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Induction Motors

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1. Construction2. Operation3. Equivalent circuit4. Losses and efficiency5. Torque – speed characteristics6. Approximate equivalent circuit7. Max power, max torque, max

efficiency criteria8. Starting9. Speed control10.Single phase induction motors

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1. Construction

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Stator

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Stator• Made of a stack of highly permeable steel laminations

-> reduce the eddy current losses

• Identical coils are wound into the slots and

connected to form a balanced 3-phase winding

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Two types:Squirrel-cage rotorWound rotor

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Rotor

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Squirrel cage rotor•Widely used in low starting torque requirements•Series of conducting bars laid into slots in the rotor•End rings – to short circuit the bars on both ends

Wound rotor

• Used in high starting torque requirements

• 3-phase windings are internally connected to form an internal neutral connection

• Other 3 ends are connected to the slip-rings

• With the brushes riding on the slip-rings, we can add external resistances in the rotor circuit - can control the developed torque

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Disadvantages:• Expensive• Less efficient• Heavier, large in size• Increased maintenance

2. Operation

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Stator winding is connected to a 3-phase power source

Produces a magnetic field

Synchronous speed of the revolving field is,

f = frequency of the stator currentP = number of polesEE2802

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Induces an emf in the rotor winding -> induce a current in rotor coils

Current carrying coil is placed in a magnetic field

-> force (torque)-> Starting torque

Rotor starts rotating

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Slip speed and slipTwo terms used to describe the

relative motion of the rotor and the magnetic filed

Relative speed of the revolving filed (Slip speed);

Nm = Rotor speedNs = Synchronous speed

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Slip;

If rotor is stationary, slip is 1If rotor runs at synchronous

speed, slip is 0

When the rotor rotates, frequency of the induced emf is;

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If the IM is operating at low slip -> frequency of the induced

emf is low -> Core loss can be ignored

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Phase currents must be equal in magnitude and 1200 apart - both in stator and rotor windings

IM - 3-phase transformer - with a rotating secondary winding

Per phase equivalent circuit :

3. Equivalent Circuit

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Rotor winding current

= Effective resistance

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By referring to the stator:

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4. Losses and Efficiency

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5. Torque – Speed Characteristics

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Developed torque is proportional to square of the rotor current hypothetical rotor resistance

However those two quantities are inversely proportional

Torque increases or decreases depends upon which parameter plays a dominant role

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At standstill, s = 1As slip deceases, R2/s increases

As long as

Rotor current is almost constant.Developed torque is proportional to

hypothetical rotor resistance->Torque increases with the

decrease in the slipEE2802

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When the slip falls below the breakdown slip (Sb)

• Developed torque is proportional to the slip

• Torque decreases with the decrease in slip

At no load,

• Slip = 0 • Rotor current = 0 • Torque = 0 EE2802

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Example:A 6-pole, 230V, 60Hz, Y connected 3-phase induction motor has the following parameters on a per-phase basis. The friction and windage loss is 150W. Determine the efficiency and the shaft torque of the motor at its rated slip of 2.5%.

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In a well designed 3-phase IM;• R1 & X1 are small • Rc & Xm are high

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6. Approximate Equivalent Circuit

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7. Max Power, Max Torque & Max Efficiency

1) Max Power Criteria

Developed power is a function of the slip

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2) Max Torque Criteria

Developed torque is a function of the slip

• Max torque is independent of R2

• R2 influences only the breakdown slip (or breakdown speed)

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Motor develops maximum power at a slip lower than that at which it develops maximum torque

When stator impedance <<< rotor impedance

Approximate equation for developed torque;

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Example:

A 8-pole, 208V, 60Hz, Y connected 3-phase induction motor has negligible stator impedance and a rotor impedance of 0.02+j0.08Ω per phase at standstill. Determine the breakdown slip and the breakdown torque. What is the starting torque developed by the motor? If the starting torque has to be 80% of the maximum torque, determine the external resistance that must be added in series with the rotor.

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3) Max Efficiency Criteria

• Core loss as a part of the rotational loss• Assume magnetization current is negligible

• Efficiency is a function of rotor current• For max efficiency

• Stator copper loss + Rotor copper loss = Rotational loss

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8. Starting

At starting, s=1

R2/s is very small at starting -> I2(s) = (400% to 800%) I2(fL)

Td(s) = (200% to 350%) Td(fL)

High starting current -> line voltage drop -> affects the operation 37 EE2802

Solutions:

1) Giving low voltage at starting

- Starting torque reducing- Suitable for low starting torque requirements

2) Increase the rotor resistance

- Starting torque increasing- Suitable for high starting torque requirements

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Giving low voltage at starting

1) Stator impedance starting- Adding external resistance with the stator winding

2) Auto-transformer starting- Using one 3-phase auto-transformer or three 1-phase auto-

transformers- Can achieve lower starting current than previous method

3) Star – delta startingStator winding - at starting - star connection

- when running - delta connection

IL (Y) = IL (delta) / 3

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Increase the rotor resistance

High rotor resistance;- Reduces developed torque at full load- High rotor copper loss -> reduces efficiency

To overcome;

For wound rotor motor:Add a high external resistance through slip rings only at starting

For squirrel cage motor:1) Double cage rotor 2) Skewing

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1. Frequency control

2. Changing stator poles

3. Rotor resistance control

4. Stator voltage control

5. Injecting an emf in the rotor circuit

9. Speed Control

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Can obtain a wide variation in speed Needs a variable frequency supply

Induced emf is directly proportional to the frequency Applied voltage must change in direct proportion to the

frequency> to maintain constant flux > constant maximum torque

Frequency Control

When frequency increases;• Slip at max torque decreases• Starting torque decreases

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Changing Stator Poles

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Suitable for squirrel-cage rotor induction motors Stator has 2 or more independent windings Each winding has different number of poles -> different

speeds At any time, only one winding is in operation

Good speed regulation High efficiency at any speed

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Rotor Resistance Control

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Suitable for wound rotor motors Add external resistance in the rotor circuits

Increase rotor copper loss Increase operating temperature Reduce efficiency

Can be used only for short periods

Stator Voltage Control

• For small change in speed -> large change in voltage is required• Difficult to use

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Injecting an emf in the rotor circuit(equal to rotor resistance control)

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Used in wound rotor induction motors Frequency of the injected emf must be equal to the rotor

frequency

Changing the phase of the injected voltage is equivalent to changing the rotor resistance

Further control by varying the magnitude of the injected emf

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Operates on a single-phase source Requires one single phase winding

Not self-starting

-> must provide some external means to start

Built in the fractional-horsepower range

Used in heating, cooling and ventilating systems

10. Single Phase Induction Motors

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2-pole, single-phase induction motor with a squirrel-cage rotor

Current in each winding produces a magnetic field 2 rotor conductors (180 degrees apart) form a closed loop

-> rotor conductors can be paired as shown

Force by 1, 2, 3 & 4 and 1’, 2’, 3’ & 4’ -> rotate in counterclockwise

Force by 5, 6, 7 & 8 and 5’, 6’, 7’ & 8’ -> rotate in clockwise

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At standstill: Produced magnetic field B can be resolved into two components (B1 & B2)

B1 & B2 are equal in magnitude and rotates in opposite directions

Induced emf in rotor circuit is in opposite directions Rotor currents in opposite directions s=1for 2 directions -> rotor impedance same Starting torques from 2 revolving fields is equal and

opposite Net torque is zero

Double Revolving Field Theory

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We can think of a 1-phase IM as it consists of 2 motors

- common stator winding

- rotors revolving in opposite direction

- At standstill

- Core loss considered with rotational losses(Core loss resistance is omitted)

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If the rotor rotates in clockwise direction with a speed Nm;- magnetic field revolving in clockwise direction has Ns- magnetic field revolving in counter-clockwise direction has – Ns.

Slip in forward direction:

Slip in backward direction:

Td forward branch >

Td backward branch

Resulting torque is in forward

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Example:

A 115V, 60Hz, 4-pole, single-phase induction motor is rotating in the clockwise direction at a speed of 1710 rpm. Determine its per-unit slip in both directions. If the rotor resistance at standstill is 12.5Ω, determine the effective rotor resistance in each branch.

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Analysis of Single Phase Induction Motors

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Developed power;

Developed torque;

Power available at the shaft; (rotational loss include the core losses too)

Load torque;

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Types of 1-Phase IMs

Based on the method used to make it self-starting;

1) Split-phase motor

2) Capacitor-start motor

3) Capacitor-start capacitor-run motor

4) Permanent split-capacitor motor

5) Shaded-pole motor

To be self-starting, • Must have at least 2 phase windings • Must be excited by a 2-phase source• Currents in the 2 phase windings are 900 electrically out of phase

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1) Split Phase Motor

• Used in fractional horsepower range

• Employs 2 separate windings -> connected in parallel to a single-phase source

• ‘Main winding’ - low resistance and high inductance. -> carry current and establish flux

• ‘Auxiliary winding’ - high resistance and low inductance-> disconnected from the supply when the motor

attains 75% of its synchronous speed

• Phase difference between the 2 currents may be as around 600

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2) Capacitor Start Motor

• Capacitor is included in series with the auxiliary winding

• Capacitor can be chosen such that -> main winding current lags the auxiliary current by

exactly 900

• Auxiliary winding & capacitor -> disconnected from the supply when the

motor attains 75% of its synchronous speed

• At rated speed -> operates just like a split-phase motor

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3) Capacitor Start – Capacitor Run Motor

• Above two methods have low power factor at the rated speed • Lower power factor -> high power input for same output power• Efficiency is low

• To improve efficiency -> another capacitor can be used at the rated speed

• •Two-value capacitor motor

• Start capacitor – for starting torque requirements• Run capacitor – for running performance

• Auxiliary winding stays in circuit at all times• Centrifugal switch -> switching from start capacitor to run capacitor

(at about 75% of the synchronous speed)

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4) Permanent Split Capacitor Motor

• Same capacitor is used for starting and running

• No centrifugal switch is needed

• Capacitor is selected to have high efficiency at rated load-> not properly matched for the starting-> starting torque is lower

• Suitable for low starting torque applications

• Used in applications that require frequent starts(other types tend to overheat when started frequently)

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5) Shaded Pole Motor

• Auxiliary winding is in the form of a copper ring (around the salient poles)

• Simple construction -> least expensive

• Efficiency is low compared with other types

• Develop low starting torque

• Built to satisfy the load requirements up to 1/3 horsepower-> low efficiency is of no interest

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Comparison between 5 types

Can be ranked from best to worst

1.Capacitor start – capacitor run motor2.Capacitor start motor3.Permanent split capacitor motor4.Split phase motor5.Shaded pole motor

•Best one is more expensive

•All techniques are not available for all size ranges

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