department of electrical and computer engineering ee20a - electromechanical energy conversion...
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Department of Electrical and Department of Electrical and Computer EngineeringComputer Engineering
EE20A - Electromechanical Energy EE20A - Electromechanical Energy ConversionConversion
Induction MachineInduction Machine
Principle of Operation• The stator coils, when energised, create a
rotating magnetic field.• Rotating magnetic field cuts through the
rotor inducing a voltage in the rotor bars.• This voltage creates its own magnetic field
in the rotor.• The rotor magnetic field will attempt to line
up with the stator magnetic field.• The stator magnetic field is rotating, the
rotor magnetic field trying to line up with the stator magnetic field causes the rotor to rotate.
• The rotor magnetic field, never catches up, but follows slightly behind.
Motor AnalysisMotor Analysis
• Slip is the difference between the speed of the stator magnetic field and the speed of the rotor
• SLIP,S, = (NS - N) / NS
• When motor is stationary, it behaves like a transformer
• At a given Speed, flux cutting rate is reduced => thereby reducing output voltage by a factor of the slip.
AnalysisAnalysis
Xm
IN L
Rs jXs
V ph
I IN I1 I2
RO
a : 1IO Im
V1 V2
R rjX r
Per Phase Equivalent Circuit
AnalysisAnalysis
Xm
IN L
Rs jXs
V ph
I IN I1 I2
RO
a : 1I O I m
V1 V2
R rs
jX r
Per Phase Equivalent Circuit
AnalysisAnalysis
Xm
IN L
Rs jXs
V ph
I IN I1
RO
IO Im R rs
jX r
Pair gap
Per Phase Equivalent Circuit
Power per Phase Power per Phase
• Total Torque =
(3Pmech_gross- PF&W)/m
• Pag = I12Rr`/s
• Pcu = sPag
• Pmech_gross = (1-s)Pag
Xm
IN L
Rs jXs
V ph
I IN I1
RO
I O I m R rs
jX r
Pair gap
Per Phase Equivalent Circuit
Power per Phase Power per Phase
m oNL I I I
Pag = Power across the air gap
)X X j( s
R R
V I
rsr
s
ph1
s
R x I P r2
1ag
Power per Phase Power per Phase
P mech_gross = (1-s) Pag per phase
r2
1cu R I P rotor,in lossesCu
m
W&Fmech_gross
ω
P - P x 3 Torque Total
s
s)-(1 R R I P rr
21ag
Power per Phase Power per Phase
s
s)-(1R I RI P r
21r
21ag
Pcu_losses_in_rotor Pmech_gross
PPag ag : P: Pcu cu : P: P
mechmech = 1:s:(1-s) = 1:s:(1-s)
Power per Phase Power per Phase
r2
1
r21_per_phasemech_gross
RIs
s)-(1
s
R I s)-(1 P
Slip is variable and affects only rotor circuit
Ignoring Stator values
rr
ph1
X j s
R
V I
Power per Phase Power per Phase
2
r
2
r
r2
ph
m
m
2r
2
r
r2
ph
r2
1mech_gross
X s
R
R . V x
ns2
s)-(1
2 ω
ω
phaseper Power Torque
Xs
R
R . V x
s
s)-(1
s
s)-(1 R I P
n
Torque Torque Simple Algebraic manipulations yield
22
r
r
2
r
r2ph
r
2r
2
2
r
r
2r
2ph
mech_gross
s X
R
s . X
R . V
x nsX2
s)-(1
X s X
R
s . R . V x
ns2
s)-(1 T
Torque Torque
22r
2ph
2
22ph
rmech_gross
r
r
s
. s x
nX2
V . s)-(1
s
. s . V x
nsX2
s)-(1 Tget Then we
X
R let Now
2
Torque Torque
22rs
2ph
mech_gross
s
s
s
s
s x
Xn2
V T
:get n wefor ngsubstitutiBy
s)-(1n n
n
n - n s slip,But
Since the above calculations was derives as power per phase, then the total torque for all three phases would be three times the gross mechanical torque for each phase calculated above.
22
rs
2ph
22rs
2ph
s
s. .k Torque TotalThen
Xn2
3V k Let
s
s x
Xn2
V x 3 Torque Total
Torque Torque
The maximum torque is obtained when:
sor X
R s slip,
r
r
Torque CharacteristicsTorque Characteristics
Speed-Torque characteristicsSpeed-Torque characteristics
Modifications in the design of the squirrel-cage motors permit a certain amount of control of the starting current and torque characteristics. These designs have been categorised by NEMA Standards (MG1-1.16) into four main classifications:
1. Normal-torque, normal-starting current motors (Design A) 2. Normal-torque, low-starting current motors (Design B) 3. High-torque, low-starting-current, double-wound-rotor motors (Design C) 4. High-slip motors (Design D)
Design A MotorDesign A Motor
• Hp range 0.5 – 500 hp. • Starting current 6 to 10 times full-load current. • Good running efficiency (87% - 89%). • Good power factor (87% - 89%). • Low rated slip (3 –5 %). • Starting torque is about 150% of full load torque. • Maximum torque is over 200% but less than 225% of full-
load torque. • Typical applications – constant speed applications where high
starting torque is not needed and high starting torque is tolerated.
Design B MotorDesign B Motor
•Hp range – 0.5 to 500 hp •Higher reactance than the Design A motor, obtained by means of deep, narrow rotor bars. •The starting current is held to about 5 times the full-load current. •This motor allows full-voltage starting. •The starting torque, slip and efficiency are nearly the same as for the Design A motor. •Power factor and maximum torque are little lower than class A, •Design B is standard in 1 to 250 hp drip-proof motors and in totally enclosed, fan-cooled motors, up to approximately 100 hp. •Typical applications – constant speed applications where high starting torque is not needed and high starting torque is tolerated.
•Unsuitable for applications where there is a high load peak
Design C MotorDesign C Motor
•Hp range – 3 to 200 hp •This type of motor has a "double-layer" or double squirrel-cage winding. •It combines high starting torque with low starting current. •Two windings are applied to the rotor, an outer winding having high resistance and low reactance and an inner winding having low resistance and high reactance. •Operation is such that the reactance of both windings decrease as rotor frequency decreases and speed increases. •On starting a much larger induced currents flow in the outer winding than in the inner winding, because at low rotor speeds the inner-winding reactance is quite high.
Design C MotorDesign C Motor
•As the rotor speed increases, the reactance of the inner winding drops and combined with the low inner-winding resistance, permits the major portion of the rotor current to appear in the inner winding. •Starting current about 5 times full load current. •The starting torque is rather high (200% - 250%). •Full-load torque is the same as that for both A and B designs. •The maximum torque is lower than the starting torque, maximum torque (180-225%).
•Typical applications – constant speed loads requiring fairly high starting torque and lower starting currents.
Design D MotorDesign D Motor •Produces a very high starting torque-approximately 275% of full-load torque.
•It has low starting current,
•High slip (7-16%),
•Low efficiency.
•Torque changes with load
•Typical applications- used for high inertia loads
The above classification is for squirrel cage induction motor
Wound RotorWound Rotor
•Hp 0.5 to 5000hp •Starting torque up to 300% •Maximum torque 225 to 275% of full load torque •Starting current may be as low as 1.5 times starting current •Slip (3 - 50%) •Power factor high •Typical applications – for high starting torque loads where very low starting current is required or where torque must be applied very gradually and where speed control is needed.
Current Effects on the MotorCurrent Effects on the Motor
•Induction motor current consists of reactive (magnetizing) and real (torque) components. •The current component that produces torque (does useful work) is almost in phase with voltage, and has a high power factor close to 100%•The magnetizing current would be purely inductive, except that the winding has some small resistance, and it lags the voltage by nearly 90°. •The magnetizing current has a very low power factor, close to zero.•The magnetic field is nearly constant from no load to full load and beyond, so the magnetizing portion of the total current is approximately the same for all loads.
•The torque current increases as the load increases
•At full load, the torque current is higher than the magnetizing current. •For a typical motor, the power factor of the resulting current is between 85% and 90%. •As the load is reduced, the torque current decreases, but the magnetizing current remains about the same so the resulting current has a lower power factor. •The smaller the load, the lower the load current and the lower the power factor. Low power factor at low loading occurs because the magnetizing remains approximately the same at no load as at full load
Current Effects on the MotorCurrent Effects on the Motor
Methods to vary speed of theMethods to vary speed of the Induction Motor Induction Motor
An induction motor is a constant-speed device. Its speed depends on the number of poles in the stator, assuming that the voltage and frequency of the supply to the motor remain constant.
•One method is to change the number of poles in the stator, for example, reconnecting a 4-pole winding so that it becomes a 2-pole winding will double the speed. This method can give specific alternate speeds but not gradual speed changes.
•Another method is to vary the line voltage this method is not the best since torque is proportional to the square of the voltage, so reducing the line voltage rapidly reduces the available torque causing the motor to stall
Methods to vary speed of theMethods to vary speed of the Induction Motor Induction Motor
•Sometimes it is desirable to have a high starting torque or to have a constant horsepower output over a given speed range. These and other modifications can be obtained by varying the ratio of voltage to frequency as required. Some controllers are designed to provide constant torque up to 60 Hz and constant hp above 60 Hz to provide higher speeds without overloading the motor.
•An excellent way to vary the speed of a squirrel-cage induction motor is to vary the frequency of the applied voltage. To maintain a constant torque, the ratio of voltage to frequency must be kept constant, so the voltage must be varied simultaneously with the frequency. Modern adjustable frequency controls perform this function. At constant torque, the horsepower output increases directly as the speed increases.
NO LOAD TESTNO LOAD TEST
Watt
meter
AC
I
V
C urren tC o il
Volta
geCo
il
Xm
IN L
Rs jXs
V ph
I IN I1
RO
I O I m R rs
jX r
Pair gap
Per Phase Equivalent Circuit
NO LOAD TESTNO LOAD TEST
n - ns = 0 ‘No load Speed Synchronous Speed’
i.e. no power transfer which implies that Torque = 0
I1 = 0 & T = 0
Power Consumed = Core Losses + Friction & Windage
Measure Vph , IIN and Wph
( Infinite Impedance ) since I1 = 0
E
sr
R
• INL = I0 – jIm
= INL ( cos NL - jsin NL )
• cos NL = Wph
Vph INL
• Ro = Vph Xm = Vph
I0 Im
NO LOAD TESTNO LOAD TEST
Lock Rotor TestLock Rotor Test
Wattm
eter
AC
I
V
C urren tC o il
Volta
ge Coil
Xm
IN L
Rs jXs
V ph
I IN I1
RO
I O I m R r
jX r
Pair gap
s
Lock Rotor TestLock Rotor Test
• In the Lock Rotor test, No Load Speed, n = 0
Slip, s = ns – 0 = 1, s = 1
ns
• Then Rr Rr
s
•Apply Voltage to Variac, VLR = (10% - 25% ) Vph
• Since INL<< I1 Then INL 0
• Measure values VLR , ILR and WLR
Lock Rotor TestLock Rotor Test•Zeq = VLR / ILR
•cos LR= WLR
VLR ILR
• Zeq = Zeq {cos LR - jsin LR}
= Zeq cos LR - Zeq jsin LR
Rs+ Rr Xs + Xr
•At Standstill Under d.c. conditions = 0
X= L
X = 0
•R1 & R2 can be measured using an ohmmeter over two stator windings, which gives a value of Rs
• Rr = Zeq cos LR - Rs
Lock Rotor TestLock Rotor Test
Rs jXs
Ohmmeter
R 1
R 2
STATOR ROTOR
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