Note: Descriptions are shown in the official language in which they were submitted.
20~TR--664 ~ ~:
07 `:
This invention is related to a Canadian patent~
application Serial ~o. 287,908 filed September 29, ~ :
1977,D. D'Atre, T.A. Lipo, and A.B. Plunkett and .~.
assigned to the General Electric Company. :
.~ This invention relates generally to a scheme for :-:
stabilizing the operation of an adjustable speed a-c .
electric motor ~hat is driven by static electric power. .
conversion apparatus. More particularly, the invention
~ relates to method and apparatus for stabilizing the operation
- 10 of a current fed induction motor drive system, and it is: ``.
~: also applicable to voltage fed induction motors and to::-:; .
drive systems employing synchronous or synchronous-
reluctance motors.
I The background of this invention is the same as the
. "Background of the Invention" set forth in the above-
~ reference Canadian patent application Serial No.
287j908 filed September 29, 1977. That :. :
application discloses an improved a-c motor stabilizing
~. .
scheme comprising suitable means for deriving an angle
feedback signal representative of`the actual phase angle .. ..
between eLectric current and electromagnetic flux that
interact to produce torque in the motor when excited
and means responsive to the angle feedback signal for ``~
controlling the power conversion apparatus so as to
control the stator excitation frequency of the motor
as a function of the angle feedback signal.
, :
20-TR-1184 .': ~
9V~7 i,,
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Summary oi! t}le In~rention ~-
A general object of the present invention iY to provide mean3 for ~,'
improving the perfomsance of the above-~ummarized ~tab~lizing arheme
when the ml)tor drive sy~tem is running wil~bi zero torque, ~'
A furth~r object of the i~vention ia the provision, in a ~tabilizing .'.
~cheme similar to the one claimed in the concurrently filsd application, ~,
. o~ an alternative angle processing means for deriving thc angle feedback
~ignal. ~ ~
. ~ . In carrying out our invention is- one form, fir~t mean3 i~ provided ,- . -
for deriving from an a-c electric motor an angle feedback 8ignal ~, :
representative of the actual phase angle betwreen current and magnetic ,^ `
flux that interact in the motor to develop an electromagnetic torgue ~'
~ . tending to move the rotor of the motor relative to the ~tator when . . '.. .
excited, and the angle feedback ~ignal i8 ~upplied to second means .
~or controLliDg the excitation source of the motor a9 a function of the . ~
angle feedback ~ignal. Preferably the excitation 30urce comprises .':. :
electric power conversion apparatu~ l~at supplies a-c power of ,~
; variable frequency and amplitude to the windings on the motor dtator,
~: and tihe ~econd means is arranged to control that frequency. In
',
accordance with the present invention, additional means is provided
for controlling the conversîon apparatus 90 as to control the amplitude
:1~: of a-c power ~upplied to the stator windings a9 a function o a'; .
; ! variable command signal, and the additional means includes rneans ~ .
for preventing any deviation o thc~ command signal below a predetermined ::
ZS ~ mi~imum limit. This ~will prevent the excitation amplitude from alling 't'
' ~ ''' '
r~
~ . , 20-TR-1184
,:, 1'~` ~'
1'-' '
below a certain minimum level when the motor i9 operating at zero ~', .
torque, thereby advantageously avoiding ~e lOEi8 of the angle feedback
signal under such conditions.
In ano~her a~pect of ~he present invention, ~e afore~aid ir~t ~, '' .
nleans comprises means for deriving a fir~t periodic signal ~ynchronized
with the fundamental component of tl e a,ctual 'flux produced acro~s the
~. .
air gap between the stator and tlle rotor of the motor in a predetermined '~ ' '
'.1 .~;;
axi8 of the stator, means for deriving a ~econd periodic signal ,' ,.. ~" j,
synchronized with the fundamental stator wind~g current in anO~er .,
stato r aXiB di~po 8 ed e~ctively in quadrature ,with said predetermined '`
, ~, axis, and phase discriminating mean~ respon~*e to the irst and second , ~,
. . .
,, periodic ~ignals for producing a ~ignal (the ang,le feedback signal)
~-.
representative of the 'complement of the electrical phase displacement
between said periodic signal~
. :
~, 15 The invention will be better understood and it'~ variOu~ objects
and advantages will be more fully appreciated from tbe following
~ I description taken in conjunction wil~h the accompanying drawings. ,~
: j~ Brie Descri~?tion c>f the Drawin~s ;;`, .
' I Fig, 1 is a unctional block diagram illustrating an '~.' .
......
~1 20 ad~ustable speed a-c electric motor dri~e ~yste~m embodying our ,~
~"~'.',.
in~rentiOn;
,
20 -TR -1184
,;
~Ig(J~7 !~
.
Fig~. 2A and 2B are, respectively, schematic diagram~ o~ the ~,
stator winding~ and of the stator current waveformE in the 3-phase ~
motor illu~trated in Fig" 1; i`7
Fig. 3 is a schematic repre~enta~ion of the motor rotor ~howing
~ector~ that re~pec~vely represent rotor and stator currents and air
gap flux and also ~howing a set of three coil& for sensing the flu~
acro~s three diff~rent sectors of ~he air gap;
Fig. 4 i~ a simplified equivalent ci rcuit diagram oiE a typical ~
a-c induction motor; ~
Fig. 5 is a vector diagram showing changes in the ~Sator ~,
terminal voltage vector durlng a motor ~peed reversal with constant
load;
Fig. 6 jB a vector diagram showing changes in the statOr and 7
roto r cu rrent vecto rs with changing load at constant speed; ' ,~
1 Fig. 7 is a graph showing the ~rariations of torque and torque '~
angle as a function of motor alip frequency;
Fig. 8 is a ~chematic diagram of an angle feedback signal ~,
., ;
~1 deriving circuit shown as a single block in the Fig. 1 embodiment ~'
~ of ~e prt~ent invention; and
; 1 20 Fig, 9 is a schematic diagram of another angle feedback signal
. ~ .
deri~ring circuit that i- also use~ul in 1~he motor drive system ~'
illu~trated in Fig. 1.
Referring noW to Flg. 1, our invention is shown embodied in ;-
an adju~table ~peed motor drive sy~tem ba~ically comprising the
combination of ~lectric power conversion apparatus 11 and an adjustable ~'
peed a-c motor l2 havine 3~-phase ~tar-connected stator windings ~_
., j . . ..
n~
~,, 1
I A I :
~08900~7 !.
~!
that are connected for energization to the polypha~e output of the
conversion apparatus and a rotor coupled to a mechanical load such
a~ ~e wheel~ of a traction vehicle ~not shown). The ap~aratus 11;~
-.
suitably constructed a~d arranged to ~upply a-c power of variablo ~.l -
,;
frequency and amplitude to the stator wlndings of the motor 12. In its
pre~erred çmbodiment, the ColXVer~ion ~Lpparatu~ 11 ha~ a front end ~!~
comprising a controlled d-c power ~upply 13 adapted to be connected
,
to an electric e~ergy source (not shown), a ~ack end comprising a '
variable requency static electric power inverter 14 having d-c and
a-c terminal set~, and a d-c lir~ 15 interconnecting the d-c terminal
set o~ 1he inverter 14 and the d-c terminals of the power supply 13.
The~e more or less conventional parts of the illustra1ed motor drive ~
system will now be briefb described, and following that description i~.
the concept and pre~erred implementation of our invention will be ~:
! .e~plained in detail. At the outset, however, it should be understood
that our invention serves the primary purpose of stabilizing the operation
of t~e motor 12, ànd it can be advantageou~ly u~ed for this purpo~e in
motor drive systems different than the particular one illustrated in
~1~ 20 The d-c power supply 13 can take any one of a variety of known
orms, such as, for example, a d-c/d-c chopper whose input terminals
are coupled to an uncontrolled d-c source, a phase controlled rectifier
circuit coupled to fixed frequency a-c ~e, and an uncontrolled ~ `
. . .j:, . . .
t~ rectifitr coupled to a variable alternaUng voltage ~ource. By varying ; ;;
25 ~ t~e~duty cycle of the chopper o~r the îiring angle o~ the electric valves
forming lhe phase controlled~rectifier circuit or t~e voltage a~plitude ;
~;. ~ :~; . .
-~ . . ...
,' .:
~ ~ f ~
20 TR-1184 .,
.;
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~,~8~ZO~Z7
of the alternating voltage 30urce, as ~he caZ~ie may be, She a~erage ¦.
magnitude of 1he unipolarity ou~put voltage ~R that the power Zsiupply
13 impresses on the d-c link 15 can be varied as desired. The d-c link ~,~
15 includeZ~i a suîtable filter, shown in Fig. 1 aZ3 a sin~le inductor or
choke 16, or ~moothing the undulating direct current flo~ving between
t~e power supply 13 and the inYerter 14, whereby controlled magnitude l~
direct current is supplied to the inverter 14. This reZrZultEi in a current '~
fed a-c motor drive syZstem. In Z3uch a sy~item the d-c power supply
i "
13 will be Z3uitably arraIlged to accommodate a polarity Ieversal of the ~ ;
!.
unipolarity voltage VR in the event o electric braking which i3 an '~
operating mode wherein the motor 12 i3 driven by the inertia of its
mechanical load and consequently serves as a generator delivering .
electric power So the ront end of the con~ersion apparatus 11. ~`
jl The inverter 14 may comprise any suitable conventional inverter. Z.
In l~e preZsently preferred embodiment o our inventlon, it is particularly ,~advantageous to use a 3-phaZse auto-sequential commutated inverter; an
improved form of such an inverter is disclosed and claimed in U.S.
',
patent No. 3, 980, 941 granted to P~. F. Griebel and assigned to the ~'
: , ' :' .
Gen~ral Electric Company. The reZspectiv~ terminals of the 3-phase
a-c terminal set o~ the inverter 14 are connected by way of three
alSexnating current conductors or lineZ~ 179 18, a~d 19 to t~e corresponding
. ':
terrninals of the 3-phase Z~tator winding3 of the motor 12, and *le
inverter 19 operative to switch the d-c link current in ~equence bel;ween
. Z . .
ie respective phaseeZZ of the Z3tator windings.
i~ :
f` ~ ~ 25 The motor 12 may be selected from a variety o~ conventional
typel~i known generally as ~induction, synchronouZs, and sync~ronou~
reluctance, and it can be eii~er round or linear. A round induc~on
-6- `
~ . 20-TR-1184
. . .
.....
90'7
,1,',. .
motor iB a,~sumed in the present description, it being under~tood that ~1,,4~ .
if a synchronou~ motor were u~ed the source of excitation would .
addltionally include ~uitable mean~ for ~upplying direct current to
the field winding~. The motor drive sy~tem may co~npri~e a single ~.
tor 12 a~ shown, or alternati-rely it may compri~e a plurality o
sucll motor~, in which event separate inverters and d-c links may be -
provided for connect1ng the respecti~re rnotor~ in parallel to a ~har0d
d-c power ~upply. While a 3-phase motor has been ~hown~ the
number of phase~ i8 not critical, and motors having single, double,
~ix, or more phases can be alternatively u~ed if desirea. ,.
The 3-pha~e stator windings of the illustrated motor }2 are .~`
shown schematically in Fig. 2A. Each winding compri~es a plurality
.... .
.o main coils ~at are conventionally distributed in slots a~round the . ~ :
stationary magnetizable core of the motor and that are electrically
. 1 . .
connected between a neutrai bus N and the as~ociated phase (A, B,
or C) of the 3-phase power lines 17-19. The alternating currents iA~ :
iB~ and ic exciting the re~pective pha~es o the stator windings during
one full cycle of operation are illu~trated in Fig. 2B wherein the
c:ommutation intervals are idealized and ripple is neglected. It wlll
, J, be 3een that a symmetrically staggered phase sequence A-B-C is
l~ assumed. In each phase the fundamental stator winding excitation
¦ current has an amplitudè determined by the magnitude of current in
i~ the d-c link 15 of ~e conversion apparatus and a frequencv determined
by the fundamental switching frequency of the electric values in the
inverter 14.
~i
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~ ~ _7
20 -TR -1184
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07
By appropriately contsolling the motor excitation, the load .,
that is driven by the motor 12 can be propelled ~motoring mode~ or
retarded ~braking mode, in which the motor operates as a genera$or) .,
in either forward or reverse di~ections as desired. Preferably the '~ -excitation control i8 exercised by varying the frequency, the current
amplitude, and the phase sequence of thie polyphase a-c power that
:
e convertion apparatu~ 11 supplies to the stator of the motor 12. Aj
Toward this end, suitable means i8 provided for regulating and
,~ ." :.
control~ing the operation of the conversion apparatus in prograIslmed
response to an operator controlled i~put ~Ignal and to certain feedback
signal~. The input signal i9 applied to an input terminal 20 of a '~'
command logic module 21 and i8 representative of a desired motor `i
.~:
torque or horsepower. The feedbaclc 6tignals are representatlye of
the actual motor responses, as is more ful}y explained below.
, . . . ..
The control mean~ shown in Fig. 1 comprises a pair of outer ^.
regulating loops 30 and 40. The fir~t outer loop 30 exerts control over
the amplitude of statOr winding current in a manner to regulate the
magnitude of stator cxcitatiOn, whereas the second outer loop 40 exerts ,~
control over the ~requenc~r o ~ttator winding current in a manner to
; 1 20 regulate motor torque. The second loop 40 lncludes an inner loop 60
fo r tabilizing purposes.
The first ou1ier loop 30 regulates the statOr excitation of the
motor lZ by so adjusting the average magnitude of the voltage VR
impressed otl the d-c link 1S9 which magnitudc in turn determinest the
25 magnitude of lir~ current and hence the amplitude of the fundamental
~ttator winding current, as to minimize the error between an excitation
. .
! ~ -8- -
. . ~; .,.
~9~07 - !`
.
magnitude feedback 3ignal applied to a terminal 31 and a variable .,.'
command ~ignal on line 32. This loop compri~es a control circuit
33 in which ~e eedback and command ~ignal~ are com~ared at a
summing point to der*e, on line 34, an error signal that renecta
S any di~ference therebetvveen. As i~ s~o~ivn in Fig. 1, ~he error aignal
on line 34 is proces~ed by a conventional gain network 35 having ~.
integral plu~ proportional tranafer characteristics, whereby a zero
~teady-state error can be obtained. From the gain network 35 a
compensated signal V*R is derived and fed over a line 36 to suitable ~ ;
control means 37 for 1he controlled d-c power supply 13. ;~`
The control mean~ 37, labeled GPG (gate pulse generator) in
Fig. l, controls the operation of the d-c power supply 13 and
determines the average magnitude of the d-c lis~ voltage VR in ;
,~ ~ accordance with the compensated ~ignal V*R. It will be apparent that
t~e ~r-t reg~llating loop 30 responds to any error between the excitation
magnitude feedback signal applied to terminal 31 and the command
~ignal on line 32 to vary VR in a corrective sense, thereby increasing
or d~croasing the fundamenta~ amplitude of stator winding curxent as
necessary to reduce the value of the error to zero. The excitatlon ~;
., ~ ,
magnitude feedback slgnal i~ intended to be repre~entative of the '
Ictual level of excltation in the stator of motor 12. For example,
:j .
it can be a measure of the average magnitude of ~he actua1 flux
produced across the ~tator-rotor gap in the motor 12 when excited,
`'r ~ iIl which case thi8 feedback signal is preferably derived rom the flux - ~o
. . .~
f~edback signals a~raila~le in the circuit ~hown in Fig. 9 as described
hereinafter. The cornnand ~ignal on line 32 iB derived from a control ;-~
, ~ ., . :
20-TR-1184 , .
,~
t~
signal P*G repre~nting the desired magnitude of etator eXCitatioA~
~ "' ,. :
a~ determined by t~se command logic module 21. Thi!3 con~rol ~ignal
is supplied 'o the circuit 33 on line 38, and in accordance with our i~
in~rention a limiter 3g i6S included betlveen line~ 38 and 32 to prevsnt any ~ ?' ~ -
deviation of i~he command signal on line 32 below a predetersnined, i.' ~ :
minimum limit. . i- :-
The 3econd outer loop 40 regulate~ the motor torque by 80 ,`.~
adjusting t~e fundamental switching frequency of the inverter 14, which `.~: ;
frequency determines ~e frequeslcy of the undamental stator winding ~,'.~ . .
current, a~ to minimize any difference between a torque feedback ~,
signal T on line 41 and a variable control signal T* (representing a ^i'
,~;~.'.
de~ired motor torque) on line 32, This loop compri~e8 a control ' ;
. ~ . . .
circuit 43 in which the feedback and control signals are compared . ...
to derive, on a line 44, an error signal that reflect6S any difference . ::
~, ' , . , . '
; .15 ~erebetween. . :
~ .. .
: ~ The error 6ignal on line 44 is processed by another gain
network 45 having an integral plus proportional transer characteristic, .
whereby a zero 9tcad~ tate error can be obtained, The gain network
~: 45 provide~ on a line 46 a command signal ~* or the inner motor
; ,:~ 20 9tabilizing loop 60, which signal varies as a function of the control
signal ~T* ard will tend to as~urne whatever value results~ss in reducing
the error blstween T* and T to zero. For reason~ and in a manner ` ~:.
.. . . ..
so~)n to be de~cribed, the inner loop 60 i9 re~Spon6i~re to the command
signal on line 46 snd supplies, on :a line 51, an appr~priate ~ignal that . ~
preferabl~ i8 combined at a ~un ming point 52 wi~ a motor speed ; : ::
feedback sigDal ~i3r~ to deriYe, on line 53, an excitation frequency
20-TR-118~ .
. .. .
control signi~ * representat*e of t~eir algebraic ~um, The
speed feedback 8ignal ~)r i8 produced by suitable means, ~uch as . . :
a tachometer generats~r 54, for sensing the actual angular velocity o~
~e rotor of the mOtor 12. (This ~ignal i8 al30 fed back to the co~nmand
logic module 21. ) The excitation 4!reque:~lcy control signal ~L)*, ~vhich ~
differs from (l)r in an amOunt and in a ~ense deterrnined by ~e value ,~"
of the signal on line 51, is fed over line 53 to ~uitable control means S5
for the inverter 14. The control means 5S is operative to determine '.
the fundamental switching frequency of the inverter 14, and hence the . -
fundamental frequency of the atator winding current, in accordance wi1~ ... .
the value of Cl~*. Since the value of Cl)* corresponds to the stator .
. j , . ~
ex¢itation frequency and the value o ~1) corresponds to the equivalent
electrical frequency o the actual rnotor ~peed, the ~ignal on line 51
represents motor 81ip frequency (~) 1.
15 ~ The inverter coIltrol mean~ 55, labeled ~Firing Loglc & GPG~ :
: 1 ~
in Fig. 1, i~ suitably con~tructed and arranged to ~upply to the re~pective
electric valve9 in the inverter 14 a family of gate pulses that will fire
;~ ¦ the valves in a predetermined ~equence atld at a fundamental frequency
del;ermin~d by the value of the excitation frequency control signal ~ . .: ~.
The stator current conducting interval~ of the inverter valves are thu~
'1 : :
:; ~ initiated every cycle in a staggered pattern ~hat results in waveforms
. , , . . :: .
similar to tho~e shown in Fig, 2B where it can be observed that the . ` ~ ::
intenrals associated with phases B and C of the windings are phase
di~placed with~respect to the phase A interval~ by one-third and two- 1;
~ thi:rds, respectiveiy, of~ a~full cycle of fundamental frequency. The
pha3e sequence, and hence ~he direction of rotation of the motor 12,
20-TR-1184
~
corresponds to the sequencing of the gate pulses and is
practically determined by a forward/reverse command signal
derived from the command logic module 21 (terminal 56a) and
applied to the inverter control means 55 (terminal 56b).
It will now be apparent that the outer regulating loop
40 responds to any difference between the torque feedback
signal T on line 41 and the control signal T* on line 42 to ~,~
vary the switching frequency of the inverter values in a
corrective sense, thereby ,increasing or decreasing the' ~'
stator excitation frequency as necessary to reduce the value
of the difference to zero. The control signal T* is provided
by the command logic module 21, and its value is determined ',
in accordance with a predesigned schedule that will enable
the motor to exhibit desired speed-torque characteristics.
(Ordinarily the module 21 will be arranged to coordinate;~`,
the value of the control signal 0 with the value of the
~ c
control signal T*.~ The torque feedback signal T on ` ,
line 41 is intended to be representative of the actual ,~
I magnitude and direction of the torque in the rotor of the ~r'. .~, `
~.
~ 20 motor 12 when excited. I`t can be derived from the motor; ~'~
.. 1 : .- :
by any suitable means.
Preferably the torque feedback signal T is obtained
from an improved torque processing circuit 47 that is ~ ;
constructed and arranged in accordance with the teachings
o~ a U.S. Patent No. 4,023,083 dated May 17, 1977, ~or
A.B. Plunkett and assigned to the General Electric Company.
As is therein explalned more fully, this component relies
; on stator excitation current feedback signals from an
¦ array of three current trans~ormers 57 coupled to the
' 30 respective a-c power lines 17, 18, and 19, and it also '`
`'1 ::` ` :,
, :1 . .:
~ - 12 - ~
:,1 ,`
: 1 , ,,
20-TR-1184
0~7
relies on motor flux feedback signals derived from suitable
means 58 for sensing the actual electromagnetic flux across :
the rotor-stator gap inside the motor 12. The flux sensing
means 58 is advantageously constructed in accordance with
the teachings of a U.S. patent No. 4,011,489 dated
March 8, 1977 for A.s. Plunkett and J.P.Franz, and assigned to
the General Electric Company. The disclosures of both of
the noted patents cited in this paragraph are available
to the public, to assist one skilled in the art to practice
the present invention.
As is more fully disclosed by Plunkett and Franz, the
sensing means 58 comprises a plurality of multi-turn coils
71, 72, and 73 mounted proximate to the main coils of the
stator windings in preselected stator slots so as to sense
the actual flux produced across the gap between the stator
. and the rotor of the motor 12 when the stator is excited,
.`~ '
:~i whereby each sensing coil has .induced therein voltage
signals substantially proportional to the rate of change
I of flux across the adjacent sector o the stator-rotor gap,
:~, 20 and a plurality of integrating ciruits 74, 75, and 76 ~;.. :
respectively connected to the aforesaid sensing coils so as ~ :
to produce flux feedback signals that are time integrals of .
~: the induced voltage signals, whereby both magni~ude and
phasa of the actual stator-rotor gap flux are truly re-
presented by the flux feedback signals. Preferably the .::
..
coils 71, 72, and 73 are positioned around the stator-rotor
gap in alignment with the centers of flux belts associated
with the main coils of the respective phases A.B, and C of
:, :
~:~ the stator windings. In such an arrangement the flux feed- .. .
:j 30 : back signals;derived by the actual flux sensing means 58 .-
are representative of~ ~ mA: ~mBi and ~ mC' respectively,
where the symbol~" ~ " stands for flux in units of volts
: - 13 -
~, . ,
.
~- 20-TR-1184
~ 3900~ :
(equal to the product of flux linkages ~ and base frequency
GJb) and the subsc~ipt "m" denotes the mutual value of the
principal quantity (i.e., the value of flux crossing the stator- ''
rotor air gap and therefore linking both rotor and stator windings).
Each of these signals is an alternating quantity having a wave-
form that is generally sinusoidal and a frequency that equals '
the fundamental frequency of the stator magnetomotive force
(MMF~. .
For the sake of simplifying an analysis of the steady- '
state and transient performance of the above-described balanced
3-phase motor drive system, the actually sensed 3-phase a-c
. .
quantities can be transformed into equivalent 2-phase variables ';
along two perpendicular axes, respectively referred to as the
direct ~d) axis and the quadrature (q) axis. In the illustrated '
system, as is indicated in Fig. 3 (where the circle 77 represents ~'
the perimeter of the motor rotor), the quadrature axis of the
' stator is arbitrarily chosen to coincide with the centerline of '~ ''
the flux belt of the'phase A stator winding on one pole of the `
motor, and this axis is disposed 90 ahead of the effective d '
20 axis of the stator in the forward direction of rotation. In this ~f~:`
~' case the ~uadrature axis component ~ mq of the 3-phase stator-
'~ rotor gap flux is represented b~ thè phase A flux eedback signal ;
mA)~ whereas the direct axis component '~ md can be readily
deduced or derived in any one of a variety of different ways. ~ ''
' 25 One way to obtain the direct axis component of air ~'
gap flux is to use the actual flux signal processing circuit '
means disclosed in the'above-referenced U.S. Patent '-
.:, . : . .
No. 4,023,083 (see also ~ig. 9 of the present
application), which'means is operative to sum the ''
;~ 30 aforesaid phase'C flux feedback signal ( ~ mC) with the
'~ ~ . ''',,::",' j . -
~; ~ ,: '::.'
: ':: : :
U~7 "
,
,, .;
negati~e of the phase B flux ~eedback signal ( YJ~B) and to ~upply the -
difference through a circuit (show:~ at 117 in Fig. 9) that introduces a
constantproportionality factor equal to ~ . In other words
Y~md = ( ~m~ Y~mB) ~ Ano~her way to achieve the same result has - :
been illu~trated in our Fig. 3 wh~re the voltage s;gnals induced in the ~;
flux sensing coil8 72 and 73 are combined in polari~r oppo3ition and
~hen ~upplied through a component 78 having a gain of ~F to an ~ -
~: ` integrator 79 whose output consequently i~ representati~re o SV ~.
Fig. 3 shows the three flux sensors 71 72 and 73 positione~ on the -
~1 10 mag~etic axes of the respective stator phase~ A B and C. Alter~ati~tely
; ~ ~md could be taken from the in~egrated output of a sen~ing coil 1~at
.. .. .
iS 80 positioned in the motor as to ~ense the actual 1ux in a cector ~`
, `; .
.~ of the statos-rotor gap that is intersected by the e~fective d axis of
i~: ~e stator where the flux wave leads ~ A by 90 electrical degrees. :
15. . It should be noted here that i~ the phase A flux ~ensing coil 71 were ~"
;,:$:
ot physically aligned wi~ the phase A magsletic axis 5UmA and iA .
;t; ~ can neverl~eless be electricaily aligned with one another (in the
quadrature axis of the statOr) by adding apprOpriate electrical phase ~`~
~hifting means in the secondary circuits.
~ ~ 20 : It will be apparent t~at the components Y~md and ~q are:~
;, 1 alternating quantities who~e instantaneous magnitudes and relative
:polarities vary sinusoidally in accordance with the projections on 1~e
d and q axes respechvely c~ a 8ingl0 vector ~ that has a constant
.,~, ~
etoady-state magnitude (equa} to the square root o the sum of thè
. ~ ; 25 ~ qua~es of Y'md and ~mq) and that rotates around the stator-rotor . . ~-~
gap i~ synchro~ism wi1~h the stator MMF at a speed corresponding to ~.. .
~9~3 ,
A ~ ~
~he fundamental ~tator excitation frequency. ITig" 3 shows tile J3;
re~ultant vector~ at a particular mo~ent of ffme whe~ ~t coincides i~,~
with the d axis of the stator, wh~ch moment will be considered a !~
reference ~ime t=0. Normally, under steady-state condit;ions,
~ =~ cos(l)t and S~ =~m~in6Jt~ it being recognized that tran~ielltly
md m mq '
t~e time displacemellt between 1he~e component~ may di~er from 90
electrical degrees. ~ is a vector representa~ion of t~e total stator- . -
rotor gap flux. `
In a similar manner, the quadrature axi~ component iqB of
the ~tator excitation current is the same as the phase A stator ~ ding
. ;.: ,
current iA7 whereas th~ direct axis component id~ of current is provided j~
by the quantity ~ . These two component currents could produce
cactly the same magnetic fields in the motor as the actual 3-phase ;'
current~. Their resultant ~tector IB in the ~ynchronously rotating -reer~nce rame has been shown in Fig. 3 for a typical ~orward
ring condition at rated load. In thi~ mode the total ~tator current
rector Ie~ leads 1~e total ~tator-rotor gap ~lux vector~ by a po~itive
- a~gLe Q8m due to load current Ir in the shorted conductors (bars or
: ~
windings) of the motor rotor, it being well known that flux in the stator-
rotor gap i8 the result of both stator and rotor currents. The
fundamental direct and quadrature components of stator current can be
respect vely exl?ressed id9=lEicos(~ 9m) and iq8=I8sin(C~t+a8m).
,: ' ':: '
Corlventional d-q~ ~en equivalent circuits of the induction
;- ~ motor 12 will now be set forth with the aid of Figo 4 which universally
:~ t~
applies to both the d-axis and t~e q-axis clrcuit~. Parameters common ~;
¦~ to both circuitt3 are denignated in Fig. 4 by the symbols listed below
(pr~me9~ signif~rîng rotor ~alues referred to the stator by the snotor
1;urn~ ratio): ~
., ., , . ,:
- 1 6 -
i: ' .
Z0-TR -1184 ~ .
. . .
'"'',~
.... ..
r~ -- stator resistance '~.;
Ll -- stator leakage inductance , ~:
Lm -~ mutual i~ductance of ~tator winding~ and rotor 1,' :
. csnductors ( referred to the ~tator~
.: :
L'lr -- rotor leakage re~istance . ,
r'r -- rotor re~istance
The other quant:ities idelltified in Fig. 4 are more ~pecifical}y i'^~ ~;
define in ~he following table: '.
Quant~y d-axis circuit q-axiB circuit .
stator current id8 iqB '.
rotor current i~dr i qr :
~tato r - roto r gap ilux Y~md S~mq
: ~ mutually linking ~tato r
j and rotor . . . '
'I ,
~lux lin3sing rotor Sv dr $~' q~ , . . .:
conducto rs
t~ cOunter electromotive C~r y~ J dr
~rce (CEMF) ~)b ~b ,;
,
In operation, interacting currents and flux in the motor will
~ ~ 20 : ~evelop slectromagnetic orce (torque) tending to mo~re the rotor ,.
Il ~ rclati~te to the stator and hence to drivc the mechanical load that is ; .
coupl~cd:to lhe~motor ~hat. . As i~ more fully e~plained in Fitzgerald
and Kingley~s classic textbook Electric Machiner~ (McGraw-Hill Book
.
: ~ ~ Co., New York, N.lF. 2d ed, 1961, pp 285-95~ is torque is due to ' .
25 ~ ~ ~ ~e supcrimposed: intcractions~of~the d-axis magnetlc fieId cross- ` ~ ~ ~
coupléd~with q-axis MMF and the~ q~ magnetic ield cros~ -coupled ....
wi1~hd~ oMMF.:;~;It ~strèn~can~e~showntbeK(S~diq9-SUmqids), ';
wbcr~ K 1~ a coD~t~t cq~ to 3P , P being thc number o pole~
_ 1 7
J,
., .. . .. , . . . , . .. , .. . " .. . . . . .. ...... .
o~
~ ~ o~ ~
ln ~he stator of the motor. This is the same as K time~ the cros~
product o~ the vectors I5 and~, io e., K(I9 ~ ). In other word~, the ''~.
magnitude and relative direction of torque i~ dependent on the product
of ~he Dnagnibudes of ~he rnteracting current and flux vec~rs mul~plied .'~
by the ~ine of the phase angle therebet1A~een. Alternative expres~ion~ ~:
for ~he ~stantaneous motortorque are wri~e~ below, itbeing
understood ~at lhe subscripts r and 8 denote rotor a~d 3tator :~
qua~tities, respectiYely, and that ~he identified vector representationa
of current and flux in each case have d and q axes component3 in the
synchronously rotating reference frame, (It shollld be further
; I ~derstood that these e~q?ressions ~pply to s~netrical inductionmotors and would be somewhat modified to apply to sali~nt pole a-c
.
motors. )
, ( . .
K(~mXIr)
., 15 K~X~r)
: ~: K(~
:1, K(IrX~r)
Analy~is of the d-q axe~ equivalent circ~its enables the
1 , .,
interrel~ted motorvariables to be convenientlyportrayed bythe ~'
vector diagrams shown in Figs. S and 6, wherein the stator-rotor
gap flux vector~ is used as a reference. In particulart Fig. S SllOW6 ~ -
the locus of the statOr terminal voltage vector V~3 for a transition
through zero speed from braking to motoring modes of a typical
adju~table speed induction motor while maintaining a relatively
constant high~oul~put torque. It can be observed that this voltage
~ .vector varies widely in angle and magnitude as the motor decelerates . .
.
1 .~
, , ,
.
. ,
1 8 -
8~ ,.",~
,, "
from an initial speed of 300 RPM (which speed, for exa~ple, ha~ an . .
equi~ralent electrical frequency of 62. 8 radlan~ per second, or ,~-3
approximately 0.2 ~L)b~ to zero speed and then accelerates t~ a new ~,','
speed of 150 RPM. However, the statcr current vector I~, which has .~
also been shown in Fig. 5, stay~ relat~vely fixed during ~;~ same ~.
tran6ition. Therefore a current fed a^c n~otor drive system, in which ~ .
the angular relation between the vectors repre~enting ~tator current
,i;
and air gap flux depends on the inverter firing, achieves the correct ~,
flwc-current vector align~nent without dificulty for the conditions ,.
illustrated in Fig. 5. -,
Fig. 6 shows the loci of stator voltage and current vectors for ~
a range of motor loads, at the base frequency t~b~ rom 750 foot- .,.
pounds motoxing to -750 oot-pounds brakin~ (generator actiOn). At ,;'i no load, the stator current vector is in phase with the flw~ vector and
,~ .. . . .
; 15 90 out of pha~e wlth: the stator terminal voltage vector. As tlle
motor load (torque) increases, rotor current must be developed, and
li9 in turn requires a counteracting component of stator current,
Flg. 6 clearly shows the change in angular position of bath the statc)r
cus~rent vector and the rotor current vector (Ir) as a function o~ load.
~ It can be observed in Fig. 6 that the stator terrrlinal voltage
vector V~ does not ~ignificantly change po~ition with load. This
1: . . ,
means that the relative phasing of the stator excitation voltage
in a Yoltage fed a-c motor drive sy3tem need not vary with load
~1 ~ change~. Furthermore, ~a voltage fed system, contrary to a current
- ~ 25 fed sy~tem, o~fers an inherent stabilizing action by Rupplying damping
c~rrents 80 that the motor is able to rapidly align to any new operating
. ~ . . .
-, :.,:.:
` ~` ` ' ` ' ~ ;.'' ''''~
20-TR~1184
',.'
condition without assistance from the inverter. On the other hand, ,"
it can be observed in Fig. 6 that the angle ~8m of the ~tator current ~'
vector change~ rapidly with load so that in the illustrated current fed ti
a-c motor drive system, where the angular relation between ~tator t~.
1, ~
current and gap flux i8 affected by the lnverter firing, the invertsr . .
i. . : '
controls should be 3ensitive to load changes. To dii~play the relation~hip ~ ` ;
between the motor output torque T and l~he isine of the angle ~m~ both . .
of the~e variables have been plotted in Fig. 7 a~ functions of motor slip ~ ,~
- frequency f81 (in units of Hertz) for the forward motoring quadrant of
~. . . ....
operation with rated excitation magnitude.
"~, In accordance with application s. N?~7,qoP, the atability of the
., j : - . .
illustrated motor drive system under conditions of changing load i~ s
onhanced and the transient behaviour of the system is generally
1- , . ....
improved by providing the above-mentioned inner loop 60 in the ' ~
. 1 , . ~.
frequency control channel of the inverter 14 and br utili~ing this
loop to controi the rnotor excitation as a unction of the actual ~'torque
anglet~ in the machine. By torque angle we ~nean the phase angle
. . .
between two vector9 that represent, respectively, the flux and currents
that interact in the motor to develop an output torque. BPcause of its
relative acce~sibility in the illustrated embodiment of the invention,
the phæse angle 0gm between ~he stator current vector Ig and the stator- ^~
rotor gap nux vector~m 18 taken as the torque angle. This angle is
po~itive during motoring in the forward direction and negative during
braking in the forward direction.
In its preferred embodiment, the stabilizing loop 60 i9
'Ir~ , arranged 90 as to vary the stator excitation frequency as necessary to
--2 0-- r
. :' ' . :
';'
20 -TR -1184
. .
~90~
,' .
. ,,.':
minimize the value of any error between a torque angle feedback signal
representative of the actual pha~e angle ~m and the command ~ignal "-
~*Ssn that represents a de~ired phase angle. As previou~ly described, ~.
the latter signal itself varie~ in a corrective ~ense in re~ponse to any ~'~
.
non-minimum error between the actual motor torque feedback signal T ~,
on line 41 and the desired torque control signal T* on line 32 inthe outer
- regulating loop 40 shown in Fig. 1. For deriving the angle feedback
signal, suitable torque angle processing means is coupled to the motor
` 12. The angle proce~sing means is ~hown in block form at 61 in Fig, 1,
and two different embodirnents of it will soon be described with reference
' I to Figs. 8 and 9.
~; l A~ hown in Fig. 1, the angle feedback signal that is derived
by the processor 61 i~ supplied over a line 62 to sumr~ing meanY 63
where it is combined with ~he desired angle command signal on line 46.
In ~e s~:nming means 63 these command and feedback signals are
compared, and an error signal represer~tati~re of their diference is
derived. The error signal appears on a line 64 that is connected to `~
l~e ~lip requency 1ine 51 by means of a gain circuit 65 having a
¦ proportional transfer characteri~tic. Thus the value of the slip
frequency sig~al ~ a function of any difference between the torque
angle command and ~eedback signals. If desired, an integral transfer
characteri~tic can be added between lines 64 and 5i by connecting
ar~o~her gain network 66 in parallel with the circuit 65 between the ~ -
line~ 64 and a ~umming point 67. This option enables a zero steady-
: 1 . :
~2~ ~ state error to be obtained on line 64, and it ~hould be used in systems
-! :
that omit the tachometer generator 54 and that operate without a motor
peed feedback Jignal ~')r'
!
- 2 1 -
I, ~'
, . , . . , . . .. , . .. ., ~ . . . .. .. .
S~ V ~ ~ L ~ ~1~
!l
The operation of the ~tabili~ing loop 60 will now be reviewed. l:,
It is first noted that the frequency of the currerlt exciting tbe stator
windinga of the motor i~ determined by the fundamental switching
frequency of the electric valves in the inverter 14 and that variation~
in t~e latter frequency will transiently shift the stator current `~'
,. , j~, . .-
- , . .
conducting intervals and hence the relative pha~e position of the current " -
vector~8. More part;cularly, when the excitation frequency i~ '
~' increasing the stator current vector i~ advancing in pha~e (i,. e., the a~gle .
,: ".....
of thi~ vector i9 increa~ing in the positive sense with respect to a ,,j
predetermined reference position), and when the excitation frequency ~'~
- i~ decreasing the pha~e of the current vector iB being retarded (i. e., "'
the angle is decreasing in the same sen~e or increasing in the opposite .~.
sense with respect to the predetermined reference position). It will ~
~, next be assumed that the value of the desired torque control signal T*
` .
applied to ~he motor torque regulating loop 40 is suddenly reduced a ''
p~edeterminesl amount Srom its steady-state rated-load forward ~;~
.. .
''~ motoring point. Thi~ causes an abrupt decrease in the angle command ~`
signal ~*8m and a corresponding decrement in the angle error signal ,,
on l~ne 64, which decrement in turn is reflected by a proportionate
rcduction in the slip frequency s~gnal ~ 1 on line Sl and consequently
by a step dccreasc in the excitation frequency control signal *e- The ~
~iring controls 55 of the inverter 14 respond to the last-rnentioned
decrease by lowering the inSrerter switching frequency, ~hereby the ~
fundamental stator excitatiorl frequency is lowered. This reduce~ the
rnotor slip ~requency~and~in the process retardY the angular position '~
of the stator current vector with respect to the stator-rotor gap flux
vec~or (i. e., reduces l~he torque angle). As a result, both the torque
2Z-
20 -TR -1184
`~.
~!
. .1 .
feedback ~ignal on line 41 and the angle feedback ~ignal on line 62 ~'~
.~ .,
decrease in vi~lue, and lhe fundamental stator ea~cltation frequency ~.'
~.1
quickly reaches eq~ilibriu~n at a new operating point wherein equality ~,
exi~ts betwe~on the actual ~orque feedbi~ck signal and l~e value o~ ,$~
S torque commanded by the reduced control ~ignal T* in the outer tatrque
, . :.~;
regulating loop 40 and wherein no rnore than a minimum di~ference ', j
exist~ between the angle feedback signal and the new value of the a~gle ',
command ~ignal in the inner stabilizing loop 6û. .
In a manner ~imilar to that described above for a ~tep change ~ ~
:, .
in the co~nanded value of the torque angle, the inner loop 60 respond0
to random char~es of the actual angle eedback signal (due to anomalies
or disturbances of any kind in the motor or in its connected load) by ,~
~, , initiating a corrective variation in the ~tator excitation, whereby the
proper angle i~ immediately reYtored. This prevent3 the motor from ' ~
oxhibiting ~el~-sustained o~cil1ations about a Yteady-state operating ;,
point. In effect the actual angular position of the stator current vector
caused spontaneously tc~ track the de~ired angle command signal
~*~m ~ and the systembecomes ~e}-~ynchroni~ing. From ,another ',
viewpoint, the torque angle regulating esct of the inner loop 60 can be ~ '
;,..
,1 20 said to synchronize thie firl~g signals of the inverter 14 (i. e., the actual
current switching moments) to the stator-rotor gap flux and hence to '~ ~ "l~he motor counter EMFI whereby the hunting type of in~tability is ~ '
eliminated. ''
The above-described ~stabilizing 3chieme has a number of ,~,
important advantages ~at will now be briefly sumInarized. since ~^
the ~yBtem is stabilized by controlling motor excitation frequency as
., ~
, -23 - ;
20--TR-1184 !. ~ ~
._ ~
7 i~
,~
a function of the torque angle, the r~quirements are ea~ed on ~e 1,
rontrolled d-c power supply 13 which is used merely to ad~ust the 1-
steady-~tate magnitude of excitation~ Furthermore, the angle control ,.
will result in less erratic current flow in t~e d-c link 15 of the sy~tem, ~,
S whercby the size and expense of the current ~o~hing filtex 16 can 1,
be reduced, and considerably less critical link curre~t regulatioQ i ,-
- required, - Another adVantage i8 that the: effects of variable inverter ,~
cor~nutation delay are attenuated by the gain within the angle regulating -loop 60, thereby eliminating possible abnormal inverter
commutation~aonditions. ~',
The tachometer generator. 54 is not essential to the ~atisfactory ~.. ~
performance o~ our stabilizing scheme, and lt carl be omitted if desired. ~.
It has been included in the preferred ernbodiment of the invention to `.
facilltate tracking of the motor speed by the control system in the event .
. . :15 . that electric power is initially applied to the stator windings while the
rotor is in motion or if an operator calls for speed changes, but if an
ctual motor spoed eedback signal were not available the angle ..
regulating loop ~with the gain n.etwork 66 in place) would nevertheiess .
~; produce whatever excitation frequency control signal iB required to
minimize the error between the actual and desired values of the torque
glc. r; ~
. ~ Two examples of specific circuit~ for deriving the torque angle
~eedback signal will next be described. In the illustrated embodiment :
: 1' ~ , ~'.' '.:~
of our invention the most convenient torque angle to measure i~ the
S angle 3m between the stator current vector and the stator-rotor gap
n~ vector. This i8 because practical means for se~sing stator current
t'~ 4- c
: . . ', .~ .
20-TR-1184
i,
01~97 ,s
.
~,
and gap flux are presently available, which means preferably compr.ise ~i
the previously described array of current tran~folmer~ 57 and the ~
flux 3ensing means 58. It should be noted that l~e feedback s;gnal~ p
from 1~he latter means are de~irably derived directly from the actual ,~
motor fluut rather than being imputed or calculated from ~tator terminal ?;
quantities 1hat would be 3ubjes:t to er or due to motor parameter~
changing wi~ temperature, with load con~itions, and from motor ~o
motO r.
Fig. 8 illustrates one arrangement .o~ the angle proce~sing
circuit means 6.1 for deriving a signal representative of the pha~e angle '.
~8m,. This angle processor i8 specifically included in the a-c 1
motor stabili~ing bcheme ihat i9 claimed hereinafter. It has four
input terminals 81, 82, 83, and 84 supplied with signals derived by
actual flux ~ignal proce~sing circuit means 80 and by ~tator current . .
~ signal proce~sing circuit means 80'. The latter two means are .
; ~ respec~ely adapted to be connected to *~e flux sen~or3 58 and to1he current transformers 57 (Fig. 1), and they are suitably constructed
and arranged (see components 115, 117, 120, and 122 in Fig. 9, for
example) to supply to the respective terminals 81, 82, 83, and 84 first,
second, third, and fourth periodic input signals ~at are respecti~ely ,
representative of the following motor quantities:
~mq= q~mA~AsinOt
'''
" .
~- -25- S,
1~8~
~;
.i
~.,
id = ~ (IB+Ic)sin(0t+~Bmf~_)+ 2 ~ (I B IC) sm ~-,
md= C ~B =~(~B+~C)~in()t~2 )~ ~c~gin~l)t
~'?
ig8=~A~ IA~;n(C~)t+~)8m)
- . .
It wi~l be apparent ~at the first and tllird input signals are synchronized, ,:`
respectively, with the fundamental oomponents of the actu.al flwc ,
produced across the stator-rotor gap in the ef~ecti~re q and d axe8 t~,
~ of the stator. Similarly, ~he second and fourth ir~pu'c signals are i,,:
synchronized, respectively, with the fundames~tal stator winding
currents in the d and q axes of the stator. In steady-state operation, IA `
tbe system isbalanced~ the gap.flux associated with each phase has the " . .
. . .
~ame peak magnitude~mA, and the respective.phase currents in the ,~
., . .
;, stato.r windings have equal peak magnitudes IA, whereby the 3econd . ,~ . :
and third quantitles in ~he above table reduce to IAsin(~t+~3m~) . .
and~AsinG~,)t~ Z2 ), respectivelyO Thus the angle of interest is She ,. ;.
'' 'I .
"complement't of the fundamental electrical pha~e displacement ,
between i~e pair of first and second input signal~ ~upplied to the
termi:nal~ 81 and 82 or between *le pair of third and fourth input
~; ;!. ~
` slgnals supplled to the terminals 83 and 84. :By complement w~ mean
the angle by which the actual pha~e displacement differs (either moro
!; ~ 20 Oi Ie~B~ from 90
The four perlodic ~nput signals that are supplied to the input
': terminal~ 81-84 of ~e~Fig. 8 angle processor are individually
amplified and limited by means 85, 86, 87, and 88 for producing
i~ square-wave signals in phase wi~h the fundamental components of ~e
. , ~ . .. .
,'~i ~ . ,, ~
~ . : : :
26- "
' ' ' ' ~0-TR-1184 ,,
t .
Q~ $.
..
~t,
respective input signals. The respective output lines 90 and 91 of the ~,first pair of ~quaring means 85 and 86 are connected to an associated ~;,
pair of input terminals of a logic component 92 that produce~ on a line ~'
"~,:
93 a irst t~ain 94 of discrete ~ignalR indicative of the eLectrical pha~e h.
5 di~placement between the squared ~ignal3 on line~ 90 and 91. Pre~erably
the train 94 conlpri~es a serieR of flllS Rignals having a conBtant ~ ~
amplitude~ a frequency that varie~ with l~e fundamental ~tator winding '~`; '
excitation frequency, and a duration that depend~ on the pha~e angle '~,;
between the squared 3ignals on line~ 90 and 91. If, as is illustrated - ''
in Fig. 8, the logic component 92 compri~es an ~'exclusive or" circuit, " ~,
each of the "0" spaceR between consecutive ~ ' signals in the train 94 ~. '
' has an angular duration equal to the phase displacement between lhe
pe,riodic 3ignal- that are supplied to the first and second input ,~
terminals 81 and 82, and each of the ~ signals has an angular duration ;.equal to the supplement of that phase displacement. "~
The line 93 from t~e logic component 92 iR connected to ~umming '~
mean3 95 where the ~irst signal train 94 i8 preferably combined wi~ a
second train 96 of di~crete signals provided on a line 97. The second ','1 signal train 96 i8 produced by another logic component 98 having input ,'
terminals respectively connect'ed to the output line g of the second pair
~, of squaring means 87 and 88, whereby the second train 96 i9 ~imilar
1o the irst train 94 except that the angular duration of each of the 1l0'l ",:
spaces between consecutive "1" signals in the train 96 coincides with the '-
phase displacement between the third and fourl~ per~odic input ~ignals
from which this train is produced. The sum~ning means 95 iR
il ~ operative m response to the ~ignal~ on ~he two lirles 93 and 97 to ; --
. i, ....
. j
27 , ti '
, ~ ~" r ~ 7~
20-T~-1184 iff
"
2 ~
~; .
. .
produce on a line 99 a resultant signal equal to their d~ference. A ;~`
8uitable ilter 100 is connected to the line 99 for producing an output ,~
ffignal (the angle feedback f~ignal ~f8}n) that varie~ with the average "~
valuf~ of the resultant signal on the line 99, which value in turn i3
determined by the complement o the ~phase diaplacement between the ff;
paired input signals (i. e., the angle ~ly which the indicated phaae
diapla,ce~ent differ3 from 90). ~'~
f~:
It will be apparent that if the paired input signals are just 90 ~i
i- ~
out o~ phase (6~m~0), the aurations of the ~ signals in both of the .~';
signal trai~s 94 and 96 are 90, whereby the average value of the ,~f,
resultant signal on line 99 (and hence the output signal o the averaging .~,
circuit 100) is zero. Thef same result is properly obtained if the ,.,
amplitude of elther one of an input ~ignal pair is 80 am311 that the ;`
assoclated squaring means ha8 a negligible ou~ut. When fhe paired ~ff
input signala are in phase with one ano*ler (~f8m=+90)~ the resultant ,~
1 :
signal on line 99 is continuously tl and t~e output signal has a maximum
poaitive magnitude. On the other hand, when the paired input signals ` '
are 180 out of phase (08m~-9)~ the resultant signal on line 99 is
continuously -1 and the output signal has a mfaximum negative magnitude. '.'
In effect the logic componeDts 92 and 98, the summ1ng mean~ 95, and il-~
the averaging circuit 100 cooperate to perform a pha~fe discriminating j~
;., .:. .
1 ~ function. '
.;;
The above-described angle processor lends itself well to ,
dig;ital implementation~f; lt~isf preferably arranged to re3pond to both
; 25 pairs of the ~our periodic mput sigllala in order to optimi~e the accuracy
and~ apeed of tran~leDt reapoDse and to increase the smoothne9s of the ;
,28-
- .,
~.1 . .
': ` 20-TR--1184
`` ilO8~
angle feedback signal. However, an equally accurate steady-
state indication of the angle ~ sm could alternatively be
;~ obtained by replacing the second train 96 of discrete
signals with a continuous bias signal having one-half the
magnitude of the "1" signals in the first train 94, for
which purpose the line 97 could be connected to a suitable
bias source 101 shown dotted in Fig. 8. In this case the ;
excursion of the angle processor output signals on line 62
would be reduced 50
A different arrangement for deriving a feedback signal
representative of the angle sm is illustrated in Fig. 9.
(The use of this arrangement in a motor stabilizing scheme
is claimed in the above Canadian application Serial No.
~ ~7 q~ dated ~ ~e ~ e~ ~/9~ n essense it
comprises a suitable torque processing circuit for deriving
a torque feedback signal representative of the magnitude
and relative direction of the actual motor torque T, in
combination with angle processing means 61' connected to
the torque processor and arranged to produce an output
, 20 signal having a value that varies directly with the value
of the torque feedback signal but inversely with the value
~ ,
of two signals respectively of the magnitudes of current and
flux that interact in the motor to produce torque. It will
be apparent that the value of such an output signal depends
on the sine of the actual torque angle. ;
, The torque processor in the Fig~ 9 combination is shown ; -
;~l in the botted box 47, and it is advantageously constructed
and arranged according to the teachings of the above-referenced
U.S. Pat. No.4,023,083 dated May 17, 1977 - Plunkett. Its `i~
output is connected via the line 41 to the angle processor
61' in which two dividers 110 and 111 are provided for
dividing the torque feedback signal respectively by a first
l .,: :, "
~.:J ii
1 ~ - 2 9 -
. . ..
V - Ll:~ - lLO~
7 t~
signal Oll a line 112 and by a second signal on a line 113, Pr~ferably s.~
the first signal on line 112 i~ proport~onal to the magnitude of the ~i3:
stator current vector I~ and the ~econd signal on line 113 i~ representatl~re ~t~
of the magnitude of the stator-rot~r gap nux vector;~m. The tandem
dividers 110 and 111 are connected through a constant gain circuit 114
to an output line of the angle processor 61'. The gain Kl of ~he ~;.;: . .
3 C"
circuit 114 preferably is b which i8 the reciprocal of the con~tant K in '~,
the motor torque equation~ set forth above. Be:Eore de~cribin~ ~ ,'~, - .
this version o~ the angle processor in more detai~, the illu~trated ^~
: ... .
. 10 tosque processor 47 will.be briefly recapitulated. `~
A~ is indicated in Fig. 9, the torque processor 47 comprises ,~
current signal ~roce3~ing circuit means that receives from the current ~'
transformer~ 57 a set of three a-c feedback signals respectively .'
representative of the actual currents iAJ iB~ and ic in the three "'
differcnt pha~es o~ the ~tator wmdings, and it also comprises flux . .
signal processing circuit means that receives from the flux sen~ors 58
: .!
t~ree a-c ~eedback signals respectively representative of the actual flux. . ',~:
mA~ t'mB. and ~mC acro~s the stator-rotor gap adjacent to the
. ' three flux sensing coils 71, 72, and 73 ~Fig, 1). The phases B and C
~1~ 20 ~lux feedback ~ignals are combined in a ~umming circuit 115, and their ',
: l ~ di~erence i9 fed to a line 116 through a constant gain circuit 117 that
introduces the ~ proportionality constant, whereby the a-c signal ~.
~ on li.e 116 is representative of the direct axi~ motor flux ~ d~ The
¦ ~ line 116 is connected to a multiplier 118 where the latter signal is :
mult~plied with the phase A current feed~ack signal (representative of
~e quadrature axis ~tator current iq8), and the product ( ~mdiq ) of
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this multiplication is supplied a~ a first of two inputs to a ~u~nming ~'.
circuit 119. Similarly, the phasea B and C current eedback signals 1;
are combined in a surnsning circuit 120, and l~heir difference i3 ~ed to t~
a line lZl through a constant gain circuit 122 lhat introduce~ the
proportionality const~t, whereby the a-c ~ignal on line 121 is
,,
representative of the direct axi~ ~tator current id~ The line lZl is ,~;
connected to a multiplier 123 where the latter ~ignal i~ multiplied wit~
the phase A flux feedback ~ignal (represefflative of the quadrature axi~
tor flux Y~ ), and the product ( y~mqid8) of this multiplication is , '
lG supplied as the other input to the summ~ng circuit 119. In the ~umming .~.
circuit 119 the product outputs of the two multiplîers 118 and 123 are
summed together to derive a resultant sig.al proportional to their
diference, and the resultant signal is ~upplied through a colistant gain '.
....
' ~K) circuit 124 to the output line 41. ..
. j ~ ~,
~: 15 It can be ahown that the outputs of the two multipliers 118 and ~ I
123 in ~e torque processor 47 are a-c quantities consisting of the same . .
double frequency components and oppoaitely poled d-c components that
` arO proportional to motor torque, whereby the value ~magnitude and ;'
~ign) of their diference ls a true measure of the electromagnetic
torque T developed in the motor. In other words, t}~e torque feedback ,. `:
. 1 ~ signal on the line 4~wi}1 vary with the cross product of the stator current ~, .
vector I~ and t~e ~tator-rotor gap flux vector~ . By dividing ~he j' ` ~:
torque feedback signal (T) on line 41 by bol~ the stator current magnitude .~;
., ~. ..
representative signal on line ll2~and the gap flux magnitude repre3entative .~
,, ~ . , ,
~1 ~ Z5 signal on line 113, the angle proce~sing circuit 61' effectively normalizes .
: 1~ the to:rque feedback signal and hence deriYe~ at its output a signal ~ .
',,,~ ",',
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representative of the sine of the phase angle (~8m) bet~feen ~he vector~ ~2
I9 and~. ~.
;! Preferably the angle proce!3sor 61'includes suitable rectifyi~g
and 3umming circuit mean~ 125 cou~led by way of the current tr~Q3~
: f~'
formers 57 to all three phases of the ~ator wirlding~ and conr~ected
~hrough a filter 126 to the line 112 for ~3upplying to the divider 110 a , `
~ignal that represents ~e average magnitude of alternating current in
the s'cator windings. The average magnitude of stator current i~ a close ,'
. ~
approximatiOn o the magnitude o~ the stator current vector I8. A~
. j ,.
0 i8 s~own in Fig. 9, the angle procesaor 6r also includes rectifying and jT~
~' summing circuit means 127 responsive to all three flux feedback signals
from the nux sensors 58 and connected ~hrough a filter 128 to a line 129
or deriving on the latter line a ~ignal that repre~ents the average
'~ magnitude of flux produced across the stator-rotor gap in the motor.
'",~' T~' 15 The average magnitude of the gap flux i9 a close approximation of the .-
magnitude of the mutual flux vecto r ~. Note that the true magnitude of
e current or the flux Yector could be obtained i desired by utilizing
~, means for deriving the square root of the ~um of the squares of the ~
re~pective direct and quadrature a~ces components o the relevant
quantity. Ideally such means will ~Sive a smoother ~eedback signal, ;~
assuming Yinu30idal direct and quadrature components. If desired,
the flux magnitude signal on line 129 can be used as the excitation ~;
; magnitude feedback signal for the fir~t outer regulating loop 30 of the
motor drive system, in which ca~e the terminal 31 shown in Fig. 1
would be connected to a terminal 131 joined to the line 129 as ~hown
in Fig. 9.
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~f the flux magnitude signal on line 129 were ~upplied directly
to the d*ider 111 in the angle processing circuit 61~, the output of this
S,
circuit would be a true measure of sin~m. The interrelationship o t~e ~,
torque magnitude and the sin ~ has been shown in Fig. 7 where it ..
will be observed that the latter quantity i~ a double valued functio~ of
torque whe~ the motor 61ip frequency increases from a low value '.
.. . toward breakdown. In motor dr.ive systems that are intended to operate '.:
o~rer a wide range of speed and load~ the. imp~o~ed angle regulating ,~
scheme will perorm its stabilizing function more successfully if a
~. . .. :
monotonic relationship is maintained be1:ween torque and angle,
. ., , ' '. .
; Toward this end, the Fig. 9 embodiment o the an~le proces~or 'i
includes between the line8 129 and 113 a con3tant gain circuit 132 , `
connected via a line 133 to one input of a summing point 134 where the
. ~ flux magnitude signal is algebraically summed with a compensating ',
i 15 signal derived from the current ~nagnitude ~ignal on line 112 to which !;~ ~ :
.~ 1 a second input of the summing point 134 is connected over a line 135 .
: ~ 1 and ano1her constant gain circuit 136. ....
The flelx magnitude signal on t~re line 133 will vary with the ~.
a~ srage magnitude of 8tato r- roto r gap fluxt being related thereto by
~1 ~ :
1 20 the gain Kz of the ci rcuit 132. The compensating ~ignal on the line 135 , ..
i8 a~prede1:ermined fraction of the average magnitude of stator current, '~
. ;1,~ ~ being related thereto by the gain K3 of the circuit 136, which gain is ~`
; -1 cho~en to yield the desired monotonic relationship and typically i~
quiSe low te.g., of the order of O.OSj. The compen~ating 9ignal i~
subtracted from the flux magnitude 9ignal at the ~umming point 134, ; -
and 1he di~erence comprises a compensated ~lux magnitude signal
appearing on 1he line 113. As a re~ult of u~ing this compen~ated signal ~ .
. ~ .. ,
~.; ~ ~ ~ ' ' ',S .,
~ 89~
a~ the divisor for the divider lll in the angle processor 61' the angle ~,
feedback signal on the output line of this processor ac tually varie~
with the sine of an equivalent torque angle ~T that ha~ a desirable ~'
~ monotonic rel~tionship to torque, as i5 shown by the trace }abel~d
;~
5 "sin~T" in Fig. 7. It can be ob~er-re~d in Fig. 7 that the equ~valent . ~.;
.~ ~; torque angle ~T is virtually the same a~ the pha~e angle 6~m for the ~`
relatively low values of ~lip frequency in the normal operating range
of an induction motor (e~g., below approxiInately one Hertz for the '
~: . typical motor whose characteristics are displayed in Fig. 7). L,
. ~ ~. :.
:: : 10 Consequently when the motor drive ~ystem is operatlng at torque level~ '"~ :
~ ~ .
up to and including rated load, the essential inverter synchroniz;ation . ~,
of the improved stabilizing scheme i~ retained, a~d when the system S ' `.
; ~ i9. opèrating at higher torques approaching the pull-o~ut torque level ~j
xegulation problems due bo double valued alngles are avoided,
I ~ 15 In order to obtain a meallingful angle feedback signal at start-up ,~
or undcr abno~nal operating ~onditions, ~e dividers llO and lll in i~
~e embodime~t of the an~le processor ~hown in Fig. 9 should be
., ::~ , ~. .
equipped with non-linear limiters that s~t apprOpriate minimum divisor ~ ~
.. . .
~alueg 90 as to a~oid division by zero. To avoid 1088 o the angle .1 :`
.`; ,
` 1 20 feedback ~ignal when the motor i~ operating at zero torque, the command ..
1 ~ signal for lhe excitation magnitude regulating 100p 30 of the motor drive
.~ 1 ;: syst~m has a predetermined minimum limit that will prevent j~
a zoro flux condition, for which purpose we provide the previously
de~cribed limiter 39 (Fig. l).
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The present invention has utillty in a wide range of motor drive t':
application~, It can be used wi1~h a variety of outer regulating loop~ ~,
different ~han the e~emplary ones illustrated in Fig. 1. It i8 useful t;
in a voltage fed motor drive syatem t~ keep the in~erter firing pulses
S ligned at the correct phase wi1~h respect to the motor flux, thereby ,~.
pe~mitting a steples~ traneition betw~en braking and motoring mode~ ~;
(~uch as ~hown in Ftig. 5) without a transient~
W~ile a spec;~ic embodiment of our in~renf;ion ha~ been shown
s. ` ~d described by wa~ of illustration, various modification~ will '~
. 10 probably occur to those skilled in the art~ We ~erefore intend, by the ~
concluding claims, to cover all such modifications as fall wlthin the ,~ : .
true spirit and scope of the invention. ,~
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