Conclusion: Three-phase Induction Motor Three-Phase Induction Motors used for the great majority of applications that call for motor with power ratings over 5 hp. They are used in its two types:

Squirrel – cage rotor type , and Wound (or Slip-Ring) Rotor type for pumps,

fans, compressors, and grinders and in many other industrial applications.

In is called, as well as, as Asynchronous Motor or Rotating Transformer

The equivalent circuits for both types are identical and it is similar to the transformer equivalent circuit, but the only difference is in the secondary side which should be closed.

The speed of the motor can be controlled either

by the supply voltage or by inserting external

variable resistance in the rotor winding

(Sure only in case of the second type).

The most important characteristics of the

motor is the Torque - Speed (slip)

characteristics as shown in the figure

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Example 17.3

A 220-V rms, 60-Hz three-phase wye-connected induction motor draws 31.87 A at a power factor of 75% lagging. For all three phases, the total copper losses are 400 W, and the total copper losses are 500 W. Find the air gap power, Pag , the developed power, Pdev, the output power, Pout and the efficiency η.

:Solution

Vs= Vp = Vline/ 3 = 127 V rms

Pinp = 3 Vs Is cos θ = 3 x 127 x 31.87 x 0.75 = 9107 W

From the power flow diagram, we know the following:

Pag = Pinp – PSCL

Thus Pag = 9107 – 400 = 8707 W

Pdev = Pag – PRCL = 8707 – 150 = 8557 W

Pout = Pdev – Prot = 8557 – 500 = 8057 W

Efficiency = Pout / Pinp x 100 %

η% = 8057 / 9107 x 100 = 94 % (Typical value for the IM)

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Drill Exercise

•D16.2. A three-phase, four-pole, 60-Hz cage rotor induction motor runs at 1746 rpm, drawing a rotor current I’r = 100 A. The rotational loss of the

machine is 4 kW. Find the developed power, rotor copper losses and ز

output power if R’r = 0.09 Ω.

Solution:

Synchronous speed ns = 120 x f / p = 120 x 60 / 4 = 1800 rpm

Slip , S = ns – nm / ns = 1800 – 1746 / 1800 = 0.03

Pdev = 3 x (1-S)/S x R’r x (I’

r)2 = 87.3 kW

PRCL = 3 x R’r x (I’

r)2 = 2.7 kW

Pout = Pdev – Prot = 87300 – 4000 = 83300 W or 83.3 kW

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Synchronous Machines INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES

Two types

1-Cylindirical rotor: High speed, fuel or gas fired power plants

To produce 50 Hz electricity

p=12, n=500 rpm

p=24, n=250 rpm

npnp

e120602

f

To produce 50 Hz electricity p=2, n=3000 rpm p=4, n=1500 rpm

2-Salient-pole rotor: Low speed, hydroelectric power plants

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INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES

How does a synchronous generator work?

1- Apply DC current to rotor winding

(field winding)

2- Rotate the shaft (rotor) with constant

speed.

3- Rotor magnetic field will create flux

linkages in stator coils and as a result

voltage will be produced because of

Faraday’s Law

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INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES

How is DC current applied to the rotor

1- Slip Rings

Note: Magnetic field of rotor can

also be produced by permanent

magnets for small machine applications

2- Brushless Excitation System: Excitation supplied from ac exciter and solid rectifiers. The

–alternator of the ac exciter and the rectification system are on the rotor. The current is supplied directly to the field-winding without the need to slip rings

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INTRODUCTION TO POLYPHASE SYNCHRONOUS MACHINES Synchronous generators work in

parallel with the interconnected

system.

Frequency and voltage are constant.

The behivor is examined based on a

generator connected to an INFINITE

BUS

Infinite bus

f : constant

V : constant

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Motor:

Generator:

•Synchronous Reactance

EQUIVALENT CIRCUTS

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asaaafa IXjIREV ˆˆˆˆ

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Synchronous-machine equivalent circuit showing air-gap and leakage components of synchronous reactance and air-gap voltage.

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Open-circuit characteristic of a synchronous machine.

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Typical form of an open-circuit core-loss curve.

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Open- and short-circuit characteristics of a synchronous machine.

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Open- and short-circuit characteristics showing equivalent magnetization line for saturated operating conditions.

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Typical form of short-circuit load loss and stray load-loss curves.

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(a) Impedance interconnecting two voltages; (b) phasor diagram.

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Typical form of synchronous-generator V curves.

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