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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 is is ir ir im im 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 wrr - + is u s’ Rr is’ Rfe lm - a) lfr + wrr - 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 us u ' s u s i' s is i ' s i s us Rs . is 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 is’ is’ vs’ vs’ 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