U SO05272429A
United States Patent [19]
[54] AIR GAP FLUX MEASUREMENT USING
STATOR THIRD HARMONIC VOLTAGE
Dec. 21, 1993
and Thomas A. Lipo in IEEE Power Electronics Spe
cialists Conference, 573-580 (Oct. 1, 1989).
AND USES
“Low Cost Efficiency Maximizer for an Induction
[75] Inventors: Thomas A. Lipo; Julio C. Moreira,
both of Madison, Wis.
[73] Assignee: Wisconsin Alumni Research
Motor Drive”, by Julio C. Moreira, Thomas A. Lipo
and Vladimir Blasko in IEEE Industry Appl. Soc. Ann.
Meeting, 426-431 (Oct. 1, 1989).
‘
“Direct Field Orientation Control Using the Third
Foundation, Madison, Wis.
[21] Appl. No.: 591,517
[22] Filed:
5,272,429
Patent Number:
Date of Patent:
[11]
[45]
Lipo et a1.
Harmonic Component of the Stator Voltage”, Julio C.
_ Moreira and Thomas A. Lipo in Intl. Conf. on Elec.
Oct. 1, 1990
Mach. Proc., 1237-1242 (Aug. 13, 1990).
“Modeling 01' Saturated AC Machines Including Air
A
[51]
Int. Cl.5 ............................................. .. H02P 5/40
[52]
US. Cl. . . . . . . . . . . . . . .
[58]
Field of Search .............................. .. 318/798-811,
[56]
318/227, 228, 722-723
References Cited
Gap Flux Harmonic Components”, Julio C. Moreira
and Thomas A. Lipo in IEEE Industry Applns. Soc.
Ann. Meeting, 37-44 (Oct. 7, 1990).
. . . .. 318/808; 318/802
IEEE Standard 112 (The Institute of Electrical and
Electronic Engineers), "Test Procedures for Polyphase
Induction Motors and Generators”, pp. 1-32 (1984).
U.S. PATENT DOCUMENTS
4,023,083
4,112,339
4,245,181
5/1977 Plunkett ............................ .. 318/227
9/1978 Lipo .............................. .. 318/227
1/ 1981 Plunkett ........................ .. 318/805
4,280,085
7/1981
Cutler et a1
. . . . .. .
. . . ..
4,431,957 2/ 1984 Chausse et a1.
4,441,064
4/ 1984
Cutler et a1.
4,445,080
4/1984
Curtiss
4,450,398
5/1984
Bose
Primary Examiner-William M. Shoop, Jr.
Assistant Examiner-John W. Cabeca
Attorney, Agent, or Firm-—Olson & Hierl, Ltd.
318/803
318/805
... .. ..
[57]
. . . .. 318/798
. ... . . .. .. ..
. . . ..
. . .. . . . . . . . . . . .
. . . ..
318/798
ABSTRACT
2/ 1986 Lipo .......... ..
318/722
Methods and apparatus are provided wherein air gap
?ux magnitude and relative position are determined
from stator voltage harmonic components and stator
current in operating alternating current machines hav
4,585,982 4/1986 Cooper et al
318/722
ing a stator, a rotor and an air gap therebetween. Such
4,724,373
2/ 1988
Lipo .............. ..
318/805
4,912,378
3/1990
Vukosavic ........................ .. 318/254
determinations have various uses, such as for ef?ciency
control. Various new and improved efficiency control
lers are provided which utilize these measurements.
4,451,770 5/1984 Boettner et a].
4,503,377 3/ 1985 Kitabayashi et al.
4,573,003
318/803
318/757
318/ 807
OTHER PUBLICATIONS
“A New Method for Rotor Time Constant Tuning in
Indirect Field Oriented Control,” by Julio C. Moreira
18 Claims, 8 Drawing Sheets
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US. Patent
Dec. 21, 1993:
Sheet '1 of 8
5,272,429 0
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US. Patent
Dec. 21, 1993
Sheet 2 of 8
5,272,429
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Dec. 21, 1993
Sheet 3 of 8
5,272,429
FIG. 7
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Sheet 5 of 8
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pumps, and the like. In these applications, improvement
in operating efficiency is possible more economically
AIR GAP FLUX MEASUREMENT USING STATOR
THIRD HARMONIC VOLTAGE-AND USES
because a controller for ‘developing the optimum ?ux
FIELD OF THE INVENTION
This invention relates to methods and. apparatus for
condition is derivable from the same converter that is
used to vary the speed of the drive.
The art needs new and improved methods and appa
determining air gap ?ux. in an operating alternating ‘
ratus for regulating the energy consumption of alternat
current machine by using the third harmonic compo
ing current machines. The discovery of a reliable mea
nent of the stator phase voltage. The invention further ‘
relates to methods and apparatus for using the air gap '
?ux in controller applications where machine opera- I
of new and very useful devices and methods for regulat
tion, performance and efficiency are regulated.
suring technique for air gap ?ux makes possible a family
ing alternating current machine operation, performance
and efficiency.
BACKGROUND OF [THE INVENTION
SUMMARY OF THE INVENTION
The present invention provides a method and appara~
tus for measuring the amplitude of the air gap flux in
gap. However, so far as now known, it has not previ
cluding its fundamental and its third harmonic compo
ously been known that air gap flux (and, in particular,
nents and their relative rotational positions using the
the peak amplitude of the fundamental component of‘
third
harmonic voltage component. This is done in an
this ?ux and its angular position in the air gap as the flux 20
alternating current machine operating under conditions
rotates) could be accurately measured on an instanta
of magnetic saturation of adjacent portions of stator and
neous basis by using some other machine characteristic,
rotor components and also of approximate rated volt
such as the third harmonic component of the stator
In an operating alternating current machine, it is
known that a magnetic flux exists in the region of the air
phase voltage.
No simple and reliable technique or apparatus was
previously known which, when used in combination
with an operating alternating current machine, would
reliably and automatically determine the peak ampli
tude and relative position of the air gap flux using only
a sensed third harmonic component of the stator phase
age.
In another aspect, the present invention provides
methods and apparatus for using such measurements to
accomplish various control functions associated with
alternating current machine operation.
Thus, the present invention provides methods and
‘ apparatus for determining various alternating machine
voltage.
variables, such as output power, torque, slip gain, rotor
time constant, rotor magnetic‘ flux, and the like. Such
determinations make possible various new alternating
peak amplitude and location of the air gap .?ux, or an
electric signal representative thereof, would be veryv current machine controller devices and methods.
useful in any one of a variety of applications, particu 35 For example, one new method and associated appara
larly in control devices and methods for regulating‘ tus maximizes the efficiency of an alternating current
machine. Thus, the third harmonic component of phase
alternating current motor variables. Moreover, such
voltage is measured from which the air gap flux is deter
control devices would themselves also be new and very
mined to provide the machine output power. The ma
useful, as would be the methods associated with their
operation and use.
40 chine input power is measured and efficiency com
Electric motors consume much of the electric power
puted. This computation is then used to regulate the
produced in the United States. For example, motors
input power voltage and frequency so as to maintain a
consume about two-thirds of the total U.S. electrical
set power output from a minimum amount of input
power consumption of about 1.7 trillion kilowatt-hours.
power.
Over 50 million motors are estimated to be in use in U.S. 45
Also, the present invention provides a method and
industry and commerce with over one million being
apparatus for controlling the efficiency of an alternating
greater than 5 horsepower (hp). Over 7500 classi?ca
current multiphase induction machine by computing
tions for induction motors exist in the size range of
the machine rotor torque. This can bedone without
about 5 to 500-hp.
directly measuring the rotor phase current by using the
Although the efficiency of electrical machinery is 50 measured angular displacement between the third har
improving, the efficiency of the typical squirrel cage
monic component of the stator phase voltage and the
Such instantaneously existing information about the
induction motor ranges from about 78- to 95 percent for
sizes of l to 100-bp. Thus, substantial energy savings
can still be achieved. Energy can be saved ‘in conven
amplitude of one phase of the stator current. This can be
accomplished, if desired, from the direct current link
bus of an associated inverter that is used to regulate
tional constant speed applications when loadconditions 55 input voltage and frequency, and then using this compu
change considerably. Induction motor operation at nor
tation to regulate the input voltage and frequency ap
mal operating conditions can result in high efficiencies
plied to the machine.
by use of a favorable balance between copper and iron
The present invention permits the output power of a
losses. Iron losses dominate at light loads. Thus, energy
motor to be adjusted so that the efficiency of the motor
is saved by reducing motor magnetic flux at the expense
can be maximized. The torque of the motor can be
of increasing copper losses so that an overall loss mini
mum can be maintained. However, the cost of the con
determined from measurements of the stator current
and the air gap ?ux together with the lag between the
troller needed to adjust the motor flux is substantial.
stator current flux and the air gap ?ux (also sometimes
In contrast to constant speed motor systems, variable
referred to as fundamental ?ux). This is given by the
speed induction motor systems characteristically in 65 formula:
volve variable torque loads over a range of speeds.
Typical applications include compressors, pumps, fans
and blowers such as occur in air conditioners, heat
3
5,272,429
where T is the torque, K is a constant which is a func
tion of the motor used, |Ia| is the absolute value of the
phase current to the stator, |'yg| is the absolute value of
the air gap ?ux and 'y is the phase displacement (lag)
between the stator current and the air gap flux.
phase voltages of a stator of a three phase induction
motor are summed together. The fundamental voltage
components cancel each other out and the resultant
FIG. 7 is a block design of hardware circuitry which
can be used to determine the phase displacement;
FIGS. 8(a)-8(c) are ?ow charts for the efficiency
maximum control algorithm including:
(a) the initial computations for input power and
torque reference,
interaction between stator and rotor slots in the operat
ing motor. The phase position and amplitude of the
third harmonic component of stator voltage is represen
tative of the phase position and amplitude of the air gap
flux. If desired, the high frequency components can be
used to determine the rotation rate (i.e., the speed) of
(b) the main program and input power minimization,
and
(c) the interrupt service subroutine;
FIG. 9 shows simulation results for the indirect type
of efficiency maximizer with Motor #1 driving a fan
type of load. The traces shown from bottom to top are:
(i) input power, (ii) input power samples at a rate of
the motor rotor.
The third harmonic of the air gap flux maintains a
constant position with respect to the third harmonic
component of the stator voltage and also to the funda
mental of air gap flux. The third harmonic component
500ms, (iii) mechanical output power, and (iv) ampli
tude of the stator phase voltage;
FIG. 10 shows experimental results for Motor #2
can thus be used to determine the wave form and ampli
tude of the fundamental flux component or air gap ?ux.
showing the dependence of the third harmonic voltage
By comparing the air gap flux with the current phase
component on the fundamental value of the applied line
of the stator, the lag or phase displacement can be deter
mined. The torque is then calculated as described
above.
The efficiency of the motor can be determined by
voltage at rated frequency and no-load condition;
FIG. 11 shows experimental results for the efficiency
controller using Motor #2. From bottom to top: (i)
amplitude of the stator current (10 A/div), (ii) third
comparing the electrical input and mechanical output
harmonic voltage signal (ZV/div), (iii) torque measured
powers. The output power is the product of the torque
and shaft speed, which is also determined as described
by the torquemeter (l5 N.m/div), and (iv) torque com
puted by the controller (15 N.m/div);
above.
FIG. 12 is a block diagrammatic view of another
embodiment of a controller for a three phase induction
The resulting determination of efficiency can then be
used to adjust the ?eld of the motor as needed to in
crease efficiency. The desire is to adjust the flux pro
machine utilizing a slip frequency calculator assuming
invariant magnetizing inductance;
ducing component to produce the minimum input
FIG. 13 shows in block diagrammatic view of an
power for a ?xed amount of output power. The output
power maybe either a ?xed speed or torque as desired.
This system can be used with most a.c. machines includ
embodiment of model reference adaptive controller for
implementation of a rotor time constant correction
scheme with magnetizing inductance based on the am
ing induction, synchronous, single phase induction mo
BRIEF DESCRIPTION OF THE DRAWINGS
In the accompanying drawings, which comprise a
portion of this disclosure:
speed;
instead using constant torque or power;
wave contains mainly the third harmonic stator voltage
components and high frequency components due to
synchronous motors.
ment of an efficiency controller for a three phase induc
tion motor using the indirect method and constant
FIG. 6 is a block diagrammatic view of another em
bodiment of an efficiency controller for a three phase
induction machine also using the indirect method but
In accordance with the present invention, the three
tors as well as brushless d.c. and permanent magnet
4
FIG. 5 is a block diagrammatic view of one embodi- I
plitude of the third harmonic voltage signal; FIG. 14
shows a block diagrammatic view of a feedforward/
predictive feedback controller using the rotor time con
45 stant with the magnetizing inductance estimate based on
FIG. 1 is a graph showing waveforms of both the
the amplitude of the third harmonic voltage signal;
FIG. 15 shows a block diagrammatic view of a direct
rotor ?eld orientation controller using a scheme of lo
cating the absolute position of the rotor flux from the
fundamental air gap ?ux voltage Vgl and the third har
monic component Vg3 as modulated by the rotor slot
third harmonic voltage signal; and
harmonics obtained after the summation of the stator
rotor ?eld orientation control implementation system
driving the rotor ?ux angle 8 to zero.
phase voltages;
FIG. 2 is a graph showing fundamental components
for the stator phase current i“, air and the gap flux of
one phase ham and also showing the third harmonic
component V33 and of the air gap voltage the angle of
displacement ‘yin, between the current and the third
harmonic component A3 of the air gap flux;
FIG. 3 is a plot showing the interrelationship be 60
tween stator current air gap flux and third harmonic
stator voltage vector (v3) for one ?eld orientation con
FIG. 16 shows a block diagrammatic view of a direct
DETAILED DESCRIPTION
The present invention is applicable to all alternative
current machines. However, for present disclosure pur
poses, three-phase induction motors are described. For
a general discussion of the operation of motors and
terms used in the art, see Electric Machinery by Fitzger
ald et al. (5th ed.) McGraw-Hill, New York, which is
incorporated herein by reference.
_
dition in the synchronous reference frame relative to the
In an induction machine, for example, saturation of
d-axis as ordinates and the q-axis as abscissae;
the magnetic ?eld paths introduces spaced saturation
FIG. 4 is a graph showing the relationship between 65 harmonic components in the air gap flux due to the
the air gap ?ux component (plotted as ordinates) and
nonlinear nature of the flux saturation phenomenon.
the amplitude of the stator third harmonic voltage (plot
These saturation harmonic components travel in the air
ted as abscissae in volts) for a 3-hp induction machine;
gap with the same synchronous speed and direction as
5
‘5,272,429
the fundamental flux component. Among all these har~
monic components, the third is the dominant one. When
the three stator phase voltages are summed, the funda
mental and characteristic harmonic voltage compo
6
The d-axis component of the air gap ?ux, which cor
responds to the rotor flux when the machine is ?eld
oriented, is then computed as:
nents are cancelled. The resultant waveform contains
mainly the third harmonic component modulated by a 1
high frequency component resulting from the air gap
?ux variations introduced by the rotor slots. The bar-'7
monic components of this signal can then beseparated
and used as a means to located the machine air gap ?ux,‘ ,
with 0;, being computed from the prechosen reference
values for the stator currents, i4!‘ and id," indicated by:
and, if desired, to measure the rotor mechanical speed.
FIG. 1 illustrates the characteristic relationship be
tween the fundamental air gap voltage V81 and the third
0 = _m--! i
harmonic‘ component of the air gap [voltage V,3 in a
[as
three phase alternating current machine obtained after‘ 15
The
amplitude
of
the fundamental of the air gap mag
summation of the stator phase voltages. Because no
netic flux component, [Am is obtained from the third
third harmonic currents can circulate in the stator (since
harmonic air gap component amplitude, via a non-linear
the machine is assumed to be wye connected), the air
function, f;,:
gap third harmonic voltage V83 is identical to the third
harmonic component of the air gap ‘voltage V_,-3. The
iMmi=fA(|)~3i)
(3)
third harmonic component is modulated by the rotor
slot harmonics.
Values for this function are unique to a given machine
After eliminating the high frequency component,‘ and these values can be experimentally determined for
which can be optionally utilized to measure the rotor 25 an unloaded machine, or the like.
mechanical speed, and after integration of the third
harmonic voltage signal, the third harmonic air gap ?ux
component is obtained as shown in FIG. 2.,
The relative position of the fundamental component
FIG. 4 shows the experimentally determined rela
tionship for an exemplary three phase inductive motor
between the amplitude of the fundamental component
of the air gap ?ux and the amplitude of the third har
of the air gap flux in relation to the stator current is 30
monic component of the stator phase voltage (or the
obtained by measuring the phase displacement angle
amplitude of the third harmonic component of the air
gap ?ux). The third harmonic voltage is plotted as ab
and line current. For example, FIG. 2 shows the interre
scissae and the fundamental component of the air gap
lation between the fundamental component of the rep
?ux is plotted as ordinates for a 3-hp machine. The
resentative stator current for one stator phase shown as 35
values represent the amplitude of the third harmonic
i“ and the-fundamental component of the air gap flux
voltage after the summation of the three stator phase
(pm) for the third harmonic component of the air gap
voltages.
voltage (V,3). The third harmonic of the air gap flux A3
As can be appreciated from the foregoing descrip
is obtained by integrating V53. The phase displacement
tion, the present invention provides a method for mea
for the stator current and the air gap flux is represented
suring the air gap ?ux existing in an operating altemat
by the angle 'y,-,,,. The reference points, respectively,
ing
current machine. This measurement provides the
along the line current (i,,) and along the third harmonic
absolute
?ux magnitude in the air gap at any given time
voltage signal (V~,3) are appropriately taken so that yim
and the relative position of such flux.
between two ?xed points in the third harmonic voltage
corresponds to the phase displacement angle between
the maximum values of the stator current iasand the air 45
gap flux fundamental component Am.
The position of point P in the third harmonic wave
form is known in relation to the terminal current ias; and
the relative position of this fundamental component of
the air gap ?ux is known with respect to this terminal 50
variable (stator current). Thus, the position of the air
In particular, the method for indirectly determining
air gap flux in an alternating current machine having a
stator, a rotor, and an air gap therebetween comprises
the following steps:
a) measuring the third harmonic component of the
stator voltage; and
b) calculating the third harmonic component of the
air gap flux by integrating the measured third har
monic stator voltage component.
Moreover, the maximum magnitude of the third har
gap flux in relation to the terminal current (or voltage)
is known at all times if a given point on the third har-‘
monic ?ux or voltage is located and tracked. The angle
55 monic component of the air gap magnetic ?ux can be
of displacement yin. between the air gap flux and the
calculated from the third harmonic component of the
phase current of the stator is measured and can be used
air gap flux. From the maximum amplitude of the third
to compute, for example, the torque in a three, phase
induction machine, or for other purposes, as desired.
The air gap ?ux km, the stator current is‘, and the air
gap third harmonic ?ux A3 are vectorially interrelated
as shown in FIG. 3 in the synchronously rotating refer
ence frame representation for a condition of ?eld orien
tation. It is clear from this vector arrangement that the
fundamental of the air gap ?ux can be resolved into its 65
d axis and q axis components Lime and )tqm3 from a
measurement of its magnitude and also the angles yin,
and 6,3.
harmonic component of the air gap magnetic ?ux, the
maximum magnitude of the fundamental component of
the air gap flux is calculated by interpolating the maxi
mum magnitude of the third harmonic component of air
gap ?ux relative to previously measured empirical data
characteristic of the machine. From this calculation,
values for the function
)tam = f(vs3)
are obtained where
(4)
7
5,272,429
Am is the fundamental component of the air gap ?ux
8
ponent, so that the model is able to predict the satura
tion effects with good accuracy. The presence of all odd
harmonic components was found in the air gap ?ux,
for a distance of 211' radians which corresponds to
360' of rotation of said rotor, and
V,; is the third harmonic component of the stator
including the triplens. The ratio between the third and
?fth harmonic amplitudes was about 3.75, and between
voltage for the distance of 211 radians which corre
sponds to 360° of rotation of the rotor.
the third and the seventh harmonics the ratio was about
7.5. These ratios are much larger than they would be for
The previously measured empirical data is obtained
by preliminarily establishing for the machine the quanti
the case of a square wave, showing that the resultant air
tative relationship between the maximum amplitude of
the third harmonic component of the stator voltage at l0 gap ?ux is far from a square waveform. These higher
harmonics could be incorporated if a better correlation
rated line voltage for the machine and with the machine
is desirable, but given the accuracy of the results, the
operating under no mechanical load. The rotation speed
higher harmonics are not really needed.
of the rotor can be computed from higher harmonic
Testing also has shown that the loading of the ma
components associated with the third harmonic compo
chine does not introduce any noticeable phase shift in
nent of the stator voltage.
15
the third harmonic ?ux. The resultant air gap ?ux kept
In a preferred embodiment, the machine is a multi
its basic flattened top characteristic for all load condi
phase induction machine and the third harmonic com
tions.
ponent of the stator voltage is measured by summing
the voltages of each respective phase. More preferably,
the machine is a three phase induction motor.
The variation of the third harmonic voltage signal
current can be measured concurrently with the measur
with the motor speed for a constant air gap ?ux level
was evaluated. The variation of the third harmonic
voltage signal was a linear function of the speed as
ing of the third harmonic component of the stator volt
expected from the model, since the motor operated
According to the method, a representative stator
20
age; and the stator current can then be compared with
under a no-load condition. Even for an air gap ?ux
the calculated third harmonic component of the air gap
reduced to half of its rated value, the third harmonic
magnetic ?ux to determine the phase angle therebe
voltage signal had considerable amplitude. This indi
tween.
cates that this signal can be utilized to estimate the air
gap flux of the machine even at reduced ?ux levels.
The air gap magnetic ?ux information can be used to
calculate the output power of the motor. The output
power calculation can be based on rotor speed and
torque. Only a single sensor wire attached to the neutral
point of the machine need be employed to cause the
In addition, the torque of the machine can be com
puted from the equation:
T = 3+ lias| liamls'mwm
(5)
where:
|iaS| is the amplitude of the representative stator
current,
|7tam| is the amplitude of the fundamental component
of the air gap magnetic ?ux,
71m is the phase angle between the stator current and
the third harmonic component of the air gap mag
netic ?ux,
P is the number of poles, and
T is the torque.
35
respective phase voltages to be accessible.
Input power is separately calculated from the electri
cal energy being fed, for example, from a rectifier to a
voltage source inverter being used to supply power to
the induction motor.
The calculated output power and input power are
both fed into a microprocessor, or the like, which is
programmed with an efficiency maximization algorithm
that utilizes both such power inputs and produces an
output
signal that is fed to a voltage and frequency
The output power of the machine can also be com
controller. Cutputs from the controller are fed to a
puted from the equation
45 voltage source inverter and thereby used to regulate the
input power. The air gap flux is thus readily adjusted to
Po= T to
(6)
produce a minimum input power for a fixed amount of
where:
output power (fixed speed motor operation).
P0 is the output power
Although a three-phase induction motor is described
T is the torque,
50 herein for illustrative purposes, the ef?ciency maximi
zation technique of this invention can be extended to
w is the rotation speed of the rotor, and wherein a) is
computed from harmonic components higher than
other types of alternating current machines, as those
skilled in the art will readily appreciate.
the third harmonic component which are associ
ated with the stator voltage.
In the case of electrical machine static drive systems
Tests were conducted using a 3-hp, 230 V, 4 pole
which inherently involve varying load demands, im
induction motor, and a 7.5-hp, 220 V, 4 pole induction
provement in operating efficiency is possible at an in
motor (referred to, respectively, as Motor #1 and
herently relatively low price since the controller used
Motor #2) in evaluation work relating to the present
to develop the optimum ?ux condition is derived from
invention. With the exception of the tests done to evalu
the same converter used to vary the speed of the drive.
ate the operation of a machine at different frequencies, 60 In these applications, the cost of an inverter is already
all the evaluation tests were performed with the indi
justified on the basis of its energy saving impact on the
cated test machine powered by a sinusoidal voltage
load; for example, eliminating vanes to control the flow
supply.
A spectrum analysis of the frequency contents for the
of air in a compressor, or the like.
Given an induction motor drive delivering a particu
air gap flux was performed to see whether or not the 65 lar mechanical output power, many different combina
third harmonic component of the air gap magnetic flux
was the dominating saturation harmonic. The third
harmonic was found to be the dominant harmonic com
tion pairs of stator voltage and synchronous frequency
are possible once the mechanical output power is satis
?ed. The efficiency for each one of the various motor
9
5,272,429
operating conditions is different. For instance, when the ~
applied voltage is high and the frequency is low, the l
machine saturates and excessive iron losses occur.
10
speed decreases, the copper losses become dominant,
implying that a better ef?ciency is achieved with in
creased ?ux level and lower slip.
The frequency of the rotor slot pulsations, is conve
When the voltage is low and the frequency is high, the ,
iron losses are reduced because the machine is not satu
rated as much, but the slip is high, whichcontributes to
niently detected by an analog circuitry employing a
an increase in the rotor and stator copper losses.
A loss model for an induction motor such as de
chanical speed is then readily computed from that signal
using, for example, a technique similar to that described
scribed above can be used in order to evaluate the in-
duction motor ef?ciency at different values of voltage
and frequency while maintaining a constantlevel of
output power. For example, when efficiency contours
for Motor #1 for an output power level of 0.25pu were :
plotted, it was found that maximum efficiency (about 81
conventional variable band-pass-?lter. The rotor me
by Zinger in "Induction Motor Speed Control Using
‘Tapped Stator windings” Ph.D. Dissertation, Univer
sity of Wisconsin, Madison, 1988.
Two embodiments of efficiency controllers are
shown in FIGS. 5 and 6. In. FIG. 5, the amplitude of the
third harmonic stator voltage component is not used.
percent) was reached for a stator phase voltage value of 15 However, the phase of the stator voltage signal is em
110 Vrm and a vfrequency value of about 38 Hz, corre
ployed to resolve the stator current into its respective
sponding to a ratio of volts/frequency (V/f) of 2.89. For
flux producing and the torque producing components.
a voltage value of 127 Vrms and a frequency of 60 Hz,
The voltage and frequency of the inverter are then
which corresponds to the rated value of V/f=2. 12, the
adjusted to reach a minimum input power by adjusting
e?iciency of the motor was lower than 72 percent. 20 the flux producing component of motor current while
Thus, an improvement of about 10 percent in the motor
keeping the speed constant.
ef?ciency is achieved when the machine is operated
Implementation of this constant speed ef?ciency con
with V/f=2.89 instead of with the rated V/f for this
troller is shown in FIG. 5. In general, the ef?ciency
load condition.
controller operates in the background with a minimiza
As another example, efficiency contours for Motor 25 tion algorithm updating the voltage and frequency com!
#2 were plotted for a load condition of 0.25pu. It was
mands perhaps only several times per second to drive
found that a maximum efficiency value of about 91.3
the operating point to adrninimum input power while
percent was achieved for a V/f of 2.22 while a value of
keeping the output power constant. Hence, the overall
about 81 percent is encountered for the rated V/f of
dynamic response of the drive remains essentially unaf
2.12. An improvement in ef?ciency of about 10 percent 30 fected. The optimum controller should be disabled
is thus achieved in this condition.
when a new speed command is issued or when the load
Maximum voltage and maximum torque limits are
demand changes. However, such problems are resolv
thus indicated. The maximum voltage limit for the
able by prior art teachings; see, for example, D. S.
motor operation is ?xed at 20 percent above the rated
Kirschen, "Optimal Efficiency Control of Induction
voltage value, and it is reached for high values of V/f;
On the other hand, when this ratio is small, the pull out
torque can be reached, and further reduction in this
ratio would not be possible if the speci?ed output power
were to be maintained. At any rate, the maximum ef?
Machines”, Ph.D. Dissertation, University of Wiscon
sin, Madison, 1985. If the torque is reasonably constant
with speed, or varies only slightly, a maximum ef?
ciency condition can still be maintained even while the
torque is changing.
ciency is always achieved for the V/f ratio between
these two limit values. These limits, however, have to
be monitored in order to avoid operational problems.
The second ef?ciency controller embodiment shown
in FIG. 6 is applicable in cases where the torque speed
The ef?ciency contours for Motor #1 for the same
output power level of 0.25 pu (as above described with
three different values for the load torque, T1=O.25 pu,
T1=O.36 pu and T1=0.43 pu) were studied. It was
pensed with since regulation at constant torque implies
found that the solution pair voltage/frequency has to
satisfy the torque constraint, causing the efficiency to
become a function of the torque that the motor has to
supply at the output power level. Thus, a maximum
ef?ciency of 81.2 percent for a Pm of 0.25 pu is possible
only if the torque supplied by the motor is in the neigh
borhood of 0.36 pu. As the load torque is reduced to
curve is essentially ?xed, such as fans, pumps, and the
like. In such cases, the speed measurement can be dis
that-output power is also maintained constant. An im
plementation for this constant torque and/or constant
power ef?ciency controller is shown in FIG. 6.
While these illustrative embodiments each employ a
series connected recti?er and inverter between the
power supply and the induction motor, it will be appre
ciated by those skilled in the art that the inventive con
troller does not require the use of such particular com
ponents, and that other components performing equiva
0.25 pu, for instance, the maximum ef?ciency attainable
lent functions can be used.
drops to approximately 77 percent.
55
In such ef?ciency controllers, the torque is computed
For such variation of ef?ciency with the torque level
from the stator current and air gap ?ux as shown by:
at a given constant output power, it is found that there .
exists an optimal value for the load torque for which a
maximum global efficiency is achieved; higher or lower .
torque values result in lower values for the ef?ciency.
Speci?cally, in the case of Motor #1, this torque value
corresponds to 0.36 pu. At this value of torque, and at
0.25 pu of output power, the balance between the iron
and copper losses favors a maximum ef?ciency. Lower
values of torque imply higher speeds when the iron loss 65
becomes dominant. Consequently, a reduction of air
- gap ?ux is necessary in order to improve the ef?ciency
of the drive. On the other hand, as torque increases and ‘
r. = 3,5- li...| Mammy...
(7)
where the angle 7,7,, is de?ned as shown in FIG. 2. The
amplitude of the air gap ?ux lhaml isobtained fromthe
third harmonic ?ux component amplitude via a non-lin
ear function de?ned as f),:
llami =f>.(l>\3l)
(8)
This function relating the amplitudes of the funda
mental and third harmonic components of the air gap
11
5,272,429
magnetic ?ux is associated with the saturation level of
the machine. Values for this function are obtainable
12
amplitude. The fact that the amplitude of the square
wave is known is important when normalizing the resul
tant signal which is used to compute the angle yim. The
experimentally using the conventional no-load test.
The third harmonic component of air gap ?ux A3, in
resultant squared current signal can be written as:
turn, is obtained from an integration of the third har
monic stator voltage signal, V53:
(l3)
A3 (+)= V8504;
(9)
Alternatively, torque T,, can be computed from:
T
e
SP
In the same way, the third harmonic voltage signal is
also applied to a zero crossing detector, and the resul
tant square wave is represented by:
(10)
we
where |vg| is the amplitude for the fundamental com
(14)
ponent of the motor air gap voltage, which can be ob
a = i 1?"; [Si-13w. - Vim) + -§- sinswe - 1...) +
tained directly from the amplitude of the third har
monic signal stator signal voltage V33 via another non
linear function:
20
While this alternative way of computing the motor
torque does not need any integration as in the method
described above, it does require a knowledge of the
synchronous frequency we.
Most of the loads driven by adjustable frequency
induction motor drives are of the type wherein the
torque is a function of the speed to a positive power:
T,_.= w,'<
(12)
with the exponent k being positive and normally higher
than 1. Therefore, the implementation of the efficiency
maximization controller presented in FIG. 6 is pre
ferred, for its simplicity, rather than the scheme pro
posed in FIG. 5.
In FIG. 5, a simple analog adder circuit is used to
obtain the third harmonic stator signal V,3, which, after
being ?ltered by LPF (low pass ?lter), is free of high
frequency contents due to the inverter switching fre
quency and rotor slot ripple. The line current ia, is also
?ltered by a low pass ?lter (LPF) to compensate for the
phase shift introduced into the signal V33 by the ?lter.
Signal VS3 is then one of the input signals to a digital
controller, which can be a Motorola DSP 56001, or the
like, where it is sampled and integrated in order to gen
erate the third harmonic component of the air gap flux
signal A3. The amplitude for the air gap third harmonic
flux {MI is then computed, and the amplitude of the
fundamental air gap flux is next obtained by means of a
reference table which includes function f)" as described
in Eq. 8.
Angle y,-,,, is thus determined. V53 is the only signal
available for flux sensing. Normally, when air gap ?ux
sensing is employed, two sensors are positioned in the
air gap in a quadrature arrangement such that sine and
cosine functions are generated. This arrangement al
By multiplying these two square waves, a signal is
produced containing direct current and oscillatory
terms. Filtering this product signal with an LPF, a
resultant signal is produced containing only a direct
current component which is a function of the angle 'y,-,,,,
as shown in Eq. 15:
M,
(1s)
16
Elig- [cosB'yim + % cos9'yi”, +
11.2
005157;", + .. .1
Angle 71", can be obtained from the signal My. A
reference table can be implemented in the digital con
troller. The input signal to this table is the normalized
signal:
16
c e l
My/7F3IS?,
( 16)
which varies from —1 to +1. Here, the desirability of
knowing the amplitudes I53 and I; is appreciated. The
squaring of the current and third harmonic flux, and the
multiplication of the two square waves, are each per
formed with associated software. The option for the
software solution is possible due to the high speed of the
commercially available digital signal processors. In
order to have a good resolution for the squaring of the
third harmonic flux, a sampling period of 50 1.1.5 is used;
however, longer and shorter time intervals can be used.
Alternatively, if desired, a hardware solution can be
employed, for example, if the controller is to be imple
mented with a slower processor. In this case, it is advan
tageous to perform the squaring and the multiplication
of the two signals using a conventional hardware cir
cuit, or the like. A simple hardware solution is pres
lows the instantaneous estimation of the air gap ?ux
position with respect to the stator mmf. Here, since one
has a single signal (sine or cosine) for use, the position of 60 ented in FIG. 7. Since each of these two signals to be
the air gap ?ux with respect to the stator current has to
multiplied are square waves, a simple solution for the
be determined indirectly.
multiplier circuit is possible, making the need for a true
multiplier unnecessary.
'
Since no third harmonic component for the current
signal exists, the current signal is applied to a non-linear
After computing the angle between the fundamental
network to generate a third harmonic output signal. A
components of the air gap ?ux and stator current, the
comparator, con?gured, for example, as a zero crossing
output torque is computed as in Eq. 7. The torque thus
detector, or the like, is chosen for use as such a network.
The output signal is a square wave of ?xed and known
computed is then used as a feedback variable for a
torque regulator. The reference value for the torque, To
13
5,272,429
in FIG. 6, is theyalue that is obtained from a sample and
hold block. The input to the sample and hold block is,
the same value of the torque computed using Eq. 7.
A brief description of the operation of the controller '
of FIG. 6 follows. The input power to the inverter is
measured and its statistical variation (Spin) computed.
When this variation is close to zero, or to a low de?ned
value, it implies that the output power is constant and
that the drive has reached a steady state condition. Only
then does the efficiency algorithm such as the algorithm‘
of FIG. 8 act by enabling a timer interrupt that is pro-‘
grammed to be internally generated by the micro
FIG. 9 shows some illustrative simulation results
obtained from the efficiency controller used with Motor
#1. The traces shown from bottom or top are: (l) alter
nating current active input power to the converter, (ii)
input power sampled at a rate of approximately 1 Hz,
(iii) output mechanical power, and (iv) amplitude of the
stator phase voltage. The output power corresponds to
approximately 0.25‘ pu with the motor running at rated
speed. As the applied voltage was reduced by the con
troller, the torque regulator kept the torque at a con
processor every 50 [LS or more or less as desired. Before
stant level. As a result, since the load driven by the
motor has a quadratic torque speed characteristic (fan
type), the output power was kept constant. From this
enabling the interrupt, the torque at the steady state
simulation case, a gain of approximately 120 Watts was
condition is estimated and de?ned as the referencevalue
achieved which implies a gain of about 15 percent in
(To) for the torque regulator. This torque reference
value is kept constant throughout the optimization pro
efficiency.
A situation where the actual torque, and the torque
computed via the third harmonic ?ux, and the funda
mental current signals for a positive step change in the
trol, is required. When such change in command oc 20 applied voltage of about 0.35 V, was studied. The out
put signal of the torque regulator, was added to the
curs, or when the optimization process is over, the timer
cess, or until an external change in the operating condi
tions, coming from an operator or any automatic con»
interrupt is disabled. The program is directed to com
frequency command sent to the inverter. In this case,
the motor was started from rest with rated voltage,
pute the input power variation only when an external
frequency, and rated load. The voltage change oc
command change occurs in the command. When the
optimization process is over, the timer interrupt is dis 25 curred after the efficiency controller detected no
change in the input power when the starting transient
abled, and the controller then keeps waiting for any
had ended. The increase _in voltage did not produce a
change coming externally.
change in the output torque because the torque regula
After the system reaches a steady state condition, the
tor decreased the synchronous frequency applied to the
efficiency algorithm takes over by decrementing the
voltage command to the inverter by AVS. The output 30 inverter. The necessary correction for the frequency
was small because the torque did not vary much from its
torque then decreases, and the torque error increases,
value prior to the voltage disturbance. For this simula
which makes the torque regulator generate a change in >
tion case, the torque estimation was performed at a rate
the synchronous frequency in order to adjust the torque
of
10ms, and, because of that, it followed the actual
back to its original value prior to the voltage change. 35
torque with some delay. It was noticed that the torque
After the torque is regulated, the efficiency algorithm
response was much better for the experimental imple
compares the new input power level with the value
before the voltage and frequency changes, and decides
if further changes in these variables are necessary in
order to achieve a minimum input power.
FIG. 8 presents a ?ow chart for a digital implementa
tion of one suitable controller. The torque regulator is
activated every time that an interrupt occurs (such as,
for example, 50 us, or more or less), while the optimiza
mentation where the torque is computed at a rate of 50
us.
In another simulation, the actual torque, speed, input
power and variation of the stator voltage were plotted.
Relatively large power and torque oscillations were
found to occur at every change in the stator voltage.
However, the steady state torque was kept constant
while the input power decreased to a value that was
tion of the input power and the changes of voltage 45 approximately
75 Watts lower than the initial power
occur at a much lower rate, such as, for example, 400rns,
or more or less, which values were employed in the case
of a test and evaluation implementation.
The whole input power minimization process can
take several seconds. Enough time is given to the torque
regulator to adjust the torque of the machine according
to the reference value.
A digital simulation model for the proposed ef?- ‘
ciency controller was developed and utilized as a tool to
aid in the design and evaluation of the software and 55
hardware implementation of the system. The simulation
program assumes a third harmonic air gap ?ux compo
nent which amplitude is governed by the saturation
function f), as in Eq. 8. A complete model for the sys
level. The conditions in which these traces were ob
tained are the same as those used in acquiring the data in
the referenced FIG. 9.
.
The third harmonic voltage waveform and one of the
phase currents for Motor #2, were obtained for a rated
load condition and sinusoidal voltage supply. A'Spec
trum Analyzer was utilized to measure the harmonic
contents of the third harmonic. The third harmonic was
clearly the dominant component followed by the rotor
slot harmonic. The amplitude of the third harmonic
signal was a function of the saturation level of the ma
chine, and, consequently, was a function of the excita
tion voltage.
These same quantities were obtained for Motor #2 at
tem, such as the one developed for a controller as de 60 a no-load condition and fed by the PWM inverter de
scribed hereinabove is not applicable in this case. The
solution for the complete model requires a very small
integration step size in order to accommodate the varia
scribed below. The third harrnonic voltage contained
the high frequency components due to the inverter
switchingfrequency and the rotor slot harmonic. The
rotor slot harmonic had a signi?cant amplitude when
plete loss model for the induction machine (such as the 65 compared to the rest of the harmonics in the spectrum,
tions of the saturation factor. On the other hand, a com
one described hereinabove) is, however, suitable for use
in this exemplary embodiment and in this simulation
program.
allowing the speed detection to be implemented, if de
sired,.or needed. As the motor load increased and the
terminal voltage was kept constant, the third harmonic
5,272,429
15
voltage amplitude dropped due to a reduction in air gap
flux while the rotor slot harmonic amplitude increased,
mainly because of the increase in the rotor mrnf har
monic components. The high frequency noise still pres
ent in the third harmonic signal was further reduced
16
machines so that the mechanical load was measurable.
The voltage source PWM inverter described herein was
modi?ed so that a direct and independent control of
both voltage and frequency could be possible. The con
trol software as described previously and illustrated in
FIG. 8 was implemented in a development system using
without any difficulty by ?ltering the signal. The spec
trum for the third harmonic signal showed a low fre
a CPU (central processing unit) board commercially
quency content which was due to a slight imbalance in
obtained from Motorola which utilizes the Digital Sig
nal Processor 56001. Analog to digital (a/d) and digital
the inverter output voltage. Such conditions, however,
do not pose any problem in the processing of the third
harmonic signal which is by far the dominant compo
to analog (d/a) converters were built, as well as an
interface circuitry between the controller and the in
verter signals. Anti-aliasing low pass ?lters commer
cially obtained with cut off frequencies around 10 KHz
nent.
Experimental results were obtained and plotted as
shown in‘ FIG. 10 showing the variation of the sensed
third harmonic rms voltage, V3, with the fundamental
rms line voltage, V11, for Motor #2 operating without
load with sinusoidal excitation at fundamental fre
were installed in each one of the analog to digital con
verters.
Three channels of a/d were employed to input the
line current, third harmonic voltage, and the input
quency. It was found that a very useful signal for the
power signals. An interface circuit was built to obtain
third harmonic voltage existed even for terminal volt
the third harmonic signal. It consisted of an isolation
ages approaching 30 percent of the rated value.
20 differential ampli?er for each one of the stator phase
As the machine mechanical load increased, the angle
'Yim between ?xed points in the third harmonic voltage
voltages and an adder for the three signals. Independent
control of the gain for each one of the isolation ampli?
waveform and the line current increased as mentioned
ers was chosen in order to guarantee that the three
previously. Motor #2 was loaded from zero to rated
phase voltages had the same amplitude before being
load while keeping the stator voltage at rated value. 25 added. The input power to the machine was measured
The motor output power was computed from the
via a wattmeter (Yokogawa) which offers an analog
third harmonic signal where the third harmonic stator
voltage itself gives information about the air gap ?ux
output signal proportional to the power measured. The
motor stator current was measured by a circuit includ
ing a Hall effect sensor.
while the slot harmonic was used to estimate the me
chanical speed. Table II (below) shows the experimen
The traces shown in FIG. 11 were obtained from the
ef?ciency controller thus constructed. From bottom to
top, the Figure shows: (i) amplitude of the stator cur
tal and estimated results obtained for Motor #2. The
torque estimate, Tmest, was computed from Eqs. 7 and
8. Values for the function relating the third harmonic
rent, (ii) third harmonic voltage signal, (iii) torque mea
sured by the torquemeter, and (iv) torque computed by
amplitude of the air gap flux and the air gap fundamen
tal ?ux amplitude expressed by Eq. 8 were derived from 35 the ef?ciency controller. A torque step from rated to
the preliminarily acquired machine characteristic data
zero was applied to the motor at approximately 3 sec
which, as measured, yielded results as presented in FIG.
onds. It is clear that the computed torque follows very
8. The speed estimation, when, was obtained from the
rotor slot ripple, as mentioned before.
TABLE II
well the actual torque variation as measured by the
torquemeter. The correlation between the computed
Experimental and Estimated Results Obtained
From the Third Hannonic Voltage Signal for Motor #2
P in
Tm
w!
P0
(W)
6613.00
5673.00
5049.00
4433.00
3816.00
3227.00
2693.00
2120.00
1559.00
994.00
479.00
(N - m)
29.82
25.56
22.72
19.88
17.04
14.20
11.36
8.52
5.68
2.84
0.00
(rpm)
1744.30
1753.00
1758.70
1764.10
1770.30
1775.20
1779.80
1784.50
1789.00
1793.30
1797.40
(W)
5447.01
4692.16
4184.37
3672.56
3158.97
2639.77
2117.28
1592.16
1064.11
533.34
0.00
17
0.82
0.83
0.83
0.83
0.83
0.82
0.79
0.75
0.68
0.54
0.00
Trmest.
(?nest.
Pa 2:1.
(N - 111)
29.80
26.17
22.95
20.08
17.32
14.54
12.09
9.08
5.69
3.32
0.00
(rpm)
1740.28
1750.99
1756.34
1761.70
1767.05
1772.41
1777.76
1783.12
1788.47
1792.04
1797.39
(W)
5430.80
4799.43
4220.18
3704.56
3204.18
2699.47
2251.18
1696.00
1064.74
622.91
0.00
7hr!
0.82
0.85
0.84
0.84
0.84
0.84
0.84
0.80
0.68
0.63
0.00
The results in Table II demonstrate that the estimated 55
values are very close in the values actually measured
demonstrating that the third harmonic signal is highly
suitable for purposes of estimating the machine speed,
value and the measured value for the torque was veri
?ed for several values of load and it was very good. As
torque, and output power. The measured and estimated
FIG. 11 shows, the change that occurs in the amplitude
mechanical load torques applied to Motor #2 as a func 60 of the third harmonic voltage as the motor load was
tion of the speed for a constant frequency of 60 Hz and
reduced to zero. The increase in the third harmonic
rated voltage of 220 volts were compared and a very
voltage amplitude came from the fact~that the saturation
good correlation was obtained.
level of the machine increases as the motor load de
The indirect type of ef?ciency controller as depicted
in FIG. 6 was implemented for Motor #2. The motor 65
Study of a more detailed plot for the torque variation
was coupled in line with a direct current dynamometer
shown in FIG. 11 reveals a very small response delay
creases.
that served as a controllable mechanical load. A torque
meter (Himmelstein) was installed between the two
'
computed torque. It has been veri?ed that delays in the
order of 5 to 10 ms occurred for the computed torque
17
5,272,429
with respect to the actual torque variation. This delay is
characteristic for this kind of controller since the ampli
18
tively low torque and medium speed (0.6 pu speed and
tude of the air gap ?ux was detected every half cycle of
the third harmonic flux signal. Another factor that con
tributes to this delay was the fact that the angle yim.
between the current and'?ux was obtained via a low
0.2 pu load torque) was evaluated. The results were
- obtained from an experimental procedure where the
input power P,-,, was measured by a digital wattmeter
'while the machine mechanical output power was kept
constant.
pass ?lter which was, in the implementation above,
The experimental results for the same motor relate
the increase in the machine efficiency as a function of
programmed to have a cut off frequency at 10 Hz. This
delay was reducible by increasingfor instance, the cut
off frequency of the ?lter used to extract the angle 7;," .
information. Some care should be taken in doing so
however, because of the low frequency contents pres
ent in the input signal M-,, to the ?lter.
Another solution to the problem of detecting the.
angle 'yim was implemented and evaluated. It consisted
in detecting the zero crossing of both the third har
speed for both relatively heavy and light torque loads of
0.8 and 0.2 pu. The efficiency increase was computed
with reference to the efficiency obtained when the ma
chine was operating at the same load torque with rated
volts per Hertz.
It was observed that when the motor was heavily
loaded, efficiency was improved primarily for low
speed operation, while, when the motor was lightly
loaded, efficiency improvement was obtained at high
speeds, due to the change in the optimum balance in
monic ?ux and stator current. This solution, unfortu
nately, did not allow a better measurement for the angle
since it was found to be somewhat dif?cult to obtain an
iron and copper losses for the two load conditions. A
accurate zero crossing detection for current and third 20 substantial increase in efficiency was achieved at high
harmonic flux. These signals appear to always have ' speeds and lowtorque suggesting that good induction
some oscillatory components superimposed on them.
motor efficiencies are maintained over a wide speed
However, when the switching frequency of the invertor
range.
was higher, as it was in the case for the current regula
The present invention can also provide an adaptive
tor described below, this solution of estimating th angle ‘ , controller for correction of the rotor time constant used
‘Yim was found to work well and is presently preferred to
for the calculation of slip frequency in indirect ?eld
the solution utilized in the efficiency controller embodi
oriented control (IFOC) of induction machines. Two
ment.
'
different embodiments of the controller method and
The operation of the efficiency controller was veri
means are provided. This can provide IFOC-type
?ed by further tests and traces showing the evolution of 30 adaptive controllers which are simple, reliable, and
the command voltage applied to the inverter, in com
independent as much as possible of the induction ma
parison to the load torque, the actual stator voltage
chine parameters. The adaptive controllers can be re
amplitude, and the input power to the motor. This data
trofitable into. existing induction machine systems.
was obtained for Motor #2 running at rated speed and
The adaptive controllers depend on one variable, the
3 percent of the rated load. When the efficiency con
air gap ?ux. Thus, in the present invention, a model
troller started its operation, the motor was running with
reference adaptive controller (MRAC) and also a feed
rated voltage and frequency. The controller then de
creased the applied voltage while keeping the torque
constant by adjusting the frequency. A minimum input
forward/predictive feedback controller (FPFC) are
provided which are each useful with an induction ma
chine for indirect field oriented control.
power was reached after approximately 20 seconds, 40 The MRAC depends only on a single, easily measur
when the reduction in power amounted to about 380
able machine parameter estimate, namely, the magnetiz
Watts. This was a signi?cant power saving, showing
ing inductance. Moreover, a correction strategy to
that, for this load condition, the iron losses were very
compensate for changes in the magnetizing inductance
high if the machine was operated with rated ?ux. Part
due to changes in the air gap ?ux level is also provided.
of the noise noticed in the signals was the result of
Such strategy is based on a function which relates the
transient oscillation occurring due to the step changes in
value of this inductance to the third harmonic voltage
the applied stator voltage.
amplitude. As a result, the controller is very reliable
As mentioned earlier, in the sample embodiment, the
with regard to dependence on machine parameters.
sampling time used for torque computation was selected
However, the MRAC tends to exhibit high sensitivity
to be 50 us and the voltage command was updated
to the machine operating condition.
every 400rns. In operation, this meant that the torque
The FPFC utilizes the rotor magnetic ?ux which is
regulator used 8,000 samples to perform the proper
computed from the air gap magnetic flux as estimated
regulation, while the optimization algorithm, in this,
particular sample embodiment, took about 50 samples of
input power to converge to the minimum value.
The same variables were employed for the condition
where the motor was running at rated speed and at 20
percent of rated torque. The efficiency controller was
able in this case to reduce the input power by about 127
Watts, while keeping the load torque constant. In this
case, it took longer for the voltage command signal to
settle down around a constant level. This was because
the input power as a function of the voltage and fre
from the third harmonic voltage signal. Consequently,
this controller is dependent on the rotor leakage induc
55 tance which contributes to a certain loss of reliability.
Its response, however, characteristically tends to be less
sensitive to the machine operating condition than the
MRAC.
These controllers do not require any sensors in the air
gap of the machine nor complex computations of ma
chine parameters or variables. Only access to the stator
neutral connection is necessary in order to estimate the
air gap flux.
quency did not have a well pronounced minimum
Both the MRAC and the FPFC IFOC adaptive con
value.
65 trollers of this invention utilize the method of estimating
The saving of electrical input power, Pin, that was
the air gap ?ux and/or rotor flux from the third har
obtained as a function of the fundamental component of
monic component of the stator phase voltages that is
the applied line voltage for Motor #2 operating at rela
provided by this invention. Similarly to what is done in
5,272,429
19
the hereinabove described ef?ciency controller of this
invention, the amplitude of the fundamental air gap flux
component, [Mm], is ?rst obtained from the amplitude
of the third harmonic component of stator voltage, V3
as derived from the integration of the third harmonic
stator voltage signal VS; resulting from the summation
of the three phase voltages in a three phase induction
motor. Then, the amplitude of the fundamental compo
nent of the flux linkage is expressed in terms of the third
harmonic ?ux component by the non-linear function of
Eq. 8. Values for lkaml are measured for a given ma
chine or machine type. An example of values obtained
for this function for one motor is given herein involving
simulation and experimental results.
The relative position of the fundamental component
of the air gap ?ux with respect to the stator current is
obtained by measuring the phase displacement between
20
q components. Therefore, changes in the torque or flux
commands produce variations in the air gap ?ux level,
and, consequently, in the magnetizing inductance, espe
cially if the machine operates in the non-linear segment
of the magnetization characteristic curve, as is common.
A function has been discovered which relates the
actual value of the magnetizing inductance with the
magnitude of the third harmonic ?ux component. This
function can be considered to have been obtained from
the function relating the fundamental air gap ?ux ampli
tude and third harmonic air gap ?ux amplitude de
scribed by f), in Eq. 8. This function, designated as f]_,,,,
15:
Lm=fLm(lA3l)
(17)
This function relating L,” and [MI is optionally but
two ?xed points, one in the third harmonic air gap
preferably incorporated in the MRAC controller in
magnetic ?ux T3 and the other in the stator line current
FIG. 12, which is easily accomplished, and the resulting
waveform in, (see FIG. 2) so that such waveform dis 20 adaptive control scheme becomes independent of varia
placement corresponds to the phase displacement be
tions in the magnetizing inductance. FIG. 13 shows an
tween the maximum values for each of the fundamental
embodiment of such an IFOC MRAC-type controller
components of current in, and air gap flux Am.
for correcting the rotor time constant which incorpo
The fundamental and third harmonic components of
rates this function.
the air gap flux, and also the stator current, are depicted 25
The performance of the MRAC is demonstrated by
in a vector representation in FIG. 4 from which it is
plots which show the steady state value of the normal
clear that the air gap flux is resolvable into its d and q
ized d-axis component of the air gap ?ux as a function of
components from a knowledge of its magnitude and the
the normalized detuning of the rotor time constant for
respective angles 71,-", and 0b.
The dependence of the MRAC type of controller on
machine parameters is minimizable when a convenient
machine variable is chosen. In accord with the present
Motor #3, which is characterized below. These quanti
ties are normalized with respect to the values at ideal
?eld orientation condition. Plots for three different
values of torque at rated flux are prepared. The results
shown demonstrate that the correct value of rotor time
constant is always obtained because the Ad"? is not a
tance of the machine to establish an IFOC-type adapt 35 doubly valued function and because it presents a zero
ive controller for the rotor time constant.
flux error at the correct rotor time constant for all
The MRAC controller utilizes the air gap ?ux mea
torque conditions. These results also demonstrate that
sured from the third harmonic content of the stator
the controller is always stable regarding the direction of
voltages for both rotor time constant estimation as well
change in the rotor time constant.
as magnetizing inductance estimation. The air gap mag
A possible potential problem for this MRAC-type of
netic flux so measured is resolved into its d and q com
controller is its low sensitivity to detuning for low
invention, which variable is the air gap magnetic flux,
one needs only a knowledge of the magnetizing induc
ponents. The d component is utilized in the adaptation
scheme for the rotor time constant. The q component is
utilized to show the magnitude of the flux or to estimate
the magnetizing inductance.
The d-axis component of the air gap ?ux, which has
the same value as the rotor ?ux when the machine is
?eld oriented, is then computed as shown in Eqs. 1 and
2 above.
The air gap flux d-axis component computed from
Eq. 1 above is utilized by the MRAC. FIG. 12 illustrates
an embodiment of the MRAC for rotor time constant
correction.
‘
The simplicity of the MRAC is striking. It requires
only an estimate for the magnetizing inductance, L,,,', in
order to set the flux reference value, Mme‘, which,
together with the flux computed as in Eq. 1 de?nes a
?ux error signal, Altdmll. This error is driven to zero by
a regulator as the rotor time constant, T}, is adjusted to
its correct value. The MRAC simplicity is possible only
because of the choice for the model output chosen, Mm
in this case.
torque conditions. The results of the indicated perfor
mance evolution suggest that a low sensitivity to detun
ing exists when the exemplary machine is running at 10
45 percent of its rated torque. This could perhaps represent
a problem if a correct tuning is desired when operating
at light load conditions. A solution for this potential
problem is to increase the controller gains which should
be done with caution in order not to compromise the
dynamic response capability of the entire system of
which this controller is a part.
The dynamic response capability of the MRAC is
also sensitive to the operating condition of the system.
The simulation and experimental results obtained in
evaluation of an embodiment of the MRAC show that
the MRAC response is a function, for instance, of the
direction of change in the rotor time constant. This type
of behavior can be explained by the fact that the
MRAC, which is implemented with constant controller
gains, is actuating in a non-linear system. Consequently,
the eigenvalues of the system including the MRAC
controller are space variant, changing as the operating
In spite of the simpli?cation obtained, the MRAC still
conditions of the drive are changed.
depends on the magnetizing inductance, a parameter
Despite these potential problems with sensitivity and
that is likely to vary with changes in the machine oper 65 variant dynamics, the MRAC presents the very attrac
ating conditions. Variations in the magnetizing induc
tive characteristic of being practically independent of
tance are characteristically associated with the air gap
machine parameters. The only machine-derived data
flux level which is a function of the stator current d and
desirable for its implementation is the function fL",
21
5,272,429
relating the magnetizing inductance and the amplitude A
22
terms that correspond to the de?nition for w, can be
of the third harmonic of the air gap ?ux. The result is 'a .
written as:
controller with high reliability. Evaluation results have
shown that the MRAC. is capable of estimating the
0= Amid,"- liq; -r'r‘:A)td,3_ 1iq,3— 5A4, — 1M4,’
correct optimum air gap ?ux value for a wide range of 5
rotor speeds.
(23)
Assuming that the actual stator currents follow ex~
In most practical applications, the detuning of the slip
actly the references, the division of Eq. 23 by Eq. 22
calculator is a result of changes in the rotor resistance
yields an expression for the error in the slip gain as a
function of the error in the rotor ?ux components, as
which has a thermal time constant that is much larger ‘
than any relevant electrical or mechanical time con-'
follows: .
stants in the system. As a result, the variant dynamic
response of the MRAC is not necessarily an issue with
which to be concerned if stability is guaranteed. Fur
thermore; in applications where the motor operates
close to its rated torque during most of the operating 15
cycle, the potential problem of low sensitivity presented
Alternatively, the expression for Am above is express
by this controller is not important.
ible in terms of the actual d-axis rotor ?ux instead of its
To improve the MRAC sensitivity to detuning at
reference value:
light loads and also its dynamic response, another em
bodiment of an IFOC adaptive controller is presented,. 20‘
identi?ed as FPFC.
The FPFC generates a rotor ?ux error which is used
as a feedback signal to the controller while the slip
frequency calculator generates the feedforward input
signal. A principal operational feature of the FPFC is
As a result, the deviation in the parameter estimation
25 represented by Am is readily computed as a function of
the way in which the error in the rotor ?ux is related to
the error in the d and q components of the rotor ?ux.
This error is used by a controller algorithm to compute
the error in the slip gain when detuning-occurs. The
two rotor ?ux components are affected by any amount
the necessary change in the slip gain commanded to the
slip frequency calculator. When Am is added to the
estimate in, Eq. 22 yields:
of detuning due to changes in the machine parameters,
and this error is used to predict the change that occurs
in the machine parameters. The derivation for the rela
w.'=<a+Am)iq.">are’-1=(K;+AK.)iqs"
tionship between the rotor ?ux error and the changes in
the machine parameters follows.
The q-axis rotor voltage can be written as:
o=r,iq,i+paq,,3+w,xd,3
(26)
where the symbol K,‘ is the rated slip gain computed
35 from Eq. 27, and K, is its variation obtained from Eq.
25:
(18)
Considering that the detuning is mainly caused by
changes in the rotor resistance which occur at a slow I
rate, the assumption can be made that the term p hqre is 40
close to zero. Hence, the foregoing equation above can '
be rewritten as:
The rotor ?ux used in Eq. 25 to compute the error in
the slip gain error is estimated from a processing of the
third harmon'ic voltage signal. As explained previously
45 herein, the third harmonic stator voltage signal and one
The q-axis rotor for ?ux a non-saturated machine is
of the stator currents are used to estimate the air gap
given by:
?ux d and q components. The rotor flux is then readily
computed from these quantities according to:
50
The slip frequency ws from Eq. 19, after substituting
ie therewith from Eq. 20, is given by:
A
L,
l
(28)
X2, = T'hzm — 14,12,
In
'
<29)
(21)
55
Although dependent on machine parameters, the
rotor ?ux is obtainable with'reasonable accuracy since
With the machine operating under ?eld orientation,
the commanded slip frequency w;'=ms, and the esti
the rotor leakage inductance, L1, andv the ratio Lr/Lm
are only moderately dependent on the saturation level.
mates of m and n coincide with the actual values for m 60 The rotor ?ux references needed in the computation of
and n in the Eq. 21 above, as shown by:
a,‘=ri1q,¢‘td,3‘—1
the ?ux error are simply de?ned as zero for the q-axis
component, and as a constant value for the d-axis com
(22)
‘ponent. This last value can be originated from a ?ux
regulator, if desired.
where the q-axis component of the rotor ?ux is zero.
When a detuning occurs, an error in the parameter
estimates appears as well as in the rotor ?ux compo
nents, such that the slip frequency, after identifying the
65
-
FIG. 14 illustrates an embodiment of an FPFC imple
mented in an induction machine indirect ?eld orienta
tion system. As for the case of a MRAC, the estimate
for the magnetizing inductance is obtained from the