A Family of Low-Voltage High-Current Rectifiers

Pekik Argo DahonoDepartment of Electrical Engineering, Bandung Institute of Technology,

Jl. Ganesa No. 10, Bandung 40132, Indonesia.Tel. 62-22-2503316 Fax 62-22-2508132

Email pekik@konversi.ee.itb.ac.id

Abstract – A new family of three-phase low-voltage high-current rectifiers is proposed in this paper. The proposedrectifiers do not need a complex input transformer beyond theone that is needed by a conventional 6-pulse three-phaserectifier. Analysis of the input and output ripples of theproposed rectifiers are presented. Influences of the couplingcoefficient of the output filter inductor on the input and outputcurrent ripples are investigated. Simulated and experimentalresults are included to verify the proposed concept.

I. INTRODUCTIONA low-voltage high-current rectifier is commonly used inelectrochemical industries and cathodic protection powersupplies. At present, such rectifiers are usually implementedby parallel connection of several rectifiers with the associatedcomplex input transformer[1-3]. In this paper, a new family of three-phase low-voltagehigh-current rectifiers is presented. The schemes of theproposed rectifiers are shown in Fig. 1. For comparisonpurpose, the scheme of a conventional six-pulse three-phaserectifier is also shown in Fig. 1. This figure shows that theproposed rectifiers do not need a complex input transformerbeyond the one, which is needed by the conventionalrectifiers. Analysis of the input and output ripples of theproposed rectifiers are presented. Analysis results show thatthe mutual coupling coefficient of the output filter inductorhas a strong influence on the input and output ripples.Simulated and experimental results are included to verify theproposed concept.

II. BASIC ANALYSISIn the circuit of Fig. 1(a), the proposed rectifier can beconsidered as three single-phase center-tap rectifiers that areconnected in parallel through a three-phase output filterinductor. Each rectifier is supplied by one of three separatelycenter-tapped secondary windings of the transformer.Because of the 120o phase differences among the transformersecondary voltages, the full-wave output voltage of eachrectifier will be displaced 60o among the others. Theoreticaloutput voltages of the rectifier are shown in Fig. 2(a). Thisfigure shows that the output voltage has a ripple at six timesthe fundamental input frequency as in the case of aconventional 6-pulse three-phase rectifier. The average valueof the output voltage is

so VVπ

22= (1)

where Vs is the rms value of secondary phase-to-center-tapvoltage of transformer.

In the circuit of Fig. 1(b), the proposed rectifier can beconsidered as six single-phase half-wave rectifiers that areconnected in parallel through a 6-phase output filter inductor.Each single-phase rectifier is supplied by each phase of thesecondary winding of three-phase transformer that isconnected as a three-phase-to-six-phase converter. The totaloutput voltage of the rectifier can be considered assuperposition of the output voltage of six single-phase half-wave rectifiers. Fig. 2(b) shows the voltage waveforms of the rectifier inFig. 1(b). Once again, this figure shows that the outputvoltage waveform of the proposed rectifier has the samenumber of pulse as in the case of a conventional 6-pulsethree-phase rectifier. The average value of the output voltageis

so VVπ2= (2)

Several performance indexes of the rectifiers can besummarized as shown in Table 1. For comparison purpose,the results for the conventional rectifier, which is shown inFig. 1(c), are also shown. This table shows that the proposedrectifiers need smaller power diodes than the conventionalones.

III. OUTPUT RIPPLE ANALYSISIn this section, the output ripple analysis of the rectifier inFig. 1(a) will be discussed in detail. Output ripple analysis forthe rectifier in Fig. 1(b) can be done in similar way. For thispurpose, the system is assumed perfectly balanced, the sourceand transformer leakage inductances are negligible, thediodes are ideal, and the conduction is continue. Based on thecircuit in Fig. 1(a), the following expression can be obtained:

+

=

w

v

u

ttt

ttt

ttt

w

v

u

tLL

LtL

LLt

w

v

u

i

i

i

p

LMM

MLM

MML

i

i

i

RRR

RRR

RRR

v

v

v

(3)

where

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(a)

(b)

(c)

Fig. 1. Low-voltage high-current rectifiers.

(a)

(b)

Fig. 2. Voltage waveforms of low-voltage high-currentrectifiers.

Lt LLL += (4)

Lt RRR += (5)

Lt LMM += (6)

R, L, and M are the resistance, self inductance, and mutualinductance of the filter inductor, respectively. If the voltagesand currents are separated into the average and ripplecomponents, eqn. (3) can be written as

+++

+

+++

=

+++

ww

vv

uu

ttt

ttt

ttt

ww

vv

uu

tLL

LtL

LLt

ww

vv

uu

ii

ii

ii

p

LMM

MLM

MML

ii

ii

ii

RRR

RRR

RRR

vv

vv

vv

~

~

~

~

~

~

~

~

~

(7)

where bar and tilde over the voltages and currents areindicated the average and ripple components, respectively.From eqn. (7), the expressions for average and ripplecomponents can be obtained as follows.

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Table 1. Performance indexes of low-voltage high-current rectifiers

Circuit Fig. 1(a) Fig. 1(b) Fig. 1(c )Average output voltage π/22 sV π/2 sV π2/63 sV

Average current of diode 6/oI 12/oI 6/oI

RMS current of diode 23/oI 26/oI 32/oI

VA of secondarywindings of transformer

2/oo IVπ 2/oo IVπ 2/oo IVπ

=

w

v

u

tLL

LtL

LLt

w

v

u

i

i

i

RRR

RRR

RRR

v

v

v

(8)

+

=

w

v

u

ttt

ttt

ttt

w

v

u

tLL

LtL

LLt

w

v

u

i

i

i

p

LMM

MLM

MML

i

i

i

RRR

RRR

RRR

v

v

v

~

~

~

~

~

~

~

~

~

(9)

where

sowvu VVvvvπ

22==== (10)

The ripple voltage drop, that is resistance times the ripplecomponent of current, is usually small and can be neglectedand, therefore, eqn. (9) can be simplified into

=

w

v

u

ttt

ttt

ttt

w

v

u

i

i

i

p

LMM

MLM

MML

v

v

v

~

~

~

~

~

~

(11)

Based on eqn. (11), the ripple component of currents can beobtained as

∫∫∫

−−−−−−−−−

=

dtv

dtv

dtv

MLLMMLMM

LMMMLLMM

LMMLMMML

Zi

i

i

w

v

u

tttttttt

tttttttt

tttttttt

dw

v

u

~

~

~1

~

~

~

2222

2222

2222

(12)where

( )( )22 ttttd MLMLZ −+= (13)

ouu Vvv −=~ (14)

ovv Vvv −=~ (15)

oww Vvv −=~ (16)

The output current ripple is

wvuo iiii~~~~ ++= (17)

Combination of eqns. (12) and (17) results in

( )∫ +++

= dtvvvML

i wvutt

o~~~

2

1~ (18)

In the interval from t1 up to t2 of Fig. 2(a), the expressions forthe ripple voltages are

( )[ ] ssu VttVvπ

ω π 22sin2~

31 −+−= (19)

( )[ ] ssv VttVvπ

ω π 22sin2~

31 −−−−= (20)

( )[ ] ssw VttVvπ

πω 22sin2~

1 −+−−= (21)

where ω is the angular frequency of the source voltage. Fromeqns. (19)-(21), the following is obtained.

( )[ ] sswvu VttVvvvπ

ω π 26sin22~~~

31 −+−=++ (22)

Based eqn. (22), eqn. (18) can be solved as

( ) ( )[ ] ( ) KttttML

Vi

tt

so +−++−

+−

= 13

31cos2

22~πωπω

ω (23)

where K is a constant to be determined. This constant can bedetermined based on the fact that the average value of theoutput current ripple over the interval from t1 to t2 is zero andthe result is

( )tt

s

ML

VK

2

23

+=

ω (24)

Eqn. (23) can be used to determine the peak-to-peak and rmsvalue of the output current ripple. Eqn. (23) shows that theoutput current ripple is reduced if an output filter inductorthat having positive coupling coefficient is used.

IV. INPUT CURRENT RIPPLEOnce again, only the input current ripple analysis of therectifier in Fig. 1(a) is detailed. Analysis of the rectifier inFig. 1(b) can be done in similar way. From eqn. (12), thecurrent ripple of phase u can be obtained as:

( )∫ +−

−∫−

= dtvvZ

MLMdtv

Z

MLi wv

d

tttu

d

ttu

~~)(~~22

(25)

If it is assumed that the output current ripple is very smalland can be neglected (which is equivalent to assume that theload inductance is very large) then eqn. (25) can beapproximated as

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( )∫ −−= dtvvvL

i wvul

u 23

1~ (26)

where Ll = L-M. This current ripple will be circulated amongthe phases of the filter inductor. Based on the voltagewaveforms in Fig. 2(a), the above integration can be solvedand the result is

( )[ ] ( )[ ] [ ]

( )[ ] ( )[ ] for

2sin32cos

for cos

for 2sin3cos2~

32

32

232

2

2131

1

ttt

ttttI

ttt)I

tttttttIi

r

r

oooru

≤≤++−−+−−=

≤≤+−=≤≤−−+−−=

ππ

π

ωω

ωω

(27)where

l

sr

L

VI

ω3

2= (29)

The fundamental frequency of the above current ripple istwice the input voltage frequency. This circulating currentwill be minimum if a filter inductor that having negativecoupling coefficient is used.The primary winding current of the transformer consists of acurrent component due to the dc load current plus the currentdue to the above current ripple. The expressions for theprimary winding current can be written as

≤≤−−−

≤≤+=

πωππω

πωω

2for )(~

3

0for )(~

3

ttiI

ttiI

N

Ni

uo

uo

p

sab (30)

where Np and Ns are the number of turns of the primary andsecondary windings of the transformer, respectively. Eqn.(30) can be used to determine the ripple content of thetransformer currents and the input line currents of therectifier.

V. EXPERIMENTAL RESULTSIn order to verify the proposed concept, small experimentalsystems with the schemes as shown in Fig. 1(a) wasconstructed. In the circuit of Fig. 1(a), the input line-to-linevoltage is rated at 380V, 50 Hz. The transformer is designedin such a way so that a dc voltage of about 20 Vdc is resultedunder rated condition. The maximum output current is 20 A.In this experiment, the rated current of the diode is 8 A. Thecoupled output filter inductor is constructed by using a zig-zag transformer rated at 50V and 5 A and, therefore, thecoupling coefficient is negative. The load that was used inthis experiment is a series connection of a variable resistanceand an 8-mH inductor. Fig. 3 shows the waveforms of the load current and one ofthe single-phase rectifiers current. This figure shows that thecurrent in one of single-phase rectifier is equal to the loadcurrent divided by three. Fig. 4 shows the input voltage andcurrent waveforms. This figure shows that the input current

waveform is the same as the conventional 6-pulse three-phaserectifier. At present, a power supply for cathodic protection systemswith the scheme as shown in Fig. 5 is under construction. Theoutput rated values of the system are designed at 5Vdc and500 Adc. The dc chopper is switched at 5 kHz and the switchis implemented by using an IGBT. The IGBT inverter isoperated as a six-step three-phase inverter with a fundamentalfrequency of 5 kHz. By using this high-frequency inverter,the required transformer will be small. Because the inverter isoperated as a six-step inverter, the output voltage of therectifiers will be similar to the output voltage of a three-phasechopper under 2/3 duty cycle. In reference [4], it was shownthat at duty cycle equal to 2/3, the output current ripple willtheoretically be zero. Thus, the system in Fig. 5 will producea very small output current ripple. Fig. 6 shows the simulatedresults of the system in Fig. 5. In this simulation, a positivecoupled inductor that having 0.5 mH self-inductance and 0.4mH mutual- inductance was used. The output filtercapacitance is 100 µF. The load was a series connection of0.01 Ω resistance and 0.1-mH inductance. Simulated resultshows that the output current ripple is very small as expected.

Fig. 3. Waveforms of total output current (upper) and outputof one of single-phase rectifiers (lower). [5 A/div]

Fig. 4. Input current waveforms of rectifier.

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Fig. 5. A power supply for cathodic protection system.

Fig. 6. Simulated results of output current (upper) and voltage (lower).

VI. CONCLUSIONA new family of low-voltage high-current rectifiers has beenpresented and compared to the conventional ones. Analysisof the input and output current ripples that is useful in thefilter design is also presented. Experimental results have beenpresented to verify the validity of the proposed rectifiers.

ACKNOWLEDGMENTThis research is funded by the Ministry of Research andTechnology of Indonesia under the RUT-V project. Theauthor wishes to thank Mr. T. Desmana and Mr. T.Handoyo for their assistance during the preparation ofthis paper and experiments.

REFERENCES[1] R. A. Zielke, A 50-MW Thyristor Controlled Power

Converter, IEEE Trans. Ind. Appl., Vol. 11, May/June1975, pp. 263-266.

[2] G. Seguier, Power Electronic Converters – AC-DCConversion, North Oxford Academic, London, 1986.

[3] G. Olivier, G. E. April, E. Ngandui, and C. Guimaraes,Novel Transformer Connection to Improve CurrentSharing in High-Current Rectifiers, IEEE Trans. Ind.Appl., Vol. 31, Jan./Feb. 1995, pp. 127-133.

[4] P. A. Dahono, S. Riyadi, A. Mudawari, and Y. Haroen,Output Ripple Analysis of Multiphase DC-DC Converters,Proc. IEEE 1999 Int. Conf. Power Electronics and DriveSystems, Hong Kong, pp. 626-631.

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