A New Rotor Time Constant Adaptation Method fop a VSI Fed Indirect Field
Oriented Induction Motor Drive
S. Palani vel
P. Srinivas
V. T. Ranganathan
Research Student
Student
Associate Professor
Department of ]Elt?ctncalEngineering Department Of Electrical Engineering D e p a a e n t of Electrical Engineering
Indian Institute of Science
Indian Institute of Science
Indian Institute of Science
Bangalore-12 INDIA
Bangalore42 INDiA
Bangalore12 INDIA
ROTOR TD~E
CONSTANT ADAPTATION
tfbstmct-Field Oriented control of an Induction Motor
requires the rotor time constant as an essential parameter to
calculate both the magnitude and phase of the rotor flux
vector. There fore it becomes necessary to adapt the rotor time
constant. A simple method based on current measuremeuts
alone is proposed. Since this method uses current
measurements, which are smoother, compared to the voltage
wave forms in a VSI fed drive, the implementation i s easy and
noise free. The method works during transients also. The stator
direct and quadrarture current components are predicted,
assuming a perfect value of rotor time constant in the control
side. This is compored with the measured currents. A
mismatch in this comparison, is an indication of an error in
phase Of tbe rotor flux. This information is used to correct the
control side rotor time constant.
One of the earliest methods of adaptation by Luis J
Garces[4], is based on the modified reactive power
e@ression. The expression is
nt on the rotor time
_consiant. The expression is
ted both on the control
side and on the motor side in real time. The difference in
these two expressions means a mismatch between control
side and motor side rotor time constants.
INTRODUCTION
Field oriented control gives an elegant way of achieving
high perfomce control of induction motas. Estimating
the magnitude and phase of the rotor flux is very crucial for
the implementation of this “d.Direct ways of sensing
the rotor flux by fabricating suitab€e hardware around the
motor have proved to be inaccqrate and impractical at very
low speeds of operation. Indirect methods of sensing the
rotor flux employ a mathematid model of the rotor, which
is exited by measurable machine state variables, like
currents and voltages. This model calculates both magnitude
and phase of the rotor flux The aauacy of this method
depends very much on accolfacy of the model parameters,
especially rotor titne constant. The accuracy of this
on the accuracy of rotor resistance m
i
rotor inductance.
The actual motor parameters may change during the
operation of the drive, which will introduce inaccursbcies in
the flux estimation, ifl& madapkd The resistance of the
Due to
stator and rotor windings change with.-et
time constants, compared to many electrid
, these variations are slow. Parameter changes
due to mer excitation or under excitation of the magnetic
circuit happen very fast, on the other hand This affects
mutual inductance of the machine largely, and leakage
inductances slightly.
0-7803-2795-0
If there is a complete decoupling between d and q axes, a
random signat in d-axis current will have zero correlation
with the q-axis response. This idea is used
el and
Leonhard[S] for adapting the rotor time constant. A Pseudo
Random Binary Seqtence (PRBS) is added to the d-axis
current reference. A non-zero correlation between the d and
q axes control system outputs indicates a cross coupling and
this information is used to adapt the rotor time constant. But
the undesired
.
effect of the PRBS signal in the performance
of the drive has limited the usage of this method.
A method to adapt the rotor time constant in real time wing
a Kalman filter was proposed by Zai and Lipf9l. This
method is limited to situations where the lsad conditions are
cbanging slowly and a h requires s m a t least above 5% of
the ratedspeed
Li and VenkatesaMl3] have used the mismatch between the
control side torque feedback and the actual motor torque to
adapt the rotor time constant. This scbeme, although simple,
has large dynamc errors and inaccurate at low speeds.
Koyama et al 171 have used a simplified reactive power
expression for the adaptation valid only for steady state
operation.
Each of the above methods has some limiting factor while
almost all of them are not suitable to be applied at or around
zero speed conditions. Holtz and Thimm[l2] describe a
method to adapt all parameters even at zero speed. An
analytical model of the machine, with the stator voltages
and mechanical speed as inputs, is operated in parallel with
the machine in real time. Then, by comparing current
trajectories of the model and the machine, all the model
parameters are corrected using nonlinear optimization
method. But the implement&ion is saphisticated and
requires lot of computational power.
222
The present method, apart from being extremely simple.
works during transients and at near zero speeds.
Taking the inverter gain to be unity for analysis purposes.
the motor side d q axis voltages can be found as follows.
U
':
THE PROPOSED METHOD
In a voltage source inverter fed induction motor the field
o r i c ~ t dcontroller output and the d q axis stator model is
represented as shown in the Fig. 1, under coupled
conditions. The following notations are used
i& - ~ a x i s a m e n t s i n ~ x t u a l ~ .
* i d is, -dqaxiscwrerd~measuredinthecimtrolside.
.UG U& - d q a x i s w ~ i n t h e a c t u a l ~ .
'USd, U, -dqaxisanrentcontN)lleroutpasinthecontrd
side.
after
*U:'
U;'
dq &S \Q&S hl the 4
COoTdinate r
.
"
. andbefOreE%k"gthe
O i L ,
U;'
= uS,cosp'
= -U,sinp'
+ Usbsinp' ..._.....2a
+ Us~cosp'..........2b
When the control side motor m&l parameters match with
those of the actual motor, these two coordinate
transformations cancel each other. Then the following
relations hold.
U; =U;'
p=p'
Dd=D$
U; =U;'
DSq=DIq
-
Under non-ideal conditions, the control side motor
parameters will not match with those of the motor. In
particular, if the rotor time constant values on control side
ckxmphgterms.
-U;
U; - d q a x i s v d t a g e ~ i n t h e c o r c t r o s i c l e ~ and motor side differ, then it can be shown that it will result
in an error of the estimated phase of the flux. Then, all the
addulgthedecouplingttotheC a m m t m e r o u t p r t s .
above expressions are not valid
-Uw u s b -a-b(sbtiomy)a~voltaga.
*D& D& --&XIIShthedmot~~.
Defining, the error angle, 6 = p' - p , U: &U; on the
* D d D, - ~ t e r m s h d r e c o n d r o l S & .
control side, can be related to U
': &U;'
on the motor
*iL-actuaImtorftuxmagwtmg
* int the motor.
side as follows ( Refer Fig. 3 ).
m i & -eslimidedrotorftuxcumltinthecontrd
si&.
U
:
'
=
U~COSG
u ~ s i.................
n~
3a
.w; -actualspeedoftherotarworienfed-fr-dmein
U:' = -Uisin6 U;cos6 ...............3b
the motor.
*U1 - & i m a t e d s p e € d o f t h e W W ~ ~ *
These d q axis currents appear as three phase currents at the
inthecontroiside.
motor terminals, after coordinate transformation by angle p'
*u-totdleakage~ofthe~.
.
.
.
and a-b to three phase conversion, inside the motor. If p is
*Ls, L , - s t a t o r a n d r o e o r t o t a l ~ ~ .
used
to convert them back to d q axis, id $1,
on the
*RS, R r - s t a t o r a n d ~ ~ t ~'r
control
side
will
be
related
to
i$
&
i&
on
the
motor
side as
*T., T:-theachlalstatca~&ecm~&&.
follows.
*TI- ~ e s t i m a t e d r o t o r t & t ~ ~ ~ ~ & ~ & .
= p -theestimatedangledratorfhnrinthx"lside.
i$ = idcos 6 i,si 6..........6a
p' -the actual angle dratorfhnr in the motor.
i& = -idsin6 i,cos6 ..........6b
isl, is2, is3 -the thmphaseaurents iat the mdortemtinals.
The stator voltage equations in the rotor field oriented
Substituting (3) and (6) in (Ia),
reference frame is as follows
U$ = U;' - D$ = UGCOSS+ UGsinS - D$
U$ =U;/- D, -U*!(1 - O)L,$ (iloR) - u;u1,,1&1..(Ia)
U:, = U!; - DL = U!; - O l ( i - u)LsikR+ W ; ~ L . & ] ....(IIJ) U$ = (U, + D+&osS + (U, + D+hS
+
+
+
+
f
,
Ef
To ensure perfect decoupling. D d & D, will be added with
Ud & U,
the . corresponding controller outputs,
respectively. Therefore, on the controller side,
+
U; = ud + D~ = ud
- u)Ls&(imR)- oluL,i,l ..(IIa)
U; = U, + D, = U, + [wl(l - u)Lslm~+ wluL,idl .....(1%)
These d q reference frame quantities, U: &U; are
transform& into stationary reference frame quantities
U, & U& by a coordinate transformation as follows.
U, = U i c o s p - UGsinp...........l a
US = U,',sinp + UGcosp
These a-b axis voltage references are converted to three
phase voltage references and are applied to the inverter.
+w:d,(-idsin6
+ i,cosa)
- (1 - u)Ls$(iL)
The above equation relates the actual motor side Usd in the
motor to the control side quantities, through error angle, and
actualmotorimr id .
I" J
Since the stator parameters are accessible for measurement,
unlike the rotor parameters. the stator parameters are
assumed to be known accurately. When the machine T'r is
changing, due to either a change in R'r or L'r, the slip
frequency error starts increasing. The slip frequency on the
control side is 0 2 =
, while on the motor side it is
2
W$ =
Ti&
Assuming no error in speed feedback, the error
in flux angle is only due to an error in slip frequency. But,
223
after the current loop delay, i, control loop responds to the
new operating conditions, and the slip frequency is again
matched with the actual value, automatically, even without
any adaptation of the parameter. Then the error angle settles
with a non zero value. momentarily.
-I
.&(if
di
)
1+sT,
At this point , the following observations can be made. In a
typical dm7e vv%hreasonably fast current control loops, it is
I
0
1 = U*.
tnie
that
This
implies.
I
-d8= - dp'
- - = d~
- 01 E 0 . This "-in that 6 can be
taken to be independent of time. Therefore,
wi
dt
dt
dt
+[i,dcos
1 +sT,
d]
gives the sig
in the adaptation loop.
+ i,sin61
1 = +[idcos6
I+sT{
~ n signum
d
[ -T
r&(i'sd)l
= L-I
i ( i '
So 6 = 0,if and
6
+ &sin 61
=
s(1 +sT,)
1+sT!
[idcos 6 + &sin
61 ...8
IMpLEmimATIoN OF
- calculation
The error for the adaptation loop
In evaluating the above expressio
variables and parameters are kno
studid considering three ca
Substituting (8) in the expression for UL, and reorganking
the terms,
*U4 = Ud
The above equation is in the following form.
-
T..J;~
= UsdCOS 6
+ Us,sin 6
In this casealsd, as a m
Applying a first order lag to both LHS & RHS,
WhenT, # TJ,
R, l+suT,
&(t) = i d(tkos 6 + i,,(t)sin 6 ,where iL is the actual d
axis motor current.
But, as the adaptation loop proc
it can be easily seen that.
The above equation can be rewritten as follows.
id(tkos6 + i,,(t)sins
= Td(t>coss +i,(t)sins
After reorganizing the terms,
-
i sdCos6+y ,sin6
d.ying transients of
= [ T < ~ - ~ ~ ~ ] C O S *[ +i , - i + n s = o
The above equation represeots a triangle. whose sides are as
shown in Fig. 2.
his implies, if
7 sd
sins i= -+1
-a-i
~d
&
T sq has the same sign,
=
arcsin
weakened region.
I--]
i
i + T & .... 10
For small values of 6 ,
224
"TATION
LOOP.
Con t r o
w
d
~
f
Fig.1
Fig.2
Therefore, for implementation purposes, 04 can always be
taken as UA .
to take cafe of the inverter voltage output rating limitation.
This is added with the decoupling terms and applied to the
inverter as instantaneous voltage command reference. The
.
1
1
So, - i s d = i & - i & = l & - - R# I + S U T T , U ~
same d-axis voltage command reference is also applied to a
first order lag, identical to the stator lag. The output of the
2. Innferring the signum of
first order lag will be a prediction of isd. This current is
To infer the signum of i sq, we examine the following compared with the meqped machine current. as shown in
Fig. 5. The error is sign corrected to derive the information
expression.
of error angle. This should again be sign c0rrecteQ before
applying to the adaptive controller. The output of the
adaptive controller adds a correction term to the cold value
-k h
+ (I - u)L,otimR- (1 - u ) ( ~ ~ i.1 - iof the controller side rotor time constant. The adaptive
controller time constant is designed to
large to avoid
=I 1
l
l
R~ I + ~ ~ T , ( ~ M+-L z
) m [ ( 1 - c)Ls@limR
unwanted nonlinear interaction with the dynamics of the
1
1
5
drive during adaptation. The adapted time constant affects
---- iw the
& I+sff, ]+ST,[(’ slip frequency and in turn corrects the error angle by
From the above expression, following observations can be suitably increasing or decreasing the fr ency of the
made.
supply voltage of the motor. The factor
acts as a
1
1
thi
sensitivity
factor
for
the
correction.
When
designing
R g t+sifT,[Uwl
i%
adaptive controller gain this factor should be taken into
*insteadystate,
account. The design should be made for the worst case
( I + S ~ T , \ ] + ~ T , ) [ ( ~- u)Tsi.(ll =
(largest value) of this factor. This value typically depends on
* E ~ e n d u h g ~ t h e i i b v e a p p r o ? c i m a t i o n i s f o u n d t o the desired maximum speed.
-
-
bq
r$1
.--
5
3. Imurovement gadaptation performance in low weed and
i ~ ~ n e o f t h e f a s t e s t s t a t e v a r i a b l e s . ~ h e r e ~ i t ~ i thh ee rm loading conditions.
catchestheoommandorhitsthe limirsdsiaysthere. mDst
The adaptation performance in very low speed and heavy
ofthetime,itisconstantSo,tkck”isvalidfol:mostcrf
loading conditions can be done as follows.
thetime.
So the signum of the above expression is dependent only on At very low speeds, using 01 alone for knowing the
- a ) T S w l i ~ ]whose
,
signum in turn signum i
the term &&$l
is
not
accurate.
1-4
introchwza m y small error for speeds abm 5%
.i,
*,
[-1,
depends on~yon w 1 . t his implies, the signum of
decides the direction of correction. If we are adapting the
parameter veq slowly, we can take the signum of w itself for
the direction of correction.
This gives the necessary information about the error angle.
The error angle information is used for correcting the
control side rotor time constant. This error angle
information should be sign corrected Mith the signum[i,,]
before it is used to correct Tr. An example VSI fed vector
controlled induction motor drive scheme is shown in Fig. 4.
The current loop controller output becomes the d-axis
voltage command reference after the limiter, which is meant
f q1
signum &{wid
- &(iq)}l can be usxi. his
requires more logic in the implementation, but gives better
adaptation response at very low speeds.
THE EXPERIMENTALRESULTS.
The adaptation method is tested on two drives. The first
system is a 40 hp. 51 Amps. 4 pole, wound rotor machine.
This \7ector control drive has been implemented using
TMS320G50 DSP processor. The adaptation is made tc
correct$, which can be easily achieved by reversing thc
signum of the 7 pd. This drive has a tacho-generate
feedback of the speed. A three phase resistance is connecte’
of shorted in the rotor circuit, to effect a change in the rotc
225
resistance. This changes rotor time conWnt and the
adaptation method was made to adapt for this change. The
results are presented in the following the figures.
A step change in speed is issued to the drive, from 40% of
the rated speed to W'%Oof the rated speed. The resulting
speed response. along with the step speed command is
shown in Fig. 6.4. The noise in the wave forms are mostly
due to measurement. This response, with the adaptation
enabled, has a settling time of 2 seconds, while it takes
around 2.4 seconds to settle without adaptation nith added
rotor resistance. The next wave form shows the response of
the adaptation, i.e. the correction in the
along with the
i ~d . The adaptation when the Rr is increased from 0. lohms
to 0.45ohm is shown in Fig. 6.5. The increase in i s d for a
step change in the Rr should be noted. This increase causes
the to be increased. Finally the predicted and actual id s
become equal, which means the settling of the adaptation
loop. The adaptation response is fast in the field weakening
region. It is mainly because of the sensitivity factor in the
adaptation loop. This factor increases in the field weakening
region. which convibutes for the faster adaptation response.
k,
2
The second drive is 550 Watts. 1.5 Amps, 4 pole squirrel
cage machine. The vector control is implemented using
ADSF72101 DSP processor. The rotor position of the motor is
measured with an incremental encoder. The performance of
the drive is shown here with the exact value of the rotor
resistance.The exact rotor resistance value is obtained by the
following method.
If the rotor time constant value is not correct on the control
side, then for a change in the speed within the base
operating region, the direct axis loop gets disturbed The
amount of dishirbance in the direct axis can be a criteria io
obtain the correct value of the rotor time cbnstant. The direct
axis current will usually be very noisy. So, the disturbance
in the i, can be used as an indication of the discrepancy.
Fig. 6.3 shows the disturbances in for various values of
rotor time constant. The minimum disturbance in i, means
the best possible value of rotor time constant.
The performance of the drive is shown in the hse speed
region, in Fig. 6.1. Fig. 6.la shows & & i d , while Fig.
6. Ib shows the speed and i, response for a reversal of speed
COmMand from -35.8% to +35.8% of the rated speed in the
base speed region. The wave forms are shown for tuned
condition. The coupling between direct and quadrature axis
can be observed to be minimal. The noise in the speed wave
form i s mainly due to the differentiation done to obtain the
speed from the enuxler position feedback. The rotor time
constant adaptation method can be verified in t h i s machine
by deliberately assuming a wrong value on the control side.
This activates the adaptation algorithm to correct the control
side value to the correct value. The adaptation is made to
work very slow to observe the adaptation response during
repeated reversals in the speed, for every six seconds. The
correction in is shown in Fig. 6.2. The method is found io
work very well in the field weakening region and at low
speeds. The method does not work at zero stator frequency,
because the flux vector stops rotating, and the loop corrects
Fig 4 A. Typical JndireQ Vedor Control Dnve v f i VSI
Signum
I+
s Siama Ts
ed Tr
-1
Fig. 5 The proposexi Adaptation SQenie
226
only the rotor time constant which is a factor in the slip
frequency.
49'
CONCLUSIONS
From the above results, the effectiveness of this simple
scheme of adaptation can be seen. The main drawback of
this scheme is that it assumes that the stator resistance, gain
of the inverter and stator time constant are known
accurately. When the stator inductance is not known
perfectly, this scheme can be left to act only in steady state.
In steady state. this scheme assumes a much more simple
form as follows.
Of course, the scheme again depends on the stator resistance
and gain of the inverter. Stator resistance can be meaured
periodically. If the gain of the inverter i s varying due to dc
link voltage, the variation can be modelled.
ACKNOWLEDGMENT
Our sincere thanks are due to both Dr.Z.V.Lakaparampi1
and
Mr.V K.Neelakantan
of
ERBiDC,
Thiruvananthapuram, for allowing us to use their facilities.
The timely help of Mr. Hector Kesari and Mr. Srikant
Pandit of Infosys Technologies Ltd, Bangalore, 1s also
deeply appreciated.
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&Field Orientalion as m
e
d to
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' -i
colrtro)
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$1 R
I(nshnan and PRllay, 'I SemhwQ Analqsls and
C o n y x " of Parameter Compensat~onS c l m m Vector
227
Fig 6 ‘la Currents during a speed reversal
Time in 0.2 msec
Fig. 6.2 Adaptation of One @Tr
Time in 0.2msec
0
Time in sec
Time in 0.2 m s w
I
I
j
22%