Transcript electrical engineering technology emt 113/4

FUNDAMENTAL OF
ELECTRICAL ENGINEERING
EMT 113/4
CHAPTER 3:
AC MACHINES
Introduction
2 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 energy
Generators = mechanical energy  ac electrical energy
AC Machinery Fundamental
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 produceconstant and uniform magnetic field, B.
Rotation of the loop induced a voltage in the wire.
V
eind
•
Current flows in the loop, a torque will be induced on the wire loop.
THE 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 LOSSES
The efficiency of an AC machines is defined as:

Pout
X 100%
Pin

Pin  Ploss
X 100%
Pin
Four types of losses in AC machines:
 Electrical or copper losses (I2R losses)
 Core losses
 Mechanical losses
 Stray load losses
VOLTAGE REGULATION AND SPEED REGULATION
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:
VR 
Vnl  V fl
V fl
X 100%
SR is a measure of the ability of a motor to keep a constant
shaft speed as load varies.
SR 
N nl  N fl
N fl
X 100%
nl   fl
SR 
X 100%
 fl
INDUCTION 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).
Two types of rotor which can placed inside the stator:
a) Squirrel-cage induction motor (Cage rotor)
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 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
The speed of the magnetic field’s rotation in a cage rotor induction motor (Figure
7.6, Chapman) is given by
nsync 
Where
120 f e
P
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.
.
This rotating field BS passes over the rotor bars and induces a voltage in them
eind  (v  B)  l
Where :
v = velocity of the bar relative to the magnetic field
B = magnetic flux density vector
l = length of conductor in the magnetic field
It 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;
 ind  kBR  BS
So, resulting torque is counterclockwise.
The voltage induced in a rotor bar depends on the speed of the rotor
relative to the magnetic fields
THE CONCEPT OF ROTOR SLIP
Slip speed is defined as the differences between synchronous speed and
rotor speed:
nslip  nsync  nm
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 :
Where
s
s
nslip = slip speed of the machines
nsync = speed of the magnetic field
nm = mechanical shaft speed of motor
nslip
nsyns
 100%
nsyns  nm
nsyns
 100%
The previous equation also can be expressed in term of angular velocity 
(radians per second) as :
sync  m
s
100%
sync
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
nm  (1  s)nsync
m  (1  s)sync
These equation are useful in the derivation of induction motor torque and power
relationship.
THE 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.
n n
s
sync
nsync
m
THE ELECTRICAL FREQUENCY ON THE ROTOR
Since the slip of the rotor is defined as :
s
nsync  nm
Then the rotor frequency can be expressed as :
nsync
f r  sf e
Substituting between these two equation become :
But nsync = 120fe/P, so
P
f r  (nsync  nm )
fe
120 f e
Therefore,
P
fr 
(nsync  nm )
120
fr = frequency rotor; fe = frequency stator
fr 
nsync  nm
nsync
fe
Induction Motor : Equivalent Circuit
a) Transformer model
model of the transformer action-induction of voltages and
currents in the rotor circuit of an IM is essentially a
transformer operation.
as in transformer model – certain resistance, self
inductance in
primary (stator) windings; magnetization
curve and etc.
b)Rotor circuit model
- The greater the relative motion between the rotor and the
stator magnetic fields, the greater the resulting rotor voltage
and frequency.
- Locked-rotor or blocked-rotor –the largest relative motion
when the rotor is stationary.
c) Final Equivalent circuit
- Refer the rotor part of the model over the stator side.
A) TRANSFORMER MODEL
STATOR
Symbol Description
aeff
Effective turn ratio – ratio of the
conductors per phase on the
stator to the conductors per phase
on the rotor
IDEAL TRANSFORMER
ROTOR
Xm
Resistance losses (correspond
to iron losses, windage and
friction losses)
E1
Primary internal stator voltage
ER
Secondary internal rotor
voltage
R1
Stator Resistance
X1
Stator Leakage Reactance
RR
Rotor Resistance
Rc
Magnetizing reactance
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=2fL) 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.
jXR=jsXR0
Then, resulting rotor equivalent circuit as
below.
The rotor current flow can be found as
:
ER
IR 
RR  jX R
ER
IR 
RR  jsX R 0
ER = sER0
The rotor circuit model of
an induction motor
sE R 0
IR 
RR  jsX R 0
IR 
ER 0
RR
s
 jX R 0
ZReq
RR
Then the rotor equivalent circuit become:
jsXR0
IR 
ER 0
RR
s
 jX R 0
ER0
ZReq
The rotor circuit model with all
the frequency (slip) effects
concentrated in resistor RR
RR
s
C) FINAL EQUIVALENT CIRCUIT
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 :
VP  V ' s  aVs
IP  I 'S 
IS
a
Z 'S  a 2 Z S
The same transformation can be used for the induction motor’s rotor circuit by
using effective turn ratio aeff
E1  E ' R  aef fER 0
I2 
IR
a eff
Z2  a
2
ef
RR
f (  jX R 0 )
s
The rotor circuit model that will be referred to the stator side as shown below
The per-phase equivalent circuit of an induction motor.
Input is 3 phase system of
voltages and currents.
Output is
mechanical.
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
I1 
V
Z eq
Where
R2
Z eq  R1  jX1  [( Rc  jX m ) //(  jX 2 )
s
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
MACHINE
Synchronous Machine : Introduction
Transformer – 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 operation
The 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.
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.
•
•
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)
Synchronous Machine : Construction
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 of
the rotor and the inside of the stator
Origin of name: syn = equal, chronos = time
Synchronous machines are called ‘synchronous’ because their mechanical
shaft speed is directly related to the power system’s line frequency.
STATOR
•The stator of a synchronous
machine carries the armature or
load winding which is a threephase 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 magnetomotive
force (mmf) proportional to the current
magnitude.
ROTOR
•2 types of rotors
- cylindrical (or round) rotors
- salient pole rotors.
Salient pole rotor less expensive than round rotors
and rotate at lower speeds
•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
The rate of rotation of the magnetic fields in the machine is related to
the stator electrical frequency, given as:
nm P
fe 
120
f e  electrical frequency, in Hz
nm  mechanical speedofmagnetic field , in r / min
P  number of poles
The internal generated voltage of a synchronous generator is given as,
EA  K
This equation shows the magnitude of the voltage induced in a given stator
phase.
The per phase equivalent circuit
Voltage Regulation:
 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;
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.
Lagging P.F
Leading 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:
Pin  appm
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
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 : Synchronous Generator.
A three-phase, wye-connected 2500 kVA and 6.6 kV generator operates at fullload. 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