Ism 11
RogerRozario
21 views
138 slides
Nov 23, 2021
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About This Presentation
ism 2020
Slide Content
UEEC007
Induction and
Synchronous Machines
Alternators
Induction and
Synchronous Machines
Alternators
Alternators
UEEC007 -ISM
Mechanical Energy Electrical Energy
Specific Voltage
Frequency
UEEC007 -ISM
Mechanical Energy Electrical Energy
Specific Voltage
Frequency
Applications
UEEC007 -ISM
Automotive alternators
Diesel-electric locomotive alternators
Marine alternators
Brushless alternators
Radio alternators
used in modern automobiles
used in diesel electric multiple units
used in marine applications
used in electrical powergeneration plants as the main source of power
used for low band radio frequency transmission
UEEC007 -ISM
Automotive alternators
Diesel-electric locomotive alternators
Marine alternators
Brushless alternators
Radio alternators
used in modern automobiles
used in diesel electric multiple units
used in marine applications
used in electrical powergeneration plants as the main source of power
used for low band radio frequency transmission
Construction
UEEC007 -ISM
Stator
Rotor
Armature
Field
Three phase windings distributed in space by 120 degrees
UEEC007 -ISM
Stator
Rotor
Armature
Field
Three phase windings distributed in space by 120 degrees
Types
UEEC007 -ISM
Salient Pole Type Smooth Cylindrical Type
UEEC007 -ISM
Salient Pole Type Smooth Cylindrical Type
Working Principle
UEEC007 -ISM
Similar to DC generator
Faraday’s law of electromagnetic induction
Current is induced in the conductor inside a magnetic field when there is a
relative motion between that conductor and the magnetic field
Conductor
MagneticField
RelativeMotion
UEEC007 -ISM
Similar to DC generator
Faraday’s law of electromagnetic induction
Current is induced in the conductor inside a magnetic field when there is a
relative motion between that conductor and the magnetic field
Conductor
MagneticField
RelativeMotion
Position 1
UEEC007 -ISM
single turn loop ABCD rotate against axis a-b clockwise
UEEC007 -ISM
single turn loop ABCD rotate against axis a-b clockwise
Position 2
UEEC007 -ISM
Rotate 90 degrees
AB of the loop comes in front of S-pole
CD of the loop comes in front of N-pole
Rate of flux cutting by the conductor AB is maximum
Tangential motion of the conductor AB is just perpendicular to the magnetic flux lines from N to S pole
direction of the induced currentFleming’s right-hand rule.
A-B C-D
UEEC007 -ISM
Rotate 90 degrees
AB of the loop comes in front of S-pole
CD of the loop comes in front of N-pole
Rate of flux cutting by the conductor AB is maximum
Tangential motion of the conductor AB is just perpendicular to the magnetic flux lines from N to S pole
direction of the induced currentFleming’s right-hand rule.
A-B C-D
Position 3
UEEC007 -ISM
ABCD comes at the vertical position
Rotate 90 degrees
Tangential motion of conductor AB and CD is just parallel to the magnetic flux lines
No flux cutting that is no current in the conductor
UEEC007 -ISM
ABCD comes at the vertical position
Rotate 90 degrees
Tangential motion of conductor AB and CD is just parallel to the magnetic flux lines
No flux cutting that is no current in the conductor
Position 4
UEEC007 -ISM
Rotate 90 degrees
The turn comes at a horizontal position from its vertical position
The current in the conductors comes to its maximum value from zero
One Stationary Brush on
each slip ring
A-B C-D
A-BC-D
A-BC-D
UEEC007 -ISM
Rotate 90 degrees
The turn comes at a horizontal position from its vertical position
The current in the conductors comes to its maximum value from zero
One Stationary Brush on
each slip ring
A-B C-D
A-BC-D
A-BC-D
Three Phase Windings
UEEC007 -ISM
UEEC007 -ISM
EmfEquation
The average value of the induced emfin a conductor is =
�??????
��
In one revolution of the rotor the each stator conductor is cut by a flux of �??????webers
Speed of the rotor in rps=
�
�
60
Time taken for one revolution =
1
��
60
=
60
��
UEEC007 -ISM
The average value of the induced emfin a conductor is =
�??????
��
In one revolution of the rotor the each stator conductor is cut by a flux of �??????webers
Speed of the rotor in rps=
�
�
60
Time taken for one revolution =
1
��
60
=
60
��
UEEC007 -ISM
EmfEquation
The average value of the induced emfin a conductor is
�??????
��
=
??????��
�
60
Frequency of the induced emfis f =
��
�
120
Synchronous speed �
�=
120�
�
The average value of the induced emfin a conductor is =
??????�
60
.
120�
�
= 2�??????volts
UEEC007 -ISM
The average value of the induced emfin a conductor is
�??????
��
=
??????��
�
60
Frequency of the induced emfis f =
��
�
120
Synchronous speed �
�=
120�
�
The average value of the induced emfin a conductor is =
??????�
60
.
120�
�
= 2�??????volts
UEEC007 -ISM
EmfEquation
If there are �
�ℎconductors in series per phase
Average Induced emfper phase = Average Induced emfper conductor x �
�ℎ
= 2�??????. �
�ℎ
Average Induced emfper phase = 2�??????.2�
�ℎ
= 4�??????.�
�ℎ
RMS value of the induced emfper phase = Form factor x Average Induced emfper phase
= 1.11.4�??????.�
�ℎ
= 4.44�??????.�
�ℎvolts
UEEC007 -ISM
�
�ℎ=2�
�ℎ
If there are �
�ℎconductors in series per phase
Average Induced emfper phase = Average Induced emfper conductor x �
�ℎ
= 2�??????. �
�ℎ
Average Induced emfper phase = 2�??????.2�
�ℎ
= 4�??????.�
�ℎ
RMS value of the induced emfper phase = Form factor x Average Induced emfper phase
= 1.11.4�??????.�
�ℎ
= 4.44�??????.�
�ℎvolts
UEEC007 -ISM
�
�ℎ=2�
�ℎ
Coil span –Distributed windings
UEEC007 -ISM
123456789 101112131415161718
18 slots
2 poles
3 phase
Coil Span =
�����
����
Coil Span =
18
2
Coil Span = 9
m = �����
����
�ℎ??????��
m = 18
2
3
m = 3
180 degrees
n = ���������
UEEC007 -ISM
123456789 101112131415161718
18 slots
2 poles
3 phase
Coil Span =
�����
����
Coil Span =
18
2
Coil Span = 9
m = �����
����
�ℎ??????��
m = 18
2
3
m = 3
180 degrees
n = ���������
Reactance Resistance and
Impedance
•Resistance -Friction against the flow of current
(Resistors)
(Voltage drop in phase with current [alternating current])
•Reactance –Inertia against the flow of current
(Capacitors and Inductors)
(Proportional to the applied voltage and current)
Impedance –Phase and magnitude (complex)
UEEC007 -ISM
Impedance
•Resistance -Friction against the flow of current
(Resistors)
(Voltage drop in phase with current [alternating current])
•Reactance –Inertia against the flow of current
(Capacitors and Inductors)
(Proportional to the applied voltage and current)
Impedance –Phase and magnitude (complex)
UEEC007 -ISM
Reactance Resistance and
Impedance
UEEC007 -ISM
Impedance
UEEC007 -ISM
Synchronous Reactance
•Imaginary reactance
•Voltage effects in the armature circuit
•Armature leakage reactance
•Change in the airgap flux caused by the armature
reaction
UEEC007 -ISM
•Imaginary reactance
•Voltage effects in the armature circuit
•Armature leakage reactance
•Change in the airgap flux caused by the armature
reaction
UEEC007 -ISM
Synchronous Impedance
•Imaginary Fictitious Impedance
•Voltage effects of the armature circuit
•Armature resistance
•Change in airgap flux produced by the armature
reaction
UEEC007 -ISM
•Imaginary Fictitious Impedance
•Voltage effects of the armature circuit
•Armature resistance
•Change in airgap flux produced by the armature
reaction
UEEC007 -ISM
Leakage Reactance
•Flux setup by the load current (R,L,C)
•Not all the flux are useful
•Effect of the leakage flux –self induced emf(voltage) in
armature winding
•Proportional and in phase with the armature current
producing it
UEEC007 -ISM
•Flux setup by the load current (R,L,C)
•Not all the flux are useful
•Effect of the leakage flux –self induced emf(voltage) in
armature winding
•Proportional and in phase with the armature current
producing it
UEEC007 -ISM
Voltage Drop
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
UEEC007 -ISM
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
UEEC007 -ISM
VOLTAGE DROP
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�+??????
??????�
??????�
•�
�+�
??????�=�
�SynchronousReactance
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????(�
�+�
??????�)
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�
UEEC007 -ISM
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�+??????
??????�
??????�
•�
�+�
??????�=�
�SynchronousReactance
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????(�
�+�
??????�)
•�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�
UEEC007 -ISM
Phasor diagram of a loaded
alternator
UEEC007 -ISM
�
�ℎ-REFERENCE PHASOR
������??????�������??????��
??????
?????? ??????
??????�
??????
??????
??????�
�
??????
??????�
??????�
�
�ℎ
�
�ℎ
??????
??????�
�
φ-lag
alternator
UEEC007 -ISM
�
�ℎ-REFERENCE PHASOR
������??????�������??????��
??????
?????? ??????
??????�
??????
??????
??????�
�
??????
??????�
??????�
�
�ℎ
�
�ℎ
??????
??????�
�
φ-lag
PHASOR DIAGRAM OF A LOADED
ALTERNATOR
UEEC007 -ISM
�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�+??????
??????�
??????�
??????
??????
??????
??????�
??????
??????
??????�
�
??????
??????�
??????�
�
�ℎ
�
�ℎ
??????
??????
??????
??????
�
�ℎ
�
�ℎ??????
??????�
??????
??????
??????�
??????
??????
??????�
�??????
??????�
??????�
�
�ℎ
??????
??????�
�
??????
??????�
??????�
??????
??????�
�
??????
??????�
�
φ-lag φ= 0
φ-lead
??????
??????-REFERENCE PHASOR
������??????�������??????��
??????
??????�
�
�
�ℎ
ALTERNATOR
UEEC007 -ISM
�
�ℎ=�
�ℎ+??????
??????�
??????+??????
??????�
�+??????
??????�
??????�
??????
??????
??????
??????�
??????
??????
??????�
�
??????
??????�
??????�
�
�ℎ
�
�ℎ
??????
??????
??????
??????
�
�ℎ
�
�ℎ??????
??????�
??????
??????
??????�
??????
??????
??????�
�??????
??????�
??????�
�
�ℎ
??????
??????�
�
??????
??????�
??????�
??????
??????�
�
??????
??????�
�
φ-lag φ= 0
φ-lead
??????
??????-REFERENCE PHASOR
������??????�������??????��
??????
??????�
�
�
�ℎ
EMF EQUATION -lag ,lead,unity
UEEC007 -ISM
??????
??????
??????
??????�
??????
�
�ℎ
�
�ℎ
??????
??????�
�
��
�
�
��
��
2
= ��
2
+ ��
2
��
2
= (��
2
+ ��
2
)+(��
2
+ ��
2
)
�
�ℎ
2
=(�
�ℎcosφ+??????
??????�
??????)
2
+ (�
�ℎsinφ+??????
??????�
�)
2
�
�ℎ(���)=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ+??????
??????�
�)
2
�
�ℎ(����)=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ−??????
??????�
�)
2
�
�ℎ(��??????��)=(�
�ℎ+??????
??????�
??????)
2
+(??????
??????�
�)
2
φ−���
�
�ℎ=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
??????
??????�
??????
??????
??????�
�
�
�
2
=�
�
2
+�
??????
2
�
�
2
=�
�
2
-�
??????
2
�
�= �
�
2
−�
??????
2
In OEC
UEEC007 -ISM
??????
??????
??????
??????�
??????
�
�ℎ
�
�ℎ
??????
??????�
�
��
�
�
��
��
2
= ��
2
+ ��
2
��
2
= (��
2
+ ��
2
)+(��
2
+ ��
2
)
�
�ℎ
2
=(�
�ℎcosφ+??????
??????�
??????)
2
+ (�
�ℎsinφ+??????
??????�
�)
2
�
�ℎ(���)=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ+??????
??????�
�)
2
�
�ℎ(����)=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ−??????
??????�
�)
2
�
�ℎ(��??????��)=(�
�ℎ+??????
??????�
??????)
2
+(??????
??????�
�)
2
φ−���
�
�ℎ=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
??????
??????�
??????
??????
??????�
�
�
�
2
=�
�
2
+�
??????
2
�
�
2
=�
�
2
-�
??????
2
�
�= �
�
2
−�
??????
2
In OEC
Voltage Regulation
•TheVoltageRegulationofaSynchronousGeneratoristheincreaseintheterminal
voltageexpressedasapercentageoftheratedterminalvoltagewhentheloadatagiven
powerfactoristhrownoff,withspeedandfieldcurrentremainingthesame.
•It depends upon the power factor of the load.
UEEC007 -ISM
Voltage Regulation =
??????�−??????
??????
% Voltage Regulation =
??????
�−??????
??????
∗100
�
�-No Load Terminal voltage per phase
�–Full Load Terminal voltage per phase
•TheVoltageRegulationofaSynchronousGeneratoristheincreaseintheterminal
voltageexpressedasapercentageoftheratedterminalvoltagewhentheloadatagiven
powerfactoristhrownoff,withspeedandfieldcurrentremainingthesame.
•It depends upon the power factor of the load.
UEEC007 -ISM
Voltage Regulation =
??????�−??????
??????
% Voltage Regulation =
??????
�−??????
??????
∗100
�
�-No Load Terminal voltage per phase
�–Full Load Terminal voltage per phase
Voltage Regulation
Case 1: Lagging power factor:
A generator operating at a lagging power factor has a positive voltage regulation.
Case 2: Unity power factor:
A generator operating at a unity power factor has a small positive voltage regulation.
Case 3: Leading power factor:
A generator operating at a leading power factor has a negative voltage regulation.
UEEC007 -ISM
Case 1: Lagging power factor:
A generator operating at a lagging power factor has a positive voltage regulation.
Case 2: Unity power factor:
A generator operating at a unity power factor has a small positive voltage regulation.
Case 3: Leading power factor:
A generator operating at a leading power factor has a negative voltage regulation.
UEEC007 -ISM
Determination of Voltage
Regulation
UEEC007 -ISM
The method of direct loading is suitable only
for small alternators of the power rating less
than 5 kVA
For large alternators, the indirect methods
are used to determine the voltage regulation
Regulation
UEEC007 -ISM
The method of direct loading is suitable only
for small alternators of the power rating less
than 5 kVA
For large alternators, the indirect methods
are used to determine the voltage regulation
Synchronous Impedance Method
UEEC007 -ISM
Replaces the effect of armature reaction by an imaginary reactance
(synchronous reactance)
2.Open Circuit Characteristic (OCC) -Generated voltage vs field current
1.Armature Resistance per phase
3.Short Circuit Characteristic (SCC) –Short circuit armature current vs field current
UEEC007 -ISM
Replaces the effect of armature reaction by an imaginary reactance
(synchronous reactance)
2.Open Circuit Characteristic (OCC) -Generated voltage vs field current
1.Armature Resistance per phase
3.Short Circuit Characteristic (SCC) –Short circuit armature current vs field current
Armature Resistance per phase
UEEC007 -ISM
The DC resistance between each pair of terminals is measured either
by using an ammeter –voltmeter method or by using the
Wheatstone’s bridge
The average of three sets of resistance value R
tis taken
Skin Effect -DC resistance is multiplied by a factor 1.20 to 1.75 (Usually 1.25) depending on the size of the machine
The value of R
tis divided by 2 to obtain a value of DC resistance per phase
UEEC007 -ISM
The DC resistance between each pair of terminals is measured either
by using an ammeter –voltmeter method or by using the
Wheatstone’s bridge
The average of three sets of resistance value R
tis taken
Skin Effect -DC resistance is multiplied by a factor 1.20 to 1.75 (Usually 1.25) depending on the size of the machine
The value of R
tis divided by 2 to obtain a value of DC resistance per phase
Open Circuit Test
UEEC007 -ISM
Alternator is running at the rated synchronous speed,theload
terminals are kept open
After setting the field current to zero, the field current is
gradually increased step by step
The excitation current may be increased to get 25% more than
the rated voltage
The terminal voltage E
tis measured at each step
A graph is drawn between the open circuit phase voltage
E
p= E
t/√3 and the field current I
f.
Field current I
f Open circuit
phase voltage
E
p= E
t/√3
UEEC007 -ISM
Alternator is running at the rated synchronous speed,theload
terminals are kept open
After setting the field current to zero, the field current is
gradually increased step by step
The excitation current may be increased to get 25% more than
the rated voltage
The terminal voltage E
tis measured at each step
A graph is drawn between the open circuit phase voltage
E
p= E
t/√3 and the field current I
f.
Field current I
f Open circuit
phase voltage
E
p= E
t/√3
OPEN CIRCUIT CHARACTERISTICS
UEEC007 -ISM
Open circuit Voltage (
�
��
)
Field Current (??????
�)
Residual Voltage
Air Gap Line
occ
UEEC007 -ISM
Open circuit Voltage (
�
��
)
Field Current (??????
�)
Residual Voltage
Air Gap Line
occ
Short Circuit Test
UEEC007 -ISM
The armature terminals are shorted through three ammeters
The field current should first be decreased to zero before starting the
alternator
The alternator is then run at synchronous speed
The field current is increased to get armature currents up to 150% of
the rated value
A graph is plotted between the armature current ??????
��and the field current
??????
�
Field current I
f Armature S.C
current ??????
��
UEEC007 -ISM
The armature terminals are shorted through three ammeters
The field current should first be decreased to zero before starting the
alternator
The alternator is then run at synchronous speed
The field current is increased to get armature currents up to 150% of
the rated value
A graph is plotted between the armature current ??????
��and the field current
??????
�
Field current I
f Armature S.C
current ??????
��
SHORT CIRCUIT CHARACTERISTICS
UEEC007 -ISM
Short Circuit Current (
??????
��
)
Field Current (??????
�)
scc
UEEC007 -ISM
Short Circuit Current (
??????
��
)
Field Current (??????
�)
scc
Calculation of Synchronous Impedance
UEEC007 -ISM
Open circuit Voltage (
�
��
)
Field Current (??????
�)
occ
Short Circuit Current (
??????
��
)
O
B
C
scc
����ℎ������??????���������
�=
�����??????���??????������������ℎ���
�ℎ����??????���??????����������������
(����ℎ�������������??????����������)
�
�=
��
��
(for the same OA)
A
UEEC007 -ISM
Open circuit Voltage (
�
��
)
Field Current (??????
�)
occ
Short Circuit Current (
??????
��
)
O
B
C
scc
����ℎ������??????���������
�=
�����??????���??????������������ℎ���
�ℎ����??????���??????����������������
(����ℎ�������������??????����������)
�
�=
��
��
(for the same OA)
A
Calculation of Synchronous
Reactance &Voltage Regulation
UEEC007 -ISM
����ℎ����������������
�= �
�
2
−�
??????
2
�
�=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
% Voltage Regulation =
??????
�−??????
??????
∗100
??????
??????�
??????
??????
??????�
��
�
2
=�
�
2
+�
??????
2
�
�
2
=�
�
2
-�
??????
2
EMF METHOD –All
Quantities are EMF
quantities
Reactance &Voltage Regulation
UEEC007 -ISM
����ℎ����������������
�= �
�
2
−�
??????
2
�
�=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
% Voltage Regulation =
??????
�−??????
??????
∗100
??????
??????�
??????
??????
??????�
��
�
2
=�
�
2
+�
??????
2
�
�
2
=�
�
2
-�
??????
2
EMF METHOD –All
Quantities are EMF
quantities
Salient Points
•Regulationobtainedbyusingasynchronousimpedancemethodishigherthanthat
obtainedbyactualloading.
•Hence,thismethodisalsocalledthePessimisticmethod.
•Theoreticallycorrectfornonsalientpolemachineswithdistributedwindingswhen
saturationisnotconsidered.
UEEC007 -ISM
??????
���??????
At lower excitations,Z
Sisconstant,
since the open circuit characteristics
coincide with the air gap line. This value
of Z
Sis called thelinearorUnsaturated
Synchronous Impedance
However, with increasing excitation, the
effect of saturation is to decrease Z
Sand
the values beyond the linear part of the
open circuit called asSaturated
Valueof the Synchronous Impedance
Open circuit Voltage (
�
��
)
Field Current (??????
�)
Air Gap Line
occ
•Regulationobtainedbyusingasynchronousimpedancemethodishigherthanthat
obtainedbyactualloading.
•Hence,thismethodisalsocalledthePessimisticmethod.
•Theoreticallycorrectfornonsalientpolemachineswithdistributedwindingswhen
saturationisnotconsidered.
UEEC007 -ISM
??????
���??????
At lower excitations,Z
Sisconstant,
since the open circuit characteristics
coincide with the air gap line. This value
of Z
Sis called thelinearorUnsaturated
Synchronous Impedance
However, with increasing excitation, the
effect of saturation is to decrease Z
Sand
the values beyond the linear part of the
open circuit called asSaturated
Valueof the Synchronous Impedance
Open circuit Voltage (
�
��
)
Field Current (??????
�)
Air Gap Line
occ
Problem
Theopencircuitandshortcircuittestconductedona3phasestarconnected866V100kva
alternatorgavethefollowingdata,
Thefieldcurrentof1Aproducedashortcircuitcurrentof25A.Thearmatureresistanceperphaseis
0.15Ω.Calculateitsfullloadregulationat0.8laggingpowerfactor.
UEEC007 -ISM
Field current
I
f 1 2 3 4 5 6 7
Open Circuit
Voltage �
��
173 310 485 605 728 790 840
Theopencircuitandshortcircuittestconductedona3phasestarconnected866V100kva
alternatorgavethefollowingdata,
Thefieldcurrentof1Aproducedashortcircuitcurrentof25A.Thearmatureresistanceperphaseis
0.15Ω.Calculateitsfullloadregulationat0.8laggingpowerfactor.
UEEC007 -ISM
Field current
I
f 1 2 3 4 5 6 7
Open Circuit
Voltage �
��
173 310 485 605 728 790 840
Steps
UEEC007 -ISM
���=3�
????????????
??????10
−3
Given Line Voltage –convert to phase voltages-draw the OCC
Calculate the armature current using the formula
Draw the SCC
and check whether the alternator is star or delta connected ??????
??????=??????
�ℎ
% Voltage Regulation =
??????
�−??????
??????
∗100
�
�=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
����ℎ����������������
�= �
�
2
−�
??????
2
�
�=
��
��
(for the same OA)
Open circuit Voltage per phase (
�
��
)
occ
Short Circuit Current (
??????
��
)
O
B
C
scc
A Field Current (??????
�)
UEEC007 -ISM
���=3�
????????????
??????10
−3
Given Line Voltage –convert to phase voltages-draw the OCC
Calculate the armature current using the formula
Draw the SCC
and check whether the alternator is star or delta connected ??????
??????=??????
�ℎ
% Voltage Regulation =
??????
�−??????
??????
∗100
�
�=(�
�ℎcosφ+??????
??????�
??????)
2
+(�
�ℎ�??????�φ +??????
??????�
�)
2
����ℎ����������������
�= �
�
2
−�
??????
2
�
�=
��
��
(for the same OA)
Open circuit Voltage per phase (
�
��
)
occ
Short Circuit Current (
??????
��
)
O
B
C
scc
A Field Current (??????
�)
UEEC007 -ISM
MMF METHOD
•AmpereturnsmethodorRothert'sMMFmethod
•MMFisproductoffieldcurrentandturnsofthefieldwinding-??????
��
�
1.ItmusthaveanMMFnecessarytoinducetheratedterminalvoltageontheopen
circuit.
2.ItmusthaveanMMFequalandoppositetothatofarmaturereactionMMF.
UEEC007 -ISM
•AmpereturnsmethodorRothert'sMMFmethod
•MMFisproductoffieldcurrentandturnsofthefieldwinding-??????
��
�
1.ItmusthaveanMMFnecessarytoinducetheratedterminalvoltageontheopen
circuit.
2.ItmusthaveanMMFequalandoppositetothatofarmaturereactionMMF.
UEEC007 -ISM
Voltage Drops
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
UEEC007 -ISM
SMALL
MMF -??????
��
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
UEEC007 -ISM
SMALL
MMF -??????
��
Open Circuit Test
ThefieldMMFwhichisrequiredforinducingtherated
terminalvoltageontheopencircuitcanbeobtainedfrom
opencircuittestresultsandopencircuitcharacteristics.
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
�
�
Rated Terminal Voltage MMF -??????
�
ThefieldMMFwhichisrequiredforinducingtherated
terminalvoltageontheopencircuitcanbeobtainedfrom
opencircuittestresultsandopencircuitcharacteristics.
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
�
�
Rated Terminal Voltage MMF -??????
�
Armature Resistance
•Whenthearmatureresistanceisneglectedthen??????
�isfieldmmfrequiredtoproducerated
Voltageattheoutputterminals.
•Butiftheeffectivearmatureresistance�
??????,isgiventhen??????
�istobecalculatedfrom
O.C.C.suchthat??????
�representstheexcitation(fieldcurrent)requiredtoproduceavoltage
of??????
??????�+??????
????????????��
??????????????????????????????
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
�
�
??????
??????�+ ??????
????????????��
??????????????????????????????
•Whenthearmatureresistanceisneglectedthen??????
�isfieldmmfrequiredtoproducerated
Voltageattheoutputterminals.
•Butiftheeffectivearmatureresistance�
??????,isgiventhen??????
�istobecalculatedfrom
O.C.C.suchthat??????
�representstheexcitation(fieldcurrent)requiredtoproduceavoltage
of??????
??????�+??????
????????????��
??????????????????????????????
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
�
�
??????
??????�+ ??????
????????????��
??????????????????????????????
Short Circuit Test
•Inshortcircuittest,fieldMMFcirculatesthefullload
currentbalancingthearmaturereactioneffect.The
valueofampere-turnsrequiredtocirculatefullload
currentcanbeobtainedfromshortcircuit
characteristics.
UEEC007 -ISM
MMF -??????
��
Short Circuit Current (??????
��)
Field Current (??????
�)
scc
�
��
Full Load Short Circuit Current (??????
��)
•Inshortcircuittest,fieldMMFcirculatesthefullload
currentbalancingthearmaturereactioneffect.The
valueofampere-turnsrequiredtocirculatefullload
currentcanbeobtainedfromshortcircuit
characteristics.
UEEC007 -ISM
MMF -??????
��
Short Circuit Current (??????
��)
Field Current (??????
�)
scc
�
��
Full Load Short Circuit Current (??????
��)
OCC and SCC
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
Short Circuit Current (??????
��)
scc
�
�
Rated Terminal Voltage
�
��
Full Load Short Circuit Current
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
Short Circuit Current (??????
��)
scc
�
�
Rated Terminal Voltage
�
��
Full Load Short Circuit Current
Resultant MMF
•Ifthealternatorissupplyingfullload,thentotalfieldMMFis
thevectorsumofitstwocomponents�
�and�
��
•TheresultantfieldMMFisdenotedas�
�
•�
�=�
�+�
��
•Thisdependsonthepowerfactoroftheloadwhich
alternatorissupplying.
UEEC007 -ISM
•Ifthealternatorissupplyingfullload,thentotalfieldMMFis
thevectorsumofitstwocomponents�
�and�
��
•TheresultantfieldMMFisdenotedas�
�
•�
�=�
�+�
��
•Thisdependsonthepowerfactoroftheloadwhich
alternatorissupplying.
UEEC007 -ISM
Zero lagging p.f
UEEC007 -ISM
�
�
�
��
ARMATURE REACTION -DEMAGNETIZING
O A
B
�
�= �
�+�
��
OA = �
�
AB= �
��
OB=�
�= OA+AB = �
�+�
��
�
�
O
B
UEEC007 -ISM
�
�
�
��
ARMATURE REACTION -DEMAGNETIZING
O A
B
�
�= �
�+�
��
OA = �
�
AB= �
��
OB=�
�= OA+AB = �
�+�
��
�
�
O
B
Zero leading p.f
UEEC007 -ISM
�
�
�
��
ARMATURE REACTION -MAGNETIZING
O A
A
�
�= �
�−�
��
OB = �
�
BA= �
��
OA=�
�= OB-BA = �
�−�
��
�
�
O
B
UEEC007 -ISM
�
�
�
��
ARMATURE REACTION -MAGNETIZING
O A
A
�
�= �
�−�
��
OB = �
�
BA= �
��
OA=�
�= OB-BA = �
�−�
��
�
�
O
B
Unity p.f
UEEC007 -ISM
ARMATURE REACTION –CROSS MAGNETIZING
�
�
�
��
O A
B
�
�
�
�= �
�+�
��
OA = �
�
AB= �
��
OB=�
�= OA+AB = �
�+�
��
UEEC007 -ISM
ARMATURE REACTION –CROSS MAGNETIZING
�
�
�
��
O A
B
�
�
�
�= �
�+�
��
OA = �
�
AB= �
��
OB=�
�= OA+AB = �
�+�
��
OCC and SCC
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
Short Circuit Current (??????
��)
scc
�
�
Rated Terminal Voltage
�
��
Full Load Short Circuit Current
�
�
�
�
% Voltage Regulation =
??????�−??????
??????
∗100
UEEC007 -ISM
Open circuit Voltage (�
��)
Field Current (??????
�)
occ
Short Circuit Current (??????
��)
scc
�
�
Rated Terminal Voltage
�
��
Full Load Short Circuit Current
�
�
�
�
% Voltage Regulation =
??????�−??????
??????
∗100
O
cos Φ, lagging p.f
UEEC007 -ISM
�
�ℎ
??????
??????�ℎ
??????
�
�
−�
���
�
�
�
90°
90°
�
��
?????? 90°
�
�ℎ
?????? �
�ℎ
90°
90°+??????
??????
�
��cos??????
�
��sin??????
A
B C
��=�
���=�
�
��=�
��
��=�
��sin??????
��=�
��cos??????
��C
OCB
��
2
=��
2
+��
2
��
2
=(��+��)
2
+��
2
�
�
2
=(�
�+�
��sin??????)
2
+(�
��cos??????)
2
�
�=(�
�+�
��sin??????)
2
+(�
��cos??????)
2
??????
90°
90°+??????
cos Φ, lagging p.f
UEEC007 -ISM
�
�ℎ
??????
??????�ℎ
??????
�
�
−�
���
�
�
�
90°
90°
�
��
?????? 90°
�
�ℎ
?????? �
�ℎ
90°
90°+??????
??????
�
��cos??????
�
��sin??????
A
B C
��=�
���=�
�
��=�
��
��=�
��sin??????
��=�
��cos??????
��C
OCB
��
2
=��
2
+��
2
��
2
=(��+��)
2
+��
2
�
�
2
=(�
�+�
��sin??????)
2
+(�
��cos??????)
2
�
�=(�
�+�
��sin??????)
2
+(�
��cos??????)
2
??????
90°
90°+??????
Cos Φ, leading p.f
UEEC007 -ISM
�
�ℎ
??????
??????�ℎ
�
��
??????
O
�
�
A−�
��
�
�
90°
�
�
90°
??????
90°
90°−??????
B
C
�
��sin??????
��=�
���=�
�
��=�
��
��=�
��sin??????
��C
OCB
��
2
=��
2
+��
2
��
2
=(��−��)
2
+��
2
�
�
2
=(�
�−�
��sin??????)
2
+(�
��cos??????)
2
�
�=(�
�−�
��sin??????)
2
+(�
��cos??????)
2
MMF METHOD –All
Quantities are MMF
quantities
UEEC007 -ISM
�
�ℎ
??????
??????�ℎ
�
��
??????
O
�
�
A−�
��
�
�
90°
�
�
90°
??????
90°
90°−??????
B
C
�
��sin??????
��=�
���=�
�
��=�
��
��=�
��sin??????
��C
OCB
��
2
=��
2
+��
2
��
2
=(��−��)
2
+��
2
�
�
2
=(�
�−�
��sin??????)
2
+(�
��cos??????)
2
�
�=(�
�−�
��sin??????)
2
+(�
��cos??????)
2
MMF METHOD –All
Quantities are MMF
quantities
Cosine Rule to Triangle
UEEC007 -ISM
�
�
B
�
��
O A
90°+??????for Lagging90°−??????forleading
O A
�
�
B
�
��
�
�
�
�
90°−??????
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(�
��
��)
90°+??????
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°+??????))
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°−??????))
UEEC007 -ISM
�
�
B
�
��
O A
90°+??????for Lagging90°−??????forleading
O A
�
�
B
�
��
�
�
�
�
90°−??????
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(�
��
��)
90°+??????
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°+??????))
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°−??????))
Salient Points
•Thisampere turn methodgives thevoltage regulation of
analternatorwhich is lower than that actually observed.
Hence this MMF method is calledoptimistic method.
•The excitation required to overcome the armature
reaction is determined on the unsaturated part of the
saturation curve.
UEEC007 -ISM
•Thisampere turn methodgives thevoltage regulation of
analternatorwhich is lower than that actually observed.
Hence this MMF method is calledoptimistic method.
•The excitation required to overcome the armature
reaction is determined on the unsaturated part of the
saturation curve.
UEEC007 -ISM
Problem
Theopencircuitandshortcircuittestconductedona3phasestarconnected1905V1000kva50Hz
alternatorgavethefollowingdata,
Thearmatureresistanceperphaseis0.2Ω.Calculateitsfullloadregulationat0.8laggingpower
factorbyEMFandMMFmethod.
UEEC007 -ISM
Open Circuit
Voltage ??????
????????????
7601500 1700 1905 2300 2600
Field current I
f10 20 25 30 40 50
ShortCircuit
current I
sc - - - 335 - -
Theopencircuitandshortcircuittestconductedona3phasestarconnected1905V1000kva50Hz
alternatorgavethefollowingdata,
Thearmatureresistanceperphaseis0.2Ω.Calculateitsfullloadregulationat0.8laggingpower
factorbyEMFandMMFmethod.
UEEC007 -ISM
Open Circuit
Voltage ??????
????????????
7601500 1700 1905 2300 2600
Field current I
f10 20 25 30 40 50
ShortCircuit
current I
sc - - - 335 - -
STEPS
•??????
??????�+ ??????
????????????��
??????????????????????????????, from OCC find �
�
•Find the full load short circuit armature current per phase
•Filed current of 30A produces a short circuit current of 335 A , from SCC
find�
�������������??????�������������������������������������.
•Find �
�corresponding to the calculated �
�
•Find Voltage Regulation
??????
�−??????
??????
∗100
UEEC007 -ISM
���=3�
????????????
??????10
−3
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°+??????)
•??????
??????�+ ??????
????????????��
??????????????????????????????, from OCC find �
�
•Find the full load short circuit armature current per phase
•Filed current of 30A produces a short circuit current of 335 A , from SCC
find�
�������������??????�������������������������������������.
•Find �
�corresponding to the calculated �
�
•Find Voltage Regulation
??????
�−??????
??????
∗100
UEEC007 -ISM
���=3�
????????????
??????10
−3
�
�
2
=�
�
2
+�
��
2
-2�
��
��cos(90°+??????)
MMF METHOD
UEEC007 -ISM
UEEC007 -ISM
MMF METHOD
UEEC007 -ISM
UEEC007 -ISM
MMF METHOD
UEEC007 -ISM
UEEC007 -ISM
EMF METHOD
UEEC007 -ISM
UEEC007 -ISM
EMF AND MMF Quantities
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
•EMF Method –All drops as EMF quantities
•MMF Method –All quantities as MMF quantities
UEEC007 -ISM
EMF Quantity
MMF Quantity
EMF Quantity
•Armature Reaction Reactance ??????
??????�
??????�(fictitious)
•Armature Resistance ??????
??????�
??????
•Leakage Reactance ??????
??????�
�
•EMF Method –All drops as EMF quantities
•MMF Method –All quantities as MMF quantities
UEEC007 -ISM
EMF Quantity
MMF Quantity
EMF Quantity
ZPF Method
•ThisZPFmethodisbasedontheseparationof
armatureleakagereactanceandarmaturereaction
effects
•Thearmatureleakagereactance�
�iscalledPotier
reactanceinthismethod,henceZPFmethodisalso
calledPotierreactancemethod
UEEC007 -ISM
•ThisZPFmethodisbasedontheseparationof
armatureleakagereactanceandarmaturereaction
effects
•Thearmatureleakagereactance�
�iscalledPotier
reactanceinthismethod,henceZPFmethodisalso
calledPotierreactancemethod
UEEC007 -ISM
OCC and ZPF Test
•Todeterminearmatureleakagereactanceandarmature
reactionMMFseparatelytwotestsareperformedon
thealternator.
1. Open circuit test
2. Zero power factor test
UEEC007 -ISM
•Todeterminearmatureleakagereactanceandarmature
reactionMMFseparatelytwotestsareperformedon
thealternator.
1. Open circuit test
2. Zero power factor test
UEEC007 -ISM
Open Circuit Test
UEEC007 -ISM
Alternator is running at the rated synchronous speed,theload
terminals are kept open
After setting the field current to zero, the field current is
gradually increased step by step
The excitation current may be increased to get 25% more than
the rated voltage
The terminal voltage E
tis measured at each step
A graph is drawn between the open circuit phase voltage
E
p= E
t/√3 and the field current I
f.
Field current I
f Open Circuit
Voltage per phase
E
p= E
t/√3
UEEC007 -ISM
Alternator is running at the rated synchronous speed,theload
terminals are kept open
After setting the field current to zero, the field current is
gradually increased step by step
The excitation current may be increased to get 25% more than
the rated voltage
The terminal voltage E
tis measured at each step
A graph is drawn between the open circuit phase voltage
E
p= E
t/√3 and the field current I
f.
Field current I
f Open Circuit
Voltage per phase
E
p= E
t/√3
ZPF Test
UEEC007 -ISM
UEEC007 -ISM
ZPF Steps
•Toconductzeropowerfactortest,theTPSTswitchiskeptclosed.
•Duetothis,apurelyinductiveloadgetsconnectedtoanalternatorthrough
anammeter.
•Apurelyinductiveloadhasapowerfactorofcos90°i.e.zerolagginghence
thetestiscalledzeropowerfactortest.
UEEC007 -ISM
•Toconductzeropowerfactortest,theTPSTswitchiskeptclosed.
•Duetothis,apurelyinductiveloadgetsconnectedtoanalternatorthrough
anammeter.
•Apurelyinductiveloadhasapowerfactorofcos90°i.e.zerolagginghence
thetestiscalledzeropowerfactortest.
UEEC007 -ISM
ZPF Steps
•Themachinespeedismaintainedconstantatitssynchronousvalue.
•Theloadcurrentdeliveredbyanalternatortopurelyinductiveloadis
maintainedconstantatitsratedfullloadvaluebyvaryingexcitationandby
adjustingvariableinductanceoftheinductivebed.
•Duetopurelyinductiveload,thealternatorwillalwaysoperateatzero
powerfactorlagging.
UEEC007 -ISM
•Themachinespeedismaintainedconstantatitssynchronousvalue.
•Theloadcurrentdeliveredbyanalternatortopurelyinductiveloadis
maintainedconstantatitsratedfullloadvaluebyvaryingexcitationandby
adjustingvariableinductanceoftheinductivebed.
•Duetopurelyinductiveload,thealternatorwillalwaysoperateatzero
powerfactorlagging.
UEEC007 -ISM
Zero Power Factorsaturation curve
•Firstpointforthiscurveiszeroterminalvoltage(shortcircuitcondition)
andthefieldcurrentrequiredtodeliverfullloadshortcircuitarmature
current.
•Secondpointfieldcurrentrequiredtoobtainratedterminalvoltagewhile
deliveringratedfullloadarmaturecurrent
UEEC007 -ISM
•Firstpointforthiscurveiszeroterminalvoltage(shortcircuitcondition)
andthefieldcurrentrequiredtodeliverfullloadshortcircuitarmature
current.
•Secondpointfieldcurrentrequiredtoobtainratedterminalvoltagewhile
deliveringratedfullloadarmaturecurrent
UEEC007 -ISM
ZPF CURVE
UEEC007 -ISM
Terminal Voltage
and Induced EMF
per phase
Field Current (??????
�)
Air Gap Line occ
O
A
R
Q
P
S
A-at zero terminal voltage (short circuit condition)
and the field current required to deliver full load
short circuit armature current
P-field current required to obtain rated terminal
voltage while delivering rated full load armature
current
Rated Voltage
when delivering
full current at zero
power factor
lagging
R’
Q’
P’
S’
R’
Q’
P’
S’
R’
Q’
P’S’
B
C
Full Load Zero pf Saturation Curve
POTIER TRIANGLE
A’
UEEC007 -ISM
Terminal Voltage
and Induced EMF
per phase
Field Current (??????
�)
Air Gap Line occ
O
A
R
Q
P
S
A-at zero terminal voltage (short circuit condition)
and the field current required to deliver full load
short circuit armature current
P-field current required to obtain rated terminal
voltage while delivering rated full load armature
current
Rated Voltage
when delivering
full current at zero
power factor
lagging
R’
Q’
P’
S’
R’
Q’
P’
S’
R’
Q’
P’S’
B
C
Full Load Zero pf Saturation Curve
POTIER TRIANGLE
A’
Steps
1.Plot open circuit characteristics
2.Plot the excitation corresponding to zero terminal voltage i.e. short
circuit fullzero power factorarmature current. This point is A.
3.Another point is the rated voltage when thealternatoris delivering
full current at zero p.f. lagging. This point is P.
UEEC007 -ISM
1.Plot open circuit characteristics
2.Plot the excitation corresponding to zero terminal voltage i.e. short
circuit fullzero power factorarmature current. This point is A.
3.Another point is the rated voltage when thealternatoris delivering
full current at zero p.f. lagging. This point is P.
UEEC007 -ISM
Steps
4.Draw the tangent to O.C.C. through origin. This is called the airline.
5.Draw the horizontal line PQ parallel and equal to OA.
6.From the point, Q draw the line parallel to the airline which intersects
O.C.C. at point R. Join RQ and join PR. The triangle PQR is calledPotier
triangle.
UEEC007 -ISM
4.Draw the tangent to O.C.C. through origin. This is called the airline.
5.Draw the horizontal line PQ parallel and equal to OA.
6.From the point, Q draw the line parallel to the airline which intersects
O.C.C. at point R. Join RQ and join PR. The triangle PQR is calledPotier
triangle.
UEEC007 -ISM
Steps
7.FrompointR,dropaperpendicularonPQtomeetatpointS.
8.Thezeropowerfactorfullloadsaturationcurveisnowbeconstructedby
movingtrianglePQRsothatRremainsalwaysonOCCandlinePQalways
remainshorizontal.
Note:Potiertriangleonceobtainedisconstantforagivenarmaturecurrent
andhencecanbetransferredasitis.
UEEC007 -ISM
7.FrompointR,dropaperpendicularonPQtomeetatpointS.
8.Thezeropowerfactorfullloadsaturationcurveisnowbeconstructedby
movingtrianglePQRsothatRremainsalwaysonOCCandlinePQalways
remainshorizontal.
Note:Potiertriangleonceobtainedisconstantforagivenarmaturecurrent
andhencecanbetransferredasitis.
UEEC007 -ISM
Steps
9.ThoughpointA,drawalineparalleltoPRmeetingOCCatpointB.
FromB,drawaperpendicularonOAtomeetitatpointC.
TrianglesOABandPQRaresimilartriangles.
UEEC007 -ISM
P
R
SQ
A
CO
B
9.ThoughpointA,drawalineparalleltoPRmeetingOCCatpointB.
FromB,drawaperpendicularonOAtomeetitatpointC.
TrianglesOABandPQRaresimilartriangles.
UEEC007 -ISM
P
R
SQ
A
CO
B
Potier Triangle
UEEC007 -ISM
P
R
SQ
A
CO
B
∆���??????��∆���??????�������??????����??????������
The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. ??????
????????????
�
The length PS gives field current necessary to overcome the demagnetizing effect of armature reaction at full load
The length SQ represents field current required to induce an EMF for balancing leakage reactance drop RS
Length of (RS) = Length of (BC)= ??????
????????????�(??????.??????)??????
�??????�Potier Reactance ??????
�??????�=
Lengthof(RS)orLengthof(BC)
??????
????????????�(??????.??????)
UEEC007 -ISM
P
R
SQ
A
CO
B
∆���??????��∆���??????�������??????����??????������
The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. ??????
????????????
�
The length PS gives field current necessary to overcome the demagnetizing effect of armature reaction at full load
The length SQ represents field current required to induce an EMF for balancing leakage reactance drop RS
Length of (RS) = Length of (BC)= ??????
????????????�(??????.??????)??????
�??????�Potier Reactance ??????
�??????�=
Lengthof(RS)orLengthof(BC)
??????
????????????�(??????.??????)
Phasor Diagram
UEEC007 -ISM
??????
�
�ℎ
??????
??????�ℎ ??????
??????�ℎ�
??????�ℎ
??????
????????????�(??????.??????)??????
�??????�
�
�ℎ
�
�1
�
��
�
�
�
1�ℎ
Armature Reaction Drop
o
A
B
C
D
E
F
G
H
90°+??????
90°
90°
UEEC007 -ISM
??????
�
�ℎ
??????
??????�ℎ ??????
??????�ℎ�
??????�ℎ
??????
????????????�(??????.??????)??????
�??????�
�
�ℎ
�
�1
�
��
�
�
�
1�ℎ
Armature Reaction Drop
o
A
B
C
D
E
F
G
H
90°+??????
90°
90°
STEPS
1.Drawtheratedterminalvoltage�
�ℎasareferencephasor.
Dependinguponatwhichpowerfactor(cos??????)theregulationistobe
predicted,drawtheCurrentphasor??????
??????�ℎlaggingorleading�
�ℎby
angle??????.
2.Draw??????
??????�ℎ�
??????�ℎvoltagedropto�
�ℎwhichisinphasewith??????
??????�ℎ.While
thevoltagedrop??????
????????????�(??????.??????)??????
�??????�istobedrawnperpendicularto??????
??????�ℎ�
??????�ℎ,
vectorbutleading??????
??????�ℎ�
??????�ℎattheextremityof�
�ℎ.
UEEC007 -ISM
1.Drawtheratedterminalvoltage�
�ℎasareferencephasor.
Dependinguponatwhichpowerfactor(cos??????)theregulationistobe
predicted,drawtheCurrentphasor??????
??????�ℎlaggingorleading�
�ℎby
angle??????.
2.Draw??????
??????�ℎ�
??????�ℎvoltagedropto�
�ℎwhichisinphasewith??????
??????�ℎ.While
thevoltagedrop??????
????????????�(??????.??????)??????
�??????�istobedrawnperpendicularto??????
??????�ℎ�
??????�ℎ,
vectorbutleading??????
??????�ℎ�
??????�ℎattheextremityof�
�ℎ.
UEEC007 -ISM
STEPS
3.The�
??????�ℎistobemeasuredseparatelybypassingad.ccurrentand
measuringthevoltageacrossarmaturewinding.While??????
�??????�isPotier
reactanceobtainedbyPotiermethod.
4.Phasorsumof�
�ℎrated,??????
??????�ℎ�
??????�ℎand??????
????????????�(??????.??????)??????
�??????�givesthee.m.f.
whichissay�
1�ℎ
�
1�ℎ=�
�ℎ+??????
??????�ℎ�
??????�ℎ+??????
????????????�(??????.??????)??????
�??????�
UEEC007 -ISM
3.The�
??????�ℎistobemeasuredseparatelybypassingad.ccurrentand
measuringthevoltageacrossarmaturewinding.While??????
�??????�isPotier
reactanceobtainedbyPotiermethod.
4.Phasorsumof�
�ℎrated,??????
??????�ℎ�
??????�ℎand??????
????????????�(??????.??????)??????
�??????�givesthee.m.f.
whichissay�
1�ℎ
�
1�ℎ=�
�ℎ+??????
??????�ℎ�
??????�ℎ+??????
????????????�(??????.??????)??????
�??????�
UEEC007 -ISM
STEPS
5.Obtaintheexcitationcorrespondingto�
1�ℎfromOCCwhichis
drawn.Letthisexcitationbe�
�1.Thisisexcitationrequiredfor
inducingEMFwhichdoesnotconsidertheeffectofarmaturereaction.
6.Thefieldcurrentrequiredtobalancearmaturereactioncanbe
obtainedfromPotiertrianglemethod,whichissay�
��.
�
��=Lenght(PS)=Lenght(AC)
UEEC007 -ISM
P
R
SQ
A
CO
B
Open circuit Voltage (�
��)
Field Current (??????
�)
�
1�ℎ
�
�1
5.Obtaintheexcitationcorrespondingto�
1�ℎfromOCCwhichis
drawn.Letthisexcitationbe�
�1.Thisisexcitationrequiredfor
inducingEMFwhichdoesnotconsidertheeffectofarmaturereaction.
6.Thefieldcurrentrequiredtobalancearmaturereactioncanbe
obtainedfromPotiertrianglemethod,whichissay�
��.
�
��=Lenght(PS)=Lenght(AC)
UEEC007 -ISM
P
R
SQ
A
CO
B
Open circuit Voltage (�
��)
Field Current (??????
�)
�
1�ℎ
�
�1
STEPS
6.Thetotalexcitationrequiredisthevectorsumofthe�
�1and�
��.
ThiscanbeobtainedexactlysimilartotheprocedureusedinMMF
Method.
7.Drawvector�
�1tosomescale,leading�
1�ℎby90°.Add�
��to
�
�1bydrawingvector�
��inphaseoppositionto??????
??????�ℎ.Thetotal
excitationtobesuppliedbyfieldisgivenby�
�.
UEEC007 -ISM
B
O A
90°+??????
�
�1
�
��
�
�
6.Thetotalexcitationrequiredisthevectorsumofthe�
�1and�
��.
ThiscanbeobtainedexactlysimilartotheprocedureusedinMMF
Method.
7.Drawvector�
�1tosomescale,leading�
1�ℎby90°.Add�
��to
�
�1bydrawingvector�
��inphaseoppositionto??????
??????�ℎ.Thetotal
excitationtobesuppliedbyfieldisgivenby�
�.
UEEC007 -ISM
B
O A
90°+??????
�
�1
�
��
�
�
STEPS
8.Once the total excitation is known which is �
�, the corresponding
induced emf �
�ℎcan be obtained from OCC
This �
�ℎlags �
�by 90°
The length CD is the drop due to the armature reaction
UEEC007 -ISM
Open circuit Voltage
(�
��)
Field
Current (??????
�)
�
�ℎ
�
�
8.Once the total excitation is known which is �
�, the corresponding
induced emf �
�ℎcan be obtained from OCC
This �
�ℎlags �
�by 90°
The length CD is the drop due to the armature reaction
UEEC007 -ISM
Open circuit Voltage
(�
��)
Field
Current (??????
�)
�
�ℎ
�
�
STEPS
9.Draw perpendicular from A and B on current phasor meeting at
points G and H respectively, the triangle OHC as right-angle triangle.
Hence �
1�ℎcan be determined, analytically.
UEEC007 -ISM
% Voltage Regulation =
??????
??????ℎ−??????
??????ℎ
??????
??????ℎ
∗100
9.Draw perpendicular from A and B on current phasor meeting at
points G and H respectively, the triangle OHC as right-angle triangle.
Hence �
1�ℎcan be determined, analytically.
UEEC007 -ISM
% Voltage Regulation =
??????
??????ℎ−??????
??????ℎ
??????
??????ℎ
∗100
Drawbacks
TheonlydrawbackoftheZPFmethodisthattheseparatecurvefor
everyloadconditionisnecessarytoplotifPotiertrianglesforvarious
loadconditionsarerequired.
UEEC007 -ISM
TheonlydrawbackoftheZPFmethodisthattheseparatecurvefor
everyloadconditionisnecessarytoplotifPotiertrianglesforvarious
loadconditionsarerequired.
UEEC007 -ISM
Assumptions
•lntheentirecalculationprocedureofPotiermethod,thearmature
resistanceisneglected.Butpracticallyarmatureresistanceisvery
smallandhencethisassumptiondoesnotcausesignificanterrorin
theaccuracy.
•InPotiermethod,azeropowerfactortestisrequiredtobedone.But
practicallywheninductorsareused,aperfectzeropower
factorcannotbeachieved.
UEEC007 -ISM
•lntheentirecalculationprocedureofPotiermethod,thearmature
resistanceisneglected.Butpracticallyarmatureresistanceisvery
smallandhencethisassumptiondoesnotcausesignificanterrorin
theaccuracy.
•InPotiermethod,azeropowerfactortestisrequiredtobedone.But
practicallywheninductorsareused,aperfectzeropower
factorcannotbeachieved.
UEEC007 -ISM
Assumptions
•the distances RS, R' S' and BC are assumed equal
•This indicates that the point P in thezero power factor methodand
point A in the short circuit test represent the same leakage reactance
of the machine.
•Length OA<OA’
UEEC007 -ISM
P
R
SQ
A
CO
B
•the distances RS, R' S' and BC are assumed equal
•This indicates that the point P in thezero power factor methodand
point A in the short circuit test represent the same leakage reactance
of the machine.
•Length OA<OA’
UEEC007 -ISM
P
R
SQ
A
CO
B
Assumptions
•Hencepracticallytheleakagereactancecorrespondingtosaturated
conditionsishigherthanthatassumedinthemethod.This
introducestheerrorinthecalculations.
UEEC007 -ISM
•Hencepracticallytheleakagereactancecorrespondingtosaturated
conditionsishigherthanthatassumedinthemethod.This
introducestheerrorinthecalculations.
UEEC007 -ISM
Air Gap
UEEC007 -ISM
UEEC007 -ISM
Non Salient Pole Alternators
•Non-salient pole type alternators the air gap is uniform.
•Due to the uniform air gap, the field flux, as well as armature flux vary sinusoidally in the
air gap.
•In non salient polealternators, air gap length is constant and reactance is also constant.
•Due to this, the MMFs of armature and field act upon the same magnetic circuit all the
time hence can be added vectorially.
UEEC007 -ISM
•Non-salient pole type alternators the air gap is uniform.
•Due to the uniform air gap, the field flux, as well as armature flux vary sinusoidally in the
air gap.
•In non salient polealternators, air gap length is constant and reactance is also constant.
•Due to this, the MMFs of armature and field act upon the same magnetic circuit all the
time hence can be added vectorially.
UEEC007 -ISM
Salient Pole Alternators
•Insalient pole type alternators, the length of the air gap varies and the reluctance also
varies.
•Hence the armature flux and field flux cannot vary sinusoidally in the air gap.
•The reluctances of the magnetic circuits on which MMFs act are different in the case of
salient pole alternators.
UEEC007 -ISM
•Insalient pole type alternators, the length of the air gap varies and the reluctance also
varies.
•Hence the armature flux and field flux cannot vary sinusoidally in the air gap.
•The reluctances of the magnetic circuits on which MMFs act are different in the case of
salient pole alternators.
UEEC007 -ISM
Field and Armature MMF
UEEC007 -ISM
UEEC007 -ISM
D-axis and q-axis
•The reluctance offered to the MMF wave is lowest when it is aligned
with the field pole axis.
•This axis is called the direct axis of pole i.e. d-axis.
•The reluctance offered is highest when the MMF wave is oriented at
90°to the field pole axis which is called quadrature axis i.e. q-axis.
UEEC007 -ISM
•The reluctance offered to the MMF wave is lowest when it is aligned
with the field pole axis.
•This axis is called the direct axis of pole i.e. d-axis.
•The reluctance offered is highest when the MMF wave is oriented at
90°to the field pole axis which is called quadrature axis i.e. q-axis.
UEEC007 -ISM
d-axis and q-axis
•Thecomponentwhichisactingalongthedirectaxiscanbe
magnetizingordemagnetizing.
•Thecomponentwhichisactingalongquadratureaxisiscross
magnetizing.
UEEC007 -ISM
•Thecomponentwhichisactingalongthedirectaxiscanbe
magnetizingordemagnetizing.
•Thecomponentwhichisactingalongquadratureaxisiscross
magnetizing.
UEEC007 -ISM
Field MMF
•Theairgapisleastinthecentreofthepolesandprogressively
increase,onmovingawayfromthecentre.
•Duetosuchshapeofthepole-shoes,thefieldwindingwoundon
salientpolesproducestheMMFwavewhichisnearlysinusoidaland
italwaysactsalongthepoleaxiswhichisdirectaxis.
UEEC007 -ISM
•Theairgapisleastinthecentreofthepolesandprogressively
increase,onmovingawayfromthecentre.
•Duetosuchshapeofthepole-shoes,thefieldwindingwoundon
salientpolesproducestheMMFwavewhichisnearlysinusoidaland
italwaysactsalongthepoleaxiswhichisdirectaxis.
UEEC007 -ISM
Armature MMF
The armature m.m.f. can be divided into two components as,
1.Component acting along the pole axis calleddirect axis.
2. Component acting at right angles to the pole axis calledquadrature
axis.
UEEC007 -ISM
The armature m.m.f. can be divided into two components as,
1.Component acting along the pole axis calleddirect axis.
2. Component acting at right angles to the pole axis calledquadrature
axis.
UEEC007 -ISM
Field MMF AND EMF
•Let �
�be the MMF wave produced by field winding, then it always
acts along the direct axis.
•This MMF is responsible for producing an excitation EMF �
�which
lags �
�by all angle 90°.
UEEC007 -ISM
•Let �
�be the MMF wave produced by field winding, then it always
acts along the direct axis.
•This MMF is responsible for producing an excitation EMF �
�which
lags �
�by all angle 90°.
UEEC007 -ISM
Armature MMF
•Whenarmaturecarriescurrent,itproducesitsownMMFwave�
��
•Thiscanberesolvedintotwocomponents,oneactingalongd-axis
(magnetisingordemagnetising)andoneactingalongq-axis(cross-
magnetising).
•Similarly,armaturecurrent??????
??????alsocanindividedintotwo
components,onealongthedirectaxisandonealongquadrature
axis.
UEEC007 -ISM
•Whenarmaturecarriescurrent,itproducesitsownMMFwave�
��
•Thiscanberesolvedintotwocomponents,oneactingalongd-axis
(magnetisingordemagnetising)andoneactingalongq-axis(cross-
magnetising).
•Similarly,armaturecurrent??????
??????alsocanindividedintotwo
components,onealongthedirectaxisandonealongquadrature
axis.
UEEC007 -ISM
??????
��VS ??????
??????
Thereluctanceofferedtofluxalongthedirectaxisislessthanthe
reluctanceofferedtofluxalongquadratureaxis.
Duetothis,theflux??????
��isnolongeralong�
��or??????
??????.
Dependinguponthereluctancesofferedalongthedirectand
quadratureaxis,theflux??????
��lagsbehindarmaturecurrent??????
??????.
UEEC007 -ISM
��VS ??????
??????
Thereluctanceofferedtofluxalongthedirectaxisislessthanthe
reluctanceofferedtofluxalongquadratureaxis.
Duetothis,theflux??????
��isnolongeralong�
��or??????
??????.
Dependinguponthereluctancesofferedalongthedirectand
quadratureaxis,theflux??????
��lagsbehindarmaturecurrent??????
??????.
UEEC007 -ISM
UEEC007 -ISM
d-axis
q-axis??????
�
??????
�
??????
��
�
�
�
�
�
��
??????
�
??????
�
??????
??????
�
�
??????
�
�
�
����������������??????���ℎ����
d-axis
q-axis??????
�
??????
�
??????
��
�
�
�
�
�
��
??????
�
??????
�
??????
??????
�
�
??????
�
�
�
����������������??????���ℎ����
Induced EMF
UEEC007 -ISM
�−��??????�����??????
�= �
��
�
�−��??????�����
�=�
��.??????
�
�
�= Permeance along the direct axis
Permeance is the reciprocal of reluctance and
indicates ease with which flux can travel along the
path
�
��is the armature reaction coefficient
Flux =
���
������??????���
UEEC007 -ISM
�−��??????�����??????
�= �
��
�
�−��??????�����
�=�
��.??????
�
�
�= Permeance along the direct axis
Permeance is the reciprocal of reluctance and
indicates ease with which flux can travel along the
path
�
��is the armature reaction coefficient
Flux =
���
������??????���
Induced EMF
UEEC007 -ISM
�−��??????�����??????
�= �
��
��.??????
�
�−��??????�����??????
�= �
��
��.??????
�
�
�> �
�
�
�= �
�??????
�∠−90°
�−��??????�����
�=-j �
�??????
�
�
�= �
�??????
�∠−90°
�−��??????�����
�=-j �
�??????
�
�
�is the emf constant of the armature winding
UEEC007 -ISM
�−��??????�����??????
�= �
��
��.??????
�
�−��??????�����??????
�= �
��
��.??????
�
�
�> �
�
�
�= �
�??????
�∠−90°
�−��??????�����
�=-j �
�??????
�
�
�= �
�??????
�∠−90°
�−��??????�����
�=-j �
�??????
�
�
�is the emf constant of the armature winding
Induced EMF
UEEC007 -ISM
�������������
�=�
�+�
�+�
�
�
�=�
�−j�
�??????
�−j�
�??????
�
�
�=�
�−j�
��
��
��.??????
�−j�
��
��
��.??????
�
���??????�������������������������??????�����−��??????��
??????��=�
��
��
��
���??????�������������������������??????�����−��??????��
??????��=�
��
��
��
�
�=�
�−j�
??????��.??????
�−j�
??????��.??????
�
UEEC007 -ISM
�������������
�=�
�+�
�+�
�
�
�=�
�−j�
�??????
�−j�
�??????
�
�
�=�
�−j�
��
��
��.??????
�−j�
��
��
��.??????
�
���??????�������������������������??????�����−��??????��
??????��=�
��
��
��
���??????�������������������������??????�����−��??????��
??????��=�
��
��
��
�
�=�
�−j�
??????��.??????
�−j�
??????��.??????
�
Induced EMF
UEEC007 -ISM
??????
??????= ??????
�+??????
�
�
�=�
�+??????
??????�
??????+??????
��
??????+??????
��
??????
�
�+??????
??????�
??????+??????
��
??????+??????
��
??????=�
�−j�
??????��.??????
�−j�
??????��.??????
�
�
�=�
�+??????
??????�
??????+j(�
??????+�
??????��)??????
�+ j(�
??????+�
??????��) ??????
�
�
�=�
�+??????
??????�
??????+j(�
�)??????
�+ j(�
�) ??????
�
�
�-direct axis synchronous reactance
�
�−Quadratureaxissynchronousreactance
UEEC007 -ISM
??????
??????= ??????
�+??????
�
�
�=�
�+??????
??????�
??????+??????
��
??????+??????
��
??????
�
�+??????
??????�
??????+??????
��
??????+??????
��
??????=�
�−j�
??????��.??????
�−j�
??????��.??????
�
�
�=�
�+??????
??????�
??????+j(�
??????+�
??????��)??????
�+ j(�
??????+�
??????��) ??????
�
�
�=�
�+??????
??????�
??????+j(�
�)??????
�+ j(�
�) ??????
�
�
�-direct axis synchronous reactance
�
�−Quadratureaxissynchronousreactance
UEEC007 -ISM
Three Phase Induction Motor
UEEC007 -ISM
UEEC007 -ISM
Three Phase Induction motor
UEEC007 -ISM
UEEC007 -ISM
Types of Rotor
UEEC007 -ISM
UEEC007 -ISM
Squirrel Cage vs Slip Ring
UEEC007 -ISM
UEEC007 -ISM
Three phase stator winding
UEEC007 -ISM
UEEC007 -ISM
Three Phase Flux Waveforms
UEEC007 -ISM
UEEC007 -ISM
At Point 0 –0 degrees
UEEC007 -ISM
UEEC007 -ISM
At Point 1 –30 degrees
UEEC007 -ISM
UEEC007 -ISM
At Point 2 -60 degrees
UEEC007 -ISM
UEEC007 -ISM
At Point 3 –90 degrees
UEEC007 -ISM
UEEC007 -ISM
UEEC007 -ISM
Principle of Operation
•Three Phase supply –stator
•Rotating Magnetic Filed is produced –Synchronous
Speed
•A)Rotating Flux b) Stationary Rotor Conductors
•Stator Flux cut by the rotor conductor –emf induced
•Rotor Short Circuited –Current Flows to the rotor
•Current Carrying Conductor in a magnetic field –
Mechanical Force
UEEC007 -ISM
•Three Phase supply –stator
•Rotating Magnetic Filed is produced –Synchronous
Speed
•A)Rotating Flux b) Stationary Rotor Conductors
•Stator Flux cut by the rotor conductor –emf induced
•Rotor Short Circuited –Current Flows to the rotor
•Current Carrying Conductor in a magnetic field –
Mechanical Force
UEEC007 -ISM
Synchronous Speed and Slip
•Synchronous speed �
�=
120�
�
•Slip =
�
??????−�
�
�
??????
•%Slip=
�
??????−�
�
�??????
*100
UEEC007 -ISM
•Synchronous speed �
�=
120�
�
•Slip =
�
??????−�
�
�
??????
•%Slip=
�
??????−�
�
�??????
*100
UEEC007 -ISM
UEEC007 -ISM
Equivalent circuit of Induction
Motor
UEEC007 -ISM
Motor
UEEC007 -ISM
Basic Equivalent Circuit
UEEC007 -ISM
UEEC007 -ISM
Basic Equivalent Circuit
UEEC007 -ISM
UEEC007 -ISM
Equivalent Circuit of Rotor
UEEC007 -ISM
UEEC007 -ISM
Equivalent Circuit Referred to the
Stator
UEEC007 -ISM
Stator
UEEC007 -ISM
Approximate Equivalent Circuit
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Equation
UEEC007 -ISM
UEEC007 -ISM
Torque Slip Characteristics
UEEC007 -ISM
UEEC007 -ISM
Torque Slip Characteristics
UEEC007 -ISM
UEEC007 -ISM
Torque Slip Characteristics
UEEC007 -ISM
UEEC007 -ISM
Effect of Rotor Resistance on Slip
UEEC007 -ISM
UEEC007 -ISM
UEEC007 -ISM
UEEC007 -ISM
UEEC007 -ISM
UEEC007 -ISM
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R
UEEC007 -ISM
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UEEC007 -ISM
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