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Power Transmission And Distribution (LAB)
Report
Malik Muhammad Zaid
2013-EE-37

Abstract
Now-a-days electricity is generating on a large scale.The main purpose is
to deliver this generated electricity to every corner of the country , for this
purpose there are some important issues that we should never forget and
here I reported these issues that are important in electric transmission.In
this I reported what is the effect of different loads on the efficiency , voltage
regulation and power factors on the short , medium and long transmission
lines and what two different types of transmission lines can be used in series
and parallel and what will be the affect on efficiency of using two different
types of transmission lines in series and in parallel.In this I also reported that
what will be the affect of shunt and series compensation on the transmission
lines and how it is usefull in transmission lines and I reported the major and
most important fact of power factor in transmission lines and what should we
do to increase the power factor of transmission lines to increase the efficiency
of transmission system.

Contents
1 Performance analysis of a Short-Transmission Line 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Effect of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Voltage Regulation . . . . . . . . . . . . . . . . . . . . 2
1.2.3 Power Factor . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Phasor Diagrans . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Lagging Power Factor . . . . . . . . . . . . . . . . . . 4
1.3.2 Unity Power Factor . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Leading Power Factor . . . . . . . . . . . . . . . . . . 4
1.4 Performance And Its Analysis . . . . . . . . . . . . . . . . . . 5
1.4.1 Highly Inductive Load . . . . . . . . . . . . . . . . . . 5
1.4.2 Highly Capacitive Load . . . . . . . . . . . . . . . . . 6
2 Performance analysis of a Medium-Transmission Line 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Different Models . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 End Condenser Method . . . . . . . . . . . . . . . . . 7
2.2.2 Nominal τ Representation . . . . . . . . . . . . . . . . 8
2.2.3 Nominal π representation . . . . . . . . . . . . . . . . 9
2.3 Effect of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Efficiency: . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Voltage Regulation . . . . . . . . . . . . . . . . . . . . 11
2.3.3 Power Factor . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Performance And Its Analysis . . . . . . . . . . . . . . . . . . 12
2.4.1 Highly Inductive Load . . . . . . . . . . . . . . . . . . 12
2.4.2 Highly Capacitive Load . . . . . . . . . . . . . . . . . 13
3 Series Connection Of Different Transmission Lines 14
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Power Transmission And Distribution (LAB) Report
3.3 Effect of Using Two Short Transmission Lines . . . . . . . . . 14
3.3.1 Load-Voltage ( VR.E ) via Load-Current ( IS.E or IR.E ) 15
3.3.2 Mid voltage ( VMID ) via Load-Current ( IS.E or IR.E . 15
3.4 Effect of Using Two Medium Transmission Lines . . . . . . . . 16
3.4.1 Load-Voltage ( VR.E ) via Load-Current ( IR.E) . . . . . 16
3.4.2 Mid-Voltage ( VMID ) via Load-Current ( IR.E) . . . . . 17
3.4.3 Load-Voltage ( VR.E ) via Mid-Current ( IMID) . . . . 17
3.4.4 Mid-Voltage ( VMID ) via Mid-Current ( IMID) . . . . . 18
4 Effect of shunt compensation on performance of Transmis-
sion Lines 19
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Shunt Capacitive Compensation . . . . . . . . . . . . . . . . . 19
4.3 Shunt Inductive Compensation . . . . . . . . . . . . . . . . . 19
4.4 Effect of Shunt Capacitive Compensation On Short Transmis-
sion Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4.1 Short Transmission Line Without Compensation . . . . 20
4.4.2 Phasor Diagram . . . . . . . . . . . . . . . . . . . . . . 20
4.4.3 Graphical Behaviour . . . . . . . . . . . . . . . . . . . 21
4.4.4 Short Transmission Line With Compensation . . . . . 22
4.4.5 Phasor Diagram . . . . . . . . . . . . . . . . . . . . . . 22
4.4.6 Graphical Behaviour . . . . . . . . . . . . . . . . . . . 22
4.5 Effect of Shunt Capacitive Compensation On Medium Trans-
mission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.5.1 Medium Transmission Line With Compensation . . . . 24
4.5.2 Graphical Behaviour Without Compensation . . . . . . 24
4.5.3 Graphical Behaviour With Compensation . . . . . . . . 25
5 Power Factor Improvement By using Static Capacitors 26
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2 Power Factor Improvement . . . . . . . . . . . . . . . . . . . . 26
5.3 Methods of Power Factor Improvement . . . . . . . . . . . . . 26
5.3.1 By use of Static Capacitor . . . . . . . . . . . . . . . . 28
5.3.2 Static Capacitor In Series . . . . . . . . . . . . . . . . 28
5.3.3 Static Capacitor In Parallel . . . . . . . . . . . . . . . 29
5.4 Graphical Behaviour of Shunt Compensation . . . . . . . . . . 30
5.4.1 For Short Transmission Line . . . . . . . . . . . . . . . 30
5.4.2 For Medium Transmission Line . . . . . . . . . . . . . 32
Page

6 Determination of Circuit Parameters of Diﬀerent Transmis-
sion Lines 34
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.2 Circuit Discription of Transmission Line . . . . . . . . . . . . 35
6.3 Parameters In Open Circuit Recieving End . . . . . . . . . . . 35
6.4 Parameters In Short Circuit Recieving End . . . . . . . . . . . 36
7 Assignment Question/Answers 37
Page

List of Figures
1.1 Equivalent circuit of a short transmission line where the resis-
tance R and inductance L are values for the entire length of
the line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Load Power Factor = 70 % Lag. . . . . . . . . . . . . . . . . . 4
1.3 Load power factor = 100 % unity . . . . . . . . . . . . . . . . 4
1.4 Load power factor = 70 % Lead . . . . . . . . . . . . . . . . . 5
1.5 Graphical behavior of highly inductive load . . . . . . . . . . . 5
1.6 Graphical behavior of highly capacitive load . . . . . . . . . . 6
2.1 End condenser model . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 End condenser phasor diagram . . . . . . . . . . . . . . . . . . 8
2.3 Nominal τ model . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Nominal τ model phasor diagram . . . . . . . . . . . . . . . . 9
2.5 Nominal π model . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Nominal π model phasor diagram . . . . . . . . . . . . . . . . 10
2.7 Graphical behavior of highly inductive load . . . . . . . . . . . 12
2.8 Graphical behavior of highly capacitive load . . . . . . . . . . 13
3.1 Graphical behavior between VR.E and IR.E . . . . . . . . . . . 15
3.2 Graphical behavior between VMID and IS.E . . . . . . . . . . . 15
3.3 Graphical behavior between VR.E and IR.E . . . . . . . . . . . 16
3.4 Graphical behavior between VMID and IR.E . . . . . . . . . . . 17
3.5 Graphical behavior between VR.E and IMID . . . . . . . . . . . 17
3.6 Graphical behavior between VMID and IMID . . . . . . . . . . . 18
4.1 Short transmission line without compensation . . . . . . . . . 20
4.2 Short transmission line phasor diagram . . . . . . . . . . . . . 21
4.3 Graphical behavior of STL without compensation . . . . . . . 21
4.4 Short transmission line without compensation . . . . . . . . . 22
4.5 Short transmission line phasor diagram . . . . . . . . . . . . . 22
4.6 VR.E and IR.E with 2.5 µF compensation . . . . . . . . . . . . 23

4.7 VR.E and IR.E with 5 µF compensation . . . . . . . . . . . . . 23
4.8 VR.E and IR.E without compensation . . . . . . . . . . . . . . 24
4.9 VR.E and IR.E with 2.5 µF compensation . . . . . . . . . . . . 25
4.10 VR.E and IR.E with 5 µF compensation . . . . . . . . . . . . . 25
5.1 Power factor improvement using static shunt capacitor . . . . 27
5.2 Power factor improvement . . . . . . . . . . . . . . . . . . . . 27
5.3 Series capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4 Voltage and phasor diagrams for a circuit of lagging power
factor (a) and (c) without series capacitors (b) and (d) with
series capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.5 STL without shunt compensation . . . . . . . . . . . . . . . . 30
5.6 STL with 2.5 µF shunt compensation . . . . . . . . . . . . . . 31
5.7 STL with 5 µF shunt compensation . . . . . . . . . . . . . . . 31
5.8 Medium Transmission Line without shunt compensation . . . 32
5.9 Medium Transmission Line with 2.5µF shunt compensation . . 32
5.10 Medium Transmission Line with 5µF shunt compensation . . . 33
6.1 Transmission Line Model . . . . . . . . . . . . . . . . . . . . . 34
7.1 Voltage Curve As Function of Load Current . . . . . . . . . . 37
7.2 Short Transmission Line . . . . . . . . . . . . . . . . . . . . . 38
7.3 Medium Transmission Line . . . . . . . . . . . . . . . . . . . . 39
7.4 Long Transmission Line . . . . . . . . . . . . . . . . . . . . . 40
Page

Chapter 1
Performance analysis of a
Short-Transmission Line
1.1 Introduction
The transmission lines which have length less than 80 km are generally re-
ferred 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,
Figure 1.1: Equivalent circuit of a short transmission line where the resis-
tance R and inductance L are values for the entire length of the line.
1.2 Effect of Loads
Effect of Different Loads on the short transmission lines are as follow:
1

1.2.1 Efficiency
Basically Efficiency can be defined by the formula given below:
Percentage Efficiency = Power recieved at recieving end
Power delivered at sending end
× 100
Power recieved at recieving end + copper losses
× 100
• When we add inductive load in the short transmission lines then
the voltage at the receiving end is less than the voltage at the sending end
because inductor drew lagging current from circuit due to which voltage at
receiving end is less as compared to voltage at sending end thus efficiency
decreases by adding inductors as loads.
• Similarly, When we add capacitive load in the short transmission
lines then the voltage at the receiving end is greater than the voltage at
the sending end because capacitor drew leading current from circuit which
cancels the lagging current that are driven by the inductor present in short
transmission lines due to which voltage at receiving end is greater as com-
pared to voltage at sending end thus efficiency increases ultimately by adding
capacitors as loads.
• When we add resistor as load in Short transmission lines then it
drew more current due to which more copper losses occurs and power at
output is less as compared to power at input and efficiency decreases.
1.2.2 Voltage Regulation
The expression of voltage regulation of short transmission line is:
V oltage Regulation = V oltage of recieving end at no load − V oltage of recieving end at full load
V oltage of recieving end at full load
because inductor drew lagging current from circuit due to which voltage
at receiving end is less as compared to voltage at sending end thus voltage
regulation is positive for inductive or lagging load as described in the formula
Page 2

given below
Percentage Regulation = I R cos φR + I XL sin φR
VR
× 100 (for lagging pf)
lines then the voltage at the receiving end is greater than the voltage at the
sending end because capacitor drew leading current from circuit which cancels
the lagging current that are driven by the inductor present in short trans-
mission lines due to which voltage at receiving end is greater as compared to
voltage at sending end thus voltage regulation is negative for capacitive or
leading load as described in the formula given below
Percentage Regulation = I R cos φR − I XL sin φR
VR
× 100 (for leading pf)
1.2.3 Power Factor
receiving end is less as compared to voltage at sending end thus power factor
decreases by adding inductive load
the lagging current that are driven by the inductor present in short trans-
mission lines due to which voltage at receiving end is greater as compared
to voltage at sending end thus power factor increases by adding capacitor on
loads.
• By adding Resistors on loads there is no aﬀect on power factor
because it does not draw lagging current nor leading current.
1.3 Phasor Diagrans
Phasor diagrams of short transmission lines relating leading power factor ,
lagging power factor and of unity power factor is described below:
Page 3

1.3.1 Lagging Power Factor
By adding inductive or lagging load phasor diagram will be as:
Figure 1.2: Load Power Factor = 70 % Lag.
1.3.2 Unity Power Factor
By balancing inductor and capacitors power factor will be unity as ashown
below in phasor diagram as:
Figure 1.3: Load power factor = 100 % unity
1.3.3 Leading Power Factor
By adding capacitor or leading load phasor diagram will be as:
Page 4

Figure 1.4: Load power factor = 70 % Lead
1.4 Performance And Its Analysis
Performance analysis of short transmission line is described below as:
1.4.1 Highly Inductive Load
The graphical Behaviour of Highly inductive load is as:
• VS.E = 240 V. VR.E = 220V θ = 37◦
lagging I = 0.27 A.
Figure 1.5: Graphical behavior of highly inductive load
Page 5

1.4.2 Highly Capacitive Load
• VS.E = 240 V. VR.E = 248V θ = 35◦
leading I = 0.28 A.
Figure 1.6: Graphical behavior of highly capacitive load
Page 6

Chapter 2
Performance analysis of a
Medium-Transmission Line
2.1 Introduction
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 medium transmission lines. For this reason the modelling of a medium
length transmission line is done using lumped shunt admittance along with
the lumped impedance in series to the circuit.
2.2 Different Models
These lumped parameters of a medium length transmission line can be rep-
resented using two different models, namely
• End Condenser Method.
• Nominal τ representation.
• Nominal π representation
2.2.1 End Condenser Method
In this the capacitance of the line is lumped at the receiving end.Its circuit
and phasor diagram is shown below:
7

Figure 2.1: End condenser model
Figure 2.2: End condenser phasor diagram
2.2.2 Nominal τ Representation
In this method the whole capacitance is assumed to be connected at the
middle point of the line and half the line resistance and reactance are lumped
on its either side .Its circuit and phasor diagram is shown below:
Figure 2.3: Nominal τ model
Page 8

Figure 2.4: Nominal τ model phasor diagram
2.2.3 Nominal π representation
In this method, capacitance of each conductor (i.e line to neutral) is divided
into two halves; one half being lumped at the sending end and the other half
at the receiving end. Its circuit and phasor diagram is shown below:
Figure 2.5: Nominal π model
Page 9

Figure 2.6: Nominal π model phasor diagram
2.3 Effect of Loads
Effect of Different Loads on the medium transmission lines are as follow:
2.3.1 Efficiency:
Basically Efficiency can be defined by the formula given below:
Power delivered at sending end
× 100
Power recieved at recieving end + power losses in conductor
× 100
• When we add inductive load in the medium transmission lines then
receiving end is less as compared to voltage at sending end thus efficiency
decreases by adding inductors as loads.
• Similarly, When we add capacitive load in the medium transmission
sending end because capacitor drew leading current from circuit which can-
cels the lagging current that are driven by the inductor present in medium
transmission lines due to which voltage at receiving end is greater as com-
pared to voltage at sending end thus efficiency increases ultimately by adding
capacitors as loads.
Page 10

• When we add resistor as load in medium transmission lines then
it drew more current due to which more copper losses occurs and power at
output is less as compared to power at input and eﬃciency decreases.
2.3.2 Voltage Regulation
The expression of voltage regulation of medium transmission line is:
V oltage Regulation = V oltage of recieving end at no load − V oltage of recieving end at full load
V oltage of recieving end at full load
because inductor drew lagging current from circuit due to which voltage
at receiving end is less as compared to voltage at sending end thus voltage
regulation is positive for inductive or lagging load as described in the formula
given below
Percentage V oltage Regulation = I R cos φR + I XL sin φR
VR
× 100 (for lagging pf)
the lagging current that are driven by the inductor present in medium trans-
mission lines due to which voltage at receiving end is greater as compared to
voltage at sending end thus voltage regulation is negative for capacitive or
leading load as described in the formula given below
Percentage V oltage Regulation = I R cos φR − I XL sin φR
VR
× 100 (for leading pf)
2.3.3 Power Factor
receiving end is less as compared to voltage at sending end thus power factor
decreases by adding inductive load
Page 11

the lagging current that are driven by the inductor present in medium trans-
mission lines due to which voltage at receiving end is greater as compared
to voltage at sending end thus power factor increases by adding capacitor on
loads.
• By adding Resistors on loads there is no aﬀect on power factor
because it does not draw lagging current nor leading current.
2.4 Performance And Its Analysis
Performance analysis of short transmission line is described below as
2.4.1 Highly Inductive Load
• VS.E = 241 V. VR.E = 226V θ = 26◦
lagging I = 0.27 A.
Figure 2.7: Graphical behavior of highly inductive load
Page 12

2.4.2 Highly Capacitive Load
The graphical Behaviour of Highly capacitive load is as:
• VS.E = 241 V. VR.E = 257V θ = 32◦
lagging I = 0.29 A.
Figure 2.8: Graphical behavior of highly capacitive load
Page 13

Chapter 3
Series Connection Of Different
Transmission Lines
3.1 Introduction
In this we add the two models of different transmission lines in series and we
calculate the the voltages at sending end and receiving end of first model and
ultimately we find the final receiving end voltages and currents after second
transmission line model. We call the first receiving end voltage as mid point
voltage and current as mid point current.
3.2 Effects
The effects of using two different transmission lines are described graphically
for short , medium and long transmission lines as described below:
3.3 Effect of Using Two Short Transmission
Lines
In this we used two short transmission line models in series.In this sending
end current,mid point current and load current ( receiving end current ) will
be same and we described this affect graphically as:
• Load-Voltage ( VR.E ) via Load-Current ( IS.E or IR.E )
• Mid voltage ( VMID ) via Load-Current ( IS.E or IR.E )
14

3.3.1 Load-Voltage ( VR.E ) via Load-Current ( IS.E or
IR.E )
In this load voltage is along y-axis and sending end current or receiving end
current is along x-axis as described below:
Figure 3.1: Graphical behavior between VR.E and IR.E
3.3.2 Mid voltage ( VMID ) via Load-Current ( IS.E or
IR.E
In this load voltage is along y-axis and sending end current or receiving end
current is along x-axis as described below:
Figure 3.2: Graphical behavior between VMID and IS.E
Page 15

3.4 Eﬀect of Using Two Medium Transmis-
sion Lines
Eﬀects on transmission Lines are:
• Load-Voltage ( VR.E ) via Load-Current ( IR.E)
• Mid-Voltage ( VMID ) via Load-Current ( IR.E)
• Load-Voltage ( VR.E ) via Mid-Current ( IMID)
• Mid-Voltage ( VMID ) via Mid-Current ( IMID)
3.4.1 Load-Voltage ( VR.E ) via Load-Current ( IR.E)
In this load voltage is along y-axis and load current or receiving end current
is along x-axis as described below:
Figure 3.3: Graphical behavior between VR.E and IR.E
Page 16

3.4.2 Mid-Voltage ( VMID ) via Load-Current ( IR.E)
In this mid voltage is along y-axis and load current or receiving end current
is along x-axis as described below:
Figure 3.4: Graphical behavior between VMID and IR.E
3.4.3 Load-Voltage ( VR.E ) via Mid-Current ( IMID)
In this load voltage is along y-axis and mid current is along x-axis as described
below:
Figure 3.5: Graphical behavior between VR.E and IMID
Page 17

3.4.4 Mid-Voltage ( VMID ) via Mid-Current ( IMID)
In this mid voltage is along y-axis and mid current is along x-axis as described
below:
Figure 3.6: Graphical behavior between VMID and IMID
Page 18

Chapter 4
Eﬀect of shunt compensation
on performance of Transmission
Lines
4.1 Introduction
In shunt compensation, power system is connected in shunt (parallel) with
the FACTS. It works as a controllable current source. Shunt compensation
is of two types:
• Shunt Capacitive Compensation
• Shunt Inductive Compensation
4.2 Shunt Capacitive Compensation
This method is used to improve the power factor. Whenever an inductive load
is connected to the transmission line, power factor lags because of lagging
load current. To compensate, a shunt capacitor is connected which draws
current leading the source voltage. The net result is improvement in power
factor.
4.3 Shunt Inductive Compensation
This method is used either when charging the transmission line, or, when
there is very low load at the receiving end. Due to very low, or no load
19

– very low current flows through the transmission line. Shunt capacitance
in the transmission line causes voltage amplification (Ferranti effect). The
receiving end voltage may become double the sending end voltage (generally
in case of very long transmission lines). To compensate, shunt inductors are
connected across the transmission line.
4.4 Effect of Shunt Capacitive Compensation
On Short Transmission Line
In this static shunt capacitors are connected at the end of short transmis-
sion line ,in which voltage at sending end increases by adding static shunt
capacitors at sending end , similarly by adding more and more capacitors at
the sending end , voltage at sending end increases and improved ultimately
due to which power factor of short transmission line increases.The circuit
of short transmission line without compensation along with its phasor dia-
gram and graphical behavior is shown below and short transmission line with
compensation along with its all other features also shown below:
4.4.1 Short Transmission Line Without Compensation
Short transmission line circuit without compensation is as follow:
Figure 4.1: Short transmission line without compensation
4.4.2 Phasor Diagram
Short transmission line phasor diagram without compensation is as follow:
Page 20

Figure 4.2: Short transmission line phasor diagram
4.4.3 Graphical Behaviour
Graphical behavior of short transmission line without compensation is as
follow:
• VR.E = 198V θ = 50.2◦
lagging I = 0.441 A.
Figure 4.3: Graphical behavior of STL without compensation
Page 21

4.4.4 Short Transmission Line With Compensation
Short transmission line circuit with compensation is as follow:
Figure 4.4: Short transmission line without compensation
4.4.5 Phasor Diagram
Short transmission line phasor diagram with compensation is as follow:
Figure 4.5: Short transmission line phasor diagram
4.4.6 Graphical Behaviour
Graphical behavior of short transmission line with 2.5 µ F compensation is
as follow:
• VR.E = 212V θ = 51◦
Page 22

Figure 4.6: VR.E and IR.E with 2.5 µF compensation
• VR.E = 224V θ = 50.2◦
lagging I = 0.5 A.
Figure 4.7: VR.E and IR.E with 5 µF compensation
Page 23

4.5 Eﬀect of Shunt Capacitive Compensation
On Medium Transmission Line
In this static shunt capacitors are connected at the end of medium transmis-
due to which power factor of medium transmission line increases.The circuit
of medium transmission line without compensation along with its phasor di-
agram and graphical behavior is shown below and medium transmission line
with compensation along with its all other features also shown below:
4.5.1 Medium Transmission Line With Compensation
In this static shunt capacitors are connected at the end of medium transmis-
due to which power factor of medium transmission line increases.
4.5.2 Graphical Behaviour Without Compensation
Graphical behavior of medium transmission line without compensation is as
follow:
• VR.E = 204V θ = 48◦
Figure 4.8: VR.E and IR.E without compensation
Page 24

4.5.3 Graphical Behaviour With Compensation
Graphical behavior of medium transmission line with 2.5 µ F compensation
is as follow:
• VR.E = 217V θ = 49.5◦
Figure 4.9: VR.E and IR.E with 2.5 µF compensation
• VR.E = 230V θ = 48.7◦
lagging I = 0.51 A.
Figure 4.10: VR.E and IR.E with 5 µF compensation
Page 25

Chapter 5
Power Factor Improvement By
using Static Capacitors
5.1 Introduction
The power factor of a circuit implies that how eﬃciently power is being
consumed or utilized in the circuit. The greater the power factor of a circuit,
greater is the ability of the circuit to utilize apparent power. Thus if the
power factor is 0.5, it means that 50% of the power is being utilized. However,
it is desired that power factor of a circuit to be as close to unity as possible.
The cosine of angle between voltage and current in an a.c circuit is known
as power factor ( p.f ) .
5.2 Power Factor Improvement
The low power factor is mainly due to the fact that most of the power loads
are inductive and,therefore take lagging currents. In order to improve the
power factor,some device taking leading power should be connected in parallel
with the load.One of such devices can be a capacitor.The capacitor draws
the leading current and partly or completely neutralizes the lagging reactive
component of load current.This raise the power factor of the load as shown
in ﬁgure5.1:
5.3 Methods of Power Factor Improvement
The low power factor is due to the inductive nature of the load i.e a device
that draws lagging reactive power. If a device drawing leading reactive power
26

Figure 5.1: Power factor improvement using static shunt capacitor
is connected in parallel with the inductive load, then the lagging reactive
power of the load will be partly neutralized, resulting in improvement of the
power factor of the system.
Therefore, when such a device is connected across the load, which takes
leading reactive power such as static capacitors, synchronous machines or
synchronous condensers, the leading reactive component of current drawn by
power factor correcting device neutralizes the lagging reactive component of
current drawn by the load partly or completely.
Power factor of the system will approach unity when lagging reactive
component of load current is completely neutralized by the leading reactive
component of current drawn by power factor correcting device as shown in
ﬁgure:
Figure 5.2: Power factor improvement
Page 27

Mainly there are three methods to improve the power factor an inductive
load
• By use of Static Capacitor
• By use of Synchronous Motors
• By use of Phase Advancers
Here we discuss only static capacitor for power factor improvement
5.3.1 By use of Static Capacitor
Power factor can be improved by connecting the capacitors in parallel with
the load operating at lagging power factor such as induction motors, fluores-
cent tubes, etc.
It has following advantages
• Small losses
• High efficiency (approximately 99.6%)
• Low initial cost
• Low maintenance due to absence of rotating parts.
• Easy installation being lighter in weight.
5.3.2 Static Capacitor In Series
Power factor can also be improved by connecting static capacitors in series
with the line, as shown in fig 5.3 Capacitors connected in series with the line
neutralize the line reactance. The capacitors, when connected in series with
the line, are called the series capacitors as shown below: Series Capacitors
Figure 5.3: Series capacitors
are connected in series with lines but they are hardly used in the distribu-
tion system because there is a requirement for a large amount of complex
Page 28

engineering investigation. Figure 5.4 shows that how series capacitor com-
pensates for inductive reactance. A series capacitor is a capacitive (negative)
reactance in series with the circuit’s inductive (positive) reactance with the
effect of compensating for part or all of it. Therefore, the primary effect of
the series capacitor is to minimize the voltage drop caused by the inductive
reactance in the circuit. A series capacitor can even be considered as a volt-
age regulator that provides voltage rise which increases automatically and
instantaneously as the load increases.
Also, a series capacitor produces more net voltage rise than a shunt
capacitor at lower power factors, which creates more voltage drop. However,
a series capacitor improves the system power factor much less than a shunt
capacitor and has a little effect on the source current.
Figure 5.4: Voltage and phasor diagrams for a circuit of lagging power factor
(a) and (c) without series capacitors (b) and (d) with series capacitors
5.3.3 Static Capacitor In Parallel
Shunt capacitors are connected in parallel with lines and they are used ex-
tensively in distribution systems. Shunt capacitors supply reactive power or
Page 29

current to counterbalance the out-of-phase component of current by an in-
ductive load.
Shunt capacitors modify the characteristic of inductive load by drawing a
leading current, which balances some or the entire lagging component of the
inductive load current at the point of installation.
By the application of shunt capacitor to a feeder, the magnitude of the source
current can be reduced, the power factor can be improved, and consequently
the voltage drop between the sending end and the load is also reduced.
However, shunt capacitors do not aﬀect current or power factor beyond their
point of application.
5.4 Graphical Behaviour of Shunt Compen-
sation
Graphical behavior of short and medium transmission line with and without
shunt compensation is as follow:
5.4.1 For Short Transmission Line
Graphical behaviour of short transmission line with and without shunt com-
pensation is described below:
Without Shunt Compensation
• VR.E = 198V θ = 50.2◦
Figure 5.5: STL without shunt compensation
Page 30

With Shunt Compensation
• VR.E = 212V θ = 51◦
Figure 5.6: STL with 2.5 µF shunt compensation
• VR.E = 224V θ = 50.2◦
lagging I = 0.5 A.
Figure 5.7: STL with 5 µF shunt compensation
Page 31

5.4.2 For Medium Transmission Line
Graphical behaviour of short transmission line with and without shunt com-
pensation is described below:
Without Compensation
• VR.E = 204V θ = 48◦
Figure 5.8: Medium Transmission Line without shunt compensation
With Compensation
• VR.E = 217V θ = 49.5◦
Figure 5.9: Medium Transmission Line with 2.5µF shunt compensation
Page 32

• VR.E = 230V θ = 48.7◦
lagging I = 0.51 A.
Figure 5.10: Medium Transmission Line with 5µF shunt compensation
Page 33

Chapter 6
Determination of Circuit
Parameters of Different
Transmission Lines
6.1 Introduction
A major section of power system engineering deals in the transmission of
electrical power from one particular place (eg. generating station) to an-
other 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 simpli-
fied to a two port network for the sake of easier calculations. The circuit of
a two port network is shown in the diagram below. As the name suggests, a
two port network consists of an input port PQ and an output port RS. Each
port has two terminals to connect itself to the external circuit. Thus it is
essentially a two port or a four terminal circuit as shown below
Figure 6.1: Transmission Line Model
34

6.2 Circuit Discription of Transmission Line
Various Parameters of transmission lines are as
Supply End Voltage = VS
Supply End Current = IS
Recieving End Voltage = VR
Recieving End Current = IR
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. Thus the relation
between the sending and receiving end speciﬁcations are given using ABCD
parameters by the equations below.
VS = A VR + B IR
IS = C VR + D IR
Now in order to determine the ABCD parameters of transmission line let us
impose the required circuit conditions in diﬀerent cases.
6.3 Parameters In Open Circuit Recieving End
The receiving end is open circuited meaning receiving end current IR = 0
Applying this condition we get,
VS = A VR + B 0 → VS = A VR + 0
A =
V S
V R
at IR =0
Thus it implies that on applying open circuit conditions to ABCD param-
eters, we get parameter A as the ratio of sending end voltage and receiving
end voltage. Since dimension wise A is a ratio of voltage to voltage, A is a
dimension less parameter.
Applying the same open circuit condition i.e IR = 0
Thus it implies that on applying open circuit condition to ABCD parameters
of transmission line, we get parameter C as the ratio of sending end current
and receiving end voltage. Since dimension wise C is a ratio of current to
voltage, its unit is mho.
Thus C is the open circuit conductance and is given by
C =
IS
V R
mho
Page 35

6.4 Parameters In Short Circuit Recieving
End
The receiving end is open circuited meaning receiving end voltage VR = 0
Applying this condition we get,
VS = A 0 + B IR → VS = 0 + B IR
B =
V S
IR
at VR =0
Thus its implies that on applying short circuit condition to ABCD pa-
rameters, we get parameter B as the ratio of sending end voltage to the short
circuit receiving end current. Since dimension wise B is a ratio of voltage to
current, its unit is Ω. Thus B is the short circuit resistance and is given by
B =
V S
IR
Ω
Applying the same open circuit condition i.e IR = 0
Thus its implies that on applying short circuit condition to ABCD param-
eters, we get parameter D as the ratio of sending end current to the short
circuit receiving end current. Since dimension wise D is a ratio of current to
current, it’s a dimension less parameter.
The ABCD parameters of transmission line can be tabulated as:-
A =
V S
V R
→ Voltage Ratio → unit less
B =
V S
IR
→ Short Circuit Resistance → Ω
C =
IS
V R
→ Open Circuit Conductance → mho
D =
IS
IR
→ Current Ratio → unit less
Page 36

Chapter 7
Assignment Question/Answers
Assignment No. 1 Plot the voltage curves as a function of the load current
in a combined diagram for short , medium and long transmission Lines.
The Voltage curves as a function of the load current in a combined diagram
for short,medium and long transmission lines are as follow
Figure 7.1: Voltage Curve As Function of Load Current
37

Assignment No. 2 Plot all the currents ( IS.E and IMID ) as a function of
the load current for short , medium and long transmission Lines.
The currents ( IS.E and IMID ) as a function of the load current for short ,
medium and long transmission Lines are as follow
Figure 7.2: Short Transmission Line
Page 38

Figure 7.3: Medium Transmission Line
Page 39

Figure 7.4: Long Transmission Line
Page 40

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