phase1

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Published in IET Power ElectronicsReceived on 4th August 2013Revised on 7th December 2013Accepted on 7th January 2014doi: 10.1049/iet-pel.2013.0605

566The Institution of Engineering and Technology 2014

ISSN 1755-4535

Compensation of three-phase diode rectifier withcapacitive filter working under unbalanced supplyconditions using series hybrid active power filterMahmadasraf Abdulhamid Mulla, Chudamani Rajagopalan, Anandita Chowdhury

Department of Electrical Engineering, S. V. National Institute of Technology, Ichchhanath, Surat, Gujarat 395007, India

E-mail: [email protected]

Abstract: The currents drawn by three-phase diode rectifiers with capacitive filters under unbalanced supply conditions are highlynon-linear and unbalanced. This configuration draws significantly unbalanced currents even with smaller percentage of unbalancein supply voltages and more unbalance in supply voltages leads to an extreme unbalanced situation like single phasing. This studyhighlights the unbalance line current problem observed in three-phase diode rectifier and proposes its compensation using serieshybrid active power filter (SHAPF) working with appropriate control strategy. Four distinct modes of operation under unbalancedsupply are identified. A new control algorithm which simultaneously compensates for supply voltage unbalance and sourcecurrent harmonics is applied to compensate the configuration. An experimental model of three-phase diode rectifier withcapacitive filter working under different supply situation is developed to establish identified modes of operation. Thisconfiguration is compensated with SHAPF, manufactured using ARM Cortex M4-based microcontroller and the results ofcompensation are described in this study.

1 Introduction

Majority of modern power converters are supplied withunregulated dc voltage from ac lines via diode rectifiers.Two popularly used configuration of diode rectifier are: therectifiers having sufficiently large dc inductor to supplyconstant dc current to the load and the rectifiers havingsufficiently large capacitance on dc side to supply constantdc voltage to the load. The source current characteristics ofdiode rectifiers are not friendly to supply lines because oftheir non-linear nature and hence it has drawn muchattention [1–5]. The situation is worst for diode rectifiersaccompanied by large dc capacitive filter. The capacitorfilter keeps the dc voltage very close to the peak ofline-to-line voltage, resulting into highly non-linear sourcecurrents flow for brief period.In addition to source current harmonics, the unbalance of

source current is another primary concern of thisconfiguration. In field applications, small unbalance is alwayspresent in source voltage which may cause significantunbalance in source currents. Unbalance rectifier currents cancause effects like uneven current distribution over the legs ofthe rectifier, increased rms ripple current in the smoothingcapacitor, increased total rms line current, harmonics and inparticular, non-characteristic triplen harmonics that do notappear under balanced condition [3–5]. As small unbalanceis always present in most industrial and commercial powerlines, care should be taken in designing and installing dioderectifiers to keep the current unbalance within an acceptablelevel and to avoid the above undesirable effects.

Load compensation in power engineering is the procedureused to obtain the source currents sinusoidal and balanced.One approach is to integrate power-factor correction (PFC)circuit in the converter configuration. Diode rectifier withthe continuous-conduction-mode boost converter [6–8],pulse-width modulated (PWM) rectifier [9], PWM ACchoppers [10] are the different topology for implementingPFC. The closed-loop operation of the static powerconverter with PFC assures satisfactory performance toachieve high input power factor and regulate converteroutput voltage over a wide operating range. Increasedcomplexity, conducted electromagnetic interference andreduced robustness are the distinct characteristics of theseapproaches [7]. These approaches address the compensationof source current harmonics, but they do not compensatefor source voltage unbalances.In an alternative approach active power filter (APF) are

suggested as power electronic solutions for loadcompensation. Various APF configurations and controlstrategies have been investigated during the last decades.Popularly used APF configurations are: shunt APF, whichinjects compensation currents [11]; series APF, whichinjects compensation voltages through a transformer [12];and the series hybrid APF (SHAPF) which is a combinedsystem of shunt passive power filter (PPF) and series APF[13–17]. In order to reduce inverter capacity and because ofmulti-functionality, SHAPF is becoming very popular inrecent developments. To obtain efficient SHAPFperformance, it is important to choose proper referencegeneration algorithm. The objective of control strategy for

IET Power Electron., 2014, Vol. 7, Iss. 6, pp. 1566–1577doi: 10.1049/iet-pel.2013.0605

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SHAPF is to extract source current harmonics or load voltageharmonics or combination of both [12]. Using vector algebra,it is possible to decompose voltage vector into quantities thatrepresent different components of power [18, 19]. Theseparated components of voltage are useful for generatingreference of SHAPF that compensates for source currentharmonics. Moreover, the reference for unbalance in sourcevoltages can be added to this reference for compensatingunbalance in source voltages.This paper is intended to highlight the problem of current
unbalance in three-phase diode rectifier working underunbalance source voltages and provide power electronicsolution to this problem using SHAPF. Operation ofthree-phase diode rectifier under four distinct modes areidentified that ranges from balance currents to extremeunbalance currents equivalent to single phasing. SHAPFalong with a new control strategy which simultaneouslycompensate the source voltage unbalances and sourcecurrent harmonics is proposed as a solution to compensatethis problem. The proposed solution is verified with anexperimental study. The main components of experimentalprototype are three-phase diode rectifier with capacitivefilter working under different unbalance power supply,SHAPF and a control circuit developed using ARM CortexM4 microcontroller STM32F407x. The source current ofthree-phase diode rectifier with capacitive filter, workingunder four possible modes of operation is compensatedusing the experimental prototype and results are reported.

2 Operating modes of three-phase dioderectifier

Detailed analysis of line current characteristics of three-phasediode rectifiers working under unbalance supply is given byJeong and Choi [5]. Following are the four possible modesof operation of this configuration, which depends on theunbalance in source voltages and the ripple in rectifiedvoltage.

Mode I – Six pulse operation under balanced source voltages:with perfectly balanced source voltages, six line-to-linevoltages appear sequentially in the dc rectified voltage. Abalance pulse shaped current around the peak of linevoltages is drawn by each line in this mode of operation.Fig. 1a shows the source current waveform while workingunder this mode. It is observed that the peaks of two pulsesin each line currents are equal in this mode.

Mode II – Six pulse operation under unbalanced sourcevoltages: with a small unbalance in source voltages, the dcrectified voltage still touches peak of all six line voltages.As shown in Fig. 1b, unbalance current is drawn fromdifferent lines in this situation which is pulse shaped aroundthe peak of the line voltages. The two peaks of currentpulses appear in each line currents are of unequal height inthis mode of operation.

Mode III – Four pulse operation under unbalanced sourcevoltages: in this mode, because of the small unbalance insource voltages, the dc rectified voltage is not touching peakof one set of line voltages, resulting into four pulses inrectified dc voltage. As shown in Fig. 1c, the line voltagehaving highest peak voltage still draws a current similar toMode II. One set of line current pulse are finding return paththrough second line and another set of line current pulse arefinding return path through the third lines. This will resultinto third harmonic intensive unbalance line currents.


Mode IV – Two pulse operation with unbalanced sourcevoltages: in this mode, as one of the three line voltages issignificantly larger than the others, only two chargingperiods appear over a cycle in the rectified voltage. Asshown in Fig. 1d, this will result into extreme unbalancecondition similar to single phasing in three-phase circuitwhere there is no current flowing in one of the line.The profiles of line current in this mode of operation arethird harmonic intensive harmonic rich extreme unbalancecurrents.The unbalance and high distortion caused in the source

current because of this load is compensated using SHAPFworking with appropriate control strategy, which isdiscussed in the following section.

3 Details of SHAPF system configuration

The complete system configuration of SHAPF used forcompensation of three-phase diode rectifier is as shown inFig. 2. The SHAPF consists of shunt passive filters andseries active filter. The arrangement is controlled to act as acurrent harmonic isolator by forcing all the harmoniccurrents to sink into passive filter.The series active filter in SHAPF works as active

impedance which offers low impedance at fundamentalfrequency and high impedance at harmonic frequency. Thiswill force all harmonic current to sink through passive filterand allow only fundamental current to come from source.The shunt passive filter consists of fifth harmonic (250 Hz)tuned filter, seventh harmonic (350 Hz) tuned filter and ahigh-pass filter. Since, the dominant (lower order)harmonics are eliminated by the passive filter and the seriesactive filter has to compensate only higher order harmonicsand thus the rating of the active filter needed will be lesscompared with conventional shunt active filters [16].The power circuit of the series power filter is made up of the

three-phase PWM voltage source inverter (VSI), the couplingtransformers and the ripple filter. The arrangement of theseries active filter and shunt passive filter reduces the needfor precise tuning of the passive filter and eliminatespossibility of series and parallel resonance. The purpose ofthe three coupling transformers is not only to isolate thePWM inverters from the source but also to match the voltageand current ratings of the PWM inverters with those of thesystem. The ripple filter inductor and capacitor are used tosuppress the switching ripples generated because of thehigh-frequency switching of the PWM inverter. In additionto remove source current harmonics, this configuration canalso be used to compensate for source voltage unbalances byadding appropriate voltage component of fundamentalfrequency in the series injected voltage.SHAPF topology is practically more viable, cost-effective

and enables the use of significantly small rated active filters.SHAPF improve the compensation characteristics of passivefilters and thus realise a reduction in the active filter rating.SHAPF effectively mitigate problems of both active andpassive filters and offer several additional value-addedfeatures such as line voltage regulation, reactive powercompensation and harmonic isolation which increase theirpractical viability [16, 17].

4 Details of control algorithm

The reference signal to compensate supply voltage unbalanceand source current harmonics is calculated in two steps. First

1567& The Institution of Engineering and Technology 2014

Fig. 1 Different operating modes of three-phase diode rectifier

a Mode I – six pulse mode balanceb Mode II – six pulse mode unbalancec Mode III – four pulse moded Mode IV – two pulse mode

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of all, the unbalance fundamental component of the sourcevoltage is derived using sequence analysis. The positivesequence component of source voltage derived using sequenceanalysis is used further as the fundamental voltage applied tothe load. In the second step, the reference voltage tocompensate supply current harmonics is derived bydecomposing the voltage vector into different components thatrepresent different power quantities. Generalised instantaneouspower theory is used to define instantaneous powers and thenthe appropriate voltage component is separated and chosen asreference voltage to compensate supply current harmonics[18]. These two reference voltage components are addedtogether to obtain resultant reference voltage for SHAPF. Thereference voltage signals are compared with high frequencycarrier wave in order to generate gate pulses for VSI.


4.1 Reference generation for compensation ofsource voltage unbalance

For generating the reference for compensating the sourcevoltage unbalance, first of all the positive sequencecomponents of the source voltage is derived using sequenceanalysis of unbalanced source voltage are as follows

v+sav+sbv+sc

⎡⎢⎣

⎤⎥⎦ = 1

3

1 a a2

a2 1 aa a2 1

⎡⎣

⎤⎦

vsavsbvsc

⎡⎣

⎤⎦ (1)

where operator a≡ ej (2π/3).


Fig. 2 SHAPF system configuration with control circuit

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The unbalance fundamental component of the sourcevoltage is then calculated as

vsaubvsbubvscub

⎡⎣

⎤⎦ =

v+sa − vsav+sb − vsbv+sc − vsc

⎡⎢⎣

⎤⎥⎦ (2)

This is the first part of reference voltage which compensates


source voltage unbalance. The positive-sequence componentof source voltage is used in further calculations as thefundamental voltage applied to the non-linear load.

4.2 Reference generation for compensation ofsource current harmonics

For a three-phase system the instantaneous quantities ofsource voltage and currents are expressed as


Table 1 System parameters considered in experimentalprototype

Sr.No.

Parameters of thesystem

Value

1 balanced supply voltage 110 V, 50 Hz (line–line)2 DC-link capacitor 1000 µF3 DC-link voltage 100 V4 ripple filter Lf = 1.35 mH and Cf = 50 µF5 tuned PPF (250 Hz) L5 = 12.32 mH and C5 = 32.88 µF6 tuned PPF (350 Hz) L7 = 6.29 mH and C7 = 32.88 µF7 high pass PPF L = 2.36 mH, C = 29.88 µF and

R = 17.758 series transformer 1:1, 1 kVA9 carrier frequency 20 kHz10 load RC load (470 µF and 265 Ω

connected parallel) fedthrough diode rectifier

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v = v+sa, v
+sb, v

+sc

[ ]Tand i = [ia, ib, ic]

T. Instantaneous activepower ‘p’ is defined as the inner product of voltage andcurrent vectors and expressed as

p(t) = v(t)†i(t) = vTi = v+saia + v+sbib + v+scic (3)

Instantaneous inactive power q(t) is defined as the outerproduct of voltage and current vectors and expressed as

q(t) = v(t)× i(t) =0 −qab qcaqab 0 −qbc−qca qbc 0

⎡⎣

⎤⎦ (4)

where qab = v+saib − v+sbia; qbc = v+sbic − v+scib; and qca =v+scia − v+saic.The applied voltage vector v(t) can be decomposed into

two components viz., vp(t) that correspond to active powerand vq(t) that corresponds to inactive power. This can befurther expressed as [18]

p(t) = vp(t)†i(t) (5)

q(t) = vq(t)× i(t) (6)

The component of instantaneous voltage vector ‘vp’, can beexpressed as

vp(t) = vpa, v pb, v pc

[ ]T= i−1(t)p(t) = i(t)

i‖ ‖2 p(t) (7)

The component of instantaneous voltage vector ‘vq’ isobtained by multiplying both right- and left-hand sides of(6) by current vector i(t) and expanding the cross productof three vectors as follows

i(t)× q(t) = i(t)× vq(t)× i(t) (8a)

i(t)× q(t) = (i(t)†i(t))vq(t)− (vq(t)†i(t))i(t) (8b)

i(t)× q(t) = i‖ ‖2vq(t)− 0 (8c)

vq(t) = vqa, vqb, vqc[ ]

= i(t)× q(t)

i‖ ‖2 (8d)

In the geometric algebra framework, the conversion of thisouter product multiplication to matrix multiplication is doneusing relations, i × q = i[ ]xq = q

[ ]Txi where [q]x =

(viT)T−viT and q = v × i. Using this, vq(t) is expressed as

vq(t) =1

i‖ ‖20 qab −qca

−qab 0 qbcqca −qbc 0

⎡⎣

⎤⎦

iaibic

⎡⎣

⎤⎦ (9)

The quantity p(t) that appears in (3) can be further dividedinto two components, namely, average active power �p(t)and oscillating active power p(t). Voltages corresponding tothese two components of active powers are

vp =i

i‖ ‖2 �p+ p[ ] = vp + vp (10)

Similarly, the total inactive power calculated using (4) is alsodivided into average inactive power �q(t) and oscillatinginactive power q(t). Voltages corresponding to these two


components of inactive powers are

vq(t) = v�q(t)+ vq(t) (11)

The required components of active and inactive power thatneed to be considered for harmonic compensation arepc(t) = p(t), qc(t) = q(t). The corresponding referencevoltage for harmonic compensation is vc(t) = vp(t)+ vq(t)

vhavhbvhc

⎡⎣

⎤⎦ =

vap + vaqvbp + vbqvcp + vcq

⎡⎣

⎤⎦ (12)

The overall resultant reference voltage for SHAPF iscalculating by adding (2) and (12) as

vcavcbvcc

⎡⎣

⎤⎦ =

vsaub + vhavsbub + vhbvscub + vhc

⎡⎣

⎤⎦ (13)

SHAPF injecting voltages that follows this reference voltagecan compensate for the source voltage unbalances and supplycurrent harmonics simultaneously. The distinct features ofthis approach are: simple expression for separatingharmonic voltage component, less computational intensiveas compared with existing techniques, fast in hardwareimplementation; and the expression is valid for balance aswell as unbalance source conditions.

5 Experimental results and discussion

For verification of compensation of three-phase diode rectifier,an experimental prototype of SHAPF is developed. Thecontrol circuit is realised digitally with STM32F407x, whichis ARM Cortex-M4 based 32-bit microcontroller. Theprototype is designed for 110 V, 50 Hz, three-phase systemhaving system parameters as shown in Table 1. The VSI isimplemented using six STGW30NC120HD IGBTs from STMicroelectronics and three-phase bridge driver IR2130 frominternational rectifier. Three single-phase matchingtransformers with turns-ratio of 1:1 are used. A reasonablyhigh switching frequency of 20 kHz is considered forimplementation and the kVA rating of the VSI used is 2kVA. The PCC voltages and source currents are sensed andare interfaced with six number of controller pins, which areconfigured as analogue-to-digital converter. Calculation of


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reference voltage signal and its comparison with carrier waveare part of controller program. Mathematical calculations onsampled data are performed to derive reference signals as perthe control strategy. The comparison of this calculatedreference signals and carrier wave is performed using a fasttime-base timer in order to generate six gate pulses for PWMinverter. Six gate pulses generated by the controller areoptically isolated before it is connected to bridge driver.The SHAPF experimental setup is tested for compensating
three-phase diode rectifier working in four distinct modesof operation explained in Section 2. For testing theperformance of SHAPF configuration under different modes,

Fig. 3 Compensation of three-phase diode rectifier working in Mode I


the system is supplied with following set of supply voltages:

Mode I: Vab =��2

√ ∗104.2 sin(vt),Vbc =

��2

√ ∗104.7 sin(vt − 1200) andVca =

��2

√ ∗104.5 sin(vt + 1200).Mode II: Vab =

��2

√ ∗96.1 sin(vt),Vbc =

��2

√ ∗99.2 sin(vt − 1200) andVca =

��2

√ ∗99.1 sin(vt + 1200).Mode III: Vab =

��2

√ ∗88.7 sin(vt),Vbc =

��2

√ ∗82.3 sin(vt − 1200) andVca =

��2

√ ∗90 sin(vt + 1200).

using SHAPF


Table

2Pe

rforman

cewith

differen

tunbalan

cedsu

pply

Modeofoperation

Compen

satoruse

dSourceac

tivepow

erLo

advo

ltages

(lineva

lues

)Sourcecu

rren

ts%

THD

inso

urce

curren

t

Vab

Vbc

Vca

%UB

I aI b

I c%UB

I aI b

I cAve

rage%THD

Inoco

mpen

satio

n18

110

4.2

104.7

104.5

0.28

1.29

1.25

1.71

22.43

71.6

75.9

73.4

73.63

with

SHAPF

182

104.4

103.7

103.1

0.72

1.73

1.78

1.75

1.66

4.6

4.1

4.2

4.30

IInoco

mpen

satio

n15

896

.199

.299

.12.06

1.28

0.89

1.44

26.87

79.3

77.3

66.1

74.23

with

SHAPF

178

103.1

103.5

103.3

0.22

1.72

1.73

1.77

1.76

4.9

4.5

3.8

4.40

IIInoco

mpen

satio

n13

488

.782

.390

5.41

1.56

0.91

1.23

32.27

54.8

98.2

100.7

84.57

with

SHAPF

138

86.7

85.9

85.8

0.66

1.52

1.49

1.51

1.17

4.8

54.6

4.77

IVnoco

mpen

satio

n12

389

63.9

75.2

19.65

1.84

1.85

010

079

.40

80.30

0.00

79.85

with

SHAPF

113

77.1

75.9

75.5

1.27

1.36

1.36

1.35

0.49

4.7

4.5

4.8

4.67

%UB=%

Unb

alan

ce

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Mode IV: Vab =
��2

√ ∗89 sin(vt),Vbc =

��2

√ ∗63.9 sin(vt − 1200) andVca =

��2

√ ∗75.2 sin(vt + 1200).

These voltages are generated using the three single-phaseauto transformers connected across three-phase source. Theperformance of the system is first tested withoutcompensation and then compensation is done with SHAPFand the performance of the system is observed. Percentageunbalance in load voltages, percentage unbalance in sourcecurrent and percentage total harmonic distortion (THD) ofsource current are measured towards performanceparameters of the system. The experimental results arediscussed in following subsections.

5.1 Compensation in Mode I of operation

When the diode rectifier is supplied with balanced supply asspecified for Mode I, it draws balance current from thesource. Fig. 3 shows the load voltages and source currentbefore and after compensation. It is observed that beforecompensation, the source current is balance but rich inharmonic content. All the harmonics are considerablyremoved after compensation is done with SHAPF and sourcecurrent shapes near to sinusoidal wave. The magnitude ofload voltages, source currents, individual harmonics and THDof source current are measured using MECO make Power andHarmonic Analyzer, model PHA-5850. Table 2 shows theoverall performance of the system. In this mode of operation,the average THD of source current is 73.63% beforecompensation, which reduces to 4.30% after compensatingthe system using the SHAPF. The reduced THD implies thatnearly sinusoidal current is drawn from the source.

5.2 Compensation in Mode II of operation

When the diode rectifier is supplied with a small unbalancedsupply voltage as specified for Mode II, it draws unbalanced,non-linear current from the source. Fig. 4 shows the loadvoltages and source current before and after compensation.It is observed that although the unbalance in sourcevoltages is very small, it results into significantlyunbalanced source currents.After compensation is done with SHAPF, all the harmonics

are considerably removed and the source currents shape almostnear to balanced sinusoidal wave. Table 2 shows the overallperformance of the system where the percentage unbalancehave been calculated, according to standard EN 50160 [20].The percentage unbalance observed in the source voltage is2.06% before compensation which is reduced to 0.22% aftercompensation. The percentage unbalance observed in thesource current is 26.87% before compensation which isreduced to 1.76% after compensation. The average THD ofsource current is 74.23% before compensation whichreduces to 4.40% after compensation. The reduced THD andreduced percentage unbalance implies that nearly sinusoidalbalanced current is drawn from the source and load voltagesare balanced set of voltages.

5.3 Compensation in Mode III of operation

When the diode rectifier is supplied with an unbalancedsupply as specified for Mode III, it draws unbalanced,non-linear current similar to the one explained for Mode IIIoperation. Fig. 5 shows the load voltages and source current



Fig. 4 Compensation of three-phase diode rectifier working in Mode II using SHAPF

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before compensation and after compensation. It is observedthat all the harmonics are considerably removed aftercompensation is done with SHAPF and source currentsshapes almost nearer to balanced sinusoidal wave. Table 2shows the overall performance of the system. In this modeof operation, the average THD of source current is 84.57%before compensation, which reduces to 4.77% aftercompensation. The percentage unbalance observed inthe source voltage is 5.41% before compensation whichreduces to 0.66% after compensation. The percentageunbalance observed in the source current is 32.27%before compensation which reduces to 1.17% aftercompensation.


5.4 Compensation in Mode IV of operation

When the diode rectifier is supplied with an unbalancedsupply as specified for Mode IV, it draws unbalanced,non-linear current similar to the one explained for Mode IVoperation. Fig. 6 shows the load voltages and source currentbefore compensation and after compensation. It is observedthat the unbalance in source currents is very significant andsimilar to single phasing observed in three-phase circuits.From Table 2, in this mode of operation the average THD

of source current observed is 79.85% before compensationwhich reduces to 4.67% after compensation. Thepercentage unbalance observed in the source voltage is


Fig. 5 Compensation of three-phase diode rectifier working in Mode III using SHAPF

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19.65% before compensation, which reduces to 1.27% aftercompensation. The percentage unbalance observed in thesource current is 100% before compensation, which reducesto 0.49% after compensation. The reduced THD andpercentage unbalance in load voltage and source currentimplies that the system is properly compensated in thismode of operation.Fig. 7 shows the intermediate control circuit waveforms,

which are unbalanced source voltages sensed by the controlcircuit, its positive sequence components, fundamentalunbalance voltage and the overall reference voltagecalculated from (13). These waveforms are acquired on


oscilloscope using two number of digital-to-analogueconverters available on the controller.

5.5 Dynamic response of the system

Fig. 8 presents the dynamic response obtained for a suddenchange in the source current. Another equal value resistanceis added on the DC side of diode rectifier to double theload current. Figs. 8a, b and c show the source current withno filter, with PPF and with SHAPF connected in thecircuit, respectively. Fig. 8d shows the expanded view ofsource current during this sudden change in the load. It can


Fig. 6 Compensation of three-phase diode rectifier working in Mode IV using SHAPF

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be noted that, in less than one cycles period the source currentreaches its new steady state.Table 3 shows the active, reactive and apparent power

drawn by the system under different modes of operation.These measurements are taken using MECO make Powerand Harmonic Analyzer, model PHA-5850. It can be seenfrom the active power readings that the active power drawnfrom each phase is approximately balance aftercompensation in all the modes of operation. There is anincrease in apparent power because of increase infundamental leading VARs drawn by the PPF banks. The


load considered in the experiment does not requirefundamental reactive power, but this could be utilised in auseful way in case of a load that requires fundamentallagging VARs. In case of a grid connected systeminvariably there is a demand for lagging VARs and that canbe met partially by PPF banks.The reduced THD of source current, while compensating all

four modes of operation of three-phase diode rectifier, workingunder unbalanced supply means in all the cases, sinusoidalcurrent is drawn from the source. The reduced percentageunbalance implies that the load voltages are balanced set of


Fig. 7 Control circuit waveforms

Fig. 8 Dynamic performance of the system

a Source current without any filterb Source current after connecting PPFc Source current after connecting SHAPFd Source current after connecting SHAPF (expanded view)

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Table 3 Power values with different unbalanced supply

Mode of operation Compensator used Active power, watts Reactive power, VAr Apparent power, VA

P1 P2 P3 Total Q1 Q2 Q3 Total S1 S2 S3 Total

I no compensation 60 59 62 181 −43 −44 −45 −132 74 74 77 224with PPF 69 63 64 196 91 93 96 280 115 113 116 341

with SHAPF 61 58 63 182 81 88 82 251 102 106 104 310II no compensation 50 39 69 158 −48 31 47 30 70 50 84 161

with PPF 55 46 65 166 68 77 83 228 88 90 106 284with SHAPF 54 56 53 163 79 88 87 254 96 105 101 302

III no compensation 76 23 35 134 −44 −35 46 −33 88 42 58 136with PPF 71 33 36 140 64 51 79 194 96 61 87 239

with SHAPF 49 46 43 138 60 56 57 173 78 73 72 221IV no compensation 75 48 0 123 74 −70 0 4 106 85 0 123

with PPF 72 47 3 122 109 67 27 203 131 82 28 237with SHAPF 41 44 40 125 52 40 41 133 66 60 57 183

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voltages. These experimental results confirm the good filteringcapabilities of suggested SHAPF configuration incompensating three-phase diode rectifier system.

6 Conclusions

In this paper, power quality problems introduced bythree-phase diode rectifier working under unbalanced sourcevoltages is addressed. Four distinct modes of operation ofthree-phase diode rectifier are identified which are six pulsebalance mode, six pulse unbalance mode, four pulse modeand two pulse mode. SHAPF with appropriate controlstrategy is suggested as power electronic solution tocompensate this power quality problem. The controlstrategy used for SHAPF compensates the source voltageunbalances and source current harmonics simultaneously.Experimental prototype of SHAPF is developed where the

control circuit is implemented using ARM Cortex M4microcontroller STM32F407x. In order to establish theoperation of diode rectifier in four modes of operation, thediode rectifier is fed from four different values of sourcevoltages. The compensation of diode rectifier in fourdifferent modes of operation is done with SHAPFconfiguration and it has been observed that in all the modesof operation the system is properly compensated.In experimental evaluation it is observed that in Mode II, a

small unbalance in source voltages (2.06%) results insignificantly high (26.87%) unbalance in source currentswhich is reduced to a small value (1.76%) when the systemis compensated using SHPAF configuration. In another testcase of Mode IV, it is observed that with more unbalance insource voltages, the unbalance in source currents leads toextreme unbalance situation of single phasing. Thesuggested SHAPF configuration effectively compensatesthis situation and compensates source currents and loadvoltages to a balanced sinusoidal set as well. In all thecases of compensation, the THD of source currents is lessthan 5% and load voltage unbalance is less than 2%, whichmeets the guidelines of IEEE 519 and EN 50160 standards.This confirms the effectiveness of suggested SHAPFconfiguration in compensating three-phase diode rectifierhaving capacitive filter working under unbalanced sourceconditions.

7 References

1 Rice, D.E.: ‘A detailed analysis of six-pulse converter harmoniccurrents’, IEEE Trans. Ind. Appl., 1994, 30, pp. 294–304


2 Sakui, M., Fujita, H., Shioya, M.: ‘A method for calculating harmoniccurrents of a three-phase bridge uncontrolled rectifier with DC filter’,IEEE Trans. Ind. Electron., 1989, 36, pp. 434–440

3 Bauta, M., Grotzbach, M.: ‘Noncharacteristic line harmonics of AC/DCconverters with high DC current ripple’, IEEE Trans. Power Deliv.,2000, 15, pp. 1060–1066

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20 European standard EN 50160: ‘Voltage characteristics of electricitysupplied by public distribution systems’, CENELEC, November 1994


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current unbalance

supplyconstant dc current

unbalance ofsource current

withunregulated dc voltage

power engineering

line voltage

converteroutput voltage

constantdc voltage