Φ

Abstract-- This work presents a computation technique to analyze the high frequency over-voltage problem in long cable PWM drives. Differential Mode (DM) analysis for voltage and its resulting current along the cable is first developed in the frequency domain. The cable length, its electrical characteristics (R,L,G,C), the motor impedance, the inverter impedance as well as voltage rise and fall times are all considered. Then, by applying the boundary conditions at the cable ends and assuming the cable without losses, delay equations, describing the voltage at the inverter side as well as the voltage at the motor side, are developed in time domain. From these equations, an appropriate algorithm has been deduced to model the voltage at the motor terminals. This paper includes computation results, carried out using Matlab software, and important experimental outcomes on an industrial 5 kVA ASD prototype.

Index Terms-- Cables, electromagnetic interference (EMI), electromagnetic transient propagation, insulated gate bipolar transistors, over-voltage, pulse width modulation, variable speed drives.

I. INTRODUCTION

N many applications, PWM drives require long motor leads. Consequently, motors undergo over-voltages stress due to the traveling waves. These over-voltages increase

with the length of the feeding cables (up to a critical cable distance) and the dv/dt generated by the inverter IGBT switches. They can cause the destruction of the motor insulation, in particular in the early turns, and affect the common mode (CM) voltage. They can also cause partial discharges in the drive-to-motor cable thereby reducing its lifespan [1]. As it will be shown in this paper, they are also associated with oscillating currents in differential mode (DM) with a frequency range that can go up to several MHz (depending on the cable length). The paths of the CM current ICM and the DM current IDM are presented in Fig. 1. These currents can radiate EMI noises thus producing an adverse effect on electronic devices around the system.

In the last decade, the application of the traveling-wave theory to PWM motor-drives has been addressed by several researchers. Qualitative analysis relating to the over-voltage phenomenon has been reported in the literature [2-5] as well as its impact on the motor and/or the cable [1, 6-9]. Some mitigation techniques, especially to design output filters capable of matching the cable’s characteristic impedance, have

This research was made possible by the generous support of the Canada

Research Chair in Energy Conversion and Power Electronics. Saïd Amarir is with Canada Research chair in Electric Energy

conversion and power electronics, ‘École de technologie supérieure’, 1100 Notre-Dame Ouest, Montréal, Québec, H3C 1K3, Canada. (e-mail: said.amarir.1@ens.etsmtl.ca).

Kamal Al-Haddad is the holder of Canada Research chair in Electric Energy conversion and power electronics, École de technologie supérieure, 1100 Notre-Dame Ouest, Montréal, Québec, H3C 1K3, Canada. (e-mail: Kamal.Al-Haddad@etsmtl.ca).

also been proposed [10,11]. Some authors focused on the frequency modeling of the motor and resorted to known traveling wave methods to analyze over-voltage at the motor terminals [12,13]. The cable was often represented by multiple Pi equivalent sections. The cable eigen frequencies will increase with the number of Pi sections. But, as more sections are added, the step time must be very small to get accurate results. This implies convergence problems, as well as longer time simulations.

Recently, we have developed a precise modeling technique to evaluate the impact of high frequency over-voltages in long cable PWM drives [15,16,17]. This technique was based on a mathematical development that led to time domain sets of equations for the computation of the over-voltages not only at the motor terminals, but at any point along the cable. It does not require any representation of the ASD-system components.

This paper presents an alternative algorithm to analyze these high frequency overvoltages at the over all 3-phase of the cable, particularly at the motor terminals. This modeling takes into account the cable characteristics (type, length), the motor impedance, the inverter impedance and its voltage rise and fall times. This paper includes simulations and experiments that were carried out on an industrial 5 kVA ASD prototype using a 4-wire braided-shielded long cable. The measurements of the cable, inverter and motor required characteristics are investigated in detail. The computation results are then compared with the obtained experimental waveforms so as to validate the proposed technique.

II. SINGLE-PHASE REPRESENTATION

In a typical application, a converter feeds the inverter which is driven by a PWM unit that controls both the voltage and the frequency to ensure variable speed operation of the motor at constant flux. The motor is fed by a power cable made of 3, 4 or 5 conductors with or without a shield.

Fig.2 presents an ASD system with a shielded 4-wire cable, where the shield and the 4th conductor are connected together to the ground.

Fig.1 Motor-drive system: common and differential mode currents

Over-voltages computation algorithm for motors fed from Long Cable PWM Drives

Saïd Amarir, Member, IEEE, and Kamal Al-Haddad, Fellow, IEEE

I

554978-1-4244-1633-2/08/.00 ©2008 IEEE

The conduction state of each power switch is represented by a binary variable qi (i= 1,2,3), where qi = 1 indicates that the upper switch is ON and qi = 0 indicates that the lower switch is OFF. Considering that the switches of each inverter leg are operated in complementary switching, the ph-ph voltages at the inverter output are expressed, at steady state, by the equations hereafter:

( )1 2AB

v q q E= − ; ( )2 3BC

v q q E= − ; ( )1 3CA

v q q E= −Fig.2 shows an example of the inverter state variation when

the switching is from ‘110’ state to ‘100’ state. Initially, the IGBTs T1, T3 and T2 (resp. T4, T6 and T5) were ON (resp. OFF). The switching from ‘110’ state to ‘100’ state is produced when T3 switches off and T6 switches on. At the motor terminals, the voltage vRS will transient from 0 to E, vST

from E to 0 while vRT will stay at its initial value E; E being the dc bus voltage. Thus, for this transient, vRS determination will be sufficient to analyze the high frequency over-voltages at the over all 3-phase motor terminals since vST could be determined by vST = -vRS + vRT = -vRS + E.

So, at each state variation, the ASD system can be represented by the equivalent single-phase circuit as shown in Fig.3, where �S(t) is a single-phase PWM generator that models one of ph-ph inverter output voltages under no-load condition; eS (t) is the inverter output voltage when the cable feeds the motor. ZS is the inverter impedance and ZR the motor impedance at an operating point. The cable is represented by infinite infinitesimal single-phase portions with the length dx; � being the cable length. R and G respectively are the cable resistance and conductance per unit length. L and C are the equivalent phase inductance (including mutual inductance) and the ph-ph capacitance per unit length.υ (x, t) and i(x, t) represent the voltage and current vs. time t at a given point x units away from the sending end.

This proposed representation has the advantage of modeling the system in single-phase, which enormously facilitates the analysis of the voltage and current transients in the over all 3-phase circuit. To supplement this representation, delay equations are developed in time domain to express the relationship between the transient of the voltage vR (t) and the current iR (t) at the motor side and the voltage eS (t) and current iS (t) at the inverter side (and vice versa) taking into account the propagation time.

Fig.2. ASD-Motor : Switching from ‘110’ state to ‘100’ state

υ υ

Fig.3. ASD-Motor equivalent single-phase circuit representation

III. DIFFERENTIAL MODE ANALYSIS

Transient states are evaluated at each point along the cable by determining the voltage and current vs. time when each pulse is transmitted by the inverter. The equations describing the voltage and current at the point x, as a function of the circuit parameters are given in (1). Laplace Transform of �(x,t) and i(x,t) are given by equations (2); where Z(s) and Y(s) are given by (3).

( ) ( ) ( )

( ) ( ) ( )

, ,,

, ,,

x t i x tRi x t L

x ti x t x t

G x t Cx t

υ

υυ

∂ ∂�= − −�� ∂ ∂

�∂ ∂� = − −� ∂ ∂�

(1)

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

,, ,0

,, ,0

V x sZ s I x s Li x

xI x s

Y s V x s Cv xx

∂�= − +�� ∂

�∂� = − +� ∂�

(2)

( )( )

Z s R Ls

Y s G Cs

= +���

= +�� (3)

Before the transient (at t = 0), �(x,t) and i(x,t) don’t depend on x; moreover, if the cable is not charged then �(x,0)=0. Therefore, we can deduce the equations (4). If we note � as given by (5), from (4), (5) and (2) we deduce that the solution of this equation system is given by (6); V+(s) and V-(s) are Laplace transforms of incident voltage wave V+(t) and the reflected one V-(t) respectively. Current I(x,s) is made of a current Î(x,s) associated to the voltage traveling wave and a current K(s) due to the initial condition (i(x,0) ≠ 0). So, one can deduce the cable’s surge impedance as given by (7). From (6) and (7), Equation (8) is thereafter obtained.

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

2

2

2

2

,,

,, ( ) ( , 0)

V x sZ s Y s V x s

x

I x sZ s Y s I x s Y s Li x

x

∂=

∂

∂= −

∂

�������

(4)

( ) ( )2 Z s Y sγ = (5)

555

( ) ( ) ( )( )

( )( ) ( )( )

,

ˆ, ( , ) ( )

1ˆ( , )

x x

x x

V x s V s e V s e

I x s I x s K s

I x s V s e V s eZ s

γ γ

γ γγ γ

+ − −

+ − −

= +

= +

= − − +

���������

(6)

( ) 1/ 2

C

Z s R LsZ

G Csγ+� �= = � + �

(7)

( ) ( ) ( )

( ) ( ) ( )( ),

1ˆ ,

x x

x x

C

V x s V s e V s e

I x s V s e V s eZ

γ γ

γ γ

+ − −

+ − −

� = +�� = −��

(8)

IV. DEVELOPED DELAY EQUATIONS AND THEIR ASSOCIATED

EQUIVALENT CIRCUIT

The proposed approach results from a time domain analysis, assuming that, due to the high frequency, the cable losses could be neglected. By applying the boundary conditions at the cable ends, system of equations (8) implies (9) and (10). From (9) and (10) we deduce (11) and (12) respectively. Let us recall that for a lossless cable, γ becomes as expressed by (13), ZC by (14), the propagation velocity by (15) and the propagation delay by (16). So, if we note eS and iS (resp. vR (t) and iR (t)) the voltage and current versus time at the inverter side (resp. the motor side), equations (12) become (17). Equations (17) could be transformed back into a time domain solution to give the delay equations (18). From (18) we deduce easily (19) where vSh (t) and vRh(t) are historical voltages given by (20). The single phase circuit of fig. 2 is now assembled at every time t as shown in the equivalent circuit of Fig. 4.

( ) ( ) ( )

( ) ( ) ( )( )0,

10,

C

V s V s V s

Î s V s V sZ

+ −

+ −

� = +�� = −��

(9)

( ) ( ) ( )

( ) ( ) ( )( ),

1,

C

V s V s e V s e

Î s V s e V s eZ

γ γ

γ γ

+ − −

+ − −

� = +�� = −��

� �

� �

�

� (10)

( ) ( ) ( )( ) ( ) ( )0, 0, 2

0, 0, 2

C

C

V s Z Î s V s

V s Z Î s V s

+

−

� + =��

− =�� (11)

( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( )

, , 0, 0,

, , 0, 0,

C C

C C

V s Z Î s V s Z Î s e

V s Z Î s V s Z Î s e

γ

γ

−� + = +��

− = −��

�

�

� �

� � (12)

s LCγ = (13) C

LZ

C= (14)

1

LCν = (15) τ

ν= � (16)

( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( )

sR C R S C S

sR C R S C S

V s Z Î s E s Z Î s e

V s Z Î s E s Z Î s e

τ

τ

−� + = +��

− = −�� (17)

Fig.4 Equivalent circuit

( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( )

sR C R S C S

sR C R S C S

V s Z Î s E s Z Î s e

V s Z Î s E s Z Î s e

τ

τ

−� + = +��

− = −�� (17)

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

S C S R C R

R C R S C S

e t Z î t v t Z î t

v t Z î t e t Z î t

τ ττ τ

− + − = +���

− − − = −�� (18)

( ) ( ) ( )( ) ( ) ( )

R C R sh

S C S Rh

v t Z î t v t

e t Z î t v t

= − +���

= +�� (19)

( ) ( ) ( )( ) ( ) ( )

Sh S C S

Rh R C R

v t e t Z î t

v t v t Z î t

τ ττ τ

= − + −���

= − − −�� (20)

V. THE PROPOSED ALGORITHM

From equation (19) and (20), an appropriate algorithm has been developed to model the voltage at the motor terminals. This algorithm is presented in Fig. 5; it consists in 6 main steps: Step1: Required parameters are reported, namely: L, C, ZR, ZS. Other parameters are also implicitly reported (by calculation): ν, τ et ZC. The following variables are declared as vectors: vS, îS, eS, vR, îR, vRh, vSh. The calculation step Δt is set in order to have τ as an integer multiple of the calculation step Δt ( τ = kΔt; k integer). Step2: An indexation (defined by x (k) = x(kΔt) is applied for each of the previous variables. The initial conditions and the simulation time tsim are set. Step3: Time t is increased with one calculation step (“t = t + Δt“), as well as the index k (“k = k +1“). The value of time t is stored at each calculation step in another variable tout. Step4: While time t does not exceed τ, the values of

; ; ;R R Rh Sh

î v vυ will be kept at their initial values. This is due to

the fact that traveling voltage wave will not reach the motor terminals if the propagation time τ is not exceeded. Step5: When time t exceeds the propagation time τ, the calculation and storage will be proceeded for the following

variables respectively: Rh

v , S

î , Sh

v , R

î , eS and vR. The

formulas used in these calculations are referred directly to the algorithm of the Fig. 5. As shown, this step is divided into 6 sub-steps. Step6: While time t does not exceed the simulation time tsim, set in advance, return to step 3. Step7: When time t exceeds the simulation time tsim, the obtained motor terminal voltage vR (tout) is plot. The current îR

(tout) as well as the voltage eS (tout) and the current îS (tout) can also be plot.

556

�������������

�� τ

�����

���

�

�

���

( ) ( ) ( )1Rh R C Rv k v k t Z î k tτ τ+ = Δ − − Δ −

( ) ( ) ( )1 11 S Rh

SS C

v k v kî k

Z Z

+ − ++ =

+

( ) ( ) ( )1Sh S C Sv k e k t Z î k tτ τ+ = Δ − + Δ −

����������������������( ) ( ) ( )1 1 1S S S Se k v k Z î k+ = + − +

���������������������������;Rυ ;Rî ;Rhv Shv

�������������������������� �����

����� �������� �! �"# #!$"��� �

( ) ( ) ( )1 1 / //R Sh C Rî k v k Z Z+ = +

������������������������ ����� ������

�����������������������

����������������������

����������������������

�����������������������

%����&���'(��&���'(��&���'(��&���'

Fig.5 The proposed algorithm

The proposed algorithm was computed using Matlab tool. It was first validated using a real distributed parameters model (RDPM) of the cable, using SimPowerSystems software. RDPM is an acronym for ''Real Distributed Parameters line Model''. It is a representation of the cable by multiple RLC branches uniformly distributed along its length.

Parameters of a tested cable (see paragraph VI) are used. For a cable length of 50 ft, 100 units of LC (or RLC) circuits are used to build the RDPM.

Simulation results given in Fig. 6 show that the developed algorithm and the LC DPM agree well. In addition, the small difference on the voltage level, which we can notice in the result obtained with RLC DPM, shows that the cable resistance can be neglected. This confirms that the cable could be considered lossless.

VI. EXPERIMENTAL RESULTS

The experiments were carried out on a 5 kVA- ABB ASD-Motor. The system is made of a three-phase diode rectifier and a three-phase IGBT voltage inverter. The DC bus voltage is at 300V. The inverter uses third-generation IGBTs driven by a PWM Direct Torque Controller (DTC). The motor is 3 HP 380Y/220Δ, 1750 rpm, type ABB. The chosen cable (VFD TC 29501) is a 14 AWG, VFD 1000V UL 4-conductors Flexible cable with a tinned copper braid shield, made by BELDEN (manufacturer).

6.65 6.7 6.75 6.8 6.85 6.9 6.95 7 7.05 7.1

x 10-5

0

50

100

150

200

250

300

350

400

450

Time (s)

Vol

tage

(V

)

Zs = 0.2Zc; Zr = 9Zc; length=50 ft; E=300V; tr=300nsDeveloped algorithmLC RDPM

RLC RDPM

Fig. 6 Comparison result with the distributed parameters models. Simulation results

A. Measurement characteristics

A.1 Inverter parameter determination: At each pulse, the inverter behaves as a charged electrolytic DC bus capacitor connected in series with stray inductance and resistance. Its impedance was measured by applying its phase to phase output voltage to a pure unwounded resistance of 80 Ω. The obtained PWM voltage at this resistive load shows that the DC voltage is reduced from 300 V to 286 V. As a result, the inverter impedance could be retained at about 4 Ω. The rise time tr of the inverter output voltage is 232 ns (the fall time tf is about 300 ns), which is equivalent to dv/dt of 1293 V/μs and corresponds to an equivalent frequency of 1.37 MHz.

A.2 Motor impedance: The induction motor load surge impedance ZR to traveling waves with fast rising edges is not well documented and is difficult to measure. Authors in the literature usually mention that the motor reflection coefficient KR depends on the motor size. For small motors, the motor impedance ZR is higher, that implies higher KR (KR > 0.9 for motor size less than 25 hp). However, no precision is given on how to evaluate the value of ZR (in frequency domain). But, a high frequency motor model reported in [8] shows that at 1 MHz the motor could be considered as an ‘’open circuit’’. In fact, this work confirms by means of experiments that, for an infinite no-load cable, the same voltage is obtained at the motor terminals; the motor being fed by the same cable. This proves that the surge impedance of the cable ZC is very negligible compared to that of the motor ZR. In addition, taking into account the reflection coefficient expression, it is verified that the peak voltage at the cable ends varies very little for a ZR variation beyond 100 ZC. Simulations with ZR varying from 100 ZC to 1000ZC have given similar results.

A.3 Cable parameter measurements: In a typical application, the fourth conductor and the shield are connected together to the ground. Measurements were carried out for various frequencies up to 2 MHz, using a precise magnetic LCR analyzer (WAYN KERR, type 3260B). The cable representation per unit length is given in Fig. 7. In Fig. 7-a, LAA , LBB and LCC represent the phase inductance which are supposed to be equal, M is the mutual inductance between any two active conductors, MAg, MBg, and MCg represent the mutual inductances between active conductors and the shield, which is connected to the fourth conductor. But, since the tests were done in a Delta configuration, the sum of all phase currents is null, so that the MAg effect could be neglected.

557

Fig. 7. Typical cable representation (the 4th conductor is connected to the shield)

Fig. 7-b shows the capacitance Ccc between any two pairs of conductors, as well as the capacitance Ccg between each active conductor and the shield. In order to measure the line-to-ground capacitance measurement, the method suggested by [2] was resorted to. The measurements show a neglecting frequency dependency on the cable parameters between 0.8 MHz and 2MHz. This is why the obtained results at 1 MHz frequency were retained: R = 91mΩ/ft; LAA = 440 nH/ft; G = 32 nS/ft and C = 22 pF/ft. The mutual inductance was measured at 60 Hz by injecting a 10 A sinusoidal current into one phase and by measuring the induced voltage into the other phases. A coupling coefficient of k = 0.6536 was obtained. Then, Equations (21) allowed to deduce L = 152.41 nH/ft. Finally, using (15) and (14), ν and ZC are calculated: ν = 546 ft/μs and ZC = 83 Ω.

( )AAL L M 440 1 0.6536 152.41nH / ft= − = − = (21)

0.8 0.9 1 1.1 1.2 1.3 1.4

x 105

-200

-100

0

100

200

300

400

500

600

Time (s)

volta

ge (

V)

Belden cable Zr=100Zc, Zs=0.05Zc, tr=232 ns, cable length = 250 ft

x10-3

Fig. 8 Motor terminal voltage (ph-ph) Cable length of 250ft ; Peak voltage is 580V (1.933 p.u) - Computation result

1.935 1.94 1.945 1.95 1.955 1.96 1.965 1.97 1.975

x 10-3

-200

-100

0

100

200

300

400

500540

Time (s)

Vol

tage

(V

)

ABB ASD-Motor, DC bus = 300V, tr = 232 ns, Zs = 0.1Zc, Zr = 100 Zc, Belden cable l = 50 ft

Fig. 9 Motor terminal voltage (ph-ph); cable length of 50 ft; Peak voltage reaches 540 V (1.8 p.u) - Computation result

B. Computation and experimental results

Computation results were compared to experimental results assuming that at high frequency motor impedance equals at least ZR = 100 ZC and that of the inverter varies from ZS = 0.05 ZC to ZS = 0.1 ZC.

Fig. 8 and Fig. 9 present computation results for cable lengths of 250 ft and 50 ft respectively. Fig. 10 and fig. 11 present experimental results when a cable length of 250 ft is used. Fig. 12 gives experimental result for a 50 ft. cable. Comparing the peak voltage value and the frequency oscillation, we concluded that computation results of Fig. 8 and Fig. 9 are comparable respectively to experimental results of Fig. 11 and Fig. 12.

Fig. 10: (1) Motor terminal voltage (ph-ph); (2) Motor terminal voltage (Phase to shield voltage) ; cable length of 250 ft - Experimental result

Fig. 11 Motor terminal voltage (ph-ph); Cable length of 250 ft ; Peak voltage is 580 V (1.933 p.u) - Experimental result

Fig. 12 Motor terminal voltage (ph-ph); Cable length of 50 ft Experimental result

558

VII. CONCLUSION

A practical tool to model over-voltages in PWM motor drives has been presented. The proposed algorithm could be used to evaluate the risk of motor insulation deterioration that can be caused by severe overvoltages created by PWM voltage source inverters. It allows coordination between the ASD-Motor systems and the length (and type) of their feeding cables. Indeed, by using this technique, we can define, for each ASD-Motor system, the maximum cable length that should not be exceeded in order to protect the motor. We can also define, for each cable length, the optimum DC voltage and the dv/dt that should be respected taking into account the motor insulation. The proposed algorithm could be useful in design; it could also serve to put forth recommendation to protect the motor against over-voltage problems.

VIII. REFERENCES

[1] Lawrence A.Saunders; Gary L. Skibinski; Steve T.Evon; David L.Kempkes ‘‘Riding the Reflected Wave IGBT Drive Technology Demands New Motor and Cable Considerations ’’ IEEE IAS-Petroleum & Chemical Industry. Conference, Philadelphia, PA., Sept. 23-25, 1996 pp.75-84

[2] R. Kerkman, Senior Member, IEEE, D. Leggate, Member, IEEE, G. Skibinski, Member, IEEE ‘‘Interaction of Drive Modulation & Cable Parameters on AC Motor Transients’’ Industry Applications, IEEE Transactions on, Vol.33, N°3, pp.722-731, May-June 1997.

[3] Persson, E. ‘‘Transient effects in application of PWM inverters to induction motors’’ Industry Applications, IEEE Transactions on, Volume: 28. Issue: 5 , Sept.-Oct. 1992 Page(s): 1095 –1101

[4] v. Jouanne, A.. Enjeti, P. Gray, . ‘‘The effect of long motor leads on PWM inverter fed AC motor drive systems’’ Applied Power Electronics. Conference and Exposition, 1995. APEC '95. Conference Proceedings 1995.Tenth Annual Part: 2 , 1995 Pages: 592 -597 vol.2

[5] C. J. Melhorn and L. Tang, ‘‘Transient effects of PWM ASDs on standard squirrel cage induction motors, ’’ Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, 1995, pp.2689-2695 vol.3

[6] R.H.Daugherty, C.H Wennerstrom,. ‘‘Need for industry standards for AC induction motors intended for use with adjustable frequency control,’’ Industry Applications, IEEE Transactions on, Volume: 27 Issue: 6 , Nov.-Dec. 1991, pp. 1175 –1185

[7] G. Skibinski, D. Leggate and R. Kerkman, ‘‘Cable characteristics and their influence on motor over-voltages,’’ Applied Power Electronics Conference and Exposition, 1997. APEC '97 Conference Proceedings 1997., Twelfth Annual, 1997, pp.114-121 vol.1

[8] C. J. Melhorn and L. Tang, ‘‘Transient effects of PWM ASDs on standard squirrel cage induction motors,’’ Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, 1995, pp.2689-2695 vol.3

[9] J. M. K. Erdman, R.J.; Schlegel, D.W.; Skibinski, G.L. ‘‘Effect of PWM inverters on AC motor bearing currents and shaft voltages,’’ Industry Applications, IEEE Transactions on, Vol.32, N°2, Mar-Apr, 1996, pp.250-259

[10] S. Ogasawara, H. Akagi, ‘‘Analysis and reduction of EMI conducted by a PWM inverter-fed AC motor drive system having long power cables,’’ Power Electronics Specialists Conference PESC, IEEE 31st Annual Vol. 2, 18-23 June 2000 pp. 928 – 933.

[11] H. Akagi, S. Tamura, S.; ‘‘ A Passive EMI Filter for Eliminating Both Bearing Current and Ground Leakage Current From an Inverter-Driven Motor,” Power Electronics, IEEE Transactions on Volume 21, Issue 5, Sept. 2006, pp.1459 – 1469.

[12] G. Skibinski,; R. Kerkman, D. Leggate, J. Pankau, D. Schlegel, ‘‘ Reflected wave modeling techniques for PWM AC motor drives,’’ Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual Vol. 2, 15-19 Feb. 1998, pp.1021 - 1029

[13] G. Oriti, A.L. Julian, ‘‘Application of the transmission line theory to the frequency domain analysis of the motor voltage stress caused by PWM inverters,’’ Proc. of Industry Applications Conference, 39th IAS Annual Meeting, vol.3, 2004, pp. 1996-2002

[14] G. Skibinski, R. Tallam, R. Reese, B. Buchholz, R. Lukaszewski, ‘‘Common Mode and Differential Mode Analysis of Three Phase Cables for PWM AC Drives,’’ Proceedings of IAS Annual Meeting 2006, pt. 2, p 9 pp. vol.2

[15] S. Amarir, K. Al-Haddad, ‘‘A new approach to analyze the overvoltages due to the cable lengths and EMI on adjustable speed drive motors,’’ 2004 IEEE 35th PESC Record - IEEE Annual Power Electronics Specialists Conference, v 5, PESC04, 2004, pp. 3964-3970

[16] Amarir, S., Al-Haddad, K (2006) ‘A New High Frequency Modeling Technique of Travelling Waves in Long Cable PWM Drives’ IEEE Industrial Electronics, IECON 2006 - 32nd Annual Conference on Publication Date: Nov. 2006, page(s): 1119-1124

[17] Amarir. S., Al-Haddad, K (2007) ‘A Modeling Technique to Analyze the Impact of Inverter Supply Voltage and Cable Length on Industrial Motor-Drives’ IEEE transactions on Power Electronics, Volume 23, Issue 2, March 2008 Page(s): 744-752.

IX. REFERENCES

Saïd Amarir (S’07) was born in Casablanca- Morocco in 1966. He received a state engineering diploma from ‘École Nationale Supérieure d’Électricité et de Mécanique’ (ENSEM), Hassan II University, Casablanca, Morocco in 1992, and the M.S. degree from ‘École de Technologie Supérieure (ÉTS)’, Québec University, Montreal, QC, Canada in 2003; where he is currently pursuing his Ph.D. degree in Electrical Engineering. He has been lecturing Power

Electronics at the same university (ÉTS) since 2001. After having worked for several years as an engineer for different industrial companies whose activities are in the electrical engineering field, he returned to the university to do research in Power Electronic systems. His field of interest is modeling, analysis, design and control of power electronic converters. His areas of research include motor drives and the interaction between power electronic converters and motors. Saïd Amarir is a member of IEEE and of the Order of Quebec Engineers: ‘Ordre des Ingénieurs du Québec’.

Kamal Al-Haddad (S’82-M’88-SM’92-FM’07) was born in Beirut, Lebanon, in 1954. He received the B.Sc.A. and the M.Sc.A. degrees from the University of Québec à Trois-Rivières, Canada, and the Ph.D. degree from the Institut National Polythechnique, Toulouse, France, in 1982, 1984, and 1988, respectively. From June 1987 to June 1990, he has been a professor at the Engineering Department, Université du Québec à Trois Rivières. In June 1990, he joined the

teaching staff as a professor of the Electrical Engineering Department of the École de Technologie Supérieure, Montreal, Canada. Since 2002, he has been the holder of Canada Research Chair In Electric Energy Conversion and Power Electronics CRC-EECPE. He has supervised more than 60 Ph.D. and M. Sc.A. students working in the field of power electronics and has been the director of graduate study programs at the ETS from1992 till 2003. His fields of interest are high efficient static power converters, harmonics and reactive power control using hybrid filters, switch mode and resonant converters including the modelling, control, and development of prototypes for various industrial applications in electric traction, power supply for drives, telecommunication etc. He is a co-author of the Sim Power System software of Matlab. He is a consultant and has established very solid link with many Canadian industries working in the field of power electronics, electric transportation, aeronautics, and telecommunications. He is the chief of ETS-Bombardier Transportation North America division, a joint industrial research laboratory on electric traction system and power electronics. He has supervised more than 60 Ph.D. and M. Sc.A. Students and coauthored more than 250 Transactions and conference papers. He is a life member of the Circle of Excellence of the University of Quebec, and received the outstanding researcher award from ETS in 2000. He is very active in the IEEE Industrial Electronics society where he is an Adcom member and serves as an associate editor of the IEEE Transactions on industrial Electronics and guest editor of the special issue on hybrid and active filters.

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