Asynchronous motor drive loss optimization

Journal of Materials Processing Technology 181 (2007) 301–306

Asynchronous motor drive loss optimization Nikolaos Tsouvalas, Ioannis Xydis, Ioannis Tsakirakis, Z. Papazacharopoulos ∗ ASPETE, Department of Education in Electrical Engineering, BO Neou Herakleiou, 14121 Athens, Greece

Abstract This paper presents a methodology for determination of harmonic iron losses in laminated iron cores under non sinusoidal excitation. The methodology adopted is based on a particular 3D finite element model by using a reduced scalar potential formulation. Eddy currents in iron laminations are considered by means of convenient surface current densities. Experimental verification is performed by comparing computed and measured leakage field in an E-shape laminated core case. A convenient modification of induction motor equivalent circuit parameters is proposed enabling consideration of switching frequency iron losses in case of inverter supply. © 2006 Elsevier B.V. All rights reserved. Keywords: Eddy currents; Finite element methods; Harmonic analysis; Losses

1. Introduction Harmonic iron losses consideration due to eddy currents in laminated iron cores constitutes a complicated task, even in cases of cores with simple geometry. Such phenomena are even more complex in cases of electrical motors supplied by converters. Adjustable frequency drives operating over a wide range of frequencies require accurate determination of the motor behavior in order to avoid possible consequences on the motor drive system and control units involved. This can be implemented by combining equivalent circuit and detailed field calculations by means of utilizing appropriate finite element techniques. However, the motor representation by means of the standard equivalent circuit may lead to inaccurate results, due to inappropriate evaluation of harmonic response and associated iron losses. A first model for the consideration of harmonic iron losses in PWM inverter fed induction motors has been proposed by using harmonic decomposition and superposition principle. This model is limited to steady state operating conditions and off line analysis. In the present work the authors extend this technique to dynamic phenomena and on line analysis. The methodology adopted is based on a high fidelity transient model of an induction motor simulated on a stationary synchronous reference frame, fed by an appropriately designed voltage-source sinusoidal pulse width modulated (VS∗

Corresponding author. Fax: +30 210 2896944. E-mail address: [email protected] (Z. Papazacharopoulos).

0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.03.062

SPWM) inverter, serving as a variable voltage variable frequency (VVVF) three-phase power supply. This model includes harmonic iron losses representation as well as motor equivalent circuit parameter variations. The parameter variations are considered by appropriate field calculations based on finite element techniques. The proposed model validity has been checked through measurements on a 20 kW experimental set-up. 2. Induction motor drive dynamic model 2.1. Inverter representation The drive system model adopted consists of a three-phase IGBT-bridge voltage source converter using PWM technique, as shown in Fig. 1. Specifically, the power unit model simulates the specific IGBT-module used for high power switching and motor control applications, consisting of a two-element halfbridge. Each module serves as a phase branch for the inverter and it is driven by two voltage pulses generated by appropriately designed PWM 6-pulse generator. The IGBT model realizes mathematically the characteristic curves for simultaneous operation of both the switching element and the antiparallel connected free-wheeling diode, without any operating limitations. Obviously the solution of the real module constitutes a rather difficult task due to the non-linearity of the characteristics of the semiconductor elements. For this reasons an approximating procedure was adopted representing each characteristic curve by four equivalent linear segments and by linearizing the system.

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Fig. 1. Motor drive system configuration.

Fig. 4. Flux density distribution (core edge).

Fig. 2. Modified equivalent circuits for induction motor dynamic model. (a) d-axis equivalent circuit (b) q-axis equivalent circuit.

2.2. Motor modified dynamic model The model is based on a convenient modification of the two axes equivalent circuit representation of the motor according

Fig. 3. Flux density distribution (half core configuration).

to Park’s transformation for dynamic phenomena analysis. The parameters of these equivalent circuits are determined by using appropriate finite element techniques. The standard two axes equivalent circuits for stationary synchronous reference frames according to Park transformation have been used. These circuits have been modified in order to take into consideration the high frequency iron losses, as shown in Fig. 2a and b. In these figures Vds and Vqs denote the direct and quadrature axes voltage components respectively, we and wr the stationary synchronous and rotor angular velocities, Rs the stator winding resistance, Rr the corresponding rotor resistance, Lls and Llr the stator and rotor leakage inductances, Lm the magnetizing inductance and Rm the core loss resistance. The newly defined parameters Rls and Rlr are resistors representing

Fig. 5. One phase windings configuration at the end part of the machine.

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λqs = Lls Iqls + Lls1 Iqs + Lm Iqm ,

(2)

λdr = Llr Idlr + Lm Idm ,

(3)

λqr = Llr Iqlr + Lm Iqm ,

(4)

where Idls , Iqls , Idlr , Iqlr , Idlm , Iqlm are the direct and quadrature axes current components flowing in the respective inductances Lls , Llr and Lm . These current components constitute the state variables of the system of linear differential equations of sixth order describing the electrical part of the motor. The differential equation corresponding to the state variables are as follows:

Fig. 6. No load current time variation.

stray load losses associated with stator and rotor leakage fluxes, placed in parallel with the corresponding leakage inductance terms. The stator and rotor two axes flux linkage components are defined by the following relations: λds = Lls Idls + Lls1 Ids + Lm Idm ,

(1)

dIdls Rls (Ids − Idls ), = dt Lls

(5)

dIqls Rls (Iqs − Iqls ), = dt Lls1

(6)

Rlr dIdlr = (Idr − Idlr ), dt Llr

(7)

dIqlr Rlr = (Iqr − Iqlr ), dt Llr

(8)

Fig. 7. Light load motor operation analysis. (a) Measured voltage time variation. (b) Measured current time variation. (c) Simulated current time variation by the modified equivalent circuit. (d) Simulated current time variation by the conventional equivalent circuit.

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Table 1 Comparison of measured and calculated flux densities and losses Waveform

Measured B (mT)

Calculated B (mT)

Measured losses (W)

Calculated. losses (W)

Sinusoidal Fs = 1 kHz Fs = 2 kHz

438 471 512

445 463 503

22.5 40 35

19.75 38.5 33.2

dIdm 1 = [(ωe − ωr )(Llr Iqlr + Lm Iqm ) dt Lm + Rlr Idlr − (Rr + Rlr )Idr ],

cies, where the skin effect enables to express the corresponding induced surface current density JI as follows: (9)

dIqm −1 [(ωe − ωr )(Llr Idlr + Lm Idm ) = dt Lm − Rlr Iqlr + (Rr + Rlr )Iqr ].

(10)

The system of state equations can be solved by considering Kirchhoff’s laws corresponding to the equivalent circuits shown in Fig. 2a and b. The mechanical part is modeled by means of a single rotating mass. The corresponding equation is of the form:
 2 dwr J− (11) + Dwr = Tm − Te , P dt where, J is the moment of inertia, P is the number of poles, D is the viscous damping constant, Tm is the mechanical torque on the shaft and Te the electromagnetic torque. The evaluation of the parameters of the equivalent circuits shown in Fig. 2a and b as well as their variations are determined through detailed field calculations for the respective regimes by using finite element techniques. 3. Methodology Three dimensional eddy current problems have been successfully modeled by means of finite element formulations involving vector quantities. On the other hand scalars, involving only one unknown per node of the mesh, seem to be more efficient. The use of scalar potential formulations in 3D configurations usually necessitates a prior source field calculation by using Biot-Savart’s Law, which presents the drawback of considerable computational effort. We have developed a particular scalar potential formulation enabling treatment of 3D magnetostatics. It permits one to model efficiently laminated iron cores with or without air-gaps and needs no prior source field calculation. According to our method the magnetic field strength H is conveniently partitioned to a rotational and an irrotational part as follows: H = K − ∇Φ,

(12)

where Φ is a scalar potential extended all over the solution domain while K is a vector quantity (fictitious field distribution), defined in a simply connected subdomain comprising the conductor, that satisfies Ampere’s law and is perpendicular on the subdomain boundary. This technique has been extended for cases involving eddy currents developed in iron laminations due to harmonic frequen-

JI = (∂/∂t)(grad T × n),

(13)

where T is a scalar quantity existing only on the lamination surface while n is the unit normal to the lamination surface. The flux density distribution on the surface of the magnetic circuit and along the core edge is given in Figs. 3 and 4, respectively, while Fig. 5 shows the one-phase windings configuration at the end part of the machine. Table 1 compares also the computed and measured values of the flux density in the middle of the air gap. The new method’s efficiency and precision are checked by comparing the computed leakage field to the measured one in the case of an E-shape electromagnet. Moreover, a convenient modification of induction motor equivalent circuit parameters is proposed and validated. 4. Results and discussion The described field models have been applied for the analysis of the leakage field distribution in a typical laminated iron core case formed by E and I shape parts separated by an air-gap of 1 mm. When the excitation winding is supplied by a 50 Hz sinusoidal supply with 1000 A-t the measured losses are 22.5 W while the calculated ones are 19.75 W. In case of supply by a PWM inverter with fundamental frequency 50 Hz and switching frequency 1 kHz the losses are almost doubled while a small reduction is obtained for a switching frequency of 2 kHz. The calculated losses for the same regimes are in quite good agreement with the measured ones, as shown in Table 1. The described induction motor model represented by the two-axes modified equivalent circuits, has been applied for the analysis of a three-phase, two pole, 20 kW, 220 V squirrel cage induction motor. The parameters of the machine equivalent circuits have been calculated for operation with fundamental frequency of 50 Hz and switching frequency of 4 kHz and involve evaluation of eddy currents developed at the end parts due to leakage fluxes by using the proposed technique. The obtained parameters are given in Table 2. Fig. 6 compares the measured no load current time variation with the simulated waveforms by using the classical and modified equivalent circuits, respectively. This figure illustrates that the modified equivalent circuit enables better representation of the iron saturation in the motor magnetic circuit. Fig. 7a–d, give the results corresponding to light load motor operation. The voltage time variation supplied by the inverter is shown in Fig. 7a. Fig. 7b–d depict the corresponding measured current and the ones computed by the modified and conventional

N. Tsouvalas et al. / Journal of Materials Processing Technology 181 (2007) 301–306 Table 2 Parameters of the equivalent circuit introduced Parameter

Derived value

Rs Rr Rm Lls Llr Rls Rlr

0.1  0.122  100  0.0008 H 0.0006 H 1.6 we Lls 1.6we Llr

equivalent circuits respectively. In these figures, the better representation of the current amplitude by the modified equivalent circuit model is profound. Fig. 8a–c show, the current spectra around the modulation frequency of the waveforms given in Fig. 7b–d, respectively. These figures show that the conventional equivalent circuit underesti-

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mates the high frequency harmonics while the modified equivalent circuit provides a more accurate simulation. In the case considered, the conventional equivalent circuit underestimates the measured current value by 25% while the modified one by 4%. The obtained results illustrate the proposed model suitability for non-sinusoidal supply analysis considering harmonic iron losses. Such a technique enables to perform induction motor drive efficiency optimization, including switching frequency losses. 5. Conclusion The paper introduced a 3D finite element model for harmonic iron losses consideration in laminated iron cores. The method is based on a particular reduced scalar potential technique accounting for eddy currents by means of convenient surface current densities. The technique presented is promising for efficient energy management and optimization in drives and subsequent applications. Acknowledgements Project co-financed by the European Social Fund and National Resources from the EPEAEK II Program. Further reading

Fig. 8. Current spectra under light load motor operation analysis. (a) Measured current spectrum. (b) Simulated current spectrum by the modified equivalent circuit. (c) Simulated current spectrum by the conventional equivalent circuit.

[1] J.M.D. Murphy, V.B. Honsinger, Efficiency of inverter-fed induction motor drives, in: Proceedings of the 13th Annual IEEE Power Electronics Specialists Conference, 1982 Record, 1982, pp. 544– 552. [2] M.A. Boost, P.D. Ziogas, State-of-art carrier PWM techniques: a critical evaluation, IEEE Trans. Ind. Appl. (1988) 482–491. [3] K. Matsui, U. Mizuno, Y. Murai, Improved power regenerative controls by using thyristor rectifier bridge of voltage source inverter and a switching transistor, IEEE Trans. Ind. Appl. 28 (5) (1992) 1010– 1016. [4] A. Yahioui, F. Bouillault, 2D and 3D numerical computation of electrical parameters of an induction motor, IEEE Trans. Magn. 30 (5) (1994) 3690–3692. [5] E. Levi, M. Sokola, A. Boglietti, M. Pastorelli, Iron loss in rotorflux-oriented induction machines: identification, assessment of detuning, and compensation, IEEE Trans. Power Electr. 11 (5) (1996) 698– 709. [6] D. Lin, T. Batan, E.F. Fuchs, W.M. Grady, Harmonic losses of singlephase induction motors, IEEE Trans. Energy Convers. 11 (2) (1996) 273– 286. [7] T.J. White, J.C. Hinton, Improved dynamic performance of the 3-phase induction motor using equivalent circuit parameter correction, Int. Conf. Control 2 (1994) 1210–1214. [8] S.C. Mukhopadhyay, S.K. Pal, D. Roy, S. Bose, Software aided derating and performance prediction of cage-rotor induction motors under distorted supply conditions, Int. Conf. Ind. Growth 1 (1996) 452– 457. [9] K.S. Smith, L. Ran, A time domain equivalent circuit for the inverter-fed induction motor, in: Ninth International Conference on Electrical Machines and Drives, 1999, pp. 1–5. [10] Z. Papazacharopoulos, A. Kladas, S. Manias, J. Tegopoulos, High fidelity model for induction motor drive including iron losses due to PWM waveforms, Int. J. Appl. Electromagn. Mech. 12 (3) (2001) 44–48, IOS Press.

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N. Tsouvalas et al. / Journal of Materials Processing Technology 181 (2007) 301–306

[11] V. Kinnares, P. Jaruwanchai, D. Suksawat, S. Pothivejkul, Effect of motor parameter changes on harmonic power loss in pwm fed induction machines, IEEE Int. Conf. Power Electron. Drive Syst. 2 (1999) 1061– 1066. [12] Z.K. Papazacharopoulos, K.V. Tatis, A.G. Kladas, S.N. Manias, Dynamic model for harmonic induction motor analysis determined by finite elements, IEEE Trans. Energy Convers. 19 (1) (2004) 102–108.

[13] P. Dziwniel, F. Piriou, J.P. Ducreux, P. Thomas, A time-stepped 2D-3D finite element method for induction motors with skewed slots modeling, IEEE Trans. Magn. 35 (3) (1999) 1262–1265. [14] A. Vamvakari, A. Kandianis, A. Kladas, S. Manias, High fidelity equivalent circuit representation of induction motor determined by finite elements for electrical vehicle drive applications”, IEEE Trans. Magn. 35 (3) (1999) 1857–1860.