3-phase Induction motor

3-Phase Induction Motor

Most Common & Frequent motors in industry

Simple Design, Rugged, Low Cost and Easy to Maintain

High efficiency: no brushes and good power factor

Constant speed from zero to full load

Transformer: Electrical Magnetic Electrical Alternating field

Induction Motor: Electrical Magnetic Mechanical /Electrical

Rotating field

General Principle

Wide Range of power rating: fractional horsepower to MW

Induction Motor Construction

3-phase induction motor comprises of two main parts:

Stator(Stationary)consists of a steel frame that supports a hollow, cylindrical core of stacked laminations.Slots on the internal circumference of the stator house the stator winding.

Rotor(Revolving)composed of punched laminations, with rotor slots for the rotor winding.Two basic design: Squirrel cage and wound rotor

Electromagnetics

Stator

Rotor

A

B

C

IA

IB

IC

Rotating Magnetic Field

Stator with 6 salient poles: Windings A, B & C. Pole pairs: North and South

Windings are mechanically spaced at 120°from each other.

Each winding produces its own MMF. The 3 fluxes combine to produce a magnetic

field that rotates at the same frequency as the supply.

3-Phase System: Current displaced by 120°in time (phase)

Synchronous Speed

For p poles/phase:

synchronous speed, ns 120 f

Prev/min

sn

ExampleA 4-pole 3 phase induction motor operates from a supply whose frequency

is 50 Hz. Calculate:

(a) the speed at which the magnetic field of the stator is rotating.

(b) the speed of the rotor when the slip is 0.04

(c) the frequency of the rotor currents when slip is 0.03

(d) the frequency of the rotor current at standstill.

(a) Stator field revolves at synchronous speed, given by:

Ns 120 f

P 120

50

4 1500r.p.m

(b) Rotor (motor) speed,

N Ns(1 s) 1500(1 0.04) 1440r.p.m

(c) Frequency of rotor current,

fR sf 0.03 50 1.5r.p.s 90r.p.m

(d) At standstill = ?

ExampleA 3 phase induction motor is wound for 4 poles and is supplied from 50-Hz

system. Calculate:

(a) the synchronous speed.

(b) the rotor speed when slip is 5%

(c) the frequency of the rotor when the rotor runs at 600 r.p.m

(a) Synchronous speed:

Ns 120 f

P 120

50

4 1500r.p.m

(b) Rotor (motor) speed,

N Ns(1 s) 1500(1 0.05) 1425r.p.m

(b) When rotor speed is 600 r.p.m,

s (Ns N )

Ns1500 600 1500

0.6

rotor current frequency:

fR sf (0.6 50) 30Hz

ExampleA 6 pole induction motor is excited by a 3 phase 60 Hz source. The full

load rpm is 1140 r.p.m. Calculate the slip?

Synchronous speed:

Ns 120 f

P120 60

6 1200r.p.m

Slip:

s Ns Nm

Ns1200 1140

1200 0.05

5%

Solution:

rpmp

fns 1800

4

60*120120

rpmnsn s 17101800*05.011

(b) 1800 (same as synchronous speed)

A 4-pole 3-phase induction motor operates from a supply whose frequency is 50Hz. Calculate:1. The speed at which the magnetic field of the stator is rotating2. The speed of the rotor when the slip is 0.043. The frequency of the rotor currents when the slip is 0.034. The frequency of the rotor currents at standstill.

Example

Recap

General Principle of Induction motor is similar to transformer

Components of Motor:

Stator - mechanically spaced at 120°

Rotor - Squirrel Cage and Wound Rotor

Synchronous speed = speed of rotating field ns 120 f

Prev/min

Slip s ns nm

ns

Slip speed n ns nm

Frequency of Rotor current fR P n

120

fR sf

Rotor Rotating Field

nr 120 fr

p

120sf

p sns

Induced current in 3-phase rotor also produce a rotating field

Speed w.r.t rotor

Induced rotor field rotates in the air gap

nm nr (1 s)ns sns

Modes of Operation

Motoring Plugging(Braking) Generating

0 ≤ nm ≤ ns

1 ≥ s ≥ 0

nm < 0

s > 1

nm > ns

s < 0

n

nn

ns ns ns

Torque-Speed Curve

Torque-Speed Curve

Motoring

Where is the operating range and why?

Power Flow

Pi

n

Stator Core Loss

Stator Cu Loss ( )

Pag

Rotor Core Loss

Rotor Cu Loss ( )

3I12R1

3I22R2

Pmech

Friction and Windage Losses

Pout

(Pshaft)

Power Flow

Motoring

Generator

Equivalent Circuit Model

Stator Windings

Similar to equivalent circuit of transformer primary winding

V1 = per-phase terminal voltageR1 = per-phase stator winding resistanceL1 = per-phase stator leakage inductance

E1 = per-phase induced voltage in stator windingLm = per-phase stator magnetizing inductanceRc = per-phase stator core loss resistance

Equivalent Circuit of the Induction Motor

22

22

jsXR

sEI

2222 RIP

22

22

/ jXsR

EI

s

RIs

s

RRIPP ag

222

22

22 1

ss

RIPmech 122

2 agmech PsP *1

2

1P

s

sPmech

agsPRIP 2

222

ssPPP mechag 1::1:: 2

Torque

Mechanical torque developed per phase, Tmech

Pmech Tmechm

ωm = angular velocity of the rotor (rad/s) m 2nm60

s 2ns60

synchronous speed (rad/s)

Tmech Pag

s

N.m

Pi

n

Stator Core Loss

Stator Cu Loss ( )

Pag

Rotor Core Loss

Rotor Cu Loss ( )

3I12R1

3I22R2

Pmech

Friction and Windage Losses

Pout(shaft)

(Pshaft)

Motoring

Power

Pshaft Tshaftm

Pshaft Pmech Pf ,w

Efficiency

Useful power output:Total input power

Pshaft

Pin

Power Factor

Power Factor = cosr

Pin

Sin

For a 3 phase system: Sin 3VlineIline

Example

A 3 phase, 230V, 60Hz, 74.6KW, six pole induction motor operating

at rated conditions has an efficiency of 91.0%. It draws a line

current of 248A. The core loss, stator copper loss and rotor

conductor loss are 1697W, 2803W and 1549W respectively.

Determine:

(a) power input

(b) total loss

(c) air-gap power

(d) shaft(mechanical) speed

(e) power factor

(f) friction and windage losses and draw the power flow diagram

(g) shaft torque