Optimal AVR placement in Radial distribution system using Backtracking Technic
-
Upload
nhet-ra -
Category
Engineering
-
view
334 -
download
2
description
Transcript of Optimal AVR placement in Radial distribution system using Backtracking Technic
រកសងអបរ យវជន នងក
វទយ ថ នបេចចកវទយកមពជ
េដបតមងេទពយេកសលយ អគគសន នងថមពល
គេ ងសញញ បរតវសវករ របធនបទ : ករគណន នងេរជើសេរ ើសទ ងស ប ក AVR
េនេលើប ត ញែចកចយតងសយងមធយម ២២ គឡវល
នស ត : ែញត
ឯកេទស : អគគសន នងថមពល
រគទទលបនទក : េ ក ឃន ចនធ
ឆន សក : 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
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
រកសងអបរ យវជន នងក
វទយ ថ នបេចចកវទយកមពជ
េដបតមង េទពេកសលយអគគសន នងថមពល
គេ ងសញញ បរតវសវករ របសនស ត: ែញត
កលបរេចឆទករពរនេកខបបទ: ៣០ មថន ២០១៤
អនញញ តឲយករពរគេរមង
នយកវទយ ថ ន _________________ ៃថងទ ែខ ឆន ២០១៤
របធនបទ: ករគណន នងេរជើសេរ ើសទ ងស ប ក AVR េនេលើប ត ញែចកចយតងសយង មធយម ២២គឡវល
សហរគស : អគគសនកមពជ
របធនេដបតមង : េ ក ជ ជបក
រ ត ចរយដកនគេ ង : េ ក ឃន ចនធ
អនកទទលខសរតវកនងសហរគស : េ ក ន សហៈគរ
ជធនភនេពញ ឆន ២០១៤
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.
ii
សេចកតេសខ េប
កនខនសកេបបទសនេះបងហា ញអពកមមេកាដែលខបានសវើសៅអគគេនកមពជា អេរយេះសពលបដខ គចាបពថង ៃទ
១៧ ដខកមភេះរហតែលថង ៃ ១៥ ដខ ឧេភា ឆន ២០១៤។ សោលគនតថនការសវើនសកេបបបទសនេះស ើខគសែើមបសវើ
ការដកលអរ តខេយខមយមសោយសបើបាេ Automatic Voltage Regulator សោយសារដតមានការធលា កតខ
េយខជាសរឿយៗ សៅសលើបណតត ញតខេយខមយម។ ជាកដេតខ បណតត ញដចកចាយតខេយខកនខសខតត ថពដែខ មាន
ការធលា កតខេយខហេពេតខោររបេ អគគេនកមពជា សោយសារដតកស ើនថនអនកសបើបាេ។ សៅកនខ
នសកេបបទសនេះតែបានដបខដចកជា ៦ ជពកេខានៗ។ ជពកទ ១ គសតត តសៅសលើ បទបងហា ញទសៅ នខ កម
ហ ន (អគគេនកមពជា)។ ជពកទ ២ គបងហា ញអព។ ជពកទ ៣ បកសាយអពែសាសរេតដែលយកមកសបើបាេ
េរាបការសវើនសកេបបទសនេះ។ ជពកទ ៤ គសរៀបរាបលអតអព បណតត ញ ២២ kV សៅសលើបពន ធដែលមានសាប
រមបញជលខ Software ដែលយកមកសបើបាេ។ ជពកទ ៥ គ បងហា ញអពការេននោា នរម នខ ជពកទ ៦ ផ ត
លជា អនសាសរេតេរាបអនកដែលចខសវើការសាែជាែបនតរ។
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.
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.
v
Table of Contents
ACKNOWLEDGEMENT ............................................................................................................... i
សេចកតេសខ េប ..................................................................................................................................... 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
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
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
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
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
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
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.
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.
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.
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:
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)
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 EDC PEC IPP
7
1.2.4 ENERGY POLICY
(J.Vitor, 2014)
To provide an adequate supply for energy throughoutCambodia at reasonable and affordable price
To ensure a reliable and secure electricty supply atreasonalbe price, which facilitates investment inCambodia and development of national economy
To encourage exploration and environmentally and sociallyacceptable develpment of energy resources needed for supplyto all sectors of Cambodia economy
To encourage the efficient use of energy and to minimizedetrimental environmental effects resulted from energy supplyand consumption
Figure 1.3. Energy policy of EDC
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
DI
DI
rI cbaa
1ln
1ln
'
1ln102 7 (2.2)
Substituting for acb III I
DI
rI aaa
1ln
'
1ln102 7
'
ln102 7
r
DIa
(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
CIbI
aI
DD
D
9
kmmHD
DL
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 radius r . 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 1ln
1ln
'
1ln102
DI
DI
rI cbaa
Figure 2.2. Three-phase line with asymmetrical spacing
c
b
a
13D
23D
12D
10
2312
7 1ln
1ln
'
1ln102
DI
DI
rI cabb
2313
7 1ln
1ln
'
1ln102
DI
DI
rI bacc (2.5)
Or in matrix form
LI (2.6)
Where the symmetrical inductance matrix L is given by
'
1ln
1ln
1ln
1ln
'
1ln
1ln
1ln
1ln
'
1ln
102
2313
2312
1312
7
rDD
DrD
DDr
L (2.7)
For balanced three-phase currents with aI as reference, we have
aab IaII 2240
aac aIII 120 (2.8)
Where the operator 1201a and 12012 a . Substituting in (2.4) result in
1312
27 1ln
1ln
'
1ln102
Da
Da
rIL
a
aa
2312
27 1ln
1ln
'
1ln102
Da
Da
rIL
b
bb
2313
27 1ln
1ln
'
1ln102
Da
Da
rIL
c
cc
(2.9)
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
dd d
d
d d
d
d
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 position222111 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
422122111 babababaAB DDDDD
422122111 cbcbcbcbBC DDDDD
422122111 cacacacaAC DDDDD (2.13)
The equivalent GMD per phase is then
3ACBCAB 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
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
3SCSBSAL DDDGMR (2.16)
The inductance per phase in millihenries per kilometer is
kmmHGMR
GMDL
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 )(kx 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 n variables
1211 ),...,,( cxxxf n
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)
15
Or
n
j
jij
n
j
ijii ijVyyVI00
(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
iii
V
jQPI
(2.27)
Substituting for iI in 2.25 yields
n
j
n
j
jijiji
i
ii VyyVV
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
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
ijy
VyV
jQP
Vij
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 andsch
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 andsch
iQ has positive values. For load buses where real and reactive powers
are flowing away from the bus, sch
iP andsch
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 VyyVVP0
)(
0
)()(*)1( ij (2.30)
n
j
k
jij
n
j
ij
k
i
k
i
k
i VyyVVQ0
)(
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
ijy
VyV
jQP
Vij
k
jijk
i
sch
i
sch
i
k
i
)(
)(*)1(
(2.31)
17
n
jj
k
jijii
k
i
k
i
k
i VYYVVP
11
)()()(*)1( ij (2.32)
n
jj
k
jijii
k
i
k
i
k
i VYYVVQ
11
)()()(*)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
cxdx
fd
ix
dx
dfxf
...)(
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( xdx
dfc
Where
)( )0()0( xfcc
Adding )0(x to the initial estimate will result in the second approximation
18
)0(
)0()0()1(
dx
df
cxx
Successive use of this procedure yields the Newton-Raphson algorithm
)( )()( kk xfcc (2.35)
)(
)()(
k
kk
dx
df
cx
(2.36)
)()()1( kkk xxx (3.74)
(2.36) can be rearranged as
)()()( kkk xjc (2.37)
Where
)(
)(
k
k
dx
dfj
The relation in (2.37) demonstrates that the nonlinear equation 0)( cxf is approximated by the
tangent line on the curve at )(kx . 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( kx .
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:
19
n
j
jiji VYI1
(2.38)
In the above equation, j includes bus i . Expressing this equation in polar form, we have
n
j
jijjiji VYI1
(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 VYVjQP1
(2.41)
Separating the real and imaginary parts,
n
j
jiijijjii YVVP1
)cos( (2.42)
n
j
jiijijjii YVVQ1
)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.
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
nQk
V
nQ
k
nV
Qk
V
Q
k
n
nQk
nQ
k
n
Qk
Q
k
nV
nPk
V
nP
k
nV
Pk
V
P
k
n
nPk
nP
k
n
Pk
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
21
)sin( jiij
ij
ijji
i
i YVVP
(2.45)
)sin( jiijijji
i
i YVVP
ij (2.46)
The diagonal and the off-diagonal elements of 2J are
ij
jiijijjiiiii
i
i YVYVV
P)cos(cos2 (2.47)
)cos( jiijijji
i
i YVVV
P
ij (2.48)
The diagonal and the off-diagonal elements of 3J are
)cos( jiij
ij
ijji
i
i YVVQ
(2.49)
)cos( jiijijji
i
i YVVQ
ij (2.50)
The diagonal and the off-diagonal elements of 2J are
ij
jiijijjiiiii
i
i YVYVV
Q)cos(sin2 (2.51)
)sin( jiijiji
i
i YVV
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)
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 and4J ) 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 )(
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
jVlIiV
ijI
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)
25
R jX
VL
I
Vs Load
Figure 2.7. Line-to-neutral equivalent
I
ZI
VL
RI
jXIRéel(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)
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.
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
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 16 15
17 18
Figure 2.10. Depth tree search
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.
30
Figure 2.12. Gram tree problem example
(Ericksion, 2014)
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
lRdc
(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.
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
212
tT
tTRR
(3.2)
Where
2R : Conductor resistance in the temperature2t
1R : Conductor resistance in the temperature1t
T : is a temperature constant that depends on the conductor material
For Aluminum 228T . 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 81059.1 243.0
Copper 81072.1 234.5
Hard Copper 81077.1 241.5
Aluminum 81083.1 228
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.
33
( )ac dcR f x R (3.3)
_
0.063598
1.6093 dc km
xf
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
34
with three conductors, each with radius r . The conductors are asymmetrically spaced with
distances shown in Figure 4.8.
kmmHGMR
GMDL
L
/ln2.0
(3.4)
Where 3132312 DDDGMD
3SCSBSAL 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
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 ijVyyVI00
(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
36
Or *
i
iii
V
jQPI
(3.8)
Substituting for iI in 6.24 yields
n
j
n
j
jijiji
i
ii VyyVV
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.
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
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.
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
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
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
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 2km . (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 2km 2007
3 Population density (person/ 2km ) 238 persons/ 2km 2007
4 GDP per capita $2,200 2011
5 Population age over 18years 2007
6 Temperature 23.70C-32.90C (Average: 28.360C) 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:
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:
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)
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 0C 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 C B
A
C
0.7m 1.4m
1.8 m
Position1
Position 2
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(70oC) Ω/km.
Table 4.6. Line parameter calculation
Type Overhead Line (AAC)
70 150
Rdc(20oC)
Rac(20oC) Ω/km 0.4172 0.1964
Rac(70oC) 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.
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
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
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
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
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
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
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.
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
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 1000177.22
3 22000 3
three phasekVA kVARated 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)
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
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
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
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
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.
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.
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.
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 .
64
Appendix-A Single Line Diagram Before and
After AVR is implemented
65
Appendix-B Cable Specifications
66
67
68
69
Appendix-C Crosse-Arm 22 kV
70
71
72
73
Appendix-D AVR specifications (Cooper
Power Systems) (Voltage Regulators, October 2007)
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
75
Appendix-E The report of Interruption
76
77
78