part 13 emachines EEP 3243

8/9/2019 part 13 emachines EEP 3243

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ELECTRICAL MACHINE

EEP 3243

Cdr Ong Khye Liat RMN

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Induction Machines


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Introduction

The induction machine was invented by NIKOLATESLA in1888.

The induction machine is an AC electromechanical energy

conversion device.

There are machines available to operate from three phase orsingle phase electrical input. Single phase machines are

restricted to small power levels.

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Principle of Operation

The operation of a 3 phase induction motor is based

upon the application of Faraday's Law and the

Lorentz force on a conductor. A permanent magnet placed above this conducting

ladder, moves rapidly to the right at a speed.

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Cont.

A voltage E=Blv is induced in each conductor while it isbeing cut by the flux (Faraday's Law).

The induced voltage immediately produces a current,

which flows down the conductor underneath the pole-face,

though the end bars and back through the other

conductor.

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Cont.

Because the current-carrying conductor lies in themagnetic field of the permanent magnet, it experiences a

mechanical force (Lorentz force).

The force always acts in a direction to drag the conductor

along with the magnetic field.

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Cont. In an induction motor the ladder is closed to form a

squirrel-cage and the moving magnet is replaced by a

rotating field.

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The Rotating Magnetic Field

The principle of operation of the induction machine is

based on the generation of a rotating magnetic field.

Consider a cosine wave from 0o to 360o . This sine wave is

plotted with unit amplitude. Now allow the amplitude of the sine wave to vary with

respect to time in a sinusoidal fashion with a frequency of

50Hz.Let the maximum value of the amplitude is, say, 10

units. This waveform is a pulsating sine wave.

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Cont.

Now consider a second sine wave, which is displaced by 120ofrom the first (lagging). and allow its amplitude to vary in a

similar manner, but with a 120o time lag.

Similarly consider a third sine wave, which is at 240o lag and

allow its amplitude to change as well with a 240o time lag. Now

we have three pulsating sine waves.

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Cont. if we sum up the values of these three sine waves at every

angle we will get a constant amplitude travelling sine wave!

In a three phase induction machine, there are three setsof windings phase A winding, phase B and phase C

windings. These are excited by a balanced three-phase voltage

supply. This would result in a balanced three phasecurrent. Note that they have a 120 time lag betweenthem.

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Cont. Further, in an induction machine, the windings are not all

located in the same place. They are distributed in the machine

120 away from each other.

When currents flow through the coils, they generate mmfs.Since mmf is proportional to current, these waveforms also

represent the mmf generated by the coils and the total mmf.

Further, due to magnetic material in the machine (iron), these

mmfs generate magnetic flux, which is proportional to the mmf.

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Cont.

Thus the waveforms seen above would also

represent the flux generated within the machine.

The net result as we have seen is a travelling fluxwave. The x-axis would represent the space angle

in the machine as one travels around the air gap.

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Cont. This may be better visualized in apolar plot. The angles

of the polar plot represent the space angle in the

machine, i.e., angle as one travels around the stator

bore of the machine.

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Cont. This plot shows the pulsating wave at the zero degree axes. The

amplitude is maximum at zero degree axes and is zero at 90 axis.Positive parts of the waveform are shown in red while negative in blue.Note that the waveform is pulsating at the 0180 axis and red and bluealternate in any given side. This corresponds to the sine wave currentchanging polarity. Note that the maximum amplitude of the sine wave isreached only along the 0180 axis. At all other angles, the amplitude

does not reach a maximum of this value. It however reaches a maximumvalue which is less than that of the peak occurring at the 0 180 axis.More exactly, the maximum reached at any space angle would be equalto cos times the peak at the 0 180 axis. Further, at any space angle the time variation is sinusoidal with the frequency and phase lag being thaof the excitation, and amplitude being that corresponding to the space

angle.

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Cont.

T

his plot shows the pulsating waveforms ofall threecosines. Note that the first is pulsating about the 0 180

axis, the second about the120 300axis and the third

at 240 360axis.

This plot shows the travelling wave in a circulartrajectory. Note that while individual pulsating waves

have maximum amplitude of 10, the resultant has

amplitude of 15.

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Cont.

If f1 is the amplitude of the flux waveform in each

phase, the travelling wave can then be represented

as

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Cont.

As time goes by, the instantaneous value and direction ofthe current in each winding and thereby establish the

successive flux patterns.

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Cont.

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Cont.

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Number ofPoles - Synchronous Speed

The speed of a rotating field depends therefore upon thefrequency of the source and the number of the poles on the stator.

This equation shows that the synchronous speed increase with

frequency and decreases with the number of poles.

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Slip and Slip Speed The slip of an induction motor is the difference between the

synchronous speed and the rotor speed, expressed as a percentor per-unit of synchronous speed.

The slip is practically zero at no-load and is equal to 1 (100%)

when the rotor is locked.

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Cont.

The voltage and frequency induced in the rotor bothdepend upon the slip. They are given by the following

equations:

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? A

? A

][2

2

2

2

VrestatwhenrotortheininducedvoltagecircuitopenEsslipatrotortheininducedvoltageE

Hzsourcetheoffrequencyf

Hzrotortheincurrentandvoltagethefrequencyf

where

sEEsff

oc

oc

!

!

!

!

}

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PROBLEM 1&2

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Active Power Flow

Active power Pe flows from the line into the 3-phase stator. Due to the stator copper losses, a portion Pjs is dissipated

as heat in the windings.

Another portion Pfis dissipated as heat in the stator core,

owing to the iron losses.

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Cont. The remaining active power Pr is carried across the air

gap and transferred to the rotor by electromagneticinduction.

Due to the I2R losses in the rotor, a third portion Pjr is

dissipated as heat, and the remainder is finally availablein the form of mechanical power Pm.

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Cont.

By subtracting a fourth portion Pv, representing windageand bearing-friction losses, we finally obtain PL, the

mechanical power available at the shaft.

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Cont.

The power flow diagram enables us to indentify and tocalculate 3 important properties of the induction motor.

1. Efficiency:

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Cont.

I2

R Losses in the rotor. The rotor I2

R losses Pjrare related tothe rotor input power Prby the equation

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Cont.2. Mechanical Power Pm developed by the motor is equal to

the power transmitted to the rotor minus its I2R losses.

Thus,

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Cont.

3. Motor Torque Tm developed by the motor at any speed

is given by,

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Doubly-Fed Induction Machine

Wound rotor induction machines may have the

stator and rotor connected to separate AC sources

having different frequencies.

The speed is varies by applying a fixed frequency to

the stator and a variable frequency to the rotor.

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Cont. Doubly-Fed motor can used to drive variable speed

pumps.

Doubly-Fed generator can used as variable-speed

generators driven by wind turbines.

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Cont. In practice, this machine has known issues of instability, high

maintenance and inefficiency of an integral multiphase slip-ring assembly, and discontinuity about synchronous speedwhere induction ceases to exist.

The wound-rotor doubly-fed induction electric machine has

been forced into antiquity, except in large installations whereefficiency and cost are critical over a limited speed range,such as wind turbines.

This may change with recentBrushless Wound-Rotor Doubly-

FedElectric Machine technology development.

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PROBLEM 3

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THE END

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part 13 emachines EEP 3243