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XXIV Symposium Electromagnetic Phenomena in Nonlinear Circuits June 28 - July 1, 2016 Helsinki, FINLAND ______________________________________________________________________________________________________ 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 j1 (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 ______________________________________________________________________________________________________ 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 L2res I 2e (4) and N0 I 2e I 1 R1 j1 L1σ U 1 1 n 1 R 2 n 2 j1 L2n , 1 L2 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] ______________________________________________________________________________________________________ 72 Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND