The alternating current induction motor
was invented by Nicola Tesla in 1888. From its inception its ease of
manufacture and its power dominated the field of electromechanical energy
conversion. Considering its universal use and application the power
available from a given motor frame construction was increased from 7.5 Hp
in 1900 to 100 + Hp by 1965. With contemporary manufacturing and
application the performance characteristics of a given machine can be
specified to an accuracy of 1% or better.
IEEE standard test procedure for
polyphase develops six main parameters which characterise the performance
of a given induction motor. They are:
1) efficiency
2) power factor
3) torque
4) r.p.m.
5) watts
6) amperes
These parameters are plotted vs motor
output in horsepower and are available from the motor manufacturer. There
are additional parameters for the characterisation of polyphase motor
performance but these are subsidiary and not germane to the substance of
this report.
Slip of a.c. motors: The parameter of
importance in this discussion is the a.c. motor slip frequency which is
the difference between the unloaded motor speed, governed by the frequency
in c.p.s. of the mains supply, and the speed at which the motor rotates
under load. The torque of a polyphase motor varies almost directly as the
magnitude of the rotor slip r.p.m.
Over the range of power in which a motor
of a given capacity may be used efficiently, i.e. an efficiency greater
than 88%, manufacturer's data is available completely specifying the
relationship of rotor slip to mechanical power output. Thus the power
output of a motor may be specified completely on the basis of the slip
frequency providing the motor is operating at the standard excitation of
50 c.p.s., 30, 415 v.a.c. and the excitation waveform is
sinusoidal.
Mechanical power output of a large a.c.
motor may be accurately measured with a tachometer used in conjunction
with a set of curves of slip vs power output supplied by the motor
manufacturer. This method obviates the standard method of motor power
measurement requiring an in-line torque sensor interposed between motor
and load. In a sense the motor itself becomes the in-line torque sensor
with slip speed as the indicator.
This method of motor power indication
becomes more interesting when the mode of motor excitation is the
synthetic sinusoidal waveforms characteristic of the present generation of
variable speed drives and motor controllers.
Non-sinusoidal motor excitation may be
characterised by an alteration in the power balance within an a.c.
machine. The presence of harmonics of the fundamental 50 c.p.s. mains
supply as well as artefacts of the internal switching strategies of the
motor speed controller result in a redirection of power flow through the
machine such that rotor and stator heating increase at the expense of
motor torque and power output.
In practical terms this means that for
the same loading, rotor slip in a polyphase a.c. motor can be greatly
increased in comparison to the same motor operated at the same voltages
and frequency from a sinusoidal supply. The loss in efficiency of
electromechanical conversion in the motor under these conditions is
reflected in a redirection of energy flow such that power normally
converted to torque x r.p.m. is diverted to the heating of the rotor and
stator.
Consequently the power conversion
efficiency of an electric motor is reduced when operated on non-sinusoidal
excitation.
A correction factor may be derived from
the relationship between the slip vs load for a specific non-sinusoidal
excitation waveform by measurement of the motor slip at constant load for
sinusoidal and non-sinusoidal excitation.
Since the torque output of an a.c.
induction machine depends on the magnitude of the slip frequency if we
were to find twice as much slip from the same power input with
non-sinusoidal excitation in comparison to the sine wave, we could surmise
the torque producing properties of this waveform had been compromised to
the extent of 50% with the balance of the real power input to the machine
being dissipated in a non-torque producing manner, i.e. heat in the rotor
and stator.
We might expect from the manufacturer's
specifications an electromechanical energy conversion efficiency of 90+%
on sine waves, however, the measurements of this author on motor speed
controllers under 10 Hp using direct torque measurements of motor output
power show overall efficiencies of 40-60%, even though individually the
controller may be .97 and the motor efficiency .96.
It is easy for a motor controller
manufacturer to specify .97 efficiency into a resistive load. A motor
manufacturer specifies using sinusoidal waveforms.
Because of the way motors under 10 Hp
are generally employed it would be hard for the user to uncover the nature
and magnitude of interactive system losses, and for the small amounts of
power being consumed and dissipated the motivation for these studies would
be very low. A different rationale might apply to electromechanical
systems where energy management and efficiency were significant
parameters.
The Method of DePalma for
characterisation of polyphase a.c. electromechanical energy converters
consists of the measurement of rotor slip frequencies with sinusoidal and
non-sinusoidal motor excitation and at constant motor loading.
The ratio of these frequencies taken
under the conditions of:
1) constant motor power input
2) standardised voltage and frequency of
excitation, e.g. 50 c.p.s., 415 v.a.c., 30
3) constant motor loading
gives the correction factor to the motor
mechanical power output for operation with quasi-sinusoidal waveforms. The
necessity for such a correction factor arises because of an alteration of
the power flows within the motor excited with non-sinusoidal
waveforms.
In motor sizes under 10 Hp, increased
rotor slip and heating, and additional heating of the stator may not be
noticed because no comparisons are made and the benefits of variable speed
control outweigh the (possible) considerable reduction of
efficiency.
Знаете ли Вы, что релятивистское объяснение феномену CMB (космическому микроволновому излучению) придумал человек выдающейся фантазии Иосиф Шкловский (помните книжку миллионного тиража "Вселенная, жизнь, разум"?). Он выдвинул совершенно абсурдную идею, заключавшуюся в том, что это есть "реликтовое" излучение, оставшееся после "Большого Взрыва", то есть от момента "рождения" Вселенной. Хотя из простой логики следует, что Вселенная есть всё, а значит, у нее нет ни начала, ни конца... Подробнее читайте в FAQ по эфирной физике.
