U.S. patent number 3,781,615 [Application Number 05/299,932] was granted by the patent office on 1973-12-25 for system for phase shifting inverters to obtain a variable modulated waveform.
This patent grant is currently assigned to Westinghouse Air Brake Company. Invention is credited to Udo Meier, Boris Mokrytzki.
United States Patent |
3,781,615 |
Mokrytzki , et al. |
December 25, 1973 |
SYSTEM FOR PHASE SHIFTING INVERTERS TO OBTAIN A VARIABLE MODULATED
WAVEFORM
Abstract
A a. c. motor drive system for effecting fundamental voltage
modulation by phase shifting inverters coupled in parallel, thereby
providing a gradual voltage change between a minimum pulse width
modulated waveform and an unmodulated waveform to overcome surges
experienced in the transition therebetween. A voltage programmer
produces a control signal predicated on vehicle speed so as to
follow a preselected profile computed to control the degree of
inverter phase shift so that the phase shift modulated fundamental
precisely matches the pulse width modulated fundamental at one
extreme of the phase shift region of the voltage curve and
precisely matches the unmodulated fundamental at the other extreme
of the phase shift region.
Inventors: |
Mokrytzki; Boris (Murrysville,
PA), Meier; Udo (Luzern, CH) |
Assignee: |
Westinghouse Air Brake Company
(Wilmerding, PA)
|
Family
ID: |
23156929 |
Appl.
No.: |
05/299,932 |
Filed: |
October 24, 1972 |
Current U.S.
Class: |
318/801 |
Current CPC
Class: |
H02P
21/00 (20130101) |
Current International
Class: |
H02p 005/40 () |
Field of
Search: |
;318/227,230,231 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Rubinson; Gene Z.
Claims
Having now described the invention, what we claim as new and desire
to secure by Letters Patent, is:
1. A control system for energizing an a. c. motor in accordance
with a modulated load waveform being generated within a first
preselected speed range and in accordance with an unmodulated load
waveform being generated within a second preselected speed range,
said system comprising:
a. multi-phase load windings forming the stator of said motor,
b. a source of d. c. voltage,
c. first and second inverter means each having a plurality of phase
displaced outputs for connection with said load windings, said
inverter means including switch means for periodically reversing
the polarity of said d. c. voltage potential at said outputs to
effect energization of said load windings, and
d. control means for operating said switch means within a first
region of said first speed range to provide said modulated waveform
by pulse width modulation, and within a second region of said first
speed range to provide said modulated waveform by phase shifting
said first and second inverter means from a predetermined phase
angle effective within said first region to a phase angle which
varies with the speed of said motor, thereby effecting a smooth
voltage transition from said modulated waveform to said unmodulated
waveform.
2. The system, as recited in claim 1, wherein said control means
further comprises voltage programmer means for generating a
reference signal which varies in accordance with the speed of said
motor so as to follow a predetermined profile and thereby effect
said phase shift of said inverter means to an extent sufficient to
produce said phase shift modulated waveform having a voltage
component equal to the voltage component of said pulse width
modulated waveform at the transition between said first and second
regions of said first speed range, and to provide said
predetermined phase angle of said inverter means to effect said
unmodulated waveform at the transition from said second region of
said first speed range into said second speed range.
3. The system, as recited in claim 1, further characterized in that
the degree of phase shift of said first and second inverter means
is equal and of opposite sense relative one to the other so that
the resultant position of the voltage component of said phase shift
mdoulated waveform coincides with the position of the voltage
component of said pulse width modulated waveform.
4. The system, as recited in claim 1, wherein said switch means
includes solid state switch means.
5. The system, as recited in claim 2, wherein said first and second
inverter means are each comprised of a three-phase, solid state
bridge network consisting of said switch means.
6. The system, as recited in claim 5, wherein said control means
further comprises motor speed responsive drive means for
controlling the switching frequency of said bridge network.
7. The system, as recited in claim 6, wherein said control means
further comprises:
a. said drive means comprising a ring counter having a plurality of
outputs providing phase displaced digital control signals,
b. comparator means for providing first and second digital control
signals in accordance with the level of said reference signal
exceeding the level of a first and a second voltage signal of
triangular waveshape having a frequency corresponding to the speed
of said motor, and
c. logic means subject to said phase displaced digital control
signals and to said first and second digital control signals for
operating said switching means to produce said phase shift
modulated waveform.
8. The system, as recited in claim 7, further characterized in that
said first and second voltage signals of triangular waveshape are
180.degree. out of phase so that said switching means are operated
to effect said phase shift of said first and second inverter means
equally in opposite sense, thereby maintaining coincidence between
the relative positions of the voltage component of said phase shift
modulated waveforms and said pulse width modulated waveform.
9. The system, as recited in claim 7, wherein said control means
further comprises means for integrating a pulse signal having a
frequency corresponding to the speed of said motor to provide said
first and second voltage signals of triangular waveshape.
10. The system, as recited in claim 1, wherein said multiphase load
windings comprise first and second sets of three-phase load
windings, one mechanically displaced relative to the other an
amount corresponding to said predetermined phase angle of said
inverter means.
11. The system, as recited in claim 10, further comprising reactor
means for coupling the phase displaced outputs of said first and
second inverter means with the windings of said first and second
sets of load windings, respectively, to form said modulated and
said unmodulated waveforms.
Description
BACKGROUND OF THE INVENTION
In a. c. motor drive systems, switching means are normally employed
to convert a d. c. supply source into three waveforms symmetrically
displaced in phase by 120 electrical degrees for sequentially
energizing the three phase load windings comprising the motor
field. This results in a rotating field flux which is inductively
linked with the rotor to effect rotation of the rotor. In order to
increase motor speed, it is necessary to increase the frequency of
the rotating motor field flux by operating the switching means more
rapidly. With the advancement of solid state technology, power
inverters have been developed utilizing thyristors as the switching
elements to obtain the fast control necessary in making the a. c.
motor drive suitable for use in high speed systems such as railway
transit vehicles, which have historically relied upon d. c. motors
to provide tractive power. In one such inverter drive system,
inverter means is utilized to produce a basic unmodulated
line-to-line voltage waveform in a six-step configuration. By
employing a reactor to inductively couple two or more of these
inverters in phase displaced relationship between the power source
and the motor load windings, a more suitable twelve-step waveform
may be provided to reduce the harmonics affecting motor operation.
In providing suitable motor operation over wide speed ranges, a
"constant horsepower" mode of operation is employed at a
preselected base speed, in which mode the unmodulated waveform
produced by the system inverter is suitable for providing motor
voltage at maximum value. However, at speeds below base speed, a
"constant torque" mode of operation is employed, which requires
that the motor voltage be varied in direct proportion to motor
speed. To accomplish this, the basic unmodulated line-to-line
waveform is provided with one or more notches, the width of which
notches may be narrowed as speed increases to increase the net
voltage at the motor, by employing the technique of pulse width
modulation.
One of the difficulties encountered in employing a pulse width
modulated waveform to control power to the motor in "constant
torque" mode of operation is that of making the transition to the
unmodulated waveform produced in "constant horsepower" mode of
operation without an accompanying disruption of the voltage level.
Because of the inherent limitation of the thyristor switching time,
although extremely fast, at the base speed at which it is desired
to change from constant torque to constant horsepower mode of
operation, there exists a minimum notch width. Thus, the width of
the single notch comprising the final pulse width modulated
waveform cannot be reduced beyond this minimum value to bring the
voltage up to a value which approaches the full voltage produced by
the unmodulated waveform. Experience has shown that where a
discrete change in the voltage level occurs during this transition
a noticeable lurch in the motor results, which is discomforting to
the passengers of a transit vehicle, and detrimental to the
vehicle's gears and drive train. In addition, and perhaps more
importantly, such a sudden voltage change results in the thyristor
network of the inverter being required to momentarily support a
heavy current surge in excess of that which the thyristors can
safely commutate or turn off. This can cause a malfunction leading
to a shut down. Also, any damage to the inverter thyristors, of
course, is extremely costly.
SUMMARY OF THE INVENTION
It is therefore the object of the present invention to provide an
a. c. motor drive system capable of effecting transition from a
pulse width modulated voltage waveform to an unmodulated waveform
without creating a disruption of the motor operation due to a
distinct or discrete voltage change accompanying such transition,
as heretofore experienced in attempting to reach maximum
voltage.
It is another object of the invention to provide a smooth voltage
transition from a modulated waveform, such as may be obtained by
pulse width modulation, to an unmodulated waveform by employing an
intermediate waveform capable of being modulated by phase shifting
a pair of inverters producing the voltage waveforms.
It is still another object of the invention to phase shift
inverters to obtain a modulated voltage waveform having a
completely variable voltage component capable of being precisely
matched to another voltage component.
Another object of the invention is that of shifting the phase of a
pair of parallel coupled inverters in opposite directions by a like
number of electrical degrees from a quiescent reference point or a
pair of quiescent points so that the phase of the resultant voltage
component following the phase shift coincides with the reference
point of the component prior to the phase shift.
In accordance with the objects of the invention, there is provided
in a preferred embodiment of the invention an a. c. motor drive
system in which a pair of common loads comprising the stator
windings of a squirrel cage type induction motor are parallel
connected to the phase outputs of first and second inverters via
reactor means. The coupled inverters are normally operated .+-.
15.degree. out of phase from a neutral reference, thereby producing
a 12-step phase-to-neutral waveform substantially free of low order
harmonics.
In a "constant torque" mode of motor operation which is employed
between speeds from zero to a preselected base speed at which a
"constant horsepower" mode of operation occurs, the motor voltage
is adjusted to increase linearly with speed by employing a pulse
width modulation technique, in which one or more notches are formed
in the voltage waveform and progressively reduced in width as motor
frequency increases. Because of the switching response limitations
of the thyristors comprising the first and second inverters, it has
been found necessary to vary the ratio of notches with speed in
decreasing order from zero to base speed. A leading and a lagging
carrier generator each provide a carrier signal in the form of a
triangular-shaped wave whose frequency varies with motor speed, but
at different rates selected in accordance with a plurality of
different speed ranges to thereby establish the desired number of
notches in the waveform produced. These phase displaced carrier
signals are compared to a reference voltage signal programmed to
follow a profile generated by a voltage programmer so as to vary in
a preselected relationship with speed, thereby producing a pair of
phase displaced, square-shaped waveforms having notches which vary
in width dependent upon the frequency of the carrier and amplitude
of the reference signals. These variable waveforms together with a
speed responsive, six-phase output from a ring counter provide the
digital input signals to a modulator logic network whose otputs
generate the thyristor firing pattern to drive the inverters and in
turn produce the desired pulse width modulated waveforms from which
the fundamental motor voltage is determined.
At base speed where "constant horsepower" mode of operation begins,
an unmodulated waveform is produced to obtain full fundamental
voltage. Because of the voltage difference between the full voltage
at base speed and the maximum voltage capable of being produced by
the final pulse width modulated waveform, an inverter phase shift
technique of modulating voltage is employed following pulse width
modulation to bring the voltage up to full value in a smooth
manner. This is accomplished at a predetermined speed of the motor
by reason of the reference voltage signal generated by the voltage
programmer, when compared with the carrier signal, producing the
variable notched waveforms from which the modulator logic
determines the thyristor firing pattern desired. At the
predetermined motor speed at which phase shift modulation is
initiated, the phase shift modulated waveform is made to precisely
match the final pulse width modulated waveform in both fundamental
voltage and phase. In approaching base speed, the inverter phase
shift is gradually brough back toward the normal .+-. 15.degree.
displacement, so as to match the voltage component of the
unmodulated waveform produced in "constant horsepower" mode, thus
effecting, in conjunction with pulse width modulation, a smooth and
continuous voltage transition from zero voltage at zero speed to
full voltage at base speed.
A better understanding of the invention will be realized from the
following more detailed description when taken with the
accompanying drawings in which:
FIG. 1 is a block diagram of the system comprising the
invention;
FIG. 2 is a graph of unmodulated waveforms produced in generating
full fundamental voltage;
FIG. 3 shows the relationship of the carrier waves generated by the
carrier generator and the d. c. reference voltage signal generated
by the voltage programmer for a particular speed and ratio
frequency;
FIG. 4 shows the signal waveforms obtained by comparison of the
carrier and voltage reference signals of FIG. 3;
FIG. 5 is a graph showing the desired motor voltage versus
frequency and the several speed ranges in which the different
techniques of voltage control are employed;
FIG. 6 shows the profile of the reference voltage signal generated
by the voltage programmer with respect to speed;
FIG. 7 is a graph showing the waveforms produced in obtaining a
modulated fundamental waveform by the pulse width modulation
technique;
FIG. 8 shows the final 12-step fundamental waveforms of FIGS. 2 and
7 superimposed one on the other to readily gain an appreciation of
the voltage difference therebetween;
FIG. 9 is a graph showing the waveforms generated in obtaining a
modulated fundamental waveform by an inverter phase shift
technique; and
FIGS. 10 and 11 are vector diagrams from which the desired degree
of inverter phase shift may be determined in matching one
fundamental with another.
Referring now to FIG. 1 of the drawings, there is shown for
purposes of best illustrating the present invention, an a. c. motor
drive system suitable for use in powering a railway type transit
vehicle. The system includes a plurality of polyphase induction
type a. c. traction motors only one of which is shown, as
represented by the dotted block 10. The induction motor includes
two sets of load windings W1, W2, W3 and W4, W5, W6 forming the
motor stator and a conventional cast aluminum squirrel cage rotor
R. The respective load windings may be preferably arranged in a
conventional Y configuration, with each set of windings being
mechanically displaced by 30 electrical .degree., as shown, to
offset the normal .+-. 15.degree. phase displacement of a pair of
three-phase inverter devices 11 and 12. These inverters are
preferably of a solid state design which employs thyristors in a
manner similar to the type disclosed in U. S. Pat. No. 3,207,974,
issued Sept. 12, 1965 to W. McMurray entitled "Inverter Circuits."
Since a complete description is provided in the aforementioned
McMurray patent, no further explanation is deemed necessary except
to point out that a thyristor bridge network of each inverter
operates to convert a suitable d. c. supply source at conductor 13,
which represents either a third rail or overhead power line along a
transit system right of way into six-step, phase displaced outputs
R, S, T of inverters 11 and U. V, W of inverter 12. The advantage
of using thyristors, as is well known, lies in the fast switching
times obtained in commutating the d. c. supply. This is especially
critical in motor drives employing pulse width modulation to vary
voltage, as will hereinafter be apparent. The firing signals
controlling the state of the thyristor switches in the inverter
bridge network are supplied via inputs A, B, C of inverter 11 and
inputs A', B', C' of inverter 12. These firing signals are
represented in FIG. 2 by waveforms A, B, C and A', B', C', which
vary in a step fashion between zero and the V.D.C. line voltage,
turning the appropriate thyristors "ON" when the voltage is high
and "OFF"when voltage is low. The thyristor bridge networks thus
generate the line-to-line voltage at outputs R, S, T and U, V, W of
inverters 11 and 12, respectively for connection to the load
windings from the d. c. supply at conduit 13. These line-to-line
waveforms alternate between positive and negative polarities for
120 electrical .degree. each, being at zero potential for
60.degree. during each polarity transition, as shown in FIG. 2. It
is noted that only waveforms R and U in FIG. 2 are shown, since the
other output waveforms of inverters 11 and 12 are of identical
shape, but phase displaced by 120.degree. for symmetry. Waveforms R
and U represent corresponding outputs of the inverters 11 and 12
and are seen to be phase displaced by 30 electrical .degree., as
are the waveforms of the other corresponding inverter outputs, to
provide the normal .+-. 15.degree. inverter phase displacement. The
normal .+-. 15.degree. phase shift between inverters 11 and 12 is
thus brough about by the thyristor firing signals at inputs A, B
and C being 30 electrical .degree. out of phase relative to
corresponding signals at inputs A', B' and C', as shown by the
waveform displacements in FIG. 2.
An inductive reactor 14 couples the inverters 11 and 12 in
parallel, preferably by connecting the line-to-line voltage of one
inverter via inductors wound on a three-legged magnetic core on
which similar inductors associated with the line-to-line voltage of
the other inverter are wound. The purpose of this unique winding
configuration in parallel coupling the inverters is to cancel
unwanted low order harmonics without requiring an excessively large
reactor, as fully explained in copending U. S. Pat. application
identified by Ser. No. 187,974, filed Oct. 12, 1971, by Udo H.
Meier and entitled "Inverters Paralleled With Reactor." For an
understanding of the present invention, however, it is only
necessary to understand that inverters 11 and 12 are operated .+-.
15 electrical .degree. out of phase with respect to neutral and
that they are coupled in parallel to obtain a 12-step
phase-to-neutral voltage waveform, as represented in FIG. 2 by
waveform VW1. Of course, identical phase-to-neutral waveforms (not
shown) are generated in accordance with the waveforms effective at
the other inverter outputs S, T, V and W. These phase-to-neutral
waveforms are 120.degree.out of phase, thereby energizing the motor
windings in a symmetrical fashion so as to produce an apparent
rotating field. This particular techique of parallel coupling the
inverters to obtain the low harmonic phase-to-neutral voltage
waveforms is known as interdigitation. The resultant average
fundamental voltage produced by this waveform is represented
graphically by a quasi-sinusoidal wave X superimposed on waveform
VW1 and having a frequency equal to the frequency at which the
inverter is driven and having an RMS value proportional to the area
under the waveform VW1. In calculating the fundamental voltage from
waveform VW1, maximum and minimum values are assigned to the high
and low voltage levels of waveforms A, B, C and A', B', C', and the
formula V= 1/6 [2A-B-C + .sqroot.3 (A' - B')] is employed at each
point where any one of the A, B, C, A', B'or C' waveforms change
state to determine the actual voltage effective at that particular
step. It is to be noted, of course, that this voltage waveform is
unmodulated, and is effective during a predetermined range of motor
speed, as hereinafter explained.
The system further includes a speed sensor device, represented by
block 15 as a tachometer generator, associated with the shaft of
rotor R of induction motor 10. The tachometer generates an analog
voltage representative of the motor speed, which of course can also
be assumed to be vehicle speed. This speed signal is connected via
conduit 16 to a voltage to frequency converter 17. Also connected
to converter 17 via conduit 18 is a slip command signal generated
within the system regulator 19. The slip command signal represents
desired torque to be produced by motor 11 and is summed at the
voltage to frequency converter 17 with the speed signal effective
at conduit 16 to produce an analog voltage signal representative of
the frequency at which the motor field flux must rotate in order to
maintain a slip frequency corresponding to the slip command signal.
It is understood of course that the slip frequency expresses the
relationship between the rotating motor field flux and rotating
rotor R in terms of their different rotating frequencies.
The analog frequency voltage signal resulting from the summation of
the slip and speed signals is converted to a digital clock signal
by the voltage to frequency converter, and is connected via conduit
20 to a frequency divider network 21. The frequency divider
comprises counter means capable of dividing the input frequency
into a plurality of different output frequencies which are an
integral ratio of the input frequency. One of these outputs is
connected via conduit 22 to drive a 12-step ring counter 23 so as
to produce six symmetrical, phase-displaced outputs, as indicated
by reference numeral 24, having a frequency which establishes the
fundamental frequency at which the inverters are operated. This
basic six-phase output waveform is connected to the modulator logic
network 25, which provides at the outputs A, B, C and A', B', C'
the firing signals controlling the inverter thyristors, which in
turn generate the line-to-neutral voltage, represented by waveforms
R AND U, at the desired fundamental frequency. Modulator logic
network 25 includes conventional integrated circuits which form the
necessary logic to provide the proper thyristor firing pattern by
utilizing gates, matrixes, amplifiers and the like. Since any
programmer skilled in digital logic design could, by employing
Boolean algebra and the Mahoney Mapping technique, devise a
software program which could be reduced into appropriate hardward
circuits, an explanation of the details of such hardware comprising
logic network 25 will not be undertaken.
In addition to the ring counter input signal 22, the frequency
divider network 21 also produces a plurality of outputs 26, each of
which are a different integral ratio of the input frequency signal
at conduit 20. These different frequency clock signals are
connected to a range switch 27, which is also subject to the speed
signal effective at conduit 16. Range switch 27 operates to gate
one of the integral ratio input signals 26 to output 28,
establishing thereon a fundamental frequency clock signal in
accordance with the level of the speed signal. Range switch 27 also
generates a plurality of digital outputs 29, successive ones of
which become energized as the speed signal increases.
Outputs 28 and 29 are connected in parallel to a pair of carrier
generators 30 and 31, each of which comprise an integrator network
for converting the fundamental frequency clock signal 28 into a
carrier signal constant, as the ratio frequencies change. The
respective carrier signals are connected by conduits 32 and 33 to
comparators 34 and 35, each being subject to a d. c. reference
voltage via conduit 36, the level of which voltage may be
automatically or selectively adjusted, as hereinafter explained.
FIG. 3 shows one specific level at which the d. c. reference
voltage represented by line 37 may be assumed to lie. When the
amplitude of this d. c. reference signal exceeds the amplitude of
the carrier signal, comparators 34 and 35 produce an output 38 and
39, respectively. These comparator outputs 38 and 39 are
represented in FIG. 4 by correspondingly numbered waveforms in
which notches 40 are shown having a width determined by the point
of intersection of the reference line 37 with waveforms 32 and 33
of FIG. 3. It is apparent now that as the d. c. reference voltage
increases and decreases, the level of line 37 rises and falls
accordingly so as to effect a variation in the width of notches 40,
which may in fact disappear entirely at very low levels of the
reference voltage to produce an unnotched waveform 38 and 39.
Comparator outputs 38 and 39 are connected as inputs to the
modulator logic 25 to set up the logic therein in conjunction with
inputs 24 to generate a thyristor firing waveform at outputs A, B,
C and A', B', C' which will result in the inverters 11 and 12
varying the fundamental motor voltage in accordance with the
frequency at which the thyristor firing waveform is running.
The aforementioned portion of the control system comprising devices
17, 21, 23, 25, 27, 30, 31, 34 and 35 shown in block form and
hereinafter referred to as the modulator network is shown and fully
described in U. S. Pat. No. 3,611,086, filed Jan. 14, 1970 by Boris
Mokrytzki and Dennis L. Szymanski, entitled "Integral Carrier Ratio
Inverter." A cursory review of this patent will show that the
modulator network of the present invention differs only in that it
employs not one but two carrier generators and two comparators as
well as a six-phase ring counter instead of a three-phase counter.
Accordingly, it is not believed necessary to provide any detailed
description of the components comprising the above mentioned
devices of the modulator network. The basic operation remains the
same as described in U.S. Pat. No. 3,611,086, with the additional
duplicate circuitry being necessary in the present invention only
to accommodate the requirement of the two parallel inverters 11 and
12. Of course, the logic of the modulator 25 is also expanded to
accommodate the additional input data.
Referring now to FIG. 5 showing a plot of the desired motor voltage
versus frequency, it will be seen that motor 10 operates in a
"constant torque" mode at frequencies between 0-60 hertz. Within
this range, the upper limit of which is considered base speed,
voltage is varied with frequency, as shown by power curve 41. Above
base speed, motor 10 is operated in a "constant horsepower" mode,
wherein the voltage is held constant at a maximum value, with
increasing frequency, as shown by curve 42. It has been found that
the voltage during "constant torque" mode of operation can be
effectively controlled to follow curve 41 by a pulse width
modulation technique, such as that afforded by the aforementioned
modulator network of the present invention.
In accelerating a transit vehicle from zero, for example, a voltage
programmer 43, subject to the speed signal effective on conduit 16
generates the voltage reference signal via conduit 36 in accordance
with the function V.sub.ref /V.sub.speed =1. FIG. 6 shows a profile
of the programmed voltage reference signal 37, which jumps to a
maximum value at 45 hertz and follows a different course between 45
and 60 hertz in accordance with a new function. In accelerating up
to 45 hertz therefore, the amplitude of the d. c. reference signal
37 rises linearly to a predetermined value, thereby intersecting
the carrier waves 32 and 33 at different points. This results in
the reference voltage signal 37 exceeding the carrier signals 32
and 33 for progressively shorter periods as the speed increases. As
clearly explained in U.S. Pat. No. 3,611,086 and only mentioned at
this point as a matter of interest, the ratio selected frequency
signal 28 varies the frequency of the carrier wave at different
rates, as the speed increases through different preselected ranges,
to assure the maximum switching rate of the thyristors comprising
the inverters 11 and 12 is not exceeded by reason of the
progressively shorter periods of the notches 40 in waveforms 38 and
39 of FIG. 4.
In keeping with the aforementioned pulse width modulation technique
of voltage variation, the modulator logic is conditioned by the
notched waveforms 38 and 39 of comparators 34 and 35 to modify the
basic six-phase signal pattern, from which the thyristor firing
signals at the modulator logic outputs A, B, C and A', B', C' are
generated. This modified firing pattern is illustrated in FIG. 7 by
the notched waveforms A, B, C, A', B' and C'. The thyristor
switching times limit the motor frequency. FIG. 7 shows the
resultant fundamental voltage waveform VW1 effective at motor
winding W1, it being understood that the other motor windings are
likewise provided with identical waveforms having a phase
displacement as explained relative to the waveforms of FIG. 2,
except that notches are contained in the waveform. This notch rate
will vary in accordance with the ratio of the carrier frequency
signal 28 in effect. The waveform VW1 of FIG. 7 shows the minimum
single notched waveform which is generated at a speed corresponding
to the 45 hertz level shown in FIG. 5 and represents the maximum
fundamental voltage capable of being produced by the pulse width
modulation techinque. A quasi-sinusoidal wave Y is shown
superimposed on waveform VW1 to graphically illustrate the
fundamental voltage produced by the minimum notched, minimum width
waveform VW1. As mentioned relative to the interdigitated waveform
VW1 of FIG. 2, the precise shape of this intricate waveform VW1 of
FIG. 7 can be calculated by employing the formula V= 1/6 [ 2A- B-C
+.sqroot.3 (A' - B')] at each point where any one of the A, B, C,
A', B', C' waveforms change state.
As previously mentioned, the unmodulated waveform of FIG. 2 is
produced, beginning at base speed. It has been found from actual
experience that the voltage transition between the pulse width
modulated waveform of FIG. 7 and the unmodulated waveform of FIG. 2
produced in "constant horsepower" mode of operation is too extreme
both in the sense of disrupting the motor to the extent that it
causes passenger discomfort, and also because of the danger to the
running gear of the vehicle and the likelihood of momentarily
drawing high inrush currents which cannot be tolerated by the
thyristors comprising inverters 11 and 12. FIG. 8 shows an overlay
of the voltage waveforms of FIGS. 2 and 7, to graphically
illustrate by the shaded area that this fundamental voltage
difference can be quite substantial.
In order to avoid this extreme voltage transition, a phase shifted
technique of voltage modulation is employed between 45 and 60
hertz, which entails operating the inverters 11 and 12 so as to be
shifted in phase from a normal .+-. 15.degree. displacement toward
a preselected phase displacement in excess of the normal
displacement. The amount of phase shift is controlled by the
voltage signal 37 generated by the voltage programmer 43 along the
portion of the voltage profile shown in FIG. 6 generated between 45
and 60 hertz. In the present invention, it is desired to shift the
phase displacement of the inverters to a point where the
fundamental voltage of the resultant 12-step waveform produced
precisely matches the fundamental voltage of waveform VW1 in FIG.
7, corresponding to the final pulse width modulated waveform, and
thence bring the inverters back to their normal .+-. 15.degree.
phase displacement to produce the maximum fundamental voltage, as
represented by waveform VW1 in FIG. 2, so that a smooth transition
into "constant horsepower" mode of operation may be realized.
It can be seen from FIG. 8 that the difference in area under the
curves shown and represented by the shaded area is the voltage
difference produced by the two waveforms VW1 of FIGS. 2 and 7.
While this may be accurately calculated in accordance with the
previously mentioned formulas, let it be assumed for the purpose of
explanation that the voltage difference between the waveforms of
FIGS. 2 and 7 is 13 percent. It will be seen from FIG. 5 that as
the motor frequency exceeds a value of 45 hertz, a variable phase
shift range of inverter operation occurs, as hereinafter explained,
in order to generate a modulated waveform VW1 of FIG. 9. This
waveform produces 13 percent less voltage than waveform VW1 of FIG.
2 and thus precisely matches the voltage produced by waveform VW1
of FIG. 7, so that there is no disruption of fundamental motor
voltage at the transition between the pulse width modulated and
variable phase shift regions of FIG. 5.
The degree of phase shift of the respective inverters 11 and 12
required to produce waveform VW1 of FIG. 9 may be determined
graphically by vector diagrams, as shown in FIGS. 10 and 11, or may
be accurately calculated for a more exact determination. For
example, in FIG. 10 vector a is drawn at a .+-. 15.degree.angle
from a component C whose length is to be determined graphically. By
letting vector a equal a value of one, and closing the triangle by
drawing vector b at a 15.degree. angle with component C, the length
of the component C is found to have a value approximately 1.9 times
the length of vector a. Since it is known that the voltage
component of the phase shifted waveform VW1 of FIG. 9 must match
that of waveform VW1 of FIG. 7, the component value 1.9 must be
reduced by 13 percent, which is represented in FIG. 11 as having a
value of 1.65 times the value of vector a. By setting off this
distance along component C and plotting the point where the area
struck by the assumed voltage vector radii intersect, the angle
that the resultant vectors a and b make with the component C is
found to be .+-. 30.degree.. Consequently, each inverter is phase
shifted from .+-. 15.degree. to .+-. 30.degree. to effect a
60.degree. phase shift between inverters 10 and 11, as shown by
waveforms A, B, C, of FIG. 9, which are displaced 60.degree. from
corresponding waveforms A', B' and C'. By employing the formula V=
1/6 [2A-B-C +.sqroot.3 (A' - B')], the interdigitated waveform VW1
of FIG. 9 may be found whose fundamental voltage is that
approximated by the quasi-sinusoidal wave Z. It will be further
noted that this waveform VW1 of FIG. 9 produces a voltage level
corresponding precisely to the voltage produced by waveform VW1 of
FIG. 7.
In order to accomplish the desired .+-. 30.degree. phase shift of
inverters 10 and 11, reference voltage signal 37 is generated by
voltage programmer 43 to follow the profile shown in FIG. 6,
thereby jumping to a maximum value when the speed signal at conduit
16 corresponds to a frequency of 45 hertz at the point where
transition from pulse width modulation to phase shift modulation
occurs. From this maximum value, reference voltage signal 37 varies
as an inverse function of frequency until base speed is reached. It
will thus be understood that the reference signal 37 intersects the
carrier waves 36 in FIG. 3 at varying amplitudes, thereby varying
the width of notches 40 forming waveforms 38 and 39, which
represent the outputs of comparators 30 and 31, respectively.
It is apparent therefore that the variable input signals 38 and 39
together with the basic six-phase waveform indicated by reference
numeral 24 provide the modulator logic with the necessary input
variables from which a unique thyristor firing pattern is produced
at outpus A, B, C, A', B', C' to generate the desired line to
neutral voltage waveforms at the transition between the pulse width
modulation and the phase shift modulation region of FIG. 5. As the
motor speed increases, the voltage programmer adjusts the amplitude
of voltage reference signal 7, accordingly, thereby gradually
bringing the degree of inverter phase shift back toward the normal
.+-. 15.degree. displacement at base speed. Being 180.degree. out
of phase, waveforms 38 and 39 of FIG. 4 assure that the inverters
11 and 12 are phase shifted by equal amounts and in opposite
directions, as illustrated in FIGS. 10 and 11, so that the voltage
component resulting from a phase shift lies along the same line as
the component prior to the phase shift throughout the entire phase
shift region. Therefore, not only is a smooth and continuous change
in voltage realized in the region between the expiration of pulse
width modulation and base speed, but also the phase of the
fundamental voltages at the motor windings is properly maintained
to avoid poor motor action in the transition from pulse width
modulation to phase shift modulation, as might otherwise occur.
It is understood of course that increasing frequencies beyond base
speed can result in "constant horsepower" mode of operation, in
which the inverter phase displacement is maintained constant at
.+-. 15.degree. so that maximum voltage is produced as the speed
increases. It should also be understood that the reverse operation
occurs in response to decreasing speeds so that in passing base
speed and until pulse width modulation occurs at a frequency of 45
hertz, the phase shift modulation is effective with the inverter
phase displacement changing with speed from .+-. 15 degrees to
30.degree.. In either case, the net result is that of passing from
a pulse width modulated waveform to an unmodulated waveform or vice
versa without experiencing an extreme voltage transition
accompanied by a disruption in the motor operation.
* * * * *