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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 isto deliver this generated electricity to every corner of the country , for thispurpose there are some important issues that we should never forget andhere I reported these issues that are important in electric transmission.Inthis I reported what is the effect of different loads on the efficiency , voltageregulation and power factors on the short , medium and long transmissionlines and what two different types of transmission lines can be used in seriesand parallel and what will be the affect on efficiency of using two differenttypes of transmission lines in series and in parallel.In this I also reported thatwhat will be the affect of shunt and series compensation on the transmissionlines and how it is usefull in transmission lines and I reported the major andmost important fact of power factor in transmission lines and what should wedo to increase the power factor of transmission lines to increase the efficiencyof transmission system.

Contents

1 Performance analysis of a Short-Transmission Line 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Effect of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Voltage Regulation . . . . . . . . . . . . . . . . . . . . 21.2.3 Power Factor . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Phasor Diagrans . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.1 Lagging Power Factor . . . . . . . . . . . . . . . . . . 41.3.2 Unity Power Factor . . . . . . . . . . . . . . . . . . . . 41.3.3 Leading Power Factor . . . . . . . . . . . . . . . . . . 4

1.4 Performance And Its Analysis . . . . . . . . . . . . . . . . . . 51.4.1 Highly Inductive Load . . . . . . . . . . . . . . . . . . 51.4.2 Highly Capacitive Load . . . . . . . . . . . . . . . . . 6

2 Performance analysis of a Medium-Transmission Line 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Different Models . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 End Condenser Method . . . . . . . . . . . . . . . . . 72.2.2 Nominal τ Representation . . . . . . . . . . . . . . . . 82.2.3 Nominal π representation . . . . . . . . . . . . . . . . 9

2.3 Effect of Loads . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Efficiency: . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Voltage Regulation . . . . . . . . . . . . . . . . . . . . 112.3.3 Power Factor . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Performance And Its Analysis . . . . . . . . . . . . . . . . . . 122.4.1 Highly Inductive Load . . . . . . . . . . . . . . . . . . 122.4.2 Highly Capacitive Load . . . . . . . . . . . . . . . . . 13

3 Series Connection Of Different Transmission Lines 143.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Power Transmission And Distribution (LAB) Report

3.3 Effect of Using Two Short Transmission Lines . . . . . . . . . 143.3.1 Load-Voltage ( VR.E ) via Load-Current ( IS.E or IR.E ) 153.3.2 Mid voltage ( VMID ) via Load-Current ( IS.E or IR.E . 15

3.4 Effect of Using Two Medium Transmission Lines . . . . . . . . 163.4.1 Load-Voltage ( VR.E ) via Load-Current ( IR.E) . . . . . 163.4.2 Mid-Voltage ( VMID ) via Load-Current ( IR.E) . . . . . 173.4.3 Load-Voltage ( VR.E ) via Mid-Current ( IMID) . . . . 173.4.4 Mid-Voltage ( VMID ) via Mid-Current ( IMID) . . . . . 18

4 Effect of shunt compensation on performance of Transmis-sion Lines 194.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Shunt Capacitive Compensation . . . . . . . . . . . . . . . . . 194.3 Shunt Inductive Compensation . . . . . . . . . . . . . . . . . 194.4 Effect of Shunt Capacitive Compensation On Short Transmis-

sion Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4.1 Short Transmission Line Without Compensation . . . . 204.4.2 Phasor Diagram . . . . . . . . . . . . . . . . . . . . . . 204.4.3 Graphical Behaviour . . . . . . . . . . . . . . . . . . . 214.4.4 Short Transmission Line With Compensation . . . . . 224.4.5 Phasor Diagram . . . . . . . . . . . . . . . . . . . . . . 224.4.6 Graphical Behaviour . . . . . . . . . . . . . . . . . . . 22

4.5 Effect of Shunt Capacitive Compensation On Medium Trans-mission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.5.1 Medium Transmission Line With Compensation . . . . 244.5.2 Graphical Behaviour Without Compensation . . . . . . 244.5.3 Graphical Behaviour With Compensation . . . . . . . . 25

5 Power Factor Improvement By using Static Capacitors 265.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Power Factor Improvement . . . . . . . . . . . . . . . . . . . . 265.3 Methods of Power Factor Improvement . . . . . . . . . . . . . 26

5.3.1 By use of Static Capacitor . . . . . . . . . . . . . . . . 285.3.2 Static Capacitor In Series . . . . . . . . . . . . . . . . 285.3.3 Static Capacitor In Parallel . . . . . . . . . . . . . . . 29

5.4 Graphical Behaviour of Shunt Compensation . . . . . . . . . . 305.4.1 For Short Transmission Line . . . . . . . . . . . . . . . 305.4.2 For Medium Transmission Line . . . . . . . . . . . . . 32

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6 Determination of Circuit Parameters of Different Transmis-sion Lines 346.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346.2 Circuit Discription of Transmission Line . . . . . . . . . . . . 356.3 Parameters In Open Circuit Recieving End . . . . . . . . . . . 356.4 Parameters In Short Circuit Recieving End . . . . . . . . . . . 36

7 Assignment Question/Answers 37

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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 ofthe line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Load Power Factor = 70 % Lag. . . . . . . . . . . . . . . . . . 41.3 Load power factor = 100 % unity . . . . . . . . . . . . . . . . 41.4 Load power factor = 70 % Lead . . . . . . . . . . . . . . . . . 51.5 Graphical behavior of highly inductive load . . . . . . . . . . . 51.6 Graphical behavior of highly capacitive load . . . . . . . . . . 6

2.1 End condenser model . . . . . . . . . . . . . . . . . . . . . . . 82.2 End condenser phasor diagram . . . . . . . . . . . . . . . . . . 82.3 Nominal τ model . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Nominal τ model phasor diagram . . . . . . . . . . . . . . . . 92.5 Nominal π model . . . . . . . . . . . . . . . . . . . . . . . . . 92.6 Nominal π model phasor diagram . . . . . . . . . . . . . . . . 102.7 Graphical behavior of highly inductive load . . . . . . . . . . . 122.8 Graphical behavior of highly capacitive load . . . . . . . . . . 13

3.1 Graphical behavior between VR.E and IR.E . . . . . . . . . . . 153.2 Graphical behavior between VMID and IS.E . . . . . . . . . . . 153.3 Graphical behavior between VR.E and IR.E . . . . . . . . . . . 163.4 Graphical behavior between VMID and IR.E . . . . . . . . . . . 173.5 Graphical behavior between VR.E and IMID . . . . . . . . . . . 173.6 Graphical behavior between VMID and IMID . . . . . . . . . . . 18

4.1 Short transmission line without compensation . . . . . . . . . 204.2 Short transmission line phasor diagram . . . . . . . . . . . . . 214.3 Graphical behavior of STL without compensation . . . . . . . 214.4 Short transmission line without compensation . . . . . . . . . 224.5 Short transmission line phasor diagram . . . . . . . . . . . . . 224.6 VR.E and IR.E with 2.5 µF compensation . . . . . . . . . . . . 23


4.7 VR.E and IR.E with 5 µF compensation . . . . . . . . . . . . . 234.8 VR.E and IR.E without compensation . . . . . . . . . . . . . . 244.9 VR.E and IR.E with 2.5 µF compensation . . . . . . . . . . . . 254.10 VR.E and IR.E with 5 µF compensation . . . . . . . . . . . . . 25

5.1 Power factor improvement using static shunt capacitor . . . . 275.2 Power factor improvement . . . . . . . . . . . . . . . . . . . . 275.3 Series capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4 Voltage and phasor diagrams for a circuit of lagging power

factor (a) and (c) without series capacitors (b) and (d) withseries capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.5 STL without shunt compensation . . . . . . . . . . . . . . . . 305.6 STL with 2.5 µF shunt compensation . . . . . . . . . . . . . . 315.7 STL with 5 µF shunt compensation . . . . . . . . . . . . . . . 315.8 Medium Transmission Line without shunt compensation . . . 325.9 Medium Transmission Line with 2.5µF shunt compensation . . 325.10 Medium Transmission Line with 5µF shunt compensation . . . 33

6.1 Transmission Line Model . . . . . . . . . . . . . . . . . . . . . 34

7.1 Voltage Curve As Function of Load Current . . . . . . . . . . 377.2 Short Transmission Line . . . . . . . . . . . . . . . . . . . . . 387.3 Medium Transmission Line . . . . . . . . . . . . . . . . . . . . 397.4 Long Transmission Line . . . . . . . . . . . . . . . . . . . . . 40

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Chapter 1

Performance analysis of aShort-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 ofthis type of line is neglected and other parameters like electrical resistanceand inductor of these short lines are lumped, hence the equivalent circuit isrepresented 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 endPower delivered at sending end

× 100

Percentage Efficiency = Power recieved at recieving endPower recieved at recieving end + copper losses

× 100

• When we add inductive load in the short transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltage atreceiving end is less as compared to voltage at sending end thus efficiencydecreases by adding inductors as loads.

• Similarly, When we add capacitive load in the short transmissionlines then the voltage at the receiving end is greater than the voltage atthe sending end because capacitor drew leading current from circuit whichcancels the lagging current that are driven by the inductor present in shorttransmission lines due to which voltage at receiving end is greater as com-pared to voltage at sending end thus efficiency increases ultimately by addingcapacitors as loads.

• When we add resistor as load in Short transmission lines then itdrew more current due to which more copper losses occurs and power atoutput 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 loadV oltage of recieving end at full load

• When we add inductive load in the short transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltageat receiving end is less as compared to voltage at sending end thus voltageregulation is positive for inductive or lagging load as described in the formula

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given below

Percentage Regulation = I R cosφR + I XL sinφRVR

× 100 (for lagging pf)

• Similarly, When we add capacitive load in the short transmissionlines then the voltage at the receiving end is greater than the voltage at thesending end because capacitor drew leading current from circuit which cancelsthe 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 tovoltage at sending end thus voltage regulation is negative for capacitive orleading load as described in the formula given below

Percentage Regulation = I R cosφR − I XL sinφRVR

× 100 (for leading pf)

1.2.3 Power Factor

• When we add inductive load in the short transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltage atreceiving end is less as compared to voltage at sending end thus power factordecreases by adding inductive load

• Similarly, When we add capacitive load in the short transmissionlines then the voltage at the receiving end is greater than the voltage at thesending end because capacitor drew leading current from circuit which cancelsthe lagging current that are driven by the inductor present in short trans-mission lines due to which voltage at receiving end is greater as comparedto voltage at sending end thus power factor increases by adding capacitor onloads.

• By adding Resistors on loads there is no affect on power factorbecause 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:

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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 ashownbelow 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:

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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

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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

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Chapter 2

Performance analysis of aMedium-Transmission Line

2.1 Introduction

The transmission line having its effective length more than 80 km but lessthan 250 km, is generally referred to as a medium transmission line. Due tothe line length being considerably high, admittance Y of the network doesplay a role in calculating the effective circuit parameters, unlike in the caseof medium transmission lines. For this reason the modelling of a mediumlength transmission line is done using lumped shunt admittance along withthe 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 circuitand 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 themiddle point of the line and half the line resistance and reactance are lumpedon its either side .Its circuit and phasor diagram is shown below:

Figure 2.3: Nominal τ model

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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 dividedinto two halves; one half being lumped at the sending end and the other halfat the receiving end. Its circuit and phasor diagram is shown below:

Figure 2.5: Nominal π model

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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:

Percentage Efficiency = Power recieved at recieving endPower delivered at sending end

× 100

Percentage Efficiency = Power recieved at recieving endPower recieved at recieving end + power losses in conductor

× 100

• When we add inductive load in the medium transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltage atreceiving end is less as compared to voltage at sending end thus efficiencydecreases by adding inductors as loads.

• Similarly, When we add capacitive load in the medium transmissionlines then the voltage at the receiving end is greater than the voltage at thesending end because capacitor drew leading current from circuit which can-cels the lagging current that are driven by the inductor present in mediumtransmission lines due to which voltage at receiving end is greater as com-pared to voltage at sending end thus efficiency increases ultimately by addingcapacitors as loads.

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• When we add resistor as load in medium transmission lines thenit drew more current due to which more copper losses occurs and power atoutput 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 loadV oltage of recieving end at full load

• When we add inductive load in the medium transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltageat receiving end is less as compared to voltage at sending end thus voltageregulation is positive for inductive or lagging load as described in the formulagiven below

Percentage V oltage Regulation = I R cosφR + I XL sinφRVR

× 100 (for lagging pf)

• Similarly, When we add capacitive load in the medium transmissionlines then the voltage at the receiving end is greater than the voltage at thesending end because capacitor drew leading current from circuit which cancelsthe 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 tovoltage at sending end thus voltage regulation is negative for capacitive orleading load as described in the formula given below

Percentage V oltage Regulation = I R cosφR − I XL sinφRVR

× 100 (for leading pf)

2.3.3 Power Factor

• When we add inductive load in the medium transmission lines thenthe voltage at the receiving end is less than the voltage at the sending endbecause inductor drew lagging current from circuit due to which voltage atreceiving end is less as compared to voltage at sending end thus power factordecreases by adding inductive load

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• Similarly, When we add capacitive load in the medium transmissionlines then the voltage at the receiving end is greater than the voltage at thesending end because capacitor drew leading current from circuit which cancelsthe lagging current that are driven by the inductor present in medium trans-mission lines due to which voltage at receiving end is greater as comparedto voltage at sending end thus power factor increases by adding capacitor onloads.

• By adding Resistors on loads there is no affect on power factorbecause 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



Figure 2.7: Graphical behavior of highly inductive load

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2.4.2 Highly Capacitive Load

The graphical Behaviour of Highly capacitive load is as:


Figure 2.8: Graphical behavior of highly capacitive load

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Chapter 3

Series Connection Of DifferentTransmission Lines

3.1 Introduction

In this we add the two models of different transmission lines in series and wecalculate the the voltages at sending end and receiving end of first model andultimately we find the final receiving end voltages and currents after secondtransmission line model. We call the first receiving end voltage as mid pointvoltage and current as mid point current.

3.2 Effects

The effects of using two different transmission lines are described graphicallyfor 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 sendingend current,mid point current and load current ( receiving end current ) willbe 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 orIR.E )

In this load voltage is along y-axis and sending end current or receiving endcurrent 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 orIR.E

In this load voltage is along y-axis and sending end current or receiving endcurrent is along x-axis as described below:

Figure 3.2: Graphical behavior between VMID and IS.E

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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 currentis along x-axis as described below:

Figure 3.3: Graphical behavior between VR.E and IR.E

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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 currentis 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 describedbelow:

Figure 3.5: Graphical behavior between VR.E and IMID

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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 describedbelow:

Figure 3.6: Graphical behavior between VMID and IMID

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Chapter 4

Effect of shunt compensationon performance of TransmissionLines

4.1 Introduction

In shunt compensation, power system is connected in shunt (parallel) withthe FACTS. It works as a controllable current source. Shunt compensationis 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 loadis connected to the transmission line, power factor lags because of laggingload current. To compensate, a shunt capacitor is connected which drawscurrent leading the source voltage. The net result is improvement in powerfactor.

4.3 Shunt Inductive Compensation

This method is used either when charging the transmission line, or, whenthere 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 capacitancein the transmission line causes voltage amplification (Ferranti effect). Thereceiving end voltage may become double the sending end voltage (generallyin case of very long transmission lines). To compensate, shunt inductors areconnected 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 shuntcapacitors at sending end , similarly by adding more and more capacitors atthe sending end , voltage at sending end increases and improved ultimatelydue to which power factor of short transmission line increases.The circuitof short transmission line without compensation along with its phasor dia-gram and graphical behavior is shown below and short transmission line withcompensation 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:

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Figure 4.2: Short transmission line phasor diagram

4.4.3 Graphical Behaviour

Graphical behavior of short transmission line without compensation is asfollow:

• VR.E = 198V θ = 50.2 lagging I = 0.441 A.

Figure 4.3: Graphical behavior of STL without compensation

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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 isas follow:

• VR.E = 212V θ = 51 lagging I = 0.472 A.

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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

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4.5 Effect of Shunt Capacitive Compensation

On Medium Transmission Line

In this static shunt capacitors are connected at the end of medium transmis-sion line ,in which voltage at sending end increases by adding static shuntcapacitors at sending end , similarly by adding more and more capacitors atthe sending end , voltage at sending end increases and improved ultimatelydue to which power factor of medium transmission line increases.The circuitof medium transmission line without compensation along with its phasor di-agram and graphical behavior is shown below and medium transmission linewith 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-sion line ,in which voltage at sending end increases by adding static shuntcapacitors at sending end , similarly by adding more and more capacitors atthe sending end , voltage at sending end increases and improved ultimatelydue 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 asfollow:• VR.E = 204V θ = 48 lagging I = 0.454 A.

Figure 4.8: VR.E and IR.E without compensation

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4.5.3 Graphical Behaviour With Compensation

Graphical behavior of medium transmission line with 2.5 µ F compensationis as follow:• VR.E = 217V θ = 49.5 lagging I = 0.483 A.

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

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Chapter 5

Power Factor Improvement Byusing Static Capacitors

5.1 Introduction

The power factor of a circuit implies that how efficiently power is beingconsumed 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 thepower 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 knownas power factor ( p.f ) .

5.2 Power Factor Improvement

The low power factor is mainly due to the fact that most of the power loadsare inductive and,therefore take lagging currents. In order to improve thepower factor,some device taking leading power should be connected in parallelwith the load.One of such devices can be a capacitor.The capacitor drawsthe leading current and partly or completely neutralizes the lagging reactivecomponent of load current.This raise the power factor of the load as shownin 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 devicethat 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 reactivepower of the load will be partly neutralized, resulting in improvement of thepower factor of the system.

Therefore, when such a device is connected across the load, which takesleading reactive power such as static capacitors, synchronous machines orsynchronous condensers, the leading reactive component of current drawn bypower factor correcting device neutralizes the lagging reactive component ofcurrent drawn by the load partly or completely.

Power factor of the system will approach unity when lagging reactivecomponent of load current is completely neutralized by the leading reactivecomponent of current drawn by power factor correcting device as shown infigure:

Figure 5.2: Power factor improvement

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Mainly there are three methods to improve the power factor an inductiveload• By use of Static Capacitor• By use of Synchronous Motors• By use of Phase AdvancersHere 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 withthe 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 serieswith the line, as shown in fig 5.3 Capacitors connected in series with the lineneutralize the line reactance. The capacitors, when connected in series withthe 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

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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 theeffect of compensating for part or all of it. Therefore, the primary effect ofthe series capacitor is to minimize the voltage drop caused by the inductivereactance in the circuit. A series capacitor can even be considered as a volt-age regulator that provides voltage rise which increases automatically andinstantaneously as the load increases.

Also, a series capacitor produces more net voltage rise than a shuntcapacitor at lower power factors, which creates more voltage drop. However,a series capacitor improves the system power factor much less than a shuntcapacitor 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

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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 aleading current, which balances some or the entire lagging component of theinductive load current at the point of installation.By the application of shunt capacitor to a feeder, the magnitude of the sourcecurrent can be reduced, the power factor can be improved, and consequentlythe voltage drop between the sending end and the load is also reduced.However, shunt capacitors do not affect current or power factor beyond theirpoint of application.

5.4 Graphical Behaviour of Shunt Compen-

sation

Graphical behavior of short and medium transmission line with and withoutshunt 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 lagging I = 0.441 A.

Figure 5.5: STL without shunt compensation

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With Shunt Compensation

• VR.E = 212V θ = 51 lagging I = 0.472 A.

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

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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 lagging I = 0.454 A.

Figure 5.8: Medium Transmission Line without shunt compensation

With Compensation

• VR.E = 217V θ = 49.5 lagging I = 0.483 A.

Figure 5.9: Medium Transmission Line with 2.5µF shunt compensation

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• VR.E = 230V θ = 48.7 lagging I = 0.51 A.

Figure 5.10: Medium Transmission Line with 5µF shunt compensation

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Chapter 6

Determination of CircuitParameters of DifferentTransmission Lines

6.1 Introduction

A major section of power system engineering deals in the transmission ofelectrical power from one particular place (eg. generating station) to an-other like substations or distribution units with maximum efficiency. So itsof substantial importance for power system engineers to be thorough with itsmathematical modeling. Thus the entire transmission system can be simpli-fied to a two port network for the sake of easier calculations. The circuit ofa two port network is shown in the diagram below. As the name suggests, atwo port network consists of an input port PQ and an output port RS. Eachport has two terminals to connect itself to the external circuit. Thus it isessentially 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 = ISRecieving End Voltage = VR

Recieving End Current = IR

Now the ABCD parameters or the transmission line parameters provide thelink between the supply and receiving end voltages and currentsConsidering the circuit elements to be linear in nature. Thus the relationbetween the sending and receiving end specifications are given using ABCDparameters by the equations below.

VS = A VR + B IRIS = C VR + D IR

Now in order to determine the ABCD parameters of transmission line let usimpose 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 = 0Applying this condition we get,

VS = A VR + B 0 → VS = A VR + 0

A =V SV 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 receivingend voltage. Since dimension wise A is a ratio of voltage to voltage, A is adimension less parameter.Applying the same open circuit condition i.e IR = 0Thus it implies that on applying open circuit condition to ABCD parametersof transmission line, we get parameter C as the ratio of sending end currentand receiving end voltage. Since dimension wise C is a ratio of current tovoltage, its unit is mho.Thus C is the open circuit conductance and is given by

C =ISV R

mho

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6.4 Parameters In Short Circuit Recieving

End

The receiving end is open circuited meaning receiving end voltage VR = 0Applying this condition we get,

VS = A 0 + B IR → VS = 0 + B IR

B =V SIR

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 shortcircuit receiving end current. Since dimension wise B is a ratio of voltage tocurrent, its unit is Ω. Thus B is the short circuit resistance and is given by

B =V SIR

Ω

Applying the same open circuit condition i.e IR = 0Thus 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 shortcircuit receiving end current. Since dimension wise D is a ratio of current tocurrent, it’s a dimension less parameter.The ABCD parameters of transmission line can be tabulated as:-

A =V SV R

→ Voltage Ratio → unit less

B =V SIR

→ Short Circuit Resistance → Ω

C =ISV R

→ Open Circuit Conductance → mho

D =ISIR

→ Current Ratio → unit less

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Chapter 7

Assignment Question/Answers

Assignment No. 1 Plot the voltage curves as a function of the load currentin a combined diagram for short , medium and long transmission Lines.

The Voltage curves as a function of the load current in a combined diagramfor short,medium and long transmission lines are as follow

Figure 7.1: Voltage Curve As Function of Load Current

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Assignment No. 2 Plot all the currents ( IS.E and IMID ) as a function ofthe 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

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Figure 7.3: Medium Transmission Line

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Figure 7.4: Long Transmission Line

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