Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

CLASS NOTES
ON

ELECTRICAL POWER TRANSMISSION AND
DISTRIBUTION
A COURSE IN 6TH SEMESTER OF
BACHELOR OF TECHNOLOGY PROGRAMME IN ELECTRICAL ENGINEERING
(COURSE CODE-BEE605)

DEPARTMENT OF ELECTRICAL ENGINEERING
VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY
BURLA
2015

2

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

D ISCLAIMER
This document does not claim any originality and cannot be used as a substitute for
prescribed textbooks
...
Further, this document is
not intended to be used for commercial purpose and the committee members are not accountable
for any issues, legal or otherwise, arising out of use of this document
...
To facilitate the electric power has to be generated and transmitted to the
consumers via a transmission and distribution network
...

The original electrical distribution system developed by Thomas Edison was an
underground direct current (DC) system
...
Ferranti constructed a 10kV link from Deptford, Kent to New Bond Street
in London
...
In 1928, the first 33kV machine was commissioned
...

Thus the study of transmission and distribution has become very fundamental for electrical
engineering students
...


5

6

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

ELECTRIC POWER TRANSMISSION AND DISTRIBUTION (3-1-0)
SYLLABUS
MODULE-I (10 HOURS)
General Introduction to power transmission by D
...
and A
...
overhead lines
Lines Constants: Resistance, inductance and capacitance of single and three phase lines with symmetrical
and unsymmetrical spacing transposition, charging current, skin effect and proximity effect
Performance of transmission Lines: Analysis of short, medium and long lines, equivalent circuit,
representation of the lines and calculation of transmission parameters, use of static or synchronous
condensers for improvement of regulation
...
H
...
transmission lines and its
advantages
Overhead line Insulators: Voltage distribution in suspension type insulators, method of equalizing, voltage
distribution, economic use of insulators
...


MODULE-IV (10 HOURS)
Substation & Earthing: Types of substations, arrangement of bus-bars and control equipments, solid
earthing, resistance earthing and Peterson coil
Per unit system one line diagram Power flow through transmission line, Power circle diagram, Series and
shunt compensation
...


John J Grainger, W
...
Stevenson, “Power System Analysis”, TMH Publication

7

8

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

[2]
...
J
...
P
...
As we know the transmission line are used for delivering electrical
power from one end to other end or one node to other node, the path of power flow i
...
the
transmission line can be represented as an electrical circuit having its parameters connected in a
particular pattern
...

RESISTANCE OF TRANSMISSION LINE
The resistance of the conductor thus transmission line can be determined by (1
...

R

l
A

(1
...

When alternating current flows through a conductor, the current density is not uniform over
the entire cross section but is somewhat higher at the surface
...
Moreover in a stranded conductor, the
length of each strand is more that the length of the composite conductor thus increasing the value
of the resistance from that calculated in (1
...

INDUCTANCE OF TRANSMISSION LINE
In order to determine the inductance of transmission line, we shall first drive expression
for the inductance of a solid conductor and it will be extended to a single phase transmission line
...

INDUCTANCE OF SOLID CONDUCTOR
The inductance of solid conductor can be determined by calculating the flux linkage due
to current flowing and using (1
...


9

10

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

L



(1
...

INDUCTANCE OF SOLID CONDUCTOR DUE TO INTERNAL FLUX
Let us consider a solid conductor of radius 'r ' cm and the current flowing is ' I ' A as shown
in Fig
...
1
...
-1
...


As we know Ampere's law states that the magnetomotive force (mmf) in ampere-turns
around a closed path is equal to the net current in amperes enclosed by the path
...
3)
...
3)

Where H is the magnetic field intensity in At/m, s is the distance along the path in meter
...
It is constant at all points that are
at a distance ' x' from the center of the conductor
...
Let the current enclosed by this path is ' I x '
...
3) we can write as follows
...
4)
(1
...
6)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

2x 2
I
2r 2

Ix 

(1
...
6) in (1
...
7)

The flux density at a distance of ' x' is given by
Bx  H x   0  r H x

(1
...
e
...
9)
...
9)

Combining (1
...
8) and (1
...
9)

The flux linkage at ' x' can be given by

d x 

x 2
I
d x  
x 3 dx
2
4
r
2r

(1
...
10) over the range of ' x' ,
i
...
, from '0' to ' r ' as follows
...
11)

(1
...
12) can be written
as follows, which is the flux linkage due to internal flux
...
13)

Hence the inductance of the conductor due to internal flux is obtained by using (1
...
13)
...
14)

11

12

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

INDUCTANCE OF SOLID CONDUCTOR DUE TO EXTERNAL FLUX
Now we shall calculate the inductance of solid conductor due to flux linking with the
conductor externally
...
Let us consider a tubular element of thickness 'dx' of
the conductor at a distance ' x' from the center of the conductor and the field intensity as ' H x ' at
' x'
...
-1
...


o

r

x

dx

FIG
...
2 EXTERNAL FLUX LINKAGE OF A ROUND CONDUCTOR
...
e
...
Hence the fieled
intensity is given by (1
...


Hx 

I

(1
...
16)

Considering the unit length of the conductor i
...
one metre, the flux in the tubular element
of thickness 'dx' of the conductor can be given by (1
...


d x  Bx dx

(1
...
15), (1
...
17)
d x  

I
2x

dx

The flux linkage at ' x' can be given by

(1
...
19)

dx

The total internal flux linkage can be obtained by integrating (1
...

D2

D2

D1

D1

   d x   


I
2x

(1
...
21)

For relative permeability to be  r  1 we have  0  4 X 10 7 , hence (1
...


ext  2 X 10 7 I ln

D2
Wb-T/m
D1

(1
...
2) and
(1
...


Lext 

ext
I

 2 X 10 7 ln

D2
D1

(H/m)

(1
...
14) and (1
...


L  Lint  Lext 

D
1
X 10 7  2 X 10 7 ln 2
2
D1

1
D 
L  2 X 10 7   ln 2 
D1 
4

(H/m)

(H/m)

(1
...
24)

Considering the flux linking with the conductor up to a point ' P' at a distance ' D' from the
center of the conductor (1
...
25)

Or we can write



D 
 D

L  2 X 10  ln 1   2 X 10 7  ln ' 



 r 
 e 4r 
7

(H/m)

(1
...
-1
...
One conductor is the return circuit for the other
...
First let us consider
conductor 1
...
However, the flux beyond
a distance D + r2 from the center of the conductor links a net current of zero
...
-1
...
27) and (1
...


 D
L1  2 X 10 7  ln '  (H/m)
 r1 

(1
...
28)

The total inductance of the single phase transmission line is then can be calculated as the
sum of these inductances since the flux lines set up by current in conductor-1 shall have same
direction as the flux lines set up by the current in conductor-2
...
29)

If r1  r2  r then

 D
L  4 X 10 7  ln '  (H/m)
 r 

(1
...
-1
...
The total current in this group
of conductors is the phasor sum of all the currents and given by (1
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

I a  I b  I c    I j    I n  0

(1
...
-1
...
14) and (1
...
e
...

 Ia
D 
 I a ln aP 
ra 
 4

aPa  2 X 10 7 

aPa  2 X 10 7 I a ln

DaP
ra

(1
...
33)

The flux linkage of conductor  a up to point ' P' due to current I b is the flux produced
by current I b between the point ' P' and conductor  a i
...
within limiting distances DbP & Dab
and can be written as (1
...


aPb  2 X 10 7 I b ln

DbP
Dab

(1
...
35)
...
35)
Let the point ' P' to move far away infinitely it mean we consider all the flux linkages with
the conductor due to all the currents in the group
...
31) in (1
...
36), which is the flux linkage of conductor  a up to point ' P'
in group of conductors
...
36)
ra
Dab
Dac
Daj
Dan 

The above derivation is true for the sum of all currents to be zero in the group
...
-1
...
Each group form one side
of a line
...
The conductor  A1
I
consists of ' n' parallel filaments each carrying ' ' current and the conductor  A2 consists of 'm'
n

parallel filaments each carrying '

I
' current
...

From (1
...


a  2 X 10 7
 2 X 10

I 1
1
1
1
1 
 ln
   ln
   ln
ln  ln

n  ra
Dab
Dac
Daj
Dan 

7

I 
1
1
1
1
1 
 ln
 ln
   ln
   ln
ln

m  Daa
Dab
Dac
Daj
Dam 

(1
...
38)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Conductor-A1

Conductor-A2

FIG
...
5 SINGLE PHASE LINE CONSITING OF COMPOSITE CONDUCTORS

The inductance of filament  a is given by
La 

 m Daa Dab Dac  Daj  Dam 

 2 X 10 7 n ln
I
n r  D D  D  D


a ab ac
aj
an
n

a

(1
...
40)

The average inductance of the filaments of conductor  A1 is
Lav 

La  Lb  Lc    Ln
n

(1
...
42)
L A1 

Lav La  Lb  Lc    Ln

n
n2

(1
...
43)

17

18

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Replacing the term ra by Daa and so on for all the filaments, we can rewrite the (1
...
44)
A closer look at the above equation for inductance conclude that the terms of numerator
consists of distances between the filaments of two groups and the terms of denominator consists
of distances between the filaments of the same group
...
The self GMD is also called as
geometric mean radius or GMR
...
44) can be written as

 D 
 mutual GMD 
L A1  2 X 10 7 ln
 2 X 10 7 ln m 

self GMD 

 Ds 

(1
...
45)
L  LA1  LA2

(1
...
As
we know for a three phase line the phasor sum of currents is zero assuming a balance system
...
-1
...


D

D

D

FIG
...
6 THREE PHASE LINES HAVING CONDUCTORS WITH SYMMETRICAL SPACING

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

For this three phase system the flux linkage with conductor  a due to all the currents is
given by (1
...
36)
...
46)

Since I a  I b  I c  0 , (1
...
47)



a  2 X 10 7  I a ln


D

ra 

(1
...
48)

Similarly the inductance for other two phase can be determined by (1
...
50) as
below
...
49)

 2 X 10 7 ln

D
rc

(1
...
-1
...


Dab

Dca

Dbc

FIG
...
7 THREE PHASE LINES HAVING CONDUCTORS WITH ASYMMETRICAL SPACING

The flux linkage of conductor  a due to all the currents can be given by (1
...
51)

19

20

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

The flux linkage of conductor  b due to all the currents can be given by (1
...
52)

The flux linkage of conductor  c due to all the currents can be given by (1
...
53)

As we see the flux linkage with all the three phases are different hence the inductance of
three phases shall be different and can be calculated as above
...
In this method each conductor occupies each position for one third
length of the transmission line total length as shown in Fig
...
8
...
54)


a1  2 X 10 7  I a ln




a 2  2 X 10 7  I a ln




a 3  2 X 10 7  I a ln


1
1
1 
 I b ln
 I c ln

ra
Dab
Dca 

(1
...
54b)

1
1
1 
 I b ln
 I c ln

ra
Dca
Dbc 

(1
...
-1
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

a 

a1  a 2  a 3

(1
...
54) and (1
...
56)

(1
...
57)

Ds

Where Deq  3 Dab Dbc Dca and Ds  ra
We have derived expression for inductance of transmission line
...
This numerator of this ratio is the mutual distances
between the conductors of different phases and the denominator is the distance between the
conductors of same group or the sub-conductors
...
e
...


INDUCTANCE OF BUNDLE CONDUCTOR
In extra high voltage transmission line bundle conductors are used to reduce the effect of
corona
...
-1
...


d
Two Sub-Conductors

d

d

d

d
d

Three Sub-Conductors

Four Sub-Conductors

FIG
...
9 BUNDLE CONDUCTORS

21

22

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

The inductance of bundle conductors can be calculated by determining its self GMD as
follows
...
094 Ds d 3

The bundle conductors have reduced reactance
...
For the calculation of inductance

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

CHAPTER-2
TRANSMISSION LINE PARAMETERS-II
INTRODUCTION
In the previous chapter we have calculated the inductance of the transmission line for single
phase and three phase transmission lines
...
It can be determined by fundamental Coulombs Law
CAPACITANCE OF LONG SOLID CONDUCTOR LINE
Let us consider a solid conductor as shown in Fig
...
1 having radius 'r '
...


r

+q

x

o

FIG
...
1 SOLID CONDUCTOR HAVING CHARGE ' q '

The cylindrical surface is the surface of equipotential and the electric flux density on the
surface is equal to the flux leaving the conductor per unit length divided by the area of the surface
in an axial length
...
1)
...
1)

Where ' q ' is the charge on the conductor per unit length
...
2)

23

24

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

E

q
V /m
2xk

(2
...
-2
...


P1
D1
r

+q

D2

P2

o

FIG
...
2 POTENTIAL DIFFERENCE BETWEEN TWO POINTS

' P1 & P2 '

The conductor is an equipotential surface in which we can assume that the uniformly
distributed charge is concentrated at the center of the conductor
...

Therefore the voltage drop between the two points can be computed by integrating the field
intensity over a radial path between the equipotential surfaces and given by (2
...

D2

D2

D1

D1

V12   Edx 

q

q

D2

 2xk dx  2k ln D

(V)

(2
...
It can be given by (2
...
4)

Let us consider two conductors having charges ' qa & qb ' on two conductors as shown in
Fig
...
3
...
-2
...
5)
Vab 

qa
r
D q
ln  b ln b (V)
2k ra 2k D

(2
...
6)

For ra  rb  r
Vab 

q
D
(V)
ln
k r

(2
...
8)

Cab 

q
k

(F/m)
V ln D
r

(2
...
-2
...
The capacitance to neutral
between the conductors is hence given by (2
...
9)

CAPACITANCE OF THREE PHASE LINE
Let us derive expression for capacitance of three phase line whose conductors are spaced
equilaterally as shown in Fig
...
6
...

Vab 

qa
q
D q
r
D
(V)
ln  b ln  c ln
2k
r 2k D 2k D

(2
...


25

26

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Similarly the voltage between two phases ' a & c" shall be expressed as follows
...
11)

Adding (2
...
11)We get
1
2k

Vab  Vac 

D
r

(V)


2
q
ln

q

q
ln
a
b
c

r
D 

(2
...
13)

Hence the capacitance is determined as

Can 

qa
2k

(F/m to neutral)
Van ln Deq r 

(2
...

Let us consider the conductors as shown in Fig
...
7 and the conductors are transposed as
shown in Fig
...
8
...
15)

Hence for position-2, the voltage between two phases ' a & b" shall be expressed as

Vab 

1
2k


D23
D 
r
 qb ln
 qc ln 31  (V)
qa ln
r
D23
D12 


(2
...
17)

Using (2
...
16) and (2
...
18)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Similarly the voltage between two phases ' a & c" shall be expressed as follows
...
19)

Using (2
...
19) we can write

Van 

Deq
qa
ln
(V)
2k
r

(2
...
21)

CAPACITANCE OF BUNDLE CONDUCTOR
The capacitance of bundles conductor can be calculated as above and given by (2
...
22)

Where ' DsC,bundle' is the modified GMR of the bundle conductor and can be given as follows
for different bundle conductors as shown in Fig
...
9
...
094 rd 3

Earth affects the calculation of capacitance of three-phase lines as its presence alters the
electric field lines
...
Therefore the effect of earth can be neglected for
capacitance calculations, especially when balanced steady state operation of the power system is
considered
...


27

28

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

CHAPTER-3
TRANSMISSION LINE PERFORMANCE
INTRODUCTION
We have derived expression for resistance, inductance and capacitance for transmission
line in last two chapters
...
Furthermore we also conclude that the parameters depend upon the length
of the transmission line
...
The circuit consisting of these parameters are shown in Fig
...
1 below
...
-3
...
The capacitance is known as shunt parameters and hence
forms shunt admittance
...
-3
...
1)

I S  CVR  DI R

(3
...
-3
...
This is the reason that the transmission line is classified into three categories
...
3)

Y  jCl

(3
...

SHORT LENGTH TRANSMISSION LINE
Since the length of the line is less, the total value of series impedance is quite comparable
with respect to shunt admittances and hence the shunt admittance is neglected and the transmission
line consists of only series impedance as shown in Fig
...
3

IS

R

VS

L

IR

VR

FIG
...
3 SHORT LENGTH EQUIVALENT OF TRANSMISSION LINE

For the circuit in Fig
...
3 the network equations are given by

VS  VR  ZI R

(3
...
6)

Hence comparing (3
...
2), (3
...
6) we get for short transmission line:

A 1 B  Z

(3
...
8)

MEDIUM LENGTH TRANSMISSION LINE
The shunt admittance cannot be neglected if the length of the line is more
...
The lumped parameters representation of
the line can be of two types (i) nominal π representation and (ii) nominal Т representation as shown
in Fig
...
4 and Fig
...
5
...


29

30

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

IS

VS

R

L

C/2

C/2

FIG
...
4 NOMINAL

IS R/2 L/2

IR

VR



VS

Y/2

IR

VR

Y/2

REPRESENTATION OF TRANSMISSION LINE

R/2 L/2 IR

VS

Z

IS

C

IS

VR

Z/2

VS

Z/2

Y

IR

VR

FIG
...
5 NOMINAL  REPRESENTATION OF TRANSMISSION LINE

NOMINAL  REPRESENTATION
Let us derive the A, B, C, D parameters of this circuit
...


' I cR ' - Current flowing in the shunt branch on receiving end side
...

' I se ' - Current flowing in the series branch
...

I cR  VR

Y
2

I se  I cR  I R  VR

(3
...
9b)

 Y

VS  I se Z  VR  VR  I R Z  VR
 2


(3
...
9)

Similarly the current at sending end is derived as follows
...
10a)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

 ZY 
Y
Y
I S  1 
VR  ZI R   VR  I R
2 
2

2

(3
...
10)

Hence comparing (3
...
2), (3
...
10) we get for medium transmission line
(nominal  representation):
A 1

ZY
2

BZ

 ZY 
C  Y 1 

4 


D 1

(3
...
12)

NOMINAL  REPRESENTATION
The A, B, C, D parameters of this circuit can be derived similar to above procedure
...


'Vc ' - Voltage at the node of shunt branch of the circuit
...


I c  VcY

(3
...
13b)

Vc  VR  I R

Z
2

(3
...
13d)

Z
Z
Z
VS  Vc    I S    I S    I R  VR
2
2
2

(3
...
13d) in (3
...
13)

From (3
...
14)

31

32

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Hence comparing (3
...
2), (3
...
14) we get for medium transmission line
(nominal  representation):
A 1

 ZY 
B  Z 1 

4 


ZY
2

C Y

D 1

(3
...
16)

LONG LENGTH TRANSMISSION LINE
The parameters of transmission line cannot approximated as lumped parameters if the
length is long as because for such line series impedance and shunt admittance both effects the
performance significantly
...
-3
...
To derive the A, B, C, D parameters of the long transmission line, let us consider the
circuit as shown in Fig
...
6
...
The series impedance and shunt admittance of this
elemental length is given by ' zdx'&' ydx' respectively, where ' z '&' y' are series impedance and
shunt admittance of transmission line per unit length
...
-3
...

I+dI

IS

zdx

V+dV ydx

VS

dx

I

IR

V

VR

x

FIG
...
6 LONG LINE REPRESENTATION OF TRANSMISSION LINE

For elemental section under consideration we can write the circuit equations as follows
...
17a)

dI  Vydx 

dI
 yV
dx

(3
...
17a) with respect to ' x' and substituting (3
...
18)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

The general solution of (3
...
19)

Where   zy
...
19) and (3
...

y



(3
...
19) and (3
...
21)

1
K1  K 2 
ZC

IR 

(3
...

K1 

1
VR  ZC I R 
2

(3
...
24)

Hence the voltage and current for the transmission line at a distance ' x' from the receiving
end is given by putting the values of ' K1 '&' K 2 ' in (3
...
20)
...
25)
(3
...
25) and (3
...
27)

 ex  e x 
 ex  e x 

VR  
 I R
2
2





(3
...
27) and (3
...
29)

33

34

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

 1

I  
Sinhx VR  Coshx I R
 ZC


(3
...


VS  Coshl VR  ZC Sinhl I R

(3
...
32)

Thus A, B, C, D parameters of the long transmission line is given by
A  Coshl

C

1
Sinhl
ZC

B  ZC Sinhl

(3
...
34)

In the derivation of A, B, C, D parameters of the long transmission line we introduce two
new parameters '  '&' Z C '
...


' Z C ' - is the characteristics impedance
...

Generally for overhead transmission line it is approximately equal to 400Ω
...
25) can be rewritten by using the components of propagation constant
...
35)

The first term increases in magnitude and advances in phase as distance ' x' from the
receiving end increases
...
This is the characteristic of a
travelling wave
...
The second term diminishes
in magnitude and retarded in phase from the receiving end towards the sending end
...
The voltage at any point on the transmission line is the sum of incident and
reflected voltage
...
Thus the line is said to be flat line or infinite line
...
Under
C

such condition the characteristics impedance is known as surge impedance and the loading under
such condition is known as surge impedance loading (SIL)
...
36)

FERRANTI EFFECT
In case of EHV very long transmission lines, the voltage at the receiving end is more that
the sending end voltage at light load or no-load condition
...
The
rise is voltage is due to the shunt capacitors of the transmission line, which draw charging current
...
-3
...
It consists of a single transmission line connected between two buses
...


S

R

FIG
...
7 TRANSMISSION LINE POWER FLOW

The line is characterized by its line constants as follows

A  A  , B  B 
So that the power received at the receiving end is given by

S R  PR  jQR  VR I R*

(3
...
38)

35

36

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

I S  CVR  DI R

(3
...
38)

VS  AV R
B

IR 

(3
...
41)

      A    VR 0

B    

(3
...
43)

(3
...
45)

(3
...
0,   0
...
45) can be fairly approximated as (3
...
47)

From (3
...
Similarly the power flow between two buses can be given by (3
...
48)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

LINE COMPENSATION
As stated above the power flow in a transmission line depends upon the voltage at both the
ends, the reactance of the line and phase difference between the voltages
...
It can be controlled by


Voltage magnitude control



Transmission line reactance control



Phase angle control

Once the installation of the transmission line is over its A, B, C, D parameters are constant
because these depend upon the size and material of conductors and the configurations of the
conductors
...
The value of reactance
X however can be controlled by providing compensation
...
The shunt admittance of the
transmission line consists of capacitive reactance, the effect of which can be compensated by
connecting a shunt reactor
...
The line
compensation are of two types
...
-3
...
The location of this capacitor is optional and
depend upon the requirement of transmission company
...
-3
...
-3
...


37

38

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

S

R

FIG
...
9 TRANSMISSION LINE WITH SHUNT COMPENSATION

The value of series compensation and shunt compensation known as degree of
compensation depend upon operational policy
...

In power system most of the loads are inductive in nature resulting in reducing the voltage
at which it is connected, it is well known to connect the capacitor at that voltage
...
Thus Fig
...
9 can be modified
to Fig
...
10
...
-3
...
If the magnitude of voltage at the bus is more than the required magnitude
then the shunt reactor is connected
...

The ' A, B, C, D' parameters of a compensated transmission line is calculated by using the
following procedure
...

A B
A B A B

C D
 


 Equivalent C D Line C D SeriesCapacitor

(3
...

A B
A B A B

C D
 


 Equivalent C D Line C D ShuntCapacitor/ Re actor

(3
...

A B
A B
A B
A B

C D






 Equivalent C D HalfLine C D SeriesCapacitor C D HalfLine

(3
...
52)

The ' A, B, C, D' parameters of shunt capacitor/reactor is given by

1
0

A B


C D 

 ShuntCapacitor/ Re actor YShuntCapacitor/ Re actor 1

(3
...
The line compensation provides:


Improvement in power flow



Power flow control



Share of power between the transmission lines



Voltage control



Improved stability



Improved security

Modern power system uses flexible AC transmission system (FACTS) devices to achieve
required degree of compensation and thus control over the system operation
...

are represented on a common base
...

Generally two base quantities ‘Base KVA or Base MVA’ and ‘Base KV’ are defined and others can
be calculated
...
54)

Base KVLN
2
Base KVLN
X 10 3
Base KVA1φ

(3
...
55) can be written as

Z Base 

2
Base KVLN
Base MVA1

(3
...
57)

3 X Base KVLL
2

Z Base

 Base KV LL 

 X 10 3
3


 Base KVA3 


3



Z Base 
Z Base 

Base KVLL 2

X 10 3
Base KVA3

(3
...
59)

Base KVLL 2

(3
...
61)

p
...
Value of the Variable 

Actual Value of the Variable
Base Value of the Variable

(3
...
62)

V p
...


V Actual
VBase

(3
...
63) to (3
...
u
...
63)

Z p
...


Z Actual
Z Base

(3
...
u
...
65)

Many a times the per unit quantities need to be calculated to a new base
...

Let the old base is given by BaseKVOld , BaseMVAOld and new base is given by

BaseKV New , BaseMVANew
...
u
...
u
...

From (3
...
u
...
u
...
66)

Base MVA3 (Old )

But the actual impedance on a new base can be given by
Z Actual  Z p
...
(New) X Z Base(New)  Z p
...
(New) X

Base KV



2

LL(New)

Base MVA3 ( New)

(3
...
66) and (3
...
u
...
u
...
u
...
u
...
u
...
u
...
68)

2

LL(New)

2

LL(Old)

LL(New)

(3
...
70) the per unit impedance can be calculated on the new base
...
70)

41

42

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

CHAPTER-4
CORONA
INTRODUCTION
When an alternating current is made to flow across two conductors of the transmission line
whose spacing is large compared to their diameters, then air surrounding the conductors
(composed of ions) is subjected to di-electric stress
...
But when the potential difference is
made to increase, then the field strength at the surface of conductor increases and then the air
surrounding it experiences stress high enough to be dissociated into ions making the atmosphere
conducting if the stress increases beyond threshold value of 30 kV (peak) known as the break down
voltage of air at normal temperature and pressure
...
This phenomena of electrical discharge occurring in transmission line for high
values of voltage is known as the corona effect in power system
...

FACTORS AFFECTING CORONA
Atmospheric Conditions: It has been physically proven that the voltage gradient for dielectric breakdown of air is directly proportional to the density of air
...

Condition of Conductors: It has an inverse proportionality relationship with the diameter
of the conductors
...
e
...
Also the presence of dirt or roughness of the conductor reduces the critical
breakdown voltage, making the conductors more prone to corona losses
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Spacing between Conductors: As already mentioned, for corona to occur effectively the
spacing between the lines should be much higher compared to its diameter, but if the length is
increased beyond a certain limit, the di-electric stress on the air reduces and consequently the effect
of corona reduces as well
...

METHODS TO REDUCE THE EFFECTS OF CORONA


The use of bundle conductors reduce corona loss



Spacing between conductors is selected so that corona is tolerable



Since the shape of conductors affect corona loss, cylindrical shape conductors have
uniform field that reduces corona loss than any other shape



The voltage stress and electric field gradient should be minimized which can be
accomplished by following good high voltage design practices
...
-4
...


Conductor-a

Conductor-b
qa

qb

o

o

D
FIG
...
1 A TWO CONDUCTOR LINE

43

44

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Let qa  qb  q and ra  rb  r , since both conductors form one transmission line
...
1)

The potential difference between two conductors is given by
r

V    Edx 
D r

V

q 1
1 
 
dx
2k  x D  x 
D r
r



q
D
ln
k r

(4
...
3)

Substituting for ‘q’ from (4
...
1) we get

E

kV 1
D
D
ln 2k xD  x 

(4
...
5)

D
xD  x  ln
r

Where V  

V
V
and for three phase line V   Line
2
3

The electric stress is maximum at x  r and given by

g max 

V D
D
r D  r  ln
r



V
D
r ln
r

(4
...
6) we can determine the expression for disruptive critical voltage
Vd  g 0r ln

D
(kV)
r

(4
...
92b
is the air density factor, in which ‘b’ is the atmospheric pressure in cm of Hg
t  273

and ‘t’ is the atmospheric temperature in degree Celsius
...
2 kV/cm (rms)
Taking into the surface condition of conductors we introduce surface irregularity factor ‘m’

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Vd  21
...
8)

For three phase line
Vd  21
...
9)

For smooth polished conductor- m  1 ,
For rough surfaces conductor- m  0
...
98
For stranded conductor- m  0
...
88
At this value of critical disruptive voltage, the corona starts but nor visible because the
charges ions do not get sufficient energy to cause further ionization by collisions
...
The expression for
critical disruptive voltage for visual corona is given by modifying (4
...


0
...
2mr 1 
(kV)(line to neutral)
 ln
r  r


(4
...
82
For stranded conductor- mv  0
...
The power loss due to corona can be calculated by
Peeks formula as given in (4
...


Pc 

241



f

 25

r
V  VD 2 X105 (kW/Phase/km)
D

(4
...
12)

Where ' f ' is the supply frequency and ' F ' is the corona factor determined by test
...


45

46

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

CHAPTER-5
OVERHEAD LINE INSULATOR
INTRODUCTION
The overhead line conductors are supported over the tower structures by means of line
insulators
...

In general, the insulators should have the following desirable properties
...




High electrical resistance of insulator material in order to avoid leakage currents to
earth
...




The insulator material should be non-porous, free from impurities and cracks
otherwise the permittivity will be lowered
...


The most commonly used material for insulators of overhead line is porcelain but glass,
steatite and special composition materials are also used to a limited extent
...
It is stronger mechanically
than glass, gives less trouble from leakage and is less affected by changes of temperature
...


There are three types of insulators used in connection with overhead lines
...




Suspension-type
...


PIN-TYPE INSULATORS
As the name suggests, the pin-type insulator shown in Fig
...
1 is attached to a steel bolt or
pin, which is secured to a cross-arm on the transmission pole
...
-5
...
It recognizes two methods:


The provision of a taper thread cut on the head of the pin, which screws into a
threaded soft metal thimble cemented into the insulator
...


For operating voltages up to about 11 kV with ordinary designs of insulator a one-piece
construction can be adopted
...
Actually, the
tendency is to use pin-type insulators for voltages up to 33 kV only, since they become
uneconomical for higher voltages
...

There should be sufficient thickness of porcelain between the line conductor and the
insulator pin (or other metal work) to give a factor of safety of up to 10 against puncture, but the
insulator should be designed so that it will spark-over before it will puncture
...
The present tendency is to use pintype insulators for low voltages only, say up to 11 kV, for which the factors of safety are 8
...
With a wet insulator, the surfaces of the various pieces, or 'sheds' as they are sometimes
called, have no insulating value, so that the total arcing distance is the sum of the shortest distances
from the edge of one shed to the nearest point on the next lower shed, plus the distance from the
edge of the next lowest shed to the pin
...
At terminal poles there is, in addition, the almost horizontal pull due to the tension
of the conductor
...
In connection with the mechanical strength, it is to be noted that the insulator is stronger
than the pin
...
For high voltages this type is therefore uneconomical, and there is the further
disadvantage that replacements are expensive
...
Several important
advantages follow from this system
...




In the event of a failure of an insulator, one unit - instead of the whole string - has
to be replaced
...
Also, since the
string is free to swing, there is an equalization of the tensions in the conductors of
successive spans
...




Owing to the free suspension, the amplitude of swing of the conductors may be
large compared with that on a pin-type insulated line, and the spacing should
therefore be increased
...
-5
...
It will be
seen that it consists of a single disc-shaped piece of porcelain, grooved on the under-surface to
increase the surface leakage path, and to a metal cap at the top, and to a metal pin underneath
...
The cap is secured to the insulator by means of cement
...
Mechanical
methods of fixing have proved unsatisfactory since they caused concentrations of mechanical
stress, which led to failure in service
...


FIG
...
2 SUSPENSION TYPE INSULATORS

The usual diameter of this type of insulator is ten inches, since it has been found that this
size gives a suitable ratio of spark-over to puncture voltage
...


49

50

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

STRAIN INSULATORS
These insulators are used to take the tension of the conductors at line terminals and at points
where the line is dead-ended, as for example some road-crossings, junctions of overhead lines with
cables, river crossings, at angle towers where there is a change in direction of the line, and so on
...
Where the tension is exceedingly high, as at
long river spans, two, three, or even four strings of insulators in parallel have been used
...
-5
...
Each insulator is represented by its capacitor
...
-5
...
1a)

CV2  CV1  KCV1

(5
...
2)
V2  1  K V1

(5
...
3a)

CV3  CV2  KC V1  V2 

(5
...
4) by using (5
...
4)

At node ' M ' using KCL we can write

I c 4  I c3  I 3

(5
...
5b)

Which can be simplified to (5
...
2) and (5
...
6)

For the whole string we have

V  V1  V2  V3  V4

(5
...
e
...
At this point let
us define string efficiency as follows:

 string 

Votlage across string
(5
...
of Insulators X Voltage across the Insulator adjacent t o the conductor

This efficiency is very low because of unequal voltage distribution
...

LENGTH OF THE CROSS ARM
As we can see the voltage distribution depends largely on the value of ' K '
...


51

52

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

It can be done by increasing the length of the cross arm
...

GRADING OF INSULATORS UNITS
It is observed from the above derivation that the insulators having same capacitors have
been used in the string
...
-5
...


C1
KC

V
J

Ic1

I1
V

C2
KC
K

Ic2
V

I2
C3

V
Ic3

KC
M
I3

V

C4
Ic4

FIG
...
4 GRADING OF STRING OF FOUR INSULATORS

I c 2  I c1  I1

(5
...
9b)

Which can be simplified to (5
...
10)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Similarly we can use for the other nodes and can determine the capacitor of each insulators
of the string
...
of insulators in
the string for very high voltage transmission line
...
The basic objective
is provide the charging current flowing through the capacitance between insulator pin and the
ground by another alternate path
...
-5
...


C
KC

V
J

Ic1

I1
V

C
KC
K

Cx(n-1)

Ic2
V

I2
C

I2

V
Ic3

KC

Cx(n)

M

I3

I3
V

C
Ic4

FIG
...
5 STATIC SHIELDING OF STRING OF FOUR INSULATORS

TESTING OF INSULATORS
The testing of insulators are made into three categories: flash-over tests, sample tests, and
routine tests
...
Flash-over tests are a design test

53

54

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

taken to three insulators only to prove the correction of the design; sample tests are to prove the
quality of manufacture, and are taken on 1/2 per cent
...

Flashover Tests


50 per cent
...




Dry flash-over and dry one-minute test
...


Sample Tests


Temperature-cycle test
...




Electro-mechanical test
...




Porosity test
...




Mechanical routine test
...

CAUSES OF INSULATOR FAILURE
Insulators are required to withstand both mechanical and electrical stresses
...
The electrical
breakdown of the insulator can occur either by flash-over or puncture
...
e
...
In case of flash-over, the insulator will continue to act in its
proper capacity unless extreme heat produced by the arc destroys the insulator
...
When such breakdown is involved, the insulator is permanently destroyed due to
excessive heat
...
The ratio of puncture strength to flashover voltage is known as safety
factor
...
These conductors, which are made of copper or aluminum or its alloys have its
own weight, especially in extra high voltage transmission line these conductors re very heavy
...
It is very important that conductors
are under safe tension
...
In order to permit safe tension in the conductors,
they are not fully stretched but are allowed to have a dip or sag
...
The conductor sag should be kept to a minimum in order to reduce the conductor
material required and to avoid extra pole height for sufficient clearance above ground level
...
However, low conductor tension and
minimum sag are not possible
...
Therefore, in actual practice, a compromise
in made between the sag and tension
...
-6
...
The
lowest point on the conductor is ‘O’ and the sag is ‘d’
...
However, if the sag is very small
compared with the span, then sag-span curve is like a parabola
...
Thus tension ‘T’ at the lowest point ‘O’ acts horizontally as shown
...
The tension at
supports is approximately equal to the horizontal tension acting at any point on the wire
...
-6
...
We can write the
vertical component and horizontal component of tension acting on the elemental length as follows
...
At point ‘P’

tan 

dy Ty ws


dx Tx H

(6
...
2)

Integrating and solving for constant we get

s

H
wx
Sinh
w
H

(6
...
1) and (6
...
4) is the equation of catenary
...
4)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

T  Tx2  Ty2  H 2  ws 

2

(6
...
3) in (6
...
6)

If the span length is ‘2l’ then half span is ‘l’, hence the length of the conductor in half span,
sag and tension can be given by (6
...
7a)
H
wl 
 Cosh  1
w
H


T  TA  TB  HCosh

wl
H

(6
...
7c)

(6
...
8a)

w 2
d
2T

(6
...
8c)

L
in (6
...
8a)

wL2
8T

(6
...
8c)

In hilly areas, we generally come across conductors suspended between supports at unequal
levels as shown in Fig
...
2
...


57

58

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

A
h

Y

B

D1

D2

O
X1

X
X2

L
FIG
...
2 SPAN OF TRANSMISSION LINE SHOWING THE CONDUCTOR SAG AND TENSION
(SUPPORTS AT DIFFERENT LEVEL)

For such case the sag calculated from two supports are given by

wx 21
2T

(6
...
9b)

D1 

h  D1  D2 



w 2
x1  x22
2T



(6
...
10)

Where

x1 

L Th
L Th

and x2  
2 wL
2 wL

EFFECT OF WIND AND ICE
The above formulae for sag are true only in still air and at normal temperature when the
conductor is acted by its weight only
...
The weight of ice acts vertically
downwards i
...
in the same direction as the weight of conductor
...
e
...
Hence, the
total force on the conductor is the vector sum of horizontal and vertical forces as given below
...

The transmission line may not have equal span throughout its length
...
11) or (6
...

Leq 

L31  L3 2  L33 
...
 Ln

Leq  Lavg 

2
Lmax  Lavg 
3

(6
...
12)

STRINGING CHARTS
There are two factors which vary the sag and tension
...

For use in the field work of stringing the conductors, temperature-sag and temperature-tension
charts are plotted for the given conductor and loading conditions
...
These charts are very helpful while stringing overhead lines
...
Where ' f1 ' is the stress tension per cross section area of the conductor
...
In general, the

59

60

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

strength of the line should be such as to provide against the worst probable weather conditions
...

Tower height: Tower height depends upon the length of span
...
It is not usually possible
to determine the tower height and span length on the basis of direct construction costs because the
lightning hazards increase greatly as the height of the conductors above ground is increased
...

Conductor clearance to ground: The conductor clearance to ground at the time of greatest
sag should not be less than some specified distance (usually between 6 and 12 m), depending on
the voltage, on the nature of the country and on the local laws
...
Special provisions must be made for melting
ice from the power lines
...
The tension
is governed by the effects of wind, ice loading and temperature variations
...
For
example, the tension increases when the temperature decreases and there is a corresponding
decrease in the sag
...

In planning the sag, tension and clearance to ground of a given span, a maximum stress is
selected
...
e
...
Wind loading
increases the sag in the direction of resultant loading but decreases the vertical component
...

Conductor spacing: Spacing of conductors should be such so as to provide safety against
flash-over when the wires are swinging in the wind
...
The use of horizontal spacing eliminates the danger caused
by unequal ice loading
...
Therefore, light wires should be given greater spacing
...
If the
wind velocity is small, the swinging of conductors is harmless provided the clearance is
sufficiently large so that conductors do not approach within the sparking distance of each other
...
Then the whole span may sail up like a kite until it reaches the limit of its slack, stops
with a jerk and falls or sails back
...
In order to protect the
conductors, Vibration Dampers are used
...
Further it is impossible to construct transmission towers
in some places
...
Underground cables have different technical requirements than overhead lines and have
different environmental impacts
...
The design and construction of underground transmission lines differ from
overhead lines because of two significant technical challenges that need to be overcome
...


The basic construction of underground cables is as shown in Fig
...
1
...

Sheath
Insulator
Conductor

FIG
...
1 BASIC CONSTRUCTION OF UNDERGROUND CABLES

Based on its application and construction there are various types of underground cables
...
The details of these cables can be referred from the Bureau of

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Indian Standard as BIS has set the guidelines for the manufacturing of cables as per applications
and criteria for safety
...
e
...
Because
XLPE cable is characterized by its ease of maintenance, the cable rapidly proliferated domestically
in the 1960s when its application began, currently constituting the majority of domestic power
cables having voltage ratings of 66-kV and higher
...

UNDERGROUND DISTRIBUTION CABLE
Underground distribution cables range from 6
...
It may be said that the
history of XLPE cable is the history of countermeasures against water tree, a process of insulation
deterioration due to water absorption
...
Moreover, water-impervious XLPE
cables were developed and applied in the late 1980s centering on the 22- kV and 33-kV XLPE
cables, with the aim of improving the reliability further by completely preventing entry of water
into the cables
...
This laminated lead layer was bonded on the
inside of the cable sheath, constituting a waterimpervious cable
...
Each conductor is made of copper or
aluminum; insulated with high-quality, oil-impregnated kraft paper insulation; and covered with

63

64

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

metal shielding (usually lead) and skid wires (for protection during construction)
...
This fluid acts as an insulator and does not conduct electricity
...
An electrical discharge
can cause the line to fail
...
The fluid is
usually static and removes heat by conduction
...
Cables with pumped fluids require
aboveground pumping stations, usually located within substations
...
There is a radiator-type device that moves the heat from
the underground cables to the atmosphere
...

HIGH-PRESSURE, GAS-FILLED PIPE-TYPE CABLE
The high-pressure, gas-filled (HPGF) pipe-type of underground transmission line is a
variation of the HPFF pipe-type, described above
...
Nitrogen gas is less effective than dielectric fluids at
suppressing electrical discharges and cooling
...
Thicker insulation and a warmer
pipe reduce the amount of current the line can safely and efficiently carry
...

Cables have a much lower inductance than overhead lines due to the lower spacing between
conductor and earth, but have a correspondingly higher capacitance, and hence a much higher
charging current
...
In the older paper insulated cables, the sheath
was of extruded lead
...
This is due to fact that the sheaths of the conductors cross the
magnetic fields set up by the conductor currents
...
This causes
eddy currents to flow in the sheaths
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Dielectrics used for cable insulation must have the following properties
...


CAPACITANCE IN A SINGLE-CORE CABLE
Let us consider a single core cable as shown in Fig
...
2
...
-7
...

g

q
(V/m)
2kx

(7
...
2)

Hence from (7
...
2) we obtain
g

V
R
x ln  
r

(7
...
e
...
e
...
So that we can write:
g max 

V
R
r ln  
r

g min 

V
R
R ln  
r

(7
...
3c)

The maximum stress should be minimum so that the cable can work satisfactorily without
rupturing the insulation
...
3b) w
...
t
...

dg max
dr





d  V
0


dr
 R
 r ln   
 r 


(7
...
3b) we get
R
 e  2
...
3e)

Thus if the overall diameter of the cable is kept fixed, then R/r = e is the condition for
minimum g max
...
Since the radius of the conductor that would be given from the above
expression is larger than is necessary for current carrying capacity, this value of radius may be
achieved by using aluminum or hollow conductors
...
4)

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

The capacitance of the cable is then given by
C

C

q

V

kr
R
18 X 10 ln  
r

(F/m)

(7
...
024k r
(μF/km)
R
ln  
r

(7
...
7
...
The filler spaces between the core insulation is also filled up with insulation, but
depriving these of voids is much more difficult
...
Over the lead sheath, there is generally
bitumen to prevent damage
...

There are two types of armouring used for these cables
...


The capacitance between the conductors to neutral of 3-core belted cables cannot be
obtained by a simple derivation as for the single core cable
...
The capacitance per unit length to neutral is given by

C

0
...
52   1
...
84 
 1
 d  
T 
T 



2

Where,
t = thickness of belt insulation
T = thickness of conductor insulation
d = diameter of conductor

(μF/km)

(7
...
-7
...
-7
...


Cs

Sheath
Conductor

Cc

FIG
...
4 CAPACITANCE OF 3-CORE CABLES

Where, Cs - Capacitance between each core and sheath and Cc - Capacitance between cores
These can be calculated as mentioned below:

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

Step-I: Strap the 3 cores together and measure the capacitance between this bundle and the
sheath as shown in Fig
...
5
...
, So that
C x  3C s

(7
...
-7
...
-7
...
Let this value to be Cy
...
9)

Sheath

Cs

Conductor

Cc

Cy
FIG
...
6 MEASUREMENT OF CAPACITANCE OF 3-CORE CABLES (STEP-II)

69

70

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Using (7
...
9) we derive the capacitance between the conductors and the conductor
and Sheath
...
10)
(7
...
12)
(7
...
The insulation is fully stressed only at the conductor, and further away near the sheath
the insulation is unnecessarily strong and thus needlessly expensive
...



Capacitance grading



Intersheath grading

CAPACITANCE GRADING
In this method of grading, the insulation material consists of various layers having different
permittivities
...
-7
...

Let the outer radii of these layers by r1 , r2 & r3  R respectively, and the conductor radius
r
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

k3

Sheath
k2
Insulator

k1
r

r1

Conductor
r3=R

r2

FIG
...
7 CAPACITANCE GRADING OF CABLES

Let the voltage across the inner-most layer of insulation be V
...

Gradient at x  r is

G
q
 1
2k1r
f

Gradient at x  r1 is

G
q
 2
2k 2 r1
f

Gradient at x  r2 is

G
q
 3
2k 3 r2
f

From the above relations,
q  2k1r

G
G1
G
 2k 2 r1 2  2k 3 r2 3 which gives k1rG1  k 2 r1G2  k3 r2G3
f
f
f

Since r  r1  r2 it means k1G1  k 2 G2  k 3G3
This shows that material of highest product of dielectric strength and permittivity should
be placed nearest to conductor and other layers be in descending order of product of dielectric
strength and permittivity
...

Then,

71

72

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

g max 

q
q
q


2k1 r 2k 2 r1 2k 3 r2

k1r  k 2 r1  k3 r2
Hence k1  k 2  k3 , thus total operating voltage of the cable becomes

V  g max (r ln

r1
r
R
 r1 ln 2  r2 ln )
r
r1
r2

Hence by grading the insulation, without increasing the overall diameter of the cable, the
operating voltage can be raised
...
8 to 4
...

In the above analysis, it has been assumed that the maximum permissible stress is the same
for all three dielectrics used
...


INTERSHEATH GRADING
In this type grading method, a single insulating material is used but separated into two or
more layers by thin metallic intersheaths maintained at appropriate potentials by being connected
to tappings on the winding of an auxiliary transformer supplying the cable as shown in Fig
...
8
...
-7
...

Since there is a definite potential difference between the inner and outer radii of each sheath, we
can treat each section separately as a single core cable
...
Thus we can write at
the surface of different intersheaths
g max 1 

V1
V2
, g max 2 
r 
r
r ln  1 
r1 ln  2
r
 r1





Hence for grading purpose we need to have g max 1  g max 2 or

V1
V2

r 
r
r ln  1 
r1 ln  2
r
 r1





Since the cable insulation now consists of a number of capacitors in series, formed by the
respective intersheaths, all potential differences V1 &V2 are in phase
...
They may be caused by the
conductor current passing through the resistance of the conductor - conductor loss (also sometimes
called the copper loss on account of the fact that conductors were mainly made out of copper),
dielectric losses caused by the voltage across the insulation, sheath losses caused by the induced
currents in the sheath, and inter-sheath losses caused by circulating currents in loops formed
between sheaths of different phases
...


73

74

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

DIELECTRIC LOSS
For a perfect dielectric, the power factor is zero
...
The current leads the voltage by an angle of less than 90o, and hence
there is a power loss
...
-

I

φ
V

As because I  VC , the dielectric loss is given by
P  VICos  VISin  V 2CSin

Where If C is the capacitance of the cable, and V is the applied voltage
...

SHEATH LOSS
The losses occurring in the sheath of a cable is usually obtained by the empirical formula
of Arnold
...
7 X 10
  (W)
Rsh  d 
3

Where rm = mean radius of sheath, d = distance between cables (centre to centre), Rsh =
resistance of full length of cable, I = current in cable
The sheath loss is usually about 2 to 5 % of the conductor loss
...
This loss is thus present only when the sheaths of adjacent cables are connected

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

together
...
The intersheath loss can be calculated as follows
...
Thus the total power loss (exclusive of the dielectric loss) is given as
PLoss(total)  PC  Psh  Pish

(7
...
In order
to transfer electrical power from an alternating-current or a direct-current source to the place where
it will be used, some type of distribution network must be utilized
...
More complex power
distribution systems are used, to transfer electrical power from the power plant to industries,
homes, and commercial buildings
...
The original electrical distribution system
developed by Thomas Edison was an underground direct current (DC) system
...
It generally consists of feeders, distributors
...
-8
...
Basically we can say, that
part of power system which distributes electric power for local use is known as distribution system
...
Generally, no tappings are taken from the
feeder so that current in it remains the same throughout
...

Distributor: A distributor is a conductor from which tappings are taken for supply to the
consumers
...

Service mains: A service mains is generally a small cable which connects the distributor to
the consumers’ terminals
...
c
...
c
...


Now-a-days, a
...
system is universally adopted for distribution of electric power as it is
simpler and more economical than direct current method
...
-8
...


Each scheme has its own advantages and disadvantages
...
C
...
One important reason for the widespread use of alternating current in
preference to direct current is the fact that alternating voltage can be conveniently changed in
magnitude by means of a transformer
...
c
...
High transmission and distribution voltages have
greatly reduced the current in the conductors and the resulting line losses
...
However, in general, the a
...
distribution system is the electrical system between the

77

78

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

step-down substation fed by the transmission system and the consumers’ meters
...
c
...

Primary distribution system: It is that part of a
...
distribution system which operates at
voltages somewhat higher than general utilization and handles large blocks of electrical energy
than the average low-voltage consumer uses
...

The most commonly used primary distribution voltages are 11 kV, 66 kV and 33 kV
...

Electric power from the generating station is transmitted at high voltage to the substation
located in or near the city
...
Power is supplied to various substations for distribution or to big
consumers at this voltage
...

Secondary distribution system: It is that part of a
...
distribution system which includes the
range of voltages at which the ultimate consumer utilises the electrical energy delivered to him
...

The primary distribution circuit delivers power to various substations, called distribution
sub-stations
...
At each distribution substation, the voltage is stepped down to 400 V and power is
delivered by 3-phase,4-wire a
...
system
...
The single phase domestic loads are connected between
any one phase and the neutral, whereas 3-phase 400 V motor, power transformer loads are
connected across 3-phase lines directly
...
C
...
c
...
c
...
For
instance, d
...
supply is required for the operation of variable speed machinery (i
...
, d
...
motors),
for electro-chemical work and for congested areas where storage battery reserves are necessary
...
c
...
c
...
g
...
The d
...
supply
from the substation may be obtained in the form of (i) 2-wire or (ii) 3-wire for distribution
...
c
...

One is the outgoing or positive wire and the other is the return or negative wire
...
are connected in parallel between the two wires
...
c
...

3-wire d
...
system: It consists of two outers and a middle or neutral wire which is earthed
at the substation
...
The principal advantage of this system is that it makes available two voltages at the
consumer terminals viz
...
Loads
requiring high voltage (e
...
, motors) are connected across the outers, whereas lamps and heating
circuits requiring less voltage are connected between either outer and the neutral
...
A single line diagram of a radial distribution system is shown in
Fig
...
2
...

Source
Main Feeder
Laterals

Load

Load

Load

Load

FIG
...
2 RADIAL DISTRIBUTION SYSTEM

79

80

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

This is the simplest distribution circuit and has the lowest initial cost
...



The end of the distributor nearest to the feeding point will be heavily loaded
...
Therefore,
any fault on the feeder or distributor cuts off supply to the consumers who are on
the side of the fault away from the substation
...


Due to these limitations, this system is used for short distances only
...

Ring main system: In this system, the primaries of distribution transformers form a loop
...
The single line diagram of ring main system is shown in Fig
...
3
...
-8
...



There are less voltage fluctuations at consumer’s terminals
...
In the event
of fault on any section of the feeder, the continuity of supply is maintained
...
Then the faulted section
the feeder can be isolated for repairs and at the same time continuity of supply is maintained to all
the consumers via the other feeder
...
The single line diagram of interconnected system is shown in
Fig
...
4
...
-8
...



It increases the service reliability
...
This reduces reserve power capacity and increases
efficiency of the system
...
Let us
consider a simple dc radial distribution system as shown in Fig
...
5
...
-8
...
The resistance of different section has been shown in the Fig
...
5
...
Let the voltages at different nodes are Va ,Vb ,Vc ,Vd & Ve and the feeder is fed at the
voltage Vo
...
1)

The current flowing in the section ‘OA’ is
I oa  I a  I b  I c  I d  I e

(8
...
2b)

The current flowing in the section ‘BC’ is

I bc  I c  I d  I e

(8
...
2d)

The current flowing in the section ‘DE’ is

I de  I e
The total voltage drop therefore, is given by

(8
...
3)

Similarly we can determine the voltage drop for ac distribution system
...
If the load is uniform then the voltage drop is calculated for a
very small length of the feeder such as dx and then integrate it over the whole length
...
Some of the requirements of a good distribution
system are proper voltage, availability of power on demand and reliability
...
The changes in voltage are
generally caused due to the variation of load on the system
...
High voltage causes lamps to burn out
permanently and may cause failure of other appliances
...

The statutory limit of voltage variations is ± 5% of the rated value at the consumer’s terminals
...

Availability of power on demand: Power must be available to the consumers in any amount
that they may require from time to time
...
As electrical
energy cannot be stored, therefore, the distribution system must be capable of supplying load
demands of the consumers
...

Reliability: Modern industry is almost dependent on electric power for its operation
...
This calls
for reliable service
...
However, the reliability can be improved to a considerable extent by


Interconnected system



Reliable automatic control system



Providing additional reserve facilities
...
For this purpose, design of feeders and
distributors requires careful consideration
...
It is because voltage drop in a feeder can
be compensated by means of voltage regulating equipment at the substation
...
It is
because a distributor supplies power to the consumers and there is a statutory limit of voltage
variations at the consumer’s terminals (± 6% of rated value)
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

CHAPTER-9
NEUTRAL GROUNDING
INTRODUCTION
System grounding is the intentional connection of the neutral points of transformers,
generators and rotating machinery to earth
...
The basic difference between system and equipment grounding is that system
grounding involves grounding circuit conductors that are current carrying under normal operation,
where equipment grounding involves grounding of all non-current carrying metallic parts that
enclose the circuit conductors
...

The best way to obtain the system neutral for grounding purposes in three phase systems
is to use source transformers or generators with Wye-connected windings
...
When the system neutral may not available, earthing transformer may be used
to obtain the neutral
...
-9
...
A three phase system with its voltage phasor diagram is
shown
...
-9
...
When the neutral of a system is not grounded, a ground
fault on one line causes full line to line voltage throughout the system, between ground and the
two unfaulted phases
...
-9
...
Usually the
insulation between each line and ground is adequate to withstand full line to line voltage
...
In spite of these considerations, ungrounded systems may
be used to gain an additional degree of service continuity
...
-9
...
-9
...
There are three typical grounding methods
...
-9
...
This reduces the problem
of transient over-voltages found on the ungrounded system and aids in the location of faults
...
-9
...
-9
...
The magnitude of the current depends on the fault location and the fault resistance
...

The main advantage of solidly earthed systems is low over voltages, which makes the earthing
design common at high voltage levels (HV)
...

Solid grounding facilitates the automatic clearing of ground faults by circuit protective
equipment (fuses and circuit breakers) because solid grounding results in the highest magnitude of
ground fault current
...

RESISTANCE GROUNDED NEUTRAL SYSTEMS
Resistance grounding provides protection of a transformer/generator by solving the
problem of transient over-voltages thereby reducing equipment damage
...
In addition, limiting fault current to predetermined maximum values permits the
designer to selectively co-ordinate the operation of protective devices, which minimizes system
disruption and allows quick location of the fault
...
-9
...

R

VR

N
Y

VY
B

VB
FIG
...
4 RESISTANCE GROUNDED THREE PHASE SYSTEM

Neutral grounding resistors will have advantage by reducing magnitude of transient overvoltages, thereby reducing equipment damage, simplifying ground fault location, improving
system and equipment fault protection, reducing maintenance time and expense, creating improved
safety for personnel, improving lightning protection and reducing fault frequency
...



Low-resistance



High-resistance

In both types of grounding, the resistor is connected between the generator/transformer
neutral and earth ground
...
These devices are then able to quickly clear the fault, usually
within a few seconds
...
The
limited fault current and fast response time also prevent overheating and mechanical stress on
conductors
...

Low-resistance grounding, typically 400 Amps for 10 seconds are commonly found on medium
and high voltage systems
...
It is typically used on low voltage systems of
600 volts or less
...
This permits
continued production, provided a second ground fault does not occur
...




The neutral point resistance can be chosen to limit the possible over voltage
transients to 2
...


Disadvantages:


Generates extensive earth fault currents when combined with strong or moderate
capacitive connection to earth
...
The ground fault that may flow is a
function of the neutral reactance, the level of the fault current is often used as a criteria for
describing the degree of grounding
...
This is considerably
higher than the level of fault current desirable in the system using resistor, and therefore reactance
grounding is usually not considered as an alternative to the system using resistor
...
In such case the reactor is used as transformer grounding to obtain the neutral
...
It is also known as resonant grounding
...
Resonance earthing makes it possible to more or less eliminate
the reactive earth fault current
...




Enables high impedance fault detection
...


The IEEE Green Book, Standard 142, contains useful reference information on system
grounding factors in selecting a system grounding method and equipment grounding and methods
...


CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

CHAPTER-10
SUB-STATION
Substations are key parts of electrical generation, transmission, and distribution systems
...
Substations also
dispatch electric power from generating stations to consumption centers
...
Substations can be generally divided into three major types:
1
...
This transmission grid is often called the bulk power system
...
Transmission substations often include
transformation from one transmission voltage level to another
...
Sub-transmission substations typically operate at 33 kV through 132 kV voltage levels,
and transform the high voltages used for efficient long distance transmission through the grid to
the sub-transmission voltage levels for more cost-effective transmission of power through supply
lines to the distribution substations in the surrounding regions
...

3
...
4 kV voltage levels, and deliver
electric energy directly to industrial and residential consumers
...
These feeders serve a
large number of premises and usually contain many branches
...

A typical sub-station connection diagram is shown in Fig
...
1
...



Power transformer or distribution transformer as the case may be of sub-station



Circuit breakers



Disconnecting switches



Isolators



Station bus

91

92

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

Source
Lightening Arrestor

Circuit Breaker

Isolator

Current Transformer

Potential Transformer

Main Transformer

Fuse

Load
FIG
...
1 A TYPICAL LAY-OUT OF SUB-STATION



Current transformer



Potential transformer



Lightening arrestor



Protective relays



Station batteries



Earthing system

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

TRANSFORMERS
...
They come in various sizes and
voltage ratings
...

In sub-station either power transformer or distribution transformers are used depending upon the
sub-station location i
...
transmission sub-station or distribution sub-station
...
Many
outdoor substations use oil-filled circuit breakers
...
Another type of high-voltage circuit
breaker is the magnetic air breaker in which the contacts separate, in the air, when the power line
is overloaded
...
A modification of this type is the compressed- air circuit breaker
...
The
compressed air aids in extinguishing the arc, which is developed when the contacts open
...
This
problem is not encountered to any great extent in low-voltage protective equipment
...
Ordinarily, disconnect switches are not operated when current
is flowing through them
...
They are opened mainly to isolate equipment
from power lines for safety purposes
...
These switches are available for indoor or outdoor use in
both manual and motor-operated designs
...
Without
lightning arresters, power lines and associated equipment could become inoperable when struck

93

94

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

by lightning
...
Their response
time must be more rapid than the other protective equipment used on power lines
...
The other side of
the arrester is connected to a power line
...
Lightning is a major cause of power-system failures and equipment damage,
so lightning arresters have a very important function
...
Large
strings of insulators are used at substations and at other points along the power distribution system
to isolate the current carrying conductors from their steel supports or any other ground mounted
equipment
...

PROTECTIVE RELAYS
Protective relays provide an accurate and sensitive method of protecting electrical
distribution equipment short circuits and other abnormal conditions
...
The response time of the relays is very important in protecting the equipment from damage
...

Each of these conditions is caused by faulty circuit conditions which draw abnormally high current
(fault currents) from the power lines
...
This protective equipment must
be designed to handle high voltages and currents
...
High-voltage fuses (those used for over 600 volts) are made in
several ways
...
Liquid fuses have a
liquid-filled metal enclosure, which contains the fuse element
...
When the fuse element melts due to an excessive current in a power line, the element is
immersed in the liquid to extinguish the arc
...
A solid material fuse is similar to a liquid fuse except that the arc is extinguished in a
chamber filled with solid material
...
These switches provide a means of switching power
lines and disconnecting them for repair
...

SUBSTATION LOCATION
Distribution substations should be located as close to the load to be served as possible
...
The level of distribution voltage is
also a consideration
...
However, they become larger in capacity and in number of customers served as
distance apart increases
...
Among these factors are the availability of land, estimated operating costs,
taxes, local zoning laws, environmental factors and potential public opinion
...
The primary voltage
level affects not only the size of conductors, but also the size of regulation equipment, insulation
and other equipment ratings
...
The connection schemes
for the buses are described herein
...
The
students are advised to discuss these in the class room
...
-10
...
-10
...
-10
...
-10
...
-10
...
-10
...
We see
that the power flow depends upon the magnitude of voltages at both the ends of the line, phase
difference between two end voltages and the reactance of the transmission link
...
Moreover the line is operated at its rated design voltage hence the power flow through the
link is limited by the magnitude of voltages i
...
operating voltage
...

LINE COMPENSATION
As stated above the power flow in a transmission line depends upon the voltage at both the
ends, the reactance of the line and phase difference between the voltages
...
It can be controlled by


Voltage magnitude control



Transmission line reactance control



Phase angle control

Once the installation of the transmission line is over its A, B, C, D parameters are constant
because these depend upon the size and material of conductors and the configurations of the
conductors
...
The value of reactance

X however can be controlled by providing compensation
...
The shunt admittance of the
transmission line consists of capacitive reactance, the effect of which can be compensated by
connecting a shunt reactor
...
The line
compensation are of two types
...
-11
...
The location of this capacitor is optional
and depend upon the requirement of transmission company
...
-11
...
-11
...

S

R

FIG
...
2 TRANSMISSION LINE WITH SHUNT COMPENSATION

The value of series compensation and shunt compensation known as degree of
compensation depend upon operational policy
...

In power system most of the loads are inductive in nature resulting in reducing the voltage
at which it is connected, it is well known to connect the capacitor at that voltage
...
Thus Fig
...
2 can be
modified to Fig
...
3
...
-11
...
If the magnitude of voltage at the bus is more than the required magnitude
then the shunt reactor is connected
...

With the insertion of compensation the circuit parameters changes and thus the operation
of the power system
...
To achieve required degree of compensation under all loading
condition, we need to have a very flexible operation, which shall provide any degree of
compensation
...
The AC transmission system,
which employs to achieve a flexible operation is known as flexible AC transmission system
(FACTS) and the devices used for such operation are known as FCATS devices
...
These devices can be divided into
two categories
...
The second group uses self-commuted static converters
as controlled voltage sources
...
These employs conventional thyristor in circuit arrangements
with capacitor or reactor or tap changing transformer, such that these can represented by variable
admittance in the circuit
...

These controllers provide superior performance characteristics and uniform applicability for
transmission voltage, effective line impedance control and angle control
...
The static synchronous compensator
(STATCOM) and static synchronous series compensator (SSSC) are the FACTS devices in this
group as counterpart to SVC and TCSC in the first group
...
Basically the SVC is more
effective in the bus voltage control at which it is connected rather than the power flow control in
the transmission line
...
The Fixed Capacitor (FC) with a
thyristor Controlled Reactor (TCR) configuration of the SVC is shown in Fig
...
4
...
-11
...


FIG
...
4 FC-TCR CONFIGURATION OF SVC
...
-11
...
The fixed reactor and bi-directional valve
can be modeled as an equivalent variable inductance using Fourier analysis on the inductor current
waveform
...

The variables are the current I svc , the reactive power Qsvc , the firing angle  svc , the
equivalent susceptance Be and the voltage reference Vsvcref
...

THYRISTOR CONTROLLED SERIES CAPACITOR (TCSC)
The thyristor controlled series capacitor (TCSC) is a capacitive reactance compensator,
which consists of a series capacitor bank shunted by a thyristor controlled reactor in order to
provide a smoothly variable series capacitive reactance
...

The same FC-TCR configuration shown above can be used as TCSC, however it is
connected in series with the transmission line
...
The minimum series compensation is reached when the TCR

103

104

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

is off
...

In the thyristor switched capacitor scheme, the degree of series compensation is controlled
by increasing or decreasing the number of capacitor bank in series
...
To minimize switching transients and
utilize natural commutation, the operation of the thyristor is coordinated with voltage and current
zero crossings
...
-11
...
The VSC is
connected to the ac system bus through a coupling transformer
...
The real power is
absorbed or supplied by VSC to the system if Vac  Vbus or Vac  Vbus respectively
...
The STATCOM is connected in shunt with the transmission line
...

Vbus

AC System Bus
Coupling Transformer

P, Q
Vac

AC terminal

Pref
Voltage Sourced
Converter

Qref

DC terminal

Vdc
FIG
...
6 FUNCTIONAL DIAGRAM OF STATCOM

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION

STATIC SYNCHRONOUS SERIES COMPENSATOR (SSSC)
The static synchronous series compensator (SSSC) is a series controller and employs the
same configuration shown in Fig
...
6
...
It inject a voltage in series with the line voltage profile and thus
improves the power transfer
...
-11
...
It is generally operated
without an external energy source thus it can only inject a variable voltage which is 900 leading or
lagging the current
...
-11
...
The SSSC
is a series controller and used to control the power transfer through the transmission line by
controlling the series impedance
...
It is controlled to provide
concurrent real and reactive series line compensation without any external energy source
...
The UPFC functional diagram is given in Fig
...
8
...
-11
...

Sl
...


SVC

STATCOM

1

It acts as a variable susceptance
...


2

It is sensitive to transmission system It is insensitive to transmission system
harmonics
...


3

It has smaller dynamic range
...


4

Its performance is slow
...


6

It has difficulty in operating during It can maintain stable voltage in weak AC
weak AC system
...


system
...


In this chapter a brief introduction on flexible ac transmission system (FACTS) and the
devices used in FACTS are described
...
They are as follows:

CLASS NOTES ON ELECTRICAL POWER TRANSMISSION AND DISTRIBUTION



Thyristor switched capacitor



Thyristor switched reactor



Thyristor controlled capacitor



Thyristor controlled reactor



Thyristor controlled/switched series capacitor



Thyristor controlled/switched series reactor



Thyristor controlled/switched phase shifting transformer



Thyristor controlled/switched voltage regulator



Interline power flow controller etc
...


107

108

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY, ODISHA, BURLA

C ONCLUSION
This class note has been prepared for the use by the students as a supplement to this course
...
The students are advised to attend the classes
and go through this notes along with the progress of the subject in the classes
...
The author wishes best of luck
to the students

---