In Dede, E (Ed.) Proceedings of the 13th European ...eprints.qut.edu.au/29786/1/c29786.pdf · using mathematical analyse, 2-D and 3-D Finite elements simulations- is to eliminate

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Adabi Firouzjaee, Jafar, Zare, Firuz, & Ghosh, Arindam(2009)End-winding effect on shaft voltage in AC generators.In Dede, E (Ed.) Proceedings of the 13th European Conference on PowerElectronics and Applications.IEEE, Online, pp. 1-10.

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Adabi, Jafar and Zare, Firuz (2009) End-winding effect on shalft voltage in AC generators. In: Proceedings of the 13th European Conference on Power Electronics and Applications, 8-10 September 2009, Barcelona, Spain.

© Copyright 2009 IEEE

1

End-winding Effect on Shaft Voltage in AC Generators

Jafar Adabi, Student member IEEE, Firuz Zare, Senior member IEEE, Arindam Ghosh, Fellow IEEE

Queensland University of Technology, 2 George St, GPO Box 2434, QLD 4001 Brisbane, Australia

[email protected] , [email protected] , [email protected] www.qut.edu.au

Acknowledgment The authors thank the Australian Research Council (ARC) for the financial support for this project through the ARC Discovery Grant DP0774497. Keywords Shaft voltage, AC generator, Common mode, design parameters, FEM, End-winding Abstract: This paper presents effects of end-winding on shaft voltage in AC generators. A variety of design parameters have been considered to calculate the parasitic capacitive couplings in the machine structure with Finite Elements simulations and mathematical calculations. End-winding capacitances have also been calculated to have a precise estimation of shaft voltage and its relationship with design parameters in AC generators. Introduction Power converters have introduced new desires for the modelling of induction motors due to an increment in switching frequency and short rise times of the PWM voltage pulses. Development of PWM-based drive systems increased the efficiency, performance, and controllability in induction motor applications, low acoustic noise and more efficient electromagnetic power conversion. However, high speed switching of IGBTs makes high-frequency ground leakage current, bearing current and shaft voltage in inverter-fed drive systems [1-3]. One of the inherent characteristics of pulse width modulation (PWM) techniques is generating common-mode voltage which is defined as the voltage between the electrical neutral of the inverter output and the electrical ground [4].

(a)

(b)

Fig.1 (a) structure of a stator-fed induction generator system (b) common mode model of the system

End-winding Effect on Shaft Voltage in AC Generators ADABI JAFAR

EPE 2009 - Barcelona ISBN: 9789075815009 P.1

2

Fig.1.a show a cross section of a stator-fed induction generator structure where the stator windings are capacitively coupled to both the stator frame (normally grounded) and the rotor. The stator frame and the rotor form a capacitance (Csr) which results in a divider network such that a portion of common-mode voltage waveform appears as the shaft voltage (see fig.1.b) on the rotor with respect to the stator frame (or ground) [5]. When this voltage exceeds the breakdown voltage of the thin lubricant film between the inner and outer rings of the bearing, there is a miniature flash over. This causes pitting in the bearings and is the main reason for early bearing failures [6-7]. Parasitic capacitances in the motor also provide low-impedance paths for high-frequency common-mode currents. The high rates of rise and fall of line-line voltage pulses in the range of a few hundreds of nanoseconds give rise to ground currents due to cable capacitance to ground and motor winding capacitance to ground. If not properly mitigated, high frequency ground currents can also interfere with the power system ground and affect other equipments on the power system [8-9]. A simple model to predict the common mode ground current from design parameters is presented at [10] based on the calculation of some capacitances. Different types of inverter-induced bearing currents [11] and a description of techniques for measuring the different parameters of importance such as calculation and measurement of bearing capacitances in different motors have been proposed in [12-13]. The influence of different parameters of a variable speed drive system on the phenomena of inverter-induced bearing currents has been studied at [14]. A three-phase induction motor model that shows the motor behaviour over a wide range of frequencies from 10 Hz to 10 MHz is presented in [15] where a common-mode, differential-mode, and bearing circuit models are combined into one three-phase universal equivalent circuit model. Two high-frequency modelling methods of induction motors for frequency- and time-domain simulation is presented in [16]. Many mitigation techniques to cancel the common mode voltage and consequently shaft voltage of inverter-fed drive system and limit other high frequency based phenomena have been presented in [4],[17]. The main goal of this work-which is to find the effect of machine parameters on the shaft voltage using mathematical analyse, 2-D and 3-D Finite elements simulations- is to eliminate the shaft voltage effects in a primary stage of design . By choosing appropriate design parameters, it is possible to decrease the shaft voltage and resultant shaft voltage without use of any other additional active and passive filter-based techniques. Based on [18], the occurrence of discharge bearing currents (also called “electric discharge machining (EDM) currents”) that can occur in machines of inverter-based drive systems depends strongly on the value of the capacitive voltage divider which can be calculated as:

srrfb

sr

com

shaftCCC

CVV

++= (1)

Where, the parasitic capacitive couplings exist between: the stator winding and rotor (Csr), the stator winding and stator frame (Csf), the rotor and stator frames (Crf), and ball bearing and outer and inner races (CBO, CBI). A full description of shaft voltage of induction generators in different structures and pulse width modulation techniques have been investigated in [19-20]. A high frequency model of AC motor is presented in [21] based on measurement results and reduction techniques of common mode voltage by a novel PWM strategy has been investigated in [22]. In this paper, calculations of different capacitances have been carried out and the results have been confirmed with FEM simulation analysis. A discussion will be conducted for the effects of each design parameters on the shaft voltage generation of ac generators. Different capacitive couplings in AC generators Fig.2 shows a view of a stator slot, a rotor and winding with different design parameters. g1 is the air gap between rotor and stator, g2 is the gap between winding and stator and gin is the thickness of the winding insulation. d is the length of slot tooth and ρ is the height of the stator slot. W and W′ are the width of winding at the top and bottom respectively. hW is the length of the stator winding at both the right and the left side of winding. In this section, simulations were conducted for a single slot for 12 design structures of Table I. The thickness of insulation (gin) is considered as 2.5 mm and rε is 2.25 and the rotor radius is 1000 mm. 2-D and 3-D FEM simulation results in a single stator slot for Csr, Crf, Csf have been shown in each section and the results compared with the calculation results. Accuracy of the mathematical analysis can be verified in this comparison.



3

Fig.2. stator slot with different design parameters

Table I. different design parameters for proposed IG structure

Design number

ρ (mm)

g2 (mm)

d (mm)

w (mm)

hw (mm)

1 3 5 50 200 289 2 5 5 50 200 287 3 3 15 50 201 278 4 5 15 50 201 276 5 3 25 50 203 268 6 5 25 50 205 266 7 3 5 150 200 289 8 5 5 150 200 287 9 3 15 150 201 278

10 5 15 150 201 276 11 3 25 150 203 268 12 5 25 150 205 266

[

The capacitive coupling between rotor and stator frame (Crf)

By considering the air gap (g1) to be much smaller than the outer diameter of the rotor, a capacitive coupling between rotor and stator frame in a single stator slot can be calculated as follows:

1

r0rf g

L)dn

r2(C

×−πε= (2)

Where r is the rotor radius and g1 is the air gap, Lr is the rotor length. This capacitance can be multiplied by the number of slots (n) to calculate the total capacitance. Fig.3 show the results for 2-D, 3-D and mathematical analysis for Crf. the results show that the calculations is accurate enough in design parameters of Table I.

Capacitive coupling betw een rotor and stator frame (Crf)

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5 6 7 8 9 10 11 12Design number

Crf

(nF)

Crf-cal Crf-2DCrf-3D

Fig.3. 2-D and 3-D simulation results for Crf and its calculated values The capacitive coupling between stator frame and stator winding (Csf) In this case, there are four surfaces which surround the winding: stator frame from right, left and bottom side and series connection of insulation capacitance and slot wedge capacitance from upper side of winding and the stator slot tooth. So, Csf can be calculated after modifications:

( ) ( )r

2rin1r2

2r1r0

in

Wr0sf L

ggdW

gh2W

C ×⎟⎟⎠

⎞⎜⎜⎝

⎛ε+ε−εεε

+×+′εε

= (3)

Where ε0 is the permittivity of free space and εr1, εr2 are the permittivity of the insulation and the slot wedge material. Fig.4 show the results for 2-D, 3-D and mathematical analysis for Csf. the results show that the calculations is accurate enough in design parameters of Table I.



4

Capacitive coupling between stator w inding and the frame(Csf)

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12Design number

Csf

(nF)

Csf-cal Csf-2DCsf-3D

Fig.4. 2-D and 3-D simulation results for Csf and its calculated values The capacitive coupling between ball bearings and inner and outer races Fig.5.a&b show the sketch of the ball bearing in the AC motor and the schematic of two capacitances of a ball bearing. During operation, the distances between the balls and races may change and vary the capacitance. At high speed, balls and shaft positions are considered symmetric and the distances between the inner race and balls (dBI) and between outer races and balls (dBO) are assumed to be equal. At low speeds, because of gravity, balls (Fig.5.c) and shaft (Fig.5.d) may shift down and the system (balls position and shaft) will be asymmetrical. In this simulation, there are 22 balls with a diameter of 30 mm, a shaft diameter of 200 mm and the range of 0.1mm oil thickness was simulated. Table II shows the capacitive coupling terms (CBO, CBI) with respect to different variables associated with the balls position assuming the equal inner and outer distances.

(a) (b) (c) (d)

Fig.5. (a) A view of ball bearings and shaft (b) ball, outer and inner races (c) Asymmetric ball position (d) Asymmetric shaft position

Table II. Capacitive coupling terms in different ball position Oil

Thickness (mm) dBO

(mm)dBI

(mm)CBO (pF)

CBI (pF)

CB (pF)

0. 1 0.01 0.09 363 78.393 64.47 0. 1 0.03 0.07 173.91 88.01 58.43 0. 1 0.05 0.05 130.07 104.44 57.927 0. 1 0.07 0.03 108.09 132.93 59.614 0. 1 0.09 0.01 94.275 216.14 65.64

Shaft centre shift down (mm)

dBO (mm)

dBI (mm)

CBO (pF)

CBI (pF)

CB (pF)

0.02 0.04 0.04 145.84 116.17 64.662 0.04 0.03 0.03 172.07 132.92 74.991 0.06 0.02 0.02 220.54 159.95 92.710



5

The capacitive coupling between rotor and stator winding (Csr) Without considering end-winding effects As shown in Fig.6.a, existing capacitive couplings are: the capacitive coupling between rotor and winding (Csr), the capacitive coupling between rotor and stator in left and right sides of the slot tooth (Cf1r, Cf2r), and capacitive coupling between winding and stator in left and right sides of the slot tooth (Cf1s, Cf2s). Fig.6.b shows a model to calculate the capacitive couplings. In fact, the electric fields between stator slot teeth on both sides influence the total electric field between the rotor and stator. Fig.6.b shows a typical electric field in the proposed system (the voltages applied to upper, lower and besides objects are 50, 100 and 0 volts respectively).

(a) (b) Fig.6. (a) capacitive couplings in a stator slot (b) a simplified model with electric fields and the capacitive couplings

Considering the electric field between sides of the slot tooth (S1, S2), the effective area to calculate capacitive couplings between rotor and stator will decrease and Csr is d-ρ and Csr can be calculated as:

210sr gg

dC++ρρ−ε= (4)

Fig.7 show the results for 2-D, 3-D and mathematical analysis for Csr the results show that the calculations is accurate enough in design parameters of Table I.

Capacitive coupling between rotor and stator w inding (Cst)

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12Design number

Csr

(pF)

Csr-cal Csr-2DCsr-3D

Fig.7. 2-D and 3-D simulation results for Csr and its calculated values



6

With considering end-winding effects As Csr is very important in shaft voltage generation, a precise calculation of this capacitance is crucial. In all previous analysis, capacitances were calculated based on without consideration of end-winding effects. Calculation of the end-winding capacitances is rather complex because of diversity of end winding shapes and complexity of its geometry. A typical shape of the stator end-winding is considered to calculate the capacitances (see Fig.8.a). This model is very simple and just to address the effectiveness of this issue. There are two capacitors in this system between: shaft and end-winding (Csh-end), rotor frame and end-winding (Cr-end). A model of end-winding and the rotor for a single slot is shown in Fig.8.b in which the winding come out of the slot by length of L1 and bend with the length of L2 to go to another slot.

(a)

(b)

Fig.8. (a) structure of an IG with (b) a model for calculation of end-winding capacitances

For capacitance calculation purposes, the end-winding of a single slot can be approximately modelled with three surfaces (2 surfaces with width of W/2 and length of L1, a plate with width of W1 and length of L2). W is the width of winding at the slot and W1 is the width of winding at the end winding. To calculate the capacitance between these surfaces, structure of two surfaces with the voltage difference of V0 and the angle of ϕ needs is shown in Fig.9. The small gap between two surfaces is ρ1 and the length of the surface is ρ2. Based on [23], the capacitance can be calculated as:



7

⎟⎟⎠

⎞⎜⎜⎝

⎛ρ

ρ+ρϕ

ε=

1

120 Lnt

C (5)

ϕ

Fig.9. Two surfaces with the voltage difference of V0 and the angle of ϕ For the simplicity of the equation and the simulation ϕ is considered as π/2. End-winding capacitances can be calculated based on the Eq.5 as:

⎪⎪

⎩

⎪⎪

⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+

++π

ε=

⎟⎟⎠

⎞⎜⎜⎝

⎛ +π

ε=

gLgLL

LnW2

C

ggL

LnW2

C

1

21102end

101end

(6)

Therefore, the capacitor between rotor and the end-winding of a single slot can be calculated as:

⎟⎟⎠

⎞⎜⎜⎝

⎛+

++π

ε+⎟⎟

⎠

⎞⎜⎜⎝

⎛ +π

ε=+=− gL

gLLLn

W2g

gLLn

W2CCC

1

2110102end1endendr (7)

Where g is ( ρ+++ in21 ggg ) and W1 can be defined as ( ) ngR2 rotor +×π . By substitution of W1=k× W in Eq.7, one can have:

( )( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛

+×++

πε

= −− 1k1

k210

endrgLg

gLLLnW2C (8)

A shaft to end-winding capacitance is also exists which is equal to:

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

+πε=−

ggR

Ln

)Lk

L(

2Crotor

21

0endsh (9)

End-winding capacitance for an IG (Csr-end) is the sum of Equations 8 and 9.. The calculated capacitors should multiply by 2n (n is the number of slots) as the calculations are for a single slot and one side of the end-winding. In this section, only end winding capacitances has been simulated with the changes of L1, L2, W and shaft diameter (Dshaft) to validate the calculations. Table III shows a variety of design parameters for end-winding simulations and calculation. Fig.10.a, b, c and d show the calculated and simulated end-winding versus variation of L1 and L2 for two rotor radiuses of 1000 and 600mm with different winding widths (W). The results show that the equations are valid for a broad range of the design parameters. Therefore, total capacitive couplings between rotor and stator winding for an n slot generator structure can be calculated as:

( )( )

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ +

+π+⎟

⎟⎠

⎞⎜⎜⎝

⎛

+×++

π+

++ρρ−ε= −−

ggR

Ln

)Lk

L(4

gLggLLLnW4

ggdnC

rotor

21

1k1

k21

210totalsr (10)



8

Table III : design parameters for end-winding simulations Figure #

Rrotor (mm)

Dshaft (mm)

W (mm)

L1 (mm)

L2 (mm)

g (mm)

10.a 1000 200 150 variable variable 21 10.b 1000 200 200 variable variable 21 10.c 600 150 75 variable variable 14 10.d 600 150 125 variable variable 14

(a)

(b)

(c)



9

(d)

Fig.10. calculated and simulated end-winding capacitances versus variation of end-winding lengths (a) Rrotor=1000mm, W=150mm (b) Rrotor=1000mm,W=200mm (c) Rrotor=600mm, W=75mm (d) Rrotor=600mm, W=125mm Effective parameters on shaft voltage of an induction generator: In a variety of design parameters changes, the ratio between Csr and Crf is between 0.05 and 0.1. Also, the ratio between Cb and Cwr (α) is almost equal to 1. To simplify the calculation, β is defined as the ratio between end-winding Csr and without end-winding Csr. So, Csr-total is (1+β) times of Csr without end-winding which is calculated in Eq.4. By substituting equations 2&4 in Eq.1, the ratio between shaft voltage and common mode voltage can be written as:

ρ>−π++ρ+ρ−β+α+

ρ−β+≈ d,

)dn

r2)(gg()d)(1)(1(g

)d)(1(gVV

211

1

com

sh (11)

As shown in this equation, the effective parameters on shaft voltage are d, ρ, g1 and g2 and β. It is clear that g1 can not be changed for a large range of variation and can not be an effective parameter in shaft voltage reduction. Fig.11 shows the variation of Vsh/Vcom versus variation of d and g2 stator slot height of ρ=5 mm. According to simulation results in different parameters, Csr is an important capacitance in case of shaft voltage generation in an IG because it can be changed by variation of the design parameters while other capacitances has not such a freedom to change. So, exact calculation of this capacitance is very important in shaft voltage estimation based on the design parameters. An increment of stator slot tooth increases the shaft voltage while increasing the gap between the slot tooth and winding decreasing the shaft voltage.

Fig.11. Vsh/Vcom versus d and g2 (ρ=5 mm, x=1)



10

Conclusions This paper presented a mathematical analysis to calculate shaft voltage phenomena based on different design parameters. Analysis has been verified with a 2-D and 3-D FEM simulation results to explore effective designs in which a lowest possible shaft voltage can be achieved. Also, the range of variation has to meet the electromechanical and thermal considerations of the generator design. This information can be taken into account in the design procedure of the motor structure and the motor designer can choose design parameters which are a trade off between shaft voltage issue and other design considerations. References [1] P. Maki-Ontto, J. Luomi, “Induction motor model for the analysis of capacitive and induced shaft voltages” IEEE

International Conference on Electric Machines and Drives, pp.1653 –60, May 2005 [2] H.Akagi, T.Doumoto, “An approach to eliminating high-frequency shaft voltage and ground leakage current from an

inverter-driven motor” IEEE Transactions on Industry Applications, Volume 40, Issue 4, pp.1162-69, July-Aug. 2004 [3] D. Macdonald, W. Gray, “PWM drive related bearing failures”, IEEE Industry Applications Magazine, Vol.5, Issue 4,

pp.41-47, July-Aug. 1999 [4] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current attenuation techniques for use with PWM drives,"

Power Electronics, IEEE Transactions on, vol. 16, pp. 248-255, 2001. [5] Rajendra Naik,Thomas A. Nondahl, Michael J. Melfi, Rich Schiferl, Jian-She Wang, “Circuit Model for Shaft Voltage

Prediction in Induction Motors Fed by PWM-Based AC Drives” , IEEE Transactions on Industry Applications, vol. 39, no. 5, Sep/Oct 2007

[6] S. Chen, T. A. Lipo, and D. Fitzgerald, “Source of induction motor bearing currents caused by PWM inverters” Energy Conversion, IEEE Transaction on, vol. 11, pp. 25-32, 1996.

[7] S. Chen, T.A.Lipo, D. Fitzgerald, “Modelling of motor bearing currents in PWM inverter drives” IEEE Trans. on Industry Applications”, Vol. 32, Issue 6, pp. 1365-70, Nov.-Dec. 1996

[8] J. M. Erdman, R. J. Kerkman, D. W. Schlegel, and G. L. Skibinski, “Effect of PWM inverters on AC motor bearing currents and shaft voltages” , Industry Applications, IEEE Transactions on, vol. 32, pp. 250-259, 1996.

[9] D.Busse, J.Erdman, R.J.Kerkman, D.Schlegel, G.Skibinski, “Bearing currents and their relationship to PWM drives IEEE Transactions on Power Electronics” ,Volume 12, Issue 2, pp.243 - 252 March 1997

[10] O.Magdun, A. Binder, A. Rocks, O. Henze, “Prediction of common mode ground current in motors of inverter-based drive systems”, ACEMP '07, pp. 806-811, Sept. 2007

[11] Annette Muetze, Andreas Binder, “Techniques for Measurement of Parameters Related to Inverter-Induced Bearing Currents”, IEEE Transactions on Industry Applications, Vol. 43, No. 5, September/October 2007

[12] Annette Muetze, Andreas Binder, “Calculation of Influence of Insulated Bearings and Insulated Inner Bearing Seats on Circulating Bearing Currents in Machines of Inverter-Based Drive Systems”, IEEE Transactions on Industry Applications, Vol. 42, No. 4, July/August 2006

[13] A. Muetze, A. Binder, “Calculation of motor capacitances for prediction of the voltage across the bearings in machines of inverter-based drive systems” , IEEE Transactions on Industry Applications, vol. 43, no. 3, pp. 665-672, May/June 2007

[14] Annette Muetze, Andreas Binder, “Practical Rules for Assessment of Inverter-Induced Bearing Currents in Inverter-Fed AC Motors up to 500 kW”, IEEE Transactions on Industrial Electronics, vol. 54, No. 3, June 2007

[15] B. Mirafzal, G.L. Skibinski, R.M. Tallam, D.W. Schlegel, R.A. Lukaszewski, “Universal induction motor model With low-to-high frequency-response characteristics” IEEE Transactions on Industry Applications, vol. 43, no. 5, pp. 1233 - 1246, Sep/Oct 2007

[16] N.Idir, Y.Weens, M.Moreau, J.J.Franchaud, “High-Frequency Behaviour Models of AC Motors” IEEE Transactions on Magnetics, Volume 45, Issue 1, Part 1, pp.133 - 138, Jan. 2009

[17] M.M. Swamy, K.Yamada, T. Kume, “Common Mode Current Attenuation Techniques for Use with PWM Drives” IEEE Transactions on Power Electronics”, Volume 16, No. 2, March 2001

[18] Annette Muetze, Andreas Binder, Calculation of Motor Capacitances for Prediction of the Voltage Across the Bearings in Machines of Inverter-Based Drive Systems IEEE Transactions on Industry Applications, Vol. 43, No. 3, pp.665-672, May/June 2007

[19] Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Analysis of Shaft Voltage in a Doubly-fed Induction Generator”, ICREPQ’09, Valencia, Spain, April 2009

[20] Jafar Adabi, Firuz Zare, “Analysis, Calculation and Reduction of Shaft Voltage in Induction Generators”, ICREPQ’09, Valencia, Spain, April 2009

[21] Firuz Zare, “High frequency model of an electric motor based on measurement results”, Australian Journal of Electrical & Electronics Engineering (AJEEE), Vol 4, No 1, 2008, page 17-24.

[22] Hoda Ghoreishy, Firuz Zare, Hamid Hassanpour, “Controlling the Common-mode Voltage in Multilevel Inverters”, The International Journal of Engineering, Vol. 21, No. 3, September 2008

[23] Matthew N.O.Sadiku, “Elements of Electromagnetics” third edition, New York, Oxford University Press, 2001 [24] ANSYS® Academic Research, Release 11.0, Help System, Electromagnetic Field Analysis Guide, ANSYS, Inc



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In Dede, E (Ed.) Proceedings of the 13th European ...eprints.qut.edu.au/29786/1/c29786.pdf · using mathematical analyse, 2-D and 3-D Finite elements simulations- is to eliminate