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Essentials of IM Parameters Measurement for FOC Drives Tuning
Conference Paper · January 2002
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Silverio Bolognani
Mauro Zigliotto
University of Padova
University of Padova
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Essentials of IM Parameters Measurement
for FOC Drives Tuning
S. Bolognani* and M.Zigliotto**
*Department of Electrical Engineering, University of Padova
Via Gradenigo 6/a, 35131 Padova, Italy
phone: + 39 049 8277509 – fax +39 049 8277599 – e-mail: bolognani@die.unipd.it
**Department of Electrical, Mechanical and Management Engineering, University of Udine
Via delle Scienze 208, 33100 Udine, Italy
Phone: +39 0432 558295 – fax +39 0432 558251 - e-mail zigliotto@uniud.it
Abstract — This paper deals with a simple measurement
procedure for characterising an induction motors according to
the requirement of that arise from the drive manufacturers
and/or users. The proposed measurement procedure requires
only a conventional instrumentation and a test bench equipped
with a brake, but without torque measurement facility.
Therefore, any motor manufacturer can perform it, without
the need of a specific inverter drive. This simple and reliable
procedure should represent a smart-testing tool that gives the
motor manufacturer the chance to complete the product with a
comprehensive drive-oriented motor nameplate, in a way
similar to that widely used for PM synchronous motors
(brushless motors).
1. Introduction
Field oriented control (FOC) of induction motors has
gained a plain maturity in the drive market. Industrial
applications of induction motors are continuously growing,
for the inherent rugged structure, reduced maintenance
requirements and high dynamic performance of actual FOC
drives. Recent trends are both the reduction of
commissioning costs and the increase of the drive
reliability. The ultimate research advances are in the
development of sensorless techniques that, eliminating the
need for mounting and calibration of mechanical sensors,
well fit the aim. Nevertheless, both sensored and sensorless
techniques make large use of motor models as a part of the
control algorithm. Many efforts have been devoted to the
determination of motor parameters [1-4] since their exact
knowledge and tracking is a key-factor for high
performances. Usually, off-line measurements are
accomplished by supplying the motor by a PWM inverter,
in which likely current control loops have been already
implemented. High complexity algorithms, as Kalman
filtering, artificial neural networks, observers, or model
reference adaptive systems, obtain on-line parameter
estimation and tracking. All of these studies are intended to
give the drive manufacturer a fine tool to design and tune
properly the IM FOC drive. On the other hand, a very weak
link exists between the induction motor manufacturers and
modern drive designers. The models used for induction
motor testing and characterisation normally do not coincide
with the models used in the control algorithm. As a result,
quite often the parameters supplied by the motor
manufacturer are insufficient or ill correlated to the ones
required by the drive as ”good starting set” for the control
algorithm. This paper intends to be a contribution to fill the
gap, merging the requirement of simplicity put forth by
motor industry with the demand of completeness of
information that arises from drive manufacturers. The
proposed measurement procedure requires only a
wattmeter, an adjustable ac supply and a test bench
equipped with a brake, but without torque measurement
facility. Therefore, any motor manufacturer can perform it
also on off-the-shelf induction motors, without the need of a
specific inverter drive. The measurement data are logged
into an electronic spreadsheet, that implements the
equivalence between the measurement model and the
parameters used in most commonly used control schemes.
This simple and reliable procedure should represent a
smart-testing tool that gives the motor manufacturer the
chance to complete the product with a comprehensive
drive-oriented motor nameplate, in a way similar to that
widely used since a long time for PM synchronous motors
(brushless motors)..
2. Equivalent circuit for FOC drives
FOC induction motor drives are usually based on the
control of the stator current components in phase (flux
current) and in quadrature (torque current) with respect to
the rotor flux linkage referred to the stator. Flux current is
used to control the level of the rotor flux linkage, while
torque current controls the torque delivered by the motor,
so emulating the control scheme of a separately excited DC
motor drive: flux current of the IM plays the role of the
field voltage on the Dc motor and torque current that of the
armature current.
Operation of an IM FOC drive can be described by using
the space vector notation and putting in evidence the
control and the controlled quantities. With reference to a
stationary reference frame, stator and rotor equations are:
u ss = R s i ss +
0=
R r i rs
d λss
dt
d λs
+ r + jω m λsr
dt
(1)
where variables are defined in the Nomenclature. Flux
linkages are given by:
λss = L s iss + L M i rs
(2)
λsr = L M iss + L r i rs
By the equation system (2), the stator flux linkage can be
rewritten as:
λss = L t i ss + λsrs
(3)
where the transient inductance and the rotor flux linkage
referred to the stator are defined by:
L2
L t = Ls − M
Lr
λsrs
(5)
At last, rotor current can be derived from the second
equation of (2) and substituted into the second equation of
(1). After some manipulations it results:
R
s
L
s
j ωm λrs
+
M
(9)
is the well-known slip quantity.
Eq. (8) points out that under steady state operation the
torque component of the current is due to a resistive branch
of resistance Rrs/s in parallel to LM, yielding to the
equivalent circuit of Fig. 2. Really, Fig. 2 is valid under any
operation with rotor flux presenting constant amplitude
even if a transient occurs in the angular frequency.
R
s
L
t
R
+
+
-
(8)
ωs − ω m
ωs
s
t
L
s=
(6)
in which Rrs=Rr(LM/Lr)2 is the rotor resistance referred to
the stator.
Eqs. (5) and (6) are represented by the equivalent circuit of
Fig. 1.
s
s d λsrs
R rs dt
i s

λs
1  d λsrs
= rs +
− jω m λ rs 

L M R rs  dt

us
(7)
where
d i s d λs
u ss = R s i ss + L t s + rs
dt
dt
s
 d λsrs

L
s

− jω m λ rs  = i rs r = i rs
 dt

L
M


(4)
L
= M λsr
Lr
i s
1
R rs
that is the stator current torque component coincides with
the rotor current referred to the stator.
Under steady state operation, the space vector of the rotor
flux referred to the stator has constant magnitude Λrs and
rotates with angular speed ωs (equal to the angular
frequency of any stator quantity). Therefore from (7) under
steady state operation it results
issτ =
By substituting (3) into the first equation of (1), the stator
voltage equation becomes
iss
issτ =
R
is
rs
sλ
is
sτ
Fig. 1 – FOC-oriented equivalent circuit of an IM.
In the circuit of Fig. 1, λsrs is the flux linkage of the
inductor LM whose current is therefore the field component
issλ of the stator current. Conversely, issτ is the torque
component; the power absorbed by the voltage source
jω m λsrs is related to the mechanical power delivered by the
motor while that absorbed by Rrs represents the rotor joule
losses.
By comparing the second addendum in the right term of (6)
with the second equation in (1), it can be easily proved that:
s
u
s
-
Ro
LM
rs
s
i ss
λ
is
sτ
Fig. 2 – Steady-state FOC-oriented equivalent circuit of an IM.
Fig. 2 is the well-known Γ-circuit widely used in FOC
drives. Ro has been included to represent the stator iron
losses, without affecting significantly the voltage drop
across Rs since the amplitude of the current through Ro is
very low. Parameters of the circuit of Fig. 2 have to be
defined for implementing and tuning any IM FOC drive,
both those of them based on a direct approach with
estimation of the rotor flux space vector and those others
based on a indirect approach that uses a feedforward or
feedback slip control scheme.
3. Equivalent circuit for the measurement
Basically, the proposed measure procedure is firstly
devoted to the parameters identification of the
measurement-oriented per-phase equivalent circuit of an
induction motor, reported in Fig.3, where capital case is
used for the symbols as they refer to a sinusoidal operation.
I
R
s
L
s
d
+
R
U
L
o
R
o
k
s
s
I
-
I
µ
k
(2)
(1)
Fig. 3 – Measurement-oriented equivalent circuit of an IM.
Then, the parameters of Fig.2 will be related to those of
Fig.3 by the following equations
The no-load test is performed without dragging the motor
and therefore active power P(1) at section (1) (Fig.3) is the
sum of mechanical Pfw and iron Pfe losses. Since the motor
speed during the test is constant (and very close to the rated
speed) mechanical losses are constant, while iron losses
vary with the squared value of the voltage U(1).
Fig.4a plots the active power P(1) at different input
voltages. Fig.4b is a zoom on the first part of the curve.
180
160
P(1)=f(U(1)2)
140
L2o
=
LM =
Ld + Lo
Lt =
Ld Lo
=
Ld + Lo
120
Lo
L
1+ d
Lo
100
80
60
20
Ld
L
1+ d
Lo
 L + Lo
R rs = R k  d
 Lo
a
40
(10)
0
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
10
2


L 
 = R k 1 + d 


L o 


2
9
P(1)=f(U(1)2)
8
7
6
5
4
which assure the same impedance of the two circuits.
Parameters of Fig. 3 can be easily measured by a no-load
test and an increasing load test as described in the next
Sections.
3
b
2
1
0
0
500
1000
1500
2000
Fig. 4 – Iron and mechanical losses as a function of U(1)
4. No-load test
As previously mentioned, a key-feature of the proposed
procedure is the simplicity of operations. The first test is
the classic no-load test. It utilises the voltage and current
measurements to find the impedance of the per-phase
equivalent circuit of Fig.3, simplified by imposing s≈0, that
is an approximately null rotor current. Stator resistance can
be measured by a DC test. The no-load test returns the
active input power P, the rms phase-to-phase voltage Uph-ph
and the rms phase current Is. The post-processing procedure
implemented in the spreadsheet is resumed in the Tab. I:
Tab. I – Procedure for data post-processing in the no-load test
Step (1)
(2)
(3)
S = 3U ph − ph I s
Q = S2 − P 2
P (1) = P − 3R I 2
(5)
Q (1) = Q
(6)
(7)
S (1) =
(P ( ) ) + (Q ( ) )
1 2
I (1) = I s
U (1) =
S (1)
3I (1)
140
120
100
80
60
40
20
0
0
s s
(4)
The mechanical power Pfw, due to friction and windage
torque, can be found by extrapolation of the curve of Fig.
4b for a null applied voltage. Then Ro is evaluated by
Ro=3U(1)2/Pfe, which results almost independent of the
voltage. For the 169 V, 50 Hz, 1 HP, 2-pole motor under
test it has been found Rs=3.45 Ω and Ro= 454 Ω.
The no-load test, performed at different stator voltages, has
been used also to determine the magnetisation curve of the
motor and, in particular, the values of current Iµ for the
subsequent test at increasing load.
1
2
3
4
5
6
Fig. 5 – Magnetisation curve U(1) as a function of Iµ
1 2
5. Test at rated voltage and increasing load.
The determination of the remaining parameters of Fig.3,
after the no-load test, is usually performed with the lockedrotor test that is simple as well. On the other hand, in the
locked-rotor test the rotor itself is interested by
magnetomotive forces rotating at frequency several times
the maximum slip frequency, and this condition deteriorates
the quality of the results. In this paper a test with rotating
rotor and increasing load is performed instead. The
increasing load test returns the active input power P, the
rms phase-to-phase voltage Uph-ph and the rms phase
current Is, as well as the motor speed ωm (in elec. rad/s) and
the slip s. Measurement data are then post-processed and Ld
and Rk (Fig.3) are determined with good accuracy.
The post-processing procedure implemented in the
spreadsheet is resumed in the Tab. II:
Tab. II – Algorithm for data post-processing in the increasing load test
U s = U ph −ph / 3
Step (1)
S = 3U s I s
(2)
Q = S2 − P 2
Q (1) = Q
P (1) = P − 3R s I 2
S (1) = P (1) 2 + Q (1) 2
U
(3)
(1)
=S
(1)
/(3I
I (1) = I s
(1)
Lo = U
(4)
/ Iµ
Pfe = 3U
P ( 2) = P (1) − Pfe
S
( 2)
= P
( 2) 2
+Q
(1) 2
/ Ro
Q ( 2) = Q (1) − Q o
( 2) 2
U
( 2)
=U
L d = Q ( 2) /(3ωI ( 2) 2 )
R k = sP ( 2) /(3I ( 2) 2 )
After the steps of Tab II have been performed, eqs. (10) are
applied for deriving the parameters of Fig. 2.
A straightforward result is that the rotor time constant,
essential in FOC algorithm, is simply given by
τr =
420.81 413.75 420.51 415.86 425.21
S(1)
[VA]
502.28 532.54 618.74 708.46 816.33
I(1)
[Arms]
U(1)
[Vrms]
Iµ
Qo
[Arms]
1.529 1.5008 1.4589 1.4266 1.3772
[var]
405.27 392.94 374.56 360.31 338.53
Lo
[H]
0.1839 0.1851 0.1867 0.1878 0.1893
Ro
[Ω]
Pfe
[W]
51.582 50.330 48.396 46.837 44.363
P(2)
[W]
222.65 284.94 405.48 526.72 652.48
Q(2)
[var]
15.541 20.810 45.958 55.542 86.687
S(2)
[VA]
223.19 285.70 408.08 529.64 658.21
U(2)
[Vrms]
88.352 87.273 85.580 84.190 81.937
I(2)
[A]
0.8420 1.0912 1.5894 2.0970 2.6777
Ld
[H]
0.0232 0.0185 0.0193 0.0134 0.0128
s
[-]
0.0243 0.0306 0.0446 0.0589 0.0793
Rk
[Ω]
2.5437 2.4436 2.3880 2.3544 2.4055
LM
[H]
0.1632 0.1682 0.1692 0.1753 0.1773
Lt
[H]
0.0206 0.0168 0.0174 0.0125 0.0120
Rrs
[Ω]
2.0047 2.0189 1.9615 2.0513 2.1099
τr
[s]
0.0814 0.0833 0.0862 0.0854 0.0840
1.895
2.034
2.41
2.805
3.321
88.352 87.273 85.580 84.190 81.937
454
454
454
454
454
(1)
I ( 2) = S ( 2) /(3U ( 2) )
(5)
[var]
)
I µ = f ( U (1) ) (Fig. 5); Q o = 3U (1) I µ
(1)
Q(1)
Lo
Rk
(11)
Definitive parameters are obtained by averaging the results
of different tests. For the motor considered in this paper the
measurement yields to
Rs = 3.45 Ω
Rk = 2.0 Ω
Ro = 454 Ω
Lt = 16.8 mH
LM = 176 mH (at rated voltage)
In order to verify the results, the predicted torque
characteristics of the motor has been compared with some
measured points.
40
Tab III gives the measured data and their post-processing
under some different increasing torque and rated voltage.
35
30
25
20
Tab. III Measurement data ad elaboration
Uph-ph
[Vrms]
159.5
159.1
159.1
159.7
159.2
Is
[Arms]
1.895
2.034
2.41
2.805
3.321
P
[W]
311.4
378.1
514
655
811
n
[rpm]
2927
2908
2866
2823
2762
15
10
5
ωm
[rad/s]
Rs
[Ohm]
306.51 304.52 300.12 295.62 289.23
3.45
3.45
3.45
3.45
3.45
Us
[Vrms]
92.090 91.859 91.859 92.205 91.916
S
[VA]
523.50 560.49 664.10 775.86 915.71
Q
[var]
420.81 413.75 420.51 415.86 425.21
P(1)
[W]
274.23 335.28 453.88 573.56 696.84
0
2400
2500
2600
2700
2800
2900
3000
Fig. 6. – Predicted and measured torque-speed characteristic
[Kgcm vs. rpm].
As pointed out by Fig. 6, a good matching exists between
measured and predicted values.
6. Conclusions
References
The paper has proposed a simple and effective procedure
for characterising an induction motor to be used in a FOC
drive. By the results of the procedure the drive
manufacturer is able to tuning any FOC control scheme as
done since a long time with brushless motor drives.
[1] P.Vas, “Parameter Estimation, Condition Monitoring, and
Diagnosis of Electrical Machines”, Oxford Science
Publications, ISBN 0-19-859375-9, Clarendon Press, 1993.
[2] D.J.Atkinson,
P.P.Acarnley,
J.W.Finch,
“Parameter
Identification Techniques for Induction Motor Drives”,
European Power Electronics Conference, pp.307-312, 1989.
[3] J.Holtz, T.Thimm, “Identification of Machine Parameters in a
Vector-Controlled Induction Motor Drive”, IEEE Trans. on
Industry Applications, vol.27, no.6, pp.1111-1118, 1991.
[4] A.M.N.Lima, C.B.Jacobina, E.B. de Souza “Non-linear
Parameter Estimation of Steady State Induction Motor
Models”, IEEE Transactions on Industrial Electronics, vol.44,
no.3, pp.390-397, 1997.
7. Nomenclature
Variables
i
L
P
Q
R
S
s
u
λ
ω
Current
Self or mutual inductance
Active power
Reactive power
Resistance
Apparent power
Slip
Voltage
Flux linkage
Angular frequency or speed (elec. rad/s)
Subscripts
d
k
m
M
r
rs
s
sλ
sτ
t
µ
ο
Leakage
Rotor in measurement-oriented circuit
Mechanical
Mutual
Rotor
Rotor referred to the stator
Stator
Flux component
Torque component
Transient
Magnetising
No load
Superscripts
(1), (2)
s
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Referred to section (1) , (2) in Fig. 3.
Referred to a stationary reference frame