XXIV Symposium
Electromagnetic Phenomena in Nonlinear Circuits
June 28 - July 1, 2016 Helsinki, FINLAND
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ESTIMATION OF MAGNETIC AND ELECTROMECHANICAL QUANTITIES
OF PWM INVERTER FED INDUCTION MOTOR
Andrzej Kaplon, Grzegorz Utrata*, Jarosław Rolek
Kielce University of Technology, Power Electronic, Electrical and Drive Chair
Aleja 1000-lecia Panstwa Polskiego 7, 25-314 Kielce, Poland, e-mail: akaplon@tu.kielce.pl, jrolek@tu.kielce.pl
* Czestochowa University of Technology, Institute of Environmental Engineering
J.H. Dabrowskiego 73, 42-201 Czestochowa, Poland, e-mail: gutrata@is.pcz.pl
Abstract - The estimation methodology of induction motor (IM)
angular velocity and rotor flux space vector is presented in the
paper. The estimation algorithms are based on the knowledge of
the measured IM Inductance Frequency Characteristic (IMIFCh) and its approximation resulting from the machine
secondary multi-loop equivalent circuit (SML-EC). The
waveforms of motor speed an rotor flux space vector
reconstructed with the use of the proposed estimation algorithms
are compared with the waveforms of adequate quantities
determined by the simulation of the mathematical model of the
IM fed by a Voltage Source Inverter employing the Pulse Width
Modulation technique (PWM-VSI).
I. INTRODUCTION
The IM-IFCh reproduces variability of rotor
electromagnetic parameters, resulting from the skin effect in
rotor conductive elements. Moreover, as it was presented in
[1], the characteristic is unequivocal at any supply voltage
frequencies in the case of the maintenance of the linear Voltsper-Hertz relationship. Therefore, the IM-IFCh can be used in
the estimation process of IM magnetic and electromechanical
quantities, which in turn can be applied in a sensorless AC
motor drives [2–4].
1.30
Measurement
SML-EC
L
_ 1(2) [pu]
1.08
II. ESTIMATION OF ANGULAR VELOCITY AND
ROTOR FLUX SPACE VECTOR
The actual simulation studies of IM angular velocity and
rotor flux space vector estimation have been conducted for
two cases. The difference between them is that in the first
case the voltage and current space vectors determined from
the mathematical model of the drive are delivered to the
estimator input directly, while in the second case they have
been filtered before (in this case estimated quantities are
denoted with the subscript (F)). In the present study, a digital
filtering algorithm with a frequency response of the
Butterworth filter and cut-off frequency of 1 kHz is used.
The operation accuracy of estimators of the considered
state variables is evaluated on the basis of the instantaneous
relative errors (2) between the values of specified motor state
variables derived from the mathematical model of the
investigated IM and the values of corresponding state
variables determined through an estimation process.
xi 
0.86
xi  xie
100 %
xi
(2)
where: x, xe – instantaneous values of a specified state
variable determined from the scalar-controlled IM drive
simulation model with the machine SML-EC and an
estimated one, respectively.
0.64
0.42
0.20
s – motor slip, R1, L1σ – stator phase winding resistance and
leakage inductance, respectively, L1(ω2) – inductance
associated with the magnetic flux in the motor air gap,
j – imaginary unit, j2=-1.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2 [pu]
Fig. 1. Modulus of the IM-IFCh
The IM-IFCh modulus of the four-pole induction motor of
Sg 132S-4 type with a solid rotor manufactured from the
magnetic material S235JR and its approximation by means of
the machine SML-EC have been presented in Fig. 1.
The measurement method of the IM-IFCh results from (1),
whereas the procedure of machine SML-EC construction,
based on that characteristic, has been discussed in detail in i.a.
[1], [5].
U 1 1  I 1 1 ,s  R1
 L1σ  L1δ  2  L1  2 
j1
(1)
where: U1(ω1), I1(ω1,s) – stator voltage and current space
vectors, respectively, ω1 – stator supply angular frequency,
For the instantaneous operating point of the IM
mathematical model, determined by stator current and voltage
space vectors, a rotor current angular frequency 2 is
estimated with the use of the IM-IFCh [6]. Basing on the
knowledge of estimated angular frequency ω2 and that of
stator supply voltage ω1, the motor angular velocity is
reconstructed according to the equation (3) [6].
me 
1 2
pp
(3)
where: pp – number of pole pairs.
Waveforms of the tested IM angular velocity during startup to ω1ref=0.8ωsN and step changes of the motor load torque
TL (TL=0.05TN→TN→0.05TN, ω1ref – stator reference angular
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71
b)
20
15
10


__ 2 [%]
frequency, ωsN, TN – nominal synchronous angular velocity
and torque of the tested IM, respectively) are presented in
Fig. 2a. The estimated angular velocity waveforms ωem, ωem(F)
are in good agreement with the ωm determined through the
scalar-controlled IM drive simulation model with PWM-VSI.
The instantaneous relative errors of the IM angular velocity
Δωm estimation, determined according to the equation (2),
can be seen in Fig. 2b).
5
0
-5
-10
e

__ 
-15
a)
-20
0.9
0
0.5
1
1.5
2
2.5
3
3.5
2(F)
4
4.5
5
5.5
t [s]
0.8
Fig. 3. Waveforms of the rotor flux space vector magnitude a) and estimation
instantaneous relative errors b)
0.7
0.6
m [pu]
e


__
2
0.825
0.5
0.4
0.775
0.3
0.725

Im
__ 2
0.85
0.2
0
0
0.5
1
1.5
2
2.5
3
m
em(F)
3.5
4
4.5
5
0.45
 2 [pu]
__
em
0.1
5.5
t [s]
b)
40
4
2
0
-2
-4
30
m [%]
20
10
-1.15
2.5


__ 2

Re
__ 2
2.505
2.51
2.515
2.52
2.525
2.53
2.535
2.54
Fig. 4. Waveforms of the rotor flux space vector real and imaginary
components
-20
 e
-30
 e
m
m(F)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
t [s]
Fig. 2. Waveforms of the tested IM angular velocity a) and estimation
instantaneous relative errors b)
The rotor flux space vector can be estimated in accordance
with the following formulas [6]:


Ψ 2e Lμ I 1  Lμ  L2res I 2e
(4)
and
N0
I 2e 
I 1 R1  j1 L1σ U 1
1
n 1 R 
2 n 
2
 j1 L2n 
,
1
L2 res

N0
1
n 1
2 n 
 L
(5)
The rotor flux space vector Ψ•2 magnitude waveform
determined by the considered motor drive mathematical
model is put together with the appropriate waveforms Ψ•e2,
Ψ•e2(F) of this quantity reconstructed by means of the
presented estimation algorithm in Fig. 3a). The instantaneous
relative errors of rotor flux space vector magnitude estimation
are shown in Fig. 3b).
a)
1.15
1.05
0.95
0.85
e

__ 2
0
0.5
1
1.5
Examining the waveforms of the real and imaginary
components of the rotor flux space vector derived from
mathematical model of the considered motor drive and the
corresponding waveforms of reconstructed quantities (Fig. 4),
it should be pointed out that both components of the rotor flux
space vector, i.e. magnitude and argument, are accurately
reconstructed, which is important from the point of view of a
vector-controlled AC motor drive.
III. CONCLUSIONS
The conducted simulation studies indicate the possibility
of applying the presented methodology of the considered
magnetic and electromechanical quantities estimation also to
the case of IMs supplied from a PWM-VSI.
REFERENCES
where: R•2(n), L•2(n) – lumped parameters of the n–th branch of
a machine secondary equivalent circuit referred to the primary
side, n = 1, 2, …, N0, N0 – number of parallel connected twoterminals composed of R•2(n), L•2(n) elements of the machine
SML-EC [1], [5].


__ 2 [pu]
e

__ 2(F)
t [s]
0
0.75
e

__ 2
-0.35
-0.75
-10
-40
0.05
2
2.5
3
 e
__
2(F)
3.5
4
 2
__
4.5
5
[1] J. Rolek, G. Utrata, A. Kaplon, “Estimation of Electromagnetic
Parameters of an Induction Motor Multi-loop Equivalent Circuit Based
on the Machine Inductance Frequency Characteristic”, Proc. of WZEE
2015, Kielce, Poland, pp. 141-146, 2015.
DOI:10.1109/WZEE.2015.7394018.
[2] C. Schauder, “Adaptive speed identification for vector control of
induction motors without rotational transducers”, IEEE Transaction on
Industry
Applications
28(5):
1054-1061
(1992).
DOI:10.1109/28.158829.
[3] C. Lascu, I. Boldea, F. Blaabjerg, "A class of speed-sensorless slidingmode observers for high-performance induction motor drives", IEEE
Transactions on Industrial Electronics, vol. 56, issue 9, pp. 3394 - 3403,
2009. DOI:10.1109/TIE.2009.2022518.
[4] T. Orłowska-Kowalska, M. Dybkowski, “Stator-Current-Based MRAS
Estimator for a Wide Range Speed-Sensorless Induction-Motor Drive”,
IEEE Transactions on Industrial Electronics, vol. 57, issue 4, pp. 12961308, 2010. DOI:10.1109/TIE.2009.2031134.
[5] G. Utrata, J. Rolek, A. Kaplon, "The Genetic Algorithm for an
Electromagnetic Parameters Estimation of an Induction Motor Secondary
Multi-Loop Equivalent Circuit", IREE, vol. 9 no. 6, pp. 1111-1118,
2014. DOI:10.15866/iree.v9i6.4599.
[6] G. Utrata, J. Rolek, A. Kaplon, “Speed and Rotor Flux Estimation Based
on the Induction Machine Inductance Frequency Characteristic –
Simulation
Studies”,
Przeglad
Elektrotechniczny,
1(12),
pp. 242-247, 2015. DOI:10.15199/48.2015.12.62A.
5.5
t [s]
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72
Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND