Download Compensation of Iron loss in EKF-based speed estimation of vector

Compensation for the Iron loss Effect in EKF-based Speed Estimation
of Vector Controlled Induction Motors
Kheldoun A., Chetate B.
Research laboratory in electrification of industrial enterprises, Boumerdes University
Rue de l’indépendance 35000, Boumerdes, Tel/fax: 213 24 81 70 50
[email protected]
Abstract-In vector controlled induction motor drives, the instantaneous rotor speed is measured using whether sensors or
estimators. Since the basic Kalman filter is a state observer, its use in vector controlled schemes has received much
attention. However, these schemes are based on the assumption that the existence of iron loss in an induction motor may be
neglected. The paper shows the effect of iron loss on the extended Kalman filter performance that is designed on the basis
if the ironless induction machine model. Simulation results are carried out to demonstrate this effect as well as the
effectiveness of the suggested approach to minimise the speed estimation error without modifying the observer algorithm.
Keywords – Indirect vector control, Extended Kalman Filter, iron loss, sensorless speed control
1. Introduction
The problem of speed estimation in induction motor drives has received over the last two decades a great attention.
Many examples of open speed estimators are given in Guanghui W. [1]. They are based on the measure of current or
voltage or both of them. However no feed back is used to check the correctness of the estimation, therefore they are very
sensitive to parameters variations. Many schemes using saliency have been elaborated to estimate the rotor velocity and
that are subdivided into two large groups. The first group is based on the geometrical effect and the second on the
saturation effect. As an example of geometrical methods, the reader can refers to Peter Vas’s book [2] where two estimators
using rotor slot harmonics are given in details. The frequency of the slot harmonic voltage (or current) depends on the rotor
speed, so they can be utilised to estimate the rotor speed. However, these estimators have not been directly used for rotor
speed estimation in high performance torque control due to the measurement bandwidth limitation. In another hand,
methods using saliency based on saturation effects proposed by Janson et al. [3] who suggested a scheme based on varying
the depth of the rotor slot opening and the injection of high frequency voltage in the stator. Good performances have been
shown using this estimation especially at low speeds but requires rotor speed modifications and they may lead torque
ripples vibration and audible noise.
Model Reference Adaptive Scheme (MRAS) is proposed in [4] where one of the flux estimators acts as a reference model
and the other acts as the adaptive estimator. The estimation is based on the comparison between the output of the two
estimators and the output errors are used to drive a suitable adaptation mechanism that generates the estimated speed. The
schemes require integration and to overcome the integration problem Peng [5] suggested the use of back-EMF and
instantaneous reactive power as alternative ways to estimate the speed. However, still limited by parameters variations and
the iron losses have not been considered.
Adaptive observers-based approaches [6] can have preferred performances using the derived adaptive laws with relatively
simple computation time. However their robustness to parameters uncertainties and noises is never guaranteed [7].
Extended Kalman filters have been proposed in [8, 9]. They can be used both under steady state and transient conditions of
the induction motor. For Furthermore, they have the advantage of the ability to estimate the rotor velocity in very large
wide range, down to very low speed (but not at DC excitation), however, its computational burden is relatively heavy, for
this raison if the iron loss must be considered, the computational time will be very large since the number of differential
equations will increase, and consequently, its implementation will be very complicated. In this paper, the effect of the iron
loss is shown through simulation framework for indirect control scheme. It will be shown also that even when the modified
indirect filed oriented controller, introduced by Levi et al. [10] is used to enhance the decoupling performances, the
estimation speed error cannot be eliminated. A mechanism to reduce this estimation error is suggested without modifying
the EKF’s algorithm or at least retune the covariance matrices.
2. Suggested solution
To improve the estimation process, the first solution which is very obvious is to use the state space IM model that takes
iron loss into account [10] to elaborate the extended kalman algorithm. In this case the state vector becomes
xT x1 x2
x3
x4
x5
x6
x7   is is ir ir im im  r  and the Jacobean matrix’s dimension
will increase. The increase in the state vector dimension will indeed increase in the dimension of the EKF covariance
matrices (1) and makes their adequate tuning more difficult.
P0 [5 x1] 
 P0 [7 x1]
Q[5 x1] 
 Q[7 x1]
(1)
Rs
+ is
us
-
lfs
Rr
lfr
+
Rfe
lm
Rfe
lfs
Rs
wrr
-
+ is
u s’
Rr
is’
Rfe
lm
-
a)
lfr
+
wrr
-
b)
Fig. 1 Steady state equivalent circuit of IM: a) before and b) after modification
We can obviously notice that modifying the EKF algorithm to take care of iron loss will increase substantially the
computational time. This change requires therefore more sophisticated hardware. To address this problem without
increasing the computational time and avoid consequently the fastidious task, i.e. retuning the covariance matrices, we can
use the steady state equivalent circuit of IM. In other words, we change the inputs of the EKF in such a way the iron loss is
not fed to the observer. By using the equivalent circuit of IMs in steady state (fig.1. a) and we ignore the voltage drop
across the stator leakage inductance lfs when compared to that due to Rs, a new equivalent circuit is obtained. This scheme
allows us to eliminate the iron loss from input power by using equations (2) deduced from fig.1.b
u' s  us
u ' s  u s
i' s  is 
i ' s  i s 
us  Rs . is
R fe
(2)
u s  R s . i s
R fe
By using the new input to observer, a new configuration system for sensorless indirect vector controlled induction
motor is obtained (fig. 2).
3. Simulation results
In order to find out to improvement in speed estimation, the configuration shown in fig.2 has been simulated with and
without changing the EKF input parameters; namely voltages and currents. Fig. 3.a illustrates to estimation error of rotor
speed if the iron loss is not compensated for. This error is about 10RPM for desired speed of 140 rad/s and this error will
increase if the motor speed increases. Better speed estimation is obtained by the same EKF without adjusting its parameters
(P0, Q and R) but in this case, the iron loss is compensated for by using the inputs given by equation (2), as shown in the
configuration of Fig. 3.
4. Conclusion
In the paper, the effect of iron loss on the Extended Kalman Filter is analysed. The main advantage of such observer is
the ability to deal with noisy systems and its robustness against parameters uncertainties. This is the main raison to find it in
sensorless speed control of induction motor drives. However, it has been shown that the iron loss decreases the estimation
accuracy and consequently degrades sensorless induction motor drives particularly when used in position control. In this
work, it has been suggested a mechanism based on the power analysis to reduce the iron loss effect without retuning the
covariance matrices of the observer. This later is the most fastidious and time consuming task to design kalman filter
algorithm. The obtained results have indicated the effectiveness of the suggested approach.
5. References
1. Guanghui W. (2004), “Speed senseless control of induction machine based on carrier signal injection and smooth-air-gap induction machine model”,
Phd Dissertation, the Pennsylvania State University.
2. Peter Vas (1998), “Sensorless vector and direct torque control”, Oxford university press.
3. P.L. Jonson, R.D. Lorenz (1994), “Transducerless position and velocity estimation in induction and salient AC machines”, IEEE Indus. Applica.
Society Annual meeting, pp. 488-495.
4. Schauder C. (1992), “Adaptive speed identification for vector control of induction motors without rotational transducers”, IEEE Transactions on
Industry Applications, Vol. 28, pp. 1054-1061.
5. Penz F. Z, Fukuo T, (1994) “Robust speed identification for speed sensorless vector control of induction motors”, IEEE Transactions on Industry
Applications, Vol. 30, pp. 1234-1240.
6. Kubota H, Matsuse K, Nakano T, (1993)“DSP-based adaptive flux observer of induction motors”, IEEE Transactions on Industry Applications, Vol. 29,
pp. 344-348.
r*=1
r*
Decoupling
scheme
suggested
by LEVI
[10]
Te*
PI
_
ias*
ids*
T-1
iqs*
CCPWM
inverter
ibs*
ics*
e
3->2
IM
p
Eq. 2

EKF
est
r
is’
is’
vs’
vs’
r
150
150
100
100
r , rest (rad/s)
r , rest (rad/s)
Fig.2 Configuration system of sensorless indirect vector control of IMs
50
0
-50
0
0.2
0.4
0.6
0.8
0
-50
1
0
12
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
10
Estimation error (RPM)
Estimation error (RPM)
50
10
8
6
4
2
0
8
6
4
2
0
-2
-4
-2
0
0.2
0.4
0.6
0.8
1
0
Time (s)
a)
Fig.3 EKF-based sensorless vector control results a) without core loss compensation
Time (s)
b)
b) with core loss compensation
7. Jingchuan Li, (2005), “Adaptive sliding mode observer and loss minimizing for senseless field orientation control of induction machine” Phd
Dissertation, The Ohio State University.
8. M.S.Nait Said, M.H. Benbouzid, A.Benchaib, (2000) “Detection of brocken bars in induction motors using an extended kalman filter for rotor
resistance sensorless estimation”, IEEE Trans. On Energy Conversion, Vol. 15, NO. 1, pp.66-70.
9. A.V. Leite, R.E. Araujo, D. Freitas, (2004), “Full and reduced order extended Kalman filter for speed estimation in induction motor drives: a
comparison study”, IEEE Power Electronics Specialists Conference, Aachen, Germany, pp. 2293-2299.
10. E.Levie, M.Sokola, A.Boglietti, M.Pastrolli, (1996), “Iron loss in rotor flux oriented induction machines: Identification, Assessment of detaining and
Compensation”, IEEE Trans. on Power Electronics, Vol.11, n°05, pp.698-709.
Appendix: induction motor's data
Rs=4.85 , Rr= 3.805 , Rfe = 500 , Lm= 0.258 H, Ls=0.274 H, Lr= 0.274 H, J= 0.031 Kg.m2, B= 0.008 Nm.s/rd, Pn= 1.5 kW, P=2x2, Vn=220/380 V
In(Y/)=3.64/6.31 A, r=1420 RPM, frequency= 50 Hz, Rated torque=10 N.m