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A Transformer Assisted Zero Voltage Switching Scheme ... - Ivo Barbi

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A <strong>Transformer</strong> <strong>Assisted</strong> <strong>Zero</strong> <strong>Voltage</strong> <strong>Switching</strong><br />

<strong>Scheme</strong> for the Neutral-Point-Clamped (NPC) Inverter<br />

Xiaoming Yuan<br />

Power Electronics and Electrometrology Laboratory<br />

Swiss Federal Institute of Technology Zurich<br />

ETH-Zentrum / ETL, CH-8092 Zurich<br />

Switzerland<br />

Phone: +41-1-632-6973 Fax: +41- 1-632-1 212<br />

<strong>Ivo</strong> <strong>Barbi</strong><br />

Power Electronics Institute<br />

Federal University of Santa Catarina<br />

P. 0. Box: 51 19,88040-970, Florianopolis-SC<br />

Brazil<br />

Phone: +55-48-33 1-9204 Fax: +55-48-234-5422<br />

Abstruct-This paper proposes a transformer assisted<br />

PWM zero voltage switching Neutral-Point-Clamped (NPC)<br />

inverter. With the assistance of a transformer assisted small<br />

rating lossless auxiliary circuit, the main switches work<br />

with zero voltage switching without suffering from any<br />

voltage/current spikes, under simple explicit control. The<br />

technique allows for higher operating frequency and better<br />

device utilization of the NPC inverter. Operation, analysis,<br />

designing as well as testing results from a 7kW prototype<br />

are presented in details.<br />

when possible mismatch between the DC link storage<br />

capacitors are taken into account [12]. Protection of the<br />

auxiliary devices from voltage spikes during their reverse<br />

recoveries constitutes the other difficulty of the circuit.<br />

Moreover, the auxiliary devices in the circuit are subject<br />

to 1.5 times of the main devices blocking voltage, raising<br />

significantly the cost for the auxiliary circuit.<br />

I. INTRODUCTION<br />

Neutral-Point-Clamped (NPC) inverter [ 13 has<br />

been playing an growing role in the recent decade in drive<br />

[2] [4] and power system applications [3], due to the<br />

expanded capacity with the existing devices without the<br />

problematic series association, as well as the reduced<br />

output harmonics. To limit the dv/dt and di/dt rates of<br />

change when GTO is used, different snubber schemes<br />

utilizing either RCD snubbers [4] or low-loss snubbers [5]<br />

[6] have been developed, where the switching frequency<br />

is limited to a few hundreds Hz due to the significant<br />

snubber loss. Regenerative snubbers avoid the loss at the<br />

expense of the considerable hardware complexity [7],<br />

which includes even baby snubbers €or the recovery<br />

choppers [SI. Moreover, snubbers either dissipative or<br />

regenerative, suffer from such other problems as<br />

voltagdcurrent spikes, series inductor loss, as well as the<br />

adverse effects from the snubbing diodes etc..<br />

Several previous publications have resorted to soft<br />

switching techniques for snubbing of NPC inverter.<br />

Besides the early thyristor three-state inverter [9] which<br />

works actually with zero current switching, zero voltage<br />

switching realized with resonant DC link and Auxiliary-<br />

Resonant-Commutated-Pole-Inverter (ARCPI) have also<br />

been investigated [ 101 [ 111.<br />

In particular, the ARCPI NPC inverter [ll], as<br />

shown in Fig. 1, is deemed a more promising scheme for<br />

high power applications due to the small power auxiliary<br />

circuit and full PWM operation capability. However, the<br />

scheme requires complicated current monitoring and<br />

controlling to ensure zero voltage switching, especially<br />

I,<br />

T<br />

Fig. 1. Configuration of the ARCPI NPC inverter proposed in [I I].<br />

T I<br />

Fig. 2. Configuration of the proposed transfonner assisted PWM zero<br />

voltage switching pole NPC inverter.<br />

0-7803-5160-6/99/$10.00 0 1999 IEEE. 1259


As shown in Fig. 2, this paper proposes an alternative<br />

zero voltage switching scheme for the NPC inverter. By<br />

setting the transformer ratio k (k=N2/N I ,=NdN 12) to less<br />

than 1/4 according to the potential resonant loop losses,<br />

the proposal requires no additional monitoring or<br />

controlling circuit for ensuring zero voltage operation.<br />

Moreover, as the auxiliary devices are now all clamped to<br />

the rails by the NPC configuration, overvoltage protecting<br />

circuit is no longer necessary. Besides, all the auxiliary<br />

devices now block the same voltage as the main devices,<br />

rendering the circuit more practically interesting.<br />

Operation, analysis, designing and testing of the circuit<br />

will be presented in this paper.<br />

11. CIRCUIT OPERATION<br />

Neglecting the affects from the second order circuit<br />

parasitics as stray inductances and capacitances etc., the<br />

whole circuit can be decoupled into two independent zero<br />

voltage switching poles, as shown in Fig. 3(a)(b). The DC<br />

link neutral potential is assumed stable and is not<br />

addressed further for the sole purpose of this paper.<br />

For the first pole, as shown in Fig. 3(a), the output can<br />

be switched between the plus rail and the zero rail by<br />

gating SI and S3 alternatively, while S2 is always ON and<br />

S4 is always OFF in the main circuit, Sa4 is always ON<br />

and Sd is always OFF in the auxiliary circuit. As a result,<br />

for the main circuit, DcI serves as the freewheeling path of<br />

the down-arm, and S3 in series with Dc2 serves as the<br />

forward path of the down-arm. In the meanwhile, Cr2 sees<br />

always zero voltage whereas Cr3 serves as the snubbing<br />

capacitance for the down-arm. Moreover, for the auxiliary<br />

circuit, DaCl serves as the freewheeling path of the downarm,<br />

and Sal in series with Dac2 serves as the forward path<br />

of the down-arm,<br />

For second pole, as shown in Fig. 3(b), the output can<br />

be switched between the zero rail and the minus rail by<br />

gating S2 and S4 alternatively, while S3 is always ON and<br />

SI is always OFF in the main circuit, and Sal is always<br />

ON and Sa3 is always OFF in the auxiliary circuit.<br />

Similar to the first pole, in the main circuit, Dc2 forms the<br />

freewheeling path of the up-arm and S2 in series with DcI<br />

forms the forward path of the up-arm. Cr3 sees always<br />

zero voltage whereas Cr2 serves as the snubbing<br />

capacitance for the up-arm. Also, in the auxiliary circuit,<br />

Dac2 forms the freewheeling path and Sa4 in series with<br />

Dacl forms the forward path of the up-arm.<br />

Evidently, both of the decoupled circuits work as a<br />

transformer assisted PWM zero voltage switching pole<br />

inverter [13]. In Fig. 3(a), auxiliary switches Sal and Sa3<br />

assist the commutations of SI and S3 respectively in the<br />

first zero voltage switching pole. On the other hand, in<br />

Fig. 3(b), auxiliary switches Sa2 and Sa4 assist the<br />

commutations of SL and S4 respectively in the second zero<br />

voltage switching pole.<br />

As operation of one pole is identical to the other, only<br />

the operation of the first pole will be described. Assume<br />

that for each snubbing capacitance, a zero voltage<br />

detecting circuit is installed across it for releasing the<br />

gating signal of its corresponding main device (CrI-Sl;<br />

Cr2-S2; Cr3-S3; Cr4-S4)[ 131. Assume further that the<br />

transformer ratio k is set less than 1/4 that ensures the<br />

pole voltage swinging to the rail level during the<br />

commutation resonance with the presence of commutation<br />

loop losses [13]. Referring to Fig. 4 for the commutation<br />

step diagrams and Fig. 5 for the predicted commutation<br />

waveformes, the commutations between SI(Dl) and S3<br />

during a switching cycle under negative load current will<br />

proceed in the steps described as following.<br />

(a) First zero voltage switching pole of the<br />

transformer assisted PWM zero voltage switching NPC inverter.<br />

SZ is always ON, S4 is always OFF in the main circuit.<br />

Sad is always ON, Sa* is always OFF in the auxiliary circuit.<br />

n<br />

(c) Second zero voltage switching pole of the<br />

transformer assisted PWM zero voltage switching NPC inverter.<br />

S, is always ON and SI is always OFF in the main circuit. S,, is always<br />

ON and Sa3 is always OFF in the auxiliary circuit.<br />

Fig. 3. Decoupling of the transformer assisted PWM zero voltage<br />

switching pole NPC inverter into two independent poles.<br />

1260


Step 1 (to-tl): Circuit steady state. Freewheeling diodes<br />

D2 and DI carry the load current. Circuit output is<br />

connected to the plus rail.<br />

Step 2 (tl-t2): Turn off SI and turn on Sa,<br />

simultaneously at tl, leading to conduction of the auxiliary<br />

diode DI2. A voltage source valued at kVd, is induced on<br />

N2. Currents in D1 and D2 start decreasing.<br />

Step 3 (t2-t3): D1 and D2 becomes blocking at t2. CrI is<br />

then charged and Cr3 is discharged.<br />

Step 4 (t3-t4): CrI voltage rises to vd& at t3. Currents<br />

transfer from C,, and Cr3 to DCI instantly. S3 gating signal<br />

is then released by the zero voltage detecting circuit<br />

installed across Cr3.<br />

Step 5 (t4-t5): Resonant inductor current iLr decreases<br />

to the load current level iload at t4. D,I becomes blocking<br />

and S3 starts conduction.<br />

Step I: b-tl (step 9: ts-b) Step 2: tl-tz Step 3: tz-t3<br />

Step 7: t& Step 8: t7-k Step 9 t&<br />

Fig. 4. Step diagrams for the commutations between SI and S3 when the load current is negative. (k is the transformer ratio, k=NlNl,=N2/N12


sa3<br />

f<br />

<strong>Switching</strong> period: T=l /f,<br />

f Commutation process SI to s, , Commutation process ~3 to SI .C:<br />

t<br />

S,I<br />

s3<br />

SI<br />

V,,,<br />

WSt,I>!)<br />

ISl",,<br />

. . ,<br />

. . ,<br />

. . ,<br />

il,<br />

VS,<br />

lw . . .,<br />

. . . . 8<br />

, I<br />

I<br />

4, fl 12 13 t4 15 k t7 t cu<br />

Fig. 5. Predicted theoretical waveforms for the commutations between St and Ss in the first zero voltage switching pole<br />

with negative load current during a switching cycle.<br />

Step 6 (t&: Resonant inductor current iLr and the<br />

auxiliary diode current in DI2 decreases to zero at t5. Sal<br />

gating signal can be withdrawn. Circuit reaches another<br />

steady state. The output is connected to the zero rail. S3<br />

and Dc2 carry the load current.<br />

Step 7 (t6-t7): Turn off S3 and turn on Sa3 at k, leading<br />

to conduction of the auxiliary diode DI1. An induced<br />

voltage source of kVdc appears on N2. Cr3 is charged and<br />

CrI is discharged.<br />

Step 8 (t&: Crl voltage declines to zero at t,.<br />

Currents in C,, and CrS transfer to D1 instantly. SI gating<br />

signal is released by the zero voltage detecting circuit<br />

installed across it.<br />

Step 9 (tg-tg): Currents in the resonant inductor Lr and<br />

the auxiliary diode DI I extinct at t8. Sa3 gating signal can<br />

be withdrawn. Circuit returns to the original state. D2 and<br />

DI carry the load current. Circuit output is connected to<br />

the plus rail.<br />

Note that the inner device S3 may not work exactly at<br />

zero voltage switching in practice when the parasitic<br />

inductances and capacitances of the circuit are taken into<br />

account. Assume a parasitic inductance with the neutral<br />

rail and a negative load current flowing through S3 and<br />

Dc2 connecting the output to the neutral rail. Now, to<br />

transfer the load current from S3 and Dc2 to D2 and D1, the<br />

neutral rail current will decrease leading to discharging of<br />

the resonant capacitor Cr4 via Dc2. Upon reaching the<br />

steady state (D2 and DI conducting), both Cn and Cr4 will<br />

be charged by C2 via the parasitic inductance of the<br />

neutral rail. Consequently, voltage across CR will not be<br />

zero. Thus for the next commutation, the turn-on of S3<br />

will see the discharging of Cr2 and will not exactly be<br />

zero voltage switching as a result.<br />

Analogously, inner device S2 will see the same<br />

problem in the second pole when load current is positive.<br />

This problem is essentially resulted from the<br />

topological drawback of the NPC inverter--the inner two<br />

devices of a NPC leg are actually not directly clamped as<br />

in the two level inverter. For example, it is S3 in series<br />

with D,z that is clamped to C1, rather than S3 itself. In<br />

the same sense, it is S2 in series with DcI that is clamped<br />

to C2, rather than SI itself. Therefore, when S3 and S4 are<br />

both OFF, S3 can block higher voltage than S4 and Dc2 can<br />

see some voltage rather than zero. Or, alternatively, when<br />

SI and S2 are both OFF, S2 can block higher voltage than<br />

SI and DcI can see some voltage rather than zero.<br />

Obviously this problem can not be removed without<br />

changing the main circuit topology. However, it can be<br />

mitigated by careful busbar designing.<br />

111. CIRCUIT ANALYSIS AND DESIGNING<br />

Since each pole works in the same way as the<br />

transformer assisted PWM zero voltage switching pole<br />

inverter, the characteristics of the transformer assisted<br />

PWM zero voltage switching pole inverter applies also in<br />

the current circuit. Under the following assumptions, the<br />

commutation duration, the resonant inductor peak current<br />

and the resonate inductor RMS current (averaged over the<br />

switching cycle) in relation to load current, transformer<br />

ratio and switching cycle are shown in Fig. 6, Fig. 7 and<br />

Fig. 8 respectively. Details of the mathematical process<br />

have been included in [ 131.<br />

I262


16.893<br />

3.704<br />

14.601<br />

3.142<br />

12.309<br />

2.58<br />

w5 I<br />

10.017<br />

2.01 7<br />

7.725<br />

1.455<br />

5.433<br />

0.893<br />

3.142<br />

0 0.5 I 1.5 2 2.5 3<br />

-<br />

iload<br />

0.33<br />

0 0.5 1 1.5 2 2.5 3<br />

iload<br />

(a) Diode to switch commutation<br />

(b) Switch to diode commutation<br />

Fig. 6. Variations of commutation durations t5, and tg6 with load current and auto-transformer ratio.<br />

3.65<br />

0.65<br />

3. I25<br />

0.549<br />

2.6<br />

-<br />

ibi 2.075<br />

0.447<br />

0.346<br />

I .55<br />

0.244<br />

1.325<br />

0.143<br />

ns "._<br />

0<br />

0.5 I 1.5 2 2.5 3<br />

0.041<br />

0 0.5 1 1.5 2 2.5<br />

(a ) Diode to switch commutation (b ) Switch to diode commutation<br />

Fig. 7. Variations of the resmant inductor peak currents with load current and auto-transformer ratio.<br />

I .42<br />

0 136<br />

I .2<br />

0.114<br />

.D. k=0.25, _T=90<br />

'-* k=O. 15. T=45<br />

0.91<br />

0092<br />

__<br />

'Lmrms 0.069<br />

0.5:<br />

. . . . . . . .<br />

0.047<br />

0.3<br />

0.024<br />

0.a<br />

038 0.53 1.03 1.52<br />

-<br />

2.01 2.Sl 3<br />

iload<br />

0.002<br />

0.0110.509 1.008 1.506 2.004 2.502<br />

-<br />

'load<br />

(a) diode to switch commutation<br />

(b) switch to diode commutation<br />

Fig. 8. Variations of the resonant inductor RMS currents with load current, transformer ratio and switching cycle.<br />

1263


Snubbing capacitance CrI=Cr2=Cr3=Cr4=Cr, resonant<br />

frequency cw=lIm,<br />

0<br />

and switching cycle T. Unit current j=q,/(& /2),<br />

-<br />

unit voltagev=v/&.//2), unit time t = tu,.<br />

resonant impedance z =r~,<br />

Circuit parasitics, device switching delays, losses etc.<br />

are neglected in the analysis.<br />

From Fig. 6, for diode to switch commutation, the<br />

commutation duration increases with load current but<br />

decreases with transformer ratio. For switch to diode<br />

commutation, it decreases with both load current and<br />

transformer ratio. From Fig. 7, for diode to switch<br />

commutation, the peak resonant inductor current<br />

increases with load current but decreases with transformer<br />

ratio. For switch to diode commutation, it decreases with<br />

both load current and transformer ratio. Moreover, from<br />

Fig. 8, the resonant inductor Rh4S current resulted from<br />

diode to switch commutation increases with load current,<br />

but decreases with transformer ratio and switching cycle.<br />

The resonant inductor RMS current resulted from switch<br />

to diode commutation, however, decreases with load<br />

current, transformer ratio and switching cycle.<br />

The reverse proportional relation of the commutation<br />

duration, resonant inductor peak current and resonant<br />

inductor RMS current with load current for switch to<br />

diode commutation highly justifies the auxiliary switch<br />

gating strategy in this paper to trigger the corresponding<br />

auxiliary switch simultaneously with the main switch not<br />

only for diode CO switch commutation where such<br />

triggering is indispensable for achieving zero voltage<br />

switching, but also for switch to diode commutation where<br />

such triggering becomes dispensable above certain load<br />

current level. Such triggering strategy facilitates<br />

significant control simplification while the extra loss so<br />

accrued during switch to diode commutation is negligible.<br />

Note that the auxiliary switch RMS current equals the<br />

diode to switch commutation component for one load<br />

current direction. It equals the switch to diode<br />

commutation component for the other load current<br />

direction. The peak current and RMS current stresses of<br />

the auxiliary diode in the transformer primary are given<br />

accordingly from the transformer ratio.<br />

For designing of the auxiliary circuit, the transformer<br />

ratio should be set less than 114 dependent on the actual<br />

resonant loop resistance to ensure the pole voltage<br />

swinging to the rail level during the commutation<br />

resonance. This requirement is hard and allows no<br />

bargaining. In addition, the resonant capacitance can be<br />

designed as per the device turn-off loss and the thermal<br />

condition associated. Resonant inductance can then be<br />

decided according to the accepted resonant circuit RMS<br />

stress based on Fig. 8, taking into account the system<br />

operating frequency. Rating of the auxiliary device can be<br />

made according to the auxiliary device RMS current<br />

stress, and the peak current stress as well given in Fig. 7.<br />

Gating signal width for the auxiliary switch must<br />

cover the maximum commutation duration given in Fig. 6<br />

and remains constant over the low frequency cycle. In the<br />

meantime, the minimum pulse width in the inverter PWM<br />

pattern should not be less than this duration. The next<br />

commutation should not start before the conclusion of the<br />

previous commutation.<br />

On the other hand, transformer designing can be<br />

based on the knowledge of commutation (magnetization)<br />

duration and the RMS resonant inductor current stress.<br />

With peak and RMS resonant inductor currents<br />

information, the resonant inductor can be designed.<br />

IV. EXPERIMENTATION RESULTS<br />

A 7kW IGBT half bridge NPC inverter prototype has<br />

been built. The specifications of which are given in Table<br />

1. Circuit parameters of the prototype are: Lr=12uH,<br />

Crl=CiL=Cr3=Cr4=0. luF, k=0.2. Auxiliary switch gating<br />

signal width is set at 14.4uS. Maximum and Minimum<br />

PWM widths are set at 136.8uS and 16.8uS respectively.<br />

Main switches S1-S4 and auxiliary switches Sal-Sa4<br />

used are semikron SKMSOGB123D (1200V/50A).<br />

Auxiliary diodes Dc,-DCz and DacI-Da,z, used are ultra-fast<br />

HFA30T60C (600V/30A). Inverter output is installed<br />

with a second order filter Lf=l.45mH and Cf=12uF.<br />

Four 350V/3300uF capacitors are used at the DC link.<br />

It is worth mentioning that the prototype is modulated<br />

with normal sub-harmonic PWM pattern under which the<br />

neutral potential has been proved to be self-balancing<br />

when the load is not pure-reactive [14]. No specific<br />

measures are taken for stabilizing the neutral potential.<br />

Four simple zero voltage detecting circuits [14] are<br />

employed to interface the four semikron SKHlO drivsrs to<br />

the main IGBT devices for releasing the gating signals<br />

once the detected voltage reaches zero.<br />

Fig. 9 shows the main device S3 voltage and current<br />

waveformes during S3 to DI and DI to S3 commutations.<br />

Obviously, the main device works with zero voltage turnon<br />

and capacitive turn-off. No voltage/current spikes are<br />

produced in the process. In the meanwhile, Fig. 10 shows<br />

the waveforms of the auxiliary device Sa3 voltage and<br />

current as well as the load current during D,, to SI<br />

commutation. With a predicted commutation duration of<br />

7.2uS according to Fig. 6(a) and a predicted peak<br />

resonant current of 47.8A according to Fig. 7(a), at load<br />

current of 20A, the experimental values ace 6.7uS and<br />

40.5A respectively. The analysis results in Section I11 are<br />

well validated. Errors are due to the losses in the<br />

commutations neglected in the analysis.<br />

1264


REFERENCES<br />

DC input<br />

voltage<br />

output<br />

power<br />

V&= Output V, Modulation M=<br />

8OOV voltage =164V index 0.62<br />

P,= Load I,,,, <strong>Switching</strong> f,=<br />

7kW current =42.5A frequency 6.5kHz<br />

loOV/DIv. IOA/DIv, 4uSDiv<br />

Fig. 9. Experimental waveforms of the main switch S3 voltage and current<br />

during S, to DI commutation and DI to S3 commutation..<br />

, . . :<br />

:................................................................. .,.... .................. . .<br />

. .<br />

I ....:.......................................<br />

Fig. 10. Experimental waveforms of the auxiliary switch Sa3 voltage and<br />

current as well as the load current during D,I to SI commutation.<br />

V. CONCLUSIONS<br />

The analysis and experimentation presented verify<br />

that the proposed small rating zero current switching<br />

auxiliary circuit guarantees the zero voltage switching of<br />

the NPC main switches, without requiring any extra<br />

monitoring or controlling and without incurring any<br />

voltagdcurrent spikes or modulation constraints. The<br />

auxiliary switches block the same voltage as the main<br />

switches. The scheme can be used to advantage for high<br />

frequency application of the GTO NPC inverter where<br />

conventional snubbers are not expected to offer adequate<br />

performance.<br />

[l] A. Nabae, I. Takahashi, and A. Akagi, “A New<br />

Neutral-Point Clamped PWM Inverter”, IEEE Trans.<br />

Ind. App., Vol. 19, No. 5, Sep./Oct. 1981, pp. 518-<br />

523.<br />

H. Stemmler, “Power Electronics in Electric Traction<br />

Applications”, Record of IEEE IECON, 1993, pp.<br />

707-713.<br />

B. A. Renz, A. J. F. Heri, A. S. Mehraban, J. P.<br />

Kessinger, C. D. Cchauder, L. Gyugyi, L. J. Kovalsky<br />

and A. A. Edris, “World’s First Unified Power Flow<br />

Controller on The AEP System”, CIGRE Paper 14-<br />

107, 1998.<br />

[4] A. Steimel, “Electric Railway Traction in Europe”,<br />

IEEE Industry Applications Magazine, Nov./Dec.<br />

1996, pp. 7-17.<br />

[5] T. Salzmann, G. Kratz, C. Daubler, “High Power<br />

Drive System with Advanced Power Circuitry and<br />

Improved Digital Control”, IEEE Trans. on Ind. App.,<br />

Vol. 29, No. 1, Jan./Feb. 1993, pp. 168-174.<br />

[6] H. Schambock and K. Schiftner, “A New Snubber for<br />

GTO Applications with Energy Recovery by an<br />

ActivePassive Circuit”, Record of EPE Conference,<br />

1989, pp. 707-711.<br />

[7] H. Okayama etc., “Large Capacity High Performance<br />

3-Level GTO Inverter System for Steel Rolling Mill<br />

Drives”, Record of IEEE IAS, 1996, pp. 174-179.<br />

[8] J. A. Tarfiq and Y. Shakweh, “New Snubber Energy<br />

Recovery <strong>Scheme</strong> for High Power Traction Drive”,<br />

Record of IPEC-Yokohama, 1995, pp. 825-830.<br />

[9] J. Holtz and S. Stadtfeld, “An Economic Very High<br />

Power PWM Inverter for Induction Motor Drives”,<br />

Record of EPE Conference, 1985, pp. 3.375-3.380.<br />

[lo] W. Yi and G. H. Cho, “Novel Snubberless Three-<br />

Level GTO Inverter with Dual Quasi-Resonant DC-<br />

Link”, Record of IEEE PESC, 1991, pp.880-884.<br />

Ill] J. G. Cho, J. W. Baek, D. W. Yo0 and C. Y. Won,<br />

“Three Level Auxiliary Resonant Commutated Pole<br />

Inverter for High Power Applications”, Record of<br />

IEEE PESC, 1996, pp.1019-1026.<br />

[12] Xiaoming Yuan and <strong>Ivo</strong> <strong>Barbi</strong>, “Control<br />

Simplification and Stress Reduction in A Modified<br />

PWM zero voltage switching Pole Inverter”, Record of<br />

IEEE APEC, 1999.<br />

[13] Xiaoming Yuan and <strong>Ivo</strong> <strong>Barbi</strong>, “<strong>Transformer</strong><br />

<strong>Assisted</strong> PWM <strong>Zero</strong> <strong>Voltage</strong> <strong>Switching</strong> Pole Inverter”,<br />

Record of IEEE PESC, 1999.<br />

[ 141 Xiaoming Yuan, “Soft <strong>Switching</strong> Techniques for<br />

Multilevel Inverters”, Ph. D Thesis, INEP-UFSC-<br />

Brazil, May 1998.<br />

1265

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