DFG FOR575 Annual Report 2007...Oliver Magdun (Romania), Tutor: Prof. A. Binder Starting date: 17th...

Annual report 1 of 26 High Frequency Parasitic Effects in Inverter-fed Electric Drives

TU Darmstadt FB18 ETiT DFG Forschergruppe FOR575 Sprecher: Prof. Dr.-Ing. habil. A. Binder

2.Annual Report for 2007 Zwischenbericht für den Zeitraum 2007

DFG Research Group FOR575

High Frequency Parasitic Effects in

Inverter-fed Electric Drives

Höherfrequente Parasitäreffekte in umrichtergespeisten elektrischen Antrieben

Darmstadt, November 2007

Responsible for the report:

Prof. Dr.-Ing. habil. Andreas Binder, geb. 16.7.1957

Technische Universität Darmstadt Institut für Elektrische Energiewandlung

Fachbereich 18 - Elektrotechnik und Informationstechnik Landgraf-Georg-Straße 4, D-64283 Darmstadt Telefon: 06151/16-2167, Fax: 06151/16-6033

E-Mail: [email protected]

Prof. Dr.-Ing. habil. Andreas Binder (Sprecher) Prof. Dr.-Ir. Herbert De Gersem Prof. Dr.-Ing. Volker Hinrichsen Prof. Dr.-Ing. Peter Mutschler Prof. Dr.-Ing. Thomas Weiland



1. Summary This report summarizes the results of the research work of the DFG Forschergruppe FOR575 for the year 2007. A short overview on the done work is given. 2. Introduction During the year 2007, the DFG Research Group FOR575 has continued its work in the same componence of the group as in the previous year. Different meetings were held regularly between the members of the DFG group. They are related on the FOR575 homepage, where the meeting protocols are available:

http://www.ew.e-technik.tu-darmstadt.de/for575/DEUTSCH/ http://www.ew.e-technik.tu-darmstadt.de/for575/ENGLISH/.

The 6 projects of the DFG Research Group FOR575 are mentioned in Table 2.1 and the starting date for each project is given. TP1-Binder Calculation of parasitic high frequency current distribution in inverter-fed electrical

machines Dipl.-Ing. Oliver Magdun (Romania), Tutor: Prof. A. Binder

Starting date: 17th July 2006 ( half norm until 16th January 2007)

TP2-Binder Comparative analysis of losses in inverter-fed machines caused by high frequency current components using time-stepping

Dipl.-Ing. Ljubisa Petrovic (Serbia), Tutor: Prof. A. Binder

Starting date: 15th December 2005

TP3-DeGersem Simulation of wave propagation phenomena in inverter-fed drives Dr.-Ing. Dipl.-Phys. Olaf Henze (Germany), Tutor: Prof. De Gersem

Starting date: 15th August 2006

TP4-Hinrichsen

Ageing mechanisms and energy handling capability of metal-oxide varistors for overvoltage protection in inverter-fed drives

Dipl.-Ing. Alexander Rocks (Germany), Tutor: Prof. Hinrichsen

Starting date: 1st January 2006 (No financial support from DFG)

TP5-Mutschler Influencing the voltage slope at the inverter output by modifying the switching behaviour of the IGBT power modules, accomplished by special gate drivers

Dipl.-Ing. Calin Purcarea (Romania), Tutor: Prof. Mutschler

Starting date: 1st February 2006

TP6-Weiland

Multiscale modelling and extraction of parameters in the simulation of inverter-fed drives M.Sc. Zarife Cay (Turkey), Tutor: Prof. Weiland

Starting date: 1st January 2006

Table 2.1. The 6 projects of the DFG Research Group FOR575 3. Overview on the research topics In the first subproject TP1, Mr. Magdun gives a method to calculate the common mode ground current for the motors fed by inverters. He uses an equivalent ladder circuit from the transmission line theory to model the stator winding of two different 110 kW induction motors. The results are fitting well with the experiments when analytical methods are used for the parameter calculation of this model.



Mr Petrovic presents in the second subproject TP2 simplified methods to calculate the iron losses for big machines with FEM. The results of Mr. Petrovic show that not all the methods applied with FEM to calculate the iron losses give correct results. In agreement with the simplified methods proposed by Mr.Petrovic, Prof. Reicherd will implement the best method in the new version of FEMAG to calculate the iron losses.

Mr. Henze presents in the third subproject TP3, the 3D model of a slot with parts of the stator yoke and winding. Using the basic equations of the Transmission Line Theory, Mr. Henze calculated the impedance of one phase of a 110kW induction motor used for investigations in TP1.

In the fourth subproject TP4, Mr. Rocks deals with the protection of the machine windings of inverter-fed drives against overvoltages caused by traveling waves on electrically long lines. The operating mode of two varistor types in inverter-fed drives has been clarified. Further, a 7.5 kW motor has been prepared in the way that the voltage distribution can be measured directly.

Mr. Purcarea presents, in the fifth subproject TP5, an equivalent network model for the behavioural description of a converter and methods to model the HF cables with more conductors. The cable modelling is done in collaboration with Mr. Magdun (TP1) who has computed the cable parameters with FEM.

In the last subproject TP6, Ms. Cay presents an extended circuit model of a roller bearing and a ball bearing. The models were checked in 2D with CST EM Studio. The study analyzes the linear electroquasistatic field behaviors of motor bearings in 2D in the time harmonic and transient case and estimates the bearing equivalent circuit parameters for the EDM (Electric Discharge Machining) bearing current. 4. List of publications The obtained results of the research work are presented in the below papers:

1. O. Magdun, A. Binder, A. Rocks, O. Henze, “Prediction of common mode ground current in motors of inverter-based drive systems”, Proceedings of Electromotion & ACEMP‘07, pp.824-830, 10-12 September, Bodrum, 2007

2. Lj. Petrovic, A. Binder, Cs. Deak, D. Irimie, K. Reichert, C. Purcarea: “Numerical Methods for Calculation of Eddy Current Losses in Permanent Magnets of Synchronous Machines”, ISEF 2007, Prague, Czech Republic, September 2007, CD-ROM, 6 pages

3. O. Henze, H. De Gersem, T. Weiland,”A Stator Coil Model for Studying High-Frequency Effects in Induction Motors”, SPEEDAM 2008 (proposed)

4. O. Henze, A. Rocks, H. De Gersem, T. Weiland, V. Hinrichsen, A. Binder, “A network model for inverter-fed induction-motor drives”, EPE 2007, Aalborg, September 2007

5. A. Rocks, V. Hinrichsen, “Application of varistors for overvoltage protection of machine windings in inverter-fed drives”, The 6th IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, Cracow (Poland), September 6-8, 2007

6. A. Rocks, V. Hinrichsen, O. Henze, A. Binder, „Neuer Einsatz von Energievaristoren zum Überspannungsschutz an umrichtergespeisten Antrieben“, Symposium Maritime Elektrotechnik, Elektronik und Informationstechnik, Rostock, 8. bis 10. Oktober 2007

7. A. Rocks, V. Hinrichsen, “Overvoltage Protection of inverter-fed drives with the help of energy varistors – dimensioning and lifetime considerations”, IEEE APEC 2008, February 24th-28th 2008, Austin Texas (proposed)

8. Z. Cay, O. Henze and T. Weiland, ” Modeling and simulation of rolling element bearings in inverter-fed ac motors”, SPEEDAM, 2008 (proposed).



5. Subproject 1: Calculation of Parasitic High Frequency Current Distribution in Inverter-Fed Electrical Machines Dipl.-Ing. Oliver Magdun Prof. Dr.-Ing. habil. Andreas Binder Institut für Elektrische Energiewandlung, TU Darmstadt E-Mail: [email protected]

5.1. Introduction The present report is dedicated to the calculation of the common mode ground current for the motors fed by inverters. In earlier papers [5.1], [5.2] the calculation of the common mode ground current was done with equivalent RLC lumped circuits, which models both the stator iron and stator winding of AC motors. The obtained results by simulation were in good agreement with experiments, when the model parameters are measured. Unfortunately, a method to calculate the parameters R, C and L is missing. After a checking of an equivalent lumped circuit for three levels of power: 11 kW, 110 kW and 500 kW, it has been concluded in the previously report (December 2006) that the model can not be applied for any motor and winding configuration to calculate the CM current. The measured CM current is not fitting well with the calculated CM current. However, treating the stator winding as a simple RLC lumped circuit is neglecting the travelling wave phenomenon within the winding. Hence, the winding transient phenomena are neglected. In a study of the voltage distribution in the stator winding of an induction machine [5.3], it is clearly indicated that the stator winding of the induction machine at very high frequency must be treated as a transmission line. Therefore, papers from the last years [5.4-5.7] considered ladder circuits for the winding in order to calculate the CM current. These different models of more or less complex circuits have been proposed, but the parameters of the models are always experimentally identified. Unfortunately this method is not available in the design stage, as no experimental apriori data are available. 5.2. Ladder circuit model of stator winding Considering the iron core as an impenetrable wall for the HF magnetic flux and the insulation as an uniform perfect dielectric inside of the slots ( r0 εεε ⋅= ), the velocity of wave propagation is

taken to be r

0c ε

cv = [8]. With 4r ≈ε this velocity is half of the velocity of light in vacuum c0.

The rise time tr of the voltage at the inverter due to the fast switching IGBT converter is typically less than 50 … 200 ns and at the motor terminal 200 … 300 ns [5.9]. It is converted to an

equivalent sine wave frequency 6.111

re ÷≈

⋅=

tf

πMHz and a corresponding wavelength

m15090ec ÷≅= fvλ . The value of λ is big enough to approximate the winding according to the transmission line theory, as a ladder circuit with only few Γ-sections in series. However, the wire length of one turn is much smaller than the wavelength λ . So, a model of the stator winding per phase with a number of Γ-sections equal to the number of turn per phase seems to be more appropriate. Each Γ-section is constituted by ΔR- the resistance per turn, ΔL- the inductance per turn, ΔCWS – the capacitance between turn and iron stack between two turns. The capacitance ΔCS between two turns is neglected, as its influence is big only at the very first moment after the switching occurs (see Fig. 5.1). By considering all turns in the model, the windings with more branches in parallel can be also modeled properly.

The CM current is constituted by a sum of impulses iCM as a linear superposition. At each voltage step at the motor terminals, which is caused by the switching of the voltage source inverter, a common mode current impulse iCM with a decay time td in the range of some μH is



generated. The decay time td of the current impulse iCM is much shorter than the average time interval between two sequential switching instants, which is determined by the switching frequency fT and the phase count 3=m : ( )TQr 31 ft = . For example, if kHz5T =f we get:

dQr μs67500031 tt >>=

⋅= . Hence, it is sufficient to calculate iCM for one voltage step of positive

DC link voltage to get the magnitude and shape of the CM current waveform.

Fig.5.1. Equivalent circuit of a stator winding ( ΔR, ΔL are the resistance and inductance per turn, ΔCS is the

capacitance between two turns and ΔCWS is the stator winding – frame capacitance per turn of one stator phase)

5.3. Parameters calculation The calculation of the parameters has been done analytically and the results were checked numerically with the Finite Element Method simulation (FEM). In order to simplify the parameters calculation, the assumptions from the transmission line theory for considering the travelling wave phenomena are accepted [5.8].

Considering the electric field energy enclosed inside the slots and the air gap, the stator winding – frame capacitances per turn ΔCWS (see Fig. 5.1) may be calculated both analytically and numerically. No differences between results have been pointed out if simplifying assumptions are considered: all the surface of the stator slot winding has the same electric potential and the distance between the stator slot surface and the stator winding surface is constant along the slot circumferential length. To compute the turn resistance and inductance per unit length in the slot area, a sinusoidal current with a high frequency (1 MHz) according to the HF voltage ripple caused by the voltage wave reflection at the motor terminals, is introduced in the turns. The distribution of wires in the slot is considered as an arrangement of wires with rectangular cross section as in the case of form-wound coils and the oval slot shape is modified to a rectangular shape with the same surface. If the iron stack is assumed to be nonconductive, the resistance calculated analytically using the Field’s formula may be compared to the resistance computed with FEM [5.10]. For the slot of a 110 kW motor the results fitted well, but they should be checked in the future for different slots and winding configurations.

At high frequency, in the MHz range, the magnetic field does not penetrate the stator and rotor core and the leakage field lines are confined inside of the stator slot [5.11]. In this case, the results obtained for the resistance per turn computed with FEM seem to be unrealistic, the resistance being underestimated. Then, the chosen value of the resistance for a ladder model is the value calculated analytically. Different measurements should be done in the future in order to confirm this choosing. The inductance per turn ΔL is given by the sum of the slot leakage inductance and the leakage inductance of the winding overhang per turn. As the leakage flux lines are confined within the stator slot due to the HF eddy currents in the iron sheets, the HF slot leakage inductance may be computed using a simple magnetic resistance network. The HF slot leakage inductance is reduced at a very low value comparative to the HF leakage inductance of the winding overhang (smaller than 10%). The HF leakage inductance of the winding overhang is also reduced due to the skin effect in the stator iron sheets. It will be roughly estimated to 30% from the leakage inductance of the winding overhang at low frequencies.



5.4. Results The line-to-earth voltage measured at the motor terminals [5.9] is used to calculate the CM current. The CM current calculated is shown in Fig. 5.2 for two motors of 110 kW (Fig.5.3) manufactured by two different manufacturers, comparative to the measured values. The first motor (M1) has 2 branches in parallel and a single layer and the second motor (M2) has 4 branches in parallel and two layers. The simulated peak value of the current and the measured peak value are fitting well.

Fig. 5.2. Common mode ground current for two motors of 110 kW, 2p = 4: (a) – motor M1 ( turn/4.2Δ Ω=R , turn/μH2Δ =L , nF/turn33.0Δ WS =C ) (b) –motor M2 ( turn/7Δ Ω=R , turn/μH2.3Δ =L ,

nF/turn202.0Δ WS =C )

Fig.3. The two induction motors of 110 kW used for experiments

For almost the same frame of 110 kW motor, using the ladder circuit model with all turns

and the real configuration of the windings, one can see in Fig. 2 the influence of the number of parallel winding branches on the amplitude of the CM current; the CM current is bigger for the motors with a bigger number of parallel branches.

The common mode ground current can be predicted using only the inverter output voltage. In this case, the cable parameters must be calculated using numerical methods. In cooperation with the project TP5 a few numerical methods presented in literature [5.12], [5.13] have been checked experimentally and analytically for different cables. The values obtained for the unshielded cable used in experiments, type NYY-J 4x70 SM, for HF at 1 MHz at 20 ºC are the phase resistance R’ph

= 13.4 mΩ/m, phase inductance L’ph = 0.172 μH/m and phase capacitance C’ph = 153.9 pF/m. Because the dielectric medium has been considered as perfect dielectric for the cable parameters computation, a further work will analyze whether there is any influence of the dielectric on the obtained results.

To introduce the cable in a complete circuit model consisting of inverter, cable and motor, the cable has been modeled with a minimum number of RLC Γ-sections. For 10 m of cable and a rise time of 200 ns determined at the inverter terminal we need at least 7 Γ-sections [5.10]. In Fig.5.4 it is given the line-to-ground voltage at the motor terminals when a ramp voltage with a rise time of 200 ns is applied at the entry of the cable terminal, in comparison with the measured



voltage. The voltages are not fitting well due to the fact that the simulated input voltage at the cable terminal is an ideal ramp. But even so, the common mode current is estimated quite well (Fig. 5.5).

Fig. 5.4. Comparative results between the

measured and computed voltage at the motor terminals for the 110 kW motor (M1)

Fig.5.5. Common mode ground current: A - computed current, when the measured motor line-to-ground voltage is applied at the motor M1 terminals, B – computed current, when an ideal

voltage ramp is applied at the motor cable entry terminals 5.5. Conclusion When the prediction of the common mode ground current is done with a ladder model for the motor winding and for the motor cable, the comparison of the simulated common mode ground current for two cage induction motor of 110 kW with the measured value (Fig. 5.2, length of measured unshielded cable: lc=10 m) shows good coincidence. Further experimental comparison for motors with different power levels will be done in the future. References [5.1] S. Ogasawara, H. Akagi, “Modeling and Damping of High-Frequency Leakage Currents in PWM Inverter-Fed AC Motor Drive Systems”, IEEE Transactions on Industry Applications, vol. 32, no. 5, pp. 29-36, September/October 1996. [5.2] Y. Murai, T. Kubota, “Leakage Current Reduction for a High-Frequency Carrier Inverter Feeding an Induction Motor”, IEEE Transaction on Industry Applications, vol. 28, no. 4, pp. 858-862, July/August 1992. [5.3] B. S. Oyegoke, “Voltage distribution in the stator winding of an induction motor following a voltage source”, Electrical Engineering, vol. 82, pp. 199 – 205, 2000. [5.4] E. Zhong, T. Lipo, “Improvements in EMC Performance of Inverter-Fed Motor Drives”, IEEE Transaction on Industry Applications, vol. 31, no. 6, pp. 1247-1256, November/December 1995. [5.5] T. Halkossari, H. Tuusa, “Reduction of Conducted Emissions and Motor Bearing Currents in Current Source PWM Inverter Drives” Power Electronics Specialists Conference, PESC 99, vol. 2, pp. 959 – 964, 1999. [5.6] G. Grandi, D. Casadei, U. Reggiani, “Common and Differential-Mode HF Current Components in AC Motors Supplied by Voltage Source Inverters”, IEEE Transaction on Industry Applications, vol. 19, no.1, pp. 16-24, January 2004. [5.7] A. Muetze, A. Binder, “Generation of High-Frequency Common Mode Currents in Machines of Inverter-Based Drive Systems”, European Conference on Power Electronics and Applications, EPE 2005, CD-ROM, no. 492, 10 pages, Dresden, Germany, 2005 [5.8] M.T. Wright, S.J. Yang, K. McLeay, “General Theory of Fast-Fronted Interturn Voltage Distribution in Electrical Machine Windings”, IEE Proceedings, vol.130, Pt. B, no. 4, pp. 245-256, July 1983. [5.9] A. Muetze, Bearing Currents in Inverter-Fed AC Motors, Ph.D. thesis, Darmstadt Univ. of Technology, Shaker Verlag, Aachen 2004. [5.10] O. Magdun, A. Binder, A. Rocks, O. Henze, “Prediction of common mode ground current in motors of inverter-based drive systems”, Proceedings of Electromotion & ACEMP‘07, pp.824-830, 10-12 September, Bodrum, 2007 [5.11] S. G. Suresh, H.A. Tolyat, D.A. Rensdussara, P.N. Enjeti, “Predicting the Transient Effects of PWM Voltage Waveform on the Stator Windings of Random Wound Induction Motors”, IEEE Transaction on Power Electronic, vol. 14, Issue 1, pp. 135-141, Jan. 1999. [5.12] P. Mäki-Ontto, H. Kinnunen, J. Luomi “AC motor cable model suitable for bearing current and over-voltage analysis”, Proceedings of International Conference on Electrical Machines, ICEM’04, CD-ROM, no. 365, 6 pages, Cracow, Poland, 2004. [5.13] A. Darcherif, A. Raizer, G. Meunier, J. F. Imhoff, and J. C. Sabonnadiere, “New techniques in FEM Field calculation applied to power cable characteristic computation”, IEEE Transaction on Magnetics, vol. 26, no. 5, pp. 2388-2390, September 1990.



6. Subproject 2: Comparative analysis of losses in inverter-fed machines caused by high frequency current components using time-stepping Dipl.-Ing. Ljubisa Petrovic Prof. Dr.-Ing. habil. Andreas Binder Institut für Elektrische Energiewandlung, TU Darmstadt E-Mail: [email protected]

6.1. Introduction In the first part of the project the synchronous permanent magnet machine was considered. When dealing with machine of this kind, the focus was on eddy current losses in permanent magnets, being the topic of great interest nowadays, when the well conductive rare-earth magnets are widely applied. Of the exceptional importance are these losses under inverter operation. A comprehensive comparative analysis of more different machines concerning this matter couldn’t be find in the literature. In the second year also iron losses of the machines were calculated. 6.2. Calculation of losses with time-step method As stated in the previous annual report, the first year was finished with the simulation of the permanent magnet synchronous machine I-C with inverter supply at rated speed of 1000 rpm. In the second year of the work the analysis of this machine was completed with analogous simulation at maximum speed of 3000 rpm and calculation of iron losses in stator. As this motor belongs to a series of 45 kW high torque machines (described in [6.1] and [6.2]), in the next step the research was extended to the other 5 machines of the series. Machines of this series are in fact combinations of two stators, EW2 and I, and four rotors, A,C,D (see Figures 6.1-6.5) and E. Yet, please note that rotor E was only designed but not built. It is analogous to rotor C, with only one difference, as stated below.

Fig. 6.1. Stator I Fig. 6.2. Stator EW2



Fig. 6.3. Rotor A Fig. 6.4. Rotor C Fig. 6.5. Rotor D Two machines are equipped with surface-mounted magnets, namely EW2-A and EW2-D, the others are with buried magnets (C and A denote segmented magnets, E and D denote massive magnets). All the machines have tooth-wound coils. The most important results are shown in Figures 6.6-6.13. Please note that iron losses are given here without deterioration factors.

no load 1000 rpm

0,19

27

0,006 0,29

8,48,6

0

5

10

15

20

25

30

I-C I-E EW2-A EW2-D EW2-C EW2-E

Pm

[W]

no load 3000 rpm

1,7

70 75

238

0,05 2,150

50

100

150

200

250


Pm

[W]

Fig. 6.6. Losses in permanent magnets at generator no

load with speed 1000 rpm Fig. 6.7. Losses in permanent magnets at generator no

load with speed 3000 rpm

load 1000 rpm

25,5

784

28

211

16,5

217

33

999

0

200

400

600

800

1000

1200

I-C/sinus I-E/sinus EW2-A EW2-D EW2-C EW2-E I-C/inverter I-E/inverter

P m [W

]

load 3000 rpm

57

2112

89

486

51,3 66

2597

715

0

500

1000

1500

2000

2500

3000


P m [W

]

Fig. 6.8. Losses in permanent magnets at load with speed 1000 rpm

Fig. 6.9. Losses in permanent magnets at load with speed 3000 rpm



no load 1000 rpm

205 205

337 330 331 331

0

50

100

150

200

250

300

350

400


PFe

,s [W

]

no load 3000 rpm

1212 1210

1959 19491776 1776

0

500

1000

1500

2000

2500


PFe

,s [W

]

Fig. 6.10. Iron losses in stator at no load with speed 1000 rpm

Fig. 6.11. Iron losses in stator at no load with speed 3000 rpm

load 1000 rpm

540 526549

527

627 624645 663

0

100

200

300

400

500

600

700


P Fe,

s [W

]

load 3000 rpm

728 734

552 555

1048 1048

875 874

0

200

400

600

800

1000

1200


P Fe,

s [W

]

Fig.6.12. Iron losses in stator at load with speed 1000 rpm

Fig. 6.13. Iron losses in stator at load with speed 3000 rpm

The most interesting conclusion for us is that the inverter supply yields from 15% to 30% higher losses. This is valid for both eddy current losses in permanent magnets and iron losses in stator. It is confirmed for one more time that segmentation of magnets is sufficiently effective technique for decreasing eddy current losses in permanent magnets. This is equally true in the case of inverter supply as for the other cases, which are at the moment more thoroughly researched. Machines I-C and I-E possess stator which produces higher content of MMF harmonics than EW2-C and EW2-E, and therefore are the magnet losses greater. Here is particularly important the presence of subharmonic of stator MMF, which has nearly the same amplitude as torque-producing harmonic. The magnet losses at no load reflect well the on-load loss component due stator slotting (although the superposition of MMF and slotting loss component is not really correct, as shown in [6.3]). I checked, supported by Mr. Purcarea (TP5), what influence do the parameters of semiconductor switches have over the magnet losses. (The results presented above are for idealized switches.) However, the influence appeared to be negligible.

As expected, it is noticeable that field weakening, present at maximum speed 3000 rpm, diminishes the stator iron losses. Of course, the difference in accomplishment of magnets doesn’t influence stator iron losses, therefore each pair of the machines has almost identical stator iron losses. There was a temptation to use the extended iron loss model offered by FLUX2D, i.e. the one with inclusion of excess eddy current losses (or Bertotti losses [6.4] and [6.5]), which is successfully done.

It is worth noting that the results of these simulations in FLUX2D (not only losses, but also torque, back electromotive force and flux density profiles, etc.) fit well to the results of



simulations with another program based on another magnet loss computation method (FEMAG). The agreement with measurements is satisfactory as well.

A special problem here was that the treatment of high saturation region of the hysteresis curve inside the FLUX2D program didn’t function as explained in the Users’ Guide. Therefore, the results for machines EW2-C and EW2-E, having both rotor which is especially high saturated, didn’t show at the beginning good correlation between FLUX2D and FEMAG. This was later corrected through a workaround.

Besides the abovementioned machines, one more high torque permanent magnet synchronous motor was examined. It is designed in special way, so that it has two rated powers, namely 272 kW and 544 kW at rotational speeds 65 rpm (supply frequency 13 Hz) and 130 rpm (supply frequency 26 Hz), respectively. Rated torque is 40 kNm and rated voltage 400 V. The motor has 24 poles, 2 slots per pole and phase, 144 slots in total, pitched distributed two-layer winding, semi-closed slots. This machine has massive surface-mounted magnets and massive rotor iron. The corresponding eddy-current losses are to be found in Table 6.2. Hysteresis losses in rotor are negligible.

The conclusions for this big machine are mostly similar with those for the other machines. The great difference is only the relation between losses under inverter supply and losses under supply with sinusoidal currents, because the ratio of increase is now very big. An explanation is that content of stator MMF harmonics, which dominantly cause eddy currents in rotor in the case of load by sinusoidal supply, is for this machine much lower. According to this, the losses in the case of sinusoidal current are relatively low (also with respect to no load they are not that much higher).

rot. speed operating condition Pm [W] Pr,Fe [W]

no load 3.7 0.19

sinusoidal current 11.5 1.25 65 rpm

inverter 331 85

no load 15 0.50 130 rpm

sinusoidal current 45.8 2.86

Table 6.2. Eddy current losses in permanent magnets Pm and rotor iron Pr,Fe

In time-step simulations, when eddy-currents in a region are taken into account, there is a transient before the solution of parabolic partial differential equation comes into steady state. As the rotor is consisted of massive iron, having higher specific electric conductivity, magnetic permeability, and bigger geometric dimensions (this dependence is with the second power) than the magnets, this time constant is for it much bigger. So long transient is almost impossible to calculate with the available computer resources, but this is not really needed, as the losses are in steady state concentrated near the surface (especially in so called skin depth). Therefore, the following trick was applied here:

• eddy currents were allowed to flow only in the area beneath the rotor surface, with the depth in radial direction equal to ten times skin depth by sinusoidal supply.



In fact there are more such tricks in this simulation. To the abovementioned statement one should add a trick used already in simulations with smaller 45 kW machines in order to shorten the transient by inverter operation:

• injecting the rated current by the three ideal current sources at the beginning, just for one time step (at least), and after that to switch on the inverter (current sources couldn’t be disconnected in FLUX2D, but their current was thereafter set to zero)

And there is another additional point, applied also to on-load operation with sinusoidal current: • keeping the speed always constant, and taking care that mutual position of rotor field and

stator MMF space vector corresponds to the desired working point (of course, it was important to keep the speed constant also at no load, only the mutual position then has no real importance)

With this strategy comprising all the three points, the eddy current iron losses were successfully calculated and the duration of in this way shortened simulation was 2 days, while taking almost 13 GB of hard disk space for the solution, which was still acceptable. 6.3. Comparative analysis of time-step and quasistatic method Further, the quasistatic (cascading) method was mentioned already in the previous annual report. The development of this method was enabled by the simulations with time-step method. The quasistatic simulations were done as part of Master thesis of Mr. Irimie, whose supervisor was Mr. Deak. By examining more machines in this second year, a better insight was yielded. The amount of losses calculated by the latest version of quasistatic method was normally inside the range of ±35% around the value obtained by time-step method. Although this is not a small discrepancy, one should keep in mind that time step method is much more expensive way of calculation. In addition, eddy current losses in permanent magnets are just one of the numerous loss components influencing power balance and thermal design of electrical machines. It is also worth noting that losses for different operating conditions of the machine EW2-C differ even up to four orders of magnitude (i.e. load at 3000 rpm vs. no load at 1000 rpm). Therefore, the novel approximate quasistatic method with its accuracy still has some practical meaning. This topic represented the focus of our conference paper [6.6]. An advanced version of this method, developed by Prof. Reichert, is part of the commercially available program FEMAG. Nevertheless, the relation between losses under inverter supply and losses by sinusoidal stator current was discussed as well. 6.4. Conclusion and outlook To conclude, in the period between January 1st, 2007 and November 14th, 2007 the simulations of 6 synchronous permanent magnet machines were fully done, and of one another machine it was partially done, i.e. finished. The simulations with inverter connected to the finite element region were included. All these results enabled better insight into the issue of eddy current losses, especially those generated by inverter-caused harmonics. One method for the loss computation in permanent magnets was significantly improved. One conference paper was published at the ISEF 2007 (International Symposium on Electromagnetic Fields 2007), please see [6.6]. Two diploma theses were proposed for students: “Three-dimensional Thermal Calculation of Synchronous Permanent Magnet Machines” and “Calculation of Losses in Inverter-fed Synchronous Permanent Magnet Machine”. Parts of this work will be also presented at FEMAG Users’ Meeting in Stuttgart at November 26th, 2007. In the continuation of this subproject, induction machines will be examined. Or to be more precise, only the induction machines constructed for the inverter operation. The losses and heating are going to be computed. After that, the switched reluctance machine will be treated in the same manner.



References [6.1] C. Deak, A. Binder, K. Magyari: “Magnet Loss Analysis of Permanent-Magnet Synchronous Motors with Concentrated Windings”, ICEM 2006, Chania, Greece, September 2006, 6 pages [6.2] C. Deak and A. Binder, “Highly utilised permanent magnet synchronous machines with tooth-wound coils for industrial applications,” in Proc. Electromotion‘05, Lausanne, Switzerland, September 2005, CD-ROM, 6 pages [6.3] S. M. Abu Sharkh, M.R. Harris, N. Taghizadeh Irenji, “Calculation of rotor Eddy-Current Loss in High-Speed PM Alternators”, EMD’97, Cambridge, England, 1997 [6.4] G. Bertotti: “General properties of power losses in soft ferromagnetic materials”, IEEE Trans. Mag., Vol. MAG-24, No. 1, January 1988, pages 621-630 [6.5] G. Bertotti, A. Boglietti, M. Chiampi, D. Chiarabaglio, F. Fiorillo, M. Lazzari: “An Improved Estimation of Iron Losses in Rotating Electrical Machines“, IEEE Trans. Mag., Vol. MAG-27, No. 1, November 1991, pages 5007-5009 [6.6] Lj. Petrovic, A. Binder, Cs. Deak, D. Irimie, K. Reichert, C. Purcarea: “Numerical Methods for Calculation of Eddy Current Losses in Permanent Magnets of Synchronous Machines”, ISEF 2007, Prague, Czech Republic, September 2007, CD-ROM, 6 pages 7. Subproject 3: Simulation of wave propagation phenomena in inverter-fed drives Dr. Olaf Henze Prof. Dr.-Ir. Herbert De Gersem Institut für Theorie Elektromagnetischer Felder, TU Darmstadt E-Mail: [email protected] Meanwhile Prof. De Gersem moved to the Catholic University of Leuven, Belgium, but can manage to be regularly in TU Darmstadt to supervise Dr. Henze. 7.1. Network-Model The network model which was created last year is compared with measurements. The simulation results are compared to measurements for a case where the direct current link voltage of the inverter is 780 V and the cable length is 130 m. The experimental and simulation results are shown in [7.1]. 7.2. Stator coil model of an induction motor For modelling the stator coils in an induction motor, the wires of one slot of the coils are considered as a Transmission Line in z-direction. By considering of one slot of the stator coils and using the basic equations of Transmission Line Theory, it is possible to calculate the voltage and current at every position. The equations can be summarized to a vector-matrix form where the voltages and currents are defined as vectors with a length equal to the numbers of conductors in one slot. The capacitances of the model are determined by electrostatic field solutions and the inductances are determined by magnetostatic field calculations. For the calculation of the resistance, the skin effect occurring at high frequencies is considered. The conductivity of the insulating material is neglected. It is obvious that in this equation all wires are still independent to each other. To interconnect the wires to coils further conditions are necessary. To get the additional coil conditions, it is necessary to consider that in one coil certain current and potentials of the end of one forward wire are equal to the potentials and currents of the beginning of a certain backward wire. The principle of this method is explained in [7.2]. The three phases of the winding are connected in star. The impedance of one phase of the coil system is calculated. The other two phases are grounded in this case. The results are compared with experimental values.

The results are shown as in Figure 7.1. At lower frequencies inductive effects are dominating: the impedance is increasing. At higher frequencies capacitive effects become



important. The impedance shows different resonant frequencies. By comparing the experimental results with the simulation one can see that the resonant frequencies of the impedance in the simulation are too high. The overhang as well as the influence of the iron yoke is not considered yet. Further investigations are still necessary.

621,80

4570,00

1430,00

277,411,17

-75,91

5,65

-22,06

78,73

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

1 10 100 1000 10000 100000 1000000 10000000

f / Hz

Z /

-100

-80

-60

-40

-20

0

20

40

60

80

100

/ °

104

105

106

0

500

1000

1500

2000

2500

3000

f/Hz

Z/oh

ms

Fig.7.1. Impedance of the stator (Experiment and Simulation)

7.3. 3-Dimensional slot-yoke model To examine the influence of the yoke on the common-mode effects, it is necessary to model the stator with a part of the yoke in three dimensions. In two dimensions this is done in [7.3], [7.4]. Because of limitations of the numerical program, the model is reduced to one slot with a quadratic part of the yoke. The model and 2D mesh configurations are shown in Figure 7.2. Both ends of the wires of the slot are connected together as a coil.

Fig.7.2. 3D model of one slot with parts of the yoke

The amount of sheets of the yoke is reduced. The thickness and the permittivity of the insulation layers are increased and the conductivity of the sheet is decreased; both in that way that the field configuration is not changed. The excitation voltage is the common-mode voltage at 1 MHz. To get the absolute value of the voltage at this frequency it is necessary to develop the voltage in a Fourier series (Figure 7.3). With a given switch frequency one can find a voltage of 0.49 % of the common-volt amplitude.

Fig.7.3. Common-mode voltage in time and frequency domain



During the simulations, solver problems related to the MHz-frequencies arise which can be solved by using the direct solver. This reduces the highest amount of mesh cells which can be processed by the solver with the given hardware to nearly 1 million. In Figure 7.4 the used mesh is shown at side direction.

Fig.7.4. Meshing of stator-yoke model 7.4. Outlook Further investigations are necessary for results of the 3D model which have to be compared with the stator coil model. Furthermore a deeper insight of the coil model is necessary. After that, a coupling with the cable model with the stator model can be done. References [7.1] O. Henze, A. Rocks, H. De Gersem, T. Weiland, V. Hinrichsen, A. Binder, “A network model for inverter-fed induction-motor drives”, EPE 2007, Aalborg, September 2007 [7.2] Luff, Norris,“High Frequency Theory of Power Transformers“, School of Engineering and Applied Science, Aston University, Birmingham [7.3] Mäki-Ontto, Luomi,”Common-Mode Flux Calculation of AC-Machines”, Proc. ICEM02, Bruges, Belgium, 25-28 August 2002 [7.4] Mäki-Ontto, Luomi,”Circumferential flux as a source of bearing current of converter-fed AC machines”, Proc. Of 2002 Nordic Workshop on Power and Industrial Electronics, NORPIE/2002 Stockholm Sweden [7.5] O. Henze, H. De Gersem, T. Weiland,”A Stator Coil Model for Studying High-Frequency Effects in Induction Motors”, SPEEDAM 2008 (proposed) [7.6] Binder,“CAD and System Dynamics of Electrical Machines”,Vorlesungsskriptum 2006 8. Subproject 4: Ageing mechanisms and energy handling capability of metal-oxide varistors for over-voltage protection in inverter-fed drives Dipl.-Ing. Alexander Rocks Prof. Dr.-Ing. Volker Hinrichsen Fachgebiet Hochspannungstechnik, Institut für Elektrische Energiesysteme, TU Darmstadt E-Mail: [email protected] 8.1. Introduction The described subproject deals with the protection of the machine winding of inverter-fed drives against overvoltages caused by traveling waves on electrically long lines. Under supposition of almost ideal reflection factors at the machine and at the inverter U,machine 1r <≈ and

U,inverter 1r >≈ − the voltage at the end of the line gets reduplicated compared to the intermediate-



circuit voltage when the inverter and the drive are connected to each other by an electrically long line. At an impulse rise time of 100 ns “electrically long” means a length of 7.50 m and longer. 8.2. Results In the given subproject the reduction of the aforementioned overvoltages with the help of metal-oxide (MO) varistor discs is investigated. Under these particular operating conditions the varistor is permanently stressed by overvoltage impulses. Therefore this is a new and non-conventional application for varistors, and the most severe problems are correct dimensioning and aging and lifetime issues, respectively.

During the last year the operating mode of two varistor types (see Table 8.1) in inverter-fed drives has been clarified. A varistor consists of a voltage dependent resistor connected in parallel to a concentrated capacitance. This capacitance itself expands the dU/dt at the machine terminal drastically to more convenient values. The extended rise time is caused by a resonance circuit consisting of the cable inductance, cable resistance and the varistor capacitance. Cycle time of the resulting oscillation can be calculated by

2p, U cable varistort L C= ⋅ (comp. Fig. 8.1).

EDC (1 mA)* E8/20(130 A/cm²)** C' *** Type 1 127,5 V/mm 217 V/mm 8,9 pF·mm·mm-2 Type 2 170 V/mm 288 V/mm 5,8 pF·mm·mm-2

Table 8.1: Data of the used varistor discs:

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120 140

cable length (m)

cycl

e tim

e ( μ

s)

varistor type 2, measured varistor type 2, calculated

varistor type 1, measured varistor type 1, calculated

Fig. 8.1 Calculated and measured cycle time of two varistor types depending on the cable length In Fig. 8.2, measurement results for the two different varistors Type 1 and Type 2 are shown. Type 1 causes a lower voltage level at the machine terminals (approx. 1000 V) than Type 2 (approx. 1100 V), but it is in turn stressed more severely during normal service than Type 2. Both varistors cause an increase of rise time to values above 500 ns. Without a varistor the maximum line to earth voltage reaches values of about 1200 V for cables longer than the critical length. Due the increasing cable capacitance the rise time increases also with cable length. Furthermore first results of the proposed method for an accelerated aging test (comp. last annual report) can be presented here. Some samples of varistor type 1 had to withstand the new accelerated aging procedure. With 20 W and 15 kHz the test parameters were chosen in this way that the parameters of the material must change due to too hard stressing during the test. With only 15 W and 15 kHz

* EDC(1 mA) represents the voltage across the varistor related to a disc of 1 mm thickness measured at a current of 1 mA DC

** E8/20(130 A/cm²) represents the voltage across the varistor related to a disc of 1 mm thickness at a lightning impulse current 8/20 μs of 130 A/cm² *** C' represents the capacitance of a disc of 1 mm thickness and a crossectional area of 1 mm2



almost no change in the parameters has been observed. One typical outcome for an overstressed varistor is shown in Fig.8.3.

800

850

900

950

1000

1050

1100

1150

1200

1250

0 20 40 60 80 100 120 140

cable length (m)

volta

gedr

op a

t the

mac

hine

(V)

without varistor varistor type 1 varistor type 2

0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80 100 120 140

cable length (m)

riset

ime

(ns)

without varistor varistor type 1 varistor type 2

Fig. 8.2. Maximum line to earth voltage (left) and rise time (right) at the machine clamps depending on the cable length

0,99

1

1,01

1,02

1,03

0 200 400 600 800 1000

Time / h

Volta

ge re

late

d to

initi

al v

alue

Fig. 8.3. Example for an outcome of a accelerated aging test with overstressing

The operating point of the varistor on the U/I characteristic was measured before and after the aging procedure. Aging of the MO leads to a conspicuous voltage increase which causes higher power losses and higher temperatures at the aged material. In the face of thermal stability this fact has to be considered when dimensioning a varistor for a special application. When considering the conventional interpretation of such an accelerated aging test which is done by the arrhenius law, this applied test procedure was the stress of almost 100 years lifetime. But one can hardly say if the arrhenius law is still valid for the given application.

Before aging After aging

Voltage / V Current / A (resistive component) Voltage / V Current / A (resistive

component)

265 10,5 290 10,5 Table 8.2. Comparison of the operation point before and after aging:

no parameter changing chart as usual

U/I characteristic changes slowly

dramatic voltage decline voltage breakdown at the varistor after 958 h



8.3. Outlook Near future work will deal with changing of the voltage distribution over the first coil in an electrical machine when using a varistor. For this investigation a 7,5 kW motor (Fig.8.4) has been prepared in the way that the voltage distribution can directly be measured.

Fig.8.4. A 7.5 kW motor prepared for investigation

It is planed as well to determine partial discharge inception voltage in the machine winding

to get knowledge about the maximum acceptable voltage and thus about the necessary protection level which has to be ensured by the varistor. Moreover we will investigate a huge number of varistor samples under reel inverter stress in order to get knowledge about the aging mechanisms about the lifetime of the MO material. References [8.1] Rocks, A., Hinrichsen, V.: “Application of varistors for overvoltage protection of machine windings in inverter-fed drives”, The 6th IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, Cracow (Poland), September 6-8, 2007 [8.2] Rocks, A., Hinrichsen, V., Henze, O., Binder, A, „Neuer Einsatz von Energievaristoren zum Überspannungsschutz an umrichtergespeisten Antrieben“, Symposium Maritime Elektrotechnik, Elektronik und Informationstechnik, Rostock, 8. bis 10. Oktober 2007 [8.3] Debus, J., Studienarbeit mit dem Thema „Untersuchung der Leistungsaufnahme von Varistoren als Überspannungsschutz pulsumrichter gespeister Antriebe“, Nov.2006- March 2007. [8.4] Rocks, A., Plenarvortrag beim 6. Technischen Tag der Fa. VEM in Wernigerode am 4. September 2007 mit dem Thema „Varistoren zum Überspannungsschutz pulsumrichter-gespeister Antriebe“ [8.5] Rocks, A., Hinrichsen, V.: “Overvoltage Protection of inverter-fed drives with the help of energy varistors – dimensioning and lifetime considerations”, IEEE APEC 2008, February 24th-28th 2008, Austin Texas (in press) 9. Subproject 5: Influencing the voltage slope at the inverter output by modifying the switching behaviour of the IGBT power modules, accomplished by special gate drivers Dipl.-Ing. Calin Purcarea Prof. Dr.-Ing. Peter Mutschler Institut für Stromrichtertechnik und Antriebsregelung, TU Darmstadt E-Mail: [email protected]

tapping of the winding



9.1. Aim of the work Modelling the Converter. The next step after building the physical set-up is to develop a suitable model for inverter, cable and motor. To simulate the 6-pack IGBT module a behavioural model must be chosen because it is very complicated or almost impossible to model such a circuit without any knowledge about the parameters of semiconductor’s internal layout [9.1], [9.2]. The parasitic capacities between chip and heat sink, together with wires inductances, must be considered. If they are not given in the data-sheet they must be determined by measurements.The IGBT- drivers have to be modelled first as ideal voltage sources and different values for RGON and RGOFF must be used in simulations.For the DC-link layout and capacitors equivalent networks have to be developed and the components of this networks must be (approx.) determined.

The aim of simulation is to obtain reliable IGBT behaviour similar like reality. Therefore a comparison with the measurements on the set-up is necessary specially for the voltage slope. Selecting the Simulator. For simulating a voltage slope of around 100ns an integration step in the order of ns must be considered. P-Spice is suited for time-domain simulation for HF-phenomena but also other simulation programs must be investigated. Modelling the Cable and Motor. For cable, equivalent circuits from literature have to be selected and developed. The lossy cable is modelled with a sufficient number of such equivalent circuits. The elements of these circuits can be obtained analytically, by direct measurements on cable or by numerical field simulations (cooperation with TP3–DeGersem).

In TP1-Binder using numerical field simulations the HF-current displacement inside the motor is determined when applying common/differential-mode voltage at motor clamps. Thus the parameters for the motor model are obtained. Due to the fact that such models are based on the knowledge of motor construction, an alternative method would be to build ‘behavioural’ models based on parameters determined from direct measurements on motor clamps. The proof of both motor and cable models is realised by comparisons between simulations and measurements on the real set-up. 9.2. Realized work and achieved knowledge Modelling the converter. For the converter a 6-pack IGBT module was used for converting the DC-voltage into a sinusoidal voltage. The IGBT considered is FS35R12YT3 (Infineon). It is a six-pack module with integrated NTC-thermistor. The type of the IGBT is Trench-Gate, Field Stop with a very fast turn on time which represents the state of the art in IGBT semiconductor technique.The IGBT is modelled regarding only the electrical behaviour between connectors. For this, several electrical components are used, like inductances, resistors, capacities and voltage controlled current sources. This electrical components are then parameterised from the data available in data sheet and from own measurements at the module.

Using a network simulation program (Simplorer 6.0) the model from Fig. 9.1 was implemented and simulated. Then the simulations are compared with measurements on the FS35R12YT3 IGBT module from Infineon. Fig. 9.1 shows the internal variable capacities between IGBT main clamps: gate-emitter CGE, gate-collector CGC, collector-emitter CCE, diode junction CDj. Additionally the parasitic wire inductances (LCE1 and LCE2) and internal wire resistance RCC’+EE’ are considered. Also two supplementary networks were added to simulate the tail current in the IGBT and in the diode.

The turn-on and turn-off transients are very crucial for feeding motors via long cables, hence it is necessary to simulate this transients as accurate as possible. The gradient of collector emitter voltage dVCE/dt is the most important because a high value (larger than 1kV/1μs) determines the over-voltage at motor terminals for long cables (longer than 15m).

Fig. 9.2 shows, that the measured voltage slope dVCE/dt at turn off is a little bit larger (250V/μs larger) than the simulated VCE. This 7% difference is due to lack of knowledge about



gate-collector capacitance GCC at high negative gate-collector voltage GCV . In simulation the value of CGC for VGC= –36V was extrapolated for VGC << –36V. In reality CGC decreases a little bit if VGC << –36V so that another measurement with VGC = –600V is required.

Fig.9.1. The equivalent network model for behavioural description

a) b) Fig.9.2. a) Measured and b) simulated collector-emitter voltage CEV at turn-off

For turn-on transient VGE is compared between measurement and simulation. In Fig. 9.3a the measured gate-emitter voltage VGE shows at the beginning of Miller-plateau an overshoot which can be caused by measuring set-up (measure probes). The level and duration of Miller-plateau is similar for measured and simulated model. The level is about 10V due to high gate current which produces a voltage drop across the internal gate resistance. Also the duration of Miller-plateau is around 500ns in this case (see Fig. 9.3a and b). Finally the model was incorporated in the inverter. The inverter is controlled with a standard Space Vector PWM algorithm which delivers the switching times. Also the interlock time was implemented and has a value of 3μs. SV-PWM and interlock time are used on the real set-up.

skV51,3

dtdVCE

μ=

skV26,3

dtdVCE

μ=



a) b)

Fig 9.3. Measured a) and simulated b) gate-emitter voltage GEV at turn-on

Selecting the simulator. Simplorer v6 simulation software was found to be the most suited for its user friendly interface and particularity for electrical circuits. It is a network simulator for time domain and is suited for power electronic simulations. Also the minimal and maximal integration step can be adjusted to small values of the order of ns. Modelling the Cable and Motor. To drive the ac-machine a 34m long LAPP Classic 115CY cable is used in the set-up. To model the cable a Γ circuit was adopted like in [9.3] (see Fig. 9.4) where the inductances for each phase and the coupling between each phase is considered. This equivalent circuit characterise the cable for 1m length having totally 34 such segments connected together. To determine the parameters of one segment three methods were applied in parallel:

- analytical calculation starting from general equations [9.4] and applying them to the particular case (LAPP Classic 115CY, 5-core shielded cable);

- Numerical field simulations (FEM) for the same cable with the given geometry (this part was made by Mr. Magdun (TP1-Binder));

- direct measurements on the cable with Impedance analyser HP 4192A.

Following table summarises the results obtained for LAPP Classic 115CY cable: Analytical method Measurements FEM simulations CA=C10+2C12+2C13 167pF/m 187pF/m 189,43pF/m LA=2(L1-M12) 560nH(LF) / 460nH(HF) 638nH(LF) / 421nH(HF) 560nH(LF) / 286nH(HF) RDC 7,66mΩ/m 7,66mΩ/m 7,66mΩ/m R(1MHz) - 172mΩ/m 171mΩ/m

Further the model was implemented in Simplorer simulation software and the results from Fig.9.5b regarding the line-line voltage VLL are obtained. The case was considered for an open end of the cable. In parallel the VLL is measured (see Fig. 9.5a) at the setup. It can be noticed that the

Fig.9.4 Model for 1m cable segment.



skin and proximity effect plays an important role in damping the waves across the cable. In the model the damping is far to low (only the DC resistance is used). On the other hand the simulated propagation velocity corresponds to the measured one (see wave propagation time across the cable tp= approx. 225 ns from Fig. 9.5).

a) b) Fig.9.5. Measured a) and b) simulated (without skin effect) line-line voltage

First the skin and proximity effect is implemented with the help of a ladder circuit of resistors and inductances [9.5]. The parameters of this circuit are then parameterised using an algorithm. Comparisons between measurements and simulation can be seen in Fig. 9.6a. In Fig. 9.6b the measured voltage wave form is the input for the cable model as a lookup up table. The effect on first and second peak as also on wave form is obvious (there is a difference between simulated and measured inverter output as well).

a) b)

Fig.9.6. a) Inverter model cable input; b) Lookup table cable input

Another method to represent the losses from cable at high frequency is adopted from [9.6]. Now the AC resistance at cable oscillation frequency (around 1MHz) is considered (constant) and implemented in each model segment (distributed). Again there are presented the two situations where the cable input is from inverter model (Fig. 9.7a) or from measurements (Lookup table). The last model [9.6] is found to be less accurate regarding the wave shape due to the fact that a constant value for AC resistance has been used. The first model [9.5] tends to be more appropriate because it considers a variation of AC resistance with frequency.

tp tp

10% 10% 10%10%

simulatedmeasured

simulatedmeasured



a) b)

Fig.9.7. a) Inverter model cable input; b) Lookup table cable input 9.3. Conclusions and Outlook A behavioural model for the power semiconductor was developed and compared with measurements. The results are in good agreement. For the cable a model has been developed and compared with measurements. For the skin and proximity effect .

For the motor model there is a good opportunity for collaboration and change of ideas with other colleagues from Electrical Machines department (TP1-Binder and TP2-Binder).Another collaboration takes place between TP5-Mutschler and TP7-Weiland regarding a 3D model for inverter which is used to compute the HF effects which cause the EMI inside an inverter.

Having an appropriate model for inverter and cable, measurements on reducing the voltage overshoot and common-mode current can be adopted, first using the simulation tools for proof and later by building on the real set-up and conducting measurements. For reducing the overvoltage on motor clamps two methods are intended: the use of inverter-output filters (Task B1) and the use of optimised IGBT switching command (Task B3). For reducing the common-mode current by reducing the common-mode voltage applying different pulse patterns for the 6-IGBT bridge. References [9.1] A. Wintrich "Verhaltungsmodellierung von Leistungshalbleitern für den rechnergestützten Entwurf leistugselektronischer Schaltungen", PhD thesis at TU-Chemnitz, Germany, 1996 [9.2] S. H. Stier, P. Mutschler "An Investigation of a reliable behavioural IGBT Model in comparison to PSpice and measurement in Hard- and Softswitching applications", European conference on Power Electronics and Applications, 2005 [9.3] Mäki-Ontto, P. ‘AC Motor Cable Model Suitable for Bearing Current and Over-Voltage Analysis’ ICEM 2004 [9.4] Küpfmüller, K. ‘Einführung in die theoretische Elektrotechnik’ 10. Auflage, 1973 [9.5] Kim, S. “Compact Equivalent Circuit Model for the Skin Effect”, IEEE 1996 [9.6] Skibinski, G. “Common Mode and Differential Mode Analysis of Three Phase Cables for PWM AC Drives”, IEEE 2006 10. Subproject 6: Multi-scale modelling and extraction of parameters in the simulation of inverter-fed drives

M.Sc. Zarife Çay Prof. Dr. –Ing. Thomas Weiland Institut für Theorie Elektromagnetischer Felder, TU Darmstadt [email protected]

10.1. Introduction High performance induction motor drives require fast switching transition and high switching frequency from PWM inverters to fully realize such advantages as fast dynamic response, high

simulatedmeasured

simulatedmeasured



efficiency, and low acoustic noise [10.1]. Unfortunately, the rapid switching of these power devices induces undesired currents which flow through the bearings causing premature motor bearing failures. This study analyzes the linear electroquasistatic field behaviors of motor bearings in 2D in the time harmonic and transient case and estimates the bearing equivalent circuit parameters for the EDM (Electric Discharge Machining) bearing current. 10.2. An Extended Circuit Model of a Roller Bearing An extended equivalent circuit model of a roller bearing is developed. Its parameters are evaluated analytically in 1D and computationally in 2D. Only half of the bearing is modeled by utilizing the symmetry property. It is partitioned into three sections. Each steel (white) subsection is represented as a resistor, each lubricant (yellow) subsection is represented as a capacitor (Fig.10.1).

1.6+d_film 8

1.551.55+d_film

6.35-d_film6.35

7.9

z0

0

5.39

2.51

x1/ 2 V=V

1.6eq 2 *=Z Z

Dimensions in mm

4

R1

C1

R2

R3

C2

R4

R5

C3

R6

C4

R7

Analytical Computed 1R 1.52 5 e − Ω 1.08 5 1.32 5 4.87 4 e e e− → − → − Ω

1CX 9.11 9 e + Ω 1.13 9 1.58 10 6.81 8 e e e+ → + → + Ω

2R 3.11 4 e − Ω 6.30 3 2.19 4 8.51 3 e e e− → − → − Ω 3R 6.95 3 e − Ω 7.42 3 7.21 3 6.04 3 e e e− → − → − Ω

2CX 1.35 13 e + Ω 1.40 10 3.52 15 1.57 10 e e e+ → + → + Ω

4R 2.34 1 e − Ω 1.44 1 1.56 1 6.29 e e− → − → Ω 5R 5.80 6 e − Ω 5.97 6 5.87 6 5.51 6 e e e− → − → − Ω

3CX 2.51 6 e + Ω 2.51 6 2.50 6 2.46 6 e e e+ → + → + Ω

6R 3.74 5 e − Ω 0 (Due to the truncation error!)Ω

4CX 1.03 7 e + Ω 1.03 7 1.02 7 1.01 7 e e e+ → + → + Ω

7R 1.95 4 e − Ω 1.20 4 1.26 4 5.40 3 e e e− → − → − Ω

Fig. 10.1. Top view of 2D CST EM Studio model with its dimensions, and circuit parameters of each

subsection

Table 10.1. Analytically and computationally calculated circuit parameters of the extended model for the roller bearing

Three different currents (current entering the subregion, current flowing through the intermediate cylinder of the subregion and current leaving the subregion) and the potential difference of each subregion are roughly estimated from the results of the time harmonic simulator. By dividing the voltage by three different currents, three different values are obtained for each circuit parameter. The real values must be somewhere in between. As seen from Table 10.1, the computed parameter values match the analytically calculated ones fairly well. 10.3 Linear Time Harmonic and Transient Analyses of a Ball Bearing 10.3.1 Linear Time Harmonic Analysis A time harmonic voltage source whose peak voltage is well below the breakdown threshold voltage of the lubrication film is applied between the cylindrical surfaces at minr and at maxr of the ball bearing. The potential distribution over the bearing cross section is simulated at different time instants (Fig. 10.2). The space monitors used are shown in Fig. 10.3. At these space points, the magnitude of the volume current density is monitored (Fig. 10.4). The calculated and computed bearing currents, impedances and capacitances for the roller and ball bearing are given in Table 10.2.



0 5 10 15 200

1

2

3

Time/ms

Mag

nitu

de o

f Cur

rent

Den

sity

/mA

/m 2

abcdefg

0 5 10 15 200

1

2

3

4

Time/msMag

nitu

te o

f Cur

rent

Den

sity

/mA

/m 2

hijklmn

10.3.2 Linear Transient Analysis A pulse train voltage source whose voltage level peak( 1 V)V = is well below the breakdown threshold voltage of the lubrication film is applied between the cylindrical surfaces at minr and at

maxr of the ball bearing. The potential distribution over the bearing cross section is simulated at different time instants (Fig. 10.5). The space monitors used are shown in Fig. 10.3. At these space points, the magnitude of the volume current density is monitored (Fig. 10.6).

0 5 10 15 20 25 30 35 40 4505

1015202530354045

Time/ms

Mag

nitu

de o

f Cur

rent

Den

sity

/mA

/m 2

abcdefg

0 5 10 15 20 25 30 35 40 450

10

20

30

40

50

60

70

Time/ms

Mag

nitu

de o

f Cur

rent

Den

sity

/mA

/m 2

hijklmn

Fig. 10.5. Potential distributions at:

(a) 17.8 ms,t = (b) 18 ms,t = (c) 22 ms,t = (d) 22.2 mst =

Fig. 10.6. Magnitude of the volume current density

10.4. Conclusions

• The analytical and simulation results verify that a bearing can be modeled by a single capacitor without losing much accuracy, as long as the lubrication film is insulating.

• The bearing capacitances before the lubrication film breakdown is found to be several hundred picofarads that matches the typical bearing capacitance value ( 200 pF)bC =

Analytical Computed

Roller Bearing Roller Bearing Ball Bearing

b /I A * 1.11 7j e − * 1.68 7j e − * 1.13 7j e −

b /Z Ω * 6.38 6j e− + * 4.21 6j e− + * 6.26 6j e− +

b /pFC 499 756 508

Fig.10.2. Potential distributions at: (a) ,t T= (b) / 6,t T= (c) / 4,t T= (d) 2 * / 3t T=

41

1

1.5492

3

0

3.95

4.9

5.96.351

6.9

z

Space Monitor 1Space Monitor 20

hi

j

k

l

mn

a

c

b

d

e

f

g

Fig. 10.3. Space monitors (Dimensions in

Fig. 10.4. Magnitude of the volume current densiy Table 10.2. Bearing current, impedance and capacitance



reported in [10.2]. • The bearing current that flows through the bearing before the lubrication film breaks down

has no unfavorable effects on bearing lifetime because of its low amplitude. • Conclusions based on Fig. 10.2, 10.4, 10.5 and 10.6: • Since steel is a good conductor, the races and the rolling element of the ball bearing behave

approximately like equipotential volumes. • The electric field strength inside the steel parts produces very small conduction current

density, which is comparable with the displacement current density in the insulating film. The displacement current density between the races, on the other hand, is extraordinarily small.

• The time derivative of potentials generates a 90° phase shift between the time harmonic voltage applied and the resulting volume current density.

• The time derivative of potentials generates impulses in the volume current density at the on and off instants of the pulse train voltage source.

10.5. Outlook The 2D nonlinear transient analysis of the ball bearing with the consideration of the electrical breakdown of the lubricant film is being done at the moment. The nonlinear bearing resistance will be extracted from this simulation. Unfortunately, since the lubricating film thickness is too small relative to the dimensions of the other parts of the motor bearing, a 3D fine mesh requires too many mesh cells to simulate the motor bearing in 3D. The bearing network model is essential to estimate the bearing voltage and the endangerment of the motor bearing due to the EDM bearing current and to determine the convenient mitigation methods, if necessary, which ensures the safe drive operation in the design phase of an inverter-driven ac motor. Finally, we will focus on the computation of parameters to induction influences in power electronic circuits using magnetoquasistatic field simulations. References [10.1] Y. Xiang, “Method and apparatus for active common-mode voltage compensation in induction motor systems”, United States Patent 5936856, 1999. [10.2] J. M. Erdman, R. J. Kerkman, D. Schlegel, and G. Skibinski, “Effect of PWM inverters on ac motor bearing currents and shaft voltages”, IEEE Trans. on Ind. Appl., vol. 32, no. 2, pp. 250-259, 1996. [10.3] A. Muetze, “Bearing currents in inverter-fed AC-motors,”,PhD dissertation in Technische Universitaet Darmstadt, 2003. [10.4] F. Ferreira, P. G. Pereirinha and A. T. de Almeida, “Study on the bearing currents activity in cage induction motors using finite element method”, ICEM, 2006.

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DFG FOR575 Annual Report 2007...Oliver Magdun (Romania), Tutor: Prof. A. Binder Starting date: 17th...

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