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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The field of the invention is AC motor drives for variable speed control of
AC induction motors, and more particularly, AC motor drives using pulse
width modulation (PWM) techniques.
2. Description of the Background Art
A motor drive for an AC induction motor includes a power section and a
logic and control section. The power section receives power from a 3-phase
AC source operating at 60 Hz frequency. The AC power is converted to DC
power to provide a PWM inverter with a source for synthesizing voltages of
different frequencies which are necessary to control the speed of an AC
motor.
The effective value of the output pulses from a PWM inverter approximates
one cycle of a sinusoidal AC waveform. The pattern is repeated to generate
additional cycles of the AC waveform.
Signals from the logic and control section of the motor drive are applied
to the PWM inverter to control the frequency and magnitude of AC power
signals to the motor.
In one type of open-loop PWM motor control, speed commands are translated
into torque commands by applying a specified volts/hertz ratio, which can
be selected through a user-selectable switch or a jumper wire interfaced
to the logic and control section of the motor control. Frequency is
determined by speed profiles, referred to as "accel/decel" rates which are
selected and adjusted through switches interfaced to the logic and control
section of the motor control. Open loop controls of this type are moderate
in cost and are widely used in industry for applications requiring low and
medium horsepower, and moderate speed range.
In a typical AC open loop motor control, a PWM mode of operation is
provided during starting and when running in the constant torque range of
operation below base speed. At the upper end of its speed range, in the
constant horsepower range of operation, the control operates with a
six-step square wave output. PWM operation helps reduce harmonics and
torque pulsations at the lower end of the speed range.
The PWM region of operation may also be considered a linear region of
operation for the gain of the PWM inverter which determines how much
output voltage is applied to the motor in response to a motor voltage
command input to the inverter. In the linear region, sine-triangle
modulation is complete, and a modulation index (Mi) is less than unity.
There is a transition region or pulse dropping region, in which the
sine-triangle modulation required for PWM operation is less effective and
some pulses of the carrier wave are not effective to modulate the motor
voltage command. This transition region precedes a six-step square wave
mode of operation for the inverter.
In the non-linear region of inverter operation, the inverter gain drops
significantly. While investigations have been made into solving the
problem of operation in this region, the present invention provides a
simplified model for on-line motor control as transition is made from PWM
to sixstep operation.
SUMMARY OF THE INVENTION
The invention relates to a method of motor control in which a phase voltage
command controls the input to the PWM inverter in response to a
volts/hertz function at low speeds, in which the PWM inverter is a
sine-triangle modulator, in which a modulation index is calculated as a
ratio of the magnitude of the phase voltage command to the peak of the
triangle wave reference to detect a nonlinear region of operation, and in
which the voltage command to the PWM inverter is adjusted in the nonlinear
region to compensate for reduced gain of the PWM inverter caused by pulse
dropping.
Because the modulation index is itself a function of the DC bus voltage,
the invention may include the additional step of controlling the phase
voltage command in response to variations in the DC bus voltage from rated
DC bus voltage.
The largest error in the compensated modulation index occurs for modulation
indices from 1.0 to 1.1. In a more detailed aspect of the invention, this
error is limited by limiting the maximum gain of the PWM inverter during
operation in the pulse-dropping or nonlinear region to the gain of the PWM
inverter in the linear region of operation, and limiting the minimum
compensated modulation index to the modulation index in the linear region.
The invention is preferably carried out using a solid state PWM inverter
and DC bus sensing circuitry interfaced to a microelectronic processor.
Digital circuitry offers manufacturing cost advantages in that many of the
control functions can be performed by executing programmed routines rather
than by processing analog signals. This reduces the size and cost of the
circuit components.
While the invention is disclosed in a preferred embodiment as an open-loop,
volts/hertz motor drive, the invention may also be practiced in a closed
loop control with speed feedback.
Other objects and advantages besides those discussed above shall be
apparent to those familiar with the art from the description of several
preferred embodiments of the invention which follow. In the description,
reference is made to the accompanying drawings, which form a part hereof,
and which illustrate examples of the invention. Such examples, however,
are not exhaustive of the various embodiments of the invention, and
therefore reference is made to the claims which follow the description for
determining the scope of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a circuit diagram of a motor drive for practicing the method of
the invention;
FIGS. 2a-2c are graphs of voltage vs. time each showing a triangle
reference waveform and a sinusoidal voltage command waveform in three
respective regions of operation: PWM, transition, and six-step operation;
FIG. 3 is a graph of PWM inverter gain as a function of frequency in the
linear and nonlinear operating regions; and
FIG. 4 is a flow chart of a program routine that is executed by a processor
shown in FIG. 1.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
FIG. 1 illustrates a control for carrying out the present invention in
controlling an AC induction motor 10. The motor control (also called a
"drive") includes a power section that receives AC power at a line
frequency of 60 Hz from a 3-phase AC power source 11. The voltage for this
example is 460 volts. An AC-DC power converter 12 rectifies the AC power
signals from the AC source 11 to produce a DC voltage (VDC) on a DC bus 13
that connects to power inputs on the pulse width modulation (PWM) voltage
inverter 14, which completes the power section of the drive. The AC source
11, the AC-DC power converter 12, and DC bus 13 provide a DC source for
generating a DC voltage of constant magnitude. A voltage detector 18 is
connected to the DC bus 13 to provide an analog input signal V.sub.bus to
the A-to-D converter 20b.
The PWM inverter 14 includes a group of switching elements which are turned
on and off to convert this DC voltage to pulses of constant magnitude. The
pulse train pattern from a PWM inverter is characterized by a first set of
positive-going pulses of constant magnitude but of varying pulse width and
by a second set of negative-going pulses of constant magnitude but of
varying pulse width. The RMS or effective value of this pulse train
pattern approximates one cycle of a sinusoidal signal which is
characteristic of an AC waveform. The pattern is repeated to generate
additional cycles of the AC waveform.
To control the frequency and magnitude of the resultant AC power to the
motor, AC phase voltage commands are applied to the PWM inverter 14. The
PWM voltage inverter 14 receives three balanced AC phase voltage commands,
V*.sub.as, V*.sub.bs and V*.sub.cs which vary in phase by 120.degree..
The magnitude and frequency of these signals determines the pulse widths
and the number of the pulses in pulse trains V.sub.as, V.sub.bs and
V.sub.cs which are applied to the terminals of the stator.
These phase AC voltage command signals, V*.sub.as, V*.sub.bs and V*.sub.cs
are produced as a result of a 2-phase to 3-phase conversion which is
accomplished with a 2-to-3 phase converter 15. The sinusoidal AC voltage
command signals V*.sub.qs and V*.sub.ds have a magnitude and a frequency
and are related to a d-q reference frame in which the phase angle of the
q-axis component and the phase angle of the d-axis component are
90.degree. apart.
The sinusoidal AC voltage control signals V*.sub.qs and V*.sub.ds are
outputs from a microelectronic processor 20, which in this embodiment is
preferably a Model 8096 available from Intel Corporation, Santa Clara,
Calif. The microelectronic processing unit 20 including CPU 20a, A-to-D
converters 20b and D-to-A converters 20c, is programmable to provide
functions to be described. The CPU 20a executes a program 20d including an
interrupt routine 20e that is stored in nonvolatile memory such as a
programmable read only memory (PROM). In executing this program the CPU
20a utilizes a random access memory (RAM) (not shown) to store data and
temporary results.
The microelectronic processor 20 calculates the motor voltage command
values V*.sub.qs and V*.sub.ds in response to one of several rates of
acceleration and deceleration selected at an Accel/Decel input 23.
Accel/Decel switches are interfaced at input 23 to the processor 20 to be
read by CPU 20a. The magnitude of the motor voltage command is also
determined by a voltage/hertz ratio, which is a multiplier applied to the
frequency determined by the accel/decel rates. The voltage/hertz ratio is
set to a predetermined ratio by connecting a jumper wire on a V/Hz input
interface 24 so that an input signal is read by the CPU 20a. Another input
25 (.omega.*.sub.e) to the microprocessor 20 in FIGS. 1-3 represents
inputs from two potentiometers which determine a range for the operating
frequency .omega.*.sub.e, such as 0-90 Hz, for example, but expressed in
radians (2.pi..times. frequency in Hz). Within this range the
microprocessor 20 generates various frequency values as the motor is
brought up to a rated frequency such as 60 Hz for example.
FIGS. 2a-2c illustrates the behavior of the inverter, when operating in the
linear and nonlinear regions. As a motor starts up from zero frequency
under Volts/Hz control, it operates in a linear region in which the sine
wave command 21 intersects the triangle wave reference 22 for each cycle.
The linear region is characterized by full sine-triangle modulation seen
in FIG. 2a, i.e., the voltage command sine wave 21 intersects each of the
pulses of the triangle wave reference 22. As seen in FIG. 3, the inverter
gain (G) remains relatively constant at G.sub.nom as speed and frequency
of the motor are increased.
At some frequency (.omega..sub.t) typically below a rated frequency
(.omega..sub.RATED) which corresponds to base speed for the motor, a
nonlinear or pulse-dropping region is encountered. This is the transition
region illustrated in FIG. 2b, where some of the pulses of the triangular
wave reference 22 are not intersected by the voltage command 21. This
results in a pulse being dropped or missed from the output to the motor
and is referred to as operation in the "pulse dropping" region. This
further results in lower voltage applied to the motor from the outputs of
the PWM inverter 14. As seen in FIG. 3, inverter gain (G) drops off
substantially in this region, and the output voltage to the motor is less
than commanded, unless something is done to offset or respond to the loss
of gain.
In industrial settings, the DC bus voltage varies higher or lower than
rated voltage (460 volts) due to the electrical load on the power
distribution lines. This causes the stator terminal voltage of the motor
to go higher or lower.
While investigations have been made into solving these problems, the
present invention provides a simplified model for on-line motor control as
transition is made from PWM to six-step operation, taking into account
variations in DC bus voltage.
FIG. 2c illustrates the region beyond the transition region where virtually
no sine-triangle modulation occurs and the drive is operated in a six-step
square wave output mode.
This mode is employed at the upper end of the motor speed range, in the
constant horsepower range of operation. PWM operation, on the other hand,
is employed at lower speeds, in the constant torque range of operation, to
reduce harmonic content and inhibit torque pulsations at these speeds.
The nominal gain G nom of the PWM inverter is given by the following
equation:
##EQU1##
where V.sub.bus =the DC bus voltage (VDC), and
A.sub.t =the peak amplitude of the triangular wave.
The transition region can be detected by calculating a modulation index
(M.sub.i) which is defined as the ratio of voltage command (V .sub.com) to
the peak of the triangular wave (A.sub.t) according to the following
equation:
##EQU2##
The gain of the inverter for all regions of operation is then described by
the following equation:
##EQU3##
When the modulation index (M.sub.i) is unity, the equation reduces to
G=G.sub.nom, which describes operation in the linear region. In the
nonlinear region of operation, the gain is nonlinear and its value depends
upon the modulation index. This region begins when the output voltage is
equal to .pi./4 or the value of fundamental component of the six-step
square wave. Six-step operation begins when the modulation index
approaches infinity and the inverter gain approaches zero.
When shifting from linear to six-step operation, it is desirable to limit
motor current transients. In the present invention, this is accomplished
by correcting for bus voltage variation and pulse dropping.
Regardless of the region of operation, if the desired PWM phase output
voltage is given by V*, then the PWM phase voltage command V.sub.com may
be expressed as follows:
##EQU4##
While the PWM inverter 14 is in the linear region, the amplitude of the
phase voltage command V*.sub.LINEAR is the desired phase output voltage V*
divided by the linear gain G.sub.nom. This follows from Eqs. 1, 3 and 4
when the modulation index (M.sub.i) is set to one (1) in Eq. 3. It can now
be seen that if DC bus voltage (VDC) varies in Eq. 1, then G.sub.nom
varies as well. And according to Eq. 4, if the bus voltage increases, G
increases and the effective phase voltage command V.sub.com should be
reduced to maintain the output command V* at the same value as before the
increase in Gain.
Eq. 3 shows that gain (G) will vary as G.sub.nom varies with bus voltage,
and as the modulation index (M.sub.i) varies with pulse dropping. The
modulation index is also affected by variations in DC bus voltage (Eq. 2,
Eq. 4 and Eq. 1) as well as pulse dropping. This requires that control be
accomplished according to a complex relationship to determine the desired
phase voltage in the pulse dropping region.
One approach to the problem is to use an iteration method incorporating a
look-up table for the gain (G). This method would iterate on the voltage
command until the desired output voltage is achieved.
However, this approach has the following disadvantages: The quantization of
the gain function accentuates the output voltage discontinuities. The
convergence requirements become critical as operation approaches six-step.
An iteration method also increases computation requirements.
Instead, the invention uses a compensated modulation index, M.sub.icomp,
which incorporates the effects of bus voltage variation and the reduction
in gain. The compensated phase voltage command V*.sub.comp then becomes an
algebraic relationship between M.sub.icomp and A.sub.t according to the
following equation.
V*.sub.comp =M.sub.icomp A.sub.t (5)
Next, if Eq. 4 is solved for V*, if a binomial expansion is substituted for
G, and if Eq. 1 is substituted for G.sub.nom, then the result is given by
Eq. 6. This equation approximates the fundamental component for the
inverter, and it incorporates the modulation index (M.sub.i) and the DC
bus voltage (V.sub.bus).
##EQU5##
The compensated modulation index in Eq. 7 below is obtained from Eq. 6 by
substituting Eq. 5 for V.sub.com and solving for M.sub.icomp. Six-step
operation commences at the point where the denominator of Eq. 7 becomes
equal to zero. By using Eq. 7 a smooth transition from linear to six-step
operation is accomplished.
##EQU6##
The largest error in the simplified model occurs for modulation indices
from 1.0 to 1.1. To limit the error in this region, the gain in the
nonlinear region is limited to be no greater than the gain G.sub.nom in
the linear region. And, the compensated modulation index (M.sub.icomp) is
limited to be no less than the uncompensated modulation index (M.sub.i) in
the linear region. These limits can be maintained by limiting the voltage
output command (V*.sub.OUT) to be no less than V*.sub.LINEAR unless the
compensated voltage output command is to be greater than V*.sub.LINEAR.
Because the DC bus voltage (V.sub.bus) and desired voltage (V*) are
incorporated, the compensated modulation index (M.sub.icomp) corrects for
bus voltage and desired voltage variations, and pulse dropping. Therefore,
by performing the calculations of Eqs. 5 and 7 as part of the program that
is executed by the CPU 20a, there is an improved transition from the
linear region to six-step operation using a volts/Hz motor drive.
FIG. 4, shows the program represented by block 20c and the routine
represented by area 20d in FIG. 1. As seen in FIG. 4, the program 20c
includes a main program loop 40 for handling background functions. As
represented by decision block 41, when a timer, which may be a
programmable hardware timer or a simply a timing routine in the program,
times out and generates an interrupt signal, the CPU 20a branches to an
interrupt portion of the microprocessor program.
As represented by decision block 42, the CPU 20a compares the frequency
command signal (.omega..sub.e) with the present operating frequency signal
(.omega..sub.e). If these are not equal, this signifies that the operating
frequency value (.omega..sub.e) must be updated according to the following
equation (8), which is shown with the related equation (9) for updating
the phase angle of excitation, .theta..sub.e :
.omega..sub.e (t)=.omega..sub.e (t-1)+.DELTA..omega..sub.e (8)
.theta..sub.e (t)=.theta..sub.e (t-1)+.omega..sub.e (t).DELTA.T (9)
In equations (8) and (9), (t) is a present time and (t-1) is a previous
time. The accel/decel rate determines .DELTA..omega..sub.e as a function
of time. If .omega.*.sub.e is greater than .omega..sub.e, then the
acceleration factor is applied until .omega..sub.e has come up to the
commanded frequency. If .omega.*.sub.e is less than .omega..sub.e, then
the deceleration factor is applied until .omega..sub.e has dropped down to
the commanded frequency. Process block 43 represents the instructions that
are executed by the CPU 20a to update the operating frequency value
.omega..sub.e.
Then, as represented by process block 44, the phase angle is updated.
.theta..sub.e is the phase angle or instantaneous value for a function of
the form sin .theta..sub.e (t), and .DELTA.T is the elapsed time since the
last update.
Where .omega.*.sub.e is equal to .omega..sub.e as a result of the
comparison represented by decision block 42, no adjustment of the
operating frequency is necessary, and the CPU 20a skips block 43 and
proceeds to execute process block 44 to update the excitation angle.
After updating frequency and phase angle as necessary, the CPU 20a executes
instructions represented by process block 45 to read the DC bus voltage
from A-to-D converter 20b. Next, as represented by process block 46, the
CPU 20a calculates the theoretical limit for peak line-to-neutral output
voltage (V*.sub.LIMIT) which is provided by the following equation:
##EQU7##
The CPU 20a next executes instructions represented by block 47 to determine
a value for a desired DC motor voltage command V* according to the
following equation:
V*=.omega..sub.e (t)/2.pi..times.(V/Hz) (11)
where (V/ Hz) is the volts/hertz ratio.
As represented by block 48, this result is divided by the linear gain (G)
as provided in Eq. (4) above to determine the desired motor voltage
command V*.sub.LINEAR for the linear region of operation. As represented
by decision block 49, a check is then made to determine whether
.omega..sub.e is equal to or greater than the threshold frequency
(.omega..sub.t) for the transition region. If the result is positive as
represented by "YES" branch, the CPU 20a proceeds to execute instructions
represented by block 51 to calculate M.sub.icomp according to Eq. (7)
above. Next, the he CPU 20a proceeds to execute instructions represented
by block 52 to calculate V*.sub.comp according to Eq. (5) above. The
routine continues to decision block 53, which represents instructions
executed by the CPU 20a to compare V*.sub.comp with V*.sub.LINEAR to
prevent V*.sub.OUT from being less than V*.sub.LINEAR. If V*.sub.comp
>V*.sub.LINEAR, as represented by the "YES" result, then V*.sub.OUT is set
equal to V*.sub.comp calculated in block 52. If V*.sub.comp is less than
or equal to V*.sub.LINEAR, as represented by the "NO" result, then
V*.sub.OUT is set equal to V*.sub.LINEAR determined in block 48. As
represented by block 56, V*.sub.OUT is also set equal to V*.sub.LINEAR in
the case where the result of the comparison in block 50 is negative, i.e.
the motor is still being operated in the linear region of operation.
After the voltage output command has been set to either the compensated
value V*.sub.comp or the value in the linear region, it is checked to see
that it is within the limits imposed by the DC bus voltage. The value that
was calculated through execution of block 46, and is then compared with
V*.sub.OUT, as represented by decision block 57. If the limit imposed by
the DC bus voltage has been exceeded, as represented by the "YES" result
from decision block 57, the V*.sub.OUT command is limited on this basis.
If the limit has not been exceeded, the routine proceeds as represented by
the "NO" result branch to block 59. Next, instructions are executed, as
represented by block 59, to convert from V*.sub.OUT to the phase voltage
commands V*.sub.qs and V*.sub.ds, which are related to the q-axis and
d-axis, respectively, and which are 90.degree. apart in phase. Finally, as
represented by output block 60, these are converted to analog signals
through the D-to-A converters 20c and transmitted to the phase converter
15. This completes the cycle of the interrupt routine and the CPU 20a is
returned to the main loop routine 40.
This description has been by way of examples of how the invention can be
carried out. Those with knowledge in the art will recognize that various
details may be modified in arriving at other detailed embodiments, and
that many of these embodiments will come within the scope of the
invention. Therefore to apprise the public of the scope of the invention
and the embodiments covered by the invention the following claims are
made.
* * * * *
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