Transcript Induction Motors

Induction Machines
Introduction
 Most industrial motors are squirrel cage induction machines because
of their simple and robust construction, low cost, minimal
maintenance, and inherent overload protection.
 However, induction generators are much less widely used because
the drive speed, electrical frequency, voltage, load, and equivalent
terminal capacitance must be juggled to provide both the reactive
excitation power to the machine and the varying real power to the
load.
 This type of generator is not widely used outside the wind turbine
industry, and in small hydropower units
Construction
 An induction machine has two main parts
-
a stationary stator
•
•
consisting of a steel frame that supports a hollow, cylindrical core
core, constructed from stacked laminations, having a number of
evenly spaced slots, providing the space for the stator winding
Stator of IM
Construction
-
a revolving rotor
•
•
•
•
composed of punched laminations, stacked to create a series of rotor
slots, providing space for the rotor winding
one of two types of rotor windings
conventional 3-phase windings made of insulated wire (wound-rotor) »
similar to the winding on the stator
aluminum bus bars shorted together at the ends by two aluminum rings,
forming a squirrel-cage shaped circuit (squirrel-cage)
 Two basic design types depending on the rotor design
-
-
squirrel-cage: conducting bars laid into slots and shorted at both
ends by shorting rings.
wound-rotor: complete set of three-phase windings exactly as the
stator. Usually Y-connected, the ends of the three rotor wires are
connected to 3 slip rings on the rotor shaft. In this way, the rotor
circuit is accessible.
Construction
Squirrel cage rotor (copper)
Wound rotor
Notice the
slip rings
Construction
Slip rings
Cutaway in a
typical woundrotor IM.
Notice the
brushes and the
slip rings
Brushes
Principle of operation
 The stator is usually connected to the grid and, thus, the
stator is magnetized
 A rotating magnetic field with constant magnitude is
produced, rotating with a speed
nsync 
120 f e
P
rpm
Principle of operation contd..
 In order to generate power the rotor speed must be slightly
above the synchronous speed
 The harder the rotor is cranked, the more power will be fed
into the electrical grid
The Slip
s
nsync  nm
nsync
Where s is the slip. Slip is one of the most
important variables in the control and
operation of induction machines.
s=0
: if the rotor runs at
synchronous speed
s=1
: if the rotor is stationary
s is –ve : if the rotor runs at a speed
above the synchronous speed
s is +ve : if the rotor runs at a speed
below the synchronous speed
Frequency

The frequency of the voltage induced in the rotor is given by
fr 
Pn
120
Where fr = the rotor current frequency (Hz)
P = number of stator poles
n = slip speed (rpm)
P  (ns  nm )
fr 
120
P  sns

 sf e
120
Alternative Rotor Constructions
 High efficiency at normal operating conditions requires a low rotor resistance.
 On the other hand, a high rotor resistance is required to produce a high starting torque
and to keep the magnitude of the starting current low and the power factor high.
 The wound rotor is one way of meeting the above mentioned need for varying the
rotor resistance at different operating conditions. Wound-rotor motors are, however,
more expensive than squirrel-cage motors.
Effect of the rotor resistance
the torque-slip curves.
Double Squirrel-Cage Rotor Construction
 Following double squirrel-cage arrangements can also be used to obtained a high
value of effective resistance at starting and a low value of the resistance at fullload operation.
 It consists of two layers of bars, both short-circuited by end rings.
 The upper bars are small in cross-section and have a high resistance.
 They are placed near the rotor surface so that the leakage flux sees a path of high
reluctance; consequently, they have a low leakage inductance.
 The lower bars have a large cross-section, a lower resistance and a high leakage
inductance.
Double squirrel-cage rotor bars
Double Squirrel-Cage Rotor Construction (cont’d)
 At starting, rotor frequency is high and very little current flows through the
lower bars; the effective resistance of the rotor is then the high resistance upper
bars.
 At normal low slip operation, leakage reactances are negligible, and the rotor
current flows largely through the low resistance lower bars; the effective rotor
resistance is equal to that of the two sets of bars in parallel.
Double squirrel-cage rotor bars
Deep-Bar Rotor Construction
 The use of deep, narrow rotor bars produces torque-slip characteristics similar to
those of a double-cage rotor.
 Leakage inductance of the top cross-section of the rotor bar is relatively low; the
lower sections have progressively higher leakage inductance.
 At starting, due to the high rotor frequency, the current is concentrated towards
the top layers of the rotor bar.
 At full-load operation, the current distribution becomes uniform and the
effective resistance is low.
Deep-bar rotor construction
Equivalent Circuit with a Double Cage or Deep Bar Rotor
Equivalent circuit of a singlecage induction motor (with one rotor
winding).
Equivalent circuit of a doublecage induction motor (two rotor
windings).
Equivalent Circuit Single Rotor Circuit Representation
For system studies, the rotor should be
represented by a single rotor circuit whose
parameters vary as a function of slip, s.
R

m 2  ms 2  1
Rr 0 

Rr s   Rr 0
m2  s2
mR
Rr 0  1 
R2 

X r s   X 1 
m2  s2
where,
RR
Rr 0  1 2
R1  R2
m
R1  R2
X2
Modeling Induction Machines
In developing the model of induction machines, following aspects will
differ from those of synchronous machines:
 The d- and q-axis equivalent circuits are identical as the rotor has
symmetrical structure.
 The rotor speed is not fixed but varies with load. This has an impact
on the selection of the d-q reference frame.
 There is no excitation source to the rotor windings. Consequently, the
dynamics of the rotor circuits are determined by slip.
 The current induced in the shorted rotor windings produce a field with
the same number of poles as that produced by the stator windings.
Rotor windings may therefore be modeled by an equivalent threephase winding.
Stator and Rotor Circuits
  r t
 1  s  s t
v a 
v  
 b
 v c 
 a   R s
p  b   
  c  
v A 
v  
 B
vC 
 A   R r
p  B   
 C  
Rs
 i a 
 i 
 b 
R s  ic 
Rr
 i A 
 i 
 B 
Rr  iC 
Equivalent Circuit
 We can rearrange the equivalent circuit as follows
Actual rotor
resistance
Resistance
equivalent to
mechanical load
Power losses in Induction machines
 Copper losses
-
Copper loss in the stator (PSCL) = I12R1
Copper loss in the rotor (PRCL) = I22R2
 Core loss (Pcore)
 Mechanical power loss due to friction and windage
 How this power flow in the motor?
Power flow in IM
Power relations
Pin  3 VL I L cos   3 Vph I ph cos 
PSCL  3 I12 R1
PAG  Pin  ( PSCL  Pcore )
PRCL  3I 22 R2
Pconv  PAG  PRCL
Pout  Pconv  ( Pf  w  Pstray )
Torque, power and Thevenin’s Theorem
V1eq
jX M
 V1
R1  j ( X 1  X M )
Req  jX eq  ( R1  jX 1 ) // jX M
Torque, power and Thevenin’s Theorem
I2 
V1eq
ZT

V1eq
2
R2 

2
R


(
X

X
)
 eq

eq
2
s


Then the power converted to mechanical (Pconv)
Pconv
R2 (1  s )
I
s
2
2
And the internal mechanical torque (Tconv)
Tconv 
Pconv
m
Pconv

(1  s )s
R2
I
s

2
2
s
Torque, power and Thevenin’s Theorem
Tconv


V1eq
1 
 
2
s 
 R  R2   ( X  X ) 2
eq
2
  eq s 



  R2 
  s 
  


 R2 
V  
1
 s 

2
s 
R2 
2
R


(
X

X
)
 eq

eq
2
s


2
1eq
Tconv
2
Torque-speed characteristics
Typical torque-speed characteristics of induction motor
Maximum torque
 Maximum torque occurs when the power
transferred to R2/s is maximum.
 This condition occurs when R2/s equals the
magnitude of the impedance Req + j (Xeq + X2)
R2
 Req2  ( X eq  X 2 )2
sTmax
sTmax 
R2
Req2  ( X eq  X 2 )2
Maximum torque
 The corresponding maximum torque of an induction
motor equals
Tmax
2

V
1 
eq

2s  Req  Req2  ( X eq  X 2 ) 2





 The slip at maximum torque is directly proportional
to the rotor resistance R2
 The maximum torque is independent of R2
Maximum torque
 Rotor resistance can be increased by inserting
external resistance in the rotor of a wound-rotor
induction motor.
 The value of the maximum torque remains
unaffected but the speed at which it occurs can be
controlled.
Maximum torque
Effect of rotor resistance on torque-speed characteristic
MATLAB/SIMULINK Simulation
d-q Axis Model of IM
Model Parameters
Simulink Block Configuration
d-q Axis Frame Transformations
d-q Axis Frame Transformations cont’d..
Simulink Block Parameters
Simulink Block Parameters cont’d..
Simulink Block Advanced Properties
Input/ Output Parameters
Input/ Output Parameters cont’d..
Motor Mode Operation of IM
Speed-Torque Characteristics
Rotor Current & Stator Current Characteristics
PWM Inverter Output
Effect of Saturation on IM
Saturation Parameters
Saturation Model Accuracy