Balanced Three Phase Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

 Page 1


Unit-1 
BALANCED THREE PHASE CIRCUITS 
1.1 Introduction: 
There are two types of systems available in electrical circuits, single phase 
and three phase. In single phase circuits, there will be only one phase, i.e the 
current will flow through only one wire and there will be one return path called 
neutral line to complete the circuit. So in single phase minimum amount of power 
can be transported. Here the generating station and load station will also be single 
phase. This is an old system using from previous time. 
In 1882, new invention has been done polyphase system, that more than 
one phase can be used for generating, transmitting and for load system. Three 
phase circuit is the polyphase system where three phases are send together from 
generator to the load. Each phase are having a phase difference of 120
0
, i.e 120
0
 
angle electrically. So from the total of 360
0
, three phase are equally divided into 
120
0
 each. The power in three phase system is continuous as all the three phases 
are involved in generating the total power. The sinusoidal waves for 3 phase 
system is shown below . 
 
Fig.1.1 
The three phase can be used as single phase each. So if the load is single 
phase, then one phase can be taken from the three phase circuit and the neutral 
can be used as ground to complete the circuit. 
Page 2


Unit-1 
BALANCED THREE PHASE CIRCUITS 
1.1 Introduction: 
There are two types of systems available in electrical circuits, single phase 
and three phase. In single phase circuits, there will be only one phase, i.e the 
current will flow through only one wire and there will be one return path called 
neutral line to complete the circuit. So in single phase minimum amount of power 
can be transported. Here the generating station and load station will also be single 
phase. This is an old system using from previous time. 
In 1882, new invention has been done polyphase system, that more than 
one phase can be used for generating, transmitting and for load system. Three 
phase circuit is the polyphase system where three phases are send together from 
generator to the load. Each phase are having a phase difference of 120
0
, i.e 120
0
 
angle electrically. So from the total of 360
0
, three phase are equally divided into 
120
0
 each. The power in three phase system is continuous as all the three phases 
are involved in generating the total power. The sinusoidal waves for 3 phase 
system is shown below . 
 
Fig.1.1 
The three phase can be used as single phase each. So if the load is single 
phase, then one phase can be taken from the three phase circuit and the neutral 
can be used as ground to complete the circuit. 
 
1.1.1 Why three phase is preferred over single phase? 
There are various reasons for this question because there are numbers of 
advantages over single phase circuit. The three phase system can be used as three 
single phase line so it can act as three single phase system. The three phase 
generation and single phase generation is same in the generator except the 
arrangement of coil in the generator to get 120
0
 phase difference. The conductor 
needed in three phase circuit is 75% that of conductor needed in single phase 
circuit. 
And also the instantaneous power in single phase system falls down to 
zero as in single phase we can see from the sinusoidal curve but in three phase 
system the net power from all the phases gives a continuous power to the load. 
Till now we can say that there are three voltage sources connected 
together to form a three phase circuit and actually it is inside generator. The 
generator is having three voltage sources which are acting together in 120
0
 phase 
difference. If we can arrange three single phase circuit with 120
0
 phase difference, 
then it will become a three phase circuit. So 120
0
 phase difference is must 
otherwise the circuit will not work, the three phase load will not be able to get 
active and it may also cause damage to the system. 
The size or metal quantity of three phase devices is not having much 
difference. Now of we consider the transformer, it will be almost same size fro 
both single phase and three phase because transformer will make only the linkage 
of flux. So the three phase system will have  higher efficiency compared to single 
phase for the same or little difference in mass of transformer, three phase line will 
be out whereas in single phase will be only one. And losses will be minimum in 
three phase circuit. So overall in conclusion the three phase system will have 
better and higher efficiency compared to the single phase system.    
A balanced polyphase system is one in which there are two or more equal 
voltages of the same frequency displaced equally in time phase, which supply 
power to loads connected to the lines. In general, in a n-phase balanced polyphase 
system, there are n-equal voltages displaced in time phase by 
360
0
?? or 
2 ?? ?? (except in 
the case of a 2-phase system, in which there are two equal voltages differing in 
Page 3


Unit-1 
BALANCED THREE PHASE CIRCUITS 
1.1 Introduction: 
There are two types of systems available in electrical circuits, single phase 
and three phase. In single phase circuits, there will be only one phase, i.e the 
current will flow through only one wire and there will be one return path called 
neutral line to complete the circuit. So in single phase minimum amount of power 
can be transported. Here the generating station and load station will also be single 
phase. This is an old system using from previous time. 
In 1882, new invention has been done polyphase system, that more than 
one phase can be used for generating, transmitting and for load system. Three 
phase circuit is the polyphase system where three phases are send together from 
generator to the load. Each phase are having a phase difference of 120
0
, i.e 120
0
 
angle electrically. So from the total of 360
0
, three phase are equally divided into 
120
0
 each. The power in three phase system is continuous as all the three phases 
are involved in generating the total power. The sinusoidal waves for 3 phase 
system is shown below . 
 
Fig.1.1 
The three phase can be used as single phase each. So if the load is single 
phase, then one phase can be taken from the three phase circuit and the neutral 
can be used as ground to complete the circuit. 
 
1.1.1 Why three phase is preferred over single phase? 
There are various reasons for this question because there are numbers of 
advantages over single phase circuit. The three phase system can be used as three 
single phase line so it can act as three single phase system. The three phase 
generation and single phase generation is same in the generator except the 
arrangement of coil in the generator to get 120
0
 phase difference. The conductor 
needed in three phase circuit is 75% that of conductor needed in single phase 
circuit. 
And also the instantaneous power in single phase system falls down to 
zero as in single phase we can see from the sinusoidal curve but in three phase 
system the net power from all the phases gives a continuous power to the load. 
Till now we can say that there are three voltage sources connected 
together to form a three phase circuit and actually it is inside generator. The 
generator is having three voltage sources which are acting together in 120
0
 phase 
difference. If we can arrange three single phase circuit with 120
0
 phase difference, 
then it will become a three phase circuit. So 120
0
 phase difference is must 
otherwise the circuit will not work, the three phase load will not be able to get 
active and it may also cause damage to the system. 
The size or metal quantity of three phase devices is not having much 
difference. Now of we consider the transformer, it will be almost same size fro 
both single phase and three phase because transformer will make only the linkage 
of flux. So the three phase system will have  higher efficiency compared to single 
phase for the same or little difference in mass of transformer, three phase line will 
be out whereas in single phase will be only one. And losses will be minimum in 
three phase circuit. So overall in conclusion the three phase system will have 
better and higher efficiency compared to the single phase system.    
A balanced polyphase system is one in which there are two or more equal 
voltages of the same frequency displaced equally in time phase, which supply 
power to loads connected to the lines. In general, in a n-phase balanced polyphase 
system, there are n-equal voltages displaced in time phase by 
360
0
?? or 
2 ?? ?? (except in 
the case of a 2-phase system, in which there are two equal voltages differing in 
phase by 90
0
). Systems of six or more phases are used in polyphase rectifiers to 
obtain rectified voltage with low ripple. But three phase system is most 
commonly used polyphase system for generation and transmission of power. 
Hence we study in detail the 3-phase voltage generation and analysis of 3-phase 
circuit in this unit. 
A 3-phase system has the following advantages over single phase system. 
For a given frame size of a machine a 3-phase machine will have large capacity 
than a single phase machine. The torque produced in a 3-phase motor will be 
more uniform where as in a 1-phase motor it is pulsating. The amount of copper 
required in a certain amount of power over a particular distance, is less compared 
to a single phase system. 
1.1.2 Phase sequence: 
It is the order in which the phase voltages will attain their maximum 
values. From the fig it is seen that the voltage in A phase will attain maximum 
value first and followed by B and C phases. Hence three phase sequence is ABC. 
This is also evident from phasor diagram in which the phasors with its +ve 
direction of anti-clockwise rotation passes a fixed point is the order ABC, ABC 
and so on. The phase sequence depends on the direction of rotation of the coils in 
the magnetic field. If the coils rotate in the opposite direction then the phase 
voltages attains maximum value in the order ACB. The phase sequence gets 
reversed with direction of rotation. Then the voltage for this sequence can be 
represented as 
0
0
sin
sin( 120 )
sin( 240 )
am
cm
bm
e E t
e E t
e E t
?
?
?
?
??
??
 
The RMS values of voltage can be expressed as 
0
0
0
0
120
240
A
C
B
EE
EE
EE
??
? ? ?
? ? ?
 
1.1.3 Star and Delta connection 
Page 4


Unit-1 
BALANCED THREE PHASE CIRCUITS 
1.1 Introduction: 
There are two types of systems available in electrical circuits, single phase 
and three phase. In single phase circuits, there will be only one phase, i.e the 
current will flow through only one wire and there will be one return path called 
neutral line to complete the circuit. So in single phase minimum amount of power 
can be transported. Here the generating station and load station will also be single 
phase. This is an old system using from previous time. 
In 1882, new invention has been done polyphase system, that more than 
one phase can be used for generating, transmitting and for load system. Three 
phase circuit is the polyphase system where three phases are send together from 
generator to the load. Each phase are having a phase difference of 120
0
, i.e 120
0
 
angle electrically. So from the total of 360
0
, three phase are equally divided into 
120
0
 each. The power in three phase system is continuous as all the three phases 
are involved in generating the total power. The sinusoidal waves for 3 phase 
system is shown below . 
 
Fig.1.1 
The three phase can be used as single phase each. So if the load is single 
phase, then one phase can be taken from the three phase circuit and the neutral 
can be used as ground to complete the circuit. 
 
1.1.1 Why three phase is preferred over single phase? 
There are various reasons for this question because there are numbers of 
advantages over single phase circuit. The three phase system can be used as three 
single phase line so it can act as three single phase system. The three phase 
generation and single phase generation is same in the generator except the 
arrangement of coil in the generator to get 120
0
 phase difference. The conductor 
needed in three phase circuit is 75% that of conductor needed in single phase 
circuit. 
And also the instantaneous power in single phase system falls down to 
zero as in single phase we can see from the sinusoidal curve but in three phase 
system the net power from all the phases gives a continuous power to the load. 
Till now we can say that there are three voltage sources connected 
together to form a three phase circuit and actually it is inside generator. The 
generator is having three voltage sources which are acting together in 120
0
 phase 
difference. If we can arrange three single phase circuit with 120
0
 phase difference, 
then it will become a three phase circuit. So 120
0
 phase difference is must 
otherwise the circuit will not work, the three phase load will not be able to get 
active and it may also cause damage to the system. 
The size or metal quantity of three phase devices is not having much 
difference. Now of we consider the transformer, it will be almost same size fro 
both single phase and three phase because transformer will make only the linkage 
of flux. So the three phase system will have  higher efficiency compared to single 
phase for the same or little difference in mass of transformer, three phase line will 
be out whereas in single phase will be only one. And losses will be minimum in 
three phase circuit. So overall in conclusion the three phase system will have 
better and higher efficiency compared to the single phase system.    
A balanced polyphase system is one in which there are two or more equal 
voltages of the same frequency displaced equally in time phase, which supply 
power to loads connected to the lines. In general, in a n-phase balanced polyphase 
system, there are n-equal voltages displaced in time phase by 
360
0
?? or 
2 ?? ?? (except in 
the case of a 2-phase system, in which there are two equal voltages differing in 
phase by 90
0
). Systems of six or more phases are used in polyphase rectifiers to 
obtain rectified voltage with low ripple. But three phase system is most 
commonly used polyphase system for generation and transmission of power. 
Hence we study in detail the 3-phase voltage generation and analysis of 3-phase 
circuit in this unit. 
A 3-phase system has the following advantages over single phase system. 
For a given frame size of a machine a 3-phase machine will have large capacity 
than a single phase machine. The torque produced in a 3-phase motor will be 
more uniform where as in a 1-phase motor it is pulsating. The amount of copper 
required in a certain amount of power over a particular distance, is less compared 
to a single phase system. 
1.1.2 Phase sequence: 
It is the order in which the phase voltages will attain their maximum 
values. From the fig it is seen that the voltage in A phase will attain maximum 
value first and followed by B and C phases. Hence three phase sequence is ABC. 
This is also evident from phasor diagram in which the phasors with its +ve 
direction of anti-clockwise rotation passes a fixed point is the order ABC, ABC 
and so on. The phase sequence depends on the direction of rotation of the coils in 
the magnetic field. If the coils rotate in the opposite direction then the phase 
voltages attains maximum value in the order ACB. The phase sequence gets 
reversed with direction of rotation. Then the voltage for this sequence can be 
represented as 
0
0
sin
sin( 120 )
sin( 240 )
am
cm
bm
e E t
e E t
e E t
?
?
?
?
??
??
 
The RMS values of voltage can be expressed as 
0
0
0
0
120
240
A
C
B
EE
EE
EE
??
? ? ?
? ? ?
 
1.1.3 Star and Delta connection 
The three phase windings have six terminals i.e., A,B,C are starting end of 
the windings and A’,B’ and C’ are finishing ends of windings. For 3 phase 
systems two types of common interconnections are employed. 
1.1.3(a) Star connection: the finishing ends or starting ends of the three phase 
windings are connected to a common point as shown in. A’, B’, C’ are connected 
to a common point called neutral point. The other ends A, B, C are called line 
terminals and the common terminal neutral are brought outside. Then it is called a 
3 phase 4 wire star connected systems. If neutral point is not available, then it is 
called 3 phase, 3 wire star connection. 
 
Fig.1.2 
1.1.3(b) Delta connection: in this form of interconnection the dissimilar ends of 
the three coils i.e A and B’, B and C’, and C and A’ are connected to form a 
closed ? circuit (starting end of one phase is connected to finishing end of the 
next phase). The three junction are brought outside as line terminal A, B, C. the 
three phase windings are connected in series and form a closed path. The sum of 
the voltages in the closed path for balanced system of voltages at any instant will 
be zero fig. 
 
Page 5


Unit-1 
BALANCED THREE PHASE CIRCUITS 
1.1 Introduction: 
There are two types of systems available in electrical circuits, single phase 
and three phase. In single phase circuits, there will be only one phase, i.e the 
current will flow through only one wire and there will be one return path called 
neutral line to complete the circuit. So in single phase minimum amount of power 
can be transported. Here the generating station and load station will also be single 
phase. This is an old system using from previous time. 
In 1882, new invention has been done polyphase system, that more than 
one phase can be used for generating, transmitting and for load system. Three 
phase circuit is the polyphase system where three phases are send together from 
generator to the load. Each phase are having a phase difference of 120
0
, i.e 120
0
 
angle electrically. So from the total of 360
0
, three phase are equally divided into 
120
0
 each. The power in three phase system is continuous as all the three phases 
are involved in generating the total power. The sinusoidal waves for 3 phase 
system is shown below . 
 
Fig.1.1 
The three phase can be used as single phase each. So if the load is single 
phase, then one phase can be taken from the three phase circuit and the neutral 
can be used as ground to complete the circuit. 
 
1.1.1 Why three phase is preferred over single phase? 
There are various reasons for this question because there are numbers of 
advantages over single phase circuit. The three phase system can be used as three 
single phase line so it can act as three single phase system. The three phase 
generation and single phase generation is same in the generator except the 
arrangement of coil in the generator to get 120
0
 phase difference. The conductor 
needed in three phase circuit is 75% that of conductor needed in single phase 
circuit. 
And also the instantaneous power in single phase system falls down to 
zero as in single phase we can see from the sinusoidal curve but in three phase 
system the net power from all the phases gives a continuous power to the load. 
Till now we can say that there are three voltage sources connected 
together to form a three phase circuit and actually it is inside generator. The 
generator is having three voltage sources which are acting together in 120
0
 phase 
difference. If we can arrange three single phase circuit with 120
0
 phase difference, 
then it will become a three phase circuit. So 120
0
 phase difference is must 
otherwise the circuit will not work, the three phase load will not be able to get 
active and it may also cause damage to the system. 
The size or metal quantity of three phase devices is not having much 
difference. Now of we consider the transformer, it will be almost same size fro 
both single phase and three phase because transformer will make only the linkage 
of flux. So the three phase system will have  higher efficiency compared to single 
phase for the same or little difference in mass of transformer, three phase line will 
be out whereas in single phase will be only one. And losses will be minimum in 
three phase circuit. So overall in conclusion the three phase system will have 
better and higher efficiency compared to the single phase system.    
A balanced polyphase system is one in which there are two or more equal 
voltages of the same frequency displaced equally in time phase, which supply 
power to loads connected to the lines. In general, in a n-phase balanced polyphase 
system, there are n-equal voltages displaced in time phase by 
360
0
?? or 
2 ?? ?? (except in 
the case of a 2-phase system, in which there are two equal voltages differing in 
phase by 90
0
). Systems of six or more phases are used in polyphase rectifiers to 
obtain rectified voltage with low ripple. But three phase system is most 
commonly used polyphase system for generation and transmission of power. 
Hence we study in detail the 3-phase voltage generation and analysis of 3-phase 
circuit in this unit. 
A 3-phase system has the following advantages over single phase system. 
For a given frame size of a machine a 3-phase machine will have large capacity 
than a single phase machine. The torque produced in a 3-phase motor will be 
more uniform where as in a 1-phase motor it is pulsating. The amount of copper 
required in a certain amount of power over a particular distance, is less compared 
to a single phase system. 
1.1.2 Phase sequence: 
It is the order in which the phase voltages will attain their maximum 
values. From the fig it is seen that the voltage in A phase will attain maximum 
value first and followed by B and C phases. Hence three phase sequence is ABC. 
This is also evident from phasor diagram in which the phasors with its +ve 
direction of anti-clockwise rotation passes a fixed point is the order ABC, ABC 
and so on. The phase sequence depends on the direction of rotation of the coils in 
the magnetic field. If the coils rotate in the opposite direction then the phase 
voltages attains maximum value in the order ACB. The phase sequence gets 
reversed with direction of rotation. Then the voltage for this sequence can be 
represented as 
0
0
sin
sin( 120 )
sin( 240 )
am
cm
bm
e E t
e E t
e E t
?
?
?
?
??
??
 
The RMS values of voltage can be expressed as 
0
0
0
0
120
240
A
C
B
EE
EE
EE
??
? ? ?
? ? ?
 
1.1.3 Star and Delta connection 
The three phase windings have six terminals i.e., A,B,C are starting end of 
the windings and A’,B’ and C’ are finishing ends of windings. For 3 phase 
systems two types of common interconnections are employed. 
1.1.3(a) Star connection: the finishing ends or starting ends of the three phase 
windings are connected to a common point as shown in. A’, B’, C’ are connected 
to a common point called neutral point. The other ends A, B, C are called line 
terminals and the common terminal neutral are brought outside. Then it is called a 
3 phase 4 wire star connected systems. If neutral point is not available, then it is 
called 3 phase, 3 wire star connection. 
 
Fig.1.2 
1.1.3(b) Delta connection: in this form of interconnection the dissimilar ends of 
the three coils i.e A and B’, B and C’, and C and A’ are connected to form a 
closed ? circuit (starting end of one phase is connected to finishing end of the 
next phase). The three junction are brought outside as line terminal A, B, C. the 
three phase windings are connected in series and form a closed path. The sum of 
the voltages in the closed path for balanced system of voltages at any instant will 
be zero fig. 
 
Fig.1.3 
The main advantage of star connection is that we can have two different 3-
phase voltages. The voltage that was the line terminals between A & B, B&C, and 
C & A are called line voltages and form a balanced three phase voltage. Another 
voltage is between the terminals A & N, B& N, and C &N are called phase 
voltage and form another balanced three phase voltage (line to neutral voltage or 
wye voltage). 
1.2 Relation between line and phase voltage and currents in 
balanced systems:  
In this section we will derive the relation between line and phase values of 
voltages and currents of 3-phase star connected and delta connected systems. 
1.2.1 Star connection: 
We will employ double subscript notation to represent voltages and 
currents. The terminal corresponding to first subscript is assumed to be at a higher 
potential with respect to the terminal corresponding to second subscript. 
 
Fig.1.4