Lecture Electromechanical energy conversion: Polyphase Induction Machines - Nguyễn Công Phương

This chapter include contents: Introduction to Polyphase Induction Machines, currents and fluxes in Polyphase Induction Machines, induction – motor equivalent circuit, analysis of the equivalent circuit, torque and power by use of Thevenin’s theorem, parameter determination from no – load and blocked – rotor tests, effects of rotor resistance.

Nguyễn Công Phương

ELECTROMECHANICAL ENERGY

CONVERSION

Polyphase Induction Machines

I Magnetic Circuits and Magnetic Materials

II Electromechanical Energy Conversion

Principles

III Introduction to Rotating Machines

IV Synchronous Machines

V Polyphase Induction Machines

VI DC Machines

VII.Variable – Reluctance Machines and Stepping

Motors

VIII.Single and Two – Phase Motors

IX Speed and Torque Control

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

Introduction to Polyphase Induction Machines (1)

• Induction motor: alternating current is supplied to the stator

directly & to the rotor by induction or transformer action from the stator.

• Two kinds of rotor:

– Wound rotor (relatively uncommon)

– Squirrel-cage rotor (the most commonly used)

Introduction to Polyphase Induction Machines (2)

• The rotor speed: n (r/min).

(r/min).

• The fractional slip:

(%)

s s

Introduction to Polyphase Induction Machines (3)

• The rotor terminals of an induction motor are

short circuited.

• The rotating air – gap flux induces slip –

frequency voltages in the rotor windings.

• The operating speed can never equal the

synchronous speed.

• The rotor currents produce a rotating flux wave

which rotate at sn s (r/min) with respect to the

rotor.

• The rotor speed: n (r/min)

• The speed of the rotor’s flux wave:

sn + n = sn + n (1 – s) = n

Introduction to Polyphase Induction Machines (4)

rotates at synchronous speed and hence in

synchronism with that produced by the stator currents.

respect to each other, & produce a steady

torque, called asynchronous torque.

Introduction to Polyphase

Induction Machines (5)

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

Currents and Fluxes in Polyphase

Currents and Fluxes in Polyphase

Currents and Fluxes in Polyphase

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

Induction – Motor Equivalent

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

2 22



of the Equivalent Circuit (2)

Ex 1

A three – phase, two – pole, 60-Hz induction motor is operating at 3502 r/min with

an input power of 15.7 kW and a terminal current of 22.6 A, the stator – windingresistance is 0.20 Ω/phase Calculate the power dissipated in rotor?

P T



2 22

of the Equivalent Circuit (4)

Ex 2

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

P rot = 403W (independent of load), s = 2% Compute the speed, output torque and

power, stator current, power factor, and efficiency?

m

R

s Z

0.144

0.209 13.250.02

of the Equivalent Circuit (5)

Ex 2

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

P rot = 403W (independent of load), s = 2% Compute the speed, output torque and

power, stator current, power factor, and efficiency?

o 1

of the Equivalent Circuit (6)

Ex 2

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

P rot = 403W (independent of load), s = 2% Compute the speed, output torque and

power, stator current, power factor, and efficiency?

o 1

of the Equivalent Circuit (7)

Ex 2

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

P rot = 403W (independent of load), s = 2% Compute the speed, output torque and

power, stator current, power factor, and efficiency?

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

Torque and Power by Use of

m

jX R jX Z

ˆ ˆ

/

eq eq

V I

Torque and Power by Use of

Torque and Power by Use of

ph eq mech

n V R s T

n V R X X R s dT

R s

Torque and Power by Use of

Torque and Power by Use of

Thevenin’s Theorem (5)

Ex.

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

the corresponding speed; (c) the electromechanical starting torque T start & the

corresponding stator load current I 2,start?

j j

Torque and Power by Use of

Thevenin’s Theorem (6)

Ex.

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

the corresponding speed; (c) the electromechanical starting torque T start & the

corresponding stator load current I 2,start?

ˆ ˆ

/

eq eq

V I





Torque and Power by Use of

Thevenin’s Theorem (7)

Ex.

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

the corresponding speed; (c) the electromechanical starting torque T start & the

corresponding stator load current I 2,start?

o 2

Torque and Power by Use of

Thevenin’s Theorem (8)

Ex.

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

the corresponding speed; (c) the electromechanical starting torque T start & the

corresponding stator load current I 2,start?

R s

Torque and Power by Use of

Thevenin’s Theorem (9)

Ex.

Given a three – phase, six – pole, Y – connected, 220-V (line-to-line) 60-Hz 7.5-kW

induction motor, R1 = 0.249Ω/phase, R2 = 0.144, X1 = 0.503, X2 = 0.209, Xm = 13.25,

the corresponding speed; (c) the electromechanical starting torque T start & the

corresponding stator load current I 2,start?

1, 2,

ˆ ˆ

1

/1

eq start

ph start

s

n I R T



Torque and Power by Use of

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

a) No – Load Test

b) Blocked – Rotor Test

7 Effects of Rotor Resistance

ph nl c

core

n V R

This test is ordinarily performed

at rated frequency & with balanced polyphase voltages applied

to the stator terminals

Blocked – Rotor Test (1)

The rotor is blocked so that it can not rotate (hence the slip is equal to unity),

and balaced polyphase voltages are applied to the stator terminals

r bl bl

bl ph bl

f Q X

f n I



2 1,

bl bl

ph bl

P R

Blocked – Rotor Test (2)

m

m bl

X X

R R R

X X

Polyphase Induction Machines

1 Introduction to Polyphase Induction Machines

2 Currents and Fluxes in Polyphase Induction

Machines

3 Induction – Motor Equivalent Circuit

4 Analysis of the Equivalent Circuit

5 Torque and Power by Use of Thevenin’s

Theorem

6 Parameter Determination from No – Load and

Blocked – Rotor Tests

7 Effects of Rotor Resistance

Effects of Rotor Resistance