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 4.8. 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)


ij

jiijijjiiiii

i

i YVYVV

P)cos(cos2 (2.47)

)cos( jiijijji

i

i YVVV

P

ij (2.48)


)cos( jiij

ij

ijji

i

i YVVQ

(2.49)

)cos( jiijijji

i

i YVVQ

ij (2.50)


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



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.


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.


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




Tran1 NODE9 NODE10 ABC 93.23 21.28 21 3,351 742 8 56 3.27 22



Line8 NODE12 NODE14 ABC 81.96 20.95 21 2,783 1,061 9 11 4.77 38




48

















Line29 NODE51 NODE52 ABC 34.15 20.86 21 855 890 0 0 5.18 75






49






















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




Name 1st Node 2nd Node Phase I(a) |Va| Min

V

Total

Branch

Power

Total

Losses Regulation

(%)

Total

Dist

P Q P Q





51




















52




















53













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




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







57

Tran1~ NODE11 NODE12 ABC 121.28 21.91 22 4,593 368 13 94 0.41 34




















58
















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


59











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

69

Appendix-C Crosse-Arm 22 kV

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

optimal avr placement in radial distribution system using backtracking technic

Engineering

tension sur

tension avr sur

ltude et

moyenne tension

distribution systme

tension dans

taille et optimum

tension moins