Induction Machine - Polyphase ac Machines, Exercises of Electric Machines

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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

• (^) 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

 (^) 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

e sync

f

n rpm

P

e sync

f

n 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..

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)

r

P n

f

s m r s e

P n n

f

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 (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 Single Rotor Circuit Representation

2 1 2 1 2 1 2 0 2 2 2 1 0 1 2 2 0 (^221) 0 , X R R m R R R R R where m s R mR R X s X m s R R m ms R s R r r r r r r                       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.

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 ) = I 12 R 1
• (^) Copper loss in the rotor ( PRCL ) = I 22 R 2  (^) Core loss ( P core )  (^) Mechanical power loss due to friction and windage  (^) How this power flow in the motor?