ELECTRICAL ENGINEERING ELECTRICAL ENGINEERING TECHNOLOGYTECHNOLOGY

EMT 113/4EMT 113/4

CHAPTER 3:CHAPTER 3:

AC MACHINESAC MACHINES

Introduction2 major classes:

a) Asynchronous machines / induction machines :–

Motors or generators whose field current is supplied by magnetic induction (transformer action) into their field windings.

b) Synchronous machines :–

Motors or generators whose field current is supplied by a separate dc power source.

Note: 1) Induction motor has the same physical stator as a synchronous machine, with a different rotor construction.

2) The fields circuit of most synchronous and induction machines are located on their rotors.

Motors = ac electrical energy mechanical energyGenerators = mechanical energy ac electrical energy

AC Machinery Fundamental

A SIMPLE LOOP IN A UNIFORM MAGNETIC FIELDS.A SIMPLE LOOP IN A UNIFORM MAGNETIC FIELDS.

• A rotating loop of wire within the magnetic field.

• Magnetic field produced by a large stationary magnet produce-constant and uniform magnetic field, B.

• Rotation of the loop induced a voltage in the wire.

• Current flows in the loop, a torque will be induced on the wire loop.

eind

V

ө

THE ROTATING MAGNETIC FIELDTHE ROTATING MAGNETIC FIELD

• When two magnetic fields are present in a machine, a torque will be created which will tend to line up the two magnetic fields.

• Magnetic field is produced by the stator and rotor of an ac machine.

• Then a torque will be induced in the rotor cause the rotor to turn and align itself with the stator magnetic field.

• The induced torque in the rotor would cause the rotor to constantly “ chase “ the stator magnetic field around in circle - the basic principle of all ac motor operation.

AC MACHINE POWER LOSSESAC MACHINE POWER LOSSES

The efficiency of an AC machines is defined as:

Four types of losses in AC machines:Electrical or copper losses (I2R losses)Core lossesMechanical lossesStray load losses

%100XP

P

in

out %100XP

PP

in

lossin

VOLTAGE REGULATION AND SPEED REGULATIONVOLTAGE REGULATION AND SPEED REGULATION

%100XV

VVVR

fl

flnl

%100XN

NNSR

fl

flnl %100XSRfl

flnl

VR is a measure of the ability of a generator to keep a constant voltage at its terminals as load varies. It is defined as follow:

SR is a measure of the ability of a motor to keep a constant shaft speed as load varies.

INDUCTION MOTORSINDUCTION MOTORS

Induction Motors

Induction motors are the motor frequently encountered in industry.

It simple, rugged, low-priced and easy to maintain.

It run essentially constant speed from zero to full-load.

The speed is frequency-dependent and consequently these motors are not easily adapted to speed control

Induction machines is called induction because the rotor voltage (which produces the rotor current and the rotor magnetic field) is induced in the rotor winding rather than physically connected by wires.

Induction Motor : Construction

A 3-phase induction motor has two main parts :• A stationary stator (stationary part of the machine)• Revolving rotor (rotating part of the machine)

The rotor is separated from the stator by a small air gap (the tolerances is depending on the power of the motor).

a) Squirrel-cage induction motor (Cage rotor)

Two types of rotor which can placed inside the stator:

b) Wound rotor induction motor

a) Squirrel cage – the conductors would look like one of the exercise wheels that squirrel or hamsters run on.

Cage Induction Motor rotor consists of a series of conducting bars laid into slot carved in the face of rotor and shorted at either end by large shorting ring

Small cage rotor induction motor Large cage rotor induction motor

b) Wound rotor – have a brushes and slip ring at the end of rotor

Wound rotor has a complete set of three-phase winding that are mirror images of the winding on the stator.

- The three phases of the rotor windings are usually Y-connected, the end of the three rotor wires are tied to slip ring on the rotor shaft.

- Rotor windings are shorted through brushes riding on the slip rings.Wound-rotor induction motors are more expansive than the cage induction motors, they required much more maintenance because the wear associated with their brushes and slip rings.

Induction Motor : Concepts

INDUCED TORQUE IN AN INDUCTION MOTOR

The speed of the magnetic field’s rotation in a cage rotor induction motor (Figure 7.6, Chapman) is given by

P

fn esync

120

Where nsync = synchronous speed [r/min] fe = System frequency [Hz]

p = number of poles

This equation shows that the synchronous speed increases with frequency and decrease with the number of poles.

.

The three-phase of voltages has been applied to the stator, and three-phase set of stator current is flowing . These currents produce a magnetic field BS , rotating counterclockwise direction

lBveind )(

This rotating field BS passes over the rotor bars and induces a voltage in them

Where : v = velocity of the bar relative to the magnetic field B = magnetic flux density vector

l = length of conductor in the magnetic fieldIt is a relative motion of the rotor compared to the stator magnetic field that produces induced voltage in a rotor bar. The rotor current flow produces a rotor magnetic field, BR.

The induce torque in the machine is given by;

The voltage induced in a rotor bar depends on the speed of the rotor relative to the magnetic fields

SRind BkB So, resulting torque is counterclockwise.

THE CONCEPT OF ROTOR SLIPTHE CONCEPT OF ROTOR SLIP

The other term used to describe the relative motion is slip, which is relative speed expressed on a per unit or a percentage basis. The slip is defined as :

msyncslip nnn

Slip speed is defined as the differences between synchronous speed and rotor speed:

%100

%100

syns

msyns

syns

slip

n

nns

n

ns

Where nslip = slip speed of the machines

nsync = speed of the magnetic field

nm = mechanical shaft speed of motor

%100

sync

msyncs

The previous equation also can be expressed in term of angular velocity (radians per second) as :

If the rotor turns at synchronous speed, s=0 ; if the rotor is stationary (locked or stop) , s=1. All normal motor speeds fall somewhere between those limits.

As for mechanical speed

syncm

syncm

s

nsn

)1(

)1(

These equation are useful in the derivation of induction motor torque and power relationship.

THE ELECTRICAL FREQUENCY ON THE ROTORTHE ELECTRICAL FREQUENCY ON THE ROTOR.

The induction motor works by inducing voltages and current in the rotor of the machine-called a rotating transformer. Like a transformer; primary (stator) induced a voltage in the secondary (rotor) Unlike a transformer, the secondary frequency not necessarily the same as

primary.

If the rotor of a motor is locked so that it cannot move, the rotor will have the same frequency as the stator.

If the rotor turns at synchronous speed, the frequency on the rotor will be zero. For nm=0 r/min & the rotor frequency fr=fe slip, s = 1

nm=nsync & the rotor frequency fr=0 slip, s = 0- For any speed in between, the rotor frequency is directly proportional to the difference between the speed of the magnetic field nsync and the speed of the rotor nm.

sync

msync

n

nns

THE ELECTRICAL FREQUENCY ON THE ROTOR

er sff

Since the slip of the rotor is defined as :

Then the rotor frequency can be expressed as :

Substituting between these two equation become :e

sync

msyncr f

n

nnf

But nsync = 120fe/P, so

ee

msyncr ff

Pnnf120)(

Therefore,

fr = frequency rotor; fe = frequency stator

)(120 msyncr nnP

f

sync

msync

n

nns

Induction Motor : Equivalent Circuita)a) Transformer modelTransformer model

- - model of the transformer action-induction of voltages model of the transformer action-induction of voltages and and currents in the rotor circuit of an IM is essentially a currents in the rotor circuit of an IM is essentially a transformer transformer operation.operation.- - as in transformer model – certain resistance, self as in transformer model – certain resistance, self inductance in inductance in primary (stator) windings; magnetization curve primary (stator) windings; magnetization curve and etc.and etc.

b)Rotor circuit modelb)Rotor circuit model- The greater the relative motionThe greater the relative motion between the rotor and the between the rotor and the

stator magnetic fields, stator magnetic fields, the greater the resulting rotor voltage the greater the resulting rotor voltage and frequencyand frequency..

- Locked-rotor Locked-rotor oror blocked-rotor blocked-rotor – –the largest relative motionthe largest relative motion when the when the rotor is stationaryrotor is stationary..

c) Final Equivalent circuitc) Final Equivalent circuit- - Refer the rotor part of the model over the stator side.Refer the rotor part of the model over the stator side.

A) TRANSFORMER MODEL

ROTORIDEAL TRANSFORMERSTATOR

Symbol

Description

aeff Effective turn ratio – ratio of the conductors per phase on the stator to the conductors per phase on the rotor

R1 Stator Resistance

X1 Stator Leakage Reactance

Rc Magnetizing reactance

Xm Resistance losses (correspond to iron losses, windage and friction losses)

E1 Primary internal stator voltage

ER Secondary internal rotor voltage

RR Rotor Resistance

XR Rotor Reactance

•Induction motor operates on the induction of voltage and current in its rotor circuit from the stator circuit (transformer action).

•An induction motor is called a singly excited machine, since power is supply to only the stator circuit.

•The flux in the machine is related to the integral of the applied voltage E1.

•The curve of magnetomotive force versus flux (magnetization curve) for this machine is compared to a similar curve for a power transformer.

B) ROTOR CIRCUIT MODEL

Suppose the motor run at a slip s, meaning that the rotor speed is ns (1-s), where ns is the synchronous speed, then this modify the values of VOLTAGE and CURRENT on the primary and secondary side.

The frequency of the induced voltage at any slip will be given

fr = sfe

Assuming ER0 is the magnitude of the induced rotor voltage at LOCKED ROTOR condition the actual voltage induced because of slip (s) is,

ER = sER0

The resistor is not frequency sensitive, the value of RR remain the same.

The rotor inductance is frequency sensitive (X=L=2fL) then

XR = sXR0

Figure 6 shows the equivalent circuit when motor is running at a slip (s).

Equivalent circuit of a wound-rotor when it at locked or blocked condition

The frequency of the voltages and currents in the stator is f, but the frequency of the voltages and currents in the rotor is sf.

Then, resulting rotor equivalent circuit as below.

The rotor current flow can be found as :

0

0

0

0

0

RR

RR

RR

RR

RR

RR

RR

RR

jXsR

EI

jsXR

sEI

jsXR

EI

jXR

EI

ZReq

ER = sER0

jXR=jsXR0

RR

The rotor circuit model of an induction motor

Then the rotor equivalent circuit become:

0

0

RR

RR

jXsR

EI

ZReq The rotor circuit model with all the frequency (slip) effects concentrated in resistor RR

ER0

jsXR0

s

RR

C) FINAL EQUIVALENT CIRCUIT

SS

SS

P

ZaZ

a

IIIP

aVssVV

2'

'

'

Remember, in transformer, the voltages, currents and impedances on the secondary side of the device can be referred to PRIMARY side by turn ratio of the transformer :

The same transformation can be used for the induction motor’s rotor circuit by using effective turn ratio aeff

)(

'

02

2

2

01

RR

ef

eff

R

RefR

jXs

RfaZ

a

II

fEaEE

The rotor circuit model that will be referred to the stator side as shown below

The per-phase equivalent circuit of an induction motor.

Output is mechanical.

Input is 3 phase system of voltages and currents.

The power flow diagram of an induction motor – shows the relationship between the input electric power and output mechanical power.

Induction Motor :Power & Torque

The per-phase equivalent circuit of an induction motor

Input current Where )//()[( 22

11 jXs

RjXRjXRZ mceq

eqZ

VI 1

Induction Motor :Torque Speed Characteristics

1. The induced torque of the motor is zero at synchronous speed.

2. The torque speed curve is nearly linear between no-load and full-load. In this range, the rotor resistance is much larger than the rotor reactance. So, the rotor current increasing linearly.

3. There is maximum possible torque that cannot be exceeded (called pullout torque or breakdown torque) is 2-3 times the rated full-load torque.

4. Starting torque on motor is slightly larger than full-load.

5. The torque on the motor for a given slip varies as the square of the applied voltage.

6. If the rotor of the induction motor is driven faster than synchronous speed, then the direction of the induced torque in the machine reverse and become generator.

7. If motor turning backward, relative to the direction of the magnetic field, the induced torque will stop the machine very rapidly and will try to rotate it in the other direction (called plugging).

Induction Motor : Speed Control

• By pole changing• By line frequency control• By line voltage control• By changing the rotor resistance

Note: 1 h.p = 746 Watts

SYNCHRONOUS SYNCHRONOUS MACHINEMACHINE

Synchronous Machine : IntroductionTransformer – energy transfer device. (transfer energy from primary to secondary) - form of energy remain unchanged. (Electrical)

(DC/AC) Machines – electrical energy is converted to mechanical or vice versa.

Motor operationThe field induced voltage, E permits the motor to draw power from the line to be converted into mechanical power. This time, the mechanical output torque is also developing. The induced voltage is in opposition to the current flow-called counter emf.

• Generally, the magnetic field in a machine forms the energy link between the electrical and mechanical systems.

• The magnetic field performs two functions:– Magnetic attraction and repulsion produces mechanical torque (motor

operation)– The magnetic field by Faraday’s Law induces voltages in the coils of wire.

(generator operation)

Generator operation The field induced voltage, E is in the same direction as the current and is called the “generated voltage”. The machine torque opposes the input mechanical torque that is trying to drive the generator, and it is called the counter torque.

Synchronous Machine : Construction

Origin of name: syn = equal, chronos = timeSynchronous machines are called ‘synchronous’ because their mechanical shaft speed is directly related to the power system’s line frequency.

Have an outside stationary part, (stator) The inner rotating part (rotor)The rotor is centered within the stator. Air gap - the space between the outside ofthe rotor and the inside of the stator

STATORSTATOR

•The stator of a synchronous machine carries the armature or load winding which is a three-phase winding. •The armature winding is formed by interconnecting various conductors in slots spread over the periphery of the machine’s stator.

•When current flows in the winding, each group produces a magnetic pole having a polarity dependent on the current direction, and a magnetomotiveforce (mmf) proportional to the current magnitude.

•2 types of rotors - cylindrical (or round) rotors - salient pole rotors.Salient pole rotor less expensive than round rotors and rotate at lower speeds

ROTORROTOR

•The rotor carries the field winding. The field current or the excitation current is provided by an external dc source.•Synchronous machine rotors are simply rotating electromagnets built to have as many poles as are produced by the stator windings. •Dc currents flowing in the field coils surrounding each pole magnetize the rotor poles. The magnetic field produced by the rotor poles locks in with a rotating stator field, so that the shaft and the stator field rotate in synchronism.

Synchronous GENERATOR 1. GENERATOR

120

Pnf me

polesofnumberP

rinfieldneticspeedofmagmechanicaln

Hzinfrequencyelectricalf

m

e

min/,

,

The rate of rotation of the magnetic fields in the machine is related to the stator electrical frequency, given as:

The internal generated voltage of a synchronous generator is given as,

KEA

This equation shows the magnitude of the voltage induced in a given stator phase.

The per phase equivalent circuit

If the generator operates at a terminal voltage VT while supplying a load corresponding to an armature current Ia, then;

In an actual synchronous machine, the reactance is much greater than the armature resistance, in which case;

Among the steady-state characteristics of a synchronous generator, its voltage regulation and power-angle characteristics are the most important ones. As for transformers, the voltage regulation of a synchronous generator is defined at a given load as;

Voltage Regulation:

Phasor Diagram:

The phasor diagram is to shows the relationship among the voltages within a phase (Eφ,Vφ, jXSIA and RAIA) and the current IA in the phase.

Leading P.F.

Lagging P.F

Power and Torque:

In generators, not all the mechanical power going into a synchronous generator becomes electric power out of the machine

The power losses in generator are represented by difference between output power and input power shown in power flow diagram below.

Pconv

Losses:

•Rotor - resistance; iron parts moving in a magnetic field causing currents to be generated in the rotor body - resistance of connections to the rotor (slip rings)

•Stator - resistance; magnetic losses (e.g., hysteresis)

•Mechanical - friction at bearings, friction at slip rings

•Stray load losses - due to non-uniform current distribution

The input mechanical power is the shaft power in the generator given by equation:

The power converted from mechanical to electrical form internally is given by

The real electric output power of the synchronous generator can be expressed in line and phase quantities as

and reactive output power

mappinP

In real synchronous machines of any size, the armature resistance RA is more than 10 times smaller than the synchronous reactance XS (Xs >> RA). Therefore, RA can be ignored

Synchronous MOTOR

POWER AND TORQUE

Example

Example 3.3 : Example 3.3 : Synchronous Generator.Synchronous Generator.A three-phase, wye-connected 2500 kVA and 6.6 kV generator operates at full-load. The per-phase armature resistance Ra and the synchronous reactance, Xd, are (0.07+j10.4). Calculate the percent voltage regulation at :

(a) 0.8 power-factor lagging

(b) 0.8 power-factor leading.

END OF CHAPTER 3