Induction Machine - Polyphase ac Machines, Exercises for Electric Machines
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Induction Machine - Polyphase ac Machines, Exercises for Electric Machines

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Circuit Analysis of Induction Machine using complete and approximate equivalent circuit of the machine
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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

Cutaway in a typical wound- rotor IM. Notice the brushes and the slip rings

Brushes

Slip rings

 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

Principle of operation

120 e sync

fn rpm P

 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

Principle of operation contd..

The Slip

sync m

sync

n n s

n

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

Where fr = the rotor current frequency (Hz) P = number of stator poles n = slip speed (rpm)

120r P nf 

( ) 120

120

s m r

s e

P n nf

P sn sf

  

  

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 full-load 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 single- cage induction motor (with one rotor winding).

Equivalent circuit of a double- cage induction motor (two rotor windings).

Equivalent Circuit Single Rotor Circuit Representation

 

 

2

21

21

21 0

22 2

1 0

1

22 0

122

0

,

X RR

m

RR RR

R

where sm

R mRR

XsX

sm

R Rmsm

RsR

r

r

r

r rr

 

 

  

 



  

 

For system studies, the rotor should be represented by a single rotor circuit whose parameters vary as a function of slip, s.

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 three- phase winding.

Stator and Rotor Circuits

 

  

  

  

  

 

  

  

  

   

  

  

  

  

  

 

  

  

  

   

  

 

C

B

A

r

r

r

C

B

A

C

B

A

c

b

a

s

s

s

c

b

a

c

b

a

s

r

i i i

R R

R p

v v v

i i i

R R

R p

v v v

ts t

1

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

3 cos 3 cosin L L ph phP V I V I   2

1 13SCLP I R

( )AG in SCL coreP P P P  

2 2 23RCLP I R

conv AG RCLP P P 

( )out conv f w strayP P P P  

Torque, power and Thevenin’s Theorem

1 1 1 1( )

M eq

M

jXV V R j X X

  

1 1( ) //eq eq MR jX R jX jX  

Torque, power and Thevenin’s Theorem

Then the power converted to mechanical (Pconv)

1 1 2 2

22 2( )

eq eq

T

eq eq

V V I

Z RR X X s

        

2 2 2

(1 ) conv

R sP I s

And the internal mechanical torque (Tconv)

conv conv

m

PT

 (1 )

conv

s

P s

 

2 2 2

s

RI s

 

Torque, power and Thevenin’s Theorem 2

1 2 2

22 2

1

( )

eq conv

s

eq eq

V RT sRR X X

s

                    

2 2 1

2 22

2

1

( )

eq

conv s

eq eq

RV sT

RR X X s

     

      

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