelps Dodode International : http://pdic.co.th/Home/Customer- Services/Brochures.aspx Design Report . (November 2002). Phnom Penh: Electricity of Cambodia. Électricité Du Cambodge. (2014, June 12). Retrieved from Électricité Du Cambodge: http://www.edc.com.kh/aboutus.php Electricity of Cambodia. (2014, June 12). Retrieved from About EDC: http://www.edc.com.kh/aboutus.php Ericksion, J. (2014, June 16). Algorithms. Retrieved from Algorithms: http://www.cs.uiuc.edu/~jeffe/teaching/algorithms/ Erickson, J. (2014, June 15). Algorithms. Retrieved from Algorithms: http://www.cs.uiuc.edu/~jeffe/teaching/algorithms/ (February 1993). In McGraw-Edison, How step-Volatge regulators operate. Bulletin: Cooper Power Systems. J.Vitor. (2014). Power development strategy in Cambodia. Ministry of Mine and Energy . La, E., & Serm, H. (2014, June 15). Retrieved from Archive for the ‘ Visit Cambodia ’ Category: http://sngsokann.wordpress.com/category/visit-cambodia/ (October 2007). In Voltage Regulators (pp. 45-46). Pewaukee: Printed in USA. (2011-2012). Optimal and Sizing . Phnom Penh: Ang Solyvann.
  76. 76. 63 Prey Veng Province. (2014, March 26). Retrieved from Cambodian Ministry of Agriculture, Forestry and Fisheries: http://en.wikipedia.org/w/index.php?title=Prey_Veng_Province&oldid=598055053 PSS/ADEPT 5.2 Users Manual. (June 2005). Schenectady: Siemens Power Transmission & Distribution, Inc. (2010). PSS/ADEPT Training Course . Phnom Penh: System Analysis & GIS office. Saadat, H. (1999). Power System Analysis. Milwaukee, Wisconsin: International Edition. Sokun, S. (October 2013). Report of Power Losses . Prey Veng : Electricity of Prey Veng .
  77. 77. 64 Appendix-A Single Line Diagram Before and After AVR is implemented
  78. 78. 65 Appendix-B Cable Specifications
  79. 79. 66
  80. 80. 67
  81. 81. 68
  82. 82. 69 Appendix-C Crosse-Arm 22 kV
  83. 83. 70
  84. 84. 71
  85. 85. 72
  86. 86. 73 Appendix-D AVR specifications (Cooper Power Systems) (Voltage Regulators, October 2007)
  87. 87. 74 ADD-AMP Capacity of 50 Hz rating Rated Volts Rated kVA Load Current Ratings (A) Regulation Range (Wye and Open Delta) ±10% ±8.75% ±7.5% ±6.25% ±5% Regulation Range (Closed Delta) ±15% ±13.1% ±11.3% ±9.4% ±7.5% 6600 11000 15000 16000 22000 35000 33 66 99 132 198 264 330 396 55 110 165 220 330 440 550 660 75 150 225 300 450 600 750 160 320 110 220 330 440 660 880 175 350 525 700 50 100 150 200 300 400 500 600 50 100 150 200 300 400 500 600 50 100 150 200 300 400 500 100 200 50 100 150 200 300 400 50 100 150 200 55 110 165 220 330 440 550 660 55 110 165 220 330 440 550 660 55 110 165 220 330 440 550 110 220 55 110 165 220 330 440 55 110 165 220 60 120 180 240 360 480 600 668 60 120 180 240 360 480 600 668 60 120 180 240 360 480 600 120 240 60 120 180 240 360 480 60 120 180 240 68 135 203 270 405 540 668 668 68 135 203 270 405 540 668 668 68 135 203 270 405 540 668 135 270 68 135 203 270 405 540 68 135 203 270 80 160 240 320 480 640 668 668 80 160 240 320 480 640 668 668 80 160 240 320 480 640 668 160 320 80 160 240 320 480 640 80 160 240 320
  88. 88. 75 Appendix-E The report of Interruption
  89. 89. 76
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  91. 91. 78

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