EE 2303 TRANSMISSION AND

DISTRIBUTION

OBJECTIVE

• To become familiar with the function of different

components used in Transmission and

Distribution levels of power systems and

modeling of these components.

OBJECTIVES

• To develop expression for computation of fundamental parameters of lines.

• To categorize the lines into different

classes and develop equivalent circuits for these classes.

• To analyse the voltage distribution in

insulator strings and cables and methods to improve the same.

INTRODUCTION

INTRODUCTION

INTRODUCTION

• Various levels such as generation, transmission and distribution.

INTRODUCTION

• HVDC

High voltage direct current (HVDC) is used to transmit

large amounts of power over long distances or for

interconnections between asynchronous grids. When

electrical energy is required to be transmitted over very

long distances, it is more economical to transmit using

direct current instead of alternating current.

INTRODUCTION • EHV AC transmission

Hydro-electric and coal or oil-fired stations are located very far from

load centres for various

reasons which requires the transmission of the generated electric

power over very long distances.

This requires very high voltages for transmission. The very rapid

strides taken by development

of dc transmission since 1950 is playing a major role in extra-long-

distance transmission,

complementing or supplementing EHV AC transmission.

INTRODUCTION

Technical performance and reliability

Considerations in the design of a power line:

• • The amount of active power it has to transmit • • The distance over which the power must be

carried

• • The cost of the power line

• • Aesthetic considerations, urban congestion, ease of installation, expected load growth

INTRODUCTION

• Application of HVDC transmission system

• HVDC Light, is utilising state of the art semiconductors,

control and cable insulation and can offer many new transmission opportunities as has been demonstrated by actual projects above. It offers a lot of possibilities to enhance the power systems.

• Wind power, even big parks, can easily be connected to the grid. In many cases HVDC Light can give new opportunities to trade electric energy in the new deregulated markets.

• As HVDC Light has been developed to minimise environmental impact and impact on the connecting grids, the licence procedure is generally more favourable than more traditional solutions.

INTRODUCTION

• FACTS

INTRODUCTION

• TCSC

The Thyristor Controlled Series Capacitor (TCSC) seems to be one

of the members within the FACTS family, beside the SVC that was established long ago, which has attracted the most interest so far. One reason may be that a distinctive quality of the TCSC concept is

that it uses an extremely simple main circuit topology. The capacitor is inserted directly in series with the transmission line

and the thyristor controlled inductor is mounted directly in parallel with the capacitor.

Thus no interfacing equipment like e.g. high voltage transformers is

required. This makes TCSC much more economical than some other competing FACTS technologies.

INTRODUCTION

• SVC

• Static variable capacitor

Parallel-connected static var generator or absorber

Output is adjusted to exchange capacitive or

inductive current.

Maintain or control specific parameters of the electrical power system (typically bus voltage).

Thyristor-based Controllers

Lower cost alternative to STATCOM

INTRODUCTION

• STATCOM

Static Synchronous Compensator (STATCOM)

• Parallel-connected static var compensator

• Capacitive or inductive output current

controlled independently of the ac system voltage

INTRODUCTION

• UPFC

Unified power flow controller (UPFC) is one of the FACTS devices, which can

control power system parameters such as terminal voltage, line impedance and phase angle. Therefore, it can be used not

only for power flow control, but also for power system stabilizing control.

1

UNIT 3

MODELLING AND PERFORMANCE OF

TRANSMISSION LINES

2

Introduction

Analyze the performance of single phase and balanced three-phase transmission lines under normal steady-state operating conditions.

Expression of voltage and current at any point along the line are developed, where the nature of the series impedance and shunt admittance is taken into account.

The performance of transmission line is measured based on the voltage regulation and line loadability.

3

Transmission Line Representation

ABCD

+

VR

-

+

Vs

-

Is IR

A line is treated as two-port network for which the ABCD parameters and an equivalent π circuit are derived.

4

Transmission Line Representation

To facilitate the performance calculations relating to a transmission line, the line is approximated as a series–parallel interconnection of the relevant parameters.

Consider a transmission line to have:

A sending end and a receiving end;

A series resistance and inductance; and

A shunt capacitance and conductance

5

Transmission Line Representation

The relation between sending–end and receiving–end quantities of the two–port network can be written as:

R

R

S

S

RRS

RRS

I

V

DC

BA

I

V

DICVI

BIAVV

6

Transmission Line Representation

Short Line Model < 80 km in length

Shunt effects are neglected.

Medium Line Model Range from 80–240 km in length

Shunt capacitances are lumped at a few predetermined points along the line.

Long Line Model >240 km in length.

Uniformly distributed parameters.

Shunt branch consists of both capacitance and conductance.

7

Short Line Model

l

VRVS

IRISR XL

Z

8

Short Line Model

length line

inductance phase-per

resistance phase-per

:where

L

r

jXR

LjrzZ

L

9

Short Line Model

Thus, the ABCD parameters are easily obtained from KVL and KCL equations as below:

SCZBpuDA

I

VZ

I

V

II

ZIVV

R

R

S

S

RS

RRS

0;;1

10

1

10

Medium Line Model – Nominal π Circuit

l

VR

IRISR XL

Z

VS Y/2 Y/2

11

Medium Line Model

Shunt capacitor is considered.

½ of shunt capacitor considered to be lumped at each end of the line – π circuit

Total shunt admittance, Y

length line

kmper econductanc line

kmper ecapacitanc neutral toline

:where

g

C

CjgY

12

Medium Line Model

Under normal condition,

shunt conductance per unit length (the leakage current) over the insulators and due to corona is negligible

Thus, g = 0

13

Medium Line Model

To obtain ABCD parameters, the current in the series branch is denoted as IL.

Using KCL and KVL, the sending–end voltage is:

3..2

1

2

2 and 1 From

2..2

1..

RR

RRRS

RRL

LRS

ZIVZY

VY

IZVV

VY

II

ZIVV

14

Medium Line Model

15

Medium Line Model

16

Medium Line Model

Using KCL to obtain equation for sending–end current:

5..2

14

1

221

2

4 into 3 and 2 Substitute

4..2

RR

RRR

RS

SLS

IYZ

VYZ

Y

YZIV

YZYVII

VY

II

17

Medium Line Model

Thus, the ABCD parameters can be obtained from equation [3] and [5];

SZY

YCZBpuZY

DA

I

V

ZYZYY

ZZY

I

V

R

R

S

S

41;;

21

21

41

21

18

Medium Line Model

ABCD constant are complex since π model

is a symmetrical two-port network

A = D

The determinant of the transmission matrix is unity(1)

AD – BC = 1 (Prove this!)

19

Medium Line Model

The receiving and quantities can be expressed in terms of the sending end quantities

If, ignore the shunt capacitance of the TL, the shunt admittance, Y=0, it become the short transmission line constant.

S

S

R

R

I

V

AC

BD

I

V

20

Medium Line Model – Nominal T Circuit

l

VR

IRIS

VS Y

Z/2 Z/2

Find the ABCD Parameters for this circuit using KVL and KCL

21

Long Line Model

l

VR

IRISZ’

VS Y’/2 Y’/2

22

Long Line Model

The shunt capacitance and series impedance must be treated as distributed quantities

The ‘V’ and ‘I’ on the line must be found by solving the differential equation of the transmission line.

23

Long Line Model

2tanh

1

2

2tanh

22

'

sinhsinh

'

c

c

c

Z

YY

ZZZ

y

zZzy

CjgyLjRz

24

Long Line Model

If γl <<0 sinh (γl )/( γl ) & tanh (γl /2)/ (γl /2) ≈ 1.0

The ABCD parameters:

12

'' D 1

4

'''

' 12

''

YZYZYC

ZBYZ

A

I

V

DC

BA

I

V

R

R

S

S

25

ABCD Parameters

ABCD Parameters

A B

C D

Short

Line

1 Z

0 1

Medium

π

Medium

T

Long

Line

26

Complex Power

Sending end power

Receiving end power

lineRlineRR

phaseRphaseRR

IVS

or

IVS

*

3

*

3

3

3

lineSlineSS

phaseSphaseSS

IVS

or

IVS

*

3

*

3

3

3

phaseline VV 3

Remember!

27

Transmission Line Efficiency

Total Full–Load Line Losses

Transmission Line Efficiency

Note that only Real Power are taken into account!

333 RSL SSS

100%

3

3

3

3

S

R

S

R

P

P

P

P

28

Voltage Regulation

ABCD parameters can be used to describe the variation of line voltage with line loading.

Voltage regulation is the change in voltage at the receiving end of the line when the load varies from no–load to a specified full–load at a specified power factor, while the sending end is held constant.

29

Voltage Regulation

RRFL

S

RNL VVA

VV

100%

RFL

RFLRNL

V

VVVR

No–load receiving–end voltage

Full–load receiving–end voltage

30

??

21

VV

VV

V

;

0:

AVV

SRNL

SRNL

RNL

RNLS

LineLong

ZYLineMedium

LineShort

A

V

Thus

IConditionLoadNo

BI

s

R

R

31

Voltage Regulation

The effect of load power factor on voltage regulation is illustrated in phasor diagram.

The phasor diagrams are graphical representation of lagging, unity and leading power factor.

32

Voltage Regulation

The higher (worse) voltage regulation occurs for the lagging pf load where VRNL exceeds VRFL by the larger amount.

A smaller or even negative voltage regulation occurs in leading pf load.

33

Voltage Regulation

In practice, transmission line voltages decrease when heavily loaded and increase when lightly loaded.

EHV lines are maintained within ±5% of rated voltage, corresponding to about 10% voltage regulation.

10% voltage regulation for lower voltage lines also considered good operating practice.

34

Line Loadability

Another important issue that affect transmission line performance.

3 major line loading limits are:

Thermal limit

Short transmission lines [<80 km length]

Voltage drop limit

Longer line length [ 80–300 km length]

Steady-state stability limit

Line length over 300 km

35

Example

A 220-kV, three-phase transmission line is 40 km long. The resistance per phase is 0.15 Ω/km and the inductance per phase is 1.5915 mH/km. The shunt capacitance is negligible. Use the line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three-phase load of

a) 381 MVA at 0.8 pf lagging at 220 kV

b) 381 MVA at 0.8 pf leading at 220 kV

36

Solution (a)

Given

R = 0.15 Ω/km , L = 1.5915 mH/km

S =381 MVA with pf 0.8 lag

VR(line)=220 kV

+

Vs

_

+

VR

_

Is IR

R jXL

Z=R+jωL Ω

37

206

405915.150215.0

Z

phase;per impedance series The

40km

j

mj

lLjr

kV

kV

VV

o

o

LineR

phaseR

0127

3

0220

3

RR

RRS

I and Z,,V find Therefore,

ZIVV voltage,end sending Find

38

A

kV

MVA

MjMWMVAS

Thus

o

o

o

o

R

o

87.361000

01273

87.36381

3V

S I

3V

S I

I3VS

var6.2288.30487.36381

,

87.368.0cos MVA, 381S

*

R(Phase)

*

RR

R(Phase)

R*

R

*

RR(Phase)R

-1

39

250V

144.33

3

93.4144.3

87.3610002060127

VV

Therefore,

PhaseRS(Phase)

PhaseSLineS

o

oo

R

VV

kV

AjkV

ZI

40

SILineSS 3V S Power, end-Sending Find

MVA

MjMW

AV

AII

o

o

o

RS

8.41433

var6.2888.322

87.3610004.93144.33 3

I3VS

87.361000

o

*

RR(Phase)S

41

%6.13

100220

220250

100 %VR

RFL

RFLRNL

V

VV

Voltage Regulation,

%4.94

1008.322

8.304

100 %

S

R

P

P

Effiency,η

INSULATORS AND CABLES

Insulators:

• An insulator, also called a dielectric, is a material that resists the flow of electric current. An insulating material has atoms with tightly bonded valence electrons. These materials are used in parts of electrical equipment, also called insulators or insulation, intended to support or separate electrical conductors without passing current through themselves. The term is often used more specifically to refer to insulating supports that attach electric power transmission wires to utility poles or pylons.

• Some materials such as glass or Teflon are very good electrical insulators. A much larger class of materials, for example rubber-like polymers and most plastics are still "good enough" to insulate electrical wiring and cables even though they may have lower bulk resistivity. These materials can serve as practical and safe insulators for low to moderate voltages (hundreds, or even thousands, of volts).

http://en.wikipedia.org/wiki/Image:Ceramic_electric_insulator.jpg

Insulators:

• Insulators are used for high-voltage power transmission are made from glass, porcelain, or composite polymer materials. Porcelain insulators are made from clay, quartz or alumina and feldspar, and are covered with a smooth glaze to shed dirt. Insulators made from porcelain rich in alumina are used where high mechanical strength is a criterion.

• Porcelain has a dielectric strength of about 4-10 kV/mm. Glass has a higher dielectric strength, but it attracts condensation and the thick irregular shapes needed for insulators are difficult to cast without internal strains. Some insulator manufacturers stopped making glass insulators in the late 1960s, switching to ceramic materials.

Insulators:

• Recently, some electric utilities have begun converting to polymer composite materials for some types of insulators. These are typically composed of a central rod made of fibre reinforced plastic and an outer weathershed made of silicone rubber or EPDM.

• Composite insulators are less costly, lighter in weight, and have excellent hydrophobic capability. This combination makes them ideal for service in polluted areas. However, these materials do not yet have the long-term proven service life of glass and porcelain.

• Design

• Cap and pin insulator string (the vertical string of discs) on a 275 kV

suspension pylon. The electrical breakdown of an insulator due to excessive voltage can occur in one of two ways:Puncture voltage is the voltage across the insulator(when installed in its normal manner) which causes a breakdown and conduction through the interior of the insulator. The heat resulting from the puncture arc usually damages the insulator irreparably.

• Flashover voltage is the voltage which causes the air around or along the surface of the insulator to break down and conduct, causing a 'flashover' arc along the outside of the insulator. They are usually designed to withstand this without damage. High voltage insulators are designed with a lower flashover voltage than puncture voltage, so they will flashover before they puncture, to avoid damage.

Insulators:

Insulators:

• Dirt, pollution, salt, and particularly water on the surface of a high voltage insulator can create a conductive path across it, causing leakage currents and flashovers. The flashover voltage can be more than 50% lower when the insulator is wet. High voltage insulators for outdoor use are shaped to maximise the length of the leakage path along the surface from one end to the other, called the creepage length, to minimize these leakage currents.

• To accomplish this the surface is molded into a series of corrugations or concentric disk shapes. These usually include one or more sheds; downward facing cup-shaped surfaces that act as umbrellas to ensure that the part of the surface leakage path under the 'cup' stays dry in wet weather. Minimum creepage distances are 20-25 mm/kV, but must be increased in high pollution or airborne sea-salt areas.

Cables

• A cable is one or more strands bound together. Electrical cables may contain one or more metal conductors, which may

be individually insulated or covered. An optical cable contains one or more optical fibers in a protective jacket that supports

the fibers. Mechanical cables such as wire rope may contain a large number of metal or fiber strands.

Cables

• Electrical cables may be made flexible by stranding the wires. The technical issue is to reduce the skin effect voltage drop while using with alternating currents.In this process, smaller individual wires are twisted or braided together to produce larger wires that are more flexible than solid wires of similar size. Bunching small wires before concentric stranding adds the most flexibility.

• A thin coat of a specific material (usually tin-which improved striping of rubber, or for low friction of moving conductors, but it could be silver, gold and another materials and of course the wire can be bare - with no coating material) on the individual wires. Tight lays during stranding makes the cable extensible (CBA - as in telephone handset cords).

Cables

• Bundling the conductors and eliminating multi-layers ensures a uniform bend radius across each conductor. Pulling and compressing forces balance one another around the high-tensile center cord that provides the necessary inner stability. As a result the cable core remains stable even under maximum bending stress.

• Cables can be securely fastened and organized, such as using cable trees with the aid of cable ties or cable lacing. Continuous-flex or flexible cables used in moving applications within cable carriers can be secured using strain relief devices or cable ties. Copper corrodes easily and so should be layered with Lacquer.

SUBSTATION, GROUNDING

SYSTEM AND DISTRIBUTION

SYSTEM

High-Temperature, Low-Sag Transmission Conductors

Technical Report

EPRI Project Manager A. Edris

EPRI • 3412 Hillview Avenue, Palo Alto, California 94304 • PO Box 10412, Palo Alto, California 94303 • USA 800.313.3774 • 650.855.2121 • askepri@epri.com • www.epri.com

High-Temperature, Low-Sag Transmission Conductors

1001811

Final Report, June 2002

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES

THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM:

(A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE; OR

(B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT.

ORGANIZATION(S) THAT PREPARED THIS DOCUMENT

Power Delivery Consultants, Inc.

ORDERING INFORMATION

Requests for copies of this report should be directed to EPRI Orders and Conferences, 1355 Willow Way, Suite 278, Concord, CA 94520, (800) 313-3774, press 2 or internally x5379, (925) 609-9169, (925) 609-1310 (fax).

Electric Power Research Institute and EPRI are registered service marks of the Electric Power Research Institute, Inc. EPRI. ELECTRIFY THE WORLD is a service mark of the Electric Power Research Institute, Inc.

Copyright © 2002 Electric Power Research Institute, Inc. All rights reserved.

iii

CITATIONS

This report was prepared by

Power Delivery Consultants, Inc. 28 Lundy Lane, Suite 102 Ballston Lake, New York 12019

Principal Investigator D. Douglass

This report describes research sponsored by EPRI.

The report is a corporate document that should be cited in the literature in the following manner:

High-Temperature, Low-Sag Transmission Conductors, EPRI, Palo Alto, CA: 2002. 1001811.

v

REPORT SUMMARY

An attractive method of increasing transmission line thermal rating (uprating) involves replacing the original (typically) steel-reinforced aluminum conductor (ACSR) with a high-temperature, low-sag (HTLS) conductor with approximately the same diameter as the original conductor. The increase in thermal rating of existing lines reconductored with one of these HTLS conductors varies from 20% to 80% depending on whether the replacement HTLS conductor is able to reach its maximum operating temperature within electrical clearance limits.

Background The overwhelming majority of overhead transmission lines use ACSR. On a continuous basis, ACSR may be operated at temperatures up to 100oC and, for limited time emergencies, at temperatures as high as 125oC without any significant change in the conductor’s physical properties. These temperature limits constrain the thermal rating of a typical 230-kV line to about 400 MVA. Given the many changes in the way the power transmission system is being planned and operated, there is a need to reach higher current densities in existing transmission lines. Replacing original ACSR conductors with HTLS conductors with approximately the same diameter is one method of increasing transmission line thermal rating. HTLS conductors are effective because they are capable of (1) high-temperature, continuous operation above 100oC without loss of tensile strength or permanent sag-increase (so that line current can be increased) and (2) low sag at high temperature (so that ground and underbuild clearances can still be met without raising or rebuilding structures).

Objectives To describe HTLS conductors in various stages of development and commercialization.

Approach HTLS conductors considered in the report are

• ACSS and ACSS/TW [Aluminum Conductor Steel Supported] – Annealed aluminum strands over a conventional steel stranded core. Operation to 200oC.

• (Z)TACIR [Zirconium alloy Aluminum Conductor Invar steel Reinforced) – High-temperature aluminum strands over a low-thermal elongation steel core. Operation to 150oC (Tal) and 210oC (ZTAl).

• GTACSR [“Gapped” TAL alloy Aluminum Conductor Steel Reinforced] – High-temperature aluminum, grease-filled gap between core / inner layer. Operates to 150oC.

vi

• ACCR [Aluminum Conductor Composite Reinforced] – High-temperature alloy aluminum over a composite core made from Alumina fibers embedded in a matrix of pure aluminum. Operation to 210oC.

• CRAC [Composite Reinforced Aluminum Conductor] – Annealed aluminum over fiberglass/thermoplastic composite segmented core. Probable operation to 150oC.

• ACCFR [Aluminum Conductor Composite Carbon Fiber Reinforced]– Annealed- or high-temperature aluminum alloy over a core of strands with carbon fiber material in a matrix of aluminum. Probable operation to 210oC.

Results The HTLS conductors described in this report are at various points in this development process:

• ACSS is commercially available and needs little additional research or development. The manufacturer has performed all necessary laboratory tests to allow sag-tension calculations and it has been used extensively in line upgrading at many utilities.

• The Japanese developers of high-temperature alloy conductors with Invar steel cores (ZTACIR and TACIR) and the gapped conductor (GTACSR) have performed many laboratory tests, and stress-strain and creep data is available for sag-tension calculations. These conductors have not been used, however, in actual U.S. installations. Field testing might be useful to members in accelerating their acceptance or rejection.

• The 3M conductor, ACCR, has been laboratory tested as part of its development process, but it has only been field tested in a single span at Xcel Energy. Field tests would be useful in identifying this conductor’s strengths and weaknesses.

• CRAC and ACCFR are composed of materials (fiberglass and carbon fiber composite) that have not been defined or laboratory tested. Research on these conductors should define material properties, including conductivity, tensile, and creep elongation properties at high temperature, and corrosion resistance. Until properties of the reinforcing materials are well-defined, there is no need for nor is it possible to execute field tests.

EPRI Perspective HTLS conductors discussed in this report are in various stages of research or commercial development. The document is not an attempt to find a “best” conductor for all high-temperature applications. There is not enough data on some conductors to make this decision. This is simply a review of the known HTLS conductor traits, an assessment of their commercial state, and a limited comparison of their effectiveness as replacement conductors in existing lines. The report can serve as the basis for field test planning and for evaluating the need for laboratory testing.

Keywords High temperature conductors Transmission line sag Thermal ratings

vii

ACKNOWLEDGEMENTS

The author acknowledges the help of many very capable people in the preparation of this report. It has been prepared in a very brief period of time and could not have been done without the help of the following people.

Tracy Anderson – 3M Company, St. Paul, MN

F. Ridley Thrash – Southwire Co., Carrollton, GA

Bernie Clairmont – EPRIsolutions, Lennox, MA

Jack Smith – Applied Thermal Sciences, Saford, ME

Alonso Rodriguez – Consultant, Los Angeles, CA

Takatoshi Kikuta – Sumitomo Electric Industries, Ltd., Osaka, Japan

Mike Tunstall – National Grid, Leatherhead, England

Acknowledgement of the people listed should be taken as just that, an acknowledgement of their help. There is no implication that any or all of those acknowledged are in agreement with the report or its conclusions.

Many other friends and professional associates in both CIGRE and IEEE also helped by providing anecdotal evidence and insight.

ix

CONTENTS

1 INTRODUCTION.................................................................................................................. 1-1

2 DESIGN CONSTRAINTS ON RECONDUCTORING EXISTING LINES............................... 2-1

Sag Constraints .................................................................................................................. 2-2

Tension Constraints............................................................................................................ 2-2

3 WIRE MATERIAL PROPERTIES......................................................................................... 3-1

4 HIGH TEMPERATURE-LOW SAG CONDUCTOR CHOICES ............................................. 4-1

5 TERMINATIONS, SPLICES, HARDWARE, AND INSTALLATION ISSUES........................ 5-1

6 CONDUCTOR DEVELOPMENT PROCESS........................................................................ 6-1

7 HTLS CONDUCTOR COMPARISONS ................................................................................ 7-1

Electrical Losses................................................................................................................. 7-1

Resistance Per Unit Length............................................................................................ 7-1

Basis for Resistance Comparison .................................................................................. 7-1

Sag Increase With Conductor Temperature........................................................................ 7-2

Basis for Sag Comparison.............................................................................................. 7-2

High Temperature Sag Uncertainties ............................................................................. 7-3

“Elastic Modulus” (Tension Change With Conductor Weight).............................................. 7-6

Replacement Conductor Modulus .................................................................................. 7-6

Rated Strength of HTLS Replacement Conductors............................................................ 7-7

8 SAG COMPARISON FOR HTSL CONDUCTORS ............................................................... 8-1

9 CONCLUSIONS................................................................................................................... 9-1

Conductor Choices ............................................................................................................. 9-1

Conductor Uprating Performance ....................................................................................... 9-3

x

10 RECOMMENDATIONS FOR TESTING AND FIELD EVALUATION................................ 10-1

11 REFERENCES................................................................................................................. 11-1

Transmission Line Design................................................................................................. 11-1

Thermal Rating of Lines.................................................................................................... 11-1

High Temperature Effects - Hardware............................................................................... 11-1

Re-Conductoring Lines with Novel Conductors................................................................. 11-2

Sag-Tension Calculations for Overhead Lines .................................................................. 11-2

xi

LIST OF FIGURES

Figure 2-1 Sag Diagram .......................................................................................................... 2-1 Figure 4-1 ZTACIR.................................................................................................................. 4-1 Figure 4-2 GTACSR................................................................................................................ 4-2 Figure 4-3 ACCR..................................................................................................................... 4-2 Figure 5-1 Termination of GTACSR Conductor at National Grid [14] ....................................... 5-1 Figure 5-2 Proposed Splice Method for Fiberglass Core of CRAC Conductor[16] ................... 5-2 Figure 5-3 Termination for ACCR HTLS Conductor................................................................. 5-3 Figure 7-1 Sag Versus Conductor Temperature with 26/7 ACCR Conductor in a Single

Dead-End Span ............................................................................................................... 7-5 Figure 8-1 Typical Plot of Sag Versus Temperature for Various HTLS Conductor Types ........ 8-1

xiii

LIST OF TABLES

Table 3-1 Wire Material Properties .......................................................................................... 3-3 Table 6-1 Product Development Status for HTLS Conductors................................................. 6-2 Table 7-1 "Kneepoint" Temperature for ACSR Conductors as a Function of Steel

Content............................................................................................................................ 7-3 Table 7-2 Transmission Line Loading Districts According to the National Electric Safety

Code................................................................................................................................ 7-6 Table 8-1 Summary of Thermal Ratings for Various HTLS Conductors All Having

Approximately the Same Diameter .................................................................................. 8-2 Table 9-1 HTLS, 1.1 inch OD, Conductor Comparison on the Basis of Equal Everyday

and High Temperature Sags............................................................................................ 9-4 Table 9-2 HTLS, 1.1 inch OD, Conductor Comparison on the Basis of Maximum

Continuous Operating Temperature................................................................................. 9-6

1-1

1 INTRODUCTION

Most existing overhead transmission lines use steel reinforced aluminum conductors (ACSR). On a continuous basis, ACSR may be operated at temperatures up to 100oC and, for limited time emergencies, at temperatures as high as 125oC without any significant change in the conductor’s physical properties. These temperature limits constrain the maximum current density of ACSR to the range of 1 to 2 amps/kcmil (2 to 4 amps/mm2). This in turn limits the thermal rating of a typical 230 kv line with a single 795 kcmil ACSR conductor per phase to about 400 MVA.

In order to increase the thermal rating of existing lines, one method involves replacing its ACSR conductors with special “high-temperature low-sag” (HTLS) conductors having approximately the same diameter as the original ACSR but being capable of operation at temperatures as high as 200oC with less thermal elongation than ACSR. Ideally, these special HTLS conductors can be installed and operated without the need for extensive modification of the existing structures and foundations.

As with ACSR, HTLS conductors typically consist of aluminum wires helically stranded over a reinforcing core. Most of the electrical current flows in the high conductivity, low density, aluminum strand layers. Most of the tension load is in the reinforcing core at high temperature and under high loads. The comparative performance of the HTLS conductors depends on the degree to which the aluminum strand and reinforcing core’s physical properties are stable at high temperature and on the elastic, plastic, and thermal elongation of the combined HTLS conductor.

The HTLS conductors discussed in this report are in various stages of research or commercial development. The document is not an attempt to find a “best” conductor for all high temperature applications. There is not enough information on some conductors to make this decision. This is simply a review of the known HTLS conductor characteristics, an assessment of their commercial state, and a limited comparison of their effectiveness as replacement conductors in existing lines.

The report can serve as the basis for field test planning and for evaluating the need for laboratory testing.

2-1

2 DESIGN CONSTRAINTS ON RECONDUCTORING EXISTING LINES

Electrical, mechanical and thermal constraints on replacement conductors are considerably more restrictive than those for conductor used in new lines. Trade-offs between conductor resistance, thermal elongation, mechanical strength, and high temperature stability of such properties will be described. An understanding of such trade-offs can serve as the basis for field-testing.

The restrictions on reconductoring include the following:

• Transverse structure load and tension limits are set. Any change requires structure reinforcement.

• Attachment height and span lengths are fixed unless structures are raised or moved.

• Mid-span spacing of phases is fixed.

• The type of insulators (“I”, “V”, “horizontal V”, or “post”) is usually difficult to change.

GROUND LEVEL

Minimum ElectricalClearance

Initial Installed Sag @60F

Final Unloaded Sag @60F

Sag @ Max Ice/Wind Load

Sag @ Max ElectricalLoad, Tmax

Span Length

Figure 2-1 Sag Diagram

Design Constraints on Reconductoring Existing Lines

2-2

In order to increase the ampacity of an existing line by reconductoring, either resistance of the conductor must be decreased or the new conductor must operate at a higher temperature than the old:

• The resistance of the phase conductors can be reduced if the existing conductor is replaced with a larger conductor (i.e. greater crossectional area) and/or with a conductor having higher effective conductivity (e.g. use Alumoweld in place of galvanized steel core wires).

• In order to operate the new conductor at a high maximum allowable temperature, some way has to be found to limit the maximum sag at high temperature to that of the existing line (refer to Figure 2-1).

Sag Constraints

As shown in Figure 2-1, the original conductor was installed at the “Initial installed sag” using stringing charts. Over time, the initial unloaded sag will increase to a final “everyday” sag condition (typically at 60oF with no ice and wind). The difference in sag between initial and final sag is the result of both occasional wind/ice loading events and the normal creep elongation process of tensioned aluminum strands over time. Under final conditions, the sag may increase further due to ice/wind loading or high electrical loads. For most transmission lines, the larger reversible increase in final sag occurs as a result of electrical rather than mechanical loads as is shown in Figure 2-1. The temperature corresponding to the maximum electrical load is called the maximum allowable conductor temperature or the line design temperature. Values of between 49oC and 125oC are common. For transmission conductors with no steel core, the maximum allowable conductor temperature may be reduced in order to limit annealing of aluminum.

When reconductoring, the new conductor must be installed, such that over time, the final unloaded sag at the new maximum allowable conductor temperature does not exceed the original conductor’s final sag at the original maximum temperature.

Tension Constraints

The other important constraint on reconductoring is typically that the new conductors must not exceed the original load limits of the existing structures. For tangent structures, the governing transverse loads are primarily a function of the conductor diameter. Thus the replacement conductor diameter must be within about 10% of the existing conductor unless the tangent structures are to be reinforced. For angle and dead-end structures, the governing loads are primarily a function of the initial maximum conductor tension. Unless these structures are to be reinforced or replaced, the replacement conductor’s maximum tension should not exceed the initial maximum conductor tension used in the structure design.

3-1

3 WIRE MATERIAL PROPERTIES

Transmission conductors are constructed from helically stranded combinations of individual wires. Certain wires are primarily used for mechanical reinforcement (e.g. galvanized steel), others solely to conduct electricity (e.g. annealed aluminum or copper), and many both for their mechanical and electrical properties (e.g. “Hard-drawn aluminum or copper). In the most common type of transmission conductor, ACSR, the steel and the aluminum strands are important mechanically. With 26/7 Drake ACSR, the total tensile strength of 31,500 lbs is the sum of 13,500 lbs in the aluminum and 18,000 lbs in the steel core.

Examples of attractive material wire properties are:

• High conductivity

• High ratio of tensile strength to weight

• Retention of tensile strength at high temperature

• Low plastic elongation

• High mechanical self-damping

• Low ratio of outside diameter to crossectional area

• Easy fabrication into wire

• Weatherability (unaffected by humidity, sun, rain)

It is reasonable to assume that any HTLS conductor will consist of helically stranded wires and that it is likely to have a mechanical reinforcing core surrounded by multiple helical layers of conducting wires. Table 1 lists material properties for the various component wires used or proposed for use in HTLS conductor.

Note that normal ACSR consists of 1350-H19 aluminum wires [4], helically stranded around a core of high strength (HS) steel core wires. 1350-H19 aluminum is nearly pure aluminum that is limited to continuous operation below 100C. Above 100oC, 1350-H19 aluminum wires lose tensile strength over time and, after extended exposure to high temperature, 1350-H19 becomes “fully annealed” wire (designated 1350-H0). 1350-H0 is chemically identical to 1350-H19 but all “work-hardening” of the wires inherent in drawing the wires from rod has been removed.

1350-H0 has a tensile strength less than half that of 1350-H19 and breaks at an elongation of 10% to 20% instead of 1%. It is unaffected by further exposure to high temperatures. Annealed aluminum wires are attractive for use in HTLS conductor meet the criteriait has a greatly reduced tensile strength and can be operated to 350C without any change in its properties.

Wire Material Properties

3-2

TAL and ZTAL [12] are Zirconium aluminum alloys that can be operated at temperatures of up to 150oC and 210oC, respectively, without loss of tensile strength.

Aweld is Alumoweld which is HS steel wire with a thick cladding (10% of diameter) of aluminum that increases the wire conductivity and improves corrosion resistance in ACSR.

HS steel and EHS steel wires are typically supplied galvanized for corrosion resistance. Ordinary galvanizing limits the continuous operation of steel core wires to about 200C. High quality “Galfan” [11] coated steel wires are capable of operation to 350C.

Invar steel alloy wires [13] have a reduced rate of thermal elongation and a slightly lower tensile strength than HS steel wires. At high temperature, the sag of invar reinforced aluminum conductor increases less than ACSR with temperature.

3M’s Alumina Composite wires [15] are quite different from steel but serve the same purpose of providing mechanical strength and low thermal elongation. This composite material has the highest conductivity and the lowest thermal elongation of the commercially available reinforcing wires.

Wire Material Properties

3-3

Table 3-1 Wire Material Properties

Material

Maximum Continuous Temp [deg

C]

Max Elongatio

n [%]

Modulus/Tensile Strength [Mpsi /

Kpsi]

CTE [10-

6 per oC] Density[g/cc]

Conductivity [%IACS]

Commercially Available Conducting Wire Materials

1350-H19 100 1 7/24 23 2.703 62

1350-H0 250 20 7/10 23 2.703 63

TAL 150 1 7/24 23 60

ZTAL 210 1 7/24 23 60

Commercially Available Reinforcing Wire Materials

Aweld 250 3 23/1 6.59 20

HS Steel 200 to 350 3 28/180 11.5 7.78 8

EHS Steel 3 28/210 11.5 7.78 8

INVAR 3 22/160 6.6 7.78 15

3M Alumina Composite 250 0.7 28/200 6.3 30

Experimental Reinforcing Wire Materials

Thermoplastic Composite <150 3 7/200 ~ 6 1.5 0

Graphite fibers* 250 ~ 1 33/360 ~ -1. 1.8 0

* Graphite fibers would almost certainly be embedded in a matrix that will reduce the modulus and tensile strength shown by as much as 50%.

The exact material properties of fiberglass and graphite composite are very uncertain as these materials are presently under development.

The development of a fiberglass composite for conductor reinforcement is not complete and the effect of high temperature exposure is uncertain [16]. The mechanical and electrical parameters listed for information and are subject to change as the materials are modified in the future. The advantage of fiberglass is its low weight and low thermal elongation. Its elastic modulus, however, is only about 25% that of the other reinforcing materials being approximately the same as aluminum. It seems unlikely that a fiberglass-reinforced conductor would be suitable for use in high ice and wind load areas.

Wire Material Properties

3-4

The values shown in Table 3-1 for modulus and tensile strength of the graphite fiber is for the strand material alone. Since the strands must almost certainly be embedded in an aluminum matrix of some sort, the modulus and the tensile strength will be considerably less than the values shown for the fiber alone. The advantage of the carbon composite reinforcing material is low weight and negative thermal elongation, however, carbon fibers react chemically with aluminum.

4-1

4 HIGH TEMPERATURE-LOW SAG CONDUCTOR CHOICES

This evaluation report includes conductors that are at various stages of this normal development process. The study is too brief to provide detailed comparisons of high temperature low sag (HTLS) conductors under the many design conditions that can be encountered. In addition there are uncertainties concerning some handling and long term sag-tension-temperature behavior that can only be determined by experiment. The report does provide a description of each the mechanical and electrical characteristics of each conductor type, an evaluation of how “commercial” the conductor is at present, and some typical performance comparisons.

The HTLS conductors considered in the report are:

1. ACSS [10] and ACSS/TW [11] Commercially available HTLS conductors that can be readily purchased and installed with an extensive history of utility experience. There are multiple suppliers within the US. Initial concerns about installation and surface roughness problems due to the use of annealed aluminum strands have been overcome and the cost premium is minimal. The main limitation with ACSS is its relatively low strength and modulus that limit its use in regions experiencing high ice loads.

2. ZTACIR [12] Commercially available through importation from Japan. While there is little or no field experience with this conductor in the US, there is extensive laboratory test data on both the Invar steel core and the Zirconium aluminum alloy wire material. It is not clear whether multiple suppliers will develop in the US. There appear to be no special problems with installation and termination of ZTACIR. Invar steel is somewhat weaker than conventional steel core wire limiting its use in high ice load areas and compression effects in the aluminum strands make its thermal elongation rate at high temperature uncertain.

Figure 4-1 ZTACIR

High Temperature-Low Sag Conductor Choices

4-2

3. GTACSR [14] Commercially available through importation from Japan. Limited field experience from National Grid installation in England (A 2 km length of GTACSR was successfully installed by National Grid). Extensive laboratory test data and detailed installation instructions are available. The installation of this conductor is more complex and labor intensive than ACSR. Its termination requires the unwinding of aluminum wires at each termination and splice. The high temperature thermal elongation has been verified by test. Special semi-strain type suspension fitting required for long lines.

Figure 4-2 GTACSR

4. ACCR [15] Commercially available in limited quantities from the 3M Company. Reasonably extensive tests have been performed on several sizes of this conductor under laboratory conditions and terminations and suspension clamps are available from Preformed Line Products. Xcel Energy successfully completed a field test, with a single 800 ft span, in Minneapolis. The installation of this conductor appears to be reasonably straightforward but may require special large blocks and careful handling.

Figure 4-3 ACCR

5. CRAC [16] Not commercially available from any of the major manufacturers nor from the inventor Goldsworthy Company. A Mr. C.W.Arrington of Transmission Technology Corp. claims to be able to supply the conductor in reel lengths. Laboratory tests have been limited to tests on short samples of fiberglass core. The use of annealed trapezoidal wire aluminum strands in combination with a low modulus fiberglass core makes its use in high ice load areas unlikely. A splice has been proposed but not demonstrated.

High Temperature-Low Sag Conductor Choices

4-3

6. ACCFR [17] Carbon fiber reinforced aluminum conductor is not commercially available. The carbon fiber core has been produced in a variety of forms but only in short lengths. The negative thermal elongation behavior of carbon fibers combined with low density and “steel-like” tensile strength and modulus make this conductor potentially attractive. The low shear strength of carbon fibers, the problems of corrosion, and high fabrication and material cost are possible drawbacks.

5-1

5 TERMINATIONS, SPLICES, HARDWARE, AND INSTALLATION ISSUES

Terminations, splices, hardware, and installation procedures for standard ACSR and AAC bare overhead conductors are well understood and problems are relatively rare when manufacturer’s installation instructions are followed. The introduction of new types of conductor may require modifications of existing equipment designs and procedures. It seems likely that problems and uncertainties involving tension stringing, termination, splicing, and support of new types of HTLS replacement conductors will be a primary focus of subsequent field-tests.

Some examples of installation procedures that are peculiar to certain HTLS conductors include the following photograph [14](Figure 5-1), that shows the special termination procedure for the GTACSR conductor installed at National Grid.Here the aluminum strands are shown as the crew is separating them in order to grip the steel core.

Figure 5-1 Termination of GTACSR Conductor at National Grid [14]

Terminations, Splices, Hardware, and Installation Issues

5-2

Tension stringing concerns include the transfer of tension load from a grip to the reinforcing core, the minimum size stringing block, and short term creep elongation that may impact sagging.

With the proposed CRAC conductor, the use of a segmented fiberglass/thermoplastic core requires a special splicing technique. The proposed splice is shown in the following picture [16]. The CRAC designs include considerations for splicing, because without it the designs cannot be implemented by the utilities due to a lack of practicality. Figure 5-2 shows the splicing concept for CRAC-121.

Figure 5-2 Proposed Splice Method for Fiberglass Core of CRAC Conductor[16]

By staggering the bond lines between segments in the lengthwise direction there is a gradual transfer of load. This type of joining is regarded in the aerospace industry as the strongest bonded connection that can possibly be made. This proposed splice is not commercially available.

In contrast to some of the other HTLS conductors, the splicing, installation, and termination of ACSS is well understood. ACSS requires special two-sleeve splices [9] that are a bit longer than normal ACSR splices but are otherwise conventional in application. Similarly, ACSS requires no special suspension clamp design and tension-stringing installation is straightforward. One point of uncertainty, however, involves the ability of conventional suspension clamps to operate at temperatures of 200oC or more.

Terminations and suspension hardware for the ACCR conductor have been developed and tested. A dead-end for ACCR used in the initial field test at Xcel Energy is shown in Figure 5-3. Armor Grip suspension clamps are recommended for suspension hardware. 3M Company has performed extensive hardware tests in cooperation with EDF and Preformed Line Products.

Terminations, Splices, Hardware, and Installation Issues

5-3

Figure 5-3 Termination for ACCR HTLS Conductor

Field-testing of HTLS conductors should include verification that recommended methods of termination, support, and tension stringing work reasonably well with ordinary utility crews. No such field tests are possible until the HTLS conductor manufacturer provides installation recommendations and arranges that connectors, support clamps, and terminations work well at the extreme temperatures that are likely to be encountered in HTLS conductor applications.

6-1

6 CONDUCTOR DEVELOPMENT PROCESS

Overhead transmission lines must be very conservatively designed and built such that the public is not injured by contact with their energized conductors. To assure the public safety, any new conductor must go through a very rigorous series of tests to prove that the conductor will not break nor sag into contact with people, vehicles and other conductors. While no federal or state law specifies this process, power utility line design engineers normally require the following laboratory tests and technical data prior to the onset of field-testing:

• Stress-strain tests showing initial and final curves

• Creep elongation data showing permanent elongation as a function of time for various tension levels

• Conductor weight per unit length

• Conductor tensile strength

• Resistance per unit length

In addition to knowing these conductor parameters, it is normally necessary that methods of terminating, splicing and supporting the conductor are specified and techniques for tension stringing demonstrated. These field tests would typically include documentation of the tension stringing, sagging and clipping processes followed by a period of time during which the conductor would be monitored while carrying full line voltage and typical line current.

Following a successful field test, the manufacturer is normally required to provide a manufacturing specification that includes wire tensile strength, elongation tests, and dimensional checks on component wires, for review by the transmission line owner. The varying stages of development for HTLS conductors is illustrated in Table 6-1.

Conductor Development Process

6-2

Table 6-1 Product Development Status for HTLS Conductors

HTLS Conductor Proof of Concept Tests

Detailed Test & Fitting Data

Field Tests Manufacturing Specification

ACSS Yes Yes Yes ASTM

ACSS/TW Yes Yes Yes ASTM

TACIR Yes Yes [1] [2]

GTACSR Yes Yes [3] [2]

ACCR(3M) Yes Yes [4]

CRAC(CEC) Yes

[1] No field test in the US [2] Japanese manufacturing standards exist [3] Field Test at National Grid [4] Single span field test at Xcel Energy

7-1

7 HTLS CONDUCTOR COMPARISONS

There are many ways to evaluate the choice of replacement conductor for an existing line. In this section of the report, economic factors, practical installation procedures, inventory control, thermal rating calculations, and continuous versus contingency applications will be discussed.

It seems very unlikely that it will be possible to suggest a single common evaluation method but this discussion will include a description of the most important issues to be considered in such a comparison.

Electrical Losses

The purpose of any power transmission line is to carry electrical power. The energized conductors of the line must carry electrical current without excessive losses. Electrical losses over a given transmission path at a given level of electrical current are a function of the conductor resistance, the length of the path, and time. For a typical balanced 3-phase line, the losses in each of the phase conductors is the same.

Electrical conductor losses determine the cost of power losses per unit length for an overhead line and also the conductor temperature attained as the result of high current levels. Power flow is seldom limited because of power losses but is commonly limited to avoid excessively high temperatures.

Resistance Per Unit Length

The resistance of a stranded bare overhead conductor is equal to the product of metal resistivity and crossectional area of the strands adjusted for frequency, temperature, and ferromagnetic losses if any.

For conductors with ferromagnetic reinforcing core wires, the 60 Hz resistance may be up to 5% higher than for those with non-ferromagnetic core wires due to magnetic losses at high current levels.

Basis for Resistance Comparison

The conductivity of “electrical conductor” grade 1350-H19 aluminum is 62% of the International Annealed Copper Standard (IACS). If it is annealed, the conductivity may increase slightly to 63%. With the addition of alloying compounds, the conductivity is usually less than 62%.

HTLS Conductor Comparisons

7-2

Galvanized steel wires have a conductivity of 8%IACS, Alumoweld wires 20% IACS, and the 3M composite core wires, 30% IACS.

Generally, comparisons of conductor resistance should be made on the basis of equal crossectional area. Conductors with round wires should not be compared to conductors with trapezoidal wires having the same diameter.

Sag Increase With Conductor Temperature

Overhead transmission lines must maintain certain minimum distances to ground under all operating conditions (both high current/temperature and high ice and wind loads). This is essential to the public safety.

In most cases, sag under ice and wind loading is less than the sag that occurs for high currents. Therefore, in order to maintain adequate clearance to ground and to other conductors, a maximum power flow on transmission lines (the thermal limit) is specified and the transmission operator monitors the power flow on each line such that the thermal rating is not exceeded.

When reconductoring an existing transmission line, the replacement conductor should be capable of carrying more electrical current with the same maximum sag as the original conductor. To accomplish this, the replacement conductor should have the following characteristics:

• Low thermal elongation

• Low initial sag

• Low plastic elongation

Conventional ACSR conductors are typically installed to sags on the order of 2% of span length. Thus a 1000 ft span of Drake ACSR may be installed to an initial sag of 20ft. As a result of exposure to ice and wind loads and time, the initial sag may increase by about 15% to about 23 ft and during high current events that raise the conductor temperature to 75C, to 30 ft.

A desirable replacement conductor might be installed at 20 ft or less of sag, exhibit no plastic elongation (final sag = initial sag), elongate thermally at half the rate of DRAKE ACSR such that the 30 ft maximum sag is not reached until the conductor temperature is much higher than 75C, and with tension under maximum wind and ice loading no higher than the original design.

Basis for Sag Comparison

The various conductor characteristics that control maximum sag must be taken together. That is, a replacement conductor that does not elongate thermally is useless if it breaks under ice and wind load. On the other hand, a conductor that elongates somewhat more than the original conductor under ice and wind load may be desirable if it keeps the maximum structure tension loads down.

HTLS Conductor Comparisons

7-3

Comparisons of sag-tension behavior must be done with a computer program such as Alcoa’s SAG10. A replacement conductor that has attractive characteristics in one design situation may be less desirable in another case. To perform these kinds of calculations, the conductor manufacturer must supply adequately detailed conductor stress-strain data, creep data and thermal elongation information.

Without such detailed data it is possible to do only rough comparisons. Clearly, low thermal elongation is desirable in any replacement conductor as is adequately low elastic and plastic elongation under high loads.

High Temperature Sag Uncertainties

Until just recently, transmission lines were seldom run to temperatures in excess of 100C. In fact until the early 1970’s it was common to design transmission lines for a maximum conductor temperature of 120F (49C). Even when lines are reconductored with special high temperature conductor capable of operation up to 200C, power system conditions rarely cause such extreme temperatures to occur. As a result there is little field data to verify the calculated sag variation of conventional ACSR with temperatures above 75C.

The primary uncertainty about ACSR at high temperature involves the thermal elongation at temperatures above the “kneepoint” of the conductor. The kneepoint temperature is typically a function of the steel content:

Table 7-1 "Kneepoint" Temperature for ACSR Conductors as a Function of Steel Content

ACSR Stranding Type Number Kneepoint temperature [ C][1]

42/7 5 190

45/7 7 150

54/7 13 95

26/7 16 70

30/19,30/7 23 35

[1] Temperatures beyond which all conductor tension is transferred to the steel core

At temperatures up to the “kneepoint”, where the aluminum and steel core are both in tension, the thermal elongation of ACSR is given by Eq. 7-1and Eq. 7-2.

⋅

⋅+

⋅

⋅=

TOTAL

ST

AS

STST

TOTAL

AL

AS

ALALAS A

AEE

AA

EE ααα

Eq. 7-1

HTLS Conductor Comparisons

7-4

⋅+

⋅=

TOTAL

STST

TOTAL

ALALAS A

AEAAEE

Eq. 7-2

where

EAL = modulus of elasticity of aluminium (GPa)

EST = modulus of elasticity of steel (GPa)

EAS = modulus of elasticity of aluminium-steel composite (GPa)

AAL = area of aluminium strands, mm2

AST = area of steel strands, mm2

ATOTAL = total cross-sectional area, square units, mm2

αAL = aluminium coefficient of linear thermal expansion, per oC

αST = steel coefficient of thermal elongation, per oC

αAS = composite aluminium-steel coefficient of thermal elongation, per oC

Using elastic moduli of 55 and 190 GPa for aluminium and steel, respectively, the elastic modulus for the 500-A1/S1A conductor is:

( ) ( ) GPaEAS 5.7056565190

56550055 =

×+

×=

Eq. 7-3

and the coefficient of linear thermal expansion is:

CaAS °×=

×

××+

×

××= −−− /105.19

56565

5.70190105.11

565500

5.70551023 666

Eq. 7-4

At temperatures above the “knee point” temperature, there is a good deal of uncertainty about thermal elongation. Up until the last 5 to 10 years, calculation methods such as SAG10 [20] assumed that the conductor’s thermal elongation rate was that of steel at temperatures above the knee point. In a number of indoor and outdoor experiments with ACSR, it appears that the thermal elongation rate above the knee point is greater than that of steel alone.

The two main theories concerning this behavior are those of Rawlins [22] and Barrett [23]. There are a number of experiments that confirm that the thermal elongation rate is greater than that of steel alone. Barrett’s theory involves the natural ability of aluminum helically wound strands to

HTLS Conductor Comparisons

7-5

support limited compression. Rawlin’s theory centers on residual stresses in the aluminum strands that are caused during manufacture. In both cases, the compression stress does not exceed 1500 to 2500 psi (10 to 20 Mpa).

The applicability of these theories to HTLS conductors is uncertain but important to their evaluation. There is uncertainty even with ACSR. There is more uncertainty with other high temperature aluminum alloys and reinforcing materials intended to replace high strength galvanized steel. It appears that the collection and analysis of sag-temperature-tension field data for field installations with high current loading is essential to evaluating HTLS conductors.

3M has performed outdoor tests on the sag behavior of ACCR in cooperation with EDF. In these tests, a 0.65 inch diameter, 26/7 ACCR two-layer conductor was placed in an 750 ft span and subjected to high current levels that drove the conductor temperature above 200oC. The conductor was installed to an initial tension of 20% of its rated strength at 15C. Experimental points are shown by the symbols and calculated sag by the lines. Note the slope change (“kneepoint”) at about 120oC.

In this experiment, the impact of aluminum compression appears to be minimal.

Figure 7-1 Sag Versus Conductor Temperature with 26/7 ACCR Conductor in a Single Dead-End Span

HTLS Conductor Comparisons

7-6

“Elastic Modulus” (Tension Change With Conductor Weight)

Conductor weight per unit length increases when wind blows across or ice forms on transmission line conductors. Table 7-2 shows various ice and wind loading conditions from the National Electric Safety Code for transmission lines. HTLS conductors used for reconductoring existing lines must be able to sustain the increases in conductor weight per unit length that result from such ice and wind loads without violating electrical clearances through excessive sag.

Table 7-2 Transmission Line Loading Districts According to the National Electric Safety Code

Loading Districts

Heavy Medium Light Extreme Wind Loading

Radial thickness of ice(in) 0.5 0.25 0 0

Radial thickness of ice(mm) 12.5 6.25 0 0

Horizontal wind pressure(lb/ft2) 4 4 9 See Figure3-6

Horizontal wind pressure(Pa) 190 190 430 See Figure3-6

Temperature(°F) 0 +15 +30 +60

Temperature(°C) -18 -10 -1 +15

Constant to be added to the resultant (all conductors) (Lb/ft)

0.30 0.20 0.05 0.0

Constant to be added to the resultant (all conductors) (N/m)

4.40 2.50 0.70 0.0

In addition, since maximum tension loads on dead-end and angle structures are a function of the conductor modulus, excessively strong HTLS replacement conductors can lead to the need for structure reinforcement.

In almost all existing transmission lines using ACSR or even AAC conductors, the sag under maximum electrical load is greater than the sag under maximum ice and wind load. In using HTLS conductors (which are intended to minimize sag at high temperature) the elastic modulus of the conductor can be important.

Replacement Conductor Modulus

The 1350-H19 aluminum wires used in most existing transmission lines have an “elastic” modulus of about 10 Mpsi and, when helically stranded, a modulus of about 8 Mpsi. Similarly, individual high strength steel core wires have an elastic modulus of nearly 30 Mpsi and approximately 26 Mpsi when stranded. The composite modulus of the ACSR conductor is

HTLS Conductor Comparisons

7-7

between 8 and 26 Mpsi depending on the ratio of steel core to aluminum area (Type number). The modulus of an HTLS replacement conductor need not be equal to the original conductor but must be adequate to avoid excessive sag under ice and wind load.

Consider, for example, 26/7 ACSR Drake conductor (elastic modulus of about 10.5 Mpsi) installed to an initial 60F unloaded sag of 21.7 ft in a 1000 ft span. When this conductor is under NESC heavy load conditions (0.5 inch ice, 9 psf wind, OF) the sag increases by about 2 ft. When it is heated to 212F, the sag increases by about 10 ft. Clearance to ground is a minimum under high temperature.

Now consider the replacement of the Drake conductor were replaced by a CRAC HTLS conductor (consisting of annealed aluminum strands and a fiberglass core), where the fiberglass core has the same area as the steel core of Drake. Using the approximate modulus shown in Table 7-2 for fiberglass (i.e. 7Mpsi), then the elastic modulus of the CRAC conductor would be about 1 Mpsi. Under NESC heavy loading, the initial sag of 21.7 ft would increase to more than 30 ft but because of the low thermal expansion coefficient of fiberglass the sag at 212F only increases to about 23 ft. Here the use of CRAC HTLS conductor would result in a clearance failure regardless of the reduced high temperature sag.

Rated Strength of HTLS Replacement Conductors

The breaking strength of transmission conductors is an essential parameter in the design of lines and structures. The breaking strength must remain at or above its “rated” value throughout the life of the transmission line. If the breaking strength decreases due to annealing, corrosion, or fatigue, then the line may fail and violate the public safety.

For homogeneous conductors, the breaking strength of the conductor is normally taken as the sum of the minimum average tensile strength of its strands derated by about 5% to account for stranding.

Note that, for a non-homogeneous conductor, the conductor breaks at the minimum elongation for which either component breaks and the composite conductor’s breaking strength equals the sum of the tensile loads at which the weaker component breaks.

For example, consider conventional ACSR. The 1350-H19 aluminum strands break at an elongation of approximately 1% whereas the steel core breaks at an elongation of approximately 3%. The conductor’s breaking strength is therefore determined using the tensile strength of the aluminum strands (about 24,000 psi) and the tensile stress in steel with a 1% elongation (about 180,000 psi).

In contrast, the rated breaking strength of ACSS with annealed aluminum strands is calculated using the tensile strength of the steel core (about 210,000 psi) and the stress of annealed aluminum strands (about 8,500 psi) at 3% elongation.

Other non-homogeneous HTLS conductors must be evaluated in the same fashion.

HTLS Conductor Comparisons

7-8

The rated strength of HTLS replacement conductors does not necessarily need to be higher than the original. It cannot, however, be dramatically less or the tensile safety factors used in the design will be inadequate.

When materials other than steel are used to reinforce aluminum conductors, several observations apply:

• The physical properties of the reinforcing materials must remain stable at high temperatures.

• The reinforcing material must not react chemically with the conducting strands.

• Regardless of the reinforcing material chosen, if full hard 1350-H19 aluminum strands are used in the replacement conductor, the composite strength will decline at temperatures above 100C.

• If 1350-H0 annealed aluminum strands are used with the reinforcing core, then the rated strength of the composite conductor is essentially determined by the reinforcing core.

• If high temperature alloys of aluminum are used, then the rated strength of the HTLS replacement conductor will determined by the tensile strength of the stranded component with the smallest maximum elongation plus the stress of the other component at that elongation.

8-1

8 SAG COMPARISON FOR HTSL CONDUCTORS

One of the possible performance comparisons for HTLS conductors is sag increase with temperature. In this case, it is assumed that the original ACSR conductor is 795 kcmil 26/7 Drake ACSR installed in a 1000ft ruling span to an initial unloaded tension equal to 20% of its rated breaking strength at 60oF. The initial sag of 21.8 ft increases to 25.7 ft due to an ice load event where the conductor was covered with 1.0 inch of radial ice for several hours. The corresponding maximum tension is 15,300 lbs.

Assume that the line was designed to provide minimum clearance to ground for the ACSR Drake at 100oC (212oF). The final sag of Drake at 100oC is 31.7 ft without aluminum compression. 31.7 ft is therefore the maximum allowable sag for any of the replacement conductors. The thermal rating of DRAKE at 100oC is 990 amperes for 2 ft/sec crosswind, 40oC air temperature, and solar heating for Summer at noon.

The replacement conductors considered in the following sag calculations are ACSS, ACSS/TW, ACCR(3M), GTACSR, and TACIR. re-phrase I could not include CRAC conductor because of a lack of test data on thermal elongation and modulus. For each replacement conductor I have assumed equal final unloaded sag at 60oF.

Sag versus Temp

20

25

30

35

40

-30 70 170 270 370 470

Cond Temp - deg F

Sag

in 1

000

Span

- ft

ACSR ACSRwc ACSS ACSS/TWTACIR ACCR GTACSR

Figure 8-1 Typical Plot of Sag Versus Temperature for Various HTLS Conductor Types

Sag Comparison for HTSL Conductors

8-2

Several observations can be made:

1. Given the sag limit of 31.7 ft, the ACCR conductor with its low thermal elongation attains the highest operating temperature of 370oF. Given the higher conductivity of the composite core and the operating temperature at 188C, the thermal rating is 1550 amperes.

2. ACSS and ACSS/TW both reach the maximum sag at temperatures of 125oC and 120oC, respectively.

3. The higher rating of ACSS/TW (1270 amperes rather than 1190 amperes) is the result of increased aluminum crossectional area. A similar increase in rating would be possible for the other HTLS conductors using TW aluminum wires.

4. With TACIR at its maximum operating temperature of 270oF (132oC), it is below its continuous operation limit of 150oC and has a thermal rating of 1220 amperes.

5. GTACSR reaches the maximum sag limit of 31.6 ft at an operating temperature of 124oC. This corresponds to a thermal rating of 1170 amperes.

For all of these replacement conductors, the maximum operating temperature, determined by maximum sag of 31.6 ft, is well below their continuous operating temperature limit. The thermal rating comparison could be quite different if the line was not clearance limited, if the temperature limit on the original conductor was higher, or if the span lengths were different.

Table 8-1 Summary of Thermal Ratings for Various HTLS Conductors All Having Approximately the Same Diameter

Conductor Temperature at 31.6 ft sag

[deg C]

Thermal Rating [amps]

(%increase)

Notes [2] Maximum tension with

1.0” radial ice at 0oF

Drake ACSR 100 990

Ignores compression in

aluminum strands

15300

Drake/ACSS 125 1190 (+20%) 13970 (-9%)

Suwannee/TW/

ACSS [1] 120 1270 (+28%) 16130 (+5%)

Drake ACCR 188 1550 (+56%) Ignore comp. 15300

Drake TACIR 132 1220 (+23%) Ignore comp. 15000 (-2%)

Drake GTACSR 124 1170 (+18%) 15300

Sag Comparison for HTSL Conductors

8-3

[1] The maximum tension with heavy ice load is 830 lbs above the original design limit for Suwanee/TW/ACSS and is 1330 lbs below it for Drake/ACSS. Thus the initial tension of the Drake/ACSS replacement conductor could probably be somewhat higher and the thermal rating increased so long as the safety factor under maximum tension was adequate.

[2] The original line design calculations are assumed to have ignored aluminum strand compression. Taking compression into account would increase the high temperature sag of the original Drake ACSR such that the sag clearance limit was reached at about 70oC rather than 100oC and the thermal rating of the line with the original conductor would have to be decreased from 990 to 660 amperes. The calculations for ACCR and TACIR also ignore aluminum compression. Aluminum compression effects are less likely with annealed aluminum and gapped HTLS conductors.

[3] The higher rating of ACSS/TW (1270 amperes rather than 1190 amperes) is the result of increased aluminum crossectional area. A similar increase in rating would be possible for the other HTLS conductors using TW aluminum wires.

9-1

9 CONCLUSIONS

This report is focused on both commercially available and developing HTLS conductors. While approximate material costs are included, no attempt is made to evaluate the comparative value of these replacement conductors since this is dependent on original design assumptions and power system requirements.

HTLS conductors discussed in the preceding are at various stages of the normal development process. While the mechanical and electrical characteristics of materials such as 1350-H19 aluminum and high strength steel are well known and described in ASTM or IEC standards, materials such as segmented fiberglass/thermoplastic cores and carbon fiber composites are in early stages of development.

Given a simple application of HTLS conductors to a typical clearance-limited transmission line, the high temperature sag and thermal rating of the various commercially available replacement conductors is calculated.

Conductor Choices

Preliminary conclusions and observations about the various types of HTLS conductor is summarized as follows:

1. ACSS and ACSS/TW conductors are commercially available from multiple suppliers in the US. There is an extensive history of utility experience with ACSS and most of the initial concerns about installation and surface roughness problems due to the use of annealed aluminum strands have been proved groundless. The cost premium of these conductors is less than 50% above standard ACSR in most cases. The main limitation with ACSS is its relatively low strength and modulus that limits its use in regions experiencing high ice loads. The use of ACSS/TW can offset this problem to some extent. Little research or development is required beyond improvements in manufacturing and resolution of possible hardware and connector concerns at operating temperatures in excess of 200oC.

2. (Z)TACIR is widely used in Japan. At present, both the Invar steel core and the Zirconium aluminum strands must be imported to the US. The conductor can be stranded in the US though it is not presently available. There is extensive laboratory test data on both the Invar steel core and the Zirconium aluminum alloy wire materials (TAL and ZTAL). It is not clear whether multiple suppliers will develop in the US. There appear to be no special problems with installation and termination of (Z)TACIR. Invar steel is somewhat weaker than conventional steel core wire limiting its use in high ice load areas and compression effects in

Conclusions

9-2

the aluminum strands may increase the thermal elongation quoted by the manufacturer. Given the need to import the aluminum and steel alloys from outside the US, the cost of this conductor is likely to exceed twice the cost of ACSR.

3. G(Z)TACSR is commercially available in Japan, can be imported and there is extensive laboratory test data and detailed installation instructions. Outside of Japan, field tests of this conductor are very limited. The installation of this conductor is complex and labor intensive, requiring the unwinding of aluminum wires at each termination and splice. The high temperature CTE has been verified by test and seems likely to be stable with time. The high temperature aluminum alloy increases the strength at low temperatures allowing its use in high ice load areas. The separate movement of the core and aluminum layers, the possible flow of grease at high temperature and long periods of time, and repair methods are possible areas of study.

4. ACCR has been extensively tested by 3M Company under laboratory conditions. Terminations and suspension clamps are available domestically from PPL. A field test of a single 800 ft span was successfully completed recently. The installation of this conductor appears to be reasonably straightforward but may require special large blocks. The composite core is only available from 3M and the Zirconium alloy aluminum strands are currently imported to the US but the conductor can be stranded domestically. Field test installations are required to establish the handling properties, verify the sag behavior at extremely high temperatures and repair methods are possible topics for study. This conductor has an extremely low thermal elongation rate. The combination of alumina composite core wires and zirconium high temperature aluminum alloy yields high rated strength, high modulus, and low resistance. It yielded the largest increase in rating for the example reconductoring case considered earlier in the report.

5. CRAC conductor is in an early stage of development. Laboratory tests have been limited to tests on short samples of fiberglass core. The proposed use of annealed trapezoidal wire aluminum strands in combination with low modulus fiberglass makes its use in high ice load areas unlikely. A splice has been proposed but not demonstrated. There are no commercial sources for the stranded conductor or for fittings. Field testing of CRAC conductor should await further laboratory tests and a selection of particular fiberglass material. Terminations and fittings can only be developed after the fiberglass material properties are certain and test lengths of conductor are available. The light weight and low thermal elongation of fiberglass make this a potentially attractive conductor.

6. ZTACCFR – Carbon fiber reinforced aluminum conductor is not commercially available. The carbon fiber core has been produced in a variety of forms but only in short lengths. It is assumed that the carbon fibers will need to be embedded in an aluminum matrix but this has not been demonstrated. It is also assumed that the outer layers of this conductor would consist of one of the high temperature aluminum alloys such as ZTAL. The negative thermal elongation behavior of carbon fibers combined with low density and “steel-like” tensile strength and modulus make this conductor potentially attractive but the low shear strength of carbon fibers, the problems of corrosion, and high fabrication and material cost are possible drawbacks. The combination of carbon fibers with various matrix materials and in various

Conclusions

9-3

configurations is under study. Development of HTLS conductor with a carbon fiber core awaits the completion of studies on the core design.

Conductor Uprating Performance

The best choice of conductor depends on design conditions as is discussed in this report. It is possible, however, to compare the conductors in two simple line uprating situations:

• Temperature Limited Line - The original transmission line design includes generous ground clearances (i.e. mid-span clearance exceeds 35 feet under everyday unloaded conditions) such that the sag at elevated temperature is not a concern. Here the replacement conductor simply has to operate at high temperature without any significant loss of strength.

• Sag Limited Line - The ground clearances for the original line design are marginal. The maximum allowable sag of any replacement conductor cannot exceed the present maximum temperature sag.

In both cases it is assumed that the replacement conductor must have approximately the same outside diameter as the original to limit any increase in transverse structure loading. No such limit is placed on the maximum tensions for strain structures.

In the Sag-limited line, the final everyday unloaded sag of all the conductors is assumed to be the same. This ignores possible differences in Aeolian vibration and consequently the need for dampers.

The basic conductor design involves the use of round strands with the exception of ACSS/TW and GTACSR wherein the aluminum strands are trapezoidal. The increased thermal rating of ACSS/TW relative to ACSS (between 5% and 15%) can be realized with any of the other conductor designs if the aluminum strands are manufactured with a trapezoidal crossection.

Conclusions

9-4

Table 9-1 HTLS, 1.1 inch OD, Conductor Comparison on the Basis of Equal Everyday and High Temperature Sags

The ground clearance at the maximum conductor temperature shown is the minimum allowed by the NESC Code. Since the OD of all the HTLS conductors is nearly equal to that of the original line, the tranverse structure loads are unchanged.

Conductor Type

Maximum Continuous Temp [deg

C]

“Elastic” Modulus

for ice&wind

loads

[Mpsi]

Kneepoint Temperature

[Deg C]

Sag change per 10C above

kneepoint temp. [ft]

Temperature at original

line’s minimum ground

clearance [deg C]

Relative resistance per unit

length

Thermal Rating** at Maximum

Allowable Sag in 1000 ft span

[amps]

Relative cost per

unit length

Type 16 ACSR

100C 11.0 60C 0.9 100 1.00 990 1.0

ACSS 200C 7.0 15C 0.9 150 0.98 1190 1.1 – 1.5

ACSS/TW* 200C 7.0 15C 0.9 135 0.90 1270 1.2 – 1.5

TACIR 150C 11.0 40C 0.5 135 1.00 1220 3

ZTACIR 210C 11.0 40C 0.5 135 1.00 1220 5

GTACSR 150C 11.0 15C 0.5 140 0.95 1170 10

ZTACCR 210C 11.0 30C 0.5 210 0.90 1550 10

CRAC 150C 5.0 15C 0.5 90 1.00 900 1.5***

ZTACCFR 210C 11.0 30C 0.1 210 0.90 1550 >10***

* The increase in ampacity obtained by ACSS/TW in this comparison is the result of both increased aluminum crossectional area and increased steel core area that strengthens the conductor. Any of the other conductors listed with the exception of GTACSR could also be fabricated with trapezoidal aluminum strands

Conclusions

9-5

resulting in similar increases in ampacity. In this case, where ampacity is determined by sag limitations, the trade-off between steel and aluminum crossectional areas is complex.

** Thermal rating values are calculated for 2 ft/sec crosswind, full noon-time sun, air temperature 40C, and emissivity = absorptivity = 0.5.

*** The cost of these conductors is very uncertain since they are in the earliest stages of development.

Conclusions

9-6

Table 9-2 HTLS, 1.1 inch OD, Conductor Comparison on the Basis of Maximum Continuous Operating Temperature

The ground clearance at the maximum continuoustemperature is assumed to be adequate to meet the NESC limits. Since all the conductors have approximately the same OD as the original line, the corresponding tranverse structure loads unchanged.

Conductor Type

Maximum Continuous

Temp [deg C]

Maximum Emergency

Temp [deg C]

Relative resistance

per unit length

Thermal Rating at Max Cont.

Temp [amps]

Relative cost per unit length

Type 16 ACSR 100 125 1.00 990 1.0

ACSS 200 230 0.98 1570 1.1 – 1.5

ACSS/TW* 200 230 0.90 1745 1.2 – 1.5

TACIR 150 180 1.00 1325 3

ZTACIR 210 240 1.00 1615 5

GTACSR 150 180 0.95 1315 3

ZTACCR 210 240 0.90 1640 8-12

CRAC 150 150 1.02 1315 1.1 – 1.5***

ACCFR 210 240 0.90 1640 >10***

* The increase in ampacity obtained by ACSS/TW is the direct result of increased aluminum crossectional area not material properties. Any of the other conductors listed with the exception of GTACSR could also be fabricated with trapezoidal aluminum strands and show a similar increase in ampacity.

** Thermal rating values are calculated for 2 ft/sec crosswind, full noon-time sun, air temperature 40C, and emissivity = absorptivity = 0.5.

*** The cost of these conductors is very uncertain since they are in the earliest stages of development.

10-1

10 RECOMMENDATIONS FOR TESTING AND FIELD EVALUATION

Historically, manufacturers rather than research groups have developed transmission line conductors. The process often takes at least 20 years from inception to acceptance. This is true of AAAC, ACAR and more recently; ACSS. ACSS was patented in 1969 and only recently has become widely accepted. Few research projects can continue through such an extended period of time.

Conductor development typically involves initial material property tests (tensile strength, minimum elongation, conductivity, etc.) on new materials and manufacturability tests to see if the new material can be drawn to wire and stranded in combination with other wire materials. Finally, stranded conductor sample lengths are tested to derive stress-strain and creep elongation data.

At the conclusion of such laboratory tests, the manufacturer typically arranges field testing with a cooperative transmission company. Field tests involve tension stringing, clipping with recommended support systems, and successful sagging. Subsequent field tests may be performed to verify claimed conductor properties (high self-damping, reduced ice-galloping amplitudes.

The HTLS conductors described in this report are at various points in this development process:

• ACSS is commercially available and needs little additional research or development. The manufacturer, first Reynolds and now Southwire, has performed all necessary laboratory tests to allow sag-tension calculations and it has been used extensively in line upgrading at many utilities.

• The Japanese developers of high temperature alloy conductors with Invar steel cores (ZTACIR and TACIR) and the gapped conductor (GTACSR) have performed many laboratory tests and stress-strain and creep data is available for sag-tension calculations. These conductors have not been used, however, in actual installations in the United States and field testing sponsored by EPRI might be useful to members in accelerating their acceptance or rejection.

• The 3M conductor, ACCR, has been laboratory tested as part of it’s development process, but it has only been field tested in a single span at Xcel Energy. Field tests would be useful in identifying this conductor’s strengths and weaknesses.

• CRAC and ACCFR are composed of materials, fiberglass and carbon fiber composite, that have not been defined nor laboratory tested. Research on these conductors should emphasize

Recommendations for Testing and Field Evaluation

10-2

the definition of material properties including conductivity, tensile and creep elongation properties at high temperature, and corrosion resistance. Until the properties of the reinforcing materials are well-defined there is no need for nor is it possible to execute field tests.

11-1

11 REFERENCES

Transmission Line Design

[1]. “National Electric Safety Code”, 1997 Edition, C2-1997.

[2]. “Relationships of National Electrical Safety Code Vertical Clearances and Potentially Conflicting Activity”, Clapp, Allen L., IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 11, November 1985, pp. 3306-3312.

Thermal Rating of Lines

[3]. Douglass, Dale A., and Rathbun, L.S., "AC Resistance of ACSR - Magnetic and temperature effects," IEEE Paper 84 SM 700-1.

[4]. American Society for Testing and Materials (ASTM), "1991 Annual Book of ASTM Standards - Section 2, Nonferrous Metal Products," Volume 02.03, Electrical conductors, Including B-1 Standards.

[5]. Kennelly, A.E., Laws, F.A., and Pierce, P.H., "Experimental Researches of Skin Effect in Conductors," AIEE Transactions, Vol. 34, Part 2, 1915, pp. 1953-2021.

[6]. Lewis, W.A., and Tuttle, P.D., "The Resistance and Reactance of Aluminum Conductors Steel Reinforced," AIEE Transactions, Vol. 77, Part III, 1958.

[7]. Aluminum Association, "Aluminum Electrical Conductor Handbook," Third Edition, 1989.

[8]. IEEE, "IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors," PES, IEEE Standard 738-1993.

High Temperature Effects - Hardware

[9]. Adams, HW, Thermal Cycle Tests of SSAC and Associated Fittings, Reynolds Aluminum, Series No. 34, May 1976.

References

11-2

Re-Conductoring Lines with Novel Conductors

[10]. Adams, H.W., "Steel Supported Aluminum Conductors (SSAC) for Overhead Transmission Lines," IEEE Paper T 74 054-3, Presented at the IEEE PES Winter Power Meeting, 1974.

[11]. Thrash, F. Ridley, “ACSS/TW - An Improved Conductor for Upgrading Existing Lines or New Construction” IEEE Paper 0-7803-5515, June, 1999.

[12]. Kikuta, Takatashi, “Low Sag Up-rating Conductor”, IEEE Panel Session on Applications and Economics of New Conductor Types, Vancouver, BC, July, 2001.

[13]. Sato, K., Mori, N., et al, “Development of Extremely-Low-Sag Invar Reinforced ACSR (XTACIR), IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 4, April, 1981.

[14]. Tunstall, M.J., et al, “Maximizing the Ratings of National Grid’s Existing Transmission Lines Using High Temperature, Low-sag Conductor”, CIGRE Paper 22-202, Paris, France, August, 2000.

[15]. Johnson, Doug, "Composite Conductors - A New Overhead Conductor (ACCR)", IEEE Panel Session on Applications and Economics of New Conductor Types, Vancouver, BC, July, 2001.

[16]. Hiel, Clem, “Development of a composite reinforced aluminum conductor”, California Energy Commission Report, November, 2000.

[17]. Smith, Jack (Applied thermal Sciences), "Advanced carbon conductor project report", National Science Foundation, August, 2001.

Sag-Tension Calculations for Overhead Lines

[18]. Winkelman, P.F., "Sag-Tension Computations and Field Measurements of Bonneville Power Administration, AIEE Paper 59-900, June 1959.

[19]. Fink, D.G., and Beaty, H.W., "Standard Handbook for Electrical Engineers," 13th Edition, McGraw Hill.

[20]. Aluminum Company of America, "Graphic Method for Sag Tension Calculations for ACSR and Other Conductors."

[21]. Aluminum Association, "Stress-Strain-Creep Curves for Aluminum Overhead Electrical Conductors," Published 7/15/74.

[22]. Barrett, J.S., Ralston, P. And Nigol, O., “Mechanical Behaviour of ACSR Conductors,” CIGRE International Conference on Large High Voltage Electric Systems, September 1-9, 1982.

References

11-3

[23]. Rawlins, Charles B. “Some Effects of Mill Practice on the Stress Strain Behavior of ACSR,” presented at IEEE Winter Meeting, Tampa, FL, February, 1998.

[24]. Harvey, JR. Creep of Transmission Line Conductors. IEEE Trans., Vol. PAS-88, No. 4, pp. 281-285, April 1969.

[25]. Harvey, JR and Larson, RE. Creep Equations of Conductors for Sag-Tension Calculations. IEEE Paper C72 190-2.

[26]. Harvey, JR and Larson RE. Use of Elevated Temperature Creep Data in Sag-Tension Calculations. IEEE Trans., Vol. PAS-89, No. 3, pp. 380-386, March 1970.

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Energy Conversion Lab

TRANSMISSION LINE PARAMETERS

Parameters in the transmission lineresistance r, inductance L, capacitance CL and C are due to the effects of magnetic and electric fields around the conductor

Overhead transmission lineANSI voltage standard: 69kV, 115kV, 138kV, 161kV, 230kV, 345kV, 500kV, 765kV line-to-lineextra-high-voltage (EHV): >230kV, ultra-high-voltage (UHV): ≥765kVbundling: use more than one conductor per phase, usually used at voltage > 230kVadvantage of bundling: increase effective radius of line conductor, reduce electric field strength and reduces corona power loss, audio loss and radio interference, and reduces line reactance

Energy Conversion Lab

LINE RESISTANCE

Transmission line resistancedc flow: resistance of solid round conductor is given by Rdc=ρl/Aac flow: the current distribution is not uniform, the current density is greatest at surface of the conductor, this is called skin effect, therefore, Rac > Rdc

temperature: resistance increases when temperature increases

Transmission line inductancedefinition of inductance L: L=λ/I, λ is flux linkagemagnetic field density: Hx=Ix/2πx, x is the radius of circle, Ix induces magnetic field density Hx

Energy Conversion Lab

INTERNAL INDUCTANCE

Derivation of internal inductance Lintconsider the flux linked by the portion x ≤ r of current Ia flowing inside a cylinder of radius x, the magnetic intensity:

Since

magnetic flux density Bx: Bx=µoHx=µoxI /2πr2

µo is the permeability of free space: 4π×10-7 H/msince current flowing into the circuit of x is only a fraction of Ia, the effective turn is equivalent to the fraction N = πx2/πr2

∫ = enclosedIHdl

IrxI

rxIa 2

2

x2

2

xH2 ore theref,πππ

ππ

==

Energy Conversion Lab

INTERNAL INDUCTANCE

Derivation of internal inductance Lintπx2/πr2 turns of the current Ia linked by flux:dλx= (πx2/πr2) dφx = (πx2/πr2) (Bx×1dx)

= (πx2/πr2) (µoxI/2πr2) ×1dx = (µoI) x3/(2πr4) dxtotal flux linkage in the inductor:

inductor due to the internal flux: Lint=µo/8π=(1/2)×10-7 H/minductor Lint is independent of the conductor radius r

∫ ==r

oo IdxxrI

0

34int 82 π

µπµλ

Energy Conversion Lab

EXTERNAL INDUCTANCE

Derivation of external inductance Lextconsider Hx external to conductor at x>r, since the circle at radius x enclose entire current, Ix=I ( see Fig.4.4 ): Bx=µoHx=µoI/2πxthe entire current I is linked by the flux outside the conductor, dλx=dφx = Bxdx*1=µoI/(2πx)*dxexternal flux linkage between D1 and D2 :

inductance between two points D1 and D2 due to the external flux:

Wb/m ln10212

2

1 1

27∫ −×==D

Do

ext DDIdx

xIπ

µλ

H/mln102L1

27

DD

ext−×=

Energy Conversion Lab

INDUCTANCE OF A SINGLE-PHASE LINE

Single-phase line inductance in conductor 1 (L1)consider one meter length of two solid round conductors, radius r1 and r2 in the figure below:

internal inductance: L1(int) = (1/2)×10-7

inductance beyond D links a net current of zero and doesn’t contribute to net magnetic flux linkage, thus the external inductance L1(ext)= 2×10-7*ln(D/r1)total inductance of conductor 1:

D

1ln1021ln102ln10210

21 7

'1

7

1

77)(1(int)11

Drr

DLLL ext−−−− ×+×=×+×=+=

41

1'

1 where−

= err

r1 r2

Energy Conversion Lab

INDUCTANCE OF A SINGLE-PHASE LINE

Single-phase line inductancetotal inductance of conductor 2:

if r1=r2=r, inductance per phase per meter length of the line:

the first term is only the fraction of conductor radiusthe second term is dependent only on conductor spacingthe term r’=re-1/4 is called self-geometric meandistance of a circle with radius r by GMRGMR is called geometric mean radius

H/m1

ln1021ln102 7'

2

72

Dr

L −− ×+×=

H/m1

ln1021ln102 7'

7 Dr

L −− ×+×=

Energy Conversion Lab

FLUX LINKAGE IN TERMS OF SELF AND MUTUAL INDUCTANCES

Flux linkage in a single-phase two-wire lineflux linkage: self and mutual inductance:

for a group of n conductors: I1+I2+…+In=0the flux linkage of conductor i :

222212112111 )( )( ILLILL +−=−= λλ

DL

rL

rL 1ln102 ,1ln102 ,1ln102 7

12'2

722'

1

711

−−− ×=×=×=

ij 1ln1ln102

ij

1'

7i

1

≠

+×=

≠+=

∑

∑

=

−

=

n

j ijj

ii

n

jjijiiii

DI

rI

ILIL

λ

λ

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE TRANSMISSION LINES3-phase line with three symmetrical spacing conductors, the single-phase inductance L

balanced three-phase currents: Ia+Ib+Ic=0 total flux linkage of phase a (see fig.4.7):

substituting for Ib+Ic=-Ia, flux linkage of phase a:

per-phase per kilo-meter length L:

inductance per-phase of a three-phase circuit with equal spacingis the same as one conductor of a single-phase circuit

++×= −

DI

DI

rI cbaa

1ln1ln1ln102 '7λ

'7

'7 ln1021ln1ln102

rDI

DI

rI aaaa

−− ×=

−×=λ

mH/km ln2.0ln2.041' −

==re

DrDL

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE TRANSMISSION LINES3-phase line with three asymmetrical spacing conductors

even in balanced three-phase currents, the voltage drop due to different line inductance will be unbalancedthe phase a, b and c flux linkages:

use λ = LI the phase a, b, and c inductances:

where, a=1∠120o, the phase inductance contain imaginary term

++×=

++×=

++×=

−

−

−

'2313

7

23'

12

7

1312'

7

1ln1ln1ln102

1ln1ln1ln102

1ln1ln1ln102

rI

DI

DI

DI

rI

DI

DI

DI

rI

cbac

cbab

cbaa

λ

λ

λ

++×==

++×==

++×==

−

−

−

'2313

27

23

2'

12

7

1312

2'

7

1ln1ln1ln102

1ln1ln1ln102

1ln1ln1ln102

rDa

Da

IL

Da

rDa

IL

Da

Da

rIL

c

cc

b

bb

a

aa

λ

λ

λ

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE TRANSMISSION LINESTranspose line

practical transmission lines cannot maintain symmetrical spacingdue to the construction considerationsone way to regain symmetry and to obtain a per-phase model is to consider transpositiontransposition arrangement: interchange phase every one-thirdthe length (see Fig.4.9)for complete transposed lines, the inductance is the average value of L=(La+Lb+Lc)/3note a+a2=1∠120o+1∠240o=-1

rearrange equation L and we obtain ( pp.114-115 ):

GMD is geometric mean distance (equivalent conductor spacing)GMR is geometric mean radius (equivalent conductor radius)

H/m1ln1ln1ln1ln33102

132312'

7

−−−

×=

−

DDDrL

H/mln102ln102 7'

31323127

GMRGMD

rDDD

L −− ×=×=

Energy Conversion Lab

INDUCTANCE OF COMPOSITE CONDUCTORSIn practical transmission line, stranded conductors and bundled conductors are used. The inductance of the composite conductors are analyzed with GMR and GMDA bundled case of single phase line with n strands in xconductor and m strands in y conductor

current is assumed equally divided among strands (sub-conductor), current per strand in x is I/n, current per strand in y is I/mflux linkage about strand a: (from Eq. 4.43 pp.116)

inductance of strand a:

λ

L

anacabx

mamabaa

aDDDrDDD

IL

L'

''7 ln102 −×=

nanacabx

mamabaaa

aDDDrDDD

nnI L

L'

''7 ln102/

−×==λ

Energy Conversion Lab

INDUCTANCE OF COMPOSITE CONDUCTORSinductance of strand n:

average of the inductance in any strand in x

the equivalent inductance of conductor x in n strands

where GMD and GMRx are as follow:

nncnbnax

mnmnbnan

nDDDrDDD

nnI

LL

L'

''7 ln102/

−×==λ

nLLLLL ncba

av++++

=L

H/mln102 72

X

ncbaavx GMR

GMDn

LLLLn

LL −×=++++

==L

mnnmnbnaamabaa DDDDDDGMD )()( '''' LLL=

2 )()(nnnnbnaanabaaX DDDDDDGMR LLL=

Energy Conversion Lab

GMD AND GMR OF COMPOSITE CONDUCTORSDefinition of GMD:

mn th root of D’s product about any strand in x to strands in y

Definition of GMRX:nn th root of rx’ product about any strand in x to the other strands in x

GMR of the seven identical strands in a conductor

see example 4.1a large number of strands in GMR calculation would be tedious, usually GMRs are available in manufacturer’s data

Energy Conversion Lab

GMR OF BUNDLED CONDUCTORSExtra high voltage transmission lines are constructed with bundled conductorsAdvantages of the bundling:

reduce line reactanceincrease power capabilityreduce voltage surface gradient and corona lossreduce surge impedance

Common conductor bundling arrangementtwo sub-conductor bundling GMR:three sub-conductor bundling GMR:four sub-conductor bundling GMR:

dDD sbs ×=

9 3)( ddDD sbs ××=

16 421

)2( ××××= dddDD sbs

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE DOUBLE CIRCUITA three phase double circuit line consists of two identical three-phase circuitsThe circuits are operated with a1-a2, b1-b2, c1-c2in parallel as figure 4.13Geometric arrangement of three-phase double circuit

unbalanced with different spacing, cause unbalanced voltage dropto achieve balance, use transpose arrangement

To obtain inductance of three-phase double circuit line, we must

consider transpose effect of Lconsider bundle effect of Lcombine transpose and bundle effects together

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT

Calculation of the GMD: starting from the calculation of per-phase GMD: group identical phase togetherfind GMD between each phase group

equivalent GMD per phase isGMD

422122111

422122111

422122111

cacacacaAC

cbcbcbcbBC

babababaAB

DDDDD

DDDDD

DDDDD

=

=

=

3ACBCAB DDD=

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT

Calculation of the GMR: starting from the calculation of per-phase GMR: group identical phase togetherfind GMR between each phase group

where Dsb is the two-subconductor bundled

distanceequivalent GMR per phase is 3

SCSBSAL DDDGMR =

214 2

21

214 2

21

214 2

21

)(

)(

)(

ccbscc

bsSC

bbbsbb

bsSB

aabsaa

bsSA

DDDDD

DDDDD

DDDDD

==

==

==

Energy Conversion Lab

INDUCTANCE OF THREE-PHASE DOUBLE CIRCUIT

The per-phase inductance of the transpose line

where GMD:where GMR:for the inductance per-phase in mH/km

3SCSBSAL DDDGMR =

H/mln102ln102 7'

31323127

LGMRGMD

rDDD

L −− ×=×=

3ACBCAB DDDGMD =

mH/km ln2.0LGMR

GMDL =

Energy Conversion Lab

REVIEW OF LINE INDUCTANCEInternal inductance

Lint=µo/8π=(1/2)×10-7 H/m

External inductance

Single-phase line inductance

Three-phase line inductance (symmetrical spacing

H/mln102L1

27

DD

ext−×=

H/mln102L '7

rD−×=

H/mln102L '7

rD−×=

Energy Conversion Lab

REVIEW OF LINE INDUCTANCEThree-phase line inductance (transpose line)

Inductance of composite conductors in x group (n conductor in x, m conductor in y)

where where

Inductance of three-phase double-circuit line (per-phase)

H/mln102ln102L 7'

31323127

GMRGMD

rDDD −− ×=×=

H/mln102L 7

Xav GMR

GMD−×=

2 )()(nnnnbnaanabaaX DDDDDDGMR LLL=

mnnmnbnaamabaa DDDDDDGMD )()( '''' LLL=

H/mln102ln102L 7

3

37

LSCSBSA

CABCAB

GMRGMD

DDDDDD −− ×=×=

Energy Conversion Lab

LINE CAPACITANCE

Derivation of the line capacitanceconsider a long round conductor with radius r , carrying a charge of q coulombs per meter length:

electric flux density at a cylinder of radius x: D = q/A = q/(2πx)electric field intensityE = D/ε0 = q/(2πε0x)εo is the permitivity of free space: 8.85×10-12 F/mpotential difference between cylinders from D1 to D2

D1

D2x

1

2

0012 ln

222

1

2

1 DDqdx

xqEdxV

D

D

D

D πεπε∫∫ ===

Energy Conversion Lab

CAPACITANCE OF SINGLE-PHASE LINE

Derivation of the line capacitanceconsider two conductors with radius r , carrying a charge of q1 coulombs/meter in conductor 1 and q2in conductor 2voltage between conductor 1 and 2 by q1 or q2

potential difference due to q1 and q2 (q1=-q2)

capacitance between conductorsor

rDqV q ln

2 0

1)(12 1 πε=

rDqV q ln

2 0

2)(21 2 πε=

Drq

Drq

rDqVVV qq lnln

2ln

2 00

2

0

1)(12)(1212 21 πεπεπε

=+=+=

F/mln

012

rDC πε

= F/mln

2 0

rDC πε

=

Dq1 q2

Energy Conversion Lab

CAPACITANCE OF THREE-PHASE LINES

Derivation of the line capacitanceconsider one meter length of a three-phase line with three long conductors with radius r , transposed spacing shown in figure 4.18 a balanced three-phase system: qa + qb + qc = 0voltage between phase a and b in section I

voltage between phase a and b in section II

voltage between phase a and b in section III

++=

13

23

12

12

0)( lnlnln

21

DDq

Drq

rDqV cbaIab πε

++=

12

13

23

23

0)( lnlnln

21

DDq

Drq

rDqV cbaIIab πε

++=

23

12

13

13

0)( lnlnln

21

DDq

Drq

rDqV cbaIIIab πε

Energy Conversion Lab

CAPACITANCE OF THREE-PHASE LINESDerivation of the line capacitance (continue)

average value of Vab :

similarly, Vac :

for qb + qc=- qa, Vab+Vac :

for balanced three-phase voltagesVab+Vac=3Van from Eq.4.83

the capacitance per-phase to neutral

( )

+=++=

GMDrq

rGMDqVVVV baIIIabIIabIabab lnln

21

31

0)()()( πε

( )

+=++=

GMDrq

rGMDqVVVV caIIIacIIacIacac lnln

21

31

0)()()( πε

rGMDq

GMDrq

rGMDqVV a

aaacab ln23lnln2

21

0πεπε=

−=+

F/mln

2 0

rGMDV

qCan

a πε==

Energy Conversion Lab

EFFECT OF BUNDLINGDerivation of the line capacitance (bundling)

the effective radius of bundled conductor is rb

the capacitor per phase for bundled conductor

for two-subconductor bundle :

for three-subconductor bundle :

for four-subconductor bundle :

spacingbundleeffective

rGMDC

b

r where F/m,ln

2 b0 ==πε

drrb ×=

3 2drrb ×=

4 309.1 drrb ×=

Energy Conversion Lab

CAPACITANCE OF THREE-PHASE DOUBLE-CIRCUIT LINES

Derivation of the line capacitance (three-phase)the effective radius of bundled conductor is GMRc

the equivalent per-phase capacitance to neutral

GMRc per-phase to neutral :

effective radius for phase A, B, and C :

groupphasefor

GMRGMDC

c

is GMR where F/m,ln

2c

0πε=

3CBAc rrrGMR =

21

21

21

ccb

C

bbb

B

aab

A

Drr

Drr

Drr

=

=

=

Energy Conversion Lab

EFFECT OF EARTH ON THE CAPACITANCEThe electric flux lines for an isolated charged conductor are radial and are orthogonal to cylindrical equipotentialsurfacesEarth level is like equipotential surfaceTo simulate effect of equipotential surface, the earth level is replaced by a fictitious charged conductor

with charge equal and opposite to the charge on actual conductor at a depth below the surface of the earth the same as the heightof the actual conductor above earth

The effect of the earth can increase capacitancenormally due to the height >> distance between conductors, therefore, effect of earth is negligiblefor balanced steady-state analysis, effect of earth is neglectedfor unbalanced faults, earth’s effect is considered

Energy Conversion Lab

INDUCTIONMagnetic field induction

transmission line magnetic fields affect objects close to the linereason: line current produce magnetic field, magnetic fieldinduces voltage in objects that have a long length parallel to line

Magnetic field have been reported to affect (long term harm)

human bloodgrowth, behaviorimmune systemsneural functions

Electrostatic inductiontransmission line electric fields affect objects close to the linereason: high voltage produce electric field, electric field induces currents in objects in the area of the electric field

Concern of the Electrostatic induction (instant harm)human body may be exposed to steady current or spark discharge from charged objects

Energy Conversion Lab

CORONACorona

the partial ionization surrounding the conductor surfacereason: when surface potential gradient of a conductor exceeds the dielectric strength of the surrounding air, ionization occurs

Corona effectproduce power lossproduce audible noiseradio interference in the AM band

Corona is affected byconductor diameter, bundlingtype of conductorcondition of surface: air dust, humidity, wind

Corona can be reduced byincreasing the conductor sizeconductor bundling

1

UNIT 3

MODELLING AND PERFORMANCE OF

TRANSMISSION LINES

2

Introduction

Analyze the performance of single phase and balanced three-phase transmission lines under normal steady-state operating conditions.

Expression of voltage and current at any point along the line are developed, where the nature of the series impedance and shunt admittance is taken into account.

The performance of transmission line is measured based on the voltage regulation and line loadability.

3

Transmission Line Representation

ABCD

+

VR

-

+

Vs

-

Is IR

A line is treated as two-port network for which the ABCD parameters and an equivalent π circuit are derived.

4

Transmission Line Representation

To facilitate the performance calculations relating to a transmission line, the line is approximated as a series–parallel interconnection of the relevant parameters.

Consider a transmission line to have:

A sending end and a receiving end;

A series resistance and inductance; and

A shunt capacitance and conductance

5

Transmission Line Representation

The relation between sending–end and receiving–end quantities of the two–port network can be written as:

R

R

S

S

RRS

RRS

I

V

DC

BA

I

V

DICVI

BIAVV

6

Transmission Line Representation

Short Line Model < 80 km in length

Shunt effects are neglected.

Medium Line Model Range from 80–240 km in length

Shunt capacitances are lumped at a few predetermined points along the line.

Long Line Model >240 km in length.

Uniformly distributed parameters.

Shunt branch consists of both capacitance and conductance.

7

Short Line Model

l

VRVS

IRISR XL

Z

8

Short Line Model

length line

inductance phase-per

resistance phase-per

:where

L

r

jXR

LjrzZ

L

9

Short Line Model

Thus, the ABCD parameters are easily obtained from KVL and KCL equations as below:

SCZBpuDA

I

VZ

I

V

II

ZIVV

R

R

S

S

RS

RRS

0;;1

10

1

10

Medium Line Model – Nominal π Circuit

l

VR

IRISR XL

Z

VS Y/2 Y/2

11

Medium Line Model

Shunt capacitor is considered.

½ of shunt capacitor considered to be lumped at each end of the line – π circuit

Total shunt admittance, Y

length line

kmper econductanc line

kmper ecapacitanc neutral toline

:where

g

C

CjgY

12

Medium Line Model

Under normal condition,

shunt conductance per unit length (the leakage current) over the insulators and due to corona is negligible

Thus, g = 0

13

Medium Line Model

To obtain ABCD parameters, the current in the series branch is denoted as IL.

Using KCL and KVL, the sending–end voltage is:

3..2

1

2

2 and 1 From

2..2

1..

RR

RRRS

RRL

LRS

ZIVZY

VY

IZVV

VY

II

ZIVV

14

Medium Line Model

15

Medium Line Model

16

Medium Line Model

Using KCL to obtain equation for sending–end current:

5..2

14

1

221

2

4 into 3 and 2 Substitute

4..2

RR

RRR

RS

SLS

IYZ

VYZ

Y

YZIV

YZYVII

VY

II

17

Medium Line Model

Thus, the ABCD parameters can be obtained from equation [3] and [5];

SZY

YCZBpuZY

DA

I

V

ZYZYY

ZZY

I

V

R

R

S

S

41;;

21

21

41

21

18

Medium Line Model

ABCD constant are complex since π model

is a symmetrical two-port network

A = D

The determinant of the transmission matrix is unity(1)

AD – BC = 1 (Prove this!)

19

Medium Line Model

The receiving and quantities can be expressed in terms of the sending end quantities

If, ignore the shunt capacitance of the TL, the shunt admittance, Y=0, it become the short transmission line constant.

S

S

R

R

I

V

AC

BD

I

V

20

Medium Line Model – Nominal T Circuit

l

VR

IRIS

VS Y

Z/2 Z/2

Find the ABCD Parameters for this circuit using KVL and KCL

21

Long Line Model

l

VR

IRISZ’

VS Y’/2 Y’/2

22

Long Line Model

The shunt capacitance and series impedance must be treated as distributed quantities

The ‘V’ and ‘I’ on the line must be found by solving the differential equation of the transmission line.

23

Long Line Model

2tanh

1

2

2tanh

22

'

sinhsinh

'

c

c

c

Z

YY

ZZZ

y

zZzy

CjgyLjRz

24

Long Line Model

If γl <<0 sinh (γl )/( γl ) & tanh (γl /2)/ (γl /2) ≈ 1.0

The ABCD parameters:

12

'' D 1

4

'''

' 12

''

YZYZYC

ZBYZ

A

I

V

DC

BA

I

V

R

R

S

S

25

ABCD Parameters

ABCD Parameters

A B

C D

Short

Line

1 Z

0 1

Medium

π

Medium

T

Long

Line

26

Complex Power

Sending end power

Receiving end power

lineRlineRR

phaseRphaseRR

IVS

or

IVS

*

3

*

3

3

3

lineSlineSS

phaseSphaseSS

IVS

or

IVS

*

3

*

3

3

3

phaseline VV 3

Remember!

27

Transmission Line Efficiency

Total Full–Load Line Losses

Transmission Line Efficiency

Note that only Real Power are taken into account!

333 RSL SSS

100%

3

3

3

3

S

R

S

R

P

P

P

P

28

Voltage Regulation

ABCD parameters can be used to describe the variation of line voltage with line loading.

Voltage regulation is the change in voltage at the receiving end of the line when the load varies from no–load to a specified full–load at a specified power factor, while the sending end is held constant.

29

Voltage Regulation

RRFL

S

RNL VVA

VV

100%

RFL

RFLRNL

V

VVVR

No–load receiving–end voltage

Full–load receiving–end voltage

30

??

21

VV

VV

V

;

0:

AVV

SRNL

SRNL

RNL

RNLS

LineLong

ZYLineMedium

LineShort

A

V

Thus

IConditionLoadNo

BI

s

R

R

31

Voltage Regulation

The effect of load power factor on voltage regulation is illustrated in phasor diagram.

The phasor diagrams are graphical representation of lagging, unity and leading power factor.

32

Voltage Regulation

The higher (worse) voltage regulation occurs for the lagging pf load where VRNL exceeds VRFL by the larger amount.

A smaller or even negative voltage regulation occurs in leading pf load.

33

Voltage Regulation

In practice, transmission line voltages decrease when heavily loaded and increase when lightly loaded.

EHV lines are maintained within ±5% of rated voltage, corresponding to about 10% voltage regulation.

10% voltage regulation for lower voltage lines also considered good operating practice.

34

Line Loadability

Another important issue that affect transmission line performance.

3 major line loading limits are:

Thermal limit

Short transmission lines [<80 km length]

Voltage drop limit

Longer line length [ 80–300 km length]

Steady-state stability limit

Line length over 300 km

35

Example

A 220-kV, three-phase transmission line is 40 km long. The resistance per phase is 0.15 Ω/km and the inductance per phase is 1.5915 mH/km. The shunt capacitance is negligible. Use the line model to find the voltage and power at the sending end and the voltage regulation and efficiency when the line is supplying a three-phase load of

a) 381 MVA at 0.8 pf lagging at 220 kV

b) 381 MVA at 0.8 pf leading at 220 kV

36

Solution (a)

Given

R = 0.15 Ω/km , L = 1.5915 mH/km

S =381 MVA with pf 0.8 lag

VR(line)=220 kV

+

Vs

_

+

VR

_

Is IR

R jXL

Z=R+jωL Ω

37

206

405915.150215.0

Z

phase;per impedance series The

40km

j

mj

lLjr

kV

kV

VV

o

o

LineR

phaseR

0127

3

0220

3

RR

RRS

I and Z,,V find Therefore,

ZIVV voltage,end sending Find

38

A

kV

MVA

MjMWMVAS

Thus

o

o

o

o

R

o

87.361000

01273

87.36381

3V

S I

3V

S I

I3VS

var6.2288.30487.36381

,

87.368.0cos MVA, 381S

*

R(Phase)

*

RR

R(Phase)

R*

R

*

RR(Phase)R

-1

39

250V

144.33

3

93.4144.3

87.3610002060127

VV

Therefore,

PhaseRS(Phase)

PhaseSLineS

o

oo

R

VV

kV

AjkV

ZI

40

SILineSS 3V S Power, end-Sending Find

MVA

MjMW

AV

AII

o

o

o

RS

8.41433

var6.2888.322

87.3610004.93144.33 3

I3VS

87.361000

o

*

RR(Phase)S

41

%6.13

100220

220250

100 %VR

RFL

RFLRNL

V

VV

Voltage Regulation,

%4.94

1008.322

8.304

100 %

S

R

P

P

Effiency,η

INSULATORS AND CABLES

Insulators:

• An insulator, also called a dielectric, is a material that resists the flow of electric current. An insulating material has atoms with tightly bonded valence electrons. These materials are used in parts of electrical equipment, also called insulators or insulation, intended to support or separate electrical conductors without passing current through themselves. The term is often used more specifically to refer to insulating supports that attach electric power transmission wires to utility poles or pylons.

• Some materials such as glass or Teflon are very good electrical insulators. A much larger class of materials, for example rubber-like polymers and most plastics are still "good enough" to insulate electrical wiring and cables even though they may have lower bulk resistivity. These materials can serve as practical and safe insulators for low to moderate voltages (hundreds, or even thousands, of volts).

http://en.wikipedia.org/wiki/Image:Ceramic_electric_insulator.jpg

Insulators:

• Insulators are used for high-voltage power transmission are made from glass, porcelain, or composite polymer materials. Porcelain insulators are made from clay, quartz or alumina and feldspar, and are covered with a smooth glaze to shed dirt. Insulators made from porcelain rich in alumina are used where high mechanical strength is a criterion.

• Porcelain has a dielectric strength of about 4-10 kV/mm. Glass has a higher dielectric strength, but it attracts condensation and the thick irregular shapes needed for insulators are difficult to cast without internal strains. Some insulator manufacturers stopped making glass insulators in the late 1960s, switching to ceramic materials.

Insulators:

• Recently, some electric utilities have begun converting to polymer composite materials for some types of insulators. These are typically composed of a central rod made of fibre reinforced plastic and an outer weathershed made of silicone rubber or EPDM.

• Composite insulators are less costly, lighter in weight, and have excellent hydrophobic capability. This combination makes them ideal for service in polluted areas. However, these materials do not yet have the long-term proven service life of glass and porcelain.

• Design

• Cap and pin insulator string (the vertical string of discs) on a 275 kV

suspension pylon. The electrical breakdown of an insulator due to excessive voltage can occur in one of two ways:Puncture voltage is the voltage across the insulator(when installed in its normal manner) which causes a breakdown and conduction through the interior of the insulator. The heat resulting from the puncture arc usually damages the insulator irreparably.

• Flashover voltage is the voltage which causes the air around or along the surface of the insulator to break down and conduct, causing a 'flashover' arc along the outside of the insulator. They are usually designed to withstand this without damage. High voltage insulators are designed with a lower flashover voltage than puncture voltage, so they will flashover before they puncture, to avoid damage.

Insulators:

Insulators:

• Dirt, pollution, salt, and particularly water on the surface of a high voltage insulator can create a conductive path across it, causing leakage currents and flashovers. The flashover voltage can be more than 50% lower when the insulator is wet. High voltage insulators for outdoor use are shaped to maximise the length of the leakage path along the surface from one end to the other, called the creepage length, to minimize these leakage currents.

• To accomplish this the surface is molded into a series of corrugations or concentric disk shapes. These usually include one or more sheds; downward facing cup-shaped surfaces that act as umbrellas to ensure that the part of the surface leakage path under the 'cup' stays dry in wet weather. Minimum creepage distances are 20-25 mm/kV, but must be increased in high pollution or airborne sea-salt areas.

Cables

• A cable is one or more strands bound together. Electrical cables may contain one or more metal conductors, which may

be individually insulated or covered. An optical cable contains one or more optical fibers in a protective jacket that supports

the fibers. Mechanical cables such as wire rope may contain a large number of metal or fiber strands.

Cables

• Electrical cables may be made flexible by stranding the wires. The technical issue is to reduce the skin effect voltage drop while using with alternating currents.In this process, smaller individual wires are twisted or braided together to produce larger wires that are more flexible than solid wires of similar size. Bunching small wires before concentric stranding adds the most flexibility.

• A thin coat of a specific material (usually tin-which improved striping of rubber, or for low friction of moving conductors, but it could be silver, gold and another materials and of course the wire can be bare - with no coating material) on the individual wires. Tight lays during stranding makes the cable extensible (CBA - as in telephone handset cords).

Cables

• Bundling the conductors and eliminating multi-layers ensures a uniform bend radius across each conductor. Pulling and compressing forces balance one another around the high-tensile center cord that provides the necessary inner stability. As a result the cable core remains stable even under maximum bending stress.

• Cables can be securely fastened and organized, such as using cable trees with the aid of cable ties or cable lacing. Continuous-flex or flexible cables used in moving applications within cable carriers can be secured using strain relief devices or cable ties. Copper corrodes easily and so should be layered with Lacquer.

SUBSTATION, GROUNDING

SYSTEM AND DISTRIBUTION

SYSTEM