Analysis and implementation of a three-phase power factor correction scheme using modular Cuk rectifier for balanced and unbalanced supply conditions

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1&

Published in IET Power ElectronicsReceived on 20th May 2012Revised on 22nd July 2013Accepted on 6th August 2013doi: 10.1049/iet-pel.2012.0243

892The Institution of Engineering and Technology 2013

ISSN 1755-4535

Analysis and implementation of a three-phase powerfactor correction scheme using modular Cuk rectifierfor balanced and unbalanced supply conditionsMallapu Gopinath Umamaheswari1,2, Govindarajan Uma1, Sangeetha Viswanathan3

1Department of Electrical and Electronics Engineering, College of Engineering, Anna University, Chennai-600025,

Tamil Nadu, India2Department of Electronics and Instrumentation Engineering, R.M.K. Engineering College, Kavaraipettai-601206,

Tamil Nadu, India3Department of Electrical and Electronics Engineering, Amrita University, Coimbatore-641112, Tamil Nadu, India

E-mail: [email protected]; [email protected]

Abstract: In this study, the analysis and design of a three-phase AC–DC converter followed by DC–DC Cuk converter modulesto achieve unity power factor is presented. Two methods of reference current generation techniques are employed. In the firstscheme, reference current is generated using instantaneous symmetrical component theory under balanced supply conditions.In the second scheme, extended synchronous detection methods such as equal current criterion, equal power criterion andequal impedance criterion are used for reference current generation under unbalanced supply conditions. The control strategyuses three hysteresis current controllers for source current shaping and an outer voltage loop with proportional-integralcontroller for load voltage regulation. To validate the proposed method, a prototype controlled by dSPACE signal processor isset up. Simulation and experimental results indicate that the proposed system offers regulated output voltage for wide loadvariations and provides power factor close to unity.

1 Introduction

Recently, there is a growing awareness about line pollutionand deteriorating power factor because of the usage ofpervading inductive and power electronic loads. In powerelectronic systems, especially diode and thyristor rectifiersare commonly used in the front end of DC-link powerconverters as an interface with the AC line power. Theserectifiers are non-linear in nature and consequently generateharmonic currents into the AC line power resulting in lowpower factor. Although many solutions were offered forsingle-phase power factor correction (PFC), three-phaseactive PFC was seldom considered. As all high powerequipment derive electrical power from three-phase mains,incorporating an active three-phase PFC front end cancontribute significantly in improving overall power factorand reducing line pollution. Many literatures have beenproposed for PFC. A three-phase single-switch PFCtopology has the merits of simple control and fewcomponents [1–5]. This type of converter suffers because ofdiscontinuous conduction mode operation, causing highcurrent stresses on the power devices. Three-phase pulsewidth modulation (PWM) boost rectifier features includecontinuous input current, excellent power factor and permitspower flow in both directions, but it is too expensive formedium power applications and it is not suitable for buckoperation [6–12]. Buck and boost rectifiers are used for

PFC in [13–15]. A buck rectifier has more attractivefeatures than boost rectifier such as inherent short-circuitprotection, low-voltage output. The conduction loss is highin buck rectifier compared with boost rectifier. In boostrectifier, isolation cannot be provided and the output voltageis always higher than the input voltage. A derived versionof buck–boost rectifier is a Cuk rectifier that inverts thevoltage polarity and can also simultaneously increase ordecrease the voltage magnitude. It has excellent featuressuch as capacitive energy transfer, magnetic componentsintegrability, full transformer utilisation and goodsteady-state performance. It also provides smooth input andoutput currents because of the presence of inductors in theinput and output sides [16, 17]. A three-phase three-switchtopology composed of three single-phase single-switchmodules were proposed for PFC in [18, 19]. Even thoughthe above method offers simple control implementation, itfails to operate in case of one or two module failures.Many methods for generating the reference template were

proposed [20–24]. In [20–22], the instantaneous reactivepower theory was proposed (i.e. p–q theory) for calculatingthe reference currents. The general equation for deriving thereference current relating the instantaneous active and reactivetheory was reported in [23], but no detailed information wasgiven for DC bus voltage compensation. In [24], only thefinal formulation of the extracted reference current wasreported. In [25], the extended symmetrical component theory

IET Power Electron., 2013, Vol. 6, Iss. 9, pp. 1892–1908doi: 10.1049/iet-pel.2012.0243

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was proposed to derive a more general vector equation forcalculating the reference currents. In [26, 27], PFC using Cukrectifier modules were proposed and reference current wasgenerated using power balance control technique.Hence, a method is proposed to develop a single-stage
three-phase AC–DC converter using Cuk rectifier modulesfor achieving voltage regulation and PFC under balancedand unbalanced supply conditions. The instantaneoussymmetrical component theory is used for calculating thereference template under balanced supply conditions.Extended synchronous detection methods are used forreference current generation under unbalanced supplyconditions. Here, hysteresis control (HC) is used for sourcecurrent shaping. HC method is one of the well-known

Fig. 1 Cuk rectifier module

a Circuit of three-phase PFC Cuk converterb Closed-loop control using HC


current control methods used in voltage-fed PWMconverters. The basic advantages of HC are its simplicity,easy implementation, fast-response, lack of tracking errorand good dynamics.

2 Cuk rectifier module

The circuit diagram for the proposed three-phaseconfiguration is shown in Fig. 1a. Lia, Lib and Lic representthe input inductors and Loa, Lob and Loc are the outputinductors for the respective three phases. Cta, Ctb and Ctc

represent the transfer capacitors. vsa, vsb and vsc and Vo

represent supply voltages for the three phases and output

1893& The Institution of Engineering and Technology 2013

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voltage, respectively, Sa, Sb and Sc are active switches for thethree phases, Da, Db and Dc are freewheeling diodes and RL isthe load resistance. A single capacitor Co is connected at theoutput terminals for filtering the output voltage ripple. Theproposed converter in modular form offers high powerfactor with simple control strategy and design. It alsoprovides regulated output voltage with fast dynamicresponse. The DC–DC Cuk converter operating incontinuous conduction mode is designed with the followingspecifications. VS = 24 V, Vo = 24 V; RL = 10 Ω, fS = 50 kHz,Io = (0–2.5) A, d = 0.5, ΔILi = 4.8% of the source current,ΔILo = 9.6% of the source current, ΔVCt = 4.2% of theoutput voltage and ΔVCo = 0.000278% of the outputvoltage. Then the calculated parameter values are listed inthe Appendix.
3 Generation of reference current

The theory of instantaneous symmetrical components cancompensate any kind of harmonics under balanced supplyconditions. The extraction of reference current based oninstantaneous symmetrical component theory involvessimple computations using instantaneous source voltagesand currents and it does not require any three-phase totwo-phase conversions. The main advantage of this methodis the simplified computational task.

3.1 Instantaneous symmetrical component theory

Based on this theory, the reference currents for thethree-phase star-connected balanced supply [25] are givenas follows

isa =vsa + vsb − vsc

( )b∗

v2sa + v2sb + v2sc( ) PLavg + PLoss

( )(1)

isb =vsb + vsc − vsa

( )b∗


( )(2)

isc =vsc + vsa − vsb

( )b∗


( )(3)

Here, vsa, vsb, vsc, isa, isb and isc represent the three-phasesupply voltages and source line currents, respectively. PLoss

represents the switching losses and ohmic losses in theconverter. Owing to losses in converter, the outputcapacitor voltage will decrease. When the output capacitorvoltage falls below the reference voltage, the compensatormay not be able to track the reference current faithfully. Soa suitable proportional-integral (PI) controller is used whichregulates the output capacitor voltage to the reference value.PLoss is thus given by

PLoss = Kpe+ Ki

∫edt (4)

where e = Vref − Vo andb∗ = tan w/��3

√( ), j is the desired

phase angle between source phase voltages (vsa, vsb andvsc) and source line currents (isa, isb and isc) for thebalanced system. Under unbalanced supply voltageconditions, j is taken as phase angle between the positivesequence source voltages and the source currents in therespective phases. The average power supplied by thesource, which is also the average load power denoted by


PLavg is given by

PLavg = vsa × isa + vsb × isb + vsc × isc( )

(5)

3.2 Extended synchronous detection methods

Symmetrical component theory gives erroneous resultswhen the source voltages are unbalanced. However, thisalgorithm can be extended for non-sinusoidal conditions,if the fundamental positive sequence components of theunbalanced supply voltages can be found out. The mainadvantage of this method is simplified computational task.In this case, it is assumed that the source voltages aresinusoidal but have magnitude unbalance. A more generalmethod for generating reference current is extendedsynchronous detection method. This includes equal currentcriterion, equal power criterion and equal impedancecriterion [25] and is discussed in the following section.

3.2.1 Equal current criterion: Under this criterion, it isassumed that the peak values of the source currents areequal in magnitude, that is

Isma = Ismb = Ismc (6)

Equation (5) can be written as

PLavg =Vsma��

2√ × Isma��

2√ × cosw+ Vsmb��

2√ × Isma��

2√

(

× cosw+ Vsmc��2

√ × Isma��2

√ × cosw

)(7)

From the above equation PLavg is derived as

PLavg =Vsma + Vsmb + Vsmc��

2√

[ ]× cosw× isa (8)

From (8), isa can be written as

isa =��2

√PLavg

cosf∑

i=a, b, cVsmi

=��2

√PLavg

Vsma cosf∑

i=a, b, cVsmi

Vsma

=��2

√PLavg

Vsma cosf∑

i=a, b, cVsmi

��2

√vsa (9)

Using (9), the reference currents for the proposed system aregiven as

isa =2PLavg

cosfVsma

∑i=a, b, c Vsmi

vsa

isb =2PLavg

cosfVsmb

∑i=a, b, c Vsmi

vsb (10)

isc =2PLavg

cosfVsmc

∑i=a, b, c Vsmi

vsc

vsa, vsb and vsc are the instantaneous three-phase voltages andVsma, Vsmb and Vsmc represent the peak value of the sourcevoltages.


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3.2.2 Equal power criterion: In equal power criterion,the real power flow in each phase after compensation is tobe shared equally. For equal power criterion, the conditionto be satisfied is
Vsma��2

√ × Isma��2

√ = Vsmb��2

√ × Ismb��2

√ = Vsmc��2

√ × Ismc��2

√ (11)

Using (11), PLavg is given as

PLavg =3VsmaIsma cosw

2(12)

From (12), reference current is represented as

isi =2PLavgVsma

3��2

√cosfV 2

sma

= 2PLavg

��2

√vsa

3��2

√cosfV 2

sma

= 2PLavgvsa3 cosfV 2

sma(13)

Fig. 2 Simulated waveforms using instantaneous symmetrical compone

a Source currentb Source current in phase with the source voltagec Regulated output voltage and load current for load variationd Harmonic spectrum of source current for three phasesSimulated waveforms using instantaneous symmetrical component theory under une Source currentf Source current in phase with the source voltageg output voltage


Using (13), the reference currents for this criterion is given as

isi =2PLavg

3 cosfV 2smi

vsi for i = a, b, c (14)

3.2.3 Equal impedance criterion: In equal impedancecriterion, it is assumed that the source should see the sameimpedance in each phase. This means that the ratios of thepeak value of the source voltages to the peak value of thesource currents in each phase should be equal.

Za = Zb = Zc = Z (15)

Therefore

Vsma

Isma= Vsmb

Ismb= Vsmc

Ismc= Z| | (16)

nt theory under balanced supply conditions

balanced supply conditions:


Fig. 3 Simulated waveforms using instantaneous symmetrical component theory under balanced supply conditions for three operatingconditions: three-phase supply condition, module loss in phase a and module loss in phases a and b

a Source currentsb Input inductor currentsc Output voltaged Load currente Output power

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Substituting the above condition, (5) can be written as

PLavg =Vsma��

2√ × Isma��

2√ × cosw+ Vsmb��

2√ × Ismb��

2√

(

× cosw+ Vsmc��2

√ × Ismc��2

√ × cosw

)(17)

Substituting Isma, Ismb and Ismc from (16) in (17), |Z| isobtained as

Z| | =∑

i=a, b, c V2smi

2PLavgcosf (18)

Equation (18) can also be written as

vsiisi

=∑

i=a, b, c V2smi

2PLavgcosf (19)

Table 1 System performance parameters for load variation usingsupply conditions

Load current, A 2.402 2.18 2.002efficiency, % 87.66 86.87 85.73PF 0.9994 0.9991 0.9986THD 1.935 2.612 3.213voltage regulation,% − 0.0416 − 0.0416 − 0.0125


Therefore the computed reference currents are given as

isi =2PLavg

cosf∑

i=a, b, c V2smi

vsi (20)

4 Closed-loop control of three-phase PFCCuk converter using HC

This section presents the design of the controller. Thecontroller is comprised of an inner current loop, which usesHC for shaping the input current, and an outer voltagecontrol loop using PI controller to regulate the outputvoltage as shown in Fig. 1b. The PI controller parameters,Kp and Ki, are found by Ziegler–Nichols tuning method. Inthis method, the proposed system is providing sustainedoscillations with the ultimate gain (Ku = 4) and ultimate

instantaneous symmetrical component theory under balanced

1.848 1.716 1.601 1.50185.36 84.91 84.45 84.410.9984 0.9983 0.9981 0.99453.584 3.966 4.767 5.001

− 0.0125 − 0.2083 − 0.2083 − 0.2083


Fig. 5 Simulated waveforms using equal current criterion for three operating conditions: three-phase supply condition, module loss in phasea and module loss in phases a and b


Fig. 4 Simulated waveforms using equal current criterion

a Source currentsb Source current in phase with the source voltagec Regulated output voltage and load current for 10% increase in loadd Harmonic spectrum of source current for three phases

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Table 2 System performance parameters for load variation using equal current criterion

Load current, A 2.402 2.18 2.002 1.848 1.716 1.601 1.501Efficiency, % 87.21 86.67 86.52 86.25 86.12 85.6 85.43PF 0.9996 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995THD 2.233 2.356 2.786 3.108 3.709 4.418 5.18voltage regulation,% − 0.0417 − 0.0417 − 0.0417 − 0.0833 − 0.0833 − 0.0833 − 0.0125

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period (Pu = 0.065 s). By this method, the values forKp( =Ku / 2) and Ki are found to be 2 and 18.46 (Ti = Pu /1.2 and Ki = 1 / Ti), respectively.The output voltage is compared with the reference voltage

and the error is fed to the PI controller. Reference currentsare generated using the output of the PI controller,three-phase source voltages vsa, vsb and vsc and source

Fig. 6 Simulated waveforms using equal power criterion

a Source currentsb Source current in phase with the source voltagec Regulated output voltage and ld Harmonic spectrum of source current in phase ae Harmonic spectrum of source current in phase bf Harmonic spectrum of source current in phase cg Power in phase ah Power in phase bi Power in phase c


currents isa, isb and isc. The reference current with desiredmagnitude and shape is derived by instantaneoussymmetrical component theory under balanced supplyvoltage conditions and by using extended synchronousdetection methods under unbalanced supply voltageconditions. The instantaneous values of actual source currentand reference source current are compared using HC. The

oad current for 10% increase in load


Fig. 7 Simulated waveforms using equal power criterion for three operating conditions: three-phase supply condition, module loss in phase aand module loss in phases a and b


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result of comparison is the PWM signals, which are used fordriving the converter switches Sa, Sb and Sc. Thus, theconverter switches forces the input current to follow thedesired reference within hysteresis band. Here the hysteresisbandwidth is chosen as 0.0005.

5 Simulation studies

In this section, a modular three-phase AC–DC converterusing Cuk rectifier modules based on symmetricalcomponent theory and extended synchronous detection

Table 3 System performance parameters for load variation using eq

Load current, A 2.402 2.18 2.002efficiency, % 87 86.53 86.47PF 0.9915 0.9908 0.9901THD 2.611 3.257 3.98voltage regulation,% − 0.125 − 0.125 − 0.167


methods for unity power factor (UPF) operation on sourceside and dynamic response of load voltage are discussed.The configuration of the proposed system is simulated usingMATLAB/SIMULINK program. The control circuit usedfor simulation is shown in Fig. 1b.The simulation results of the proposed scheme under

balanced supply conditions using instantaneous symmetricalcomponent theory are shown in Figs. 2a–d. From Figs. 2aand b, it is seen that the source currents become sinusoidaland balanced and almost UPF operation is achieved. Thesimulation result of transient response of the output voltage

ual power criterion

1.848 1.716 1.601 1.50186.18 86.18 85.19 85.160.9897 0.99 0.9883 0.98644.784 5.589 6.52 7.676

− 0.167 − 0.25 − 0.25 − 0.25


Fig. 8 Simulated waveforms using equal impedance criterion

a Source currentsb Source current in phase with the source voltagec Regulated output voltage and load current for 10% increase in loadd Harmonic spectrum of source current in phase ae Harmonic spectrum of source current in phase bf Harmonic spectrum of source current in phase cg Impedance in phase ah Impedance in phase bi Impedance in phase c

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and load current waveforms for step load change is shown inFig. 2c. The proposed system provides regulated outputvoltage for load variation after 36 ms. From Fig. 2d, the %total harmonic distortion (THD) of the source current forthe balanced supply condition is 1.94%. The instantaneoussymmetrical component theory is tested for unbalancedsupply conditions and results are presented in Figs. 2e–g. Itis inferred from the results that even though the outputvoltage is regulated, the source current after compensationbecomes highly distorted. Hence, it is concluded that theuse of symmetrical component theory under the magnitudeunbalanced supply voltage conditions does not providesatisfactory performance.Figs. 3a–e show the simulation results of source currents

isa, isb and isc, input inductor currents iLia, iLib and iLic,output voltage, load current and output power under


balanced supply conditions for three operating conditions;three-phase supply condition between 0 and 0.15 s, moduleloss in phase a between 0.15 and 0.25 s, return ofthree-phase supply condition between 0.25 and 0.35 s,module loss in phases a and b between 0.35 and 0.45 s.Here, each single-phase PFC Cuk module is designed forthe rated load current. In the three-phase configuration, eachCuk module carries one-third of load current. From Figs. 3aand b, it is seen that even under single/two module lossconditions, the system continues to work. It is observedfrom Fig. 3a, during three-phase supply condition, sourcecurrent become sinusoidal and balanced after 0.114 s.Under one module loss conditions, the magnitude of thesource currents are unequal. This is due to the presence ofan oscillating component in the power PLavg. It is inferredfrom Fig. 3c that for one module loss, the steady-state error


Fig. 9 Simulated waveforms using equal impedance criterion for three operating conditions: three-phase supply condition, module loss inphase a and module loss in phases a and b


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in the output voltage is 6.25% of the reference voltage and fortwo module loss, the steady-state error in the output voltage is16.5% of the reference voltage. Table 1 presents theperformance parameters of three-phase PFC Cuk converterfor load variation using instantaneous symmetricalcomponent theory under balanced supply voltageconditions. From Table 1, it is observed that the percentageefficiency is maintained nearly 85% for all the loads andthe maximum efficiency is found to be 87.66% at ratedload. For instantaneous symmetrical component theoryunder balanced supply conditions, the %THD is maintainedaround 5% for all the loads as per IEEE Std 519.

Table 4 System performance parameters for load variation using eq

Load current, A 2.402 2.18 2.002efficiency, % 87.08 86.71 86.27PF 0.9902 0.9895 0.9887THD 3.131 4.044 5.007voltage regulation,% − 0.2083 − 0.2083 − 0.2083


In the following section, simulation results of extendedsynchronous detection methods are discussed. Thesimulation results of the proposed system under unbalancedsupply conditions using equal current criterion are presentedin Figs. 4a–d. From Fig. 4a, it is seen that source currentsbecome sinusoidal and balanced and it proves theassumption made in reference current generation. Fig. 4bdepicts that source current is in phase with the sourcevoltage after employing equal current criterion. It is evidentfrom Fig. 4c that the proposed system provides regulatedoutput voltage for load variation after 22 ms. Fig.4d showsthe harmonic spectrum of source current and the %THD is

ual impedance criterion

1.848 1.716 1.601 1.50185.77 85.23 85.16 84.980.9879 0.9875 0.9872 0.98175.918 6.911 7.816 8.998

− 0.2083 − 0.2083 − 0.1667 − 0.125


Fig. 10 Hardware implementation of the proposed control technique

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2.23% for all the three phases. Figs. 5a–e depict thesimulation results of source currents isa, isb and isc, inputinductor currents iLia, iLib and iLic, output voltage, loadcurrent and output power after employing equal currentcriterion for three operating conditions; three-phase supplycondition between 0 and 0.15 s, module loss in phase abetween 0.15 and 0.25 s, return of three-phase supplycondition between 0.25 and 0.35 s, module loss in phases aand b between 0.35 and 0.45 s. Results from Figs. 5a and breveal that the system continue to work even under onemodule loss/two module loss conditions. It is observedfrom Fig. 5a, during three-phase supply condition, sourcecurrent become sinusoidal and balanced after 0.088 s. It isinferred from Fig. 5c that for one module loss, thesteady-state error in the output voltage is 2% of thereference voltage and for two module loss, the steady-stateerror in the output voltage is 4.25% of the referencevoltage. Table 2 illustrates the performance parameters ofthe three-phase PFC Cuk converter for load variation usingequal current criterion. It is observed that the percentageefficiency is maintained above 85% for all the loads and themaximum efficiency at rated load is found to be 87.21%.Equal current criterion provides balanced, sinusoidalcompensated currents, even when the system voltage isunbalanced and hence the %THD is maintained around 5%for all the loads as per IEEE Std 519.Simulation results of equal power criterion are shown in

Figs. 6a–i. Figs. 6a and b depict that the source currentsbecome sinusoidal, but have magnitude unbalance and


source current is in phase with the source voltage. Resultsfrom Fig. 6c reveal that the converter provides a regulatedoutput voltage for load variation and gets back its referencevoltage within 28 ms. Figs. 6d–f shows the harmonicspectrum of three phases and the %THD is 2.61, 6.73 and4.38%, respectively. Results from Figs. 6g–i illustrate thatequal power is shared by all the three phases and it alsojustifies the assumptions made in generating referencecurrents using equal power method. Figs. 7a–e) show thesimulation results of source currents isa, isb and isc, inputinductor currents iLia, iLib and iLic, output voltage, loadcurrent and output power using equal power criterion forthree operating conditions; three-phase supply conditionbetween 0 and 0.15 s, module loss in phase a between 0.15and 0.25 s, return of three-phase supply condition between0.25 and 0.35 s, module loss in phases a and b between0.35 and 0.45 s. From Figs. 7a and b, it is inferred thateven under single/two module loss conditions, the systemcontinue to work. It is inferred from Fig. 7a, duringthree-phase supply condition, source current becomesinusoidal but unbalanced after 0.95 s. It is found fromFig. 7c that for one module loss, the steady-state error inthe output voltage is 7% of the reference voltage and fortwo module loss, the steady-state error in the output voltageis 16% of the reference voltage. Table 3 presents thedifferent performance parameters of the three-phase PFCCuk converter for load variation using equal powercriterion. It is observed that the percentage efficiency ismaintained above 85% for all the loads and the maximum


Fig. 11 Experimental waveforms using instantaneous symmetrical component theory under balanced supply conditions

a Source currentsb Source current in phase with the source voltagec Source currents under module loss conditionsd Output voltage and load current under module loss conditionse Regulated output voltage and load current for load variationf Harmonic spectrum of source current for three phases

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efficiency at rated load is found to be 87%. In equal powercriterion, the compensator must compensate for theoscillating real power, and hence the rms value of thereference current is minimised. Owing to this, the %THD iswithin 5% for light load variations, %THD is around 9%for heavy load variations.Simulation results for equal impedance criterion are

presented in Figs. 8a–i. It is apparent from Fig. 8a thatcompensated source currents are sinusoidal but havemagnitude unbalance. Fig. 8b also depicts that UPFoperation is possible in equal impedance criterion. FromFig. 8c, it is inferred that the proposed system providesregulated output voltage and the converter gets back itsreference voltage within 32 ms for load variation. Figs. 8d–fpresent the harmonic spectrum of three phases and the %THD is 3.13, 7.62 and 3.81%, respectively. Results fromFigs. 8g–i depict that equal impedance is present in all thethree phases and it also proves the effectiveness ofassumption made in reference current generation.Figs. 9a–e illustrate the simulation results of source

currents isa, isb and isc, input inductor currents iLia, iLib andiLic, output voltage, load current and output power usingequal impedance criterion for three operating conditions;


three-phase supply condition between 0 and 0.15 s, moduleloss in phase a between 0.15 and 0.25 s, return ofthree-phase supply condition between 0.25 and 0.35 s,module loss in phases a and b between 0.35 and 0.45 s.From Figs. 9a and b, it is observed that the proposedsystem operates continuously under module loss conditions.It is seen from Fig. 9a, during three-phase supply condition,source current become sinusoidal but have magnitudeunbalance after 0.09 s. From Fig. 9c, it is inferred that forone module loss, the steady error in the output voltage is6.5% of the reference voltage and for two module loss, thesteady error in the output voltage is 13% of the referencevoltage.Table 4 presents the different performance parameters of

the three-phase PFC Cuk converter for load variation usingequal impedance criterion. From Table 4, it is seen that thepercentage efficiency is maintained nearly 85% for all theloads and the maximum efficiency at rated current is foundto be 87.08%. In equal impedance method, the sourcecurrent is proportional to the corresponding source phasevoltage. However, this method does not guaranteesinusoidal reference current or constant instantaneous activepower drawn from the source. Owing to this, the %THD is


Fig. 12 Experimental waveforms for equal current criterion

a Source currentsb Source current in phase with the source voltagec Source currents under module loss conditionsd Output voltage and load current under module loss conditionse Regulated output voltage and load current for load variationf Harmonic spectrum of source current for three phases

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within 5% for light load variations, %THD is around 9% forheavy load variations.

6 Experimental results

A prototype model for three-phase PFC Cuk converter isdeveloped and controlled with the proposed control strategyusing dSPACE 1104 signal processor with the same designvalues as used in simulation. The dS1104 controller boardof dSPACE specifically designed for the development ofhigh-speed multivariable digital controllers is plugged intoa PCI slot of the PC. The board also includes aslave-subsystem based on the TMS320F240 digital signalprocessor (DSP). Hardware implementation of the proposedcontrol strategy is shown in Fig. 10. During closed-loopoperation, the three-phase source voltages, source currentsand output voltage are sensed by hall effect voltage andcurrent sensors and scaled down to less than ±10 V usingthe signal conditioning circuit, fed-back to the controllerthrough the analog-to-digital convertor channels of theDSP. The reference current generation using instantaneoussymmetrical component theory/extended synchronousdetection methods and HC are then designed in SIMULINKand downloaded to the DSP which provides the necessary


switching signals to the driver circuit. Figs. 11a–f depict theexperimental results of the proposed converter moduleunder balanced supply conditions using instantaneoussymmetrical component theory. It is seen from Figs. 11aand b that the source currents become sinusoidal andbalanced and almost UPF operation is achieved. Fig. 11creveals that the proposed system operates continuouslyunder module loss conditions. Fig. 11d depicts the outputvoltage and load current waveforms for module lossconditions. The transient response of the output voltage andload current waveforms for load variation is shown inFig. 11e. The output voltage attains its reference value after36 ms. The harmonic spectrum of the source current isshown in Fig. 11f and the %THD is 3.5%.The experimental results of the proposed system under

unbalanced supply conditions using equal current criterionare presented in Figs. 12a–f. Results from Fig. 12a illustratethat the source currents are sinusoidal and balanced afteremploying equal current criterion. From Fig. 12b, it isinferred that source current is in phase with the sourcevoltage. Results from Fig. 12c reveals that the system cancontinuously operate in spite of module loss in any one ortwo phases. Fig. 12d represents the output voltage and loadcurrent waveforms for module loss conditions. It is inferredfrom Fig. 12e that the converter provides a constant voltage


Fig. 13 Experimental waveforms for equal power criterion

a Source currentsb Source current in phase with the source voltagec Source currents under module loss conditionsd Output voltage and load current under module loss conditionse Regulated output voltage and load current for load variationf Harmonic spectrum of source current in phase ag Harmonic spectrum of source current in phase bh Harmonic spectrum of source current in phase c

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for load variation after 22 ms. Harmonic spectrum of sourcecurrent for all the three phases is shown in Fig. 12f. Theexperimental results of the proposed system underunbalanced supply conditions using equal power criterionare presented in Figs. 13a–h. Results from Fig. 13a showthat the source currents are sinusoidal, but have magnitudeunbalance after employing equal power criterion. FromFig. 13b, it is observed that source current is in phase withthe source voltage. Results from Fig. 13c show that thesystem can continuously operate in spite of module loss inany of the phases. Fig. 13d represents the output voltage


and load current waveforms for module loss conditions.Fig. 13e shows that the converter provides a regulatedoutput voltage for load variation after 28 ms. Figs.13f–hshow the harmonic spectrum of source current and the %THD are 3.6, 7.0 and 5.6%, respectively. Experimentalresults of the proposed system for unbalanced supplyconditions using equal impedance criterion are shown inFigs. 14a–h. Results from Fig. 14a indicate that the sourcecurrents are sinusoidal and but have magnitude unbalanceafter employing equal impedance criterion. From Fig. 14b,it is seen that source current is in phase with the source


Fig. 14 Experimental waveforms for equal impedance criterion

a Source currentsb Source current in phase with the source voltagec Source currents under module loss conditionsd Output voltage and load current under module loss conditionse Regulated output voltage and load current for load variationf Harmonic spectrum of source current in phase ag Harmonic spectrum of source current in phase bh Harmonic spectrum of source current in phase c

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voltage. Results from Fig. 14c depict that the converter cancontinuously operate in spite of module loss in any one ortwo phases. Fig. 14d shows the output voltage and loadcurrent for module loss condition. Fig. 14e reveals that theconverter provides a regulated output voltage for loadvariation after 32 ms. Harmonic spectrum of source currentfor the three phases are given in Figs. 14f–h and the %THDare 3.8, 7.6 and 4.0%, respectively.

7 Performance of three-phase Cuk PFCconverter for various control strategies

Calculation of effective apparent power plays a vital role inobtaining the power factor under unbalanced supply


conditions [28, 29]. The effective rms voltage underunbalanced supply condition is given by

Ve =��1

183 V 2

sa + V 2sb + V 2

sc

( )+ V 2sab + V 2

sbc + V 2sca

[ ]√(21)

where Vsa, Vsb, Vsc, Vsab, Vsbc and Vsca represent the rms valueof the phase and line voltages.Effective rms current is calculated by the equation

Ie =��I2sa + I2sb + I2sc

√��3

√ (22)


Table 5 Comparative analysis of different methods of the proposed system

Method used Loadcurrent,

A

Efficiency,%

PF THD inphasea, %

Loadregulation,

%

Settling timefor step loadvariation, ms

Steady-stateerror for onemodule loss

Steady-stateerror for twomodule loss

Balanced supply voltage conditionsinstantaneoussymmetricalcomponent theory

2.4 87.66 0.9994 1.94 −0.0416 36 6.25% ofreferencevoltage

16.5% ofreferencevoltage

Unbalanced supply voltage conditionsequal currentcriterion

2.4 87.21 0.9996 2.23 −0.0417 22 2% of referencevoltage

4.25% ofreferencevoltage

equal powercriterion

2.4 87 0.9915 2.61 −0.125 28 7% of referencevoltage

16% of referencevoltage

equal impedancecriterion

2.4 87.08 0.9902 3.131 −0.2083 32 6.5% ofreferencevoltage

13% of referencevoltage

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where Isa, Isb and Isc represent the rms value of the sourcecurrents.Using (21) and (22), the effective apparent power is

calculated as

Se = 3VeIe (23)

Power factor is calculated using the PLavg and effectiveapparent power Se as

power factor = PLavg

Se(24)

Based on the results obtained from simulation andexperimentation, the following analysis is made and it ispresented in Table 5. Among the three types of extendedsynchronous methods for unbalanced supply voltageconditions, it is inferred that equal current criterion givesbest results for PFC as it provides less percentage of THDand also it is seen that the source currents are sinusoidaland balanced after compensation. Output voltage is alsoregulated for load variation and it also produces the outputvoltage almost equal to reference voltage for one moduleand two module loss conditions.

8 Discussion

It is proposed to construct a single-stage Cuk converter inmodular form for achieving PFC and voltage regulation. Allthe control circuits including the PI controller, referencecurrent calculation and inner HC loop have beenimplemented using dSPACE signal processor. There is adifference in %THD between simulation andexperimentation, because the internal resistances of reactiveelements, semiconductors that may slightly influence thedynamics of the converter, which is not appearing whensimulated with ideal components. In addition to that themeasurement errors caused by high-frequency componentsmight bring more differences between the results.Moreover, the power quality analyser used inexperimentation can able to trap only up to the 49thharmonics.

9 Conclusions

In this paper, the analysis and design of a three-phase AC–DCconverter followed by DC–DC Cuk converter modules with


the common DC output for PFC is presented. Referencecurrents are generated using instantaneous symmetricalcomponent theory for the balanced supply voltageconditions and for the unbalanced supply voltage conditionsextended synchronous detection methods such as equalcurrent criterion, equal power criterion and equal impedancecriterion are used. The control strategy is based on outervoltage control loop and three inner hysteresis currentcontrollers. The proposed controller guarantees continuousoperation of the system in case of module failure. Tosupport the proposed method, a prototype controlled bydSPACE signal processor is set up. From the results, it isfound that equal current criteria offers excellent results forPFC when compared with equal power and equalimpedance criterions under unbalanced supply voltageconditions. Simulation and experimental results reveal thatthe proposed system offers the regulated output voltage forload variations and also provide power factor close to unity.

10 References

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Table 6 Design parameters for Cuk module

Converterparameters

Design values

input sourcevoltages

24 V/phase (balanced system)24 V/phase a 26 V/phase b (unbalanced

system) 28 V/phase csupply frequency 50 Hzswitchingfrequency

variable frequency (40–50) kHz

output voltage 24 VLia, Lib, Lic 2 mH/10 ALoa, Lob, Loc 1 mH/10 ACta, Ctb, Ctc 25 µF/25 VCo 9000 µF/63 VRL 10 Ω/100 WKp, Ki 2, 18.46

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11 Appendix

See Table 6


Documents

Analysis and implementation of a three-phase power factor correction scheme using modular Cuk rectifier for balanced and unbalanced supply conditions