IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 10, OCTOBER 2015 6035

A Three-Phase AC–AC Converter in Open-DeltaConnection Based on Switched

Capacitor PrincipleMauricio Dalla Vecchia, Telles Brunelli Lazzarin, Member, IEEE , and Ivo Barbi, Fellow, IEEE

Abstract—This paper proposes a new topology for athree-phase open-delta connection ac–ac converter basedon the switched capacitor principle. The topology employsonly capacitors and switches in the power stage, which canprovide high efficiency and power density. It operates inopen loop with constant values for the gain, duty cycle,and frequency. The converter is bidirectional and thus itcan step-down or step-up the output voltages. A 3.5-kWprototype was built, tested and used to verify the theoreticalanalysis for resistive, inductive, and nonlinear loads. Theefficiency of the topology is around 93% in nominal loadand the power density is 1.178 kW/kg.

Index Terms—AC–AC converter, equivalent circuit, pha-sor diagram, switched capacitor, three-phase.

I. INTRODUCTION

FOR many years, the conventional transformer/autotransformer has been used in residences and in

industry to step-up or step-down the voltage levels. Recently,research on ac–ac power converters based on the switchedcapacitor principle has been carried out as an alternative toreplace these components. The concept of switched capacitors(SCs) was firstly proposed for dc-dc power converters (e.g.,in [1]–[3]) and this principle was subsequently employedin other applications, such as ac-dc, dc-ac, resonant andmultilevel converters [4]–[12]. Currently, it has also beenextended to direct ac–ac single-phase and three-phase powerconverters [13]–[15]. In terms of efficiency, power density,weight, and volume, the aforementioned ac–ac converters showbetter performance when compared with the conventionalautotransformer, because they do not employ an inductiveelement in their power circuits.

Studies have been made, as in [16]–[19], to improve thedesign, static and dynamic models, and control strategies of SCpower converters. They have shown that the efficiency of the SCconverters is influenced by the SC operation mode (completecharge (CC), partial charge (PC) or no charge (NC) [18], [19]),which is defined by the switching frequency, switch resistanceand capacitance. The steady-state operation of SC converters

Manuscript received October 22, 2014; revised January 30, 2015 andMarch 5, 2015; accepted March 25, 2015. Date of publication April 27,2015; date of current version September 9, 2015.

The authors are with the Department of Electrical Engineering(EEL), Federal University of Santa Catarina (UFSC), 88040-970Florianópolis, Brazil (e-mail: m.dallavecchia90@gmail.com; telles@inep.ufsc.br; ivobarbi@inep.ufsc.br).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2015.2426673

Fig. 1. (a) Three-phase converter based on switched capacitor princi-ple with open-delta connection, (b) gate driver signal and (c) open-deltaconfiguration with single-phase cell representation.

can be represented by simple equivalent circuits, in which theswitching can be disregarded. Modeling approaches can beemployed, considering ideal and non-ideal switches, as in [16],to provide instantaneous and average dynamic models whichcan be used to analyze current and voltage ripples and losses.Finally, the output voltage control is still a major challenge inrelation to SCs [7], [12]–[15].

In this paper, a new topology is described for a three-phaseac–ac converter based on the switched capacitor principle witha reduced number of components compared with the converterproposed in [15]. An equivalent circuit for the structure andthe phasor analysis for different types of resistive load (deltaor wye connection) are presented herein. This topology, asin [13]–[15], operates in open loop, with constant duty cycleand constant switched frequency, and amplitude transformationoccurs with no operational frequency change. Experimentalresults obtained with resistive, inductive and nonlinear load,together with the efficiency curves with different switchingfrequencies to verify the proposed converter and the powerfactor curve are reported herein.

II. SWITCHED CAPACITOR THREE-PHASE AC–ACCONVERTER—OPEN-DELTA CONNECTION

The proposed SC three-phase ac–ac converter described inthis paper is shown in Fig. 1(a). It has two SC single-phase

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6036 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 10, OCTOBER 2015

Fig. 2. (a) Unbalanced three-phase equivalent circuit, (b) balanced three-phase equivalent circuit, (c) single-phase equivalent circuit, and(d) generic representation of the single-phase equivalent circuit used to create Table II.

cells, as presented in [14], which are connected in one open-delta, as illustrated in Fig. 1(c) (open-delta configuration similarto that in an autotransformer). The proposed converter reducesthe component number by one third when compared withthe three-phase ac–ac converter described in [15], which iscomprised of three SC single-phase cells. Each cell shown inFig. 1(a) is composed of four bidirectional switches (BS) andthree capacitors (one of them being an SC).

The converter is bidirectional and works as a multiplier(step-up operation) or a divider (step-down operation). Thewaveforms of the output voltages follow the shape of that ofthe input voltages, multiplied by a gain with no change in thefrequency. The converter operates in open loop, the switchingfrequency is constant and the duty cycle is fixed and set at closeto 0.5 [the gate driver signals are shown in Fig. 1(b)].

In the first topological stage, all odd switches are turned onand thus the C1 and C4 SCs are connected to the capacitorsC2 and C5. In the second topological stage the even switchesare turned on and thus the C1 and C4 SCs are connected tothe capacitors C34 and C6. Therefore, the C1 SC equalizes thevoltages in capacitors C2 and C3, and the C4 SC equalizes thevoltages in C5 and C6. For a step-down operation, as is shownin Fig. 1(a), the input voltages are connected at points 1, 4, and6 (VAB = V14, VBC = V46 and VCA = V61), and the outputvoltages are available at points 2, 3 (or 4) and 5 (Vrs = V23,Vst = V35 and Vtr = V52). For a step-up operation, the sourcesare connected at points 2, 3 (or 4), and 5, and the loads at 1, 4,and 6.

The theoretical voltage gain of this structure in step-downoperation is

Gstep−down =Vout

Vin=

1

2. (1)

An advantage of this topology is that the maximum voltageapplied to all capacitors and switches is

VS1= VS2

= VS3= VS4

= VC1= VC2

= VC3=

Vin

2(2)

for step-down operation. In step-up operation, the maximumvoltage applied to the components is half the load voltage.

A single-phase equivalent circuit is proposed for an open-delta converter based on [14]. First, a three-phase unbalanced

TABLE IEQUIVALENCE REACTIVE AND ACTIVE POWER ANALYSIS

TABLE IICOMPONENT VALUES FOR THE EQUIVALENT CIRCUIT IN

OPEN-DELTA CONNECTION

equivalent circuit was obtained, as shown in Fig. 2(a). A deltathree-phase balanced equivalent circuit was then generatedfrom Fig. 2(a), as seen in Fig. 2(b). To obtain a three-phasebalanced circuit for an unbalanced three-phase circuit [Fig. 2(a)and (b)], an equivalence reactive and active power analysis was

VECCHIA et al.: CONVERTER IN OPEN-DELTA CONNECTION BASED ON SWITCHED CAPACITOR PRINCIPLE 6037

TABLE IIIANALYSIS OF PHASOR DIAGRAM WITH DIFFERENT TYPES OF LOAD IN OPEN-DELTA CONNECTION

carried out, as shown in Table I (considering the line-to-linevoltages and line currents to be equal). A Δ -Y transformationwas then performed and, finally, a single-phase equivalentcircuit was obtained from Fig. 2(b), as shown in Fig. 2(c).A generic representation [Fig. 2(d)] was created and used inthe definitions given in Table II. The equivalent circuit shownin Fig. 2(d) is composed of series resistance (RS) modelingconduction losses, parallel resistance (RP ) modeling switchlosses and parallel capacitance (CP ) modeling the reactivepower flow.

The parameters of the equivalent circuit are defined by

VX =Vin

2, (3)

Ceq = 3C, (4)

Rsl =1

4Cossfs, (5)

Req =1

4fsC

(1− e−1

2fsRonC )

(1− e−D

2fsRonC − e−(1−D)2fsRonC + e

−12fsRonC )

, (6)

Rp =1

2Rsl, (7)

Rs =2

3Req, (8)

Cp = 2Ceq, (9)

where C is the capacitance employed in the power circuit(C = C1 = C2 = C3 = C4 = C5 = C6), Ron is the conduc-tion resistance of the switches, fs is the switching frequency,Coss is the intrinsic capacitance of the switches and D is theduty cycle.

The values for the equivalent circuit elements are depen-dent on the way in which the input sources and the loadsare connected. The values for all connections are defined inTable II (where VLi is the line-to-line voltage and VFa is theline-to-neutral voltage from the input sources).

On analyzing the equivalent circuit shown in Fig. 2(d), theefficiency and power factor equations are obtained and they are

presented by

η =1

1 + RS

Ro+ (RS+Ro)2

RPRo

, (10)

and

FP =Pin√

P 2in +Q2

in

. (11)

These equations are employed to design the converter andthey also give an estimate of its performance. The efficiencyis associated with the parallel and series resistances (Rp andRs), which are defined by the components and operation modeof the SC converter. As in the case of an autotransformer, thisconverter has a reactive power inherent to its structure, whichin this case is capacitive (while in the autotransformer it isinductive). Therefore, the power factor seen by the input sideis associated with two components: i) the structure (related toCeq) and ii) the load type applied to the converter (as in anautotransformer).

A detailed analysis of the voltages supplied by the converterin open-delta connection was carried out. The results are shownat Table III, which shows the phasor analysis for different typesof load and the equations that define the output voltages inrelation to the input voltages.

III. EXPERIMENTAL RESULTS

A 220-V/ 110-V/ 3.5-kW prototype was built to verify theoperation of the proposed converter. Fig. 3 shows a photographof the prototype and Table IV the design specifications. In Fig. 4the three-phase line-to-line output voltage of the structurerelated to the line-to-line input voltage can be observed forstep-down [Fig. 4(a)] and step-up [Fig. 4(b)] configurations.The step-down configuration was used in the tests shown inFigs. 5–11. The voltage stress applied to the capacitors C1,C2 and C3 and the switch S1 (a single MOSFET) are shownin Figs. 5 and 6, respectively. Note that the voltage stress, asexpected, is half of input voltage.

The waveforms of the input current IA and line-to-line inputvoltage VAB for a 3.5-kW resistive load are shown in Fig. 7.On analyzing the results it can be observed that the line voltageleads the line current at 1.1 ms (approximately 23◦), which isexpected for the capacitive circuit. In this test, an L filter of

6038 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 10, OCTOBER 2015

Fig. 3. Photograph of the 3.5-kVA prototype.

TABLE IVMAIN SPECIFICATIONS AND COMPONENTS OF THE PROTOTYPE

0.2 mH was added to filter the high frequency and provide asinusoidal waveform.

The tests carried out under inductive load (350 VA and 0.2power factor) are detailed in Fig. 8. The line-to-line input andoutput voltages are in phase, with a 1/2 gain in the step-downoperation. Line-to-neutral output voltage has a 30◦ phase-shiftand a 1/(2

√3) gain in relation to the input line-to-line voltage,

as proposed in Table III. The current Ir under an inductiveload lags in relation to the line-to-neutral output voltage, asexpected.

Fig. 9 shows the experimental results under nonlinear load(900 VA and 2.43 crest factor). The input (VAB) and output(Vrs) voltages are presented in the figure, together with theinput (IA) and output currents (Ir). Note that the input andoutput voltage remain unchanged in relation to the phase shift.

Fig. 10 shows the power factor curve for tests with resistiveload. As expected, for a lower active power flow, the reactivepower inherent to the structure prevails and the value for thepower factor is low. As the active power increases, the power

Fig. 4. Experimental waveforms: input line-to-line voltage (VAB) andthree-phase line-to-line output voltages (Vrs, Vst and Vtr) for a step-down (a) and step-up (b) configurations.

Fig. 5. Experimental waveforms: voltage stress in capacitors C1, C2,and C3.

VECCHIA et al.: CONVERTER IN OPEN-DELTA CONNECTION BASED ON SWITCHED CAPACITOR PRINCIPLE 6039

Fig. 6. Experimental waveforms: voltage stress on a single MOSFET.

Fig. 7. Experimental waveforms: line-to-line input voltage (VAB) andinput current (IA) under resistive load.

factor also increases, approximating the unitary value. Thetheoretical analysis [based on (11)] shows a power factor valueof 0.987, while the experimental result in Fig. 10 indicates avalue of 0.998, both in nominal load. This difference is due tothe fact that the proposed equivalent circuit does not considerthe parasitic inductances in the power stage that affect thestructure power factor (parasitic inductances compensate a partof the capacitive power factor originating from the structure).

The theoretical [based on (10)] and experimental efficiencycurves for the proposed converter are shown in Fig. 1(a) and(b) , respectively. Note that the shapes of the theoretical andexperimental curves are similar for all switched frequencies,with small differences due to the losses that were not consideredand simplifications that were employed. The highest experi-mental efficiency (94.5%) was obtained with almost half load(processing 1.5 kW). In the case of nominal load, the efficiencywas around 93%. Tests with different switching frequencieswere also carried out and the results showed that the efficiency

Fig. 8. Experimental waveforms: line-to-line input voltage (VAB), line-to-line output voltage (Vrs), line-to-neutral output voltage (Vrn) and line-to-neutral current (Ir) under inductive load.

Fig. 9. Experimental waveforms: line-to-line input voltage (VAB), line-to-line output voltage (Vrs), input and output currents (IA and Ir) undernonlinear load.

can be increased with a light load when the switching frequencyis reduced [as seen in Fig. 11(a) and (b)]. The results alsoshowed that with a heavy load a high switching frequency isrequired to increase the efficiency.

On comparing the proposed topology with the three-phaseac–ac converter described in [15] it can be observed that:i) both topologies have fixed amplitude transformation, withno operational frequency change; ii) the command signalsare simple and equal in the two cases; iii) for the three-phase topology in [15], the number of switches (24), capacitors(nine) and drivers (12) is higher than the number of switches(16), capacitors (six) and drivers (eight) used in the proposedtopology; and (iv) the power density increase with the converteroperating in delta configuration is 1.35 kW/kg, higher than thecorresponding value for the same converter operating in open-delta configuration, which is 1.178 kW/kg.

6040 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 10, OCTOBER 2015

Fig. 10. Experimental curve: power factor for the structure with resistiveload.

Fig. 11. Efficiency versus variation in the switching frequency:(a) theoretical and (b) experimental curves.

IV. CONCLUSION

A three-phase ac–ac open-delta connection converter basedon SCs has been proposed in this paper. The advantages of thisconverter include: i) the absence of magnetic elements, ii) highefficiency, iii) bidirectional power flow and, most importantly,iv) a reduced number of components when compared withthe three-phase ac–ac converter in delta or wye connectiondescribed in [15]. The experimental results corroborate thetheoretical analysis and enable the proposed converter to beapplied as a low cost solution to replace the conventional three-phase autotransformer.

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Mauricio Dalla Vecchia was born in Fran-cisco Beltrão, Brazil, in 1990. He received theB.Sc. degree in electrical engineering from theFederal University of Santa Catarina (UFSC),Florianópolis, Brazil, in 2014. He is currentlyworking toward the master’s degree at the Fed-eral University of Santa Catarina (PPGEEL-UFSC) in the Power Electronics Institute(INEP-UFSC).

His interests include direct ac–ac powerconverters, switched capacitor converters, hy-

brid dc–dc switched capacitor converters, and bidirectional dc–dcconverters.

VECCHIA et al.: CONVERTER IN OPEN-DELTA CONNECTION BASED ON SWITCHED CAPACITOR PRINCIPLE 6041

Telles Brunelli Lazzarin (S’09–M’12) was bornin Criciúma, Brazil, in 1979. He received theB.Sc., M.Sc., and Ph.D. degrees in electrical en-gineering from the Federal University of SantaCatarina (UFSC), Florianópolis, Brazil, in 2004,2006 and 2010, respectively.

He is currently an Adjunct Professor at theUSFC. His interests include inverters, paral-lel operation of inverters, UPS, high-voltagedc–dc converters, direct ac–ac power convert-ers, switched capacitor converters, and hybrid

switched capacitor converters.Dr. Lazzarin is a member of the Brazilian Power Electronics Society

(SOBRAEP), IEEE Power Electronics Society (PELS) and IEEE Indus-trial Electronics Society (IES).

Ivo Barbi (M’78–SM’90–F’11) was born inGaspar, Brazil, in 1949. He received the B.S.and M.S. degrees in electrical engineeringfrom the Federal University of Santa Catarina(UFSC), Florianópolis, Brazil, in 1973 and 1976,respectively, and the Dr.Ing. degree from theInstitut National Polytechnique de Toulouse,Toulouse, France, in 1979.

He is currently a visiting professor in theDepartment of Automation and Systems of theUFSC. He founded the Brazilian Power Elec-

tronics Society and the Power Electronics Institute of the Federal Uni-versity of Santa Catarina.