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1. EEE 402
Power System I
Introduction
Md Rizwanul Arafin Neyon
Dept. of Electrical and Electronics Engineering
Chittagong Independent University
neyon@ciu.edu.bd
Cell: 01750695207

2. About me
• Professional
– Received BS in EEE from CUET, MS from
Purdue University USA
– Worked as a graduate teaching assistant in
ECE department of Purdue University for two
years.
– Worked as a graduate research assistant in
mechatronics lab of school of technology of
Purdue University for two years
– Worked as a part time faculty in Ivy tech , IN,
USA
2

3. Simple Power System
• Every power system has three major
components
– generation: source of power, ideally with a
specified voltage and frequency
– load: consumes power; ideally with a constant
resistive value
– transmission system: transmits power; ideally as a
perfect conductor

4. Complications
• No ideal voltage sources exist
• Loads are seldom constant
• Transmission system has resistance,
inductance, capacitance and flow limitations
• Simple system has no redundancy so power
system will not work if any component fails

5. Notation - Power
• Power: Instantaneous consumption of energy
• Power Units
• Watts = voltage x current for dc (W)
• kW – 1 x 103 Watt
• MW – 1 x 106 Watt
• GW – 1 x 109 Watt
• Installed U.S. generation capacity is about
1000 GW ( about 3 kW per person)
• Maximum load of Champaign/Urbana about 300
MW

6. Notation - Energy
• Energy: Integration of power over time; energy is
what people really want from a power system
• Energy Units
– Joule = 1 Watt-second (J)
– kWh = Kilowatthour (3.6 x 106 J)
– Btu = 1055 J; 1 MBtu=0.292 MWh
– One gallon of gas has about 0.125 MBtu (36.5 kWh);
• U.S. electric energy consumption is about 3600
billion kWh (about 13,333 kWh per person, which
means on average we each use 1.5 kW of power
continuously)

7. Power System Examples
• Electric utility: can range from quite small, such
as an island, to one covering half the continent
– there are four major interconnected ac power systems
in North American, each operating at 60 Hz ac; 50 Hz
is used in some other countries.
• Airplanes and Spaceships: reduction in weight is
primary consideration; frequency is 400 Hz.
• Ships and submarines
• Automobiles: dc with 12 volts standard
• Battery operated portable systems

8. Electric Systems in Energy Context
• Class focuses on electric power systems, but we
first need to put the electric system in context of
the total energy delivery system
• Electricity is used primarily as a means for energy
transportation
• Use other sources of energy to create it, and it is
usually converted into another form of energy when
used
• About 40% of US energy is transported in electric
form
• Concerns about need to reduce CO2 emissions
and fossil fuel depletion are becoming main
drivers for change in world energy infrastructure

9. US Historical Energy Usage
9
Source: EIA Monthly Energy Review, July 2016

10. Renewable Energy Consumption
10
Source: EIA Monthly Energy Review, July 2016

11. Growth in US Wind Power Capacity
11
Source: AWEA Wind Power Outlook 2 Qtr, 2016
The quick
development
time for wind
of 6 months
to a year
means that
changes in
federal tax
incentives
can have
an almost
immediate
impact on
construction

12. Energy Economics
Electric generating technologies involve a tradeoff between fixed
costs (costs to build them) and operating costs
•Nuclear and solar high fixed costs, but low operating costs
(though cost of solar has decreased substantially recently)
•Natural gas/oil have low fixed costs but can have higher
operating costs (dependent upon fuel prices)
•Coal, wind, hydro are in between
Also the units capacity factor is important to determining ultimate
cost of electricity

13. Ball park Energy Costs
13
Source: Steve Chu and Arun Majumdar, “Opportunities and challenges for a
sustainable energy future,” Nature, August 2012, Figure 6
Energy costs depend
upon the capacity factor
for the generator.
The capacity factor is the
ratio of the electricity
actually produced,
divided by its maximum
potential output. It is
usually expressed on an
annual basis.

14. Natural Gas Prices 1997 to 2015
14
Marginal cost for natural gas fired electricity price
in $/MWh is about 7-10 times gas price
Source: http://www.eia.gov/dnav/ng/hist/rngwhhdW.htm

15. Coal Prices have Fallen Substantially
from Five Years Ago
15
BTU content per pound varies between about 8000
and 15,000 Btu/lb, giving costs of around $1 to 2/Mbtu
July 2016 prices
per ton range from $8.70
to
$43.35
Source: eia.gov/coal

16. Solar PV Prices
16
Image: http://cleantechnica.com/2015/08/13/us-solar-pv-cost-fell-50-5-years-government-report/screen-shot-2015-08-
12-at-12-33-53-pm/

17. Brief History of Electric Power
• First real practical uses of electricity began with the
telegraph (1860's) and then arc lighting in the 1870’s
• Early 1880’s – Edison introduced Pearl Street dc system
in Manhattan supplying 59 customers
• 1884 – Sprague produces practical dc motor
• 1885 – invention of transformer
• Mid 1880’s – Westinghouse/Tesla introduce rival ac
system
• Late 1880’s – Tesla invents ac induction motor
• 1893 – Three-phase transmission line at 2.3 kV

18. History, cont’d
• 1896 – ac lines deliver electricity from hydro
generation at Niagara Falls to Buffalo, 20 miles
away; also 30kV line in Germany
• Early 1900’s – Private utilities supply all
customers in area (city); recognized as a
natural monopoly; states step in to begin
regulation
• By 1920’s – Large interstate holding
companies control most electricity systems

19. History, cont’d
• 1935 – Congress passes Public Utility Holding
Company Act to establish national regulation,
breaking up large interstate utilities (repealed
2005)
• This gave rise to electric utilities that only operated in one
state
• 1935/6 – Rural Electrification Act brought
electricity to rural areas
• 1930’s – Electric utilities established as vertical
monopolies
• Frequency standardized in the 1930’s

20. History, cont’d -- 1970’s
• 1970’s brought inflation, increased fossil-fuel
prices, calls for conservation and growing
environmental concerns
• Increasing rates replaced decreasing ones
• As a result, U.S. Congress passed Public Utilities
Regulator Policies Act (PURPA) in 1978, which
mandated utilities must purchase power from
independent generators located in their service
territory (modified 2005)
• PURPA introduced some competition

21. PURPA and Renewable
• PURPA, through favorable contracts, caused the
growth of a large amount of renewable energy in the
1980’s (about 12,000 MW of wind, geothermal, small
scale hydro, biomass, and solar thermal)
– These were known as “qualifying facilities” (QFs)
– California added about 6000 MW of QF capacity during the
1980’s, including 1600 MW of wind, 2700 MW of
geothermal, and 1200 MW of biomass
– By the 1990’s the ten-year QFs contracts written at rates
of $60/MWh in 1980’s, and they were no longer profitable
at the $30/MWh 1990 values so many sites were retired or
abandoned

22. CONDUCTOR
Conductor is a physical medium to carry electrical
energy form one place to other. It is an important
component of overhead and underground electrical
transmission and distribution systems. The choice
of conductor depends on the cost and efficiency. An
ideal conductor has following features.
1. It has maximum conductivity
2. It has high tensile strength
3. It has least specific gravity i.e. weight / unit
volume
4. It has least cost without sacrificing other factors

23. Power Transmission line
•A transmission line is a pair of electrical conductors carrying
an electrical signal from one place to another.
• Coaxial cable and twisted pair cable are examples.
• The two conductors have inductance per unit length, which
we can calculate from their size and shape.
• They have capacitance per unit length, which we can
calculate from the dielectric constant of the insulation.
•The electrical resistance of the conductors, is significant
because it increases with frequency.
•The magnetic fields generated by high-frequency currents
drive those currents to the outer edge of the conductor that
carries them, so the higher the frequency, the thinner the
layer of metal available to carry the current, and the higher
the effective resistance of the cable.

24. Types
The transmission lines are categorized as three
types 1) Short transmission line – the line
length is up to 80 km
2) Medium transmission line – the line length is
between 80km to 150 km
3) Long transmission line – the line length is
more than 150 km

25. Equivalent circuit of short transmission
line
The transmission lines which have length less than 50 km
are generally referred as short transmission lines.
For short length, the shunt capacitance of this type of line
is neglected and other parameters like electrical
resistance and inductor of these short lines are lumped,
hence the equivalent circuit is represented as given
below,
Let’s draw the vector diagram for this equivalent circuit,
taking receiving end current Ir as reference. The sending
end and receiving end voltages make angle with that
reference receiving end current, of φs and φr,
respectively.

26. Cont….

27. Cont…..
As the shunt capacitance of the line is neglected, hence
sending end current and receiving end current is same,
i.e. Vs is approximately equal to
As there is no capacitance, during no load condition the
current through the line is considered as zero, hence at
no load condition, receiving end voltage is the same as
sending end voltage.
As per dentition of voltage regulation of power
transmission line

28. 10.1 Classification of Overhead Transmission Lines
A transmission line has *three constants R, L and C distributed uniformly along the whole
length of the line. The resistance and inductance form the series impedance. The
capacitance existing between conductors for 1-phase line or from a conductor to neutral for
a 3-phase line forms a shunt path throughout the length of the line. Therefore, capacitance
effects introduce complications in transmission line calculations. Depending upon the
manner in which capacitance is taken into account, the overhead transmission lines are
classified as :
(i)Short transmission lines. When the length of an overhead transmission line is upto
about 50 km and the line voltage is comparatively low (< 20 kV), it is usually considered as a
short transmission line. Due to smaller length and lower voltage, the capacitance effects are
small and hence can be neglected. Therefore, while studying the performance of a short
transmisison line, only resistance and inductance of the line are taken into account.
(ii) Medium transmission lines. When the length of an overhead transmission line is about
50-150 km and the line voltage is moderatly high (>20 kV < 100 kV), it is considered as a
medium transmission line. Due to sufficient length and voltage of the line, the capacitance
effects are taken into account. For purposes of calculations, the distributed capacitance of
the line is divided and lumped in the form of condensers shunted across the line at one or
more points.

29. •(iii) Long transmission lines. When the length of an overhead transmission line is
more than 150 km and line voltage is very high (> 100 kV), it is considered as a long
transmission line. For the treatment of such a line, the line constants are considered
uniformly distributed over the whole length of the line and rigorous methods are
employed for solution.
•10.2 Important Terms
While studying the performance of a transmission line, it is desirable to determine its
voltage regulation and transmission efficiency. We shall explain these two terms in
turn-
(i) Voltage regulation: When a transmission line is carrying current, there is a voltage
drop in the line due to resistance and inductance of the line. The result is that
receiving end voltage (VR) of the line is generally less than the sending end voltage
(VS). This voltage drop (VS −VR) in the line is expressed as a percentage of receiving
end voltage VR and is called voltage regulation.The difference in voltage at the
receiving end of a transmission line **between conditions of no load and full load is
called voltage regulation and is expressed as a percentage of the receiving end
voltage.

31. 10.3 Performance of Single Phase Short Transmission Lines

42. 10.6 Medium Transmission Lines
•In short transmission line calculations, the effects of the line
capacitance are neglected because such lines have smaller lengths and
transmit power at relatively low voltages (< 20 kV).
•However, as the length and voltage of the line increase, the
capacitance gradually becomes of greater importance.
•Since medium transmission lines have sufficient length (50-150 km)
and usually operate at voltages greater than 20 kV, the effects of
capacitance cannot be neglected.
•Therefore, in order to obtain reasonable accuracy in medium
transmission line calculations, the line capacitance must be taken into
consideration. The most commonly used methods for the solution of
medium transmissions lines are :
•(i) End condenser method (ii) Nominal T method (iii) Nominal π
method

48. EQUIVALENT CIRCUIT OF MEDIUM
TRANSMISSION LINE
•The transmission line having its effective length more than 80 km but
less than 250 km is generally referred to as a medium transmission
line. Due to the line length being considerably high, admittance Y of
the network does play a role in calculating the effective circuit
parameters, unlike in the case of short transmission lines. For this
reason the modeling of a medium length transmission line is done
using lumped shunt admittance along with the lumped impedance in
series to the circuit.
These lumped parameters of a medium length transmission line can be
represented using three different models, namely-
•Nominal Π representation.
•Nominal T representation.
•End Condenser Method.

49. Nominal Π representation of a
medium transmission line
•In case of a nominal Π representation, the lumped series
impedance is placed at the middle of the circuit where as
the shunt admittances are at the ends.
•As we can see from the diagram of the Π network below,
the total lumped shunt admittance is divided into 2 equal
halves, and each half with value Y ⁄ 2 is placed at both the
sending and the receiving end while the entire circuit
impedance is between the two.
•The shape of the circuit so formed resembles that of a
symbol Π, and for this reason it is known as the nominal
Π representation of a medium transmission line.

50. Cont….
As we can see here, VS and VR is the supply and receiving end voltages respectively, and Is is the
current flowing through the supply end. IR is the current flowing through the receiving end of
the circuit. I1 and I3 are the values of currents flowing through the admittances. And I2 is the
current through the impedance Z. Now applying KCL, at node P, we get.
IS = I1 + I2 —————(1)
Similarly applying KCL, to node Q.
I2 = I3 + IR —————(2)
Now substituting equation (2) to equation (1)
IS = I1 + I3 + IR
= (Y/2)Vs+(Y/2)Vr+ IR

51. Cont….

52. Cont…..
Comparing equation (4) and (5) with the
standard ABCD parameter equations
VS = A VR + B IR
IS = C VR + D IR We derive the parameters of a
medium transmission line as:

58. Equivalent circuit of long transmission line
From the provided sheet

59. Surge impedance

60. Ferranti effect

61. Inductance of Three Phase Lines With
Equilateral and Symmetrical Spacing
Consider a three phase line consisting of three phase conductors a, b
and c
as shown in the Fig. 1. These
three conductors are equally
spaced at the corners of an
equilateral triangle having
radius r . The flux linkages of
conductor a are given by,
If the currents are assumed to be balanced than
Ia+ Ib + Ic = 0
... Ia = - ( Ib + Ic )
or ( Ib + Ic) = - Ia
The inductance of conductor a is given by

62. because of symmetry, conductors b and c will
have same inductance as that of conductor a.
Each phase consists of only one conductor. So
the above equation gives inductance per
phase of the three phase lines.

63. Distribution system
•The electrical energy produced at the generating station is conveyed to the
consumers through a network of transmission and distribution systems.
•The transmission and distribution systems are
similar to man’s circulatory system.
•The transmission system may be compared with arteries in the human body
and distribution system with capillaries.
•They serve the same purpose of supplying the ultimate consumer in the city
with the life giving blood of civilization–electricity. In this chapter, we shall
confine our attention to the general introduction to distribution system.
•That part of power system which distributes electric power for local use is
known as distribution system.
•In general, the distribution system is the electrical
system between the sub-station fed by the transmission
system and the consumers meters.
• It generally consists of feeders, distributors and the
service mains. Fig. 12.1 shows the single line diagram
of a typical low tension distribution system

64. Continue…..
(i)Feeders: A feeder is a conductor which connects the sub-station (or
localized generating station) to the area where power is to be
distributed. Generally, no tapings are taken from the feeder so that
current in it remains the same throughout. The main consideration in
the design of a feeder is the current carrying capacity.
(ii) Distributor: A distributor is a conductor from which tappings are
taken for supply to the consumers. In Fig. 12.1, AB, BC, CD and DA are
the distributors. The current through a distributor is not constant
because tappings are taken at various places along its length. While
designing a distributor, voltage drop along its length is the main
consideration since the statutory limit of voltage variations is ± 6% of
rated value at the consumers’ terminals.
(iii) Service mains: A service mains is generally a small cable which
connects the distributor to the consumers’ terminals.

65. Classification of Distribution Systems
A distribution system may be classified according to –
(i) Nature of current: According to nature of current, distribution system may
be classified as (a) d.c. distribution system (b) a.c. distribution system.
Now-a-days, a.c. system is universally adopted for distribution of electric
power as it is simpler and more economical than direct current method.
(ii)Type of construction: According to type of construction,
distribution system may be classified as (a) overhead system
(b) underground system. The overhead system is generally
employed for distribution as it is 5 to 10 times cheaper
than the equivalent underground system. In general, the
underground system is used at places where overhead construction is
impracticable or prohibited by the local laws.
iii) Scheme of connection: According to scheme of connection, the
distribution system may be classified as (a) radial system (b) ring main system
(c) inter-connected system. Each scheme has its own advantages and
disadvantages

66. Overhead Versus Underground System
The distribution system can be overhead or underground.
Overhead lines are generally mounted on wooden, concrete or steel poles which are
arranged to carry distribution transformers in addition to the conductors.
The underground system uses conduits, cables and manholes under the surface of
streets and sidewalks.
The choice between overhead and underground system depends upon a number of
widely differing factors. Therefore, it is desirable to make a comparison between the
two-
(i) Public safety : The underground system is more safe than overhead system because
all distribution wiring is placed underground and there are little chances of any
hazard.
(ii) Initial cost: The underground system is more expensive due to the high cost of
trenching, conduits, cables, manholes and other special equipment. The initial cost of
an underground system may be five to ten times than that of an overhead system.
(iii) Flexibility: The overhead system is much more flexible than the underground
system. In the latter case, manholes, duct lines etc., are permanently placed once
installed and the load expansion can only be met by laying new lines. However, on an
overhead system, poles, wires, transformers etc., can be easily shifted to meet the
changes in load conditions.

67. CONT….
(iv) Faults: The chances of faults in underground system are very rare as the cables are
laid underground and are generally provided with better insulation.
(v) Appearance: The general appearance of an underground system is better as all the
distribution lines are invisible. This factor is exerting considerable public pressure on
electric supply companies to switch over to underground system.
(vi) Fault location and repair: In general, there are little chances of faults in an
underground system. However, if a fault does occur, it is difficult to locate and repair
on this system. On an overhead system, the conductors are visible and easily
accessible so that fault locations and repairs can be easily made.
(vii) Current carrying capacity and voltage drop: An overhead distribution conductor
has a considerably higher current carrying capacity than an underground cable
conductor of the same material and cross-section because of closer spacing of
conductors.
(viii) Useful life: The useful life of underground system is much longer than that of an
overhead system. An overhead system may have a useful life of 25 years, whereas an
underground system may have a useful life of more than 50 years.

68. Cont….
(ix) Maintenance cost: The maintenance cost of underground
system is very low as compared with that of overhead system
because of less chances of faults and service interruptions from
wind, ice, lightning as well as from traffic hazards.
(x) Interference with communication circuits: An overhead
system causes electromagnetic interference with the telephone
lines. The power line currents are superimposed on speech
currents, resulting in the potential of the communication
channel being raised to an undesirable level. However, there is
no such interference with the underground system

69. Requirements of a Distribution System
A considerable amount of effort is necessary to maintain an electric power supply
within the requirements of various types of consumers. Some of the requirements of a
good distribution system are :
proper voltage, availability of power on demand and reliability.
(i) Proper voltage: One important requirement of a distribution system is that voltage
variations at consumer’s terminals should be as low as possible. The changes in
voltage are generally caused due to the variation of load on the system. Low voltage
causes loss of revenue, inefficient lighting and possible burning out of motors. High
voltage causes lamps to burn out permanently and may cause failure of other
appliances. Therefore, a good distribution system should ensure that the voltage
variations at consumers terminals are within permissible limits. The statutory limit of
voltage variations is ± 6% of the rated value at the consumer’s terminals. Thus, if the
declared voltage is 230 V, then the highest voltage of the consumer should not exceed
244 V while the lowest voltage of the consumer should not be
less than 216 V.
(ii) Availability of power on demand: Power must be available to the consumers in
any amount that they may require from time to time.

70. Cont….
. For example, motors may be started or shut down, lights may be
turned on or off, without advance warning to the electric supply
company. As electrical energy cannot be stored, therefore, the
distribution system must be capable of supplying load demands of the
consumers. This necessitates that operating staff must continuously
study load patterns to predict in advance those major load changes
that follow the known schedules.
(iii) Reliability: Modern industry is almost dependent on electric
power for its operation. Homes and office buildings are lighted,
heated, cooled and ventilated by electric power. This calls for reliable
service. Unfortunately, electric power, like everything else that is man-
made,can never be absolutely reliable. However, the reliability can be
improved to a considerable extent by (a) interconnected system (b)
reliable automatic control system (c) providing additional reserve
facilities.

71. Types of D.C. Distributors
The most general method of classifying d.c. distributors is the way they are fed by the
feeders. On this basis, d.c. distributors are classified as:
(i) Distributor fed at one end
(ii) Distributor fed at both ends
(iii) Distributor fed at the centre
(iv) Ring distributor.
(i) Distributor fed at one end: In this
type of feeding, the distributor is
connected to the supply at one
End and loads are taken at
different points along the length of the
distributor. Fig. 13.1 shows the single
line diagram of a d.c. distributor
AB fed at the end A (also known as
singly fed distributor) and loads I1, I2
and I3 tapped off at points C, D and E
respectively.

72. Cont….
The following points are worth noting in a singly fed distributor :
(a) The current in the various sections of the distributor away from feeding point goes
on decreasing. Thus current in section AC is more than the current in section CD and
current in section CD is more than the current in section DE.
(b) The voltage across the loads away from the feeding point goes on decreasing. Thus
in Fig. 13.1, the minimum voltage occurs at the load point E.
(c) In case a fault occurs on any section of the distributor, the whole distributor will
have to be disconnected from the supply mains. Therefore, continuity of supply is
interrupted.
Distributor fed at both ends: In this type of feeding, the distributor is connected to
the supply mains at both ends and loads are
tapped off at different points along the length
of the distributor. The voltage at the feeding
points may or may not be equal. Fig. 13.2
shows a distributor AB fed at the ends A and
B and loads of I1, I2 and I3 tapped off at
points C, D and E respectively. Here, the load voltage goes on decreasing as we move
away from one feeding point say A, reaches minimum value and then again starts
rising and reaches maximum value when we reach the other feeding point B. The
minimum voltage occurs at some load point and is never fixed. It is shifted with the
variation of load on different sections of the distributor.
.

73. Cont….
Advantages
(a) If a fault occurs on any feeding point of the distributor, the continuity of supply is
maintained from the other feeding point.
(b) In case of fault on any section of the distributor, the continuity of supply is maintained
from the other feeding point.
(c) The area of X-section required for a doubly fed distributor is much less than that of a
singly fed distributor.
(iii) Distributor fed at the centre: In this type of feeding,
the centre of the distributor is connected to the supply
mains as shown in Fig. 13.3. It is equivalent to two singly
fed distributors, each distributor having a common
feeding point and length equal to half of the total length.
(iv) Ring mains: In this type, the distributor is in the
form of a closed ring as shown in Fig.13.4. It is
equivalent to a straight distributor fed at both
ends with equal voltages, the two ends being
brought together to form a closed ring.
The distributor ring may be fed at one or more than
one point.

74. 13.2 D.C. Distribution Calculations
In addition to the methods of feeding discussed above, a distributor may have
(i)Concentrated loading (ii) uniform loading (iii) both concentrated and uniform loading.
D.C. Distributor Fed at one End—Concentrated Loading
Fig. 13.5 shows the single line diagram of a 2-wire d.c. distributor AB fed at one end A and
having concentrated loads I1, I2, I3 and I4 tapped off at points C, D, E and F respectively.
Let r1, r2, r3 and r4 be the resistances of both wires (go and return) of the sections AC, CD,
DE and EF of the distributor respectively.
Current fed from point A = I1 + I2 + I3 + I4
Current in section AC = I1 + I2 + I3 + I4
Current in section CD = I2 + I3 + I4
Current in section DE = I3 + I4
Current in section EF = I4
Voltage drop in section AC = r1 (I1 + I2 + I3 + I4)
Voltage drop in section CD = r2 (I2 + I3 + I4)
Voltage drop in section DE = r3 (I3 + I4)
Voltage drop in section EF = r4 I4
∴ Total voltage drop in the distributor = r1 (I1 + I2 + I3 + I4) + r2 (I2 + I3 + I4) + r3 (I3 + I4) +
r4 I4
It is easy to see that the minimum potential will occur at point F which is farthest from the
feeding point A.

78. 13.4 Uniformly Loaded Distributor Fed at One End
Fig 13.11 shows the single line diagram of a 2-wire d.c. distributor AB fed at one end A and loaded
uniformly with i amperes per metre length. Let l metres be the length of the distributor and r ohm be the
resistance per meter run.
Consider a point C on the distributor at a distance x metres from the feeding point A as shown in Fig.
13.12. Then current at point C is
= i l − i x amperes = i (l − x) amperes
Now, consider a small length dx near point C. Its resistance is r dx and the voltage drop over length dx is
dv = i (l − x) r dx = i r (l − x) dx
Total voltage drop in the distributor upto point C is
The voltage drop upto point B (i.e. over the whole distributor) can be obtained by putting x = l in
the above expression.
∴ Voltage drop over the distributor AB

79. where i l = I, the total current entering at point A
r l = R, the total resistance of the distributor
Thus, in a uniformly loaded distributor fed at one end, the total voltage drop is equal
to that
produced by the whole of the load assumed to be concentrated at the middle point.

81. Distributor Fed at Both Ends — Concentrated Loading
It is desirable that a long distributor should be fed at both ends instead of at one end
only, since total voltage drop can be considerably reduced without increasing the
cross-section of the conductor. The two ends of the distributor may be supplied with
(i) equal voltages (ii) unequal voltages.
(i)Two ends fed with equal voltages: Consider a distributor AB fed at both ends with
equal voltages V volts and having concentrated loads I1, I2, I3, I4 and I5 at points C, D,
E, F and G respectively as shown in Fig. 13.14. As we move away from one of the
feeding points, say A, p.d. goes on decreasing till it reaches the minimum value at
some load point, say E, and then again starts rising and becomes V volts as we reach
the other feeding point B.
All the currents tapped off between points A and E (minimum p.d. point) will be
supplied from the feeding point A while
those tapped off between B and E will be
supplied from the feeding point B. The
current tapped off at point E itself will be
partly supplied from A and partly from B.
If these currents are x and y respectively, then,
I3 = x + y

82. Point of minimum potential: It is desired to locate the point of minimum potential.
There is a simple method for it. Consider a distributor AB having three concentrated
loads I1, I2 and I3 at points C, D and E respectively. Suppose that current supplied by
feeding end A is IA. Then current distribution in the various sections of the distributor
can be worked out as shown in Fig. 13.15(i). Thus
IAC = IA ; ICD = IA − I1
IDE = IA − I1 − I2 ; IEB = IA − I1 − I2 − I3
Voltage drop between A and B = Voltage drop over AB
or V −V = IA RAC + (IA − I1) RCD + (IA − I1 − I2) RDE + (IA − I1 − I2 − I3) REB
From this equation, the unknown IA can be calculated as the values of other quantities
are generally given. Suppose actual directions of currents in the various sections of the
distributor are indicated as shown in Fig. 13.15 (ii). The load point where the currents
are coming from both sides of the distributor is the point of minimum potential i.e.
point E in this case.

83. (ii) Two ends fed with unequal voltages: Fig. 13.16 shows the distributor AB fed with
unequal voltages ; end A being fed at V1 volts and end B at V2 volts. The point of
minimum potential can be found by following the same procedure as discussed above.
Thus in this case,
Voltage drop between A and B = Voltage drop over AB
or V1−V2 = Voltage drop over AB

91. Uniformly Loaded Distributor Fed at Both Ends
We shall now determine the voltage drop in a uniformly loaded distributor fed at both
ends. There can be two cases viz. the distributor fed at both ends with (i) equal
voltages (ii) unequal voltages. The two cases shall be discussed separately-
(i) Distributor fed at both ends with equal voltages: Consider a distributor AB of
length l meters, having resistance r ohms per meter and with uniform loading of i
amperes per meter as shown in Fig. 13.24. Let the distributor be fed at the feeding
points A and B at equal voltages, say V volts. The total current supplied to the
distributor is i l. As the two end voltages are equal, therefore, current supplied
from each feeding point is i l/2 i.e. Current supplied from each feeding point =il/2
Consider a point C at a distance x metres from the feeding point A. Then current at
point C is-

92. Now, consider a small length dx near point C. Its resistance is r dx and the voltage drop
over length dx is
Obviously, the point of minimum potential will be the mid-point. Therefore, maximum
voltage drop will occur at mid-point i.e. where x = l/2.

93. (ii) Distributor fed at both ends with unequal voltages: self

97. AC Distribution
How AC distribution differs from DC Distribution
A.C. distribution calculations differ from those of d.c. distribution in the following
respects :
(i) In case of d.c. system, the voltage drop is due to resistance alone. However, in a.c.
system, the voltage drops are due to the combined effects of resistance, inductance
and capacitance.
(ii) In a d.c. system, additions and subtractions of currents or voltages are done
arithmetically but in case of a.c. system, these operations are done vectorially.
(iii) In an a.c. system, power factor (p.f.) has to be taken into account. Loads tapped off
form the distributor are generally at different power factors. There are two ways of
referring power factor viz
(a) It may be referred to supply or receiving end voltage which is regarded as the
reference vector.
(b) It may be referred to the voltage at the load point itself.

105. 3-Phase Unbalanced Loads: The 3-phase loads that have the same impedance and power factor
in each phase are called balanced loads. The problems on balanced loads can be solved by
considering one phase only ; the conditions in the other two phases being similar. However, we
may come across a situation when loads are unbalanced i.e. each load phase has different
impedance and/or power factor. In that case, current
and power in each phase will be different. In practice, we may come across the following
unbalanced loads:
(i) Four-wire star-connected unbalanced load
(ii) Unbalanced Δ-connected load
(iii) Unbalanced 3-wire, Y-connected load
(i) Four-wire star-connected unbalanced load :
We can obtain this type of load in two ways. First, we may connect a 3-phase, 4-wire unbalanced
load to a 3-phase, 4-wire supply as shown in Fig. 14.10. Note that star point N of the supply is
connected to the load star point N′. Secondly, we may connect single phase loads between any
line and the neutral wire as shown in Fig.14.11. This will also result in a 3-phase, 4-wire
unbalanced load because it is rarely possible that single phase loads on all the three phases have
the same magnitude and power factor. Since the load is unbalanced, the line currents will be
different in magnitude and displaced from one another by unequal angles. The current in the
neutral wire will be the phasor sum of the three line currents i.e.
Current in neutral wire, IN = IR + IY + IB

106. The following points may be noted carefully :
(i) Since the neutral wire has negligible resistance, supply neutral N and load neutral N′ will be at
the same potential. It means that voltage across each impedance is equal to the phase voltage of
the supply. However, current in each phase (or line) will be different due to unequal impedances.
(ii) The amount of current flowing in the neutral wire will depend upon the magnitudes of line
currents and their phasor relations. In most circuits encountered in practice, the neutral
current is equal to or smaller than one of the line currents. The exceptions are those circuits
having severe unbalance.

111. Midterm

112. Mechanical design of overhead lines
•Electric power can be transmitted or distributed either by means of underground
cables or by overhead lines. The underground cables are rarely used for power
transmission due to two main reasons.
•Firstly, power is generally transmitted over long distances to load centers. Obviously,
the installation costs for underground transmission will be very heavy.
•Secondly, electric power has to be transmitted at high voltages for economic reasons.
It is very difficult to provide proper insulation† to the cables to withstand such higher
pressures.
•Therefore, as a rule, power transmission over long distances is carried out by using
overhead lines.

113. 8.1 Main Components of Overhead Lines
The main components of an overhead line are:
(i) Conductors which carry electric power from the sending end station to the receiving
end station.
(ii) Supports which may be poles or towers and keep the conductors at a suitable level
above the ground.
(iii) Insulators which are attached to supports and insulate the conductors from the
ground.
(iv) Cross arms which provide support to the insulators.
(v) Miscellaneous items such as phase plates, danger plates, lightning arrestors, anti-
climbing wires etc.

114. 8.2 Conductor Materials
The conductor material used for transmission and distribution of electric power
should have the following properties :
(i) high electrical conductivity.
(ii) high tensile strength in order to withstand mechanical stresses.
(iii) low cost so that it can be used for long distances.
(iv) low specific gravity so that weight per unit volume is small.
All above requirements are not found in a single material. Therefore, while selecting a
conductor material for a particular case, a compromise is made between the cost and
the required electrical and mechanical properties.
8.3 Line Supports
In general, the line supports should have the following properties :
(i) High mechanical strength to withstand the weight of conductors and wind loads
etc.
(ii) Light in weight without the loss of mechanical strength.
(iii) Cheap in cost and economical to maintain.
(iv) Longer life.
(v) Easy accessibility of conductors for maintenance

115. 8.4 Insulators
The overhead line conductors should be supported on the poles or towers in such a
way that currents from conductors do not flow to earth through supports i.e., line
conductors must be properly insulated from supports. This is achieved by securing line
conductors to supports with the help of insulators.The insulators provide necessary
insulation between line conductors and supports and thus prevent any leakage current
from conductors to earth. In general, the insulators should have the following
desirable properties :
(i) High mechanical strength in order to withstand conductor load, wind load etc.
(ii) High electrical resistance of insulator material in order to avoid leakage currents to
earth.
(iii) High relative permittivity of insulator material in order that dielectric strength is
high.
(iv) The insulator material should be non-porous, free from impurities and cracks
otherwise the permittivity will be lowered.
(v) High ratio of puncture strength to flashover

116. • Different Type of Insulators Used in Power System
The purpose of the insulator or insulation is to insulate
the electrically charged part of any equipment or
machine from another charged part or uncharged
metal part. At lower utilization voltage the insulation
also completely covers the live conductor and acts as a
barrier and keeps the live conductors unreachable from
human being or animals. In case of the high voltage
overhead transmission and distribution the
transmission towers or poles support the lines, and
insulators are used to insulate the live conductor from
the transmission towers. The insulators used in
transmission and distribution system are also required
to carry large tensional or compressive load.

117. •Different types of Insulators used in Power Transmission for supporting the
conductors on Tower are as follows:
•Pin Type Insulator:
This is the first developed insulators and being used for overhead lines for voltage
grade up to 33 kV. The live conductor is place on the top of the insulator and the
bottom of the insulator in connected to earth. The insulator has to withstand the
potential stress between conductor and earth. When insulator is wet, its outer surface
becomes almost conducting. Hence the flash over distance of insulator is decreased.
The electrical insulator is designed such that the decrease of flash over distance is
minimum when the insulator is wet. That is why the upper most petticoat of a pin
insulator has umbrella type designed so that it can protect the rest lower part of the
insulator from rain. The upper surface of top most petticoat is inclined as less as
possible to maintain maximum flash over voltage during raining.

118. •Post Insulators
•Post insulator is suitable for higher voltage. It has higher numbers of petticoats and has
greater height. This type of insulator can be mounted on supporting structure
horizontally as well as vertically. The insulator is made of one piece of porcelain and it
has fixing clamp arrangement are in both top and bottom end. For higher voltage
application Two or more insulators can be fixed together to meet the requirement.
Suspension Insulator:
Using post insulator in higher voltage is not economical and suspension
type insulator is evolved. Disc insulators are connected together in series
to make a string which is suspension type insulators. As per the voltage
grade the no of disc isolators are increased or decreased so that is is
suitable for any voltage level. When suspension insulators are used a
conductor is always hanging / suspended below the metallic tower level
and it is always protected from lightning. On the other hand in order to
maintain minimum clearance between conductor and ground/ equipment
the tower hight use to be higher. The amplitude of free swing of
conductors is larger in suspension insulator system, hence, more spacing
between conductors should be provided.

119. • String Insulators:
• When suspension string is used to sustain extraordinary tensile load of
conductor it is referred as string insulator. When there is a dead end or there is
a sharp corner in transmission line, the line has to sustain a great tensile load
of conductor or strain. A strain insulator must have considerable mechanical
strength as well as the necessary electrical insulating properties. In string
Insulator, each porcelain disc is designed for 11 kV. Thus for 132 kV overhead
line around 12 disc will be assembled.
Stay Insulators:
For low voltage lines, the stays are to be
insulated from ground at a height. The insulator
used in the stay wire is called as the stay
insulator and is usually of porcelain and is so
designed that in case of breakage of the
insulator the wire will not fall to the ground.
Shackle insulators:
It is usually used in low voltage distribution
network. It can be used both in horizontal and
vertical position. The conductor in the groove
of shackle insulator is fixed with the help of soft
binding wire.

120. Advantages of suspension type insulator
(i) Suspension type insulators are cheaper than pin type insulators for voltages beyond
33 kV.
(ii) Each unit or disc of suspension type insulator is designed for low voltage, usually 11
kV. Depending upon the working voltage, the desired number of discs can be
connected in series.
(iii) If any one disc is damaged, the whole string does not become useless because the
damaged disc can be replaced by the sound one.
(iv) The suspension arrangement provides greater flexibility to the line. The connection
at the i9kross arm is such that insulator string is free to swing in any direction and can
take up the position where mechanical stresses are minimum.
(v) In case of increased demand on the transmission line, it is found more satisfactory
to supply the greater demand by raising the line voltage than to provide another set of
conductors. The additional insulation required for the raised voltage can be easily
obtained in the suspension arrangement by adding the desired number of discs.
(vi) The suspension type insulators are generally used with steel towers. As the
conductors run below the earthed cross-arm of the tower, therefore, this arrangement
provides partial protection from lightning.

121. 8.6 Potential Distribution over Suspension Insulator String
The following points may be noted regarding the potential distribution over a string of
suspension insulators :
(i) The voltage impressed on a string of suspension insulators does not distribute itself
uniformly across the individual discs due to the presence of shunt capacitance.
(ii) The disc nearest to the conductor has maximum voltage across it. As we move
towards the cross-arm, the voltage across each disc goes on decreasing.
(iii) The unit nearest to the conductor is under maximum electrical stress and is likely to
be punctured. Therefore, means must be provided to equalise the potential across
each unit. This is fully discussed in Art. 8.8.
(iv) If the voltage impressed across the string were d.c., then voltage across each unit
would be the same. It is because insulator capacitances are ineffective for d.c.

122. The ratio of voltage across the whole string to the product of number of discs and the voltage across the
disc nearest to the conductor is known as string efficiency i.e.,
Mathematical expression. Fig. 8.11 shows the equivalent circuit for a 3-disc string. Let us suppose that
self capacitance of each disc is C. Let us further assume that shunt capacitance C1 is some fraction K of
self capacitance i.e., C1 = KC. Starting from the cross-arm or tower, the voltage across each unit is V1,V2
and V3 respectively as shown.
Applying Kirchhoff’s current law to node A, we get,
I2 = I1 + i1
or V2ω C* = V1ω C + V1ω C1
or V2ω C = V1ω C + V1ω K C
∴ V2 = V1 (1 + K) ...(i)
Applying Kirchhoff’s current law to node B, we get,
I3 = I2 + i2
or V3 ω C = V2ω C + (V1 + V2) ω C1†
or V3 ω C = V2ω C + (V1 + V2) ω K C
or V3 = V2 + (V1 + V2)K
= KV1 + V2 (1 + K)
= KV1 + V1 (1 + K)2 [ V2 = V1 (1 + K)]
= V1 [K + (1 + K)2]
∴ V3 = V1[1 + 3K + K2] ...(ii)
String Efficiency

123. Voltage between conductor and earth (i.e., tower) is
V = V1 + V2 + V3
= V1 + V1(1 + K) + V1 (1 + 3K + K2)
= V1 (3 + 4K + K2)
∴ V = V1(1 + K) (3 + K) ...(iii)

124. Method of improving string efficiency
The various methods for this purpose are :
• By using longer cross-arms
• By grading the insulators
• By using a guard ring

125. Corona
Definition: The phenomenon of violet glow, hissing noise and production of ozone gas
in an overhead transmission line is known as corona.
Theory of corona formation:
Some ionisation is always present in air due to cosmic rays, ultraviolet radiations and
radioactivity. Therefore, under normal conditions, the air around the conductors
contains some ionised particles (i.e., free electrons and +ve ions) and neutral
molecules. When p.d. is applied between the conductors, potential gradient is set up
in the air which will have maximum value at the conductor surfaces. Under the
influence of potential gradient, the existing free electrons acquire greater velocities.
The greater the applied voltage, the greater the potential gradient and more is the
velocity of free electrons.
When the potential gradient at the conductor surface reaches about 30 kV per cm
(max. value), the velocity acquired by the free electrons is sufficient to strike a neutral
molecule with enough force to dislodge one or more electrons from it. This produces
another ion and one or more free electrons, which is turn are accelerated until they
collide with other neutral molecules, thus producing other ions. This, the process of
ionization is cumulative. The result of this ionization is corona.

126. 8.11 Factors Affecting Corona
The phenomenon of corona is affected by the physical state of the atmosphere as well as by
the conditions of the line. The following are the factors upon which corona depends :
(i) Atmosphere: As corona is formed due to ionsiation of air surrounding the conductors,
therefore, it is affected by the physical state of atmosphere. In the stormy weather, the
number of ions is more than normal and as such corona occurs at much less voltage as
compared with fair weather.
(ii) Conductor size: The corona effect depends upon the shape and conditions of the
conductors. The rough and irregular surface will give rise to more corona because
unevenness of the surface decreases the value of breakdown voltage. Thus a stranded
conductor has irregular surface and hence gives rise to more corona that a solid conductor.
(iii) Spacing between conductors:If the spacing between the conductors is made very large
as compared to their diameters, there may not be any corona effect. It is because larger
distance between conductors reduces the electro-static stresses at the conductor surface,
thus avoiding corona formation.
(iv) Line voltage: The line voltage greatly affects corona. If it is low, there is no change in the
condition of air surrounding the conductors and hence no corona is formed. However, if the
line voltage has such a value that electrostatic stresses developed at the conductor surface
make the air around the conductor conducting, then corona is formed.

127. 8.13 Advantages and Disadvantages of Corona
Advantages
(i) Due to corona formation, the air surrounding the conductor becomes conducting
and hence virtual diameter of the conductor is increased. The increased diameter
reduces the electrostatic stresses between the conductors.
(ii) Corona reduces the effects of transients produced by surges.
Disadvantages
(i) Corona is accompanied by a loss of energy. This affects the transmission efficiency
of the line.
(ii) Ozone is produced by corona and may cause corrosion of the conductor due to
chemical action.
(iii) The current drawn by the line due to corona is non-sinusoidal and hence non-
sinusoidal voltage drop occurs in the line. This may cause inductive interference with
neighboring communication lines.

128. 8.14 Methods of Reducing Corona Effect
The corona effects can be reduced by the following methods :
(i) By increasing conductor size. By increasing conductor size, the voltage at which
corona occurs is raised and hence corona effects are considerably reduced. This is one
of the reasons that ACSR conductors which have a larger cross-sectional area are used
in transmission lines.
(ii) By increasing conductor spacing. By increasing the spacing between conductors,
the voltage at which corona occurs is raised and hence corona effects can be
eliminated. However, spacing cannot be increased too much otherwise the cost of
supporting structure (e.g., bigger cross arms and supports) may increase to a
considerable extent.

129. 8.15 Sag in Overhead Lines
The difference in level between points of supports and the lowest point on the
conductor is called sag. Fig. 8.23. (i) shows a conductor suspended between two
equilevel supports A and B. The conductor is not fully stretched but is allowed to have
a dip. The lowest point on the conductor is O and
the sag is S. The following points may be noted

130. The following points may be noted
(i) When the conductor is suspended between two supports at the same level, it takes
the shape of catenary. However, if the sag is very small compared with the span, then
sag-span curve is like a parabola.
(ii) The tension at any point on the conductor acts tangentially. Thus tension TO at the
lowest point O acts horizontally as shown in Fig. 8.23. (ii).
(iii) The horizontal component of tension is constant throughout the length of the
wire.
(iv) The tension at supports is approximately equal to the horizontal tension acting at
any point on the wire. Thus if T is the tension at the support B, then T = TO.
8.16 Calculation of Sag: In an overhead line, the sag should be so adjusted that tension
in the conductors is within safe limits.The tension is governed by conductor weight,
effects of wind, ice loading and temperature variations.It is a standard practice to keep
conductor tension less than 50% of its ultimate tensile strength i.e.,minimum factor of
safety in respect of conductor tension should be 2. We shall now calculate sag and
tension of a conductor when (i) supports are at equal levels and (ii) supports are at
unequal levels

131. Continue….
(i) When supports are at equal levels : Consider
a conductor between two equilevel supports
A and B with O as the lowest point as shown in Fig.
8.24. It can be proved that lowest point will be at
the mid-span.
Let
l= Length of span
w = Weight per unit length of conductor
T = Tension in the conductor
Consider a point P on the conductor. Taking the lowest point O as the origin, let the
co-ordinates of point P be x and y. Assuming that the curvature is so small that curved
length is equal to its horizontal projection (i.e., OP = x), the two forces acting on the
portion OP of the conductor are :
(a) The weight wx of conductor acting at a distance x/2 from O.
(b) The tension T acting at O.

132. Equating the moments of above two forces about point O, we get,
T y = w x × (x/2)
or y = (w x²)/(2T)
(ii) When supports are at unequal levels: In hilly areas, we generally come across
conductors suspended between supports at unequal levels. Fig. 8.25 shows a conductor
suspended between two supports A and B which are at different levels. The lowest point on
the conductor is O.
Let,
l = Span length
h = Difference in levels between two supports
x1 = Distance of support at lower level (i.e., A) from O
x2 = Distance of support at higher level (i.e. B) from O
T = Tension in the conductor

133. If w is the weight per unit
length of the conductor, then,
Sag S1 =(w x²1 )/2T
and Sag S2 = (wx²2)/2T
Also x1 + x2 = l

134. Effect of wind and ice loading
• Self

139. 10.12 ABCD Parameter
• A major section of power system engineering deals in the
transmission of electrical power from one particular place
(eg. Generating station) to another like substations or
distribution units with maximum efficiency.
• So its of substantial importance for power system engineers
to be thorough with its mathematical modeling.
• Thus the entire transmission system can be simplified to a
two port network for the sake of easier calculations. The
circuit of a 2 port network is shown in the diagram .
• As the name suggests, a 2 port network consists of an
input port PQ and an output port RS. Each port has 2
terminals to connect itself to the external circuit. Thus it is
essentially a 2 port or a 4 terminal circuit,

140. Cont…..
having ,
Supply end voltage = VS
Supply end current = IS
Given to the input port P Q. And there is the Receiving end Voltage = VR
and Receiving end current = IR
Given to the output port R S
Now the ABCD parameters or the transmission line parameters provide the
link between the supply and receiving end voltages and currents, considering
the circuit elements to be linear in nature.

141. Cont….
Thus the relation between the sending and receiving end
specifications are given using ABCD parameters by the equations
below.
VS = A VR + B IR ———————-(1)
IS = C VR + D IR ———————-(2)
The receiving end is open circuited meaning receiving end
current IR = 0
Applying this condition to equation (1) we get.
Applying the same open circuit condition i.e IR = 0 to equation
(2)

142. Cont….
Receiving end is short circuited meaning
receiving end voltage VR = 0
Applying this condition to equation (1) we get
Applying the same short circuit condition i.e VR
= 0 to equation (2) we get

144. The following points may be kept in mind :
(i) The constants A, B,C and D are generally complex numbers.
(ii) The constants A and D are dimensionless whereas the dimensions of B and C are
ohms and siemen respectively.
(iii) For a given transmission line,
A = D
(iv) For a given transmission line,
A D − B C = 1

145. 10.13 Determination of Generalized Constants for Transmission Lines
The sending end voltage (VS) and sending end current (IS) of a transmission line
can be expressed as :
VS = AVR +BIR ...(i)
IS = CVR+ DIR ….(ii)
We shall now determine the values of these constants for different types of
transmission lines-
(i)Short lines: In short transmission lines, the effect of line capacitance is neglected.
Therefore, the line is considered to have series impedance. Fig. 10.23 shows the circuit
of a 3-phase short transmission line on a single phase basis.
Here, IS = IR ...(iii)
and VS = VR+ IRZ + ...(iv)
Comparing these with eqs. (i) and (ii), we have,
A = 1 ; B = Z, C = 0 and D = 1
Incidentally ; A = D
and A D − B C = 1 × 1 − Z × 0 = 1

146. (ii) Medium lines – Nominal T method: In this method, the whole line to neutral
capacitance is assumed to be concentrated at the middle point of the line and half the
line resistance and reactance are lumped on
either side as shown in Fig. 10.24.
Here, VS = V1 +IS Z /2 ...(v)
and V1 = VR +Z R /2
Now, IC = IS − IR
= VY1 , where Y = shunt admittance
=
...(vi)
Substituting the value of V1 in eq. (v), we get,
Substituting the value of IS, we get, …(vii)
Comparing eqs. (vii) and (vi) with those of (i) and (ii), we have,
Incidentally,
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152. Insulated cables
An underground cable essentially consists of one or more conductors covered with
suitable insulation and surrounded by a protecting cover. In general, a cable must
fulfill the following necessary requirements :
(i) The conductor used in cables should be tinned stranded copper or aluminum of
high conductivity. Stranding is done so that conductor may become flexible and carry
more current.
(ii) The conductor size should be such that the cable carries the desired load current
without overheating and causes voltage drop within permissible limits.
(iii) The cable must have proper thickness of insulation in order to give high degree of
safety and reliability at the voltage for which it is designed.
(iv) The cable must be provided with suitable mechanical protection so that it may
withstand the rough use in laying it.
(v) The materials used in the manufacture of cables should be such that there is
complete chemical and physical stability throughout.

153. 11.2 Construction of Cables
Fig. 11.1 shows the general construction of a
3-conductor cable. The various parts are :
(i)Cores or Conductors: A cable may have one
or more than one core (conductor) depending
upon the type of service for which it is
intended. For instance, the 3-conductor cable
shown in Fig. 11.1 is used for 3-phase service.
The conductors are made of tinned copper or
aluminum and are usually stranded in order to
provide flexibility to the cable.
(ii)Insulation: Each core or conductor is provided with a suitable thickness of insulation, the
thickness of layer depending upon the voltage to be withstood by the cable. The commonly
used materials for insulation are impregnated paper, varnished cambric or rubber mineral
compound.
(iii)Metallic sheath: In order to protect the cable from moisture,gases or other damaging
liquids (acids or alkalies) in the soil and atmosphere, a metallic sheath of lead or aluminium is
provided over the insulation as shown in fig.

154. (iv) Bedding: Over the metallic sheath is applied a layer of bedding which consists of a
fibrous material like jute or hessian tape. The purpose of bedding is to protect the
metallic sheath against corrosion and from mechanical injury due to armoring.
(v) Armoring: Over the bedding, armoring is provided which consists of one or two
layers of galvanized steel wire or steel tape. Its purpose is to protect the cable from
mechanical injury while laying it and during the course of handling.
(vi) Serving: In order to protect armoring from atmospheric conditions, a layer of
fibrous material (like jute) similar to bedding is provided over the armoring. This is
known as serving.
Insulating Materials for Cables:
In general, the insulating materials used in cables should have the following properties
:
(i) High insulation resistance to avoid leakage current.
(ii) High dielectric strength to avoid electrical breakdown of the cable.
(iii) High mechanical strength to withstand the mechanical handling of cables.
(iv) Non-hygroscopic i.e., it should not absorb moisture from air or soil. The moisture
tends to decrease the insulation resistance and hastens the breakdown of the cable. In
case the insulating material is hygroscopic, it must be enclosed in a waterproof
covering like lead sheath.
(v) Non-inflammable.
(vi) Low cost so as to make the underground system a viable proposition.
(vii) Unaffected by acids and alkalies to avoid any chemical action.

155. 11.4 Classification of Cables
(i) Low-tension (L.T.) cables — upto 1000 V
(ii) High-tension (H.T.) cables — upto 11,000 V
(iii) Super-tension (S.T.) cables — from 22 kV to 33 kV
(iv) Extra high-tension (E.H.T.) cables — from 33 kV to 66 kV
(v) Extra super voltage cables — beyond 132 kV
11.5 Cables for 3-Phase Service
The following types of cables are generally used for 3-phase service :
1. Belted cables — up to 11 kV
2. Screened cables — from 22 kV to 66 kV
3. Pressure câbles — beyond 66 kV.
3. Pressure cables For voltages beyond 66 kV, solid type cables are unreliable because there
is a danger of breakdown of insulation due to the presence of voids. When the operating
voltages are greater than 66 kV, pressure cables are used. In such cables, voids are
eliminated by increasing the pressure of compound and for this reason they are called
pressure cables. Two types of pressure cables viz oil-filled cables and gas pressure cables
are commonly used.

156. (i) Oil-filled cables. In such types of cables, channels or ducts are provided in the cable
for oil circulation. The oil under pressure (it is the same oil used for impregnation) is
kept constantly supplied to the channel by means of external reservoirs placed at
suitable distances (say 500 m) along the route of the cable.
Fig. 11.6 shows the constructional details of a single-core conductor channel, oil filled
cable.
The oil channel is formed at the centre by stranding the conductor wire around a
hollow cylindrical steel spiral tape. The oil under pressure is supplied to the channel by
means of external reservoir. As the channel is made of spiral steel tape, it allows the
oil to percolate between copper strands to the wrapped insulation. The oil pressure
compresses the layers of paper insulation and prevents the possibility of void
formation. The system is so designed that when the oil gets
expanded due to increase in cable temperature, the extra oil
collects in the reservoir. However, when the cable
temperature falls during light load conditions, the oil from
the reservoir flows to the channel. The disadvantage of this
type of cable is that the channel is at the middle of the cable
and is at full voltage w.r.t. earth, so that a very complicated
system of joints is necessary

157. The oil-filled cables have three principal advantages. Firstly, formation of voids and
ionization are avoided. Secondly, wever, their major disadvantages are the high initial
cost and complicated system of laying. allowable temperature range and dielectric
strength are increased. Thirdly, if there is leakage, the defect in the lead sheath is at
once indicated and the possibility of earth faults is decreased. Ho
(ii) Gas pressure cables: In case of as pressure cables, an inert as like nitrogen at high
pressure is introduced. The pressure is about 12 to 15 atmospheres. Due to such a
high pressure there is a radial compression due to which the ionization is totally
eliminated. The working power factors of such cables is also high.
The Fig. 1 shows the section of a gas pressure cable. The cable is
triangular in shape and installed in the steel pipe. The pipe is
filled with the nitrogen at 12 to 15 atmospheric pressure. The
remaining construction is similar to that of solid type cable but
the thickness of lead sheath is 75% of that of solid type cable.
There is no bedding and serving. The pressure cable was firstly
designed by Hochstadter, Vogel and Bownden.
The triangle shape lead sheath acts as a pressure membrane. The shape
reduces the weight and provides the low thermal resistance. The high
pressure creates the radial compression to close any voids. The steel pipe is coated with a
point to avoid corrosion.

158. During heating, the cable compound expands and a sheath acts as a
membrane becomes circular in such a case. When cable cools down
the gas pressure acting via sheath forces compound to come back to
the noncircular normal shape. Due to good thermal characteristics, fire
quenching property and high dielectric strength, the gas SF6 is also
used in such cables.
Advantages
The various advantages of gas pressure cables are,
1. Gas pressure cables can carry 1.5 times the normal load current and
can withstand double the voltage. Hence such cables can be used for
ultra high voltage (UHV) levels.
2. Maintenance cost is small.
3. The nitrogen in the steel tube, helps in quenching any fire or flame.
4. No reservoir or tanks required.
5. The power factor is improved.
6. The steel tubes used make the cable laying easy.
7. The ionization and possibility of voids is completely eliminated.The
only disadvantages of this type of cables is very high initial cost.

160. 11.8 Capacitance of a Single-Core Cable
A single-core cable can be considered to be equivalent to two long co-axial cylinders.
The conductor (or core) of the cable is the inner cylinder while the outer cylinder is
represented by lead sheath which is at earth potential. Consider a single core cable
with conductor diameter d and inner sheath diameter D (Fig. 11.13). Let the charge
per metre axial length of the cable be Q coulombs and ε be the permittivity of the
insulation material between core and lead sheath. Obviously *ε = ε0 εr where εr is the
relative permittivity of the insulation.

161. Dielectric Stress in a Single-Core Cable
Under operating conditions, the insulation of a cable is subjected to electrostatic
forces. This is known as dielectric stress. The dielectric stress at any point in a cable is
infact the potential gradient (or *electric intensity) at that point.
Consider a single core cable with core diameter d and internal sheath diameter D. As
proved in Art 11.8, the electric intensity at a point x metres from the centre of the
cable is
By definition, electric intensity is equal to potential gradient. Therefore,
potential gradient g at a point x metres from the centre of cable is
Potential difference V between conductor and sheath is

162. Substituting the value of Q from exp. (ii) in exp. (i), we get,
It is clear from exp. (iii) that potential gradient varies inversely as the distance x.
Therefore, potential gradient will be maximum when x is minimum i.e., when x = d/2
or at the surface of the conductor. On the other hand, potential gradient will be
minimum at x = D/2 or at sheath surface.

165. Grading of Cables
The process of achieving uniform electrostatic stress in the dielectric of cables is
known as grading of cables.
The following are the two main methods of grading of cables :
(i) Capacitance grading (ii) Intersheath grading
Capacitance Grading: The process of achieving uniformity in the dielectric stress by
using layers of different dielectrics is known as capacitance grading.

169. Intersheath Grading
Consider a cable of core diameter d and outer lead sheath of diameter
D. Suppose that two Intersheath of diameters d1 and d2 are inserted
into the homogeneous dielectric and maintained at some fixed
potentials. Let V1, V2 and V3 respectively be the voltage between core
and Intersheath 1, between Intersheath 1 and 2 and between
Intersheath 2 and outer lead sheath. As there is a definite potential
difference between the inner and outer layers of each Intersheath, therefore, each
sheath can be treated like a homogeneous single core cable. Now
maximum stress between core and Intersheath 1 is

172. 11.20 Types of Cable Faults
Cables are generally laid directly in the ground or in ducts in the underground distribution
system. For this reason, there are little chances of faults in underground cables. However, if
a fault does occur, it is difficult to locate and repair the fault because conductors are not
visible. Nevertheless, the following are the faults most likely to occur in underground cables
:
(i) Open-circuit fault
(ii) Short-circuit fault
(iii) Earth fault.
(i)Open-circuit fault : When there is a break in the conductor of a cable, it is called open
circuit fault. The open-circuit fault can be checked by a megger. For this purpose, the three
conductors of the 3-core cable at the far end are shorted and earthed. Then resistance
between each conductor and earth is measured by a megger. The megger will indicate zero
resistance in the circuit of the conductor that is not broken. However, if the conductor is
broken, the megger will indicate infinite resistance in its circuit.
(ii) Short-circuit fault: When two conductors of a multi-core cable come in electrical
contact with each other due to insulation failure, it is called a short-circuit fault. Again, we
can seek the help of a megger to check this fault. For this purpose, the two terminals of the
megger are connected to any two conductors. If the megger gives zero reading, it indicates
short-circuit fault between these conductors. The same step is repeated for other
conductors taking two at a time.

173. (iii) Earth fault: When the conductor of a cable comes in contact with earth, it is called
earth fault or ground fault. To identify this fault, one terminal of the megger is
connected to the conductor and the other terminal connected to earth. If the megger
indicates zero reading, it means the conductor is earthed. The same procedure is
repeated for other conductors of the cable.
11.21 Loop Tests For Location of Faults in Underground Cables
There are several methods for locating the faults in underground cables. However, two
popular methods known as loop tests are :
(i) Murray loop test
(ii) Varley loop test
•Murray Loop Test : The Murray loop test is the most common and accurate method
of locating earth fault or short-circuit fault in underground cables.
(i) Earth fault: Fig. 11.22 shows the circuit diagram for locating the earth fault by
Murray loop test. Here AB is the sound cable and CD is the faulty cable; the earth fault
occuring at point F.
The far end D of the faulty cable is joined to the far end B of the sound cable through
a low resistance link. Two variable resistances P and Q are joined to ends A and C (See
Fig. 11.22) respectively and serve as the ratio arms of the Wheatstone bridge.

174. Let R = resistance of the conductor loop upto the fault from the test end
X = resistance of the other length of the loop
Note that P, Q, R and X are the four arms
of the Wheatstone bridge. The resistances P
and Q are varied till the galvanometer
indicates zero deflection. In the balanced
position of the bridge, we have,
If r is the resistance of each cable, then R + X = 2r.
If l is the length of each cable in metres, then resistance per metre length of cable r/l
Distance of fault point from test end is
X
R
Q
P

1
1 


S
R
Q
P
X
X
R
Q
Q
P 


X
r
Q
Q
P 2


r
x
Q
P
Q
X 2



175. (ii) Short-circuit fault : Fig. 11.23 shows the circuit diagram for locating the short-
circuit fault by Murray loop test. Again P, Q, R and X are the four arms of the bridge.
Note that fault resistance is in the battery circuit and not in the bridge circuit. The
bridge in balanced by adjusting the resistances P and Q. In the balanced position of
the bridge :

178. Sub Station layout

179. Types of sub station
Power is generated comparatively in low voltage level. It is economical to transmit
power at high voltage level. Distribution of electrical power is done at lower voltage
levels as specified by consumers. For maintaining these voltage levels and for
providing greater stability a number of transformation and switching stations have to
be created in between generating station and consumer ends. These transformation
and switching stations are generally known as electrical substations. Depending upon
the purposes, the substations may be classified as-
•Step Up Substation
Step up substations are associated with generating stations. Generation of power is
limited to low voltage levels due to limitations of the rotating. These generating
voltages must be stepped up for economical transmission of alternators power over
long distance. So there must be a step up substation associated with generating
station.
• Step Down Substation
The stepped up voltages must be stepped down at load centers, to different voltage
levels for different purposes. Depending upon these purposes the step down
substation are further categorized in different sub categories.
•Primary Step Down Substation
The primary step down sub stations are created nearer to load center along the
primary transmission lines. Here primary transmission voltages are stepped down to
different suitable voltages for secondary transmission purpose.

180. •Secondary Step Down Substation:
Along the secondary transmission lines, at load center, the secondary transmission
voltages are further stepped down for primary distribution purpose. The stepping
down of secondary transmission voltages to primary distribution levels are done at
secondary step down substation.
• Distribution Substation
Distribution substation are situated where the primary distribution voltages are
stepped down to supply voltages for feeding the actual consumers through a
distribution network.
•Bulk Supply or Industrial Substation
Bulk supply or industrial substation are generally a distribution substation but they are
dedicated for one consumer only. An industrial consumer of large or medium supply
group may be designated as bulk supply consumer. Individual step down substation is
dedicated to these consumers.
•Mining Substation
The mining substation are very special type of substation and they need special design
construction because of extra precautions for safety needed in the operation of
electric supply.

181. •Outdoor Type Substation
Outdoor type substation are constructed in open air. Nearly all 132KV, 220KV,
400KV substation are outdoor type substation. Although now days special GIS
(Gas insulated substation) are constructed for extra high voltage system which are
generally situated under roof.
•Indoor Substation
The substations are constructed under roof is called indoor type substation.
Generally 11 KV and sometime 33 KV substation are of this type.
•Underground Substation
The substation are situated at underground is called underground substation. In
congested places where place for constructing distribution substation is difficult
to find out, one can go for underground substation scheme.
•Pole Mounted Substation
Pole mounted substation are mainly distribution substation constructed on two
pole, four pole and sometime six or more poles structures. In these type of
substation fuse protected distribution transformer are mounted on poles along
with electrical isolator switches.

182. Factors Making Site Selection For a Substation
Making Site Selection and Location for a Substations. The following factors are
considered while making site selection for a substations.
1. Type of Substation
The category of substation is important for its location. For example a step-up
substation, which is generally a point where power from various sources (generating
machines or generating stations) is pooled and stepped up for long distance
transmission, should be located as close to the generating stations as possible to
minimize the transmission losses. Similarly a step-down substation should be located
nearer to the load center to reduce transmission losses, cost of distribution system
and better reliability of supply.
2. Availability of Suitable and Sufficient land
The land proposed for a substation should be normally level and open from all sides. It
should not be water logged particularly in rainy season. The site selected for a
substation should be such that approach of transmission lines and their take off can be
easily possible without any obstruction. The places nearer to aerodrome, shooting
practice grounds etc. should be avoided.

183. 3. Communication Facility
Suitable communication facility is desirable at a proposed substation both during and
after its construction. It is better, therefore, to select the site along side on existing
road to facilitate an easier and cheaper transportation.
4. Atmospheric Pollution
Atmosphere around factories, which, may produce metal corroding gases, air fumes,
conductive dust etc…, and nearer to sea coasts, where air may be more humid and
may be salt loaded, is detrimental to the proper running of power system and
therefore substations should not be located near factories or sea coast.
5. Availability of Essential Amenities To The Staff
The site should be such where staff can be provided essential amenities like school,
hospital, drinking water, housing etc,
6. Drainage Facility
The site selected for the proposed substation should have proper drainage
arrangement to avoid pollution of air and growth of micro-organisms detrimental to
equipment and health.

184. Substation Components
Electric Substations are the part of the power system and used for transferring power from
generating points to load centers. Some of the important components of substation are:
Busbars:
Various incoming and outgoing circuits are connected to busbars. Busbars receive power
from incoming circuits and deliver power to outgoing circuits.
Surge arrestors or Lightning
arrester: Surge Arresters or
Lightning Arresters discharge the
over voltage surges to earth and
protect the equipment insulation
from switching surges and lightning
surges. Surge arresters are generally
connected between phase
conductor and ground
. In a Substation surge arrester is located at the starting of the substation as seen
from incoming transmission lines and is the first equipment of the substation..

185. Isolators or Disconnecting Switches:
Isolators are provided for isolation from live parts for the purpose of maintenance.
Isolators are located at either side of the circuit breaker. Isolators are operated under
no load. Isolator does not have any rating for current breaking or current making.
Isolators are interlocked with circuit breakers
Types of Isolators are
•Central rotating, horizontal swing
•Centre-Break
•Vertical swing
•Pantograph type
Earth Switch:
Earth Switch is used to discharge the voltage on the circuit to the earth for safety.
Earth switch is mounted on the frame of the isolators. Earth Switch is located for each
incomer transmission line and each side of the busbar section

186. Current transformers:
Current transformers are used for Stepping down current for
measurement, protection and control. Current transformers are
of two types
•Protective CT
•Measuring CT
Voltage Transformer:
Voltage transformers are used to step down the voltage
for measurement, protection and control. Voltage
transformers are of two types.
•Electro magnetic type
•Capacitive VT located on the feeder side of the Circuit
Breaker.

187. Circuit Breaker:
Circuit Breaker is used for Switching during normal
and abnormal operating conditions. It is used to
interrupt the short circuit currents. It is used to
interrupt short circuit currents. Circuit Breaker
operations include.
•Closing
•Opening
•Auto – reclosing
Circuit Breaker is located near every switching point
and also located at the both ends of every protection
zone.
Power Transformers:
Power Transformers are used to step up or step –
down a.c. voltages and to transfer electrical power
from one voltage level to another. Tap changers are
used for voltage control.

188. Shunt Reactors:
Shunt Reactors are used for long EHV transmission lines to control voltage during low
– load period. Shunt reactors is also used to compensate shunt capacitance of
transmission line during low load periods.
Shunt Capacitance:
Shunt capacitors are used for compensating reactive power of lagging power factor.
Shunt Capacitors are used for improving the power factor. It is also used for voltage
control during heavy lagging power factor loads. Shunt Capacitors are located at the
receiving stations and distribution substations
Series Capacitor:
Series Capacitors are used for some long EHV a.c lines to
improve power transferability. Capacitors are located at
the sending end / receiving end of the lines. Series
Capacitors are provided with by – pass circuit breaker and
protective spark – gaps.
Shunt Capacitance

189. Lightning Protection:
Lightning protection is used to protect substation equipment
from direct lightning strokes. Lightning Masts are located at
the outdoor yard. Overhead Shielding wires are used to cover
entire outdoor yard.
Neutral Grounding Equipment:
Neutral Grounding Equipment are Resistors and reactors.
They are used to limit the short circuit current during ground
fault. They are connected between neutral point and ground
Station Earthing System:
Station Earthing System includes Earth
Mat and Earth electrodes placed below
ground level. These Earth Mat and Earth
electrode is connected to the
equipment structures, neutral points for
the purpose of Equipment earthing and
neutral point earthing.
.

190. Metering, Control and Relay panels:
To house various measuring Instruments
, control Instruments, Protective relays.
They are located in air-conditioned
building. Control Cables are laid
between Switchyard equipment and
these panels.

191. What is Flux?
Flux means an imaginary line through which a physical quantity can travel. The word
“Flux” is originated from Latin Word ‘Fluxus’ that means flow. Isaac Newton first used
this term as fluxion into differential calculus.
Types of Flux
Flux can be used in various concepts, such as
Magnetic Flux
It means the number magnetic field lines passing through a closed surface. Its SI unit is
– Weber and in CGS is – Maxwell. It is denoted as Φm.
Electric Flux
It means the number of electric field lines passing through a closed surface. It is
denoted as ΦE.

192. Inductance of a Conductor due to External Flux
we will derive an expression for the flux linkages of the conductor due to the external
flux. For this we will consider the flux linkages of an isolated conductor due to that
portion of the external flux which lies between two points distant D1 and D2 meters
from centre of conductor. P1 and P2 are two such points as shown in the Fig. 1.
The conductor shown in the Fig. 1 carries current I. The flux paths are concentric
circles around the conductor between P1 and P2.
Consider a tubular element which is x meters from centre
of conductor. The field intensity at this point is Hx. The mmf
around the element is
2∏xHx =1
The flux density Bx at this point is given by
The flux dΦ in the tubular element of thickness dx is given by,
The flux linkages dψ per meter equal to dΦ since flux external to the conductor links
all the current in the conductor. The total flux linkage between P1 and P2 are obtained
by integrating dψ from D1 to D2

194. Inductance of a single conductor
Suppose a conductor is carrying current I through its length l, x is the internal variable
radius of the conductor and r is the original radius of the conductor. Now the cross-
sectional area with respect to radius x is πx2 square – unit and current Ix is flowing
through this cross-sectional area. So the value of Ix can be expressed in term of original
conductor current I and cross-sectional area πr2 square – unit
Now consider small thickness dx with the 1m length of the conductor, where Hx is the
magnetizing force due to current Ix around the area πx2.

195. Cont….
And magnetic flux density Bx = μHx, where μ is the permeability of this
conductor. Again, µ = µ0µr. If it is considered that the relative permeability of
this conductor µr = 1, then µ = µ0. Hence, here Bx = μ0 Hx.

196. Inductance Of Single Phase Two Wire Line
Suppose conductor A of radius rA carries a current of IA in opposite direction of current
IB through the conductor B of radius rB. Conductor A is at a distance D from conductor
B and both are of length l. They are in close vicinity with each other so that flux
linkage takes place in both of the conductors due to their electromagnetic effects.
Let us consider the magnitude of current in both conductors are same and hence IA = -
IB, Now, total flux linkage in conductor A = flux linkage by
self-current of conductor A + flux linkage on conductor A
due to current in the conductor B.
Similarly, flux linkage in conductor B = flux linkage by
self-current of conductor B + flux linkage on conductor B
due to current through conductor A. Similarly, flux linkage in conductor
B = flux linkage by self-current of conductor B + flux linkage on conductor B due to
current through conductor A.
Now if we consider a point P in close vicinity both conductor A and B, the flux linkage
at point P would be, flux linkage at point P for current carrying conductor A + flux
linkage at point P for current carrying conductor B i.e.

197. Now,
shown in the figure below in figure (a) and (b).
•λAAP is the flux linkage at point P for conductor A
due to current through conductor A itself.
•λABP is the flux linkage at point P for conductor A due to current through conductor B.
•λBAP is the flux linkage at point P for conductor B due to current through conductor A.
•λBBP is the flux linkage at point P for conductor B due to current through conductor B
itself.

198. λABP and λBAP are negative in value because the directions current are opposite with
respect to each other.

199. CAPACITANCE OF A SINGLE PHASE TWO-WIRE LINE
Consider a single phase overhead transmission line consisting of two parallel
conductors A and B spaced d metres apart in air. Suppose that radius of each
conductor is r metres. Let their respective charge be + Q and − Q coulombs per metre
length. The total p.d. between conductor A and neutral “infinite” plane is

200. Both these potentials are w.r.t. the same neutral plane. Since the unlike charges attract
each other, the potential difference between the conductors is

201. Inductance of Three Phase Lines With
Equilateral and Symmetrical Spacing
Consider a three phase line consisting of three phase conductors a, b and c as shown
in the Fig. 1. These three conductors are equally spaced at the corners of an
equilateral triangle having radius r.

202. because of symmetry, conductors b and c will have same
inductance as that of conductor a. Each phase consists of only
one conductor. So the above equation gives inductance per
phase of the three phase lines.