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Lecture from 27-45
Lecture-27
Voltage Distribution over Insulator String, Improvement of String Efficiency,
String Efficiency
Expression
Method of improving String Efficiency
The potential difference across the insulator is not uniform
Lecture:-28
Insulator Failure
It is desirable that the value of safty factor is high so that flash-over take place befor the isulator gets
punctured.For pin type insulator ,the value of safty factor is about 10.
Testing of insulator
The insulator should have good mechanical strength to withstand the load condition.It should be
free from pores or voids which lead to breakdown. It electrical strength should be large enough
to withstand normal and over voltage.but the isulator should flash over at voltages which are
likely to cause damage to other equipment
Various Test of insulator
1. Mechanical strength:The insulator is mouted on the cross arm I the normal working condition.
And following test are conducted.
i) A mechanical load is given and kept for one minute ,No crack should be caused to the
insulator.
ii) At normal applied voltage load equal 1.25 times of normal load is applied and crack should be
developed in the conductor.
iii) For pin type insulator a bending stress equal to the three times the normal load to the
insulator is applied for one minute.The insulator should show any sign of damage.
2.Porosity:-This is destructive test and is performed on very selected piece usually one or two out
of a production batch.The insulator to be tested is broken into pieces and the pieces are immersed
in a 1% solution of fuchisn dye in alcohol under pressure.After time the pieces are removed from
the container and examined.A deep penetration of dye indicates porosity of insulator.
3.Power frequency Dry flashover Voltage:- The insulator should be mounted or suspended from
a crossarm extending at least 3 ft. on either side and there should be no other conducting object
in the vicinity of the conductor. A stedy increse in power frequency voltage is applied and raised
till the flash overs occurs.
4.Power Frequency Wet Flashover Voltage:In this test water is sprayed on the inbsulator at an
inclination of 45 degree and equivalent to precipitation of 3mm per minute.Then test is
continued in the same way as in dry flash over.
5. Impuse Voltage Flashover Test:Voltage impulses of increasing magnitude are applied to the
conductor in succession.The peak value of impulse voltage giving flash over is called the
impulse flashover
6.Puncture Volatage Test:- When used in design test,this test is a destructive test and very few
pieces out of batch are selected for test.The insulator with the pin in proper position and
conductor at the other end is immersed in an insulating oil and steadily increasing power
frequency voltage is applied.The voltage at which conduction starts is called the puncture
voltage.
Lecture:29
General Considerations, Line Supports, Types of Steel Towers
Steel Towers
Lecture:30
Cross Arms, Span, Conductor Configuration, Spacing and Clearances,
Cross Arms
Spacing and Clearance
A longer span means a smaller number of towers but the towers are taller and more
costly. The higher the operating voltage ,the greater shoud be the span to reduce the high cost of
insulators. The insulators constitute the weaker part of transmission line and reduction in the
number of towers per Km.increases the reliability of the line. For every proposed line there is a
definite length of the span which will give minimum cost of the line.For mechanical
consideration there is a maximum value of span for each conductor size. Many times itmhappens
that the conductor size as detrmined from electrical calculation is very small and it is possible to
reduce the cost of the line by using thicker and stronger conductor so that a longer span may be
used.some times it is not feasible to determine the tower height and span length on the basis of
cost alone because the lightning hazards increase greatly as the height of conductors above
ground is increased.modern high voltage voltage line have span between 200 and 4oo m.For
river and ravine crossing exceptionally long span upto 800
have been saticifactory
employed.Many conductors configuration are used in practice .There is no special advantage in
using symmetrical configuration and most cases flat horizontal or vertical configuration are used
from mechanical consideration.A flat horizontal cconfiguation means lesser tower height but
wider right of way .A vertical configuration means taller height and increase the lightning
hazards.In spite of fact flat horizontal and vertical configuration are used in many cases.For
single circuit lines L type configuration is popular.
There must be adequate spacing between conductors so that they do not come within
sparking distance of each other even while swinging due to wind. An empirical formula
commonly used for determining tha spacing of aluminium conductor lenes ia
Spacing= S+ V/150 meters
S= spacing,V = Line voltage in KV
These rules also specify the minimum clearance for power lines from building,railway
tracks and telecommunication lines.
LECTURE:-31
Sag and Tension Calculations, Erection Conditions, Factors affecting Sag, Sag
Template
In the fig a conductor is suspended between two equilevel supports supports A and
B.The conductor is not fully stretched but allowed to have dip.The lowest point on the
conductor is O and Sag is S.
The following points may be noted
Calculation of SAG
Lecture : 32:
Catenary, Conductor Vibration.
Conductor Vibration:
Lecture:33
Comparison of various Distribution Systems, AC three-phase four-wire Distribution System,
Comparison of Conductor Material in Overhead System
In comparing the relative amounts of conductor material necessary for different systems of
transmission, similar conditions will be assumed in each case viz
(i)same power (P watts) transmitted by each system.
(ii)the distance (l metres) over which power is transmitted remains the same.
(iii)the line losses (W watts) are the same in each case.
(iv)the maximum voltage between any conductor and earth (Vm) is the same in each case.
1. Two-wire d.c. system with one conductor earthed
In the 2-wire d.c. system, one is the outgoing or positive wire and the other is the return or
negative wire as shown in Fig.
The load is connected between the two wires.Max. voltage between conductors = Vm
Power to be transmitted =P
∴Load current,
I1= P/Vm If R1 is the resistance of each line conductor, then,
R1=ρl/a1 where
a1 is the area of X-section of the conductor.
Line losses,
W=2I21R1= 2(P/Vm)2 ρl/a1
∴Area of X-section, a1=2P2ρl/WV2m
Volume of conductor material required
=2 a1l = 2( 2P2ρl/WV2m) l= 4P2ρl2/WV2m
It is a usual practice to make this system as the basis for comparison with other systems. Therefore, volume of conductor material required in this system shall be taken as the basic quantity
i.e.
4P2ρl2/WV2m =K
(2) . Two-wire d.c. system with mid-point earthed.
Fig. shows
The two-wire d.c. system with mid-point earthed. The maximum voltage
between any conductor and earth is Vm so that maximum voltage between
conductors is 2Vm
.
Load current,I2=P/2Vm
Let a2 be the area of X-section of the conductor.
Line losses, W=2I2R2= 2 (P/2V)2m x ρl/2
∴
W=P2 ρ l/2a2V2m
∴Area of X-section, a2=P2 ρ l/2WV2m
∴Volume of conductor material required
=2 a2 l= 2 (P ρ l/2WV2m) =K/4
Hence, the volume of conductor material required in this system is one-fourthof that required in a
two-wire d.c. system with one conduc-tor earthed.
In the beginning of the electrical age, electricity was generated as a direct current and
voltages were low. The resistance losses in the lines made it impracticable to transmit
anddistribute power for more than a few localities of the city. With the development of the
transformer,a.c. has taken over the load formerly supplied by d.c. Now-a-days, electrical energy
is generated, transmitted and distributed in the form of a.c. asan economical proposition. The
transformerpermits the transmission and distribution of a.c.power at high voltages. This has
greatly reduced the current in the conductors (and hence their sizes) and the resulting line
losses.However, for certain applications, d.c. supply is absolutely necessary. For example,
d.c.supply is required for the operation of variable speed machinery (e.g. d.c. motors),
electrochemical work and electric traction. For this purpose, a.c. power is converted into d.c.
power at the sub-station by using converting machinery e.g. mercury are rectifiers, rotary
converters and motor-generator sets. The d.c. supply from the sub-station is conveyed to the
required places for distribution.
AC three-phase four-wire Distribution System,
3-phase, 4-wire system.
In this case, 4th or neutral wire is taken from the neutral point as shown in Fig. 7.13. The area of
X-section of the neutral wire is generally one-half that of the line conductor. If the loads are
balanced, then current through the neutral wire is zero. Assuming balanced loads and p.f. of the
load as cosφ,
Line losses,
W= Same as in 3 phase, 3-wire
= 2 P2ρl/3a10V2mcosφ
∴
Area of X-section, a10= 2 P2ρl/3W V2mcosφ
As the area of X-section of neutral wire is one-half that of any line conductor,
∴Volume of conductor material required
= 3·5 a10l= 3·5 (2 P2ρl/3W V2mcosφ) x l
= 7K/12 cos2φ
Hence, the volume of conductor material required for this system is 7/12 cos2φ times that
required for 2-wire d.c. system with one conductor earthed.
Lecture:34
Types of Primary Distribution Systems, Types of Secondary Distribution Systems, Voltage Drop
in DC Distributors,
Types of Secondary Distribution Systems
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. 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.
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., 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.
(ii) 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. 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 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
Advantages
(a) If a fault occurs on any feeding point of the distributor, the continuity of supply is
main tained 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.
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.
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.The
concentrated loads are those which act on particular points of the distributor. A common example of such loads is that tapped off for domestic use.
On the other hand,distributed loads are those which act uniformly on all points
of the distributor.Ideally, there are no distributed loads. However, a nearest example of
distributed load is a large number of loads of same wattage connected to the distributor at equal
distances. In d.c. distribution calculations, one important point of interest is the determination of
point of minimum potential on the distributor. The point where it occurs depends upon the
loading conditions and the method of feeding the distributor. The distributor is so designed that
the minimum potential on it is not less than 6% of rated voltage at the consumer’s terminals.
D.C. Distributor Fed at one End—Concentrated Loading
Fig. 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=r4I4
∴Total voltage drop in the distributor=r1(I1+I2+I3+I4) +r2(I2+ I3+ I4) r3(I3+ I4) +r4I4
It is easy to see that the minimum potential will occur at point F which is farthest from the feeding
Uniformly Loaded Distributor Fed at One End
Fig 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. It means that at every 1 m length of the distributor,
the load tapped is I amperes. Let l metres be the length of the distributor and r ohm be the
resistance per metre run.
Consider a point C on the distributor at a distance x metres from the feeding point
Aas shown in Fig. . 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 dxand 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
V=
=ir(lx-x2/2)
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
= i r( lxl – l2/2)
=1/2 i rl2=1/2(i l) (r l)
=1/2I R
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.
Distributor Fed at Both Ends—Concentrated Loading
Whenever possible, 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 crosssection 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 Vvolts and having concentrated loads I1, I2, I3, I4 and I5 at points C, D, E, F and
Grespectively as shown in Fig.
As we move away from one of the feeding points, sayA, p.d. goes on decreasing till it reaches
the minimum value at some load point, say E, and then again starts rising and becomes Vvolts 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 Awhile those tapped off between Band 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
Therefore, we arrive at a very important conclusion that at the point of minimum potential,
current comes from both ends of the distributor
Point of minimum potential.
It is generally 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 I3at 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.
(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= IARAC + (IA − I1) RCD+ (IA−I1−I2) RDE+ (IA−I1−I2−I3) REB
From this equation, the unknown IAcan be calculated as the values of other quantities are
generally given. Suppose actualdirections of currents in the various sections of the distributor are
indicated as shown in Fig. (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
(ii) Two ends fed with unequal voltages.
Fig. 13.16 shows the distributor AB fed with unequal voltages ; end A
being fed at V1volts 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
Lecture35
Voltage Drop in AC Distributors, Kelvin’s Law, Limitations of Kelvin’s Law, General Design
Considerations
Voltage Drop in AC Distributors
A.C. Distribution Calculations
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
i.e (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.
There are several ways of solving a.c. distribution problems. However, symbolic notation
method has been found to be most convenient for this purpose. In this method, voltages, currents
and impedances are expressed in complex notation and the calculations are made exactly as in
d.c. distribution.
Methods of Solving A.C. Distribution Problems
In a.c. distribution calculations, power factors of various load currents have to be considered
since currents in different sections of the distributor will be the vector sum of load currents and
not the arithmetic sum. The power factors of load currents may be given (i) w.r.t. receiving or
sending end voltage or (ii) w.r.t. to load voltage itself.
(i) Power factors referred to receiving end voltage.
Consider an a.c. distributor AB with concentrated loads of I1 and I2 tapped off at points C and B
as shown in Fig.
Taking the receiving end voltage VB as the reference vector, let lagging power
factors at Cand Bbe cos φ1 and cos φ2w.r.t.VB. Let R1, X1 and R2, X2 be the resistance and
reactance of sections AC and CB of the distributor.
Impedance of section AC, ZAC=R1+ j X1
Impedance of section CB,ZCB=R2+ j X2
Load current at point C,I1=I1(cos φ1−jsin φ1)
Load current at point B,I2=I2(cos φ2−jsinφ2)
Current in section CB,ICB=I2= I2(cos φ2−jsin φ2)
Current in section AC,IAC=II12+=I1(cos φ1−jsin φ1) + I2(cos φ2−jsinφ2)
Voltage drop in section CB,VCB=IZCB CB= I2(cos φ2−jsin φ2) (R2+ jX2)
Voltage drop in section AC,VAC= IACZ AC = (I1+I2) Z AC
=[I1(cos φ1−jsin φ1) + I2(cos φ2−jsin φ2)] [R1+ jX1]
Sending end voltage,VA=VB+VCB +VAC
Sending end current,IA=I1+I2
The vector diagram of the a.c. distributor under these conditions is shown in Fig. Here, the
receiving end voltage VB is taken as the reference vector. As power factors of loads are given
w.r.t. VB, therefore, I1and I2 lag behind VB by φ1and φ2 respectively.
The vector diagram of the a.c. distributor under these conditions is shown in Fig Here, the
receiving end voltage VB is taken as the reference vector. As power factors of loads are given
w.r.t.VB , therefore, I1and I2 lag behind VB by φ1and φ2 respectively
(ii) Power factors referred to respective load voltages.Suppose the power factors of loads in the
previous Fig are referred to their respective load voltages. Then φ1 is the phase anglevbetween
VC and I1 and φ2 is the phase angle between VB and I2. The vector diagram under these
conditions is shown in Fig.
Voltage drop in section CB=IZCB2= I2(cos φ2−jsin φ2) (R2+ j X2)
Voltage at point C=VB+ Drop in section CB= VC ∠α(say)
Now I1=I1∠−φ1w.r.t. voltage VC
∴I1=I1∠−(φ1−α)w.r.t. voltage VB
i.e.I1=I1[cos (φ1−α) −jsin (φ1−α)]
Now IAC=II1
=I1[cos (φ1−α)−jsin(φ1−α)] + I2(cos φ2−jsin φ2)
Voltage drop in section AC=IACZAC
∴Voltage at point A=VB+ Drop in CB+ Drop in AC
Kelvin’s Law, Limitations of Kelvin’s Law, General Design Considerations
Economics of Power Transmission
While designing any scheme of power transmission, the engineer must have before him the
commercial aspect of the work entrusted to him. He must design the various parts of
transmission scheme in a way that maximum economy is achieved. The economic design and
layout of a complete power transmission scheme is outside the scope of this book. However, the
following two fundamental economic principles which closely influence the electrical design of a
transmission line will be discussed :
(i)Economic choice of conductor size
(ii)Economic choice of transmission voltage
General Design Considerations
The choice of proper scheme is the most difficult and complex task because a number of factors
have to be taken into account and some of the factors cannot be epressed in economic
term.Economy,eliability,oltage level,egulation and feasibility of expansion are some of the
important consideration.
a) Economimy: Annual fixed cost (interest and depreciation etc) must be taken into account
during planning.
Different steps of economy study are
1. Determination of total investment for each plan
2. Determination of annual fixed costs,perating and overhead expenses.
3. Detremination of cost of electrical losses.
4. Selection of most economic plan
b) Reliability: It can be expressed in a number of ways .From the consumers points of view,the
number of interruption total interruption time and average time per outage are of main interest.
c) Voltage Level and Regulation:Following voltage control methods are used singly or in
combination.
1. Transformer tap changing under load
2.Shunt capacitors to improve power factor thereby reducing voltage drop
3.Series capacitors to compensate the line reactance.
c) Feasibility of Expansion:The expansion are usually carried out in small increaments.One of
the key concepts in the system design is therefore provision of expansion.
Economic Choice of Conductor Size
The cost of conductor material is generally a very considerable part of the total cost of a
transmission line. Therefore, the determination of proper size of conductor for the line is of vital
importance. The most economical area of conductor is that for which the total annual cost of
transmission line is minimum. This is known as Kelvin’s Law after Lord Kelvin who first
stated it in 1881. The total annual cost of transmission line can be divided broadly into two parts
viz., annual charge on capital outlay and annual cost of energy wasted in the conductor.
(i) Annual charge on capital outlay.
This is on account of interest and depreciation on the capital cost of complete installation of
transmission line. In case of overhead system, it will be the annual interest and depreciation on
the capital cost of conductors, supports and insulators and the cost of their erection. Now, for an
overhead line, insulator cost is constant, the conductor cost is proportional to the area of Xsection and the cost of supports and their erection is partly constant and partly proportional to
area of X-section of the conductor. Therefore, annual charge on an overhead transmission line
can be expressed as :
Annual charge = P1+ P2a...(i)
where P1and P2 are constants and a is the area of X-section of the conductor
(ii) Annual cost of energy wasted.
This is on account of energy lost mainly in the conductor due to I2R losses. Assuming a constant
current in the conductor throughout the year, the energy lost in the conductor is proportional to
resistance. As resistance is inversely proportional to the area of X-section of the conductor,
therefore, the energy lost in the conductor is inversely proportional to area of X-section. Thus,
the annual cost of energy wasted in an overhead transmission line can be expressed as :
Annual cost of energy wasted =P3/a.
where P3 is a constant.
Total annual cost, C= exp. (i) + exp.
(ii)
= (P1+ P2a) + P3/a
∴
`
C=P1+ P2a+ P3/a
(iii)
In exp. (iii), only area of X-section a is variable. Therefore, the total annual cost of
transmission line will be minimum if differentiation of C w.r.t.a is zero i.e.
d/da (C) = 0
or
d/da ( P1+ P2a+ P3/a) = 0
or
P2−P3/a2 = 0
or
P2 = P3/a2
or
P2 a=P3/a
i.e. Variable part of annual charge = Annual cost of energy wasted
Therefore Kelvin’s Law can also be stated in an another way i.e. the most economical area of
conductor is that for which the variable part of annual charge is equal to the cost of energy losses
per year.
Graphical illustration of Kelvin’s law.
Kelvin’s law can also be illustrated graphically by plotting annual cost against X-sectional area ‘
a’of the conductor as shown in Fig. 7.28. In the diagram,
The straight line
(1) shows the relation between the annual charge (i.e., P1+ P2a) and the area of X-section
A of the conductor. Similarly, the rectangular hyperbola (2) gives the relation between annual
cost of energy wasted and X-sectional area a . By adding the ordinates of curves (1) and (2), the
curve (3) is obtained. This latter curve shows the relation between total annual cost
(P1+P2a+ P3/a) of transmission line and area of X-section a. The lowest point on the curve (i.e.,
point P) represents the most economical area of X-section.
Limitations of Kelvin’s law.
Although theoretically Kelvin’s law holds good, there is often considerable difficulty in applying
it to a proposed scheme of power transmission. In practice, the limitations of this law are :
(i) It is not easy to estimate the energy loss in the line without actual load curves, which are
not available at the time of estimation.
(ii) The assumption that annual cost on account of interest and depreciation on the capital
outlay is in the form P1+ P2a is strictly speaking not true. For instance, in cables
neither the cost of cable dielectric and sheath nor the cost of laying vary in this
manner
(iii)This law does not take into account several physical factors like safe current density,
mechanical strength, corona loss etc.
(iv) The conductor size determined by this law may not always be practicable one because it
may be too small for the safe carrying of necessary current.
(v)
Interest and depreciation on the capital outlay cannot be determined accurately.
Lecture:36
Load Estimation, Design of Primary Distribution, Sub-Stations, Secondary Distribution Design,
Load Estimation:
The estimation of load likely to come on the distribution system immediately as weel as in the
future is the firdt step in the design of distribution system
Following estimation are needed.
a) Short term Estimation:
b) Long term estimation:
Design Considerations in Distribution System
Good voltage regulation of a distribution network is probably the most important factor
responsible for delivering good service to the consumers. For this purpose, design of feeders and
distributors requires careful consideration.
(i)Feeders.
A feeder is designed from the point of view of its current carrying capacity while
the voltage drop consideration is relatively unimportant. It is because voltage drop in a
feeder can be compensated by means of voltage regulating equipment at the substation.
(ii)Distributors.
A distributor is designed from the point of view of the voltage drop in it. 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). The size and length of the
distributor should be such that voltage at the consumer’s terminals is within the permissible
limits
Lecture:37
Economical Design of Distributors, Design of Secondary Network,
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. 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
Lecture:38
Lamp Flicker, Application of Capacitors to Distribution Systems
Lecture39:
Introduction, Insulation, Sheath, Armour and Covering
Electric power can be transmitted or distributed either by overhead system or by underground
cables. The underground cables have serveral advantages such as less liable to damage through storms or
lightning, low maintenance cost, less chances of faults, smaller voltage drop and better general
appearance.However, their major drawback is that they have greater installation cost and introduce
insulation problems at high voltages compared with the equivalent overhead system. For this
reason,underground cables are employed where it is impracticable to use overhead lines. Suchlocations
may be thickly populated areas where municipal authorities prohibit overhead lines for reasons of safety,
or around plants and substations or where maintenance conditions do not permit the use of overhead
construction.The chief use of underground cables for many
years has been for distribution of electric power in congested urban areas at comparatively low or
moderate voltages. However, recent improvements in the design and manufacture have led to
the development of cables suitable for use at high voltages. This has made it possible to employ
underground cables for transmission of electric power for short or moderate distances. In this chapter, we
shall focus our attention on the various aspects of underground cables and their increasing use in power
system.
Underground Cables
An underground cableessentially consists of one or more conductors covered with suitable insulation and
surrounded by a protecting cover.Although several types of cables are available, the type of cable to be
used will depend upon theworking voltage and service requirements. In general, a cable must fulfil the
following necessary requirements :
(i) The conductor used in cables should be tinned stranded copper or aluminium 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 chemicaland
physical stability throughout.
Construction of Cables
Fig. 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 shownin Fig. is used for 3-phase service. The conductors
are made of tinned copper or aluminium and are usually stranded in order to provide flexibility to the
cable.
(ii)Insulatian.
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 inFig.
(iv)Bedding.
Over the metallicsheath is applied a layer of bedding which consists of a fibrous material like jute or
hessiantape. The purpose of bedding is to protect the metallic sheath against corrosion and
frommechanical injury due to armouring.
(v)Armouring.
Over the bedding, armouring is provided which consists of one or two layers of galvanised steel wire or
steel tape. Its purpose is to protect the cable from mechanical injury while laying it and during the course
of handling. Armouring may not be done in the case of some cables.
(vi)Serving.
In order to protect armouring from atmospheric conditions, a layer of fibrous Insulation
Insulating Materials for Cables
The satisfactory operation of a cable depends to a great extent upon the characteristics of insulation used.
Therefore, the proper choice of insulating material for cables is of considerable importance. 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.No one insulating material possesses
all the above mentioned properties.Therefore, the type of insulating material to be used depends upon the
purpose for which the cable is required and the quality of insulation to be aimed at. The principal
insulating materials used in cables are rubber, vulcanised India rubber,
impregnated paper, varnished cambric and polyvinyl chloride.
1. Rubber.
Rubber may be obtained from milky sap of tropical trees or it may be produced from oil products. It has
relative permittivity varying between 2 and 3, dielectric strength is about
30 kV/mm and resistivity of insulation is 1017Ωcm. Although pure rubber has reasonably high insulating
properties, it suffers form some major drawbacks viz., readily absorbs moisture, maximum safe
temperature is low (about 38ºC), soft and liable to damage due to rough handling and ages when exposed
to light. Therefore, pure rubber cannot be used as an insulating material.
2. Vulcanised India Rubber (V.I.R).
It is prepared by mixing pure rubber with mineral matter such as zine oxide, red lead etc., and 3 to 5% of
sulphur. The compound so formed is rolled into thin sheets and cut into strips. The rubber compound is
then applied to the conductor and is heated toa temperature of about 150ºC. The whole process is called
vulcanisationand the product obtained is known as vulcanised India rubber.Vulcanised India rubber has
greater mechanical strength, durability and wear resistant property than pure rubber. Its main drawback is
that sulphur reacts very quickly with copper and for this reason, cables using VIR insulation have tinned
copper conductor. The VIR insulation is generally used for low and moderate voltage cables.
3. Impregnated paper.
It consists of chemically pulped paper made from wood chippings and impregnated with some compound
such as paraffinic or napthenic material. This type of insulation has almost superseded the rubber
insulation. It is because it has the advantages of low cost, low capacitance, high dielectric strength and
high insulation resistance. The only disadvantage is that paper is hygroscopic and even if it is
impregnated with suitable compound, it absorbs moisture and
thus lowers the insulation resistance of the cable. For this reason, paper insulated cables are always
provided with some protective covering and are never left unsealed. If it is required to be left unused on
the site during laying, its ends are temporarily covered with wax or tar.
Since the paper insulated cables have the tendency to absorb moisture, they are used where the
cable route has a few joints. For instance, they can be profitably used for distribution at low voltages in
congested areas where the joints are generally provided only at the terminal apparatus. However,for
smaller installations, where the lenghts are small and joints are required at a number of places,VIRcables
will be cheaper and durable than paper insulated cables.
4. Varnished cambric.
It is a cotton cloth impregnated and coated with varnish. This type ofinsulation is also known as
empire tape.The cambric is lapped on to the conductor in the form of a tape and its surfaces are coated
with petroleum jelly compound to allow for the sliding of one turn over another as the cable is bent. As
the varnished cambric is hygroscopic, therefore, such cables are always provided with metallic sheath. Its
dielectric strength is about 4 kV/mm and permittivity is 2.5
to 3.8.
5. Polyvinyl chloride (PVC).
This insulating material is a synthetic compound. It is obtained from the polymerisation of acetylene and
is in the form of white powder. For obtaining this material as a cable insulation, it is compounded with
certain materials known as plasticizers which are liquids with high boiling point. The plasticizer forms a
gell and renders the material plastic over the desired range of temperature.Polyvinyl chloride has high
insulation resistance, good dielectric strength and mechanical tough-ness over a wide range of
temperatures. It is inert to oxygen and almost inert to many alkalies andacids. Therefore, this type of
insulation is preferred over VIR in extreme enviormental conditionssuch as in cement factory or chemical
factory. As the mechanical properties (i.e., elasticity etc.) ofPVC are not so good as those of rubber,
therefore,
PVC insulated cables are generally used for lowand medium domestic lights and power installations.
Lecture:40
Classification of Cables, Pressured cable, Effective Conductor Resistance, Conductor Inductive
Resistance
Classification of Cables
Cables for underground service may be classified in two ways according to (i) the type of insulating
material used in their manufacture (ii) the voltage for which they are manufactured. However, the latter
method of classification is generally preferred, according to which cables can be divided into the
following groups :
(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
A cable may have one or more than one core depending upon the type of service for which it is intended.
It may be (i) single-core (ii) two-core (iii) three-core (iv) four-core etc. Fora 3-phase service, either 3single-core cables or three-core cable can be used depending upon the operating voltage and load demand.
Fig. shows
The constructional details of a single-core low tension cable. The cable has ordinary construction
because the stresses developed in the cable for low voltages (upto 6600 V) are generally small. It consists
of one circular core of tinned stranded copper (or aluminium) insulated by layers of impregnated paper.
The insulation is surrounded by a lead sheath which prevents the entry of moisture into the inner parts. In
order to protect the lead sheath from corrosion, an overall serving of compounded fibrous material (jute
etc.) is provided. Single-core cables are not usually armoured in order to avoid excessive sheath losses.
The principal advantages of single-core cables are simple construction and availability of larger copper
section.
Cables for 3-Phase Service
In practice, underground cables are generally required to deliver 3-phase power. For the purpose,
either three-core cable or *three single core cables may be used. For voltages upto 66 kV, 3-core
cable (i.e.,multi-core construction) is preferred due to economic reasons. However, for voltages
beyond 66 kV, 3-core-cables become too large and unwieldy and, therefore, single-core cables areused.
The following types of cables are generally used for 3-phase service :
1.Belted cables — upto 11 kV
2.Screened cables — from 22 kV to 66 kV
3.Pressure cables — beyond 66 kV.
1. Belted cables.These cables are used for voltages upto 11kV but in extraordinary cases,
their use may be extended upto 22kV. Fig. 11.3 shows the constructional details of a 3-core beltedcable.
The cores are insulated from each other by lay-ers of impregnated paper. Another layer of impreg-nated
paper tape, called paper belt is wound round the grouped insulated cores. The gap between the insulated
cores is filled with fibrous insulating material (juteetc.) so as to give circular cross-section to the
cable.The cores are generally stranded and may be of non-
circular shape to make better use of available space.The belt is covered with lead sheath to protect the
cableagainst ingress of moisture and mechanical injury. The lead sheath is covered with one or more
layers of armouring with an outer serving (not shown in the fig-ure).
The belted type construction is suitable only for low and medium voltages as the electrostatic
stresses developed in the cables for these voltages are more or less radial i.e., across the
insulation.However, for high voltages (beyond 22 kV), the tangential stresses also become important.
Thesestresses act along the layers of paper insulation. As the insulation resistance of paper is quite small
along the layers, therefore, tangential stresses set up **leakage current along the layers of paper
insulation. The leakage current causes local heating, resulting in the risk of breakdown of insulation at
any moment. In order to overcome this difficulty, screened cables
are used where leakage currents are conducted to earth through metallic screens.
2. Screened cables. These cables are meant for use upto 33 kV, but in particular cases their
use may be extended to operating voltages upto 66 kV. Two principal types of screened cables are H-type
cables and S.L. type cables.(i)H-type cables. This type of cable was first designed by H. Hochstadter and
hence the name.Fig. 11.4 shows the constructional details of a typical 3-core,
H-type cable. Each core is insulated by layers of impregnated paper. The insulation on each core is
covered with a metallic screen which usually consists of a perforated aluminium foil. The cores are laid in
such a way that metallic screens make contact with one another. An additional
conducting belt (copper woven fabric tape) is wrapped round the three cores. The cable has no
insulating belt but lead sheath, bedding,armouring and serving follow as usual. It is easy to see that each
core screen is in electrical contact with the conducting belt and the lead sheath.
As all the four screens (3 core screens and one conducting belt) and the lead sheath are at
Earth potential, therefore, the electrical stresses are purely radial and consequently dielectric losses are
reduced.Two principal advantages are claimed for H-type cables. Firstly, the perforations in the metallic
screens assist in the complete impregnation of the cable with the compound and thus the possibility of air
pockets or voids (vacuous spaces) in the dielectric is eliminated. The voids if present tend to reduce the
breakdown strength of the cable and may cause considerable damage to the paper insulation. Secondly,
the metallic screens increase the heat dissipating power of the cable.
(ii)S.L. type cables.
Fig. shows
(S.L. type cables)
the constructional details of a 3-core S.L. (separate lead) type cable. It is basically H -type cable but the
screen round each core insulation is covered by its own lead sheath. There is no overall lead sheath but
only armouring and serving are provided. The S.L. type cables have two main advantages over H-type
cables. Firstly, the separate sheaths minimise the possibility of core-to-core breakdown. Secondly,
bending of cables becomes easy due to the elimination of overall lead sheath. However, the disadvantage
is that the three lead sheaths of S.L. cable are much thinner than the single sheath of H-cable and,
therefore, call for greater care in manufacture.Limitations of solid type cables.All the cables of above
construction are referred to as solid type cables because solid insulation is used and no gas or oil
circulates in the cable sheath. The voltage limit for solid type cables is 66 kV due to the following reasons
:
(a) As a solid cable carries the load, its conductor temperature increases and the cable compound (i.e., insulating compound over paper) expands. This action stretches the lead sheath which may be
damaged.(b) When the load on the cable decreases, the conductor cools and a partial vacuum is formed
within the cable sheath. If the pinholes are present in the lead sheath, moist air may be drawn into the
cable. The moisture reduces the dielectric strength of insulation and may eventually cause the break-down
of the cable.(c)In practice, voids are always present in the insulation of a cable. Modern techniques of
manufacturing have resulted in void free cables. However, under operating conditions, the voids are
formed as a result of the differential expansion and contraction of the sheath and impregnated com pound.
The breakdown strength of voids is considerably less than that of the insulation. If the void is small
enough, the electrostatic stress across it may cause its breakdown. The voids nearest to the conductor are
the first to break down, the chemical and thermal effects of ionisation causing permanent damage to the
paper insulation.
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.
(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. Oil under pressure compresses the layers of paper insulation and is forced into any
voids that may have formed between the layers. Due to the elimination of voids, oil-filled cables can be
used for higher voltages, the range being from 66 kV upto 230 kV. Oil-filled cables are of three types viz.
single-core conductor channel, single-core sheath channel and three-core filler-space
channels.Fig 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 cylindricalsteel 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. Fig.
shows the constructional details of a single-core sheath channel oil-filled cable. In this type of cable,the
conductor is solid similar to that of solid cable and is paper insulated. However, oil ducts are provided in
the metallic sheath as shown. In the 3-core oil-filler cable shown in Fig. the oil ducts are located in the
filler spaces. These channels are composed of perforated metal-ribbon tubing and are at earth
potential.The oil-filled cables have three principal advantages. Firstly, formation of voids and ionization
are avoided. Secondly, 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.
However, their major disadvantages are the high initial cost and complicated system of laying.
(ii)Gas pressure cables.
The voltage required to set up ionisation inside a void increases as the pressure is increased. Therefore, if
ordinary cable is subjected to a sufficiently high pressure, the ionisation can be altogether eliminated. At
the same time, the increased pressure produces radial compression which tends to close any voids. This is
the underlying principle of gas pressure cables.
Fig. 11.9 shows
The section of external pressure cable designed by Hochstadter, Vogal and Bowden.The
construction of the cable is similar to that of an ordinary solid type except that it is of triangular shape and
thickness of lead sheath is 75% that of solid cable. The triangular section reduces the weight and gives
low thermal resistance but the main reason for triangular shape is thatthe lead sheath acts as a pressure
membrane. The sheath is protected by a thin metal tape. The cable is laid in a gas-tight steel pipe. The
pipe is filled with dry nitrogen gas at 12 to 15 atmospheres. The gas pressure produces radial compression
and closes the voids that may have formed between the layers of paper insulation. Such cables can carry
more load current and operate at higher voltages than a normal cable. Moreover, maintenance cost is
small and the nitrogen gas helps in quenching any flame. However, it has the disadvantage that the overall
cost is very high
.
Insulation Resistance of a Single-Core Cable
The cable conductor is provided with a suitable thickness of insulating material in order to prevent
leakage current. The path for leakage current is radial through the insulation. The opposition offered by
insulation to leakage current is known as insulation resistance of the cable. For satisfactory operation, the
insulation resistance of the cable should be very high.
Consider a single-core cable of conductor radius r1 and internal sheath radius r2
as shown in Fig.
Let l be the length of the cable and ρ be the resistivity of the insulation.
Consider a very small layer of insulation of thickness dx at a radius x.
The length through which leakage current tends to flow is dx and the area of X-section offered to this
flow is 2πxl.
∴Insulation resistance of considered layer=ρdx/2πxl
Insulation resistance of the whole cable is
πxl
R=
∴
R=ρ/2
πl
x
R = ρ/2 πl
This shows that insulation resistance of a cable is inversely proportional to its length. In other
words, if the cable length increases, its insulation resistance decreases and vice-versa
Lecture:41:
Parameters of Single core cable , Grading of Cables, Capacitance of Three phase Belted cable,
Breakdown of Cables.
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
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= ε0εr where εr is the relative permittivity
of the insulation.
Consider a cylinder of radius x metres and axial length 1 metre. The surface area of this cylinder is = 2π x
×1= 2 π x m2
∴
Electric flux density at any point P on the considered cylinder is
Dx=Q/2πx
C/m2
Electric intensity at point P, Ex=Dx/ε= Q/2πxε= Q/2π x ε0εr volts/m
The work done in moving a unit positive charge from point P through a distance dx in the
direction of electric field is Ex dx. Hence, the work done in moving a unit positive charge from conductor
to sheath, which is the potential difference V between conductor and sheath, is given by :
V=
Capacitance of cable is
=
= Q/2π x ε0εr
C=Q/V = Q/ Q/2π x ε0εr
=20πε0εr
F/m
Fm/m
If the cable has l meters, then capacitance is
C= εrl 10-9/41.4
Farad
Grading of Cables
The process of achieving uniform electrostatic stress in the dielectric of cables is known as
Grading of cables.It has already been shown that electrostatic stress in a single core cable has a maximum
value (gmax) at the conductor surface and goes on decreasing as we move towards the sheath. The
maximum voltage that can be safely applied to a cable depends upon gmaxi.e.,
electrostatic stress at the conductor surface. For safe working of a cable having homogeneous dielectric,
the strength of dielectric must be more than gmax .If a dielectric of high strength is used for a cable, it is
useful only near the conductor where stress is maximum. But as we move away from the conductor, the
electro-tatic stress decreases, so the dielectric will be unnecessarily overstrong.
The unequal stress distribution in a cable is undesirable for two reasons. Firstly, insulation of
greater thickness is required which increases the cable size. Secondly, it may lead to the breakdown of
insulation. In order to overcome above disadvantages, it is necessary to have a uniform stress distribution
in cables. This can be achieved by distributing the stress in such a way that its value is increased in the
outer layers of dielectric. This 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.In capacitance grading, the homogeneous dielectric is replaced
by a composite dielectric. The composite dielectric consists of various layers of different dielectrics in
such a manner that relative permittivity εr of any layer is inversely proportional to its distance from the
centre. Under such conditions, the value of potential gradient at any point in the dieletric is constant and is independent of its distance from the centre. In other
words, the dielectric stress in the cable is same everywhere and the grading is ideal one. However, ideal
grading requires the use of an infinite number of dielectrics which is an impossible task. In practice, two
or three dielectrics are used in the decreasing order of permittivity ; the dielectric of highest permittivity
being used near the core.referring to Fig.
There are three dielectrics of outer diameter d1, d2 and D and of relative permittivity ε1, ε2
and ε3 respectively.
If the permittivities are such that ε1 >ε2 >ε3 and the three dielec-trics are worked at the same maximum
stress, then,
1/ε1d =1/ε2d1 =1/ ε3d2
ε1 d=ε2 d1=ε3 d2
Or
Potential difference across the inner layer is
V1=
=
= gmaxd/2
Similarly, potential across second layer (V2) and third layer (V3) is given by ;
V2= gmaxd1/2
V3= gmaxd1/2
Total p.d. between core and earthed sheath isV=V1 +V2 +V3
=
If the cable had homogeneous dielectric, then, for the same values of d, D and gmax, the permissible potential difference between core and earthed sheath would have been
V′= gmaxd/2
Obviously, V > V′i.e., for given dimensions of the cable, a graded cable can be worked at a
greater potential than non-graded cable. Alternatively, for the same safe potential, the size of graded cable
will be less than that of non-graded cable. The following points may be noted :
(i)As the permissible values of gmax are peak values, therefore, all the voltages in above expressions should be taken as peak values and not the r.m.s. values.
(ii) If the maximum stress in the three dielectrics is not the same, then
V = g1maxd/2
+ g2maxd1/2
+ g3maxd1/2
The principal disadvantage of this method is that there are a few high grade dielectrics of reasonable cost
whose permittivities vary over the required range.
Intersheath Grading
In this method of cable grading, a homogeneous dielectric is used, but it is divided into various layers by
placing metallic intersheaths between the core and lead sheath. The intersheaths are held at suitable
potentials which are inbetween the core potential and earth potential. This arrangement improves voltage
distribution in the dielectric of the cable and consequently more uniform potential gradient is obtained.
Consider a cable of core diameter d and outer lead sheath of diameter D. Suppose that two intersheaths 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.
Maximum stress between core and intersheath 1 is
g1max=
Similarly
g2max=
g3max=
Since the dielectric is homogeneous, the maximum stress in each layer is the same
i.e.,g1max=g2max= g3max=gmax(say)
∴
=
As the cable behaves like three capacitors in series, therefore, all the potentials are in phase
i.e.Voltage between conductor and earthed lead sheath is
V=V1+ V2+ V3
Intersheath grading has three principal disadvantages. Firstly, there are complications in fixing
the sheath potentials. Secondly, the intersheaths are likely to be damaged during transportation and
installation which might result in local concentrations of potential gradient. Thirdly, there are
considerable losses in the intersheaths due to charging currents. For these reasons, intersheath grading is
rarely used.
Lecture:42
Cable Installation, Current Rating of Cables, System Operating Problems with Underground Cables
Cable Installation
The reliability of underground cable network depends to a considerable extent upon the proper
laying and attachment of fittings i.e., cable end boxes, joints, branch connectors etc .
There are three main methods of laying underground cables viz.,direct laying, draw-in system and the
solid system.
1. Direct lying.
This method of laying underground cables is simple and cheap and is much favoured in modern practice.
In this method, a trench of about 1·5 metres deep and 45 cm wide is dug. The trench is covered with a
layer of fine sand (of about 10 cm thickness) and the cable is laid over this sand bed. The sand prevents
the entry of moisture from the ground and thus protects the cable from decay. After the cable has been
laid in the trench, it is covered with another layer of sand of about 10 cm thickness.
The trench is then covered with bricks and other materials in order to protect the cable from mechanical
injury. When more than one cable is to be laid in the same trench, a horizontal or vertical interaxial
spacing of atleast 30 cm is provided in order to reduce the effect of mutual heating and also to ensure that
a fault occurring on one cable does not damage the adjacent cable. Cables to be laid in this way must have
serving of bituminised paper and hessian tape so as to provide protection against corrosion and
electorlysis.
Advantages
(i)It is a simple and less costly method.
(ii)It gives the best conditions for dissipating the heat generated in the cables.
(iii)It is a clean and safe method as the cable is invisible and free from external disturbances.
Disadvantages
(i)The extension of load is possible only by a completely new excavation which may cost as
much as the original work.
(ii)The alterations in the cable netwok cannot be made easily.
(iii)The maintenance cost is very high.
(iv)Localisation of fault is difficult.
(v)It cannot be used in congested areas where excavation is expensive and inconvenient.
This method of laying cables is used in open areas where excavation can be done conveniently
and at low cost.
2. Draw-in system.
In this method, conduit or duct of glazed stone or cast iron or concrete are laid in the ground with
manholes at suitable positions along the cable route. The cables are then pulled into position from
manholes. Fig. shows
Section through four-way underground duct line. Three of the ducts carry transmission cables and
the fourth duct carries relay protection connection, pilot wires. Care must be taken that where the duct
line changes direction ; depths, dips and offsets be made with a very long radius or it will be difficult to
pull a large cable between the manholes. The distance between the manholes should not be too long so as
to simplify the pull ing in of the cables. The cables to be laid in this way need not be armoured but must
be provided with serving of hessian and jute in order to protect them when being pulled into the ducts.
Advantages
(i)Repairs, alterations or additions to the cable network can be made without opening the
ground.
(ii)As the cables are not armoured, therefore, joints become simpler and maintenance cost is
reduced considerably.
(iii)There are very less chances of fault occurrence due to strong mechanical protection provided by the system.
Disadvantages
(i)The initial cost is very high.
(ii)The current carrying capacity of the cables is reduced due to the close grouping of cables
and unfavourable conditions for dissipation of heat.
This method of cable laying is suitable for congested areas where excavation is expensive and
inconvenient, for once the conduits have been laid, repairs or alterations can be made without opening the
ground. This method is generally used for short length cable routes such as in workshops,road crossings
where frequent digging is costlier or impossible.
3. Solid system.
In this method of laying, the cable is laid in open pipes or troughs dug out in earth along the cable route.
The troughing is of cast iron, stoneware, asphalt or treated wood. After the cable is laid in position, the
troughing is filled with a bituminous or asphaltic compound and covered over. Cables laid in this manner
are usually plain lead covered because troughing affords
good mechanical protection.
Disadvantages
(i)It is more expensive than direct laid system.
(ii)It requires skilled labour and favourable weather conditions.
(iii)Due to poor heat dissipation facilities, the current carrying capacity of the cable is reduced.
In view of these disadvantages, this method of laying underground cables is rarely used now-adays
Current Rating of Cables
Current-Carrying Capacity of Underground Cables
The safe current-carrying capacity of an underground cable is determined by the maximum permissible
temperature rise. The cause of temperature rise is the losses that occur in a cable which appear as heat.
These losses are :
(i)Copper losses in the conductors
(ii)Hysteresis losses in the dielectric
(iii)Eddy current losses in the sheath
The safe working conductor temperature is 65ºC for armoured cables and 50ºC for lead-sheathed
cables laid in ducts. The maximum steady temperature conditions prevail when the heat generated in the
cable is equal to the heat dissipated. The heat dissipation of the conductor losses is by conduction through
the insulation to the sheath from which the total losses (including dielectric and sheath losses) may be
conducted to the earth. Therefore, in order to find permissible current loading, the thermal resistivities of
the insulation, the protective covering and the soil must be known.
System Operating Problems with Underground Cables
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.
(iv)
(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 shortcircuit fault between these conductors. The same step is
repeated for other conductors taking two at a time.
(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.
Lecture:43
HVDC Cables ,Problem Solving
Problem 1
Calculate the capacitance and charging current of a single core cable used on a 3-phase, 66 kV system.
The cable is 1 km long having a core diameter of 10 cm and an impregnated paper insulation of thickness
7 cm. The relative permittivity of the insulation may be taken as 4 and the supply at 50 Hz.
Solution.
Capacitance of cable, C=εrl 10-9/41.4 log10(D/d)
Here,
εr=4 ;
l= 1000 m
d=10 cm;D = 10 + 2 ×7 = 24 cm
Substituting these values in the above expression,
C = 0·254 × 10–6F = 0·254 μF
Voltage between core and sheath is
Vph=66/
= 38·1 kV = 38·1 ×10-3V
Charging current =Vph/XC = 2πf C Vph
= 2π×50 ×0·254 ×10–6 ×38·1×103A = 3.04 A
Problem:2
A single core cable for use on 11 kV, 50 Hz system has conductor area of 0·645cm2 and internal diameter
of sheath is 2·18 cm. The permittivity of the dielectric used in the cable is 3·5. Find (i) the maximum
electrostatic stress in the cable (ii) minimum electrostatic stress in the cable (iii) capacitance of the cable
per km length (iv) charging current.
Solution.
Area of cross-section of condutor, a= 0.645 cm2
Diameter of the conductor,d=
=
= 0·906 cm
Internal diameter of sheath,D= 2·18 cm
(i) Maximum electrostatic stress in t
gmax=
= 2*11/0.906
= 27.65 kV/cm r.m.s
(ii)Minimum electrostatic stress in the cable is
gmin =
= 2*11/2.18
=11.5kV/cm r.m.s
(iii)Capacitance of cable,C = l εr/D 41. 4 ⋅
= 3.5 *1000*10-9/41.4
=0.22*10-6
F
(v) Charging current,IC=V/Xc=2πf C V = 2π×50 ×0·22 ×10−6 *11000 = 0·76 A
Lecture: 44
Soil Resistivity, Earth Resistance, Tolerable Step and Touch Voltage,
Soil resistivity depends upon following factor:
a) Soil Type: The type of soil governs the resistivity to a large extent.Some typical value
Sea water 2.5 ohm-m,Tap water 20ohm-m,Clay mixture 100 ohm-m.
b) moisture content: Electrical condution in soils is electrilic.Soil resistivity decrease with
increase in moisture content.However when moisture is more than 20%,the change in resistivity
is negligible.The amount of water which a soil can observe depends on soil type grain size and
compactness.
c) Temperature: When temperature is more than 0 degree ,its effect on soil resistivity is
negligible.At o degree C water in the soil starts freezing and resistivity increases.
d) Salt content: The composition and amount of soluble salts also affect resistivity considerable.
e) Magnitude of current
Earth Resistance
Hemispherical Electrode: The total resistance can be divided into three parts
i) Resistance of conductor
ii) Contact resistance between the surface of electrode and main body of earth
iii)Resistance of body of earth surrounding the electrode.
The resistance of conductor and contact resistance are negligible.Therefore the main part of
resistance is that of body of earth surrounding the electrode.
Driven Rod
Mltiple Rod Electrodes
Tolerable Step and Touch Voltage,
When fault occurs ,the flow of current to earth results in voltage gradient on the surface of the
earth in the vicinity of earthing system. This voltage gradient affect a person in two ways,step or
foot to foot contact and hand to both feet or touch contact.
Step voltage
The potential defference shunted by the body is limited to the maximum value between two
contacts points,on the ground surface,separated by one pace . Rf is the earthing resistance of one
foot. And RB is the resistance of body.
A human foot can be taken as equivalent to a circular plate electrode with a radius of about 0.08
m and its each resistance may be assumed to be 3ρs where ρs is the resistivity of the soilnear the
surface of earth RB is assumed to be 1000 ohms.Therefore tolerable value of step voltage is
Estep = (RB+2RF) IB volts
Touch Voltage
The maximum earth potential intercepted would be that which would occur over a distance along
the equal to maximum possible horizontal reach. Tolerable value of touch potential is
E touch = (RB +0.5 RF) IB = (1000 + 1.5 ρs) 0.116/
Transfer Potential
A special situation occurs when a person standing within the station area touches a conductor
grounded at a remote point or a person standing at a remote point touches a connected to station
earthing grid. This special case of a touch pontial is known as transferred and can have a very
high value .It is possible to design an earthing grid for safe transferred pontila.The only remedy
is to isolate such conductors and to lable as live conductors.
Lecture: 45
Actual Touch and Step Voltages, Design of Earthing Grid.
Exact calculation of actual touch and step voltages for a grid is very difficult and can be done
only with the help of a computer.Instead of calculating Etouch corresponding to maximum
possible horizontal reach it is preferable to calculate the maximum value of touch voltage within
a mesh of the grid.This voltage is known as mesh voltage and is given by
Em = ρ Km Ki I/L
L== Lc + 1.15 Lr
Lc = total length of horizontal grid conductor, m
Lr = total length of graund rods,m
Ki = 0.656+0.172n
N = number of parallel conductors in one derection.
Design of Earthing Grid.
The following points should be followed for desihn of an earhing grid.
(a) data needed for design:
1. Substation graund area
2. Soil resistivity at the site
3. Fault clearing time
4. Maximum grid current
5 Resistivity of soil at surface.
(b) Design of earthing system
1. Selection of electrode material
2. Determination of conductor size
3. Preliminary design
4 Determination of conductor length required for control of voltage gradient
Calculation of resistance and ground potential rise
6. Checking of step pontial and revision of design, if necessary
Generally the substation plan is prepared before the grid design. The earthing grid
should cover as much ground area as possible.
The fault clearing time is governed by systemstability consideration and depends
upon potential switchgear equipment. Generally a value of 0.5 seconds is assumed.The size of
conductor is based on time of 1 second.
A single line ground fault is more common and causes fault current as compared to a double line
to ground fault.Therefore the design is based on a single line to ground fault current..For
calculation of this current resistance and fault a reassumed to be zero.
The material for grounding grid should have good conductivity, be mechanically
rugged and resist fusing and deterioration of joints.