Note: Descriptions are shown in the official language in which they were submitted.
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1058695
REGULATING THE TORQUE OF AN INDUCTION MOTOR
Background of the Invention
This invention relates to a motor control circuit and
method for regulating the torque of an induction motor, and
more particularly to regulating the torque of an induction
motor operated at a variable frequency using a modified in-phase
component of stator current as a controlled variable.
Most traction applications specify precise regulation
of motor torque so as to provide smooth, controlled acceleration.
Smooth control of a subway car or a trolley car, for example,
is needed for passenger comfort. In the application of ac
induction motors to such applications in an adjustable speed,
variable frequency drive system, precise control of torque is
hindered by the fact that no single variable which is directly
proportional to torque is readily measurable. The torque is
proportional to the air gap flux per pole and to the in-phase
rotor current, however the present invention relates to a
technique that avoids the need for sensing the air gap flux.
Summary of the Invention
In accordance with the invention, a motor control
circuit for regulating the torque of a polyphase or single
phase ac induction motor operated at a variable frequency is
based on the principle of maintaining constant the in-phase
component of stator current compensated for the voltage drop
across the stator resistance while also holding constant the
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slip frequency. To implement this control technique, the per
phase instantaneous stator supply line current and voltage is
continuously sensed and supplied to a generating means for
deriving the per phase supply line voltage corrected for the
stator resistance voltage drop. The compensated supply line
voltage signal is then used in conjunction with the instantaneous
current sensor signal to generate the desired modified in-phase
stator current component signal, either in one half cycle or
in both half cycles. In a polyphase circuit or whenever
appropriate, the several modified in-phase stator current
component signals are summed and filtered to produce an averaged
dc signal to be used in the feedback control system for the
power converter supplying adjustable frequency and amplitude
voltage to the motor.
The preferred embodiment is a drive system for a three
phase induction motor wherein the power converter is a poly-
pha~e pulse width modulated inverter. In one feedback control
circuit, the error between the averaged dc signal and a command
signal representing the desired torque is used to actuate a
slip frequency regulator, thereby generating a slip frequency
signal which is summed with a rotor frequency signal to produce
a first control signal for determining the inverter operating
frequency. In the second feedback control circuit, a command
slip frequency signal and the aforementioned slip frequency
signal are summed to generate a second error signal, this being
used to actuate a voltage regulator for producing a second
control signal for determining the voltage amplitude of the
inverter. In a motor position, the second error signal is
inverted at the input of the voltage regulator, but is un-
inverted in a brake position. Although other applications are
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possible, this torque regulating motor controller is
advantageous in traction applications. Both positive and
negative torque are approximately linear. A method for
regulating the torque of an induction motor is in accordance
with the foregoing description.
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Brief Description of the Drawings
FIG. 1 is a schematic diagram showing a per phase
equivalent circuit of a three-phase induction motor;
FIG. 2 is a curve of torque vs. the modified in-phase
component of stator current for a typical induction motor con-
trolled according to the principles herein taught, it being
assumed that the slip frequency is increased linearly with the
modified in-phase component of stator current;
FIG. 3 is a schematic circuit diagram in block diagram
form of the preferred embodiment of a polyphase motor control
circuit constructed according to the invention; and
FIG. 4 are stator voltage and current waveforms useful
in explaining the operation of the FIG. 3 motor controller.
Description of the Preferred Embodiment
The theory and principles underlying the invention will
be discussed with regard to FIG. 1 before proceeding to a
detailed description of the exemplary torque regulating motor
control circuit of FIG. 3 for use in an adjustable speed
polyphase ac induction motor drive system especially suitable
for traction applications. Within its broader scope, the
present induction motor control circuit can be constructed in
single phase versions and is useful in a wide variety of
applications where the smooth or approximately linear control
of induction motor torque is required or is desirable.
FIG. 1 shows the well-known per phase equivalent circuit
of a three-phase induction motor, which is similar to the
usual transformer equivalent circuit. In this diagram, the
stator resistance rs, the stator leakage reactance ~eL ~s and
the magnetizing reactance ~eLm are effectively in series and
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energized by the stator voltage vl, while the rotor resistance
rr/S and rotor leakage reactance ~eL ~r are shown connected in
series across the magnetizing reactance. The stator current
is identified as il and the rotor current as i2. In general,
the torque T developed by the machine is proportional to i22rr/S,
or at an arbitrary frequency fe(~e= 2 ~ fe)
T = Ki2 rr/(feS)' (1)
where the fractional slip S = (fe ~ fr)/fe.
Thus,
T = Ki2 rr/(fe r)~ (2)
where fe is the stator supply line frequency and fr is the
rotor speed in Hz related to n, the actual mechanical rotor
speed in rpm by fr = Pn/60, P being the number of pole pairs.
One possible method of torque control is to maintain
the slip frequency fe ~ fr and the rotor current i2 constant.
Reference to equation (2) verifies that torque will then be
maintained constant. However, rotor current cannot readily be
measured so that this type of control cannot be implemented.
Another type of control is provided by maintaining
constant the real or in-phase component of the stator current
il relative to the stator voltage vl. Neglecting resistance,
it is clear from the equivalent circuit that the in-phase
stator current component il InPh which flows into the motor
terminals must also flow in the rotor resistance since all
the other circuit elements are reactive. Hence, holding the
slip frequency fe ~ fr constant and the real or in-phase
component of stator current il InPh also constant, then the
rotor current i2 is also maintained constant. This method
has one serious drawback. The stator resistance is typically
very small, and for high speeds the power flow into the motor
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terminals is nearly identical to the power crossing the air
gap into rotor resistance rr/S. However, as the stator supply
line frequency is reduced (speed is reduced), the power
dissipated by the stator resistance rs becomes appreciable
compared to the power into the motor terminals. When this
occurs, the rotor current i2 is no longer maintained constant
for a constant il InPh and, hence, the torque is no longer
maintained constant. Assuming a variable opsrating frequency
range of 50 Hz to 2.5 Hz, the change is especially pronounced
as the line frequency is reduced from about 15 Hz to 2.5 Hz,
particularly for negative torque or braking.
The difficulty involved in using and sensing the in-
phase component of stator current, il InPh~ is overcome by
compensating for the IR drop through the stator resistance.
In this case, a voltage signal vl' is derived by sensing the
motor terminal or supply line voltage (vl) and the stator
supply line current (il). It is evident from FIG. 1 that
Vl ' = V~ rs
This modified voltage signal (vl') is now used as a reference
and the modified in-phase stator current component i'l InPh
relative to this signal is determined. In an induction motor
control method and a motor control circuit employing this
technique, the modified in-phase stator current component
i'l InPh together with the slip frequency fe ~ fr is held
constant to regulate torque.
FIG. 2 shows a common curve for torque versus the
modified in-phase stator current component i'l InPh for
several different stator supply line or motor operating
frequencies, in particular 50 Hz, 12.5 Hz, 5 Hz and 2.5 Hz,
when the slip frequency fe ~ fr is increased linearly with
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i'l InPh The shape of the curve is independent of frequency,
from which it follows that torque is maintained constant for
a fixed i'l InPh and fe ~ fr and it will be noted that this
holds true at negative as well as positive torque values.
S Although the use of the modified in-phase stator current
component i'l InPh as a controlled variable for regulating
torque is not exact and more precisely can be said to give an
approximation of the torque, the distinct advantage is that
implementation of the control method and circuit based on
equation (3) requires only sensing voltage and current
parameters that are readily available external to the induction
motor itself at the motor or supply line terminals. Modifica-
tion of the motor or an appropriate air gap flux sensor is
not required.
In the exemplary embodiment of a motor control circuit
for regulating torque shown in block diagram form in FIG. 3,
a conventional three-phase, squirrel cage ac induction motor
is indicated generally at 10. As is apparent to those skilled
in the art, the invention is also applicable with appropriate
modifications to the control of wound rotor induction motors
operated at a variable frequency. The wye-connected stator
windings lla-llc are respectively connected to the motor or
supply line terminals 12a-12c, and the rotor speed at the motor
shaft is continuously measured by a tachometer 13 which
generates the signal frotor. A three-phase pulse width
modulated inverter 14 is provided to supply the variable
frequency induction motor 10 with constant volts/Hz power,
so that the amplitude of the line voltage supplied to the
motor decreases as the operating frequency decreases, and
vice versa. Other suitable converters that can be used for
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this application are a three-phase square wave inverter or
a polyphase cycloconverter. In accordance with the invention,
the instantaneous single phase stator supply line current and
voltage for each of the supply lines 14a-14c is continuously
sensed and supplied a~ input information to the motor controller.
To this end, the instantaneous line currents iaS-iCS correspond-
ing to the per phase stator current is sensed by a suitable
current sensor such as the current transformers l~a-15c.
The instantaneous supply line voltages vas-vcs corresponding
to the per phase stator voltages between the respective motor
terminals 12a-12c and neutral are also sensed by suitable
voltage sensors such as the voltage transformers 16a-16c and
filtered by the low pass filters 17a-17c to produce sine waves.
It is usually preferable to sense an equivalent set of reference
voltages that are present in the control circuits of inverter 14.
Generating means for computing and generating a dc
signal proportional to or representative of the average value
` of the modified in-phase component of stator current,
i'l InPh~ is indicated generally at 20. In each phase, a
computation circuit produces a signal representative of the
voltage vl, as defined in FIG. 1, and this is used to obtain in
each phase, preferably for both positive and negative
currents, the modified in-phase component of stator current.
These three (or six) currents are summed to produce the ac
signal i'l InPh~ which is in turn filtered to produce the dc
signal i'l InPh(av ) Only the computation and associated
circuitry for phase A will be described, corresponding
components in the other phases being designated by similar
numerals. Thus, in the phase A computation circuit, the
sensed instantaneous current iaS is fed to a sign inverter
21a and then through a resistor 22a having the value rs to
one input of a summing circuit 23a. The other input to the
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summing circuit 23a is the sensed instantaneous voltage signal
vas. Accordingly, the summing circuit 23a generates the signal
vas-rsias, and an important feature of the invention is that
this signal is compensated for the voltage drop across the
S stator resistance rs.
A comparator circuit 24a connected to the output of
summer 23a has a first binary output representing the positive
half cycles of the signal vaS-rsias. The binary "one" outputs
are used to periodically time the closing of a switch 25a and
complete a path for conduction of the positive current sensor
signal iaS through a resistor 26 to one input of the summing
circuit 27.; The value of resistor 26 is selected according
to a predetermined proportionality constant. The in-phase
component of the positive stator current iaS which is passed
by the switch 25a is more clearly understood by reference to
FIG. 4. The upper waveform diagram, of course, shows the
three-phase sine wave voltages, while in the second diagram
the component of iaS in phase with the voltage vas is
illustrated in heavy lines. It will be appreciated from the
foregoing discussion that the voltage vaS-rsias is slightly
lagging with respect to vas. The second waveform diagram
also shows the negative stator current -iaS with the in-phase
component likewise illustrated in heavy lines. The current
-iaS is obtained at the output of inverter 21a, which in
similar fashion is connected to a second switch 25a' that
is closed by the complementary binary signal at the inverse
logic output of comparator 24a. That is, switches 25a and
25a' are alternately closed for 180 intervals. The modified
in-phase component of -iaS is supplied through another resistor
26 to a second input of the summing circuit 27. The other
two phases operate in similar fashion, it being understood
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that the binary outputs of comparator 24b and 24c are
respectively displaced from one another and the output of
comparator 24a by 120. In the third and fourth diagrams
of FIG. 4, the in-phase stator current components of ibS,-ibS,
iC8, and -iCS are shown in like manner in heavy lines.
The sum of the six modified in-phase components of the stator
currents is an ac signal with a sawtooth type waveshape as
illustrated diagrammatically at 28 in FIG. 3. The low pass
filter circuit 29 converts this to the averaged dc signal
i l~Inph(av)
Referring now to the remainder of the motor controller,
the desired value of torque or the command value of the
modified in-phase stator current component, i'l InPh~ is set
manually or automatically by a suitable device such as a
potentiometer 31 connected to a source of voltage V. In
addition to adjusting the torque to a set value, it will be
recalled from FIG. 2 that the slip frequency is increased
linearly as the torque is increased. A feedback control
circuit for setting the slip frequency and therefore the
inventer operating frequency is comprised by a first summing
circuit 32 for obtaining the error between the command value
and the computed average value of the modified in-phase stator
current component signal i'l InPh. The error signal is fed
to a suitable slip frequency regulator 33 which performs
the function of zeroing the error and generating an output
signal proportional to the slip frequency fslip. Preferably,
the regulator 33 operates according to the rule Kl(l+TlS)/S,
where Kl is a gain constant, Tl is a time constant, and S is
a Laplace operator. A second summing circuit 34 determines
the error between the slip frequencY fslip and the measured
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rotor frequency frotor this error signal being a control signal
for determining the desired inverter operating frequency finverter.
It will be appreciated that the inverter operating frequency cor-
responds to the variable frequency of the voltage supplied by the
inverter 14 to the stator supply lines 14a-14c and thus to the
variable operating frequency of induction motor 10.
A second feedback control circuit for setting the
amplitude of the voltage supplied by inverter 14, which is
adjusted in complementary fashion to obtain a constant volts/Hz
as previously explained, is comprised by a proportional gain
circuit 36 for converting the command value of the modified
in-phase stator current component to a corresponding value of
fslip. The command value of the slip frequency and fslip
signal at the output of slip frequency regulator 33 are
applied to another summing circuit 37. The error signal
representing the difference between the command value of slip
frequency and the slip frequency actually being asked for is
fed to a two position switch 38 having a brake position and
a motor position. Both of these are needed, of course, in
a traction application where it is also necessary to regulate
the torque during deceleration to a stop. In the motor
position of switch 38, the error signal is fed through a sign
inverter 39 to a voltage regulator 40 for producing an output
control signal for the inverter 14 which is proportional to the
inverter voltage amplitude to be obtained. In the brake
position of switch 38, the error signal is fed directly to
voltage regulator 40, which in either case performs the function
of zeroing the error. The regulator 40 also preferably
operates according to the rule K2(1+T2S)S, where the quantities
are defined as before. The three-phase pulse width modulated
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power inverter 14 is of conventional construction, for
example as described in the book "Principles of Inverter
Circuits" by Bedford and Hoft, John Wiley and Sons, Inc.,
Copyright 1964, Library of Congress Catalog Card No.: 64-20078.
In view of the foregoing extensive discussion of the
torque regulating control circuit for an induction motor
operated at a variable frequency for traction and other
applications, further description of the operation is not
necessary. Although discussed with regard to the regulation
of torque of a polyphase induction motor, the principles of
the invention are also applicable to the control of single
phase induction motors in an adjustable speed drive system.
Instead of sensing the per phase stator supply line current
and voltage parameters using the current transformers 15a-15c
and voltage transformers 16a-16c, it will be apparent to those
skilled in the art that suitable parameters in the control
circuit for power inverter 14 which effectively determine
these output quantities may be sensed. Broadly speaking,
by way of summary, the metnod for regulating the torque of
an induction motor operated at a variable frequency comprises
the steps of continuously sensing and generating a plurality
of instantaneous sensor signals indicative of the per phase
stator supply line current and voltage to be supplied to the
stator winding, deriving from the instantaneous sensor
signals a modified in-phase stator current component signal
compensated for the voltage drop across the stator resistance,
and utilizing the derived modified in-phase stator current
component signal as a controlled variable in the motor
control circuit to adjust in complementary fashion the frequency
and the amplitude of the per phase stator supply line voltage,
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thereby regulating the torque of the induction
motor.
While the invention has been particularly shown
and described with reference to a preferred embodiment
thereof, it will be understood by those skilled in the art
that the foregoing and other changes in form and details
, may be made therein without departing from the spirit and
scope of the invention.
