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INDEX

S.L.D.G. 5 - GENERAL PARAMETERS AND RULES FOR THEDESIGN OF A.C. SUBSTATIONS

5-0 Index

5-1 General Criteria And Rules For The Design OfA.C. Substations

S.L.D.G. 6 - BUSBAR ARRANGEMENTS

6-0 Index

6-1 Switching Arrangements.

6-2 Static And Dynamic Stress On TubularConductor Busbar Systems

6-3 Miscellaneous Information On Busbar Systems

S.L.D.G. 7 - INSULATION AND CLEARANCES

7-0 Index

7-1 Insulation Levels And Creepage Distances

7-2 Electrical And Working Clearances

7-3 Standard Number Of Insulator Discs

7-4 Corona Limits

7-5 Tan Delta and Power Factor

S.L.D.G. 8 - SUBSTATION EARTHING

8-0 Index

8-1 Earth-mat Design

8-2 Copper Earthing Conductor Sizes

S.L.D.G. 9 - SUBSTATION FLEXIBLE CONDUCTORS,TUBULAR CONDUCTORS, EARTH-WIRES,EARTH-MAT COPPER AND INSULATED CABLES

9-0 Index

9-1 Substation Flexible Conductors, Earth-wiresAnd Earth-mat Copper

9-2 All Aluminium Conductors

9-3 Aluminium Alloy Conductors

9-4 SCA Conductors

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2001Transmission Substation Design & Applications

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INDEX

S.L.D.G. 9(Continued)

9-5 Copper Conductors And Earthing Materials

9-6 Tubular Conductors

9-7 Proposed Standard Aluminium TubularConductors

9-8 Insulated Cables

S.L.D.G. 10 - TERMINALS, STEMS, CLAMPS AND YARDHARDWARE

10-0 Index

10-1 Equipment Terminal Stems

10-2 Substation Current Carrying Clamps10-3 Standard Substation Clamps And Accessories

For Flexible Conductors

10-4 Standard Substation Clamps And AccessoriesFor Tubular Conductors

10-5 Standard Range Of Substation Hardware

S.L.D.G. 11 - CIRCUIT BREAKERS

11-0 Index

11-1 Standard Circuit Breaker Ratings

11-2 Application Guide

S.L.D.G. 12 - ISOLATORS

12-0 Index

12-1 General Information

12-2 Pantograph Isolators

12-3 Isolator Auxiliary Contacts

S.L.D.G. 13 - INSTRUMENT TRANSFORMERS

13-0 Index

13-1 Introduction

13-2 Current Transformers

13-3 Electromagnetic And Capacitive VoltageTransformers

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INDEX

S.L.D.G. 14 - SURGE ARRESTERS

14-0 Index

14-1 Scope

14-2 Zinc Oxide (ZnO) Surge Arrester ApplicationGuide

14-3 Schedule Of Surge Arrester ProtectiveDistances For Transformers

S.L.D.G. 15 - POWER AND AUXILIARY TRANSFORMERS

15-0 Index

15-1 Standard Power Transformers15-2 Power Transformer Application Guide

15-3 Standard Transformers : In-built CurrentTransformers

15-4 Substation Auxiliary Transformers

S.L.D.G. 16 - SHUNT AND SERIES REACTORS, ANDEARTHING COMPENSATORS

16-0 Index

16-1 Shunt Reactors

16-2 Series Current Limiting Reactors

16-3 Earthing Compensators

S.L.D.G. 17 - CAPACITORS - SHUNT AND SERIES

17-0 Index

17-1 Shunt Capacitors

17-2 Series Capacitor Application And Protection

S.L.D.G. 18 - STATIC VAR COMPENSATORS (SVCS)

18-0 Index

18-1 Static VAr Compensators

S.L.D.G. 19 - TELECOMMUNICATIONS EQUIPMENT ANDCOMMUNICATION ROOM LAYOUT

19 - 0 Index

19 - 1 Carrier Coupling Arrangements

19 - 2 Communication Room Layout

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INDEX

S.L.D.G. 20 - CIVIL WORKS

20-0 Index20-1 Standard Civil Details

20-2 Cut / Fill Calculations

20-3 Application Guide

20-4 Transformer Plinth and Fire Protection

20-5 Application Guide For Substation Fencing

S.L.D.G. 21 - STEELWORK

21-0 Index

21-1 Busbar Steelwork Details

21-2 Steelwork Schedules For Various SystemVoltages

S.L.D.G. 22 - SUBSTATION AND POWER STATION H.V. YARDOPERATIONAL LIGHTING

22-0 Index

22-1 Operations And Maintenance Standard ForThe Lighting Of High Voltage Stations

22-2 Operational Lighting Design Principles

22-3 An Example Of Operational LightingSpecifications, Design And Implementation.

S.L.D.G. 23 - SUBSTATION LAYOUT PROJECT DRAWINGSAND DESIGN DRAUGHTING STANDARDS

23-0 Index

23-1 Information For The Production Of SubstationLayout Project Drawings

23-2 Design Draughting Standards

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INDEX

S.L.D.G. 24 - BAY LAYOUT SCHEDULE

24-0 Index

24-1 Standard Bays General Philosophy

24-2 Overhead Strung Busbar Arrangements forSubstation with Protection housed in a CentralControl Room

24-3 Overhead Strung Busbar Arrangements forSubstation with Modular Bay Protection

24-4 Tubular Busbar Arrangements for Substationswith Protection Housed in a CentralizedControl Room

24-5 Tubular Busbar Arrangement for Substationswith Module by Protection

S.L.D.G. 25 - SLACKSPAN SCHEDULES

25-0 Index

25-1 Introduction

S.L.D.G. 26 - COST ESTIMATING

26-0 Index

26-1 Substation Project Cost Estimating

26-2 Transformer Cost Calculations For EstimatingAnd Budgetary Purposes

S.L.D.G. 27 - ESKOM NATIONAL CONTRACTS (ENC)

27-0 Index

27-1 ENC Details

27-2 Typical Order Forms

S.L.D.G. 28 - FAULT ANALYSIS

28-0 Index

28-1 Incident Investigations

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INDEX

S.L.D.G. 29 - HIGH VOLTAGE DIRECT CURRENT SYSTEM

29-0 Index29-1 High Voltage Direct Current (HVDC) Systems

S.L.D.G. 30 - GAS INSULATED SWITCHGEAR

30-0 Index

30-1 Introduction

30-2 Typical Bays

30-3 Containerized GIS Switchgear

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S.L.D.G. 1 - 0

GENERAL

INDEXDOCUMENT REVISION TITLE

S.L.D.G. 1-0

S.L.D.G. 1-1

S.L.D.G. 1-2

2

1

1

INDEX

INTRODUCTION

CODING, REVISIONS AND DISTRIBUTION OF DESIGNGUIDE1. Coding2. Indexing

3. Revisions3.1 Type-written Documents3.2 Diagrams

4. Distribution

S.L.D.G. 1-3 0 MISCELLANEOUS PHYSICAL, CHEMICAL ANDTECHNICAL INFORMATION1. Electrochemical Series2. Moments Of Resistance And Moments Of Inertia3. Geometry, Calculation Of Areas And Volumes Of

Solid Bodies3.1 Area Of Polygons

3.2 Areas And Centres Of Gravity3.3 Volumes And Surface Areas Of Solid Bodies3.4 Logarithmic And Trigonometrical Relationships3.5 Conversion Tables : Imperial - Metric

4. General Electrotechnical Formulae And Tables4.1 Electro-technical Symbols4.2 Alternating-current Quantities4.3 Forms Of Power In An Alternating-current Circuit4.4 Resistances And Conductances In An Alternating-

current Circuit4.5 Alternating-current Quantities Of Basic Circuits4.6 Electric Resistances

4.6.1 Definitions and specific values4.6.2 Resistances in different circuit

configurations

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INTRODUCTION

Although a great deal of information relating to the design of substations is availablein one form or another, it is often not readily accessible. Design times areconsequently prolonged unnecessarily because of the need to search for data or torepeat calculations that may have been done many times before.

The first object of this Design Guide is thus to assemble into one manual (or set ofmanuals) as much basic design data as possible.

Where applicable, reference is made to the source of the data e.g. Eskom Standard,S.A.B.S Standard, etc., and here it must be stressed that the Design Guides are inno way intended to supersede any Standard documents. The basic data is merelyrepeated for ease of reference and it follows that every effort will be made to ensurethat the manual is updated in line with any changes to the relevant Standard. This isnot expected to be necessary very often.

The second objective of the Design Guide is to introduce a measure ofStandardisation.

For a variety of reasons including site orientation, topography and environment, loadrequirements and local network configurations, the layouts of even similarsubstations can rarely be made identical. Individual components ranging formclamps through to complete bays do, however, lend themselves to standardisationand by concentrating on the development of these building-blocks, significantcontributions can be made towards:

Reduction of design times

Smaller stocks of less items

Better use of manufacturing resources and hence better deliveries

Improved estimating techniques

Greater accuracy in forecasting of material for bulk buying and productionplanning purposes.

The guides are not expected to cater for every possible case that can arise inpractice, but the general principles outlined should be followed wherever possible.

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S.L.D.G. 1 - 2

CODING, REVISIONS AND DISTRIBUTION OF DESIGN GUIDE

1. CODING

All documents comprising the Substation Layout Design Guide will be codedwith the following:

a) An alpha abbreviation - S.L.D.G.(Substation Layout Design Guide).

b) This will be followed by a series of numerals, the first group of thatdenotes the Design Guide number while the second group defines thedocument or topic. The two groups of digits will be separated by adash or hyphen.

Example: S.L.D.G. 11-4

This implies that Substation Layout Design Guide No. 11, document ortopic No. 4. Where sketches (or figures) are involved these will begiven numeric figure identifications in addition to their coding as theremay be a series of sketches associated with one topic.

Example: Fig. 1, Fig. 2, etc.

For cross-reference between sketches within the same topic, only thefigure number need be quoted e.g. See Fig. 3.

For cross-reference between sketches in different topics the full codemust be quoted e.g. See S.L.D.G. 6-2 Fig. 1.

2. INDEXING

The General Index for the full Design Guide series will be logged under theCode S.L.D.G. 0 and identifies the subject covered by each Design Guide.This appears at the very front of the manual.

Each individual Design Guide will carry its own index sheet coded with thedocument number 0.

Example: S.L.D.G. 12-0.

This means that it is the Index Sheet for Design Guide No. 12. This Indexidentifies the various topics covered by that particular Design Guide andrecords latest revisions.

3. REVISIONS

3.1 Type-written Documents

On all type written documents revisions will be recorded as a stroke

number following the document or topic number

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Example: S.L.D.G. 16-3/1

The full code shall appear in the top right -hand corner and the date inthe top left-hand corner of the document.

3.2 Diagrams

For all diagrams a revision and date column is provided in thestandard drawing format.

4. DISTRIBUTION

The publication of this manual and its updating is the responsibility of theChief Engineer (Substation Design and Applications) and the masterdocument shall be kept in his possession.

The Chief Engineer (Substation Design and Applications) will arrange forHead Office Services section to print copies of the document and to distributethese in accordance with Table 1.

Each time a revision of a type written document or diagram is issued, therevision shall be accompanied by the revised index sheet associated with therelevant Design Guide. This will enable the recipient to check that his manualis complete, up-to-date and that no previous issues have been mislaid orgone astray.

To cover minor errors such as a spelling or typing mistake an erratum sheetwill be issued form which the manuals can be corrected by hand.

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TABLE 1

DISTRIBUTION LIST FOR

SUBSTATION LAYOUT DESIGN GUIDE

No. of Copies Recipient Copy Number

1

1

1

1

1

5

1

1

1

1

1

1

1

1

5

1

MANAGER (TRANSMISSION SUBSTATION &LINES DESIGN AND APPLICATIONS)

MANAGER (NETWORK OPERATIONSENGINEERING)

MANAGER (TRANSMISSION EXPANSIONPLANNING)

MANAGER (SYSTEM OPERATIONS)

MANAGER (TRANSMISSION PROJECTS)

REGIONAL MANAGER (NORTH)

REGIONAL MANAGER (NORTH WEST)

REGIONAL MANAGER (NORTH EAST)

REGIONAL MANAGER (EAST)

REGIONAL MANAGER (CENTRAL)

REGIONAL MANAGER (SOUTH)

REGIONAL MANAGER (WESTERN)

MANAGER (NEW BUSINESS VENTURES)

CHIEF ENGINEER (SUBSTATION DESIGN &APPLICATIONS)

CHIEF ENGINEER (LINE DESIGN &APPLICATIONS)

1

2

3

4

5, 6, 7, 8 & 9

10

11

12

13

14

15

16

17

18, 19, 20, 21 &22

23

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S.L.D.G. 1 - 3

MISCELLANEOUS PHYSICAL, CHEMICAL AND TECHNICAL

INFORMATION

1. ELECTROCHEMICAL SERIES

If different metals are joined together in a manner permitting conduction, and bothare wetted by a liquid such as water, acids, etc., an electrolytic cell is formedwhich gives rise to corrosion. The amount of corrosion increases with thedifferences in potential. If such conducting joints cannot be avoided, the twometals must be insulated from each other by protective coatings or byconstructional means. In outdoor installations, therefore, aluminium / copperconnectors or washers of copper-plated aluminium sheet are used to joinaluminium and copper, while in dry indoor installations aluminium and copper maybe joined without the need for special protective measures.

Table 1 : Electrochemical Series, Normal Potentials Against Hydrogen,In Volts.

1. Lithium approx. -3,02 15. Cobalt approx. -0,26

2. Potassium approx. -2,95 16. Nickel approx. -0,20

3. Barium approx. -2,80 17. Tin approx. -0,146

4. Sodium approx. -2,72 18. Lead approx. -0,132

5. Strontium approx. -2,70 19. Hydrogen approx. -0,00

6. Calcium approx. -2,50 20. Antimony approx. +0,20

7. Magnesium approx. -1,80 21. Bismuth approx. +0,20

8. Aluminium approx. -1,45 22. Arsenic approx. +0,30

9. Manganese approx. -1,10 23. Copper approx. +0,35

10. Zinc approx. -0,77 24. Silver approx. +0,80

11. Chromium approx. -0,56 25 Mercury approx. +0,86

12. Iron approx. -0,43 26. Platinum approx. +0,87

13. Cadmium approx. -0,42 27. Gold approx. +1,50

14. Thallium approx. -0,34

If two metals included in this table come into contact, the metal mentioned first will

corrode.

The less noble metal becomes the anode and the more noble acts as thecathode. As a result, the less noble metal corrodes and the more noble metal isprotected.

Metallic oxides are always less strongly electronegative, i.e. nobler in theelectrolytic sense, than the pure metals. Electrolytic potential differences cantherefore also occur between metal surfaces that to the engineer appear very littledifferent. Even though the potential differences for cast iron and steel, forexample, with clean and rusty surfaces are small, as shown in Table 2, undersuitable circumstances these small differences can nevertheless give rise to

significant direct currents, and hence corrosive attack.

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Table 2: Standard Potentials Of Different Types Of Iron AgainstHydrogen, In Volts

SM steel, clean surface approx. -0.40 cast iron, rusty approx. -0.30

cast iron, clean surface approx. -0.38 SM steel, rusty approx. -0.25

2. MOMENTS OF RESISTANCE AND MOMENTS OF INERTIA

Table 3: Moments Of Resistance And Moments Of Inertia

Moment Of Resistance Moment Of Inertia

Cross-section

TorsionW

(cm3)

Bending (1)W

(cm3)

Polar (1)Jp

(cm4)

Axial (2)J

(cm4)

dxx

0,196.d3

0,2.d3

0,198.d3

0,2.d3

0,098.d4

0,1.d4

0,049.d4

0,05.d4

Dx d

0,096. (D4-d

4)

D0,098. (D

4-d

4)

D0,098.(D

4-d

4)

0,049.(D4-d

4)

(D4-d

4)

20

x x

a

0,208 . a3 0,018 . a

3 0,167 . a

4 0,083 . a

4

b

x x h

0,208 . k.b2.h (3)

b.h2= 0,167.b.h

2

6b.h = (b

2+h

2)

12b.h

3= 0,083.b.h

3

12

B

x x H

b

B.H3- b.h

3

6HB.H

3- b.h

3

12

B

x x Hh

b/2 b/2

B.H3- b.h

3

6HB.H

3- b.h

3

12

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Table 3 : Moments Of Resistance And Moments Of Inertia(Continued)

Cross- Moment Of Resistance Moment Of Inertia

section Torsion

W(cm3)

Bending (1)

W(cm3)

Polar (1)

Jp(cm4)

Axial (2)

J(cm4)

b

x x

B

h H

B.H3- b.h

3

6HB.H

3- b.h

3

12

x x hoh

b bo

b.h3 b0.h0

3

6hb.h

3 b0.h0

3

12

(1) Referred to CG of area.(2) Referred to plotted axis.(3) Values for k: if h: b = 1 1,5 2 3 4

then k = 1 1,11 1,18 1,27 1,36

3. GEOMETRY, CALCULATION OF AREAS AND VOLUMES OF SOLID BODIES

3.1 Area ofPolygons

S r

R

R

A d D

FIGURE 1 : REGULAR POLYGONS(n ANGLES)

The area A, length sides Sand radii of the outer andinner circles can be taken from Table 4 below.

Table 4 : Area Of Regular Polygons

No. ofsides

AreaA

SideS

Outer radiusR

Inner radiusr

n S2. R

2. r

2. Rx. rx. Sx. rx. Rx. Sx.

34568

1012

0,43301,00001,72502,59814,8284

7,694211,196

1,29902,00002,37762,59812,8284

2,93893,0000

5,19624,00003,63273,46413,3137

3,24923,2154

1,73211,41421,17561,00000,7654

0,61800,5176

3,46412,00001,45311,15470,8284

0,64980,5359

0,57740,70710,85071,00001,3066

1,61901,9319

2,00001,41421,23611,15471,0824

1,05151,0353

0,50000,70710,80900,86600,9239

0,95110,9659

0,28870,50000,68820,86601,2071

1,53881,8660

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Table 5.1 : Area Of Irregular Polygons

Irregular Polygons

h1

A1

h2

A2

g1 g2g3

A3

h3

...h.gh.g2

1

.....2

h.g

2

h.gA

2211

2211

++

Table 5.2 : Area Of Regular Polygons

Pythagoras Theorem

b2 b

ac

a2

c2

a2 = c

2 - b

2; a =

22 bc b

2 = c

2 - a

2; b =

22 ac c

2 = a

2 + b

2; c =

22 ba+

3.2 Areas and Centres of Gravity

Table 6: Areas And Centres Of Gravity

Shape ofSurface

A = areaC = perimeterS = centre of gravity(cg)e = distance of cg

Triangle

a

h c b

a

e

S

e

hc

b

S

A = a.h

C = a + b + c

halving a and b givese = . h

Trapezium

hd

a

S

e

c

b

A = (a + b).h

C = a + b + c + d

e = . (a + 2.b).ha + b

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Table 6: Areas And Centres Of Gravity (Continued)

Quadrangle

c

b

a

d

D

h1

h2

A = .(h1 + h 2).D

C = a + b + c + d

Rectangle

b

a

e

S

A = a.bC = 2.(a + b)(Square : a = b, A = a

2, C = 4.a)

Parallelogram

h

a

A = a.h C = 2.(a+b)

Circle segment b

r

s

e

S

o180

r..=

2

b.r=A

2o

o

2o

90

r..=b

C = 2.r + b

o

o

o180

.R.sin

.3

2=e

Shape OfSurface

A = areaC = perimeterS = centre of gravity (cg)e = distance of cg

Semicircle

re

S

2.R.

2

1=A

C = r . (2 + ) = 5,14 . r,425.r0.

R.

3

1=e

Circle

r

dS

A =. R2 = .d24C = 2..r = .d

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Annularsegment

B

S

b

R

e

r

)r- 22o

o

.(R.

180

=A C = 2.(R - r) + B + b

o

o22

22 180.

sin.

)r-(R

)r-(R.

3

2=e

Semi- annulus

e

b

r RS

)r- 22.(R.2

1=A

If b < 0,2.R, then

e 0,32.(R + r)

Annulus

Sr

R

dD

)r- 22.(R=A C = 2..(R + r)

Circularsegment

S

b

h1

h

s

er

22

2o

o

hr.2s

2

h.sr..

180A

=

A

s.

12

1e

.r..90

hr.2C

2

o

o22

=+

Circularsegment

h

sr

b

=+

22.r.sins

8.h

s

2

hr

2

.ssb.r.2

1A

Sin180

.2

1=A

o

o

+ [ ]h

r. 2

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Shape ofsurface

A = areaC = perimeterS = centre of gravity (cg)e = distance of cg

Ellipse

S b

a

A = .a.b. C = .(a+b) (approx.)

Solid rectangle

a

bc

V = a.b.c

O = 2.(a.b + a.c + b.c)

Cube

a

d

V = a3= d

3 (d = a)

2

O = 6.a2= 3.d

2

Prism

h

A

V = A.h

O = C.h + 2.A

A = base surface

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3.3 Volumes And Surface Areas Of Solid Bodies

Table 7: Volumes And Surface Areas Of Solid Bodies

Shape Of Body V = Volume

O = SurfaceA = Area

Pyramid

h

A

V = . A.h

O = A + Nappe

Cone

s

r A

h

V = . A.h.O = .r.s + .r 2S = (h2 + r 2)

Truncatedcone

h

r A1

A

S

R

V = (R2+ r

2+ R.r). . .h

O = (R + r)..s + .(R2 + r 2)S = h2+ (R 2 - r 2)

Truncatedpyramid

h

A1

A

V = .h.(A + A1 + A.A1)

O = A + A1 + Nappe

Sphere

r

d

V = 4. .r33

O = 4. .r2

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Table 7: Volumes And Surface Areas Of Solid Bodies (Continued)

Shape Of Body V = VolumeO = SurfaceA = Area

Hemisphere

r

V = 2..r3 3

O = 3..r2Sphericalsegment h

r

V = .h2.(r - .h)O = 2..r.h + .(2.r.h - h2)

= .h.(4.r - h)Sphericalsector h

r

s

V = 2. .r2.h3

O = ..r.(4.h + s)

Zone of sphere b

h

r a

V = ..r.(3.a2 + 2.b 2 + h 2)O = .(2.r.h + a2 +b 2)

Obliquely cutcylinder A1

h1 r

A

h

V = ..r2.(h + h1)O = .r.(h + h1) + A + A1

Cylindrical

wedge

A h

r

V = .r2.h

O = 2.r.h + ..r2 + A

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Table 7: Volumes And Surface Areas Of Solid Bodies (Continued)

Shape Of Body V = VolumeO = SurfaceA = Area

Cylinder

h

r

V = .r2.hO = 2. .r.h + 2. .r2

Hollowcylinder

h

R

r

V = .h (R2- r 2)O = 2. .h (R + r) +2. (R

2

- r

2

)

Barrel

Dd

l

V = .l.(2.D2 + D.d + 0,75.d 2)15

O = (D + d). .d + . .d2(approx.)

Frustum

A

A1

h

V = ((A + A1) + A1).h

O = A + A1 + areas of sides

Body ofrotation (ring)

A

V = 2...AA = cross-section

O = circumference of cross-

section x 2..Pappustheorem forbodies ofrevolution

A

1

Volume of turned surface (hatched) xpath of its centre of gravity

V = 2.A.. Length of turned line x path of its centreof gravity

O = 2.L.. 1

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3.4 Logarithmic and Trigonometrical Relationships

Table 8: Logarithmic And Trigonometrical Relationships

Powers nman

.am

a;n

(a.b)n

.bn

a +=

0aforn

a

1na1;

0a;

m.na

n)

m(a =

Roots

mb

m amb

a;mb.m am a.b =

Logarithms

b = Basea = Antilogarithms

in general : log ba = nlog b1 = 0; log bb = 1

Logarithms

a.logn

1alog

an.logalog

bn

b

bn

b

==

Powersnm

an

a

ma

;

n

b

a

nb

na =

Roots

m.n am n a

nm am na;

m.n nman a.m a

===

Logarithms

clogalogc

alog

clogalog(a.c)log

bbb

bbb

+

Quadratic equation

2.a

4a.cbbx

0cb.xa.x2

1,2

2

==

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Table 8 : Logarithmic And Trigonometrical Relationships(Continued)

Binomical expansion32233

222

b3.a.b.b3.aaba

b2.a.baba + Cosine theorem

a

b

c

cos.2.a.bbac

cos.2.a.ccab

cos.2.b.ccba

222

222

222

Additional theorems

sin.sincos.cos)cos(

sin.cos.cossin)sin(

m

Additional theorems=

cotcot

1cot.cot)cot(

m

Triangle

a

b

c

a

bcot

b

atan

c

bcos

c

asin

==

Sine theorem

b

c

a

sincsinbsina

Additional theorems = tan.tan1 tantan)tan( m

Transformation of trigonometrical functions

1cot.tan

cos

sin

tan1;2

cos2

sin = =

Transformation of trigonometrical functions == 2cot11

2tan1

tan2cos1sin

Transformation of trigonometrical functions == cot1

cos

cos1

sin1

sintan

2

2

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Table 8: Logarithmic And Trigonometrical Relationships(Continued)

Transformation of trigonometrical functions == 2cot1cot2tan1 12sin1cos

Transformation of trigonometrical functions == tan1cos1cos

sin

sin1cot

2

2

Functions of double angles

222 2.sin1sincos)cos(2.

.cossin)sin(2.

Functions of half-angles

2

cos1

2cos

2

cos1

2ins

==

Functions of double angles

2

tancot

2.cot

1cot)cos(2.

tancot

2

tan1

.2.tan)tan(2.

2

2

===

Functions of half-angles

======sin

cos1

cos1

sin

cos1

cos1

2cot

sin

cos1

cos1

sin

cos1

cos1

2tan

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3.5 Conversion Tables

Table 9 : Velocity

Multiply the dimension in the appropriate column below.

To obtaindimension

below

Centi-metres

persecond

Metresper

second

Metresper

minute

Kilo-metres

perminute

Kilo-metres

perhour

Feetper

second

Feetper

minute

Milesper

minute

Milesper

hour

Knots

by the factor in the same column

Centimetres/second

1 100 1,667 1667 27,78 30,48 0,5080 2682 44,70 51,48

Metres/ second

0,01 1 1,66710

-2

16,67 0,2778 0,3048 5,080. 10

-3

26,82 0,4470

0,5148

Metres /minute

0,6 60 1 1000 16,67 18,29 0,3048 1609 26,82 30,88

Kilometres/ minute

0,0006 0,06 0,001 1 1,667. 10

-2

1,829. 10

-2

3,048. 10

-4

1,609 2,682. 10

-2

3,088. 10

-2

Kilometres/ hour

0,036 3,6 0,06 60 1 1,079 1,829. 10

-2

96,54 1,609 1,853

Feet /

second

3,281

. 10-2

3,281 5,468

. 10-2

54,68 0,9113 1 1,667

. 10-2

88 1,467 1,689

Feet / minute 1,969 196,8 3,281 3281 54,68 60 1 5280 88 101,3

Miles /minute

3,728. 10

-4

3,728. 10

-2

6,214. 10

-4

0,6214 1,036. 10

-2

1,136. 10

-2

1,892. 10

4

1 1,667. 10

-2

1,919. 10

-2

Miles/ hour

2,237. 10

-2

2,237 3,728. 10

-2

37,28 0,6214 0,6818 1,136. 10

-2

60 1 1,152

Knots(Nauticalmiles / hour)

1,943. 10

-2

1,943 3,238. 10

-2

32,38 0,5396 0,5921 9,868. 10

-3

52,10 0,8684

1

Table 10 : Pressure Or ForceMultiply the dimension in the appropriate column below

To obtaindimension

below

Atmos-pheres

Bayersper

sq. cm

Centi-metre

Hg

Inches

Hg

Inches

H20

Kilo-grams

per sqmetre

Pounds

per sqfoot

Pounds

per sqinch

Tonsper sq

foot

Newtons

per sqmetre


Atmospheres(76 cm Hg at0

oC

1 9,869.10

-7

1,316. 10

-2

3,342. 10

-2

2,458. 10

-3

9,678. 10

-5

4,725. 10

-4

6,804. 10

-2

0,945 9,869. 10

-6

Baryers ordynes per sqcentimetre(bar)

1,013. 10

6

1 1,333. 10

4

3,386. 10

4

2,491. 10

-3

98,07 478,8 6,895. 10

4

9,576. 10

5

10

Centimetre ofmercury(0

oC)

76,00 7,501. 10

-5

1 2,540 0,1868 7356. 10

-3

3,591. 10

-2

5,171 71,83 7,501. 10

-4

Inches ofmercury(0

oC)

29,92 2,953. 10

-5

0,3937 1 7,355. 10

-2

2,896. 10

-3

1,414. 10

-2

2,036 28,28 2,953. 10

-4

Inches ofwater (4

oC)

406,8 4,015. 10

-4

5,354 13,60 1 3,937. 10

-2

0,1922 27,68 384,5 4,015. 10

-3

Kilogramspersquare metre

1,033. 10

4

1,020. 10

-2

136,0 345,3 25,40 1 4,882 703,1 9765 0,102

Pounds persquare foot

2117 2,089. 10

-3

27,85 70,73 5,204 0,2048 1 144 2000 2,089. 10

-2

Pounds persquare inch

14,70 1,45. 10

-5

0,1934 0,4912 3,613. 10

-2

1,422. 10

-3

6,944. 10

-3

1 13,89 1,45. 10

-4

Tons (short)per sq. foot

1,058 1,044. 10

-6

1,392. 10

-2

3,536. 10

-2

2,601. 10

-3

1,024. 10

-4

0,0005 0,072 1 1,044. 10

-1

Newtons persquare metre

1,013. 10

5

10-1

1333. 10

3

3,386. 10

3

2,491. 10

-4

9,807 47,88 6,895. 10

3

9,576. 10

4

1

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Table 11 : Length

Multiply the dimension in the appropriate column below

To obtaindimension

below

Centi-metres

Feet Inches Kilo-metres

Nauti-cal

miles

Metres Mils Miles(statute

)

Milli-metre

s

Yards


Centimetres 1 30,48 2,540 105 1,853

. 105

100 2,540

. 10-3

1,609

. 105

0,1 91,44

Feet 3,281

. 10-2

1 8,333

. 10-2

3281 6080,27

3,281 8,333

. 10-5

5280 3,281

. 10-3

3

Inches 0,3937 12 1 3,937

. 104

7,296

. 104

39,37 0,001 6,336

. 104

3,937

. 10-2

36

Kilometres 10-5

3,048

. 10-5

2,540

. 10-5

1 1,853 0,001 2,540

. 10-8

1,609 10-6

9,144

. 10-3

Nautical Miles 1,645

. 10-4

0,5396 1 5,396

. 10-4

0,8684 4,934

. 10-4

Metres 0,01 0,3048

2,540

. 10-2

1000 1853 1 1609 0,001 0,9144

Mils (10-3inches)

393,7 1,2

. 104

1000 3,937

. 107

3,937

. 104

1 39,37 3,6

. 104

Miles (statute) 6,214

. 10-6

1,894

. 10-4

1,578

. 10-5

0,6214 1,1516 6,214

. 10-4

1 6,214

. 10-7

5,682

. 10-4

Millimetres 10 304,8 25,4 106 1000 2,540

. 10-2

1 914,4

Yards 1,094

. 10-2

0,3333

2,778

. 10-2

1094 2027 1,094 2,778

. 10-5

1760 1,094

. 10-3

1

Table 12 : AreaMultiply the dimension in the appropriate column below

To obtain

dimensionbelow

Circula

rmils

Squar

einch

Squar

efeet

Square

yards

Square

miles

Acres Square

milli-metres

Square

centi-metres

Squar

emetre

s

Squar

ekilo-

metres


Circular mils 1 1,273

. 106

1,833

. 108

1973 1,973

. 105

1,973

. 109

Square inch 7,854

. 10-7

1 144 1296 4,015

. 109

6,2726

106

1,550

. 10-3

0,1550 1550 1,550

. 109

Square feet 6,944

. 10-3

1 9 2,788

. 107

4,356

. 104

1,076

. 10-5

1,076

. 10-3

10,76 1,076

. 107

Square yards 7,716

. 10-4

0,1111

1 3,098

. 106

4840 1,196

10-6

1,196

. 10-4

1,196 1,196

. 10-6

Square miles 3,587

. 10-8

3,228

. 10-7

1 1,562

. 10-3

3,861

. 10-13

3,861

. 10-11

3,861

. 10-7

0,3861

Acres 2,296

. 10-5

2,066

. 10-4

640 1 2,471

. 10-4

274,1

Square

millimetres

5,067

. 10-4

9,290

. 104

8,361

. 105

1 100 106 10

12

Square

centimetres

5,067

. 10-6

6,452 1

Square

metres

6,452

. 10-4

9,290

. 10-2

0,8361 2,590

. 106

4047 10-6 0,0001 1 10

6

Square

kilometres

6,452

. 10-10

9,290

. 10-8

8,361

. 10-7

2,590 4,047

. 10-3

10-12

10-10

10-6

1

* 1 Hectare = 2,471 Acres

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Table 13 : Energy, Heat And Work


To obtaindimension

below

BTW Centi-metregrams

Ergs Footpounds

Hph Joules Kilo-gram

calories

Kwh mkg Wh

by the factor in the same columnBritish Thermal

units (B.T.U)

1 9,297

. 10-8

9,48

. 10-11

1,285

. 103

2545 9,48

. 10-4

3,969 3413 9,297

. 10-3

3,413

Centimetre -

grams

1,076

. 107

1 1,020

. 10-3

1,383

. 104

2,737

. 1010

1,020

. 104

4,269

. 107

3,671

. 1010

105 3,671

. 107

Ergs orcentimetre

- dynes

1,055

. 1010

980,7 1 1,356

. 107

2,684

. 1013

107 4,186

. 1010

3,6

. 1013

9,807

. 107

3,6

. 1010

Foot - pounds 778,0 7,233

. 10-5

7367

. 10-8

1 1,98

. 106

0,7376 3,087 2,655

. 106

7,233 2655

Horsepower -

hours (Hph)

3,929

. 10-4

3,654

. 10-11

3,722

. 10-14

5,050

. 10-7

1 3,722

. 10-7

1,559

. 10-3

1,341 3,653

. 10-6

1,341

. 10-3

Joules orwatt - seconds

1054,8 9,807. 10

-5

10

-7

1,356 2,684. 10

6

1 4186 3,6. 10

6

9,807 3600

Kilogram -

calories

0,252 2,343

. 10-8

2,389

. 10-11

3,239

. 10-4

6413 2,389

. 10-4

1 860 2,343

. 10-3

0,86

Kilowatt - hours

(Kwh)

2,93

. 10-4

2,724

. 10-11

2,778

. 10-14

3,766

. 10-7

0,7457 2,778

. 10-7

1,163

. 10-3

1 2,724

. 10-6

0,001

Metre -Kilograms

(mkg)

107,6 10-5

1,02

. 10-8

0,1383 2,737

. 105

0,102 426,9 3,671

. 105

1 367,1

Watt - hours

(Wh)

0,293 2,724

. 10-8

2,778

. 10-11

3,766

. 10-4

745,7 2,778

. 10-4

1,163 1000 2,724

. 10-3

1

Table 14 : Power Multiply the dimension in the appropriate column belowTo obtaindimension

below

BTUper

minute

Ergsper

second

Footpound

sper

minute

Footpounds

persecond

Horsepower

kgcalorie

sper

minute

Kilowatts

Metrichorsepower

Watts


British Thermal

Units per minute

1 5,689

. 10-9

1,285

. 10-3

7,712

. 10-2

42,41 3,969 56,89 41,83 5,689

. 10-2

Ergs per

second

1,758

. 108

1 2,259

. 105

1,356

. 107

7,457

. 109

6,977

. 108

1010

7,355

. 109

107

Foot pounds

per minute

778 4,426

. 10

-6

1 60 3,3

. 10

4

3087 4,426

. 10

4

3,255

. 10

4

44,26

Foot pounds

per second

12,97 7,376

. 10-8

1,667

. 10-2

1 550 51,44 737,6 542,5 0,7376

Horsepower 2,357

. 10-2

1,341

. 10-10

3,030

. 10-5

1,818

. 10-3

1 9,355

. 10-2

1,341 0,9863 1,341

. 10-3

Kilogramcalories

per minute

0,252 1,433

. 10-9

3,239

. 10-4

1,943

. 10-2

10,69 1 14,33 10,54 1,433

. 10-2

Kilowatts 1,758

. 10-2

10-10

2,26

. 10-5

1,356

. 10-3

0,7457 6,977

. 10-2

1 0,7355 10-3

Metric

horsepower

2,39

. 10-2

1,36

. 10-10

3,072

. 10-5

1,843

. 10-3

1,014 9,485

. 10-2

1,36 1 1,36

. 10-3

Watts 17,58 10-7

2,26

. 10-2

1,356 745,7 69,77 1000 735,5 1

Table 15 : Volume

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To obtaindimension

below

Cubiccenti-metre

Cubicmetre

s

Litres Cubicinches

Cubicfeet

Gallons

lmp

Gallons

U.S.

Pints(liquid)

Quarts(liquid)

Bushels

(dry)


Cubic

centimetres

1 106 1000 16,39 2,832

. 104

3785 473,2 946,4 3,524

. 104

Cubic metres 10-6

1 0,001 1,639

. 10-5

2,832

. 10-2

3,785

. 10-3

4,732

. 10-4

9,464

. 10-4

3,524

Litres 0,001 1000 1 1,639

. 10-2

28,32 3,785 0,4732 0,9464 35,24

Cubic inches 6,102

. 10-2

6,102

. 104

61,02 1 1728 231 28,87 57,75 2150,4

Cubic feet 3,531

. 10-5

35,31 3,531

. 10-2

5,787

. 10-4

1 0,1337 1,671

. 10-2

3,342

. 10-2

1,2445

Gallons lmp. 1 0,8327

Gallons U.S. 2,642

. 10-4

264,2 0,2642

4,329

. 10-3

7,481 1,201 1 0,125 0,25

Pints (liquid) 2,113

. 10-3

2113 2,113 3,463

. 10-2

59,84 8 1 2

Quarts (liquid) 1,057

. 10-3

1057 1,057 1,732

. 10-2

29,92 4 0,5 1

Bushels (dry) 28,38 2,838

. 10-2

4,651

. 10-4

0,8036 1

Table 16 : MassMultiply the dimension in the appropriate column below

To obtaindimension

below

Grams Kilo-grams

Tons(metric)

Tons(long)

Tons(short)

Grains Ounces

Adp

PoundsAdp

Hundredweight


Grams 1 1000 106 1,016

. 106

9,072

. 105

6,481

. 10-2

28,35 453,6 5,080

. 104

Kilo grams 0,001 1 1000 1016 907,2 6,481

. 10-5

2,835

. 10-2

0,4536 50,80

Ton (metric) 10-6

0,001 1 1,016 0,9072 2,835

. 10-5

4,536

. 10-4

0,0508

Tons (long) 9,842

. 10-7

9,842

. 10-4

0,9842 1 0,8929 2,790

. 10-5

4,464

. 10-4

0,050

Tons (short) 1,102

. 10-6

1,102

. 10-3

1,102 1,120 1 3,125

. 10-5

0,0005 0,056

Grains 15,43 1,543

. 104

1 437,5 7000 784

. 103

Ounces (Adp) 3,527

. 10-2

35,27 3,527

. 104

3,584

. 104

3,2

. 104

2,284

. 10-3

1 16 1792

Pounds

Avoirdupois

2,205

. 10-3

2,205 2205 2240 2000 1,429

. 10-4

6,250

. 10-2

1 112

Hundredweights

(cwts)

0,0197

. 10-3

0,0197

19,7 20 17,8 0,128

. 10-6

558

. 10-6

0,0089 1

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4. GENERAL ELECTROTECHNICAL FORMULAE AND TABLES

4.1 Electro-technical symbols as per DIN 4897

Table 17 : Mathematical Symbols For Electrical Quantities(General)

Symbol Quantity SI unit

QEDU 0 1 CI

S,Jx, yGR

quantity of electricity, electric chargeelectric field strengthelectric flux density, electric displacementelectric potential differenceelectric potentialpermittivity, dielectric constant

electric field constant, 0 = 0,885419 . 10-11

F/m

relative permittivityelectric capacitanceelectric currentelectric current densityelectric conductivityspecific electric resistanceelectric conductanceelectric resistanceelectromotive force

CV/mC/m2

VVF/mF/m1 (ratio)

FAA/m2S/m

S

A

Table 18 : Mathematical Symbols For MagneticQuantities (General)

Symbol Quantity SI unitBHV 0 1 L

L, M

magnetic fluxmagnetic inductionmagnetic field strengthmagnetomotive forcemagnetic potentialpermeability

absolute permeability 0= 4 . . 10-7H/mrelative permeability

inductancemutual inductance

WbTA/mAAH/mH/m1 (ratio)

HH

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Table 19 : Mathemetical Symbols For Alternating-Current Quantities And NetworkQuantities.

Symbol Quantity SI unit

SPQDdZYR

GXB

apparent poweractive powerreactive powerdistortion powerphase displacementload angle

power factor, = P/S, = cos (1) loss angle

loss factor, d = tan impedanceadmittanceresistance

conductancereactancesusceptanceimpedance angle, = arctan (X/R)

W, VAWW, var

Wradrad

1 (ratio)rad

1 (ratio)

S

SS

rad

(1) Valid only for sinusoidal voltage and current

Table 20 : Numerical And Proportional Relationships

Symbol Quantity SI unit(ratios)

sp

w, Nm kvsgk

efficiencyslipnumber of pole-pairsnumber of turnstransformation rationumber of phases and conductorsamplitude factorovervoltage factorordinal number of a periodic componentwave contentfundamental wave contentharmonic content, distortion factor

increase in resistance due to skin effect, = R ~ /R_

111111111111

1

4.2 Alternating-current Quantities

With an alternating current, the instantaneous value of the current

changes its direction as a function of time i= f(t). If this process takesplace periodically with a period of duration T, this is a periodicalternation current. If the variation of the current with respect to time isthen sinusoidal, one speaks of a sinusoidal alternating current.

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The frequency fand the angular frequency are calculated from the periodictime Twith :-

T

.2f..2and

T

1f

= eq. 1-3.1The equivalent d.c. value of an alternating current is the average, taken overone period of the value :-

.tdi..2

1dti.

T

1i

2

O

T

O

eq. 1-

3.2

This occurs in rectifier circuits and is indicated by a moving-coil instrument, forexample.

The root-mean-square value (rms value) of an alternating current is the

square root of the average of the square of the value of the function withrespect to time.

2

O

2T

O

2 tdi..2

1dti.

T

1I eq. 1-3.3

As regards the generation of heat, the root-mean-square valueof the currentin a resistance achieves the same effect as a direct current of the samemagnitude.

The root-mean-square value can be measured not only with moving-coil

instruments, but also with hot-wire instruments, thermal converters andelectrostatic voltmeters.

A non-sinusoidal current can be resolved into the fundamental oscillationwith the fundamental frequency f and into harmonics having whole-numbered

multiples of the fundamental frequency. If I1 is the rms value of thefundamental oscillataion of an alternating current, and I2, I3, etc are the rmsvalues of the harmonics having frequencies 2.f, 3.f, etc, the rms value of thealternating current is:-

........IIII

2

3

2

2

2

1 + eq. 1-3.4If the alternating current also includes a direct-current component i_, this istermed an undulatory current. The rms value of the undulatory current is :-

........IIIII 2322

21

2_ + eq. 1-

3.5

The fundamental oscillation content g is the ratio of the rms value of thefundamental oscillation to the rms value of the alternating current

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I

Ig 1= eq. 1-3.6

The harmonic content k(distortion factor) is the ratio of the rms value of theharmonics to the rms value of the alternating current.

.g1I

....IIk 2

23

22 = eq. 1-3.7

The fundamental oscillation content and the harmonic content cannot exceed1.

In the case of a sinusoidalthe oscillation the fundamental content g = 1

the harmonic content k = 0.

4.3 Forms Of Power In An Alternating-current Circuit

The following terms and definitions are in accordance with DIN 40 110 for thesinusoidal wave-forms of voltage and current in an alternating-current circuit.

apparent power S = U.I = ,QP 22 + eq. 1-3.8active power P = U.I . cos = S . cos , eq. 1-3.9reactive power Q = U.I . sin = S . sin , eq. 1-3. 10power factor cos =

S

P, eq. 1-3.11

reactive factor sin =S

Q, eq. 1-3.12

When a three-phase system is loaded symmetrically, the apparent power is :-

S = 3.U1.I1 = 3 . U. I1 , eq. 1-3.13

where I1 is the rms phase current, U1 the rms value of the phase to neutralvoltage and Uthe rms value of the phase to phase voltage. Also:-

active power P = 3.U1.I1.cos = 3 . U . I1. cos , eq. 1-3.14reactive power Q = 3.U1.I1.sin = 3 . U . I 1 . sin . eq. 1-3.15The unit for all forms of power is the watt (W). The unit watt is also termed volt-ampere (symbol VA) when stating electic aparent power, and Var (symbol var)when stating electric reactive power.

4.4 Resistances And Conductances In An Alternating-current Circuit

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Impedance 222

XRI

S

I

UZ + eq. 1-3.16

Resistance 222

XZcos.ZI

P

I

cos.UR -==== eq. 1-3.17

Reactance 222

RZsin.ZI

Q

I

sin.UX -==== eq. 1-3.18

Inductive reactance Xi= .LCapacitive reactance

C.

1Xc eq.1 3.19

AdmittanceZ1BG

US

UIY 22

2 = eq. 1-3.20

Conductance2U

P

U

cos.IG ==

2

22

Z

RBYcos.Y === eq. 1-3.21

Susceptance sin.YU

Q

U

sin.IB

2===

222

ZRGY = eq. 1-3.22

Inductive susceptanceL.

1Bi eq. 1-3.23

Capacitive susceptance B C.c eq. 1-3.24= 2. .f is the angular frequencyand the phase displacement angle ofthe voltage with respect to the current. U, Iand Zare the numerical values ofthe alternating-current quantities U, Iand Z.

Complex presentation of sinusoidal time-dependent a.c. quantities

Expressed in terms of the load vector system:-

U = I . Z, I = U . Y. eq. 1-3.25The symbols are underlined to denote that they are complex quantities(DIN 1344).

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~I

UY

1Z=

Figure 2 : Equivalent CircuitDiagram

+j

- j

jXi=j.L

+

.C1jjXc

R

Vector diagram of resistance

+ j

- j

jBc=j.C

.L1jijB G+

Vector diagram of conductances

In the voltage vector Uis laid on the real reference axis of the plane of complex

numbers, for the equivalent circuit in Fig. 2 with Z = R + Xi; we have:-

U =U, eq. 1-3.26

I =I W -j I b =I.(cos -j sin ) eq. 1-3.27IW = ;

U

PI b = ;

U

Q eq. 1-3.28

S = U.I*= U.I.(cos +j sin ) = P +j Q, eq. 1-3.29S = S= U.I = ,QP 22 + eq. 1-3.30Z = R +j X i= )sinj.(cosI

U)sinj.(cosI

UIU +=+= eq. 1-3.31

where : R =I

U.cos and Xi=

I

U.sin ,

Y = G -jB =U

I

U

I = .(cos -j sin ) eq. 1-3.32where : G =

U

I.cos and Bi=

U

I.sin .

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4.5 Alternating-current Quantities Of Basic Circuits

Table 21: Alternating - Current Quantities Of Basic Circuits

Circuit Z Z1.

R

R R

2.L

j .L .L

3.C

- j / (.C) 1/ .C

4. R + j .L (1) R2+ ( .L)2 5. R - j / (.C) R2+ 1/( .L)2 6. j (.L - 1/(.C)) .L - 1/(.C)7.

C.1L.jR (2) 22

C.

1L.R

8. RL.L..R 22 )L.(R

L..R

9. 22

2

R.)C.(1

R.C.jR (3) 22 R.)C.(1R

10.C.)L./(1

j C.)L./(1 1

11.))L./(1C.(jR/1

1

L.1C.jR1=Y 2

2 L.

1C.

R

1

1

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12.

222

22

222

)C..R()C.L.1(

C.R)C.L.1(Lj

)C..R()C.L.1(

R

+

222

2222

)C..R()C.L.1(

]C.R)C.L.1.(L[R

(1) With small loss angle ( = 1/ ) tan (error at 4oabout 0,1 %) : Z .L(+ j). (2) Series resonance (voltage resonance) for .L = 1 / (.C) :

C.L.2

1f:C/LXXX resCLres : Zres= R.

Close to resonance (f

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_________________

Table22:Current/VoltageRelations

hips

OhmicresistanceR

Capacitance(cap

acitor)C

Inductance

(chokecoil)L

Generallaw

u

=

i.R

dti.C1

dt

di

.L

i=

Ru

dt

du.C

dtu.L1

Timelaw

u

=

.sint

.sint

.sint

hence

u

=

.R.sint=.sint

-

C.1 ..cost=-.cost

.L..cos

t=.cost

i=

R.sint=.sint

.C..cost=.cost

-

L.1 ..cos

t=-.cost

Elementofcalculation

=

/R

.C.

/(.L)

=

.R

/(.C)

..L

=

O uandIinphase

2

0.C.

1

arctan

=

ileadsuby90o

2

0

L.

arctan

=

ilagsuby90o

f=

.2

.2

.2

Alternating

current

Z

=

R

C.j

j.L

impedance

Z=

R

C.1

.L

Diagrams

U i

U

i

U

i

U

i

U

i

U

i

_________

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TABLE2

2:

CURRENT/VOLTAGE

RELATIONSHIPS

(Continued)

Ohmicresi

stanceR

Capacitanc

e(capacitor)C

Inductance

(chokecoil)L

Alternating

current

Z

=

R

C.j

j.L

impedance

Z=

R

C.1

.L

Diagrams

U i

U

i

U

i

U

i

U

i

U

i

_________

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4.6 Electric Resistances

4.6.1 Definitions and specific values

An ohmic resistance is present if the instantaneous values of the voltage are

proportional to the instantaneous values of the current, even in the event oftime-dependent variation of the voltage or current. Any conductor exhibitingthis proportionality within a defined range (e.g. of temperature, frequency orcurrent) behaves within this range as an ohmic resistance. Active power isconverted in an ohmic resistance. For a resistance of this kind is:-

R =2I

P eq. 1-3.33

The resistance measured with direct current is termed the d.c. resistance R_.If the resistance of a conductor differs from the d.c. resistance only as a resultof skin effect, we then speak of the a.c. resistance R~ of the conductor. The

ratio expressing the increase in resistance is :-

resistanced.c.

resistancea.c.

_R

~R = eq. 1-3.34Specific values for major materials are shown in Table 23.

TABLE 23: NUMERICAL VALUES FOR MAJOR MATERIALS

Conductor Specificelectric

resistance (mm

2/m)Electric

conductivity

s = 1/(mm

2/m)Temperaturecoeficient

(K-1

)

Density

(kg/dm3

)Aluminium : 99,5 % Al,soft

0,0278 36 4. 10-3

2,7

Al-Mg-Si 0,030 ..0,033

33 ... 30 3,6 . 10-3

2,7

Al-Mg 0,06 ... 0,07 17 ... 14 2,0 . 10-3

2,7

Al bronze : 90% Cu, 10%Al

0,13 7,7 3,2 . 10-3

8,5

Bismuth 1,2 0,83 4,5 . 10-3

9,8

Brass 0,07 14,3 1,3 .. 1,9 . 10-3

8,5

Bronze : 88% Cu, 12%Sn

0,18 5,56 0,5 . 10-3

8,6 ... 9

Cast iron 0,60 ... 1,60 1,67 ... 0,625 1,9 . 10-3

7,86 ... 7,2

Conductor copper, soft 0,01754 57 4,0 . 10

-3

8,92Conductor copper, hard 0,01786 56 3,92 . 10

-3 8,92

Constantan 0,49 ... 0,51 2,04 ... 1,96 -0,05 . 10-3

8,8

CrAl 20 5 1,37 0,73 0,05 . 10-3

-

CrAl 30 5 1,44 0,69 0,01 . 10-3

-

Dynamo sheet 0,13 7,7 4,5 . 10-3

7,8

Dynamo sheet alloy (1 to5% Si)

0,27 ... 0,67 3,7 ... 1,5 - 7,8

Graphite and retortcarbon

13 ... 100 0,077 ... 0,01 -0,8 ... -0,2 . 10-3

2,5 ... 1,5

Lead 0,208 4,8 4,0 . 10-3

11,35

Magnesium 0,046 21,6 3,8 . 10-3

1,74

Manganin 0,43 2,33 0,01 . 10-3

8,4

Mercury 0,958 1,04 0,90 . 10

-3

13,55Molybdenum 0,054 18,5 4,3 . 10-3

10,2

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U

I1 I2 I3

G1= 1

R1

I

G 2 =

1

R2

G3=1

R3

FIGURE 4 : RESISTANCESCONNECTED IN

PARALLEL

Total conductance = Sum of the individual conductances:-

G

1Ri.e......GGGG

R

1321 = eq. 1-3.36

In the case of nequal resistances the total resistance is the nth part of theindividual resistances. The voltage at all the resistances is the same. Totalcurrent:-

R

UIcomponentsofSum

R

UI

i

i= eq. 1-3.37The currents behave inversely to the resistances:-

3

3

2

2

1

1R

R.II;

R

R.II;

R

R.II = eq. 1-3.38

Rd3 Rd2

Rd1

Rs2

Rs1

Rs3

FIGURE 5 : TRANSFORMATIONDELTA-STAR ANDSTAR-DELTA

Conversion form delta to star connection with the same total resistance:-

3d2d1d

3d2d1S

RRR

.RRR + eq. 1-3.39

3d2d1d

3d1d2S

RRR

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3d2d1d

2d1d3S

RRR

.RRR + eq. 1-3.41

Conversion from star to delta connection with the same total resistance:-

1s

1s3s3s2s2s1s1d

R

.RR.RR.RRR

+= eq. 1-3.42

2s

1s3s3s2s2s1s2d

R

.RR.RR.RRR

+= eq. 1-3.43

3s

1s3s3s2s2s1s3d

R

.RR.RR.RRR

+= eq. 1-3.44

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S.L.D.G. 2 - 0

AN OVERVIEW OF THE GENERALGUIDELINES FOR THE DESIGN OF A.C. SUBSTATIONS

INDEX

DOCUMENT REVISION TITLE

S.L.D.G. 2 - 0 1 INDEX

S.L.D.G. 2 - 1 1 ESTABLISHMENT OF A NEW SUBSTATION

1. Introduction - Flow Chart.

S.L.D.G. 2 - 2 1 SYSTEM REQUIREMENTS AND BASIC CONCEPTS

1. Introduction

1.1 Functions Of The Network

1.2 Functions Of The Substation

1.3 Structure Of A Substation

1.4 System Requirements

2. Parameters Determined By The Network

2.1 Main Equipment Parameters

2.2 Fault Clearing Time With Respect To System

Stability

3. Planning Of A Substation

3.1 General Location

3.2 Extent Of The Substation

3.3 Busbar Scheme

3.3.1 Operational flexibility

3.3.2 System security

3.3.3 Reliability and availability

3.3.4 Substation control

3.4 Fault Current Levels

3.5 Neutral Point Earthing

3.6 Future Extensions

3.7 Control In General

3.8 Protection In General

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S.L.D.G. 2 - 1

ESTABLISHMENT OF A NEW SUBSTATION

1. INTRODUCTION

The purpose of this document is to provide a simple guide to the design of anout-door, AC Substation, from the System requirements point of view. Theselection of the most suitable site and the design of the equipment to beinstalled will be dealt with in S.L.D.G. 3 and 4 respectively. It gives advice onthe general principles, refers to relevant standards as appropriate, and givesan indication of the economic factors involved.

Its scope is limited to open-terminal switchgear although mention is made ofGas Insulated Switchgear as an option, in the appropriate sections. GasInsulated Switchgear is dealt with in detail in S.L.D.G. 30.

In general the guidelines cover a substation within a transmission networkalthough some sections will be applicable to other situations such as DC / ACconvertor stations.

S.L.D.G. 2 covers system requirements and basic concepts, includingnetwork considerations and the particular needs of a substation.

The diagram on the following page is a flow-chart showing the various stagesnecessary in the establishment of a new substation. It must be emphasisedthat the decision on whether or not to build a substation may depend on

different conditions in different countries.

Once the decision has been made a course of action can be determined. Theflow chart gives a typical example.

It has been necessary to adopt a simplified step by step approach to theplanning and design process whereas in practice iterative actions may oftenbe involved.

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GENERAL PLANOF THE

NETWORK

ISREINFORCEMENT

REQUIRED

LOADGROWTH

ASSESSMENT

ENDNO

IS A NEWSUBSTATION

REQUIREDEND

NO

YES

CONSIDER OTHERMEANS OF

REINFORCEMENT

* PREPAREPRELIMINARY

PLANS

TECHNICAL &COMMERCIAL

POLICY

* General Locations Line Directions

Soil Investigations

Transport Routes

YES

GENERAL

DESIGN

SPECIFICDESIGN

PREPARE MAINCONNECTIONS &

PROTECTION DIAGRAM

DETERMINE

SITE LOCATION

DETERMINE EXACT SITEPLACEMENT &

ORIENTATION

DETERMINESUBSTATION LAYOUT

PREPARECIRCUIT DIAGRAMS

PREPARE WIRINGDIAGRAM & CABLE

SCHEDULE

CARRY OUT CIVIL

DESIGN WORK

INSTALL CIVIL

WORKS

INSTALL PLANT &

EQUIPMENT

TEST COMMISSIONTAKE OVER

Figure 1: Establishment Of A New Substation Flow Chart

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S.L.D.G. 2 - 2

SYSTEM REQUIREMENTS AND BASIC CONCEPTS

1. INTRODUCTION

The transmission network has two main constituent elements :-

a) Circuits that enable power transmission.

b) Substations that enable the interconnection of these circuits and thetransformation between networks of different voltages.

1.1 Functions of the Network

The transmission network performs three different functions :-

a) The transmission of electric power from generating stations (orother networks) to load centres.

b) The interconnection function that improves security of supplyand allows a reduction in generation costs.

c) The supply function which consists of supplying the electricpower to sub-transmission or distribution transformers and insome cases to customers directly connected to thetransmission network.

1.2 Functions of the Substation

These three functions of the transmission network are fulfilled throughdifferent types of substations listed below :-

a) Substations attached to Power Stations (Power Station HighVoltage Yards)

b) Interconnection substations)

Step-down (EHV / HV, EHV / MV, HV / MV) substations.

A single substation may perform more than one of these functions.

1.3 Structure Of A Substation.

Substations generally comprise the following :-

a) Switchgear.

b) Power Transformers.

c) Control Gear

Substations usually include busbars and are divided into bays. Inspecial cases other plant such as reactive power compensators,harmonic filters, fault current limiting and load-managementequipment are included.

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1.4 System Requirements

The design of a substation depends on the functions it has to fulfil.The system planning requirements define these functions and enablethe parameters that have to be complied with, to be determined.

Some of these parameters are common for all the substations thatperform the same functions whereas others are specific to eachsubstation.

Standarised parameters are established jointly by system plannersand transmission departments by means of system studies, andeconomic considerations. Particular economic benefits are derivedfrom specifying the technical stages to allow the use of standardisedHV equipment with identical characteristics (such as short-circuitcurrent level, maximum current carrying capacity of HV equipment,characteristics of transformers, insulation level and compensatingdevices).

The location of a substation at a particular site will give rise to systemrequirements peculiar to this station :-

a) General location requirements.

b) Extent of the substation.

c) Required availability of circuits.

d) Main connections scheme.

e) Current rating.

f) Fault current level.

g) Neutral point earthing.

h) Fault elimination rapidity with respect to system stability.

i) Future extensions.

j) Control and needs of personnel.

k) Equipment characteristics.

2. PARAMETERS DETERMINED BY THE NETWORK

System planners seek to optimise the parameters that apply to the completetransmission system. They proceed to network studies that involve mainly,insulation co-ordination, transient stability, short-circuit level and load flow.

2.1 Main Equipment Parameters

When a utility determines a standardisation policy and thedevelopment of a technical stage, the main characteristics of theprimary equipment have to be specified in close link with system

planners. The following parameters may be defined :-

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a) The maximum short circuit current rating of the substationsequipment (Busbars, Isolators, Circuit Breakers, CurrentTransformers), including its supporting structures.

b) The maximum load current passing through the components ofa substation (which is related to the maximum current carryingcapacity of the lines and underground cables).

c) The transformer numbers, sizes and impedances as well as themode of voltage control required, i.e. operating mode of tapchanging, regulation range, its phase shifting characteristicsand number of taps.

2.2 Fault Clearing Time With Respect To System Stability

Transient stability characterises the dynamic behaviour of a generatorin the case of large oscillations following a major disturbance

In order to comply with the requirements of the Network (systemstability), or the specifications of particular utilities, specified faultclearance times must not be exceeded.

Fault clearing time limits and the reclosing conditions, may influencethe choice of circuit breaker and other switchgear, and also thedimensioning of the earthing grid and the mechanical strength of theequipment.

3. PLANNING OF A SUBSTATION

This section will give information helpful for dimensioning the main substationprimary parameters and for defining the general scope of the substationequipment, depending on the system requirements. The options of extendingor uprating existing substations and / or lines should have already beenevaluated.

The starting point for a substation design procedure is as follows :-

a) The need for a new substation is approved.

b) The range of its duties, loadings and general location are known.

3.1 General Location

For the location of a new substation in the network several alternativesusually exist, the total costs of which should be calculated. Thefollowing should be included :-

a) The losses in power transmission and transformation.

b) The costs of telecontrol and communications.

c) Preliminary study of reliability and busbar schemes.

d) Fault current and load flow calculations.

The building cost of new transmission lines and the reinforcement of

old ones are often of the same order as that of the substation. Thus, itis worth examining various alternatives with system planners.

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Nowadays it is not easy to get new line corridors, and their availabilityalone may determine the location of the substation. Along with theautomation of substations the costs of telecontrol andtelecommunications grow, but they do not have a decisive effect fromthe point of view of location.

3.2 Extent Of The Substation

The available area of the substation, the number of the outgoingfeeders of different voltage levels, the number of the maintransformers, the busbar schemes and the possibility of extensions aswell as compensating equipment options should be selected for theneeds of the future. It should be noted that the lifetime of thesubstations may be between 30 and 50 years.

It is very important to reserve sufficient space for the future andsophisticated network planning is needed to estimate the necessaryreserve space. If no better prognosis exists, 100 % reserve ofoutgoing feeders may be used as an estimate. The space requireddepends essentially on the function of the substation.

It is important to define the number and the size of the maintransformers at the final stage. The initial peak load of a powertransformer is dependent upon a number of factors such as thenetwork configuration, standby-philosophy and rate of load growth.An initial estimate would be in the range of 30 - 70 %. (See S.L.D.G.15 for a detailed discussion on power transformers).

In the case of GIS switchgear it is usual to reserve space for a number

of spare bays and also to make allowance for the future extension ofthe control building. (See S.L.D.G. 30 for a detailed discussion onGIS switchgear).

The outgoing line corridors should be planned so that there is aminimum number of crossings between different overhead lines.

3.3 Busbar Scheme (See also S.L.D.G. 6)

The selection of a busbar scheme and its possible extensions for aparticular substation is an important initial step of the design. Amongthe matters that affect this decision are operational flexibility, system

safety, reliability and availability, capacity to facilitate system control,and costs

3.3.1 Operational flexibility

In order to take into account both production and consumerrisks and contingent faults in system components the circuitsbetween two substations are often doubled, so that powertransfer is shared, for instance between two separateoverhead line circuits. In some instances this is alsonecessary to limit the power of a short-circuit. Theserequirements lead to the installation of a proportionally greater

number of busbars and sections in the substation when thenumber of outgoing feeders is large.

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3.3.2 System security

Faults occurring on feeders or within the substation itself, mustbe cleared rapidly by as small a number of circuit-breakers aspossible in order to avoid splitting the network and maintainnon-faulted circuits in service.

Careful selection of the electrical schematic arrangement -primary connections and protection scheme - and the detailedconstruction layout should enable these criteria to beoptimized.

3.3.3 Reliability and availability

The evaluation of how the availability performance of thesubstation elements influences the over-all performance of thesubstation is a complicated task in a meshed transmissionnetwork. The failure rates of the equipment and the choice ofthe substation scheme have a considerable effect on reliabilityand availability i.e. forced outages and planned shut-downs.Calculations can give only approximate results, because failurestatistics available are always based on an older generation ofapparatus and the likelihood of a severe outage occurringduring the life-time of the substation is quite small.

However, for a comparison of different schemes reliabilitycalculations are valuable instruments for the substation designengineer to receive additional information for choice of schemeand layout aspects.

Not only the primary equipment but also the secondaryequipment, e.g. the location and number of instrumenttransformers and the arrangement of the secondary circuitscan have a great influence on the over-all reliabilityperformance. For the looped substation schemes in particular,special attention has to be paid to the secondary wiring andcabling.

3.3.4 Substation control

The proposed scheme and layout must allow simple and

efficient performance of the usual operational steps, changesof section and planned outage for maintenance or extension.

3.4 Fault Current Levels

Fault current dimensioning depends on the neighbouring network andthe size and short-circuit impedance of the main transformers.System planning usually defined the following fault current ratings fora new substation :-

a) Maximum three-phase effective short-circuit current for thelines and the substation for the foreseeable future.

b) Duration of the effective short-circuit current.

c) Peak short-circuit current.

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d) Maximum earth fault current and corresponding time.

e) Maximum current through the neutral point of the maintransformer.

f) Minimum short-circuit current (for protection).

g) Minimum earth fault current (for protection).

3.5 Neutral Point Earthing

The transmission networks may be :-

a) Effectively earthed (earthing factor 1,4).

b) Non-effectively earthed (earthing factor e.g. 1,7).

e.g. resistance earthed or resonant earthed.

c) Isolated.

In the first case earth current may be 60 ... 120 % of the short-circuitcurrent. If the conductivity of the soil is poor (for example on theaverage 2 000 ohm-m), special attention has to be paid to themagnitude of station potential during an earth fault. In this case it ispossible to limit the earth-fault current and dimension the insulationlevel of the three-phase transformer neutral point correspondingly.Alternatively the potential rise of the earthing grid (see S.L.D.G. 8)may be limited by ensuring that the earth wires of outgoing overheadlines have cross sectional areas equivalent to those of the phasecables.

3.6 Future Extensions

For small substations performing distribution and transformationfunctions it is sometimes not necessary to consider future extensionpossibilities, on the high voltage side at all. However, it is importantthat the main transformers can be replaced by larger ones. For largejunction point substations system planning usually gives the forecastof extensions.

Extension work such as building of new bays, dismantling andreconstruction of bays, extension of the set of busbars may ratherdifficult and expensive, if there has been no previous planning for

them.

3.7 Control In General

Control includes actions to be taken under normal conditions such asenergising and de-energising a feeder, earthing of a section of a set ofbusbars etc. The way of carrying out this control depends for instanceon the following matters :-

a) Manually operated isolators.

b) Motor operated isolators.

c) Presence of earthing switches.d) Control via local control board.

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e) Control via local computer terminal.

f) Degree of substation automation, sequence control.

g) Remote control from the National or Regional control centre.

h) Regulations.

i) Station manned / unmanned.

The need for tele-control and telecommunication links depends on theneeds of the automation, remote control, data transmission andoperation of the network. A substation is often also a nodal point of adata transmission network.

Probable future development: Remote control substations automationis increasing; substations are designed as unmanned; maintenance ismanaged by the resources concentrated in control centres. Whetherthe substation is manned or unmanned may depend on theimportance of the station in the grid.

In accordance with system planning requirements load shedding,network sectioning, voltage regulation and load distribution regulationdevices may be placed on the substation.

3.8 Protection In General

The substation has to be constructed so that all possible faults can beeliminated :-

a) Selectively.

b) So that the fault current rating of the lines and equipment is notexceeded.

c) So that no danger is caused to personnel and the requirementsof safety codes are fulfilled.

d) Within such a time that stability of the network is maintained.

e) In such a way that load and production are held in balance.

For every protection item back-up protection is usually provided andimportant

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