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INTRODUCTION
The present invention relates to a system and method for starting a
synchronous motor from a static inverter without reliance upon rotor
position and speed measurements. The proposed system provides a method for
performing a start of an auxiliary power unit (APU) for jet aircraft.
Prior art includes the use of a DC motor to start the APU from a battery.
BACKGROUND ART
Exemplary of the prior art is U.S. Pat. No. 4,361,791 (Allan B. Plunkett)
which describes an apparatus for controlling a permanent magnet
synchronous motor driven by a pulse width modulated inverter. The method
forms a modified flux vector by phase shifting the measured flux vector,
and using this modified flux vector as a feedback signal for inverter
control. Further exemplary of the prior art is U.S. Pat. No. 4,855,519
(Heinrich-Karl Vogelmann) which describes an apparatus for determining the
flux vector of a machine without using a mechanical shaft position
indicator. This is done by injecting a component of stator current from
which the error between the computed flux vector and the actual flux
vector can be calculated. The error is used to modify the computed flux
vector. In contrast, the proposed system utilizes a flux estimation system
using well known synchronous machine equations with feedback added to
ensure stability of the estimated flux.
SUMMARY OF THE INVENTION
The proposed system utilizes a pulse-width-modulated static inverter to
produce a controlled AC power to drive the generator of the APU as a
synchronous motor for starting. An important feature of the present
invention includes the method in which the output of the inverter is
modified as the APU is started using only electrical system measurements.
Rather than measuring the rotor speed and position directly in an attempt
to optimize the starting torque, the supply current to the stator is
measured, filtered and is used as a feedback to estimate the motor
magnetizing flux. Then, by adjusting the supply voltage to hold the phase
angle between the current and the estimated flux at the proper angle, the
starting current can be optimized. An additional restriction is applied to
avoid exceeding the maximum supply voltage.
BRIEF DESCRIPTION OF THE DRAWINGS
Further advantages and uses of the invention will become more apparent when
considered in view of the following detailed description of a preferred
embodiment of the invention when taken in conjunction with the
accompanying drawings in which:
FIG. 1 is a schematic block diagram of a preferred embodiment of the
present synchronous motor drive system;
FIG. 2 is a diagram illustrative of the desired phase angle for controlling
and otimizing developed torque;
FIG. 3 is a block diagram showing signal processing for providing
development of the motors electrical angular velocity .omega. using
phase-locked loop with electrical angular velocity of the voltage output
of the motor drive inverter;
FIGS. 4A and 4B are block diagrams showing stabilization of flux estimation
equations, FIG. 4A being illustrative of a block diagram of original
equations showing them as equivalent to an oscillator while FIG. 4B shows
a block diagram of flux estimation equations with addition of
stabilization loops;
FIGS. 5 through 8 are graphs displaying voltage and current variables
during initial starting of the synchronous machine, more specifically
FIGS. 5 and 6 show the time history of the reference PMW voltage magnitude
and the average PMW inverter output voltage magnitude while FIGS. 7 and 8
show the time history of the inverters reference and average current
magnitudes;
FIG. 9 is a graph illustrative of motor drag torque;
FIG. 10 is a graph plotting average electrical torque;
FIG. 11 is a graph showing rotor speed versus time;
FIG. 12 is a graph showing average electrical power;
FIGS. 13 through 16 show the reference and the actual PWM voltages, as well
as the actual and filtered synchronous machine armature currents at about
10-seconds into the machine's start-up, respectively. FIG. 13 is the
reference and input voltage to the PWM inverter, while FIG. 14 is the
resulting inverter voltage. FIGS. 15 and 16 are the input and the output
of the filter respectively;
FIGS. 17 through 20 and 21 through 24 are similar to FIGS. 13 through 16,
but at about 20 and 30 seconds into the machine's start-up, respectively;
FIGS. 25 through 28 display the time history of the actual and estimated
values of q- and d-axis magnetizing fluxes during the start-up; and,
FIGS. 29 through 32 respectively show the time history of the field
voltage, flux, and current in per-unit, as well as the inverter output
power factor angle.
DESCRIPTION OF THE PREFERRED EMBODIMENT
A. Introduction
The method described hereinafter relates to a system used to start a
synchronous motor from a static inverter without relying on rotor position
or speed measurements. Features of the control system used to govern this
process are hereinafter described in detail. An overview of the system is
provided in sections B.1 and B.2, followed by details of the individual
functional blocks in sections C.1 through C.8. Section D describes a
computer simulation of the synchronous motor starting scheme and verifies
the proper operation.
B.1 System Overview
FIG. 1 shows the components of the present synchronous motor drive system.
Power to the synchronous motor is provided by a three-phase, variable
voltage and variable frequency pulse-width-modulated (PWM) static
inverter. Applicability to other forms of static inverter, e.g. six or
twelve step inverters is expected although not studied and described
hereinafter. The inverter provides AC power to the motor; the inverter's
output voltage magnitude, frequency and phase being determined by the
control system. Motor excitation is provided by a separate power source to
establish field poles in the machine. Hereinafter follows a detailed
description of the control system shown in FIG. 1. This provides control
of the PWM inverter.
B.2 Control System Description
In order to maximize the motor torque per armature ampere of the
synchronous machine it is necessary to control the phasor relationships
within the machine. The phasors of primary importance are the airgap
magnetizing flux, .PSI..sub.qdm.sup.S, and the stator current,
I.sub.qd.sup.S both represented in a stationary reference frame. By
maintaining a desired phase angle between these phasors, the developed
torque can be controlled and optimized. For a round-rotor synchronous
machine the optimum phase angle is 90 electrical degrees, that is, to have
the stator current in the rotor reference frame, I.sub.qd.sup.r, entirely
in the q-axis. However, for a salient pole synchronous machine the optimum
phase angle depends on whether the machine is saturated or not. For the
unsaturated condition, the optimum angle, .delta., is somewhat less than
90 electrical degrees, and is given by
##EQU1##
where the angle .alpha. is determined by solving equation below and is the
angle between I.sub.qd.sup.S and the d-axis as shown in FIG. 2.
(X.sub.md -X.sub.mq)I.sub.qd.sup.S.spsp.2 cos 2.alpha.+X.sub.md
I.sub.qd.sup.S I.sub.f cos .alpha.=0
For a saturated salient pole synchronous machine, on the other hand, the
optimum angle is somewhat greater than 90 degrees, and is given by
##EQU2##
where E.sub.i is the machine internal voltage and the angle .alpha. is
determined by solving the following equation
E.sub.i cos .alpha.-X.sub.mq I.sub.qd.sup.S.spsp.2 cos 2.alpha.=0
The control system will command the static inverter to maintain a phase
angle near the optimum angular displacement by injecting the appropriate
current I.sub.qd.sup.S into the motor.
The phase angle of the current vector, I.sub.qd.sup.S, is established in
relation to the estimated airgap magnetizing flux, .PSI..sub.qdm.sup.S,
developed by the "Magnetizing Flux Estimation" portion of FIG. 1.
The magnitude of the current vector is determined by measuring the power
being provided to the machine and comparing this to a reference power
input. This function is provided in the "Power Control Loop". The
calculated current magnitude is then combined with the current phase angle
to provide a current reference signal I.sub.qd.sup.ref as an input to the
"Current Control Loop". This loop then provides a reference voltage,
V.sub.qd.sup.ref, for the PWM inverter so that the inverter's output
current matches the reference value of I.sub.qd.sup.ref. As the speed of
the motor increases, the counter-voltage developed by the motor requires
that the inverter's output voltage increase in order to maintain the
desired reference current, I.sub.qd.sup.ref. At a certain speed this
counter-voltage may exceed the voltage ability of the inverter. This would
cause the inverter to lose the capability to control the motor in the
desired fashion. To avoid this loss of control, the excitation to the
motor is reduced after a certain value of line voltage is sensed. This
decrease in motor excitation reduces the motor's counter-voltage allowing
the inverter to retain control of the motor start at high speeds. The
decrease in motor excitation is accomplished by the "Field Weakening
Loop".
Sections C.1 through C.8 provide more detailed data on the individual
blocks of the system schematic of FIG. 1.
C.1 Magnetizing Flux Estimation
One of the most important functions of the control system is to determine
the magnitude and angle of the vector .PSI..sub.qdm.sup.S. This function
is accomplished within the "Magnetizing Flux Estimation" block.
Determination of .PSI..sub.qdm.sup.S is accomplished by manipulation of the
following well known synchronous machine equations in a stationary
reference frame (p denotes differentiation, d/dt):
##EQU3##
Determination of the magnetizing flux in the fashion described is
marginally stable and would often become unstable due to other system
dynamics. A method to stabilize flux estimation is described in section
C.4. In addition, the above equations require knowing the fundamental
frequency current components I.sub.qs.sup.S and I.sub.ds.sup.S for
determination of .PSI..sub.qdm.sup.S. Finding these current components is
complicated by the fact that the actual current waveform contains a
significant amount of harmonic components. Direct use of the actual
current waveform without filtering the harmonics would result in
degradation of system operation, since, the control system would then try
to respond to the harmonic components in addition to the fundamental.
Extraction of this fundamental component is accomplished by the current
measurement filter.
C.2 Current Measurement Filter
As discussed above, the filtering of the motor input current is an
important element. Inadequate filtering may result in unacceptable current
control and PWM converter operation. This is somewhat contrary to what has
been observed in typical drive system applications using induction meters
in which the motor's armature series inductance provides sufficient
filtering of harmonic currents. Synchronous motors of high rating do not
have as high a series inductance to provide inherent filtering action.
Consequently, the filter is necessary for acceptable operation. The filter
must effectively attenuate high order harmonic currents without
introducing significant phase lag in the measured armature fundamental
frequency current. In order to eliminate the harmonic components from the
control system, a narrowband filter tuned to the system fundamental
frequency .omega..sub.r is used. The mathematical representation of this
filter is:
##EQU4##
This filter has a unity gain and zero phase shift at its tuned frequency
.omega..sub.r and a sharply reduced gain at all other frequencies, hence,
it would provide the desired filtering. Also note that since the system
fundamental frequency changes with motor speed, the filter's tuned
frequency must also change with motor speed. The filter's tuned frequency
is determined by measuring the fundamental frequency of the supplied PWM
voltage as described in section C.3. below.
C.3 Determination of Electrical Frequency of the Motor
As the above description indicates, determination of the motor's electrical
angular velocity, .omega..sub.r, is critical for operation of the control
system. In the proposed scheme this is accomplished without sensing the
motor's shaft speed. Instead it is determined mathematically using a well
known phase-locked loop approach to measure the electrical angular
velocity of the voltage output of the motor drive inverter. The block
diagram is shown in FIG. 3. Signals proportional to cos .theta..sub.r and
sin .theta..sub.r, derived from the PWM reference voltages, are combined
with cos .theta. and sin .theta. terms generated by a local phase-locked
oscillator. This multiplication and subsequent subtraction results in a
signal proportional to sin (.theta..sub.r -.theta.). If .theta..sub.r
-.theta. is very small, the sin (.theta..sub.r -.theta.) term represents a
very slowly varying sine wave. Feeding this input to a
proportional-integral controller results in a change in the controller's
output, .omega. which is the frequency of the internal oscillator, until
.theta..sub.r -.theta. becomes zero. At this point the sin (.theta..sub.r
-.theta.) term equals zero, and the integrator's output remains locked
onto .omega..sub.r (=d.theta..sub.r /dt). This measurement approach is
accurate when the value of a .omega. being reasonably close to
.omega..sub.r so that the argument of the sine term is small. Otherwise,
the sin (.theta..sub.r -.theta.) may become oscillatory and the error that
this term represents may not be decreased by the rest of the loop to zero.
In the motor start system described herein we know that initially
.omega..sub.r =0. This may be used to initialize the internal oscillator
(i.e., .omega.(0)=0). Afterward, it would track the electrical angular
velocity continually as the machine speeds up.
The measured .omega. is used as an input to the harmonic filter and flux
estimator.
C.4 Stabilization of the Flux Estimation Loop
As was mentioned in section C.1, the flux estimation loop is marginally
stable and would often become unstable due to other system dynamics. In
order to see this marginal stability, it is instructive to transform the
flux equations to the rotor reference frame as follows (p denotes
differentiation, d/dt):
##EQU5##
The fact that the eigenvalues (poles) of these equations lie on the
imaginary axis means that the system is marginally stable. Other system
dynamics may push these poles to the right-half plane thus making the
overall system unstable. It would be desirable to move these poles into
the left half plane to stabilize these equations without impacting the
steady state and low frequency values of flux vector components
.PSI..sub.qs.sup.r and .PSI..sub.ds.sup.r.
To solve this instability problem, feedback loops of wash-out form have
been included in the flux estimation portion. These feedback loops are
shown in FIG. 4 and result in movement of the poles to the left half
plane. This shift in the poles causes damping of high frequency transient
components, but it does not impact the steady-state and low frequency
response of the flux estimator. The steady-state value of the flux
estimator will continue to show the correct value.
Note that the feedback loops, in their simplest form in the rotor reference
frame shown in FIG. 4, may be implemented in any reference frame. However,
they must be implemented in the stationary reference frame to eliminate
the need for rotor position information. The stabilized flux estimator
equations in the stationary reference frames are then:
##EQU6##
where K, T, .sigma..sub.q.sup.r, and .sigma..sub.d.sup.r are the washout
gain, time constant, q- and d-axis state variables, respectively, and the
caret () denotes an estimated variable.
C.5 Current Control Loop
Once the phase angle of .PSI..sub.qdm.sup.S is known the desired phase
angle of the motor current, I.sub.qd.sup.S can be calculated. To obtain
maximum motor torque the angular position of I.sub.qd.sup.ref must be set
ahead of the position of .PSI..sub.qdm.sup.S by the angle .delta., which
is determined as explained in Section B.2. This requires knowledge of the
synchronous machine parameters, in particular, the field circuit
resistance to determine the field current I.sub.f and the machine
saturation condition. However, this mathematically ellegant approach is
impractical since the field circuit resistance could significantly change
with temperature variations and the resulting field current and the
machine saturation condition could dramatically change. Fortunately, the
angle .delta. is reasonably close to 90 electrical degrees for realistic
conditions and does not need to be determined precisely for near optimum
operation. In practice, selecting a fixed value of .delta. between 70 and
110 degrees would result in an acceptable, near optimum performance. Note
that for an unsaturated machine, a .delta. of more than 90 electrical
degrees would not reinforce the magnetizing flux, while a .delta. less
than 90 electrical degrees would reinforce the magnetizing flux and
possibly cause saturation. These factors should be considered in selecting
a fixed value of .delta..
C.6 Power Control Loop Function
As described before, the magnitude of the reference current,
I.sub.qd.sup.ref, for current control is obtained via the power control
loop. Instantaneous motor voltage and the fundamental component of motor
current (obtained from the current filter described earlier) are
multiplied to obtain instantaneous motor input power. This value of power,
P.sub.e, is compared to a given reference power, P.sub.ref, and the
resulting error would be processed by an appropriate controller involving
low pass filtering and proportional-integral (PI) regulation to determine
the magnitude for the reference current. This magnitude information is
combined with the desired current phase angle to determine the reference
current, I.sub.qd.sup.ref, for the current regulators. The reference
current, I.sub.qd.sup.ref, is then compared with the filtered measured
currents to form error signals which in turn drive the PI current
regulator blocks to arrive at a reference value for the inverter output
voltage, V.sub.qd.sup.ref. See FIG. 1. The V.sub.qd.sup.ref is then
converted to phase values V.sub.abc.sup.ref which in turn are inputed to
the PWM inverter for appropriate switching actions through triangularized
pulse-width-modulation. The V.sub.qd.sup.ref is also inputted to the
frequency measurement block to determine the fundamental frequency of the
inverter output voltage which is proportional to the motor speed.
C.7 Field Weakening Loop Function
In order to provide torque control of the synchronous machine at high
speeds it is necessary that the inverter be able to inject the required
current into the machine windings. As the machine speed increases, the
internal voltage of the synchronous motor, caused by field excitation,
also increases. This acts as a back-voltage to the PWM inverter. In order
to counteract this back voltage, the voltage supplied by the inverter must
increase as the motor speed increases. With a constant field excitation, a
speed would eventually be reached at which the inverter would be unable to
satisfy the commanded current loop unless some means were in place to
reduce the internally generated synchronous machine voltage.
This means is provided by the field weakening loop. Initially the field
current is maintained at a maximum possible value to give a strong rotor
field and thus a high starting torque. The voltage commanded by the
current control loop is sensed during the motor startup process. When this
commanded voltage, V.sub.qd.sup.ref, exceeds a given reference value,
V.sub.max, the exciter current is reduced by the field weakening loop.
This maintains the motor back-voltage constant as the motor speed
increases during the start cycle. This excitation control will extend the
speed range that the converter maintains control of the motor start.
C.8 System Startup
Unfortunately, since the flux estimator is itself a dynamic system, it
takes some time (about six seconds for the example in Section D) to
overcome initial transients and correctly estimate the machine fluxes.
Therefore, early in the startup, another control means should be used to
provide starting of the synchronous machine while the flux estimator is
reaching the correct estimating condition. Afterward, the flux estimator
can be engaged in the preferred startup mode to provide a near optimum
startup characteristic as described previously.
The following early startup technique was found effective through computer
simulation studies and laboratory tests. The technique is comprised of the
following four steps:
1. Energize the synchronous machine's field circuit with a maximum possible
field voltage while the stator winding is energized by a very low
frequency voltage (about two hertz for the example) at a very small
voltage magnitude determined by a current controller regulating the stator
current to its maximum allowable level. The synchronous machine should
start rotating at a speed corresponding to the supplied frequency as the
machine's field flux increases.
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