Chapter 1:
AC Machine Fundamentals
Torque Produced:
A fixed magnetic flux density vector Bs produced by a ‘stator’ and moving magnetic
flux density vector Br existing on a ‘rotor’. The torque produced by the interaction of
these 2 fields is given by:
T = k Bs × Br
[1-1]
(vector product)
Note that one can use a permanent magnet, or an electrical magnet (coil with magnetic
core fed from a DC source) to produce these flux densities.
Br = µ 0 H (i )
Bs
α
i
Br
N
α
Bs
i
T
S
(Remember Gauss’ Law of “maximum flux density”)
Losses:
The losses in an AC machine can be divided in 4 basic categories:
•
Electrical losses
Also called ‘Copper’, or ‘Joules’, or ‘Resistive’ losses (I2R losses). These
are the heating losses due to resistive effects in windings. We also have to
include the resistive losses in the excitation windings.
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•
Core Losses
When the core sees an alternating flux, it follows a hysteresis loop. The area
of the loop is proportional to the energy lost in that cycle. Therefore the
hysteresis losses are proportional to the frequency of the supply.
A conducting material placed in a changing field sees a voltage induced by
that field ( e = − dΦ ). Hence a current will flow in the circuit (called an
dt
‘eddy current’). This circuit has a resistance, and therefore some resistive
losses in the core are going to result. These losses are called ‘eddy current
losses’ and are proportional to the square of the frequency.
•
Mechanical losses
These are associated with the mechanical motions. “Friction and Windage”
are mechanical losses due to mechanical friction of the mechanical parts
(bearings), and the fluid losses due to the air flow resistance. Note that there
would also be a component called “Stiction” at start, but this is not considered
when the machine rotates.
•
Stray losses
Unfortunately, when one adds the 3 losses above, the result comes lower than
the actual losses. The difference is called “Stray Losses”. Since the source of
these losses is unknown, one cannot measure them as such. However in
practice they can be approximated as 1% of full load.
The diagram below shows the power-flow diagram of a GENERATOR, which transforms
Mechanical Power to Electrical Power
Mechanical >>>>>
Power
Transformation
in the Air Gap
>>>>> Electrical
Power Output
3 phase
Power Input
(mechanical on the shaft):
3 V I cos
Torque x Speed
of the
“Prime Mover”
Joules Losses
Core losses
(hysteresis,eddy)
Mechanical Losses
(friction, windage)
Stray Losses
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Performance Indices:
The EFFICIENCY of a generator is given in % by:
η G=
Electrical Power Out
× 100
Mechanical Power In + Excitation Power
[1-2]
(Note that the total input power must take into consideration the power used by the
excitation power of the generator).
The VOLATGE REGULATION of a generator is defined in % as:
σ G=
No Load Voltage − Full Load Voltage
× 100
Full Load Voltage
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[1-3]