UNIT
7
AC MACHINES
ALTERNATORS
Classification and Operating Principle
• Alternators according to their construction, are divided into the following two classifications:
1. Revolving armature type
- Stationary field poles and revolving armature
- Usually of relatively small kVA capacity and low-voltage rating
2. Revolving field type
- Stationary armature, inside of which the field poles rotate
- Rotor has slip rings and brushes to supply the excitation current from an outside DC
source
- When the rotor rotates, the stator conductors are cut by the magnetic flux, hence, an
alternating emf is produced in the stator conductors.
Constructional Features
• Stator consists essentially of a cast iron or a welded-steel frame supporting a slotted ring made
of soft laminated sheet-steel punching in the slots of which the armature coils are assembled.
•
Rotor is the revolving field structure.
1. Salient pole type. They are used on low and medium speed alternators.
2. Smooth cylindrical type. They are used with high-speed prime mover.
EMF Generated
•
PN
The frequency of the emf (in Hz) generated is given by: f = 120
where P = number of poles and N = speed in rpm
•
The emf induced per phase: E = 2.22 kpkdZφf
where Z = number of conductors per phase, φ = flux per pole (in Wb), kp = pitch factor, and
kd = distribution factor
•
Pitch factor (or coil span factor)
phasor sum of induced emfs per coil
kp =
= sin(90° p)
arithmetic sum of the induced emfs per coil
where p = winding pitch
AC Machines
Special Topics 3 (EE Review)
•
Distribution (or Breadth or Belt) factor
where
nδ
induced emf in a distributed winding sin ( 2 )
kd =
=
induced emf in concentrated winding n sin (δ)
2
n = number of slots per pole per phase
δ = angle between adjacent slots in degrees = 180°/slots per pole
Alternators on Load
• When load on an alternator varies, its terminal voltage also varies due to the following reasons:
1. Voltage drop due to armature reaction
2. Voltage drop due to armature leakage reactance
3. Voltage drop due to armature resistance
-
From the simplified equivalent circuit,
|E| = √(V cos θ + IR a )2 + (V sin θ ± IX s )2
Note: + if lagging p.f., − if leading p.f.
-
-
Using complex expression,
E = (V + IR a cos θ + IX s sin θ) + j(IXs cos θ − IR a sin θ)
E = (V + IR a cos θ − IX s sin θ) + j(IXs cos θ + IR a sin θ)
(lagging p.f.)
(leading p.f.)
Using polar form,
E = V∠0° + (I∠ ± θ)(Z∠ϕ) = V∠0° + (I∠ ± θ)(R a + jX s )
Note: + if leading p.f., − if lagging p.f.
Alternator Tests and Voltage Regulation
• Synchronous impedance of the machine
open − circuit voltage per phase Voc
Zs =
=
short − circuit current per phase Isc
Then, the synchronous reactance is X s = √(Zs )2 − (R a )2
•
Percent voltage regulation
%VR =
|E| − |V|
x 100%
|V|
2
AC Machines
Special Topics 3 (EE Review)
Parallel Operation on Alternators
• The requirements for paralleling include the requirements for DC machines plus a few others
1. Voltages must be the same at the paralleling point or junction.
2. Phase sequence must be the same at the paralleling point.
3. The incoming machine must be in phase at the moment of paralleling.
4. The line frequencies must be identical at the paralleling point.
5. The prime movers must have relatively similar and drooping speed-load characteristics.
Alternator Synchronizing Procedure
• At the time of synchronizing, the following conditions must be met.
1. The effective voltage of the incoming alternator must be exactly equal to that of the others or
of the busbars connecting them.
2. The phase rotation, or sequence of the running and incoming alternators must be the same.
3. The individual phase voltages which are to be connected to each other must be in exact phase
opposition.
4. The frequencies should be the same.
Alternator Connected to Infinite Busbar
• Three-phase complex power at the generator terminal
3|E||V|
3|V|2
S3ϕ =
∠(ϕ − δ) −
∠ϕ
|Zs |
|Zs |
3|E||V|
3|V|2
3|E||V|
3|V|2
cos(ϕ − δ) −
cos ϕ] + j [
sin(ϕ − δ) −
sin ϕ]
|Zs |
|Zs |
|Zs |
|Zs |
Note: Theoretical maximum power occurs when δ = 90°.
S3ϕ = [
Load Distribution
• Amount of load taken up by an alternator running in parallel with other machines is solely
determined by its driving torque.
• Any change in its excitation merely changes its kVA output (not its kW output).
Losses and Efficiency
• The following losses occur in an alternator:
1. Copper losses
2. Core losses
•
3. Friction and windage losses
4. Load loss
The efficiency of an alternator is calculated as follows:
Alternator efficiency =
kVA(p. f. )
kVA(p. f. ) + losses
3
Special Topics 3 (EE Review)
AC Machines
THREE-PHASE INDUCTION MOTOR
An induction motor is simply an electric transformer whose magnetic circuit is separated by an air
gap into two relatively movable portion, one carrying the primary and the other the secondary
winding.
Induction motors are available with torque characteristics suitable for a wide variety of loads:
1. The standard motor has a starting torque of about 120 – 150% of full-load torque.
2. For starting loads, high-torque motors with a starting torque of twice normal full-load torque
or more are used.
3. For driving machines that use large flywheels to carry peak loads, a high-torque motor with a
slip at full-load up to 10% is available.
4. By the use of a wound-rotor with suitable controller and external resistances connected in
series with the rotor winding, it is possible to obtain any value of starting torque up to the
maximum breakdown torque.
Constructional Features
• A polyphase induction motor comprises of stator and rotor.
1. Squirrel-cage rotor
2. Wound rotor
Theory of Operation of an Induction Motor
• When a three-phase is given to the stator winding, a rotating field is set up and this field sweeps
past the rotor and an emf is induced in the rotor conductors by virtue of relative motor.
• The change is the relative motion of the rotating field and the rotor so that, to oppose this, the
rotor runs in the same direction as the field and attempts to catch up with it.
• Torque must be produced to cause rotation.
Slip
• It is the difference between the synchronous speed (Ns) and the motor speed (N), expressed as a
fraction of the synchronous speed.
s = (Ns – N) / Ns
Note: s = 1 if the rotor is standstill, s = 0 for synchronous motor
Frequency of Rotor Current (fr)
• Given the frequency of supply voltage (f),
fr = sf
Rotor EMF
• The induced emf per phase in the rotor (Er) at the instant of starting is given as:
Er = Es (N2 / N1)
where: Es = applied voltage per phase to stator, N2 = number of rotor turns, and N1 = number of
stator turns
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AC Machines
Special Topics 3 (EE Review)
Rotor Current
• Given the rotor winding impedance, R2 + jX2, at any value of slip, s:
sEr
Ir =
√(R 2 )2 + (sX 2 )2
Power Stages in Induction Motor
Stator power
input (SPI)
SCL
CL
Rotor power
input (RPI)
RCL
Rotor power
developed
(RPD)
F&W
Rotor power
output
(RPO)
where: SCL = stator copper loss, CL = core loss, RCL = rotor copper loss, and F&W = friction
and windage loss
RCL = s(RPI)
RPD = RPI (1 – s) = RCL (1 – s)/s
RPI = SPI – (SCL + CL)
RPD = RPI – RCL
RPD / RPI = N / Ns
RPO = RPD – F&W
Rotor Torque
• The torque acting on the rotor when the motor is running at any slip, s:
180
sR 2 (E2 )2
Tr =
2πNs (R 2 )2 + (sX 2 )2
•
•
•
•
Starting torque occurs at s = 1 and is proportional to the square of the applied voltage.
Torque will be maximum when s = a = R2 / X2.
Maximum starting torque occurs when R2 = X2.
Relationship between full-load torque and maximum torque
TFL
2as
= 2
Tmax a + s2
Induction Motor Test
1. Blocked rotor test. The rotor is blocked and the rotor windings are short-circuited at slip
rings (if the motor has a wound rotor). A reduced voltage is applied to the stator terminals
and the full load current flows in the stator will be adjusted to determine the equivalent
resistance referred to the stator.
2. No-load test. The actual purpose is to be able to determine the constant losses (core loss +
friction and windage loss)
Starting of Induction Motor
• Some of the starting devices for starting induction motors are:
1. Stator rheostat starter
3. Wye-delta starters
2. Auto-transformers
4. Rotor rheostat (for wound rotor)
5
Special Topics 3 (EE Review)
AC Machines
SYNCHRONOUS MOTOR
It is one type of 3-phase AC motor which operates at a constant speed from no-load and full-load and
is similar in construction to 3-phase AC generator in that it has a revolving field which must be
separately excited from a DC source.
Characteristic Features
1. It runs either at synchronous speed or not at all.
2. It is not inherently self-starting.
3. It can operate under a wide range of power factors.
4. On no load, it draws very little current from the supply to meet internal losses.
Construction
• A three-phase synchronous motor consists of the following parts:
1. Laminated stator core with 3-phase armature winding
2. Revolving field with windings and slip rings
3. Brushes and brush holders
4. Two end shields to house the bearings that support the shaft.
• The stator core and windings of a synchronous motor are similar to those of a 3-phase induction
motor.
Principle of Operation
• When the stator windings of a 3-phase synchronous motor are supplied with rated 3-phase
voltage, a rotating field travelling at synchronous speed is set up.
• The rotor is energized with DC source (it acts like a bar magnet). The strong magnetic field
attracts the strong rotor fields activated by the DC source. This results in a strong turning force in
the rotor shaft. The rotor is therefore able to turn a load as it rotates in step with the rotating
magnetic field.
EMF Equation
- From the simplified equivalent circuit,
|E| = √(V cos θ − IR a )2 + (V sin θ ± IX s )2
Note: − if lagging p.f., + if leading p.f.
-
-
Using complex expression,
E = (V − IR a cos θ − IX s sin θ) − j(IXs cos θ − IR a sin θ)
E = (V − IR a cos θ + IX s sin θ) − j(IXs cos θ + IR a sin θ)
(lagging p.f.)
(leading p.f.)
Using polar form,
E = V∠0° − (I∠ ± θ)(Z∠ϕ) = V∠0° − (I∠ ± θ)(R a + jX s )
Note: + if leading p.f., − if lagging p.f.
6
AC Machines
Special Topics 3 (EE Review)
Power Stages in Synchronous Motor
Stator power input
(SPI)
Armature
Copper
Loss
Rotor power
developed (RPD)
Core and
friction
losses
Rotor power output
(RPO)
Rotor power developed (RPD) in the armature = 3EIa cos β
where β = angle between emf and armature current
Hunting or Surging
• The phenomenon of hunting occurs when a motor carries varying load or supply voltage
frequency changes. To stop the build up of oscillations caused by this phenomenon, dampers or
damping grids (short-circuited copper bars embedded in the faces of the field poles of the
motor) are used.
Starting
• The synchronous motor can be developed synchronous torque only at synchronous speed. For
starting, it is therefore necessary to employ other methods of developing torque.
1. Pony induction motor
2. Clutch and brake gear
3. Starting as induction motor
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