induction mach slides
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Department of Electrical andDepartment of Electrical and
Computer EngineeringComputer Engineering
EE20AEE20A -- Electromechanical EnergyElectromechanical Energy
ConversionConversion
Induction MachineInduction Machine
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Principle of Operation
• The stator coils, when energised, create arotating magnetic field.
• Rotating magnetic field cuts through therotor inducing a voltage in the rotor bars.
• This voltage creates its own magnetic fieldin the rotor.
• The rotor magnetic field will attempt to lineup with the stator magnetic field.
• The stator magnetic field is rotating, therotor magnetic field trying to line up withthe stator magnetic field causes the rotor torotate.
• The rotor magnetic field, never catches up,
but follows slightly behind.
Principle of OperationThe 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.
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Motor AnalysisMotor Analysis
• Slip is the difference betweenthe speed of the stator magneticfield 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.
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
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AnalysisAnalysis
Xm
I NL
Rs
jXs
Vph
IIN
I1
I2
RO
a : 1IO I
m
V1 V2
Rr
jXr
Per Phase Equivalent Circuit
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AnalysisAnalysis
Xm
I NL
Rs
jXs
Vph
IIN
I1
I2
RO
a : 1IO I
m
V1 V2
Rr
s jX
r
Per Phase Equivalent Circuit
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AnalysisAnalysis
Xm
I NL
Rs
jXs
Vph
IIN
I1
RO
IO Im R
r
s
jXr
Pair gap
Per Phase Equivalent Circuit
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Power per PhasePower per Phase
• Total Torque =
(3Pmech_gross- PF&W)/ωm
• Pag = I12R r ̀ /s
• Pcu = sPag
• Pmech_gross = (1-s)Pag
Xm
I NL
Rs
jXs
Vph
IIN
I1
RO
IO I
m Rr
s
jXr
Pair gap
Per Phase Equivalent Circuit
Power per PhasePower per Phase
Total Torque =
(3Pmech_gross- PF&W)/ωm
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Power per PhasePower per Phase
mo NL III +=
Pag = Power across the air gap
′′ +++
=
s
R xIP r
2
1ag
′=
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Power per PhasePower per Phase
P mech_gross = (1-s) Pag per phase
r 2
1cu R IProtor,inlossesCu ′=
m
W&Fmech_gross
ω
P-Px3 TorqueTotal =
[ ] ⎥⎦⎤⎢⎣
⎡ += ′s
s)-(1 R R IP r r 2
1ag
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Power per PhasePower per Phase
[ ] [ ]s
s)-(1R IR IP r
2
1r
2
1ag += ′
Pcu_losses_in_rotor Pmech_gross
PPagag :: PPcucu :: PPmechmech = 1:s:(1= 1:s:(1--s)s)
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Power per PhasePower per Phase
[ ]
[ ] r 2
1
r 2
1 _per_phasemech_gross
R Is
s)-(1
s
R Is)-(1P
′
′
⎥⎦
⎤⎢⎣
⎡=
⎥⎦
⎤⎢⎣
⎡=
Slip is variable and affects only rotor circuit
Ignoring Stator values
r r
ph1
X j
s
R V I
′′ +
=
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Power per PhasePower per Phase
[ ]
[ ][ ]
[ ]
2
r
2
r
r
2
ph
m
m
2
r
2
r
r
2
ph
r
2
1mech_gross
X
s
R
R .V x
ns2
s)-(1
2 ω
ω
phase perPowerTorque
Xs
R
R .V x
ss)-(1
s
s)-(1 R IP
′′
′
′′
′
′
+⎥⎦
⎤⎢⎣
⎡Π⇒
Π=
=
+⎥⎦
⎤⎢⎣
⎡=
=
n
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TorqueTorque
Simple Algebraic manipulations yield
( )
⎪⎪
⎭
⎪⎪
⎬
⎫
⎪⎪
⎩
⎪⎪
⎨
⎧
+⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⇒
⎪
⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪
⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡+⎟⎟
⎠
⎞⎜⎜
⎝
⎛ ⎥⎦⎤⎢⎣
⎡=
′
′
′
′
′
′
′
′
′
22
r
r
2
r
r 2
ph
r
2
r
2
2
r
r
2
r
2
ph
mech_gross
sX
R
s.
X
R .V
xnsX2
s)-(1
XsX
R
s.R .V xns2s)-(1 T
π
π
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TorqueTorque
⎥⎦
⎤
⎢⎣
⎡
+⎥⎥⎦
⎤
⎢⎢⎣
⎡⇒
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+⎥⎦
⎤⎢⎣
⎡=
=
′
′
′
′
22r
2
ph
2
22
ph
r
mech_gross
r
r
s
.s x
nX2
V.s)-(1
s
.s.V x
nsX2
s)-(1 TgetThen we
X
R let Now
2
α
α
π
α
λ
π
α
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TorqueTorque
22
r s
2
phmech_gross
s
s
s
ss x
Xn2V T
:getn weforngsubstitutiBy
s)-(1nn
n
n-n sslip,But
+=
=⇒
=
′ α π
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.
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22
r s
2 ph
22
r s
2
ph
s
s. .kTorqueTotalThen
Xn2
3V kLet
s
s x
Xn2
V x3TorqueTotal
+=
=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+=
′
′
α
α
π
α π
TorqueTorque
The maximum torque is obtained when:
α sorX
R sslip,
r
r ==′
′
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Torque CharacteristicsTorque Characteristics
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SpeedSpeed--Torque characteristicsTorque characteristicsModifications 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)
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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.
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Design B MotorDesign B Motor•Hp range – 0.5 to 500 hp
•Higher reactance than the Design A motor, obtained by means ofdeep, 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 forthe 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
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Design C MotorDesign C Motor
•Hp range – 3 to 200 hp
•This type of motor has a "double-layer" or double squirrel-cagewinding.
•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 havinglow 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.
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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.
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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
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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.
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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
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•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 noload as at full load
Current Effects on the MotorCurrent Effects on the Motor
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Methods to vary speed of theMethods to vary speed of the
Induction MotorInduction MotorAn 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 methodcan give specific alternate speeds but not gradual speed
changes.
•Another method is to vary the line voltage this method is notthe 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
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Methods to vary speed of theMethods to vary speed of the
Induction MotorInduction 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 voltageto 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 thefrequency. Modern adjustable frequency controls perform this
function. At constant torque, the horsepower output increases
directly as the speed increases.
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NO LOAD TESTNO LOAD TEST
W a t t m
e t e r
AC
I
V
Current
Coil
V o l t a g e
C o i l
Xm
I NL
Rs
jXs
Vph
IIN
I1
RO
IO Im Rr
s
jXr
Pair gap
Per Phase Equivalent Circuit
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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 ′
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• INL = I0 – jIm
=⏐
INL ⏐ ( cos ∅NL - jsin ∅NL )
• cos∅NL = Wph
Vph ⏐ INL ⏐
• Ro = Vph Xm = Vph
I0 Im
NO LOAD TESTNO LOAD TEST
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Lock Rotor TestLock Rotor Test
W a t t m
e t e r
AC
I
V
Current
Coil
V o l t a g e
C o i l
Xm
I NL
Rs jXs
Vph
IIN
I1
RO
IO Im R
r
jXr
Pair gap
s
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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
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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
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•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
R1
R2
STATOR ROTOR
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