Single Phase to Three Phase Power ConversionUsing Reduced Rated Inverters

Anil K AdapaDepartment of Electrical Engineering

Indian Institute of ScienceEmail: aniladapa@ee.iisc.ernet.in

Vinod JohnDepartment of Electrical Engineering

Indian Institute of ScienceEmail: vjohn@ee.iisc.ernet.in

Abstract—A feature of grid interactive single phase to threephase converters is the ability to deliver a fraction of total loadpower directly from the source. This feature draws our attentionas it reduces the size and cost of the system, and results in abetter efficiency. This paper proposes control strategy for a threeleg single phase to three phase converter with active front endconverter that leads to reduced converter rating and improvedthe dc bus utilization. The proposed approach reduces the currentrating required by the converter by 50%. The results are validatedon a laboratory power converter prototype.

Keywords—Single phase to three phase, grid interactive, reso-nant controller, front end converter(FEC).

I. INTRODUCTION

Most of the electric power is consumed by motor loads,mainly induction motors. These motors are used in fans, blow-ers, pumps, compressors as well as motor driven equipment.Above 0.5 kW three phase induction motors are preferableas they are highly efficient, have smooth torque and goodstarting torque. A three phase motor is also less expensivethan a single phase motor of the same voltage and rating. Inmany countries single phase power is used for rural powerdistribution [1]. As the method of supplying power to manyhouseholds, small rural industries, railways and remote areasis only on single phase basis, they limit the use of three phasemotors. To overcome this problem, phase converters are usedto serve three phase loads.

Rotary phase converters use a motor generator set to ac-complish phase conversion. These converters are commerciallyavailable, but these have poor efficiency compared to the staticpower converters. The traditional way to generate three phasepower is by rectification of single phase using diode bridgeor active current shaping front end converter to get requireddc bus voltage, followed by the use of a 3 − φ inverter [2].For the aforementioned applications, it is not necessary tohave variable frequency power supply. Moreover these gridinteractive system are better than the traditional ones in twoaspects: (1) they require fewer number of solid state devices,and (2) these converters need not to be rated for total loadkVA, thereby reducing the size of dc bus capacitors and costof the semiconductor devices [3].

A large number of fixed frequency and reduced switchvariable frequency single phase to three phase converters withdifferent control techniques have been reported [2], [4]–[6].The control approach for fixed frequency single phase to threephase converter topologies, shown in Fig. 1 use active input

~

+

-

a

b

O

c

Front end converter

3- load

Inverter

i1

i2

i3

(a)

~

+

-

a

b

O

c

Front end converter

i1

i2

i3

n

3- load

Inverter

(b)

Fig. 1. Grid interactive single phase to three phase converters. (a) Type-aconverter; utilizing grid phase voltage as line to line voltage for the load. (b)Type-b converter; utilizing grid phase voltage as phase voltage for the load.

current shaping for the grid connected legs, and open loopcontrol of third leg. Fixed frequency single phase to three phaseconverters in Fig. 1 are divided into two Types, namely Type-a and Type-b. Converter shown in Fig. 1(a) limits the line-to-line voltage of the resulting three phase supply to singlephase grid voltage, where as the converter shown in Fig. 1(b) uses the grid voltage as one of the phase voltages of theresulting three phase supply. Low cost soft start strategies forthe configuration shown in Fig. 1(a) are proposed in [7].

Fig. 2. Voltage phasors corresponding to Type-a and Type-b convertersshowing grid voltage in solid lines and inverter voltages in dotted lines.

In this paper, a new control strategy for Type-a converteris proposed to improve the dc bus utilization and to implementadvanced PWM techniques. First the basic principle of theseconverters presented in section II. The closed loop control ofthird phase is explained in section III, followed by proposedcontrol structure of FEC IV. Experimental results are presentedthat validate the proposed control structure. Analysis of currentsharing among the three legs of the converter is presented toaid designers to built such a converter.

II. BASIC PRINCIPLE

Fixed frequency single phase to three phase converters canbe broadly divided into two categories based on the utilizationof existing single phase grid, as line to line and per phasevoltage of the created three phase supply. Phasor diagaram ofthe grid voltage and inverter voltages are shown in Fig. 2. InType-a converter two legs act as front end converter whichmaintains the required dc bus voltage. Supply mains willprovide two lines and the pole of third leg will provide otherline. The whole system can be treated as two ac voltage sourceshaving 600 phase shift with a common neutral point, one isexisting grid voltage(Vab) and other is inverter based voltagesource(Vcb). In Type-b converters the neutral of the existinggrid is connected to the dc bus mid point and phase to one legof the converter which acts as front end converter, other twolegs of the converter switches in a fashion such that poles of thetwo legs create remaining two phases of required three phasesupply. Other single phase to three phase variable frequencyconverters reported in literature are rated for total load power[1], [2].

TABLE I. COMPARISON OF TYPE A AND B CONVERTERS

Type-a Type-b

Line to line voltage Vph

√3Vph

Converter based voltage sources 1 2Throughput of the converter ≤ 1

2Pload23Pload

Availability of neutral No YesSemiconductor cost Less More

Requirement of step up transformer* Yes† No* Transformer is mandatory in few grid connected applications.† Loads like blowers can be used either in delta connection or starconnection, which can be used without a transformer.

A. Power Flow

The proposed control method has been divided into twotypes, lag control and lead control. In lag control invertervoltage Vcb lags the grid voltage Vab by 600 whereas in leadcontrol inverter voltage leads the grid voltage by 600; themagnitude of vab and vcb are the same in both lag and leadcontrol approach.

~

(a)

(b)

Fig. 3. Power exchange between grid and Type-a single phase to three phaseconverter through the load. (a) Block diagram of the grid and inverter. (b)Phasor diagram of the grid and inverter voltages and currents.

TABLE II. POWER SHARING BETWEEN GRID AND INVERTER

Load Control Power Flow

RL load Lag control Pg > Pi;Qg < Qi

RL load Lead control Pg < Pi;Qg > Qi

RC load Lag control Pg < Pi;Qg > Qi

RC load Lead control Pg > Pi;Qg < Qi

R load Lag/Lead control Pg = Pi;Qg = −Qi

Fig. 3(a) represents block diagram of the grid and inverterof Type-a single phase to three phase converter and Fig. 3(b) isthe corresponding phasor diagram under balanced three phaseload, Zab=Zbc=Zca=Z∠θl where θl=tan−1[Im(Z)/Re(Z)]is the impedance angle. Pg + jQg and Pi + jQi representpower delivered to load by the grid and inverter respec-tively. In the block diagram, I1=Ix + Iz=

√3I∠(θl − 30)

and I3=Ix − Iz=√3I∠(θl + 30) as shown in the pha-

sor diagram in Fig. 3(b). Referring to the phasor diagram|VabI∗1 |=|VcbI∗3 |=

√3V I=V IL. This implies that the load kVA

is equally shared by the grid and inverter.A qualitative relationbetween type of load, real and reactive power shared by thegrid and inverter is tabulated in Table II. For the same load,full rated single phase FEC has to deliver a real power of√3V ILcos(θl) to the inverter, where as FEC in the considered

single phase to three phase converter needs to deliver onlyV ILcos(30 + θl). For unity pf, ratio of the total powerprocessed in the two cases is 2, with decrease pf (inductiveloads) this ratio increases further. This indicates the fact thatunder inductive loading, power processed by the single phaseto three phase converter with the lag control is less than 50%.The same is true for capacitive loading and lead control.

-90 -60 -30 0 30 60 90-4

-2

0

2

4

6

8

10

impedance angle of the load (θl in deg)

curr

ent

in A

|IC

| (leg C current)

|If | (min. loading on FEC)

| Ig | (min. loading on FEC)

| If | (UPF loading at grid)

| Ig |(UPF loading at grid)

capacitive loading inductive loading

(a)

-90 -60 -30 0 30 60 90-4

-2

0

2

4

6

8

10

impedance angle of the load (θl in deg)

curr

ent

in A

| IC

| (leg C current)

| If | (min. loading on FEC)

| Ig | (min. loading on FEC)

| If | (UPF loading at grid)

| Ig | (UPF loading at grid)

capacitive loading inductive loading

(b)

Fig. 4. Variation of rms currents drawn by the load, FEC and grid currents fora 2kVA load at different impedance angles excluding losses in the converter(Vab = 230V ∠00, Z = 79.35Ω∠θ0

); (a) lag control Vcb = 230V ∠−600,

case-1 and case-2 (b) lead control Vcb = 230V ∠+600, case-3 and case-4.

The dependency of the reactive power exchange betweentwo sources Vcb and Vab on load power factor can be exploitedto minimize the reactive power supplied by the grid. Thisimproves the power handling capability of the converter. Forexample, under pure resistive loading and lag control ofthe single phase to three phase converter, grid will operateat leading power factor. Real power delivered to the loadthrough the leg C, Pi, will be drawn by FEC at unity powerfactor(UPF). In this case current loading on the FEC will beminimum. To operate grid at UPF, FEC needs to compensatefor the reactive power supplied by the grid. This will increaseloading on the FEC and decreases reactive power loading ongrid. For minimum loading on FEC, unity power factor hasto be maintained at FEC end. Based on the possible ways ofoperating the FEC and ways for drawing power from the grid,the following four cases can be analysed:Case 1) Unity power factor at grid and lag control.Case 2) Unity power factor at FEC and lag control.Case 3) Unity power factor at grid and lead control.Case 4) Unity power factor at FEC and lead control.

Absolute magnitude of the grid current, FEC current andinverter currents for all the four cases listed above are plotted inFigs. 4(a) and (b). Absolute magnitude of the currents throughlegs of the Type-a converter for both lag and lead control forcases (2) and (4) are shown in Fig. 5.

For inductive loading upto impedance angle from 120 to

-90 -60 -30 0 30 60 900

1

2

3

4

5

6

impedance angle θl in degrees

curr

ent

in A

|IC

| lag / lead control

|IB

| lag control

|IB

| lag control|I

A| lag control

|IA

| lead control

Fig. 5. RMS currents through three legs of the converter for minimum loadon FEC for 2kVA balanced three-phase load and minimum loading on FEC.

420 and lag control of the converter, power factor at the singlephase grid varies from 0.951 leading to 0.978 lagging. Forthe same loading on three phase grid it will vary from 0.978lagging to 0.743 lagging. From Fig. 4(a) one can observe thatgrid currents with and without reactive power compensationare close to each other for this impedance angle range. Ingeneral induction motors operating p.f falls in this range. Solag control of the converter will give additional advantage interms of grid power factor while maintaining the FEC underminimum loading conditions. In a similar way for capacitiveloading one can exploit the load sharing by making Vcb to belead Vab by 600(lead control).

III. CONTROL APPROACH

A. Front end converter

Front end converter consists of two legs and it is intendedto draw sufficient real power to maintain the dc bus voltageat the set value. For minimum loading on FEC it shapescurrent drawn by the FEC to be at unity power factor (UPF)where as for minimum loading operation at grid it will shapecurrent drawn from the grid to be at UPF. To meet thisobjective, second order generalized integrator based PLL hasbeen employed to track grid voltage [8]. In the single phasefront end converter(FEC) current loop proportional + resonantcontrollers(PR) have been used, these PR controllers providesufficient gain to force the actual current in phase with gridvoltage.

B. PR controller based voltage control of leg C

From the SOGI based PLL shown in Fig. 6, informationabout grid voltage vgα and its orthogonal vector vgβ areavailable, these are sufficient to estimate required instantaneousline to line voltage v∗ca from (1).

v∗cb =

1

2vgα +

√3

2vgβ for lag control

1

2vgα −

√3

2vgβ for lead control

(1)

~-

+

-+

-+

+ -+

++

++

++

-

-+

Hardware DetailsFilter inductance, Lf 5 mH

Filter Capacitance, Cf 4.7 µFDC link Capacitance, Cdc 3000 µF

Current sensor gain, ki 1/10Voltage sensor gain, kv 1/200

FEC Inner current loopProportional gain, KP (FEC,i) 2.5 Ω

Resonant gain, KR(FEC,i) 45 Ω

FEC Outer voltage loopProportional gain, KP (FEC,v) 13.91 Ω−1

Integral gain, KI(FEC,v) 12.35 Ω−1s−1

Inverter Inner current loopProportional gain, KP (INV,i) 4.61 Ω

Inverter Outer voltage loopProportional gain, KP (INV,v) 0.59 Ω−1

Resonant gain, KR(INV,v) 40 Ω−1

Fig. 6. Control structure of type-a single phase to three phase converter.

where, vgβ = vgαe−jπ/2 PR controller corrects the error in

estimated line voltage and applied line voltage, v∗cb − vcb byapplying required modulating signal to leg C of the singlephase to three phase converter. Controlling of a Type-a con-verter using conventional method, two legs as single phaseFEC and third leg independently requires the dc link voltagemore than

√3Vg(pk).

IV. PROPOSED CONTROL STRUCTURE

An approach to improve dc bus utilization is proposedwhich facilitates the use of advanced PWM techniques. Theproposed control scheme consists of the following stages:

1) Obtaining modulation index, mα of FEC in conven-tional approach.

2) Obtaining ma and mb to control FEC.3) PR controller based voltage control to leg C.

Refering to the phasor diagram for lag control shown in Fig. 7OA and OB are pole voltages of legs A and B under normalsingle phase FEC operation; unlike normal single phase FEC,the same resultant pole to pole voltage VAB can be obtained byshifting modulating signals m′a and m′b by 1200. As a result ofthese modulating signals, the dc bus mid point will be shiftedfrom O to O′ as shown in Fig. 7. To generate required polevoltage at leg C with this modification, modulating signal toswitch the devices of leg C need not be with respect to dcbus mid point at O. Use of O′ as the virtual dc bus midpointimproves dc bus utilization. This method requires minimum dcbus voltage of (2/

√3)Vg(pk). To achieve this modulating signal

mα is obtained using conventional control approach and itsorthogonal vector mβ is generated, using (3) and (5). These areused to get required modulating signals m′a and m′b with 1200

shift. Modulating signal to leg-C without common mode, m′cis same as that obtained in conventional approach. To improveoverall system stability and attenuate LC resonant oscillations,inner current loop is added [9]. As its control is based on line-line voltages, added common mode doesn’t effect m′c. In asimilar way lead control can be done.

bB

A

a

-jωₒLIf

c

-jωₒLIf /2If

o

o'n

Fig. 7. Phasor diagram of the single phase to three phase converter withproposed lag control strategy.

m′a =

mα −

1√3mβ for lag control

mα +1√3mβ for lead control

(2)

m′b =

−mα −

1√3mβ for lag control

−mα +1√3mβ for lead control

(3)

where, mβ = mαe−jπ/2

ma = m′a +mcom

mb = m′b +mcom

mc = m′c +mcom

(4)

For sine triangular PWM technique mcom = 0. Othervalues of mcom can be used based on PWM strategies [10].

V. SIMULATION RESULTS

Simulation results for Type-a single phase to three phaseconverter are shown in Fig. 8. The test load is 500W star con-nected resistive load. Grid voltage and frequency consideredwere 115V (rms) with 50Hz. It can be seen that the proposed

control structure is effective in operating three-leg inverter asa single phase FEC and also providing virtual third phase fora three-phase load.

0 5 10 15 20-20

-15

-10

-5

0

5

10

15

20

time (in ms)

i g , i f ,

i a

and v

ab

if (FEC current)

ia

ig (grid current)

vab

(grid voltage)

(a)

0 5 10 15 20 25 30 35 40 45 50-8

-6

-4

-2

0

2

4

6

8

time (in ms)

i a , i b

, i c

and v

ab

vab

(grid voltage)

ia

ic i

b

(b)

Fig. 8. Simulation results of single phase to three phase converter; (a) gridvoltage and FEC currents, vab : 50V/div, all currents 5A/div; (b) grid voltageand load currents, vab : 50V/div, all currents 2A/div.

VI. EXPERIMENTAL RESULTS

A prototype of Type-a converter has been made and testedwith the proposed control strategy (lag control). DC link of theconverter is maintained at 200V with two legs of the converteracting as a single phase FEC with 1200 phase shift betweenthe legs. The third leg is modulated to maintain the rms lineto line voltage same as that of the grid with desire phaseshift. All currents are measured with ac current clamp with10kHz bandwidth. Fig. 9 shows that the experimental resultsare agreeing with the simulation results.

VII. CONCLUSION

Power flow and current through different legs of theproposed single phase to three phase converter have beenanalyzed. A control method is proposed to improve dc linkvoltage utilization for the converter. The same control methodis verified through simulation. Practical results are obtainedwith a laboratory prototype. The obtained results agree withthe simulation results confirming the validity of the proposedcontrol method.

REFERENCES

[1] E. C. dos Santos Jr., C. B. Jacobina, E. R. C. da Silva, and N. Rocha,“Single-phase to three-phase power converters: State of the art,” IEEETrans. Power Electron., vol. 27, pp. 2437 – 2452, 2012.

(a)

(b)

Fig. 9. Experimental results of single phase to three phase converter; (a)grid voltage and FEC currents, vab : 50 V/div, all currents 5 A/div; (b) gridvoltage and load currents, vab : 50 V/div, all currents 2 A/div and time 5ms/div.

[2] P. N. Enjeti and A. Rahmant, “A new single-phase to three-phaseconverter with active input current shaping for low cost ac motor drives,”IEEE Trans. Ind. Appl., vol. 29, pp. 806–813, 1993.

[3] R. Q. Machado, S. Buso, and J. A. Pomilio, “A line-interactive single-phase to three-phase converter system,” IEEE Trans. Power Electron.,vol. 21, pp. 1628–1636, 2006.

[4] J. Nesbitt, C. Chen, D. M. Divan, and D. Novotny, “A novel single phaseto three phase converter,” in Proc. IEEE Applied Power ElectronicsConference and Exposition (APEC’91), 1991, pp. 95–99.

[5] G. A. Covic, G. L. Peters, and J. T. Boys, “An improved single phaseto three phase converter for low cost ac motor drives,” in Proc. IEEEInternational Conference on Power Electronics, Drives and EnergySystems (PEDES’95), 1995, pp. 1252–1257.

[6] C. B. Jacobina, M. B. de Rossiter Corrła, A. M. N. Lima, andE. R. C. da Silva, “Ac motor drive systems with a reduced-switch-countconverter,” IEEE Trans. Appl. Ind., vol. 39, pp. 1333–1342, 2003.

[7] J. A. A. Dias, E. C. dos Santos Jr., C. B. Jacobina, and M. B. R. Corrła,“Soft-starting techniques for low cost single-phase to three-phase drivesystem configuration,” presented at the Power Electronics SpecialistsConference, 2008, pp. 3996–4002.

[8] M. Ciobotaru, R. Teodorescu, and F. Blaabjerg, “A new single-phasepll structure based on second order generalized integrator,” in Recordof IEEE PESC, 2006, pp. 1511–1516.

[9] Y. W. Li, “Control and resonance damping of voltage-source andcurrent-source converters with lc filters,” IEEE Trans. Ind. Electron.,vol. 56, pp. 1511–1521, 2009.

[10] K. Zhou and D. Wang, “Relationship between space-vector modulationand three-phase carrier-based pwm : A comprehensive analysis,” IEEETrans. Ind. Electron., vol. 49, pp. 186–196, 2002.