ๅฐŠๆ•ฌ็š„ ๅพฎไฟกๆฑ‡็Ž‡๏ผš1ๅ†† โ‰ˆ 0.046239 ๅ…ƒ ๆ”ฏไป˜ๅฎๆฑ‡็Ž‡๏ผš1ๅ†† โ‰ˆ 0.04633ๅ…ƒ [้€€ๅ‡บ็™ปๅฝ•]
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UEEC007
Induction and
Synchronous Machines
Alternators
Alternators
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 power generation 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
Types
UEEC007 - ISM
Salient Pole Type Smooth Cylindrical Type
Working Principle
UEEC007 - ISM
Similar to DC generator
Faradayโ€™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
Magnetic Field
Relative Motion
Position 1
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 current Flemingโ€™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
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-B
C-D
A-B
C-D
Three Phase Windings
UEEC007 - ISM
Emf Equation
The average value of the induced emf in a conductor is =
๐‘‘๐œ‘
๐‘‘๐‘ก
In one revolution of the rotor the each stator conductor is cut by a flux of ๐‘๐œ‘ webers
Speed of the rotor in rps =
๐‘๐‘ 
60
Time taken for one revolution =
1
๐‘๐‘ 
60
=
60
๐‘๐‘ 
UEEC007 - ISM
Emf Equation
The average value of the induced emf in a conductor is
๐‘‘๐œ‘
๐‘‘๐‘ก
=
๐œ‘๐‘ƒ๐‘๐‘ 
60
Frequency of the induced emf is f =
๐‘ƒ๐‘๐‘ 
120
Synchronous speed ๐‘๐‘  =
120๐‘“
๐‘ƒ
The average value of the induced emf in a conductor is =
๐œ‘๐‘ƒ
60
.
120๐‘“
๐‘ƒ
= 2๐‘“๐œ‘ volts
UEEC007 - ISM
Emf Equation
If there are ๐‘๐‘โ„Ž conductors in series per phase
Average Induced emf per phase = Average Induced emf per conductor x ๐‘๐‘โ„Ž
= 2๐‘“๐œ‘. ๐‘๐‘โ„Ž
Average Induced emf per phase = 2๐‘“๐œ‘.2๐‘‡๐‘โ„Ž
= 4๐‘“๐œ‘.๐‘‡๐‘โ„Ž
RMS value of the induced emf per phase = Form factor x Average Induced emf per phase
= 1.11 . 4๐‘“๐œ‘.๐‘‡๐‘โ„Ž
= 4.44 ๐‘“๐œ‘.๐‘‡๐‘โ„Ž volts
UEEC007 - ISM
๐‘๐‘โ„Ž = 2๐‘‡๐‘โ„Ž
Coil span โ€“ Distributed windings
UEEC007 - ISM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
18 slots
2 poles
3 phase
Coil Span =
๐‘ ๐‘™๐‘œ๐‘ก๐‘ 
๐‘๐‘œ๐‘™๐‘’
Coil Span =
18
2
Coil Span = 9
m =๐‘ ๐‘™๐‘œ๐‘ก๐‘  ๐‘๐‘œ๐‘™๐‘’
๐‘โ„Ž๐‘Ž๐‘ ๐‘’
m =18 2
3
m = 3
180 degrees
n =๐‘ ๐‘™๐‘œ๐‘ก๐‘  ๐‘๐‘œ๐‘™๐‘’
Reactance Resistance and
Impedance
โ€ข Resistance - Friction against the flow of current
(Resistors)
(Voltage drop in phase with current [alternating current])
โ€ข Reactance โ€“ Inertia against the flow of current
(Capacitors and Inductors)
(Proportional to the applied voltage and current)
Impedance โ€“ Phase and magnitude (complex)
UEEC007 - ISM
Reactance Resistance and
Impedance
UEEC007 - ISM
Synchronous Reactance
โ€ข Imaginary reactance
โ€ข Voltage effects in the armature circuit
โ€ข Armature leakage reactance
โ€ข Change in the airgap flux caused by the armature
reaction
UEEC007 - ISM
Synchronous Impedance
โ€ข Imaginary Fictitious Impedance
โ€ข Voltage effects of the armature circuit
โ€ข Armature resistance
โ€ข Change in airgap flux produced by the armature
reaction
UEEC007 - ISM
Leakage Reactance
โ€ข Flux setup by the load current (R,L,C)
โ€ข Not all the flux are useful
โ€ข Effect of the leakage flux โ€“ self induced emf(voltage) in
armature winding
โ€ข Proportional and in phase with the armature current
producing it
UEEC007 - ISM
Voltage Drop
โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious)
โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž
โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™
UEEC007 - ISM
VOLTAGE DROP
โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘™+๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
โ€ข ๐‘‹๐‘™+๐‘‹๐‘Ž๐‘Ÿ=๐‘‹๐‘  Synchronous Reactance
โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž(๐‘‹๐‘™+๐‘‹๐‘Ž๐‘Ÿ)
โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘ 
UEEC007 - ISM
Phasor diagram of a loaded
alternator
UEEC007 - ISM
๐‘‰๐‘โ„Ž - REFERENCE PHASOR
๐ถ๐ฟ๐‘‚๐ถ๐พ๐‘Š๐ผ๐‘†๐ธ ๐‘…๐‘‚๐‘‡๐ด๐‘‡๐ผ๐‘‚๐‘
๐ผ๐‘Ž ๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘‹๐‘™
๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
๐‘‰๐‘โ„Ž
๐ธ๐‘โ„Ž
๐ผ๐‘Ž๐‘‹๐‘ 
ฯ† - lag
PHASOR DIAGRAM OF A LOADED
ALTERNATOR
UEEC007 - ISM
๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘™+๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
๐ผ๐‘Ž
๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘‹๐‘™
๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
๐‘‰๐‘โ„Ž
๐ธ๐‘โ„Ž
๐ผ๐‘Ž
๐ผ๐‘Ž ๐‘‰๐‘โ„Ž
๐‘‰๐‘โ„Ž ๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘‹๐‘™
๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
๐ธ๐‘โ„Ž
๐ผ๐‘Ž๐‘‹๐‘™
๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ
๐ผ๐‘Ž๐‘‹๐‘ 
๐ผ๐‘Ž๐‘‹๐‘ 
ฯ† - lag ฯ† = 0
ฯ† - lead
๐ผ๐‘Ž - REFERENCE PHASOR
๐ถ๐ฟ๐‘‚๐ถ๐พ๐‘Š๐ผ๐‘†๐ธ ๐‘…๐‘‚๐‘‡๐ด๐‘‡๐ผ๐‘‚๐‘
๐ผ๐‘Ž๐‘‹๐‘ 
๐ธ๐‘โ„Ž
EMF EQUATION- lag ,lead,unity
UEEC007 - ISM
๐ผ๐‘Ž
๐ผ๐‘Ž๐‘…๐‘Ž
๐‘‰๐‘โ„Ž
๐ธ๐‘โ„Ž
๐ผ๐‘Ž๐‘‹๐‘ 
๐ด ๐ต
๐ถ
๐ท ๐ธ
๐‘‚
๐‘‚๐ถ2 = ๐‘‚๐ธ2+ ๐ธ๐ถ2
๐‘‚๐ถ2 = (๐‘‚๐ท2+ ๐ท๐ธ2) + (๐ธ๐ต2+ ๐ต๐ถ2)
๐ธ๐‘โ„Ž
2
= (๐‘‰๐‘โ„Žcos ฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2
+ (๐‘‰๐‘โ„Žsin ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2
๐ธ๐‘โ„Ž(๐‘™๐‘Ž๐‘”) = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2
๐ธ๐‘โ„Ž(๐‘™๐‘’๐‘Ž๐‘‘) = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† โˆ’ ๐ผ๐‘Ž๐‘‹๐‘†)2
๐ธ๐‘โ„Ž(๐‘ข๐‘›๐‘–๐‘ก๐‘ฆ) = (๐‘‰๐‘โ„Ž+๐ผ๐‘Ž๐‘…๐‘Ž)2 +(๐ผ๐‘Ž๐‘‹๐‘†)2
ฯ† โˆ’ ๐‘™๐‘Ž๐‘”
๐ธ๐‘โ„Ž = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2
๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘‹๐‘ 
๐‘๐‘ 
2
= ๐‘‹๐‘ 
2
+๐‘…๐‘Ž
2
๐‘‹๐‘ 
2
= ๐‘๐‘ 
2
- ๐‘…๐‘Ž
2
๐‘‹๐‘† = ๐‘๐‘ 
2
โˆ’ ๐‘…๐‘Ž
2
In OEC
Voltage Regulation
โ€ข The Voltage Regulation of a Synchronous Generator is the increase in the terminal
voltage expressed as a percentage of the rated terminal voltage when the load at a given
power factor is thrown off, with speed and field current remaining the same.
โ€ข It depends upon the power factor of the load.
UEEC007 - ISM
Voltage Regulation =
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
% Voltage Regulation =
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
โˆ— 100
๐ธ๐‘‚ - No Load Terminal voltage per phase
๐‘‰ โ€“ 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
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
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) โ€“ 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 โ€“ voltmeter method or by using the
Wheatstoneโ€™s bridge
The average of three sets of resistance value Rt is 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 Rt is 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,the load
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 Et is measured at each step
A graph is drawn between the open circuit phase voltage
Ep = Et/โˆš3 and the field current If.
Field current If Open circuit
phase voltage
Ep = Et/โˆš3
OPEN CIRCUIT CHARACTERISTICS
UEEC007 - ISM
Open
circuit
Voltage
(๐ธ
๐‘‚๐ถ
)
Field Current (๐ผ๐‘“)
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 ๐‘ฐ๐’”๐’„ and the field current
๐‘ฐ๐’‡
Field current If Armature S.C
current ๐‘ฐ๐’”๐’„
SHORT CIRCUIT CHARACTERISTICS
UEEC007 - ISM
Short
Circuit
Current
(๐‘ฐ
๐’”๐’„
)
Field Current (๐ผ๐‘“)
scc
Calculation of Synchronous Impedance
UEEC007 - ISM
Open
circuit
Voltage
(๐ธ
๐‘‚๐ถ
)
Field Current (๐ผ๐‘“)
occ
Short
Circuit
Current
(๐‘ฐ
๐’”๐’„
)
O
B
C
scc
๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐ผ๐‘š๐‘๐‘’๐‘‘๐‘Ž๐‘›๐‘๐‘’ ๐‘ง๐‘  =
๐‘‚๐‘๐‘’๐‘› ๐‘๐‘–๐‘Ÿ๐‘๐‘ข๐‘–๐‘ก ๐‘‰๐‘œ๐‘™๐‘ก๐‘Ž๐‘”๐‘’ ๐‘๐‘’๐‘Ÿ ๐‘โ„Ž๐‘Ž๐‘ ๐‘’
๐‘†โ„Ž๐‘œ๐‘Ÿ๐‘ก ๐ถ๐‘–๐‘Ÿ๐‘๐‘ข๐‘–๐‘ก ๐ด๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐ถ๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก
(๐‘“๐‘œ๐‘Ÿ ๐‘กโ„Ž๐‘’ ๐‘ ๐‘Ž๐‘š๐‘’๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘œ๐‘“ ๐‘“๐‘–๐‘’๐‘™๐‘‘ ๐‘๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก)
๐‘ง๐‘  =
๐ด๐ถ
๐ด๐ต
(for the same OA)
A
Calculation of Synchronous
Reactance &Voltage Regulation
UEEC007 - ISM
๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘‹๐‘† = ๐‘๐‘ 
2
โˆ’ ๐‘…๐‘Ž
2
๐ธ๐‘‚ = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2
% Voltage Regulation =
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
โˆ— 100
๐ผ๐‘Ž๐‘…๐‘Ž
๐ผ๐‘Ž๐‘‹๐‘  ๐‘๐‘ 
2
= ๐‘‹๐‘ 
2
+๐‘…๐‘Ž
2
๐‘‹๐‘ 
2
= ๐‘๐‘ 
2
- ๐‘…๐‘Ž
2
EMF METHOD โ€“ All
Quantities are EMF
quantities
Salient Points
โ€ข Regulation obtained by using a synchronous impedance method is higher than that
obtained by actual loading.
โ€ข Hence, this method is also called the Pessimistic method.
โ€ข Theoretically correct for non salient pole machines with distributed windings when
saturation is not considered.
UEEC007 - ISM
๐ผ๐‘“ ๐‘ฃ๐‘  ๐œ‘
At lower excitations, ZS is constant,
since the open circuit characteristics
coincide with the air gap line. This value
of ZS is called the linear or Unsaturated
Synchronous Impedance
However, with increasing excitation, the
effect of saturation is to decrease ZS and
the values beyond the linear part of the
open circuit called as Saturated
Value of the Synchronous Impedance
Open
circuit
Voltage
(๐ธ
๐‘‚๐ถ
)
Field Current (๐ผ๐‘“)
Air Gap Line
occ
Problem
The open circuit and short circuit test conducted on a 3 phase star connected 866 V 100 kva
alternator gave the following data,
The field current of 1 A produced a short circuit current of 25 A. The armature resistance per phase is
0.15 ฮฉ. Calculate its full load regulation at 0.8 lagging power factor.
UEEC007 - ISM
Field current
If 1 2 3 4 5 6 7
Open Circuit
Voltage ๐ธ๐‘‚๐ถ
173 310 485 605 728 790 840
Steps
UEEC007 - ISM
๐‘˜๐‘ฃ๐‘Ž = 3 ๐‘‰๐ฟ๐ผ๐ฟ10โˆ’3
Given Line Voltage โ€“ 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 ๐ผ๐ฟ=๐ผ๐‘โ„Ž
% Voltage Regulation =
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
โˆ— 100
๐ธ๐‘‚ = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2
๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘‹๐‘† = ๐‘๐‘ 
2
โˆ’ ๐‘…๐‘Ž
2
๐‘ง๐‘  =
๐ด๐ถ
๐ด๐ต
(for the same OA)
Open
circuit
Voltage
per
phase
(๐ธ
๐‘‚๐ถ
)
occ
Short
Circuit
Current
(๐‘ฐ
๐’”๐’„
)
O
B
C
scc
A Field Current (๐ผ๐‘“)
UEEC007 - ISM
MMF METHOD
โ€ข Ampere turns method or Rothert's MMF method
โ€ข MMF is product of field current and turns of the field winding - ๐ผ๐‘“ ๐‘๐‘“
1. It must have an MMF necessary to induce the rated terminal voltage on the open
circuit.
2. It must have an MMF equal and opposite to that of armature reaction MMF.
UEEC007 - ISM
Voltage Drops
โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious)
โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž
โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™
UEEC007 - ISM
SMALL
MMF - ๐‘ญ๐‘จ๐‘น
Open Circuit Test
The field MMF which is required for inducing the rated
terminal voltage on the open circuit can be obtained from
open circuit test results and open circuit characteristics.
UEEC007 - ISM
Open circuit Voltage (๐ธ๐‘‚๐ถ)
Field Current (๐ผ๐‘“)
occ
๐น๐‘‚
Rated Terminal Voltage
MMF - ๐‘ญ๐‘ถ
Armature Resistance
โ€ข When the armature resistance is neglected then ๐‘ญ๐‘ถ is field mmf required to produce rated
Voltage at the output terminals.
โ€ข But if the effective armature resistance ๐‘…๐‘Ž, is given then ๐‘ญ๐‘ถ is to be calculated from
O.C.C. such that ๐‘ญ๐‘ถ represents the excitation (field current) required to produce a voltage
of ๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹
UEEC007 - ISM
Open circuit Voltage (๐ธ๐‘‚๐ถ)
Field Current (๐ผ๐‘“)
occ
๐น๐‘‚
๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹
Short Circuit Test
โ€ข In short circuit test, field MMF circulates the full load
current balancing the armature reaction effect. The
value of ampere-turns required to circulate full load
current can be obtained from short circuit
characteristics.
UEEC007 - ISM
MMF - ๐‘ญ๐‘จ๐‘น
Short Circuit Current (๐‘ฐ๐’”๐’„)
Field Current (๐ผ๐‘“)
scc
๐น๐ด๐‘…
Full Load Short Circuit Current (๐‘ฐ๐’”๐’„)
OCC and SCC
UEEC007 - ISM
Open circuit Voltage (๐ธ๐‘‚๐ถ)
Field Current (๐ผ๐‘“)
occ
Short Circuit Current (๐‘ฐ๐’”๐’„)
scc
๐น๐‘‚
Rated Terminal Voltage
๐น๐ด๐‘…
Full Load Short Circuit Current
Resultant MMF
โ€ข If the alternator is supplying full load, then total field MMF is
the vector sum of its two components ๐น๐‘‚ and ๐น๐ด๐‘…
โ€ข The resultant field MMF is denoted as ๐น๐‘…
โ€ข ๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘…
โ€ข This depends on the power factor of the load which
alternator is supplying.
UEEC007 - ISM
Zero lagging p.f
UEEC007 - ISM
๐น๐‘‚
๐น๐ด๐‘…
ARMATURE REACTION - DEMAGNETIZING
O A
B
๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘…
OA = ๐น๐‘‚
AB= ๐น๐ด๐‘…
OB= ๐น๐‘…= OA+AB = ๐น๐‘‚+๐น๐ด๐‘…
๐น๐‘…
O
B
Zero leading p.f
UEEC007 - ISM
๐น๐‘‚
๐น๐ด๐‘…
ARMATURE REACTION - MAGNETIZING
O A
A
๐น๐‘… = ๐น๐‘‚ โˆ’ ๐น๐ด๐‘…
OB = ๐น๐‘‚
BA= ๐น๐ด๐‘…
OA= ๐น๐‘…= OB-BA = ๐น๐‘‚ โˆ’ ๐น๐ด๐‘…
๐น๐‘…
O
B
Unity p.f
UEEC007 - ISM
ARMATURE REACTION โ€“ CROSS MAGNETIZING
๐น๐‘‚
๐น๐ด๐‘…
O A
B
๐น๐‘…
๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘…
OA = ๐น๐‘‚
AB= ๐น๐ด๐‘…
OB= ๐น๐‘…= OA+AB = ๐น๐‘‚+๐น๐ด๐‘…
OCC and SCC
UEEC007 - ISM
Open circuit Voltage (๐ธ๐‘‚๐ถ)
Field Current (๐ผ๐‘“)
occ
Short Circuit Current (๐‘ฐ๐’”๐’„)
scc
๐น๐‘…
Rated Terminal Voltage
๐น๐ด๐‘…
Full Load Short Circuit Current
๐น๐‘‚
๐ธ๐‘‚
% Voltage Regulation =
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
โˆ— 100
O
cos ฮฆ, lagging p.f
UEEC007 - ISM
๐‘‰๐‘โ„Ž
๐ผ๐‘Ž๐‘โ„Ž
๐œ‘
๐น๐‘‚
โˆ’๐น๐ด๐‘…
๐น๐‘…
๐ธ๐‘‚
90ยฐ
90ยฐ
๐น๐ด๐‘…
๐œ‘ 90ยฐ
๐‘‰๐‘โ„Ž
๐œ‘ ๐‘‰๐‘โ„Ž
90ยฐ
90ยฐ + ๐œ‘
๐œ‘
๐น๐ด๐‘… cos ๐œ‘
๐น๐ด๐‘… sin ๐œ‘
A
B C
๐‘‚๐ด = ๐น๐‘‚ ๐‘‚๐ต = ๐น๐‘… ๐ด๐ต = ๐น๐ด๐‘…
๐ด๐ถ = ๐น๐ด๐‘… sin ๐œ‘
๐ต๐ถ = ๐น๐ด๐‘… cos ๐œ‘
๐ด๐ตC
OCB
๐‘‚๐ต2
= ๐‘‚๐ถ2
+ ๐ถ๐ต2
๐‘‚๐ต2 = (๐‘‚๐ด + ๐ด๐ถ)2+๐ถ๐ต2
๐น๐‘…
2
= (๐น๐‘‚ + ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2
๐น๐‘… = (๐น๐‘‚ + ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2
๐œ‘
90ยฐ
90ยฐ + ๐œ‘
Cos ฮฆ, leading p.f
UEEC007 - ISM
๐‘‰๐‘โ„Ž
๐ผ๐‘Ž๐‘โ„Ž
๐น๐ด๐‘…
๐œ‘
O
๐น๐‘‚
A
โˆ’๐น๐ด๐‘…
๐น๐‘…
90ยฐ
๐ธ๐‘‚
90ยฐ
๐œ‘ 90ยฐ
90ยฐ โˆ’ ๐œ‘
B C
๐น๐ด๐‘… sin ๐œ‘
๐‘‚๐ด = ๐น๐‘‚ ๐‘‚๐ต = ๐น๐‘… ๐ด๐ต = ๐น๐ด๐‘…
๐ด๐ถ = ๐น๐ด๐‘… sin ๐œ‘
๐ด๐ตC
OCB
๐‘‚๐ต2
= ๐‘‚๐ถ2
+ ๐ถ๐ต2
๐‘‚๐ต2 = (๐‘‚๐ด โˆ’ ๐ด๐ถ)2+๐ถ๐ต2
๐น๐‘…
2
= (๐น๐‘‚ โˆ’ ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2
๐น๐‘… = (๐น๐‘‚ โˆ’ ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2
MMF METHOD โ€“ All
Quantities are MMF
quantities
Cosine Rule to Triangle
UEEC007 - ISM
๐น๐‘œ
B
๐น๐ด๐‘…
O A
90ยฐ + ๐œ‘ for Lagging 90ยฐ โˆ’ ๐œ‘ for leading
O A
๐น๐‘œ
B
๐น๐ด๐‘…
๐น๐‘…
๐น๐‘…
90ยฐ โˆ’ ๐œ‘
๐น๐‘…
2
= ๐น๐‘‚
2
+ ๐น๐ด๐‘…
2
-2๐น๐‘œ๐น๐ด๐‘… cos(๐น๐‘œ๐น๐ด๐‘…)
90ยฐ + ๐œ‘
๐น๐‘…
2
= ๐น๐‘‚
2
+ ๐น๐ด๐‘…
2
-2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ + ๐œ‘))
๐น๐‘…
2
= ๐น๐‘‚
2
+ ๐น๐ด๐‘…
2
-2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ โˆ’ ๐œ‘))
Salient Points
โ€ข This ampere turn method gives the voltage regulation of
an alternator which is lower than that actually observed.
Hence this MMF method is called optimistic method.
โ€ข The excitation required to overcome the armature
reaction is determined on the unsaturated part of the
saturation curve.
UEEC007 - ISM
Problem
The open circuit and short circuit test conducted on a 3 phase star connected 1905 V 1000 kva 50Hz
alternator gave the following data,
The armature resistance per phase is 0.2 ฮฉ. Calculate its full load regulation at 0.8 lagging power
factor by EMF and MMF method.
UEEC007 - ISM
Open Circuit
Voltage ๐„๐Ž๐‚
760 1500 1700 1905 2300 2600
Field current If 10 20 25 30 40 50
Short Circuit
current Isc - - - 335 - -
STEPS
โ€ข ๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹ , from OCC find ๐น๐‘œ
โ€ข Find the full load short circuit armature current per phase
โ€ข Filed current of 30A produces a short circuit current of 335 A , from SCC
find ๐น๐ด๐‘… ๐‘๐‘œ๐‘Ÿ๐‘’๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘๐‘Ž๐‘™๐‘๐‘ข๐‘™๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘“๐‘ข๐‘™๐‘™ ๐‘™๐‘œ๐‘Ž๐‘‘ ๐‘Ž๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐‘๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก.
โ€ข Find ๐ธ๐‘‚ corresponding to the calculated ๐น๐‘…
โ€ข Find Voltage Regulation
๐ธ๐‘‚ โˆ’๐‘‰
๐‘‰
โˆ— 100
UEEC007 - ISM
๐‘˜๐‘ฃ๐‘Ž = 3 ๐‘‰๐ฟ๐ผ๐ฟ10โˆ’3
๐น๐‘…
2
= ๐น๐‘‚
2
+ ๐น๐ด๐‘…
2
-2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ + ๐œ‘)
MMF METHOD
UEEC007 - ISM
MMF METHOD
UEEC007 - ISM
MMF METHOD
UEEC007 - ISM
EMF METHOD
UEEC007 - ISM
EMF AND MMF Quantities
โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious)
โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž
โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™
โ€ข EMF Method โ€“ All drops as EMF quantities
โ€ข MMF Method โ€“ All quantities as MMF quantities
UEEC007 - ISM
EMF Quantity
MMF Quantity
EMF Quantity
ZPF Method
โ€ข This ZPF method is based on the separation of
armature leakage reactance and armature reaction
effects
โ€ข The armature leakage reactance ๐‘‹๐‘™ is called Potier
reactance in this method, hence ZPF method is also
called Potier reactance method
UEEC007 - ISM
OCC and ZPF Test
โ€ข To determine armature leakage reactance and armature
reaction MMF separately two tests are performed on
the alternator.
1. Open circuit test
2. Zero power factor test
UEEC007 - ISM
Open Circuit Test
UEEC007 - ISM
Alternator is running at the rated synchronous speed,the load
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 Et is measured at each step
A graph is drawn between the open circuit phase voltage
Ep = Et/โˆš3 and the field current If.
Field current If Open Circuit
Voltage per phase
Ep = Et/โˆš3
ZPF Test
UEEC007 - ISM
ZPF Steps
โ€ข To conduct zero power factor test, the TPST switch is kept closed.
โ€ข Due to this, a purely inductive load gets connected to an alternator through
an ammeter.
โ€ข A purely inductive load has a power factor of cos 90ยฐ i.e. zero lagging hence
the test is called zero power factor test.
UEEC007 - ISM
ZPF Steps
โ€ข The machine speed is maintained constant at its synchronous value.
โ€ข The load current delivered by an alternator to purely inductive load is
maintained constant at its rated full load value by varying excitation and by
adjusting variable inductance of the inductive bed.
โ€ข Due to purely inductive load, the alternator will always operate at zero
power factor lagging.
UEEC007 - ISM
Zero Power Factor saturation curve
โ€ข First point for this curve is zero terminal voltage (short circuit condition)
and the field current required to deliver full load short circuit armature
current.
โ€ข Second point field current required to obtain rated terminal voltage while
delivering rated full load armature current
UEEC007 - ISM
ZPF CURVE
UEEC007 - ISM
Terminal Voltage
and Induced EMF
per phase
Field Current (๐ผ๐‘“)
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
Rโ€™
Qโ€™
Pโ€™
Sโ€™
Rโ€™
Qโ€™
Pโ€™
Sโ€™
Rโ€™
Qโ€™ Pโ€™
Sโ€™
B
C
Full Load Zero pf Saturation Curve
POTIER TRIANGLE
Aโ€™
Steps
1.Plot open circuit characteristics
2.Plot the excitation corresponding to zero terminal voltage i.e. short
circuit full zero power factor armature current. This point is A.
3.Another point is the rated voltage when the alternator is 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 called Potier
triangle.
UEEC007 - ISM
Steps
7.From point R, drop a perpendicular on PQ to meet at point S.
8.The zero power factor full load saturation curve is now be constructed by
moving triangle PQR so that R remains always on OCC and line PQ always
remains horizontal.
Note: Potier triangle once obtained is constant for a given armature current
and hence can be transferred as it is.
UEEC007 - ISM
Steps
9.Though point A, draw a line parallel to PR meeting OCC at point B.
From B, draw a perpendicular on OA to meet it at point C.
Triangles OAB and PQR are similar triangles.
UEEC007 - ISM
P
R
S
Q
A
C
O
B
Potier Triangle
UEEC007 - ISM
P
R
S
Q
A
C
O
B
โˆ†๐‘ท๐‘ธ๐‘น ๐’‚๐’๐’… โˆ† ๐‘จ๐‘ฉ๐‘ช ๐’‚๐’“๐’† ๐’”๐’Š๐’Ž๐’Š๐’๐’‚๐’“ ๐’•๐’“๐’Š๐’‚๐’๐’๐’ˆ๐’๐’†๐’”
The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. ๐‘ฐ๐’‚๐‘ฟ๐’
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)= ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ Potier Reactance ๐‘ฟ๐’๐’‘๐’‰ =
Length of (RS) or Length of (BC)
๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)
Phasor Diagram
UEEC007 - ISM
๐œ‘ ๐‘‰๐‘โ„Ž
๐ผ๐‘Ž๐‘โ„Ž ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž
๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰
๐ธ๐‘โ„Ž
๐น๐‘“1
๐น๐ด๐‘…
๐น๐‘…
๐ธ1๐‘โ„Ž
Armature Reaction Drop
o
A
B
C
D
E
F
G
H
90ยฐ + ๐œ‘
90ยฐ
90ยฐ
STEPS
1.Draw the rated terminal voltage ๐‘‰๐‘โ„Ž as a reference phasor.
Depending upon at which power factor (cos ๐œ‘ ) the regulation is to be
predicted, draw the Current phasor ๐ผ๐‘Ž๐‘โ„Ž lagging or leading ๐‘‰๐‘โ„Ž by
angle ๐œ‘ .
2.Draw ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž voltage drop to ๐‘‰๐‘โ„Ž which is in phase with ๐ผ๐‘Ž๐‘โ„Ž. While
the voltage drop ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ is to be drawn perpendicular to ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž,
vector but leading ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž at the extremity of ๐‘‰๐‘โ„Ž.
UEEC007 - ISM
STEPS
3.The ๐‘…๐‘Ž๐‘โ„Ž is to be measured separately by passing a d.c current and
measuring the voltage across armature winding. While ๐‘ฟ๐’๐’‘๐’‰ is Potier
reactance obtained by Potier method.
4.Phasor sum of ๐‘‰๐‘โ„Ž rated, ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž and ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ gives the e.m.f.
which is say ๐ธ1๐‘โ„Ž
๐ธ1๐‘โ„Ž =๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž+๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰
UEEC007 - ISM
STEPS
5.Obtain the excitation corresponding to ๐ธ1๐‘โ„Ž from OCC which is
drawn. Let this excitation be ๐น๐‘“1 . This is excitation required for
inducing EMF which does not consider the effect of armature reaction.
6.The field current required to balance armature reaction can be
obtained from Potier triangle method, which is say ๐น๐ด๐‘….
๐น๐ด๐‘… = Lenght(PS) = Lenght(AC)
UEEC007 - ISM
P
R
S
Q
A
C
O
B
Open circuit Voltage (๐ธ๐‘‚๐ถ)
Field Current (๐ผ๐‘“)
๐ธ1๐‘โ„Ž
๐น๐‘“1
STEPS
6.The total excitation required is the vector sum of the ๐น๐‘“1 and ๐น๐ด๐‘….
This can be obtained exactly similar to the procedure used in MMF
Method.
7.Draw vector ๐น๐‘“1 to some scale, leading ๐ธ1๐‘โ„Ž by 90ยฐ. Add ๐น๐ด๐‘… to
๐น๐‘“1 by drawing vector ๐น๐ด๐‘… in phase opposition to ๐ผ๐‘Ž๐‘โ„Ž . The total
excitation to be supplied by field is given by ๐น๐‘….
UEEC007 - ISM
B
O A
90ยฐ + ๐œ‘
๐น๐‘“1
๐น๐ด๐‘…
๐น๐‘…
STEPS
8.Once the total excitation is known which is ๐น๐‘…, the corresponding
induced emf ๐ธ๐‘โ„Ž can be obtained from OCC
This ๐ธ๐‘โ„Ž lags ๐น๐‘… by 90ยฐ
The length CD is the drop due to the armature reaction
UEEC007 - ISM
Open circuit Voltage
(๐ธ๐‘‚๐ถ)
Field
Current (๐ผ๐‘“)
๐ธ๐‘โ„Ž
๐น๐‘…
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 ๐ธ1๐‘โ„Žcan be determined, analytically.
UEEC007 - ISM
% Voltage Regulation =
๐ธ๐‘โ„Ž โˆ’๐‘‰๐‘โ„Ž
๐‘‰๐‘โ„Ž
โˆ— 100
Drawbacks
The only drawback of the ZPF method is that the separate curve for
every load condition is necessary to plot if Potier triangles for various
load conditions are required.
UEEC007 - ISM
Assumptions
โ€ข ln the entire calculation procedure of Potier method, the armature
resistance is neglected. But practically armature resistance is very
small and hence this assumption does not cause significant error in
the accuracy.
โ€ข In Potier method, a zero power factor test is required to be done. But
practically when inductors are used, a perfect zero power
factor cannot be achieved.
UEEC007 - ISM
Assumptions
โ€ข the distances RS, R' S' and BC are assumed equal
โ€ข This indicates that the point P in the zero power factor method and
point A in the short circuit test represent the same leakage reactance
of the machine.
โ€ข Length OA<OAโ€™
UEEC007 - ISM
P
R
S
Q
A
C
O
B
Assumptions
โ€ข Hence practically the leakage reactance corresponding to saturated
conditions is higher than that assumed in the method. This
introduces the error in the calculations.
UEEC007 - ISM
Air Gap
UEEC007 - ISM
Non Salient Pole Alternators
โ€ข Non-salient pole type alternators the air gap is uniform.
โ€ข Due to the uniform air gap, the field flux, as well as armature flux vary sinusoidally in the
air gap.
โ€ข In non salient pole alternators, air gap length is constant and reactance is also constant.
โ€ข 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
โ€ข In salient pole type alternators, the length of the air gap varies and the reluctance also
varies.
โ€ข Hence the armature flux and field flux cannot vary sinusoidally in the air gap.
โ€ข 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
D-axis and q-axis
โ€ข The reluctance offered to the MMF wave is lowest when it is aligned
with the field pole axis.
โ€ข This axis is called the direct axis of pole i.e. d-axis.
โ€ข The reluctance offered is highest when the MMF wave is oriented at
90ยฐ to the field pole axis which is called quadrature axis i.e. q-axis.
UEEC007 - ISM
d-axis and q-axis
โ€ข The component which is acting along the direct axis can be
magnetizing or demagnetizing.
โ€ข The component which is acting along quadrature axis is cross
magnetizing.
UEEC007 - ISM
Field MMF
โ€ข The air gap is least in the centre of the poles and progressively
increase, on moving away from the centre.
โ€ข Due to such shape of the pole-shoes, the field winding wound on
salient poles produces the MMF wave which is nearly sinusoidal and
it always acts along the pole axis which is direct axis.
UEEC007 - ISM
Armature MMF
The armature m.m.f. can be divided into two components as,
1. Component acting along the pole axis called direct axis.
2. Component acting at right angles to the pole axis called quadrature
axis.
UEEC007 - ISM
Field MMF AND EMF
โ€ข Let ๐น๐‘“ be the MMF wave produced by field winding, then it always
acts along the direct axis.
โ€ข This MMF is responsible for producing an excitation EMF ๐ธ๐‘“ which
lags ๐น๐‘“by all angle 90ยฐ.
UEEC007 - ISM
Armature MMF
โ€ข When armature carries current, it produces its own MMF wave ๐น๐ด๐‘…
โ€ข This can be resolved into two components, one acting along d-axis
(magnetising or demagnetising) and one acting along q-axis (cross-
magnetising).
โ€ข Similarly, armature current ๐ผ๐‘Ž also can in divided into two
components, one along the direct axis and one along quadrature
axis.
UEEC007 - ISM
๐œ‘๐ด๐‘… VS ๐ผ๐‘Ž
The reluctance offered to flux along the direct axis is less than the
reluctance offered to flux along quadrature axis.
Due to this, the flux ๐œ‘๐ด๐‘… is no longer along ๐น๐ด๐‘… or ๐ผ๐‘Ž.
Depending upon the reluctances offered along the direct and
quadrature axis, the flux ๐œ‘๐ด๐‘… lags behind armature current ๐ผ๐‘Ž.
UEEC007 - ISM
UEEC007 - ISM
d-axis
q-axis
๐œ‘๐‘‘
๐œ‘๐‘ž
๐œ‘๐ด๐‘…
๐น๐‘‘
๐น๐‘ž
๐น๐ด๐‘…
๐ผ๐‘‘
๐ผ๐‘ž
๐ผ๐‘Ž
๐ธ๐‘“
๐œ‘๐‘“
๐น๐‘“
๐ต๐‘™๐‘œ๐‘›๐‘‘๐‘’๐‘™๐‘  ๐‘‡๐‘ค๐‘œ ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘–๐‘œ๐‘› ๐‘‡โ„Ž๐‘’๐‘œ๐‘Ÿ๐‘ฆ
Induced EMF
UEEC007 - ISM
๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐น๐‘‘
๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘š๐‘š๐‘“ ๐น๐‘‘ =๐‘˜๐ด๐‘…. ๐ผ๐‘‘
๐‘ƒ๐‘‘ = Permeance along the direct axis
Permeance is the reciprocal of reluctance and
indicates ease with which flux can travel along the
path
๐‘˜๐ด๐‘… is the armature reaction coefficient
Flux =
๐‘š๐‘š๐‘“
๐‘Ÿ๐‘’๐‘™๐‘ข๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’
Induced EMF
UEEC007 - ISM
๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘
๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘ž = ๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž
๐‘ƒ๐‘‘ > ๐‘ƒ๐‘ž
๐ธ๐‘‘ = ๐พ๐‘’๐œ‘๐‘‘ โˆ  โˆ’ 90ยฐ
๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘’๐‘š๐‘“ ๐ธ๐‘‘ =-j ๐พ๐‘’๐œ‘๐‘‘
๐ธ๐‘ž = ๐พ๐‘’๐œ‘๐‘ž โˆ  โˆ’ 90ยฐ
๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘’๐‘š๐‘“ ๐ธ๐‘ž =-j ๐พ๐‘’๐œ‘๐‘ž
๐พ๐‘’ is the emf constant of the armature winding
Induced EMF
UEEC007 - ISM
๐‘…๐‘’๐‘ ๐‘ข๐‘™๐‘ก๐‘Ž๐‘›๐‘ก ๐‘’๐‘š๐‘“ ๐ธ๐‘… = ๐ธ๐‘“ + ๐ธ๐‘‘ + ๐ธ๐‘ž
๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐œ‘๐‘‘โˆ’j ๐พ๐‘’๐œ‘๐‘ž
๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘โˆ’j ๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž
๐ธ๐‘ž๐‘ข๐‘–๐‘ฃ๐‘Ž๐‘™๐‘’๐‘›๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘‹๐‘Ž๐‘Ÿ๐‘‘ =๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…
๐ธ๐‘ž๐‘ข๐‘–๐‘ฃ๐‘Ž๐‘™๐‘’๐‘›๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘ ๐‘‹๐‘Ž๐‘Ÿ๐‘ž =๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…
๐ธ๐‘… = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž
Induced EMF
UEEC007 - ISM
๐ผ๐‘Ž = ๐ผ๐‘‘ + ๐ผ๐‘ž
๐ธ๐‘… = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ
๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž
๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘ž) ๐ผ๐‘ž
๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐‘ž) ๐ผ๐‘ž
๐‘‹๐‘‘ - direct axis synchronous reactance
๐‘‹๐‘ž โˆ’ Quadrature axis synchronous reactance
UEEC007 - ISM
Three Phase Induction Motor
UEEC007 - ISM
Three Phase Induction motor
UEEC007 - ISM
Types of Rotor
UEEC007 - ISM
Squirrel Cage vs Slip Ring
UEEC007 - ISM
Three phase stator winding
UEEC007 - ISM
Three Phase Flux Waveforms
UEEC007 - ISM
At Point 0 โ€“ 0 degrees
UEEC007 - ISM
At Point 1 โ€“ 30 degrees
UEEC007 - ISM
At Point 2 -60 degrees
UEEC007 - ISM
At Point 3 โ€“ 90 degrees
UEEC007 - ISM
UEEC007 - ISM
Principle of Operation
โ€ข Three Phase supply โ€“ stator
โ€ข Rotating Magnetic Filed is produced โ€“ Synchronous
Speed
โ€ข A)Rotating Flux b) Stationary Rotor Conductors
โ€ข Stator Flux cut by the rotor conductor โ€“ emf induced
โ€ข Rotor Short Circuited โ€“ Current Flows to the rotor
โ€ข Current Carrying Conductor in a magnetic field โ€“
Mechanical Force
UEEC007 - ISM
Synchronous Speed and Slip
โ€ข Synchronous speed ๐‘๐‘† =
120๐‘“
๐‘ƒ
โ€ข Slip =
๐‘๐‘†โˆ’๐‘๐‘Ÿ
๐‘๐‘†
โ€ข %Slip=
๐‘๐‘†โˆ’๐‘๐‘Ÿ
๐‘๐‘†
*100
UEEC007 - ISM
UEEC007 - ISM
Equivalent circuit of Induction
Motor
UEEC007 - ISM
Basic Equivalent Circuit
UEEC007 - ISM
Basic Equivalent Circuit
UEEC007 - ISM
Equivalent Circuit of Rotor
UEEC007 - ISM
Equivalent Circuit Referred to the
Stator
UEEC007 - ISM
Approximate Equivalent Circuit
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Equation
UEEC007 - ISM
Torque Slip Characteristics
UEEC007 - ISM
Torque Slip Characteristics
UEEC007 - ISM
Torque Slip Characteristics
UEEC007 - ISM
Effect of Rotor Resistance on Slip
UEEC007 - ISM
UEEC007 - ISM
UEEC007 - ISM
UEEC007 - ISM
UEEC007 - ISM
๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐น๐‘‘
๐น๐‘‘ =๐‘˜๐ด๐‘…. ๐ผ๐‘‘
๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘
๐œ‘๐‘ž = ๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž
๐‘ƒ๐‘‘ > ๐‘ƒ๐‘ž
๐ธ๐‘‘ = ๐พ๐‘’๐œ‘๐‘‘ โˆ  โˆ’ 90ยฐ
๐ธ๐‘‘ =-j ๐พ๐‘’๐œ‘๐‘‘
๐ธ๐‘ž = ๐พ๐‘’๐œ‘๐‘ž โˆ  โˆ’ 90ยฐ
๐ธ๐‘ž =-j ๐พ๐‘’๐œ‘๐‘ž
๐ธ๐‘… = ๐ธ๐‘“ + ๐ธ๐‘‘ + ๐ธ๐‘ž
๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐œ‘๐‘‘โˆ’j ๐พ๐‘’๐œ‘๐‘ž
๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘โˆ’j ๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž
๐‘‹๐‘Ž๐‘Ÿ๐‘‘ =๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…
๐‘‹๐‘Ž๐‘Ÿ๐‘ž =๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…
๐ธ๐‘… = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž
๐ผ๐‘Ž = ๐ผ๐‘‘ + ๐ผ๐‘‘
๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ
๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž
๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘ž) ๐ผ๐‘ž
๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐‘ž) ๐ผ๐‘ž
R
UEEC007 - ISM
๐œ‘๐‘‘
๐œ‘๐‘ž
๐œ‘๐ด๐‘…
๐น๐‘‘
๐น๐‘ž
๐น๐ด๐‘…
๐ผ๐‘‘
๐ผ๐‘ž
๐ผ๐‘Ž
๐ธ๐‘“
๐น๐‘“

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Ism 11

  • 2. Alternators UEEC007 - ISM Mechanical Energy Electrical Energy Specific Voltage Frequency
  • 3. 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 power generation plants as the main source of power used for low band radio frequency transmission
  • 4. Construction UEEC007 - ISM Stator Rotor Armature Field Three phase windings distributed in space by 120 degrees
  • 5. Types UEEC007 - ISM Salient Pole Type Smooth Cylindrical Type
  • 6. Working Principle UEEC007 - ISM Similar to DC generator Faradayโ€™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 Magnetic Field Relative Motion
  • 7. Position 1 UEEC007 - ISM single turn loop ABCD rotate against axis a-b clockwise
  • 8. 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 current Flemingโ€™s right-hand rule. A-B C-D
  • 9. 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
  • 10. 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-B C-D A-B C-D
  • 12. Emf Equation The average value of the induced emf in a conductor is = ๐‘‘๐œ‘ ๐‘‘๐‘ก In one revolution of the rotor the each stator conductor is cut by a flux of ๐‘๐œ‘ webers Speed of the rotor in rps = ๐‘๐‘  60 Time taken for one revolution = 1 ๐‘๐‘  60 = 60 ๐‘๐‘  UEEC007 - ISM
  • 13. Emf Equation The average value of the induced emf in a conductor is ๐‘‘๐œ‘ ๐‘‘๐‘ก = ๐œ‘๐‘ƒ๐‘๐‘  60 Frequency of the induced emf is f = ๐‘ƒ๐‘๐‘  120 Synchronous speed ๐‘๐‘  = 120๐‘“ ๐‘ƒ The average value of the induced emf in a conductor is = ๐œ‘๐‘ƒ 60 . 120๐‘“ ๐‘ƒ = 2๐‘“๐œ‘ volts UEEC007 - ISM
  • 14. Emf Equation If there are ๐‘๐‘โ„Ž conductors in series per phase Average Induced emf per phase = Average Induced emf per conductor x ๐‘๐‘โ„Ž = 2๐‘“๐œ‘. ๐‘๐‘โ„Ž Average Induced emf per phase = 2๐‘“๐œ‘.2๐‘‡๐‘โ„Ž = 4๐‘“๐œ‘.๐‘‡๐‘โ„Ž RMS value of the induced emf per phase = Form factor x Average Induced emf per phase = 1.11 . 4๐‘“๐œ‘.๐‘‡๐‘โ„Ž = 4.44 ๐‘“๐œ‘.๐‘‡๐‘โ„Ž volts UEEC007 - ISM ๐‘๐‘โ„Ž = 2๐‘‡๐‘โ„Ž
  • 15. Coil span โ€“ Distributed windings UEEC007 - ISM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 18 slots 2 poles 3 phase Coil Span = ๐‘ ๐‘™๐‘œ๐‘ก๐‘  ๐‘๐‘œ๐‘™๐‘’ Coil Span = 18 2 Coil Span = 9 m =๐‘ ๐‘™๐‘œ๐‘ก๐‘  ๐‘๐‘œ๐‘™๐‘’ ๐‘โ„Ž๐‘Ž๐‘ ๐‘’ m =18 2 3 m = 3 180 degrees n =๐‘ ๐‘™๐‘œ๐‘ก๐‘  ๐‘๐‘œ๐‘™๐‘’
  • 16. Reactance Resistance and Impedance โ€ข Resistance - Friction against the flow of current (Resistors) (Voltage drop in phase with current [alternating current]) โ€ข Reactance โ€“ Inertia against the flow of current (Capacitors and Inductors) (Proportional to the applied voltage and current) Impedance โ€“ Phase and magnitude (complex) UEEC007 - ISM
  • 18. Synchronous Reactance โ€ข Imaginary reactance โ€ข Voltage effects in the armature circuit โ€ข Armature leakage reactance โ€ข Change in the airgap flux caused by the armature reaction UEEC007 - ISM
  • 19. Synchronous Impedance โ€ข Imaginary Fictitious Impedance โ€ข Voltage effects of the armature circuit โ€ข Armature resistance โ€ข Change in airgap flux produced by the armature reaction UEEC007 - ISM
  • 20. Leakage Reactance โ€ข Flux setup by the load current (R,L,C) โ€ข Not all the flux are useful โ€ข Effect of the leakage flux โ€“ self induced emf(voltage) in armature winding โ€ข Proportional and in phase with the armature current producing it UEEC007 - ISM
  • 21. Voltage Drop โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious) โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™ UEEC007 - ISM
  • 22. VOLTAGE DROP โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘™+๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ โ€ข ๐‘‹๐‘™+๐‘‹๐‘Ž๐‘Ÿ=๐‘‹๐‘  Synchronous Reactance โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž(๐‘‹๐‘™+๐‘‹๐‘Ž๐‘Ÿ) โ€ข ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘  UEEC007 - ISM
  • 23. Phasor diagram of a loaded alternator UEEC007 - ISM ๐‘‰๐‘โ„Ž - REFERENCE PHASOR ๐ถ๐ฟ๐‘‚๐ถ๐พ๐‘Š๐ผ๐‘†๐ธ ๐‘…๐‘‚๐‘‡๐ด๐‘‡๐ผ๐‘‚๐‘ ๐ผ๐‘Ž ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘‹๐‘™ ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ ๐‘‰๐‘โ„Ž ๐ธ๐‘โ„Ž ๐ผ๐‘Ž๐‘‹๐‘  ฯ† - lag
  • 24. PHASOR DIAGRAM OF A LOADED ALTERNATOR UEEC007 - ISM ๐ธ๐‘โ„Ž = ๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘…๐‘Ž+๐ผ๐‘Ž๐‘‹๐‘™+๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ ๐ผ๐‘Ž ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘‹๐‘™ ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ ๐‘‰๐‘โ„Ž ๐ธ๐‘โ„Ž ๐ผ๐‘Ž ๐ผ๐‘Ž ๐‘‰๐‘โ„Ž ๐‘‰๐‘โ„Ž ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘‹๐‘™ ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ ๐ธ๐‘โ„Ž ๐ผ๐‘Ž๐‘‹๐‘™ ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ ๐ผ๐‘Ž๐‘‹๐‘  ๐ผ๐‘Ž๐‘‹๐‘  ฯ† - lag ฯ† = 0 ฯ† - lead ๐ผ๐‘Ž - REFERENCE PHASOR ๐ถ๐ฟ๐‘‚๐ถ๐พ๐‘Š๐ผ๐‘†๐ธ ๐‘…๐‘‚๐‘‡๐ด๐‘‡๐ผ๐‘‚๐‘ ๐ผ๐‘Ž๐‘‹๐‘  ๐ธ๐‘โ„Ž
  • 25. EMF EQUATION- lag ,lead,unity UEEC007 - ISM ๐ผ๐‘Ž ๐ผ๐‘Ž๐‘…๐‘Ž ๐‘‰๐‘โ„Ž ๐ธ๐‘โ„Ž ๐ผ๐‘Ž๐‘‹๐‘  ๐ด ๐ต ๐ถ ๐ท ๐ธ ๐‘‚ ๐‘‚๐ถ2 = ๐‘‚๐ธ2+ ๐ธ๐ถ2 ๐‘‚๐ถ2 = (๐‘‚๐ท2+ ๐ท๐ธ2) + (๐ธ๐ต2+ ๐ต๐ถ2) ๐ธ๐‘โ„Ž 2 = (๐‘‰๐‘โ„Žcos ฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Žsin ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2 ๐ธ๐‘โ„Ž(๐‘™๐‘Ž๐‘”) = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2 ๐ธ๐‘โ„Ž(๐‘™๐‘’๐‘Ž๐‘‘) = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† โˆ’ ๐ผ๐‘Ž๐‘‹๐‘†)2 ๐ธ๐‘โ„Ž(๐‘ข๐‘›๐‘–๐‘ก๐‘ฆ) = (๐‘‰๐‘โ„Ž+๐ผ๐‘Ž๐‘…๐‘Ž)2 +(๐ผ๐‘Ž๐‘‹๐‘†)2 ฯ† โˆ’ ๐‘™๐‘Ž๐‘” ๐ธ๐‘โ„Ž = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2 ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘‹๐‘  ๐‘๐‘  2 = ๐‘‹๐‘  2 +๐‘…๐‘Ž 2 ๐‘‹๐‘  2 = ๐‘๐‘  2 - ๐‘…๐‘Ž 2 ๐‘‹๐‘† = ๐‘๐‘  2 โˆ’ ๐‘…๐‘Ž 2 In OEC
  • 26. Voltage Regulation โ€ข The Voltage Regulation of a Synchronous Generator is the increase in the terminal voltage expressed as a percentage of the rated terminal voltage when the load at a given power factor is thrown off, with speed and field current remaining the same. โ€ข It depends upon the power factor of the load. UEEC007 - ISM Voltage Regulation = ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ % Voltage Regulation = ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ โˆ— 100 ๐ธ๐‘‚ - No Load Terminal voltage per phase ๐‘‰ โ€“ Full Load Terminal voltage per phase
  • 27. 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
  • 28. 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
  • 29. 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) โ€“ Short circuit armature current vs field current
  • 30. Armature Resistance per phase UEEC007 - ISM The DC resistance between each pair of terminals is measured either by using an ammeter โ€“ voltmeter method or by using the Wheatstoneโ€™s bridge The average of three sets of resistance value Rt is 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 Rt is divided by 2 to obtain a value of DC resistance per phase
  • 31. Open Circuit Test UEEC007 - ISM Alternator is running at the rated synchronous speed,the load 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 Et is measured at each step A graph is drawn between the open circuit phase voltage Ep = Et/โˆš3 and the field current If. Field current If Open circuit phase voltage Ep = Et/โˆš3
  • 32. OPEN CIRCUIT CHARACTERISTICS UEEC007 - ISM Open circuit Voltage (๐ธ ๐‘‚๐ถ ) Field Current (๐ผ๐‘“) Residual Voltage Air Gap Line occ
  • 33. 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 ๐‘ฐ๐’”๐’„ and the field current ๐‘ฐ๐’‡ Field current If Armature S.C current ๐‘ฐ๐’”๐’„
  • 34. SHORT CIRCUIT CHARACTERISTICS UEEC007 - ISM Short Circuit Current (๐‘ฐ ๐’”๐’„ ) Field Current (๐ผ๐‘“) scc
  • 35. Calculation of Synchronous Impedance UEEC007 - ISM Open circuit Voltage (๐ธ ๐‘‚๐ถ ) Field Current (๐ผ๐‘“) occ Short Circuit Current (๐‘ฐ ๐’”๐’„ ) O B C scc ๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐ผ๐‘š๐‘๐‘’๐‘‘๐‘Ž๐‘›๐‘๐‘’ ๐‘ง๐‘  = ๐‘‚๐‘๐‘’๐‘› ๐‘๐‘–๐‘Ÿ๐‘๐‘ข๐‘–๐‘ก ๐‘‰๐‘œ๐‘™๐‘ก๐‘Ž๐‘”๐‘’ ๐‘๐‘’๐‘Ÿ ๐‘โ„Ž๐‘Ž๐‘ ๐‘’ ๐‘†โ„Ž๐‘œ๐‘Ÿ๐‘ก ๐ถ๐‘–๐‘Ÿ๐‘๐‘ข๐‘–๐‘ก ๐ด๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐ถ๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก (๐‘“๐‘œ๐‘Ÿ ๐‘กโ„Ž๐‘’ ๐‘ ๐‘Ž๐‘š๐‘’๐‘ฃ๐‘Ž๐‘™๐‘ข๐‘’ ๐‘œ๐‘“ ๐‘“๐‘–๐‘’๐‘™๐‘‘ ๐‘๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก) ๐‘ง๐‘  = ๐ด๐ถ ๐ด๐ต (for the same OA) A
  • 36. Calculation of Synchronous Reactance &Voltage Regulation UEEC007 - ISM ๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘‹๐‘† = ๐‘๐‘  2 โˆ’ ๐‘…๐‘Ž 2 ๐ธ๐‘‚ = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2 % Voltage Regulation = ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ โˆ— 100 ๐ผ๐‘Ž๐‘…๐‘Ž ๐ผ๐‘Ž๐‘‹๐‘  ๐‘๐‘  2 = ๐‘‹๐‘  2 +๐‘…๐‘Ž 2 ๐‘‹๐‘  2 = ๐‘๐‘  2 - ๐‘…๐‘Ž 2 EMF METHOD โ€“ All Quantities are EMF quantities
  • 37. Salient Points โ€ข Regulation obtained by using a synchronous impedance method is higher than that obtained by actual loading. โ€ข Hence, this method is also called the Pessimistic method. โ€ข Theoretically correct for non salient pole machines with distributed windings when saturation is not considered. UEEC007 - ISM ๐ผ๐‘“ ๐‘ฃ๐‘  ๐œ‘ At lower excitations, ZS is constant, since the open circuit characteristics coincide with the air gap line. This value of ZS is called the linear or Unsaturated Synchronous Impedance However, with increasing excitation, the effect of saturation is to decrease ZS and the values beyond the linear part of the open circuit called as Saturated Value of the Synchronous Impedance Open circuit Voltage (๐ธ ๐‘‚๐ถ ) Field Current (๐ผ๐‘“) Air Gap Line occ
  • 38. Problem The open circuit and short circuit test conducted on a 3 phase star connected 866 V 100 kva alternator gave the following data, The field current of 1 A produced a short circuit current of 25 A. The armature resistance per phase is 0.15 ฮฉ. Calculate its full load regulation at 0.8 lagging power factor. UEEC007 - ISM Field current If 1 2 3 4 5 6 7 Open Circuit Voltage ๐ธ๐‘‚๐ถ 173 310 485 605 728 790 840
  • 39. Steps UEEC007 - ISM ๐‘˜๐‘ฃ๐‘Ž = 3 ๐‘‰๐ฟ๐ผ๐ฟ10โˆ’3 Given Line Voltage โ€“ 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 ๐ผ๐ฟ=๐ผ๐‘โ„Ž % Voltage Regulation = ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ โˆ— 100 ๐ธ๐‘‚ = (๐‘‰๐‘โ„Žcosฯ† + ๐ผ๐‘Ž๐‘…๐‘Ž)2 + (๐‘‰๐‘โ„Ž๐‘ ๐‘–๐‘›ฯ† + ๐ผ๐‘Ž๐‘‹๐‘†)2 ๐‘†๐‘ฆ๐‘›๐‘โ„Ž๐‘Ÿ๐‘œ๐‘›๐‘œ๐‘ข๐‘  ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘‹๐‘† = ๐‘๐‘  2 โˆ’ ๐‘…๐‘Ž 2 ๐‘ง๐‘  = ๐ด๐ถ ๐ด๐ต (for the same OA) Open circuit Voltage per phase (๐ธ ๐‘‚๐ถ ) occ Short Circuit Current (๐‘ฐ ๐’”๐’„ ) O B C scc A Field Current (๐ผ๐‘“)
  • 41. MMF METHOD โ€ข Ampere turns method or Rothert's MMF method โ€ข MMF is product of field current and turns of the field winding - ๐ผ๐‘“ ๐‘๐‘“ 1. It must have an MMF necessary to induce the rated terminal voltage on the open circuit. 2. It must have an MMF equal and opposite to that of armature reaction MMF. UEEC007 - ISM
  • 42. Voltage Drops โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious) โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™ UEEC007 - ISM SMALL MMF - ๐‘ญ๐‘จ๐‘น
  • 43. Open Circuit Test The field MMF which is required for inducing the rated terminal voltage on the open circuit can be obtained from open circuit test results and open circuit characteristics. UEEC007 - ISM Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) occ ๐น๐‘‚ Rated Terminal Voltage MMF - ๐‘ญ๐‘ถ
  • 44. Armature Resistance โ€ข When the armature resistance is neglected then ๐‘ญ๐‘ถ is field mmf required to produce rated Voltage at the output terminals. โ€ข But if the effective armature resistance ๐‘…๐‘Ž, is given then ๐‘ญ๐‘ถ is to be calculated from O.C.C. such that ๐‘ญ๐‘ถ represents the excitation (field current) required to produce a voltage of ๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹ UEEC007 - ISM Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) occ ๐น๐‘‚ ๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹
  • 45. Short Circuit Test โ€ข In short circuit test, field MMF circulates the full load current balancing the armature reaction effect. The value of ampere-turns required to circulate full load current can be obtained from short circuit characteristics. UEEC007 - ISM MMF - ๐‘ญ๐‘จ๐‘น Short Circuit Current (๐‘ฐ๐’”๐’„) Field Current (๐ผ๐‘“) scc ๐น๐ด๐‘… Full Load Short Circuit Current (๐‘ฐ๐’”๐’„)
  • 46. OCC and SCC UEEC007 - ISM Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) occ Short Circuit Current (๐‘ฐ๐’”๐’„) scc ๐น๐‘‚ Rated Terminal Voltage ๐น๐ด๐‘… Full Load Short Circuit Current
  • 47. Resultant MMF โ€ข If the alternator is supplying full load, then total field MMF is the vector sum of its two components ๐น๐‘‚ and ๐น๐ด๐‘… โ€ข The resultant field MMF is denoted as ๐น๐‘… โ€ข ๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘… โ€ข This depends on the power factor of the load which alternator is supplying. UEEC007 - ISM
  • 48. Zero lagging p.f UEEC007 - ISM ๐น๐‘‚ ๐น๐ด๐‘… ARMATURE REACTION - DEMAGNETIZING O A B ๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘… OA = ๐น๐‘‚ AB= ๐น๐ด๐‘… OB= ๐น๐‘…= OA+AB = ๐น๐‘‚+๐น๐ด๐‘… ๐น๐‘… O B
  • 49. Zero leading p.f UEEC007 - ISM ๐น๐‘‚ ๐น๐ด๐‘… ARMATURE REACTION - MAGNETIZING O A A ๐น๐‘… = ๐น๐‘‚ โˆ’ ๐น๐ด๐‘… OB = ๐น๐‘‚ BA= ๐น๐ด๐‘… OA= ๐น๐‘…= OB-BA = ๐น๐‘‚ โˆ’ ๐น๐ด๐‘… ๐น๐‘… O B
  • 50. Unity p.f UEEC007 - ISM ARMATURE REACTION โ€“ CROSS MAGNETIZING ๐น๐‘‚ ๐น๐ด๐‘… O A B ๐น๐‘… ๐น๐‘… = ๐น๐‘‚+๐น๐ด๐‘… OA = ๐น๐‘‚ AB= ๐น๐ด๐‘… OB= ๐น๐‘…= OA+AB = ๐น๐‘‚+๐น๐ด๐‘…
  • 51. OCC and SCC UEEC007 - ISM Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) occ Short Circuit Current (๐‘ฐ๐’”๐’„) scc ๐น๐‘… Rated Terminal Voltage ๐น๐ด๐‘… Full Load Short Circuit Current ๐น๐‘‚ ๐ธ๐‘‚ % Voltage Regulation = ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ โˆ— 100
  • 52. O cos ฮฆ, lagging p.f UEEC007 - ISM ๐‘‰๐‘โ„Ž ๐ผ๐‘Ž๐‘โ„Ž ๐œ‘ ๐น๐‘‚ โˆ’๐น๐ด๐‘… ๐น๐‘… ๐ธ๐‘‚ 90ยฐ 90ยฐ ๐น๐ด๐‘… ๐œ‘ 90ยฐ ๐‘‰๐‘โ„Ž ๐œ‘ ๐‘‰๐‘โ„Ž 90ยฐ 90ยฐ + ๐œ‘ ๐œ‘ ๐น๐ด๐‘… cos ๐œ‘ ๐น๐ด๐‘… sin ๐œ‘ A B C ๐‘‚๐ด = ๐น๐‘‚ ๐‘‚๐ต = ๐น๐‘… ๐ด๐ต = ๐น๐ด๐‘… ๐ด๐ถ = ๐น๐ด๐‘… sin ๐œ‘ ๐ต๐ถ = ๐น๐ด๐‘… cos ๐œ‘ ๐ด๐ตC OCB ๐‘‚๐ต2 = ๐‘‚๐ถ2 + ๐ถ๐ต2 ๐‘‚๐ต2 = (๐‘‚๐ด + ๐ด๐ถ)2+๐ถ๐ต2 ๐น๐‘… 2 = (๐น๐‘‚ + ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2 ๐น๐‘… = (๐น๐‘‚ + ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2 ๐œ‘ 90ยฐ 90ยฐ + ๐œ‘
  • 53. Cos ฮฆ, leading p.f UEEC007 - ISM ๐‘‰๐‘โ„Ž ๐ผ๐‘Ž๐‘โ„Ž ๐น๐ด๐‘… ๐œ‘ O ๐น๐‘‚ A โˆ’๐น๐ด๐‘… ๐น๐‘… 90ยฐ ๐ธ๐‘‚ 90ยฐ ๐œ‘ 90ยฐ 90ยฐ โˆ’ ๐œ‘ B C ๐น๐ด๐‘… sin ๐œ‘ ๐‘‚๐ด = ๐น๐‘‚ ๐‘‚๐ต = ๐น๐‘… ๐ด๐ต = ๐น๐ด๐‘… ๐ด๐ถ = ๐น๐ด๐‘… sin ๐œ‘ ๐ด๐ตC OCB ๐‘‚๐ต2 = ๐‘‚๐ถ2 + ๐ถ๐ต2 ๐‘‚๐ต2 = (๐‘‚๐ด โˆ’ ๐ด๐ถ)2+๐ถ๐ต2 ๐น๐‘… 2 = (๐น๐‘‚ โˆ’ ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2 ๐น๐‘… = (๐น๐‘‚ โˆ’ ๐น๐ด๐‘… sin ๐œ‘)2+(๐น๐ด๐‘… cos ๐œ‘)2 MMF METHOD โ€“ All Quantities are MMF quantities
  • 54. Cosine Rule to Triangle UEEC007 - ISM ๐น๐‘œ B ๐น๐ด๐‘… O A 90ยฐ + ๐œ‘ for Lagging 90ยฐ โˆ’ ๐œ‘ for leading O A ๐น๐‘œ B ๐น๐ด๐‘… ๐น๐‘… ๐น๐‘… 90ยฐ โˆ’ ๐œ‘ ๐น๐‘… 2 = ๐น๐‘‚ 2 + ๐น๐ด๐‘… 2 -2๐น๐‘œ๐น๐ด๐‘… cos(๐น๐‘œ๐น๐ด๐‘…) 90ยฐ + ๐œ‘ ๐น๐‘… 2 = ๐น๐‘‚ 2 + ๐น๐ด๐‘… 2 -2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ + ๐œ‘)) ๐น๐‘… 2 = ๐น๐‘‚ 2 + ๐น๐ด๐‘… 2 -2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ โˆ’ ๐œ‘))
  • 55. Salient Points โ€ข This ampere turn method gives the voltage regulation of an alternator which is lower than that actually observed. Hence this MMF method is called optimistic method. โ€ข The excitation required to overcome the armature reaction is determined on the unsaturated part of the saturation curve. UEEC007 - ISM
  • 56. Problem The open circuit and short circuit test conducted on a 3 phase star connected 1905 V 1000 kva 50Hz alternator gave the following data, The armature resistance per phase is 0.2 ฮฉ. Calculate its full load regulation at 0.8 lagging power factor by EMF and MMF method. UEEC007 - ISM Open Circuit Voltage ๐„๐Ž๐‚ 760 1500 1700 1905 2300 2600 Field current If 10 20 25 30 40 50 Short Circuit current Isc - - - 335 - -
  • 57. STEPS โ€ข ๐‘ฝ๐’‘๐’‰ + ๐‘ฐ๐’‚๐’‘๐’‰๐‘น๐’‚ ๐œ๐จ๐ฌ ๐‹ , from OCC find ๐น๐‘œ โ€ข Find the full load short circuit armature current per phase โ€ข Filed current of 30A produces a short circuit current of 335 A , from SCC find ๐น๐ด๐‘… ๐‘๐‘œ๐‘Ÿ๐‘’๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘๐‘Ž๐‘™๐‘๐‘ข๐‘™๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘“๐‘ข๐‘™๐‘™ ๐‘™๐‘œ๐‘Ž๐‘‘ ๐‘Ž๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐‘๐‘ข๐‘Ÿ๐‘Ÿ๐‘’๐‘›๐‘ก. โ€ข Find ๐ธ๐‘‚ corresponding to the calculated ๐น๐‘… โ€ข Find Voltage Regulation ๐ธ๐‘‚ โˆ’๐‘‰ ๐‘‰ โˆ— 100 UEEC007 - ISM ๐‘˜๐‘ฃ๐‘Ž = 3 ๐‘‰๐ฟ๐ผ๐ฟ10โˆ’3 ๐น๐‘… 2 = ๐น๐‘‚ 2 + ๐น๐ด๐‘… 2 -2๐น๐‘œ๐น๐ด๐‘… cos(90ยฐ + ๐œ‘)
  • 62. EMF AND MMF Quantities โ€ข Armature Reaction Reactance ๐ผ๐‘Ž๐‘‹๐‘Ž๐‘Ÿ (fictitious) โ€ข Armature Resistance ๐ผ๐‘Ž๐‘…๐‘Ž โ€ข Leakage Reactance ๐ผ๐‘Ž๐‘‹๐‘™ โ€ข EMF Method โ€“ All drops as EMF quantities โ€ข MMF Method โ€“ All quantities as MMF quantities UEEC007 - ISM EMF Quantity MMF Quantity EMF Quantity
  • 63. ZPF Method โ€ข This ZPF method is based on the separation of armature leakage reactance and armature reaction effects โ€ข The armature leakage reactance ๐‘‹๐‘™ is called Potier reactance in this method, hence ZPF method is also called Potier reactance method UEEC007 - ISM
  • 64. OCC and ZPF Test โ€ข To determine armature leakage reactance and armature reaction MMF separately two tests are performed on the alternator. 1. Open circuit test 2. Zero power factor test UEEC007 - ISM
  • 65. Open Circuit Test UEEC007 - ISM Alternator is running at the rated synchronous speed,the load 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 Et is measured at each step A graph is drawn between the open circuit phase voltage Ep = Et/โˆš3 and the field current If. Field current If Open Circuit Voltage per phase Ep = Et/โˆš3
  • 67. ZPF Steps โ€ข To conduct zero power factor test, the TPST switch is kept closed. โ€ข Due to this, a purely inductive load gets connected to an alternator through an ammeter. โ€ข A purely inductive load has a power factor of cos 90ยฐ i.e. zero lagging hence the test is called zero power factor test. UEEC007 - ISM
  • 68. ZPF Steps โ€ข The machine speed is maintained constant at its synchronous value. โ€ข The load current delivered by an alternator to purely inductive load is maintained constant at its rated full load value by varying excitation and by adjusting variable inductance of the inductive bed. โ€ข Due to purely inductive load, the alternator will always operate at zero power factor lagging. UEEC007 - ISM
  • 69. Zero Power Factor saturation curve โ€ข First point for this curve is zero terminal voltage (short circuit condition) and the field current required to deliver full load short circuit armature current. โ€ข Second point field current required to obtain rated terminal voltage while delivering rated full load armature current UEEC007 - ISM
  • 70. ZPF CURVE UEEC007 - ISM Terminal Voltage and Induced EMF per phase Field Current (๐ผ๐‘“) 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 Rโ€™ Qโ€™ Pโ€™ Sโ€™ Rโ€™ Qโ€™ Pโ€™ Sโ€™ Rโ€™ Qโ€™ Pโ€™ Sโ€™ B C Full Load Zero pf Saturation Curve POTIER TRIANGLE Aโ€™
  • 71. Steps 1.Plot open circuit characteristics 2.Plot the excitation corresponding to zero terminal voltage i.e. short circuit full zero power factor armature current. This point is A. 3.Another point is the rated voltage when the alternator is delivering full current at zero p.f. lagging. This point is P. UEEC007 - ISM
  • 72. 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 called Potier triangle. UEEC007 - ISM
  • 73. Steps 7.From point R, drop a perpendicular on PQ to meet at point S. 8.The zero power factor full load saturation curve is now be constructed by moving triangle PQR so that R remains always on OCC and line PQ always remains horizontal. Note: Potier triangle once obtained is constant for a given armature current and hence can be transferred as it is. UEEC007 - ISM
  • 74. Steps 9.Though point A, draw a line parallel to PR meeting OCC at point B. From B, draw a perpendicular on OA to meet it at point C. Triangles OAB and PQR are similar triangles. UEEC007 - ISM P R S Q A C O B
  • 75. Potier Triangle UEEC007 - ISM P R S Q A C O B โˆ†๐‘ท๐‘ธ๐‘น ๐’‚๐’๐’… โˆ† ๐‘จ๐‘ฉ๐‘ช ๐’‚๐’“๐’† ๐’”๐’Š๐’Ž๐’Š๐’๐’‚๐’“ ๐’•๐’“๐’Š๐’‚๐’๐’๐’ˆ๐’๐’†๐’” The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. ๐‘ฐ๐’‚๐‘ฟ๐’ 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)= ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ Potier Reactance ๐‘ฟ๐’๐’‘๐’‰ = Length of (RS) or Length of (BC) ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)
  • 76. Phasor Diagram UEEC007 - ISM ๐œ‘ ๐‘‰๐‘โ„Ž ๐ผ๐‘Ž๐‘โ„Ž ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ ๐ธ๐‘โ„Ž ๐น๐‘“1 ๐น๐ด๐‘… ๐น๐‘… ๐ธ1๐‘โ„Ž Armature Reaction Drop o A B C D E F G H 90ยฐ + ๐œ‘ 90ยฐ 90ยฐ
  • 77. STEPS 1.Draw the rated terminal voltage ๐‘‰๐‘โ„Ž as a reference phasor. Depending upon at which power factor (cos ๐œ‘ ) the regulation is to be predicted, draw the Current phasor ๐ผ๐‘Ž๐‘โ„Ž lagging or leading ๐‘‰๐‘โ„Ž by angle ๐œ‘ . 2.Draw ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž voltage drop to ๐‘‰๐‘โ„Ž which is in phase with ๐ผ๐‘Ž๐‘โ„Ž. While the voltage drop ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ is to be drawn perpendicular to ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž, vector but leading ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž at the extremity of ๐‘‰๐‘โ„Ž. UEEC007 - ISM
  • 78. STEPS 3.The ๐‘…๐‘Ž๐‘โ„Ž is to be measured separately by passing a d.c current and measuring the voltage across armature winding. While ๐‘ฟ๐’๐’‘๐’‰ is Potier reactance obtained by Potier method. 4.Phasor sum of ๐‘‰๐‘โ„Ž rated, ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž and ๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ gives the e.m.f. which is say ๐ธ1๐‘โ„Ž ๐ธ1๐‘โ„Ž =๐‘‰๐‘โ„Ž + ๐ผ๐‘Ž๐‘โ„Ž๐‘…๐‘Ž๐‘โ„Ž+๐‘ฐ๐’‚๐’‘๐’‰(๐‘ญ.๐‘ณ)๐‘ฟ๐’๐’‘๐’‰ UEEC007 - ISM
  • 79. STEPS 5.Obtain the excitation corresponding to ๐ธ1๐‘โ„Ž from OCC which is drawn. Let this excitation be ๐น๐‘“1 . This is excitation required for inducing EMF which does not consider the effect of armature reaction. 6.The field current required to balance armature reaction can be obtained from Potier triangle method, which is say ๐น๐ด๐‘…. ๐น๐ด๐‘… = Lenght(PS) = Lenght(AC) UEEC007 - ISM P R S Q A C O B Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) ๐ธ1๐‘โ„Ž ๐น๐‘“1
  • 80. STEPS 6.The total excitation required is the vector sum of the ๐น๐‘“1 and ๐น๐ด๐‘…. This can be obtained exactly similar to the procedure used in MMF Method. 7.Draw vector ๐น๐‘“1 to some scale, leading ๐ธ1๐‘โ„Ž by 90ยฐ. Add ๐น๐ด๐‘… to ๐น๐‘“1 by drawing vector ๐น๐ด๐‘… in phase opposition to ๐ผ๐‘Ž๐‘โ„Ž . The total excitation to be supplied by field is given by ๐น๐‘…. UEEC007 - ISM B O A 90ยฐ + ๐œ‘ ๐น๐‘“1 ๐น๐ด๐‘… ๐น๐‘…
  • 81. STEPS 8.Once the total excitation is known which is ๐น๐‘…, the corresponding induced emf ๐ธ๐‘โ„Ž can be obtained from OCC This ๐ธ๐‘โ„Ž lags ๐น๐‘… by 90ยฐ The length CD is the drop due to the armature reaction UEEC007 - ISM Open circuit Voltage (๐ธ๐‘‚๐ถ) Field Current (๐ผ๐‘“) ๐ธ๐‘โ„Ž ๐น๐‘…
  • 82. 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 ๐ธ1๐‘โ„Žcan be determined, analytically. UEEC007 - ISM % Voltage Regulation = ๐ธ๐‘โ„Ž โˆ’๐‘‰๐‘โ„Ž ๐‘‰๐‘โ„Ž โˆ— 100
  • 83. Drawbacks The only drawback of the ZPF method is that the separate curve for every load condition is necessary to plot if Potier triangles for various load conditions are required. UEEC007 - ISM
  • 84. Assumptions โ€ข ln the entire calculation procedure of Potier method, the armature resistance is neglected. But practically armature resistance is very small and hence this assumption does not cause significant error in the accuracy. โ€ข In Potier method, a zero power factor test is required to be done. But practically when inductors are used, a perfect zero power factor cannot be achieved. UEEC007 - ISM
  • 85. Assumptions โ€ข the distances RS, R' S' and BC are assumed equal โ€ข This indicates that the point P in the zero power factor method and point A in the short circuit test represent the same leakage reactance of the machine. โ€ข Length OA<OAโ€™ UEEC007 - ISM P R S Q A C O B
  • 86. Assumptions โ€ข Hence practically the leakage reactance corresponding to saturated conditions is higher than that assumed in the method. This introduces the error in the calculations. UEEC007 - ISM
  • 88. Non Salient Pole Alternators โ€ข Non-salient pole type alternators the air gap is uniform. โ€ข Due to the uniform air gap, the field flux, as well as armature flux vary sinusoidally in the air gap. โ€ข In non salient pole alternators, air gap length is constant and reactance is also constant. โ€ข 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
  • 89. Salient Pole Alternators โ€ข In salient pole type alternators, the length of the air gap varies and the reluctance also varies. โ€ข Hence the armature flux and field flux cannot vary sinusoidally in the air gap. โ€ข The reluctances of the magnetic circuits on which MMFs act are different in the case of salient pole alternators. UEEC007 - ISM
  • 90. Field and Armature MMF UEEC007 - ISM
  • 91. D-axis and q-axis โ€ข The reluctance offered to the MMF wave is lowest when it is aligned with the field pole axis. โ€ข This axis is called the direct axis of pole i.e. d-axis. โ€ข The reluctance offered is highest when the MMF wave is oriented at 90ยฐ to the field pole axis which is called quadrature axis i.e. q-axis. UEEC007 - ISM
  • 92. d-axis and q-axis โ€ข The component which is acting along the direct axis can be magnetizing or demagnetizing. โ€ข The component which is acting along quadrature axis is cross magnetizing. UEEC007 - ISM
  • 93. Field MMF โ€ข The air gap is least in the centre of the poles and progressively increase, on moving away from the centre. โ€ข Due to such shape of the pole-shoes, the field winding wound on salient poles produces the MMF wave which is nearly sinusoidal and it always acts along the pole axis which is direct axis. UEEC007 - ISM
  • 94. Armature MMF The armature m.m.f. can be divided into two components as, 1. Component acting along the pole axis called direct axis. 2. Component acting at right angles to the pole axis called quadrature axis. UEEC007 - ISM
  • 95. Field MMF AND EMF โ€ข Let ๐น๐‘“ be the MMF wave produced by field winding, then it always acts along the direct axis. โ€ข This MMF is responsible for producing an excitation EMF ๐ธ๐‘“ which lags ๐น๐‘“by all angle 90ยฐ. UEEC007 - ISM
  • 96. Armature MMF โ€ข When armature carries current, it produces its own MMF wave ๐น๐ด๐‘… โ€ข This can be resolved into two components, one acting along d-axis (magnetising or demagnetising) and one acting along q-axis (cross- magnetising). โ€ข Similarly, armature current ๐ผ๐‘Ž also can in divided into two components, one along the direct axis and one along quadrature axis. UEEC007 - ISM
  • 97. ๐œ‘๐ด๐‘… VS ๐ผ๐‘Ž The reluctance offered to flux along the direct axis is less than the reluctance offered to flux along quadrature axis. Due to this, the flux ๐œ‘๐ด๐‘… is no longer along ๐น๐ด๐‘… or ๐ผ๐‘Ž. Depending upon the reluctances offered along the direct and quadrature axis, the flux ๐œ‘๐ด๐‘… lags behind armature current ๐ผ๐‘Ž. UEEC007 - ISM
  • 99. Induced EMF UEEC007 - ISM ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐น๐‘‘ ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘š๐‘š๐‘“ ๐น๐‘‘ =๐‘˜๐ด๐‘…. ๐ผ๐‘‘ ๐‘ƒ๐‘‘ = Permeance along the direct axis Permeance is the reciprocal of reluctance and indicates ease with which flux can travel along the path ๐‘˜๐ด๐‘… is the armature reaction coefficient Flux = ๐‘š๐‘š๐‘“ ๐‘Ÿ๐‘’๐‘™๐‘ข๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’
  • 100. Induced EMF UEEC007 - ISM ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘ ๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘“๐‘™๐‘ข๐‘ฅ ๐œ‘๐‘ž = ๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž ๐‘ƒ๐‘‘ > ๐‘ƒ๐‘ž ๐ธ๐‘‘ = ๐พ๐‘’๐œ‘๐‘‘ โˆ  โˆ’ 90ยฐ ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘’๐‘š๐‘“ ๐ธ๐‘‘ =-j ๐พ๐‘’๐œ‘๐‘‘ ๐ธ๐‘ž = ๐พ๐‘’๐œ‘๐‘ž โˆ  โˆ’ 90ยฐ ๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘’๐‘š๐‘“ ๐ธ๐‘ž =-j ๐พ๐‘’๐œ‘๐‘ž ๐พ๐‘’ is the emf constant of the armature winding
  • 101. Induced EMF UEEC007 - ISM ๐‘…๐‘’๐‘ ๐‘ข๐‘™๐‘ก๐‘Ž๐‘›๐‘ก ๐‘’๐‘š๐‘“ ๐ธ๐‘… = ๐ธ๐‘“ + ๐ธ๐‘‘ + ๐ธ๐‘ž ๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐œ‘๐‘‘โˆ’j ๐พ๐‘’๐œ‘๐‘ž ๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘โˆ’j ๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž ๐ธ๐‘ž๐‘ข๐‘–๐‘ฃ๐‘Ž๐‘™๐‘’๐‘›๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘‘ โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘  ๐‘‹๐‘Ž๐‘Ÿ๐‘‘ =๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘… ๐ธ๐‘ž๐‘ข๐‘–๐‘ฃ๐‘Ž๐‘™๐‘’๐‘›๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘๐‘œ๐‘Ÿ๐‘Ÿ๐‘’๐‘ ๐‘๐‘œ๐‘›๐‘‘๐‘–๐‘›๐‘” ๐‘ก๐‘œ ๐‘ž โˆ’ ๐‘Ž๐‘ฅ๐‘–๐‘ ๐‘‹๐‘Ž๐‘Ÿ๐‘ž =๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘… ๐ธ๐‘… = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž
  • 102. Induced EMF UEEC007 - ISM ๐ผ๐‘Ž = ๐ผ๐‘‘ + ๐ผ๐‘ž ๐ธ๐‘… = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž ๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘ž) ๐ผ๐‘ž ๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐‘ž) ๐ผ๐‘ž ๐‘‹๐‘‘ - direct axis synchronous reactance ๐‘‹๐‘ž โˆ’ Quadrature axis synchronous reactance
  • 104. Three Phase Induction Motor UEEC007 - ISM
  • 105. Three Phase Induction motor UEEC007 - ISM
  • 107. Squirrel Cage vs Slip Ring UEEC007 - ISM
  • 108. Three phase stator winding UEEC007 - ISM
  • 109. Three Phase Flux Waveforms UEEC007 - ISM
  • 110. At Point 0 โ€“ 0 degrees UEEC007 - ISM
  • 111. At Point 1 โ€“ 30 degrees UEEC007 - ISM
  • 112. At Point 2 -60 degrees UEEC007 - ISM
  • 113. At Point 3 โ€“ 90 degrees UEEC007 - ISM
  • 115. Principle of Operation โ€ข Three Phase supply โ€“ stator โ€ข Rotating Magnetic Filed is produced โ€“ Synchronous Speed โ€ข A)Rotating Flux b) Stationary Rotor Conductors โ€ข Stator Flux cut by the rotor conductor โ€“ emf induced โ€ข Rotor Short Circuited โ€“ Current Flows to the rotor โ€ข Current Carrying Conductor in a magnetic field โ€“ Mechanical Force UEEC007 - ISM
  • 116. Synchronous Speed and Slip โ€ข Synchronous speed ๐‘๐‘† = 120๐‘“ ๐‘ƒ โ€ข Slip = ๐‘๐‘†โˆ’๐‘๐‘Ÿ ๐‘๐‘† โ€ข %Slip= ๐‘๐‘†โˆ’๐‘๐‘Ÿ ๐‘๐‘† *100 UEEC007 - ISM
  • 118. Equivalent circuit of Induction Motor UEEC007 - ISM
  • 121. Equivalent Circuit of Rotor UEEC007 - ISM
  • 122. Equivalent Circuit Referred to the Stator UEEC007 - ISM
  • 133. Effect of Rotor Resistance on Slip UEEC007 - ISM
  • 137. UEEC007 - ISM ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐น๐‘‘ ๐น๐‘‘ =๐‘˜๐ด๐‘…. ๐ผ๐‘‘ ๐œ‘๐‘‘ = ๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘ ๐œ‘๐‘ž = ๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž ๐‘ƒ๐‘‘ > ๐‘ƒ๐‘ž ๐ธ๐‘‘ = ๐พ๐‘’๐œ‘๐‘‘ โˆ  โˆ’ 90ยฐ ๐ธ๐‘‘ =-j ๐พ๐‘’๐œ‘๐‘‘ ๐ธ๐‘ž = ๐พ๐‘’๐œ‘๐‘ž โˆ  โˆ’ 90ยฐ ๐ธ๐‘ž =-j ๐พ๐‘’๐œ‘๐‘ž ๐ธ๐‘… = ๐ธ๐‘“ + ๐ธ๐‘‘ + ๐ธ๐‘ž ๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐œ‘๐‘‘โˆ’j ๐พ๐‘’๐œ‘๐‘ž ๐ธ๐‘… = ๐ธ๐‘“โˆ’j ๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘…. ๐ผ๐‘‘โˆ’j ๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘…. ๐ผ๐‘ž ๐‘‹๐‘Ž๐‘Ÿ๐‘‘ =๐พ๐‘’๐‘ƒ๐‘‘๐‘˜๐ด๐‘… ๐‘‹๐‘Ž๐‘Ÿ๐‘ž =๐พ๐‘’๐‘ƒ๐‘ž๐‘˜๐ด๐‘… ๐ธ๐‘… = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž. ๐ผ๐‘ž ๐ผ๐‘Ž = ๐ผ๐‘‘ + ๐ผ๐‘‘ ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž + ๐ผ๐‘‘๐‘‹๐ฟ + ๐ผ๐‘ž๐‘‹๐ฟ = ๐ธ๐‘“โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘‘. ๐ผ๐‘‘โˆ’j๐‘‹๐‘Ž๐‘Ÿ๐‘ž ๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐ฟ+๐‘‹๐‘Ž๐‘Ÿ๐‘ž) ๐ผ๐‘ž ๐ธ๐‘“ = ๐‘‰๐‘ก+๐ผ๐‘Ž๐‘…๐‘Ž+j(๐‘‹๐‘‘) ๐ผ๐‘‘+ j(๐‘‹๐‘ž) ๐ผ๐‘ž
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