Research Article Control for the Three-Phase Four-Wire...

Research ArticleControl for the Three-Phase Four-Wire Four-Leg APF Based onSVPWM and Average Current Method

Xiangshun Li and Jianghua Lu

School of Automation Wuhan University of Technology 205 Luoshi Road Hongshan Wuhan Hubei China

Correspondence should be addressed to Xiangshun Li lixiangshunwhuteducn

Received 30 August 2014 Accepted 3 March 2015

Academic Editor Iqbal A Khan

Copyright copy 2015 X Li and J LuThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A novel control method is proposed for the three-phase four-wire four-leg active power filter (APF) to realize the accurate and real-time compensation of harmonic of power system which combines space vector pulse width modulation (SVPWM) with trianglemodulation strategy Firstly the basic principle of the APF is briefly describedThen the harmonic and reactive currents are derivedby the instantaneous reactive power theory Finally simulation and experiment are built to verify the validity and effectiveness of theproposed method The simulation results show that the response time for compensation is about 0025 sec and the total harmonicdistortion (THD) of the source current of phase A is reduced from 3338 before compensation to 305 with APF

1 Introduction

As the power electronic devices are extensively used in theindustrial and commercial areas a large number of nonlinearloads such as electrical machines static power convertersand electric arc furnaces have been connected to the powersystem which lead to waveforms distortion of voltage andcurrent in the grid and seriously degrade the power quality[1ndash3] Distorted currents and voltages contain a large numberof harmonics which not only cause additional heating andloss of power system components but also lead to voltagedrop at their respective harmonic frequencies distorting thevoltage waveform at the point of common coupling (PCC)Active power filter (APF) is an electrical equipment whichcan dynamically suppress the harmonic compensate reactivepower eliminate the asymmetric loads and overcome theshortcomings of passive filter (LC filter)

The compensation performances of APF depend largelyon the control method Reference [4] summarizes the controlstrategies of the main circuit for the APF There are twokinds of topologies three-leg split capacitive structure andfour-leg inverter structure for the main circuit of three-phase four-wire APF [5 6] In the split capacitor structure

the three-phase inverter essentially ismade up of three signal-phase half-bridge inverters so it suffers from insufficientutilization of the DC link voltage In addition the DC-buscapacitor of the three-leg split capacitive structure must beVoltage-Sharing So the control strategy is very complex [7]References [8ndash10] analyse the three-dimensional space vectorpulse width modulation (3D-SVPWM) control theory andintroduce 3D-SVPWM strategies based on the 120572120573120574 coor-dinate systems or the 119886119887119888 coordinate systems to the three-phase four-leg shunt APF Though these strategies providegood ideas and measures to solve the zero-sequence currentcompensation they come up with some shortcomings suchas high complexity and slow speed in computing As aresult the generated current signals based on these controlalgorithms cannot timely achieve phase synchronizationwiththe harmonic current of the power system in engineering

This paper proposes a novel kind of controlmethod basedon the three-phase four-leg inverter for the shunt APF The119860119861119862 three-legs and zero-line leg (119873 leg) can be separated andindependently controlledNot only are the control theory andcomputation of this method very simple which is based onthe two dimensional SVPWM control algorithm and triangle

Hindawi Publishing CorporationActive and Passive Electronic ComponentsVolume 2015 Article ID 528360 7 pageshttpdxdoiorg1011552015528360

2 Active and Passive Electronic Components

Rectifier load

Command current operation circuit

Command current tracking control circuit

Drive circuit

Main circuit

esis il

times

+

Figure 1 The topology of the APF

CLPF

abc

abc

PI

Voltage control

LPF

PLLea

ia

ib

ici0

times times

times

times

times

timestimes

times

minus

minus

minusminus

+

+

++ +

+

sum

3

i120572i120572f iaf iah

ibhich

ibf

icfi120573 i120573fiq

ip

120572120573

120572120573Cminus1

minus

minus

minus

+

+

+

UdcUdc_ref

sin 120596t sin 120596t

minuscos 120596t minuscos 120596tia998400

ib998400

ic 998400

ip

iq

Figure 2 The diagram of harmonic current detection

modulation strategy but also the engineering application inthe three-phase four-wire power system can come true

2 Working Principle

APF mainly consists of detecting circuit to measure theharmonic and reactive current and compensation currentgenerating circuit And the compensation circuit is made upof control circuit of the compensation current drive isolationcircuit and main circuit The topology of the APF is shownin Figure 1

The working principle of APF is through the detectingcontrol circuit to detect accurately in real time the corre-sponding harmonic components of the load current (119894119897) andat the same time the compensation current generating circuitgenerates current signals equal in amplitude and oppositein phase to the harmonic currents which is injected intothe load current circuit to offset the harmonic componentof original load current so that the source current (119894119904) justcontains the fundamental active current and a small amountof harmonic components that is the purpose of eliminatingharmonic and compensating reactive power is achieved

3 The Harmonic Extraction Method Based onthe Instantaneous Reactive Power Theory

In this paper we choose the 119894119901-119894119902 method [11ndash13] based oninstantaneous reactive power theory to detect the harmonic

current components compared with the 119901-119902 method whichcannot effectively separate the fundamental current com-ponent and harmonic current components when the gridcurrent distorts The diagram of harmonic current detectionis shown in Figure 2 Consider

1198940 =

119894119886 + 119894119887 + 119894119888

3

(1)

1198941198861015840 = 119894119886 minus 1198940

1198941198871015840 = 119894119887 minus 1198940

1198941198881015840 = 119894119888 minus 1198940

(2)

In Figure 2 119894119886 119894119887 and 119894119888 are the load currents whichcontain zero-sequence component And the zero-sequencecomponent is given in (1)The 1198941198861015840 1198941198871015840 and 1198941198881015840 are calculated by(2) which just contain the positive-sequence and negative-sequence components Then 1198941198861015840 1198941198871015840 and 1198941198881015840 are transferred tothe instantaneous active current 119894119901 and instantaneous reactivecurrent 119894119902 through the following coordinate transformations

(

119894120572

119894120573

) = radic2

3

(

1 minus

1

2

minus

1

2

0

radic3

2

minus

radic3

2

)(

1198941198861015840

1198941198871015840

1198941198881015840

)

(

119894119901

119894119902

) = (

sin120596119905 minus cos120596119905minus cos120596119905 minus sin120596119905

) sdot (

119894120572

119894120573

)

(3)

Active and Passive Electronic Components 3

Nonlinear load

C

Udc

C1

SaSb

ScSn

i1k i2k

iCk

uCk

Oc

ia ib ic in

L1 L2

Rd

C2

+

minus VT4 VT6 VT2 VT8

VT1 VT3 VT5 VT7uSa uSb uSc

Figure 3 The main circuit of the three-phase four-leg APF

Phase 119860 voltage 119890119886 is input into the phase-locked loop(PLL) module and the sine and cosine signal circuit moduleThen sine signal (sin(120596119905)) and cosine signal (minus cos(120596119905)) areproduced which is in phase with the 119890119886 The 119894119901 and 119894119902 obtainthe DC components 119894119901 and 119894119902 through low-pass filter (LPF)which correspond to the fundamental positive sequencecomponents 119894119886119891 119894119887119891 and 119894119888119891 of 1198941198861015840 1198941198871015840 and 1198941198881015840 Then thenonharmonic current components of the three-phase currentare deduced through inverse transform The 119894119886 119894119887 and 119894119888 aresubtracted from the fundamental wave components to get thereference compensation current values 119894119886ℎ 119894119887ℎ and 119894119888ℎ

119894119886ℎ = 119894119886 minus 119894119886119891

119894119887ℎ = 119894119887 minus 119894119887119891

119894119888ℎ = 119894119888 minus 119894119888119891

(4)

Then 119894119886ℎ 119894119887ℎ and 119894119888ℎ are used to calculate the cur-rent signals in the compensation current generating circuitFurthermore this paper adopts the traditional proportionalintegral (PI) control method to realize voltage regulation ofthe inverter DC voltage

4 Control Strategy of the CompensationCurrent Generation Circuit

41 3D-SVPWM Based on the 120572120573120574 Coordinate System Themain circuit of the three-phase four-leg LCL APF is shown inFigure 3 where 1198711 1198712 and 119862 are the inverter-side inductorgrid-side inductor and filter capacitor

As shown in Figure 3 the topology of the three-phasefour-leg inverter consists of four legs 119860 119861 119862 and 119873 whichincrease a degree of freedom compared with the three-phasethree-wire three-leg APF The switching function is definedas 119878119896 (119896 = 119886 119887 119888 and 119899) At any time there is one and onlyone switch which keeps turning on among the switches of thesame bridge leg That is the upper leg is on and the lowerleg is off when 119878119896 = 1 By contrast when 119878119896 = 0 this refersto the upper leg being off and the lower leg being on Sothere exist 16 different switching states from 0000 to 1111 overthe 8 switching devices which correspond to 16 switching

vectors fourteen active nonzero vectors (1198811ndash11988114) and twonull vectors (1198810 and 11988115) The relationship between the ACside voltage of the four-leg converter in 120572120573120574 coordinate and119886119887119888 coordinate is as follows

(

119880120572

119880120573

119880120574

) = radic2

3

(

(

1 minus

1

2

minus

1

2

0

radic3

2

minus

radic3

2

1

2

1

2

1

2

)

)

(

119880119886

119880119887

119880119888

) (5)

Table 1 shows the switching states the correspondingvoltages of the four-leg and the resultant voltage vectorsaccording to different switching states Furthermore Figure 4shows the switching vectors under the 120572120573120574 static coordinate

42 The Novel Control Method for Three-Phase Four-Leg APFBased on the analysis of Table 1 and Figure 4 the switchingstates of the neutral line leg just affect the value of the 119880120574when the states of the 119860 119861 and 119862 legs are determined Bycontrast the switching states of the 119860 119861 and 119862 legs onlyhave an effect on the values of the 119880120572 119880120573 and 119880120574 but donot affect the symbol of the119880120574 except the zero vectors1198810 and11988115 when the states of the 119873 leg are determined In a worldthe switching states of the119873 leg just affect the zero sequencecomponent of the three-phase output voltage and119860119861 and119862legs determine the positive-sequence and negative-sequencecomponents of the three-phase inverter output voltage Sothe 119860 119861 and 119862 legs and zero-line leg can be separated andindependently controlled

For the 119860 119861 and 119862 legs the two-dimensional SVPWMcontrol algorithm is used to generate 6 complementary PWMwaves in the 120572120573 coordinate to drive the 119860 119861 and 119862 legsof the inverter Figure 5 shows the control diagram of theSVPWM control algorithm The essence of control for the119873leg is to control the switching states of 119878119899 to make the neutralline current tracking the sum of three-phase load currentsFigure 6 shows the diagram of the control of the119873 leg basedon triangle modulation strategy


Table 1 Switching states and the corresponding voltages

119878119886 119878119887 119878119888 119878119899 119880119886119899 119880119887119899 119880119888119899 119880120572 119880120573 119880120574

1198810 0 0 0 0 0 0 0 0 0 01198811 0 0 0 1 minus119880dc minus119880dc minus119880dc 0 0 minusradic62119880dc

1198812 0 0 1 0 0 0 119880dc minusradic66119880dc minusradic22119880dc radic66119880dc

1198813 0 0 1 1 minus119880dc minus119880dc 0 minusradic66119880dc minusradic22119880dc minusradic63119880dc

1198814 0 1 0 0 0 119880dc 0 minusradic66119880dc radic22119880dc radic66119880dc

1198815 0 1 0 1 minus119880dc 0 minus119880dc minusradic66119880dc radic22119880dc minusradic63119880dc

1198816

0 1 1 0 0 119880dc 119880dc minusradic63119880dc 0 radic63119880dc

1198817 0 1 1 1 minus119880dc 0 0 minusradic63119880dc 0 minusradic66119880dc

1198818 1 0 0 0 119880dc 0 0 radic63119880dc 0 radic66119880dc

1198819 1 0 0 1 0 minus119880dc minus119880dc radic63119880dc 0 minusradic63119880dc

11988110 1 0 1 0 119880dc 0 119880dc radic66119880dc minusradic22119880dc radic63119880dc

11988111 1 0 1 1 0 minus119880dc 0 radic66119880dc minusradic22119880dc minusradic66119880dc

11988112 1 1 0 0 119880dc 119880dc 0 radic66119880dc radic22119880dc radic63119880dc

11988113 1 1 0 1 0 0 minus119880dc radic66119880dc radic22119880dc minusradic66119880dc

11988114 1 1 1 0 119880dc 119880dc 119880dc 0 0 radic62119880dc

11988115 1 1 1 1 0 0 0 0 0 0

120572

120573

120574

V6

V2

V7

V5

V3

V4

V12

V10

V8

V13

V14

V0V15

V11

V9

V1

U120574 =radic6

2Udc

U120574 =radic6

3Udc

U120574 =radic6

6Udc

U 0120574 =

U120574 = minusradic6

6Udc


3Udc


2Udc

Figure 4 The switching vectors under the 120572120573120574 coordinate


T

N

Judge the sectorXYZ

Calculate the Calculate the action time switching timeSVPWM

PI

PI

PI

abc

+ +

+

+

+

+

minus

minus

minus minus

minus

minustimes

times

times

times

times

times

ibhila

ilb

Udc

T1Tcm1

Tcm2

Tcm3

T2ilc

ich

iah

U120572

U120573120572120573

S1simS6

USa

USb

USc

Figure 5 Control diagram of the SVPWM

PILogicalcontrol

Add

++

+ +minus

minusTriangular wave

ilailb

iln

S7

S8

ilc

+

Figure 6 The diagram of the control of the119873 leg based on triangle modulation strategy

dc_refV and Vdc

a ah_refI and IAPF_

30 AlphaBlock

Pulse0

uaubuc

I_load

I_Sabc

U anda_source Ia_source

Measurements and signals

NABC

A

B

C

A

B

C C

AB

gABC

abc

ab

c

a bn

c

a

b

c

+

Discrete

U source_I source_

I source_I load_

I load_

abcIabcIabcV

i i+minus +minus

+

+

+minus

Ts = 2e minus 06 s

Figure 7 The Simulink simulation circuit for the three-phase four-wire four-leg APF

5 Simulation and Experimental Analysis

51 Simulation Analysis According to the above analysis thesimulation for the three-phase four-wire four-leg shunt APFis built inMATLABSimulink based on SVPWMand averagecurrent method The Simulink simulation circuit is shown inFigure 7 And the parameters of the simulation system aregiven in Table 2 Figure 8 shows the simulation waveformsof the load currents before compensation The load currentsand the source currents are the same without APF Figure 9shows the simulation waveforms of the source currents aftercompensation It can be observed from Figure 9 that theresponse time for compensation is about 0025 sec Further-more the source currents of the phases of 119860 119861 and 119862 arebalanced and the current of phase 119873 is improved obviously

after compensation Figure 10 shows the spectrum analysisof the current of phase 119860 before and after compensationObserved from Figure 10 the THD of the load current ofthe phase 119860 are up to 3338 and the load current of phase119860 contains numerous harmonic waves (especially third andfifth harmonic current) without APF But the THD of sourcecurrent of phase 119860 reduces to 305 with APF which meetthe IEEE-519 standard

52 Experimental Results To confirm the validity of theoryanalysis and simulation results of the proposed APF wedesign the actual prototype Control system adopts two-coreprocessor TMS320F28335 for the function of exchanging dataand real-time performances What shown in Figure 11 are


004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln

Figure 8 The load current waveforms before compensation

2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn

Figure 9 The source current waveforms after compensation

Table 2 Simulation parameters

Source load voltage magnitude 380V50HzFrequency of the main circuit 10 kHzDC bus capacitor (1198621 and 1198622) 9600 uFFilter resistance (1198711 1198712) 03mH 005mHFilter capacitor (119862) 80 uFDamping resistance (119877119889) 05Ω

Unbalanced nonlinear load 119877 = 3Ω 119871 = 2mH1198771 = 2Ω 1198711 = 15mH

the experimental waveforms of the power systems three-phase four-wire currents before and after compensationComparing Figure 9with Figure 11(b) the current waveformsare very similar when the system is stable Both of thesimulation and experiment results show that the proposedmethod can suppress the harmonic and improve the currentwaveforms of the power system

6 Conclusion

The shunt APF is a kind of new electronic device which isused to dynamically suppress the harmonic and compensatereactive power This paper makes a brief description for thebasic principle of the APF and proposes a novel controlmethod for the three-phase four-wire four-leg APF basedon SVPWM and average current method then the MAT-LABSimulink simulation and experimental platform for theAPF are built Finally the simulation and experimental resultsdemonstrate effectively the effectiveness of the proposedmethod forAPF that is themethod can improve significantlyelectric energy quality Concretely speaking not only does

0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)

Fundamental (50Hz) = 9537 THD = 3338

(a) The THD without APF

0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)


(b) The THD with APF

Figure 10 Harmonic spectrum analysis of phase119860 before compen-sation and after compensation

(a) Current waveforms on the load side before compensation

(b) The source current waveforms after compensation

Figure 11The experimental waveforms before and after compensa-tion


the proposed method for the three-phase four-wire four-leg APF dynamically suppress the harmonic and compensatereactive power but also it simplifies the calculation and hasgood performance in the engineering applications

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984

[2] ZWang J Yang and J LiuHarmonic Suppression and ReactivePower Compensation China Machine Press Beijing China2006

[3] Institute of Electrical and Electronics Engineers ldquoRecom-mended practices and requirements for harmonic control inelectrical power systemsrdquo IEEE Std 519-1992 1992

[4] J Wang and G Zhang ldquoOverviews of control strategy of activepower filterrdquo Electric Drive vol 37 no 6 pp 6ndash11 2007

[5] X-P Ren and C-P Jiao ldquoSimulation of control strategy ofthreephase four-wire four-leg APF based on MATLABrdquo Low-Voltage Apparatus no 6 pp 48ndash50 64 2010

[6] C Ravichandran L Premalatha and R Saravanakumar ldquoCon-trol methodology of three phase four wire current controlledvoltage source active power filter for power quality improve-mentrdquo in Proceedings of the International Conference on PowerEnergy and Control (ICPEC rsquo13) pp 531ndash536 February 2013

[7] S Po-Ngam ldquoThe simplified control of three-phase four-legshunt active power filter for harmonics mitigation load balanc-ing and reactive power compensationrdquo in Proceedings of the 11thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo14) pp 1ndash6 Nakhon Ratchasima Thailand May2014

[8] M A Peralest M M Prats R Portillol J L Moral and L GFranquelol ldquoThree dimensional space vector modulation forfour-leg inverters using natural coordinatesrdquo in Proceedings ofthe IEEE International Symposium on Industrial Electronics vol2 pp 1129ndash1134 May 2004

[9] Z Xiao Y Chen R Yuan and X Deng ldquoAnalysis and exper-imental validation of a space-vector-modulation algorithm forfour-leg active power filterrdquo International Journal of Control andAutomation vol 7 no 4 pp 73ndash88 2014

[10] R Cardenas R Pena M P Wheeler and M J Clare ldquoExperi-mental validation of a space-vector-modulation algorithm forfour-leg matrix convertersrdquo IEEE Transactions on IndustrialElectronics vol 58 no 4 pp 1282ndash1293 2011

[11] H Li and C Kang ldquoCao Kang Active power filter simulationbased on instantaneous reactive power theory and the PWMhysteresis control moderdquo in Proceedings of the 10th InternationalConference on Electronic Measurement amp Instruments (ICEMIrsquo11) vol 4 pp 95ndash100 Chengdu China August 2011

[12] L Chen and Z Jia ldquoThree-phase four-wire shunt active powerfilter based onDSPrdquo inProceedings of the 5th IEEEConference onIndustrial Electronics and Applications (ICIEA rsquo10) pp 948ndash951Taichung Taiwan June 2010

[13] M Marcu F-G Popescu T Niculescu L Pana and A DHandra ldquoSimulation of power active filter using instantaneousreactive power theoryrdquo in Proceedings of the 16th InternationalConference onHarmonics and Quality of Power (ICHQP rsquo14) pp581ndash585 Bucharest Romania May 2014

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DistributedSensor Networks



Rectifier load

Command current operation circuit

Command current tracking control circuit

Drive circuit

Main circuit

esis il

times

+

Figure 1 The topology of the APF

CLPF

abc

abc

PI

Voltage control

LPF

PLLea

ia

ib

ici0

times times

times

times

times

timestimes

times

minus

minus

minusminus

+

+

++ +

+

sum

3

i120572i120572f iaf iah

ibhich

ibf

icfi120573 i120573fiq

ip

120572120573

120572120573Cminus1

minus

minus

minus

+

+

+

UdcUdc_ref

sin 120596t sin 120596t

minuscos 120596t minuscos 120596tia998400

ib998400

ic 998400

ip

iq

Figure 2 The diagram of harmonic current detection

modulation strategy but also the engineering application inthe three-phase four-wire power system can come true

2 Working Principle

APF mainly consists of detecting circuit to measure theharmonic and reactive current and compensation currentgenerating circuit And the compensation circuit is made upof control circuit of the compensation current drive isolationcircuit and main circuit The topology of the APF is shownin Figure 1

The working principle of APF is through the detectingcontrol circuit to detect accurately in real time the corre-sponding harmonic components of the load current (119894119897) andat the same time the compensation current generating circuitgenerates current signals equal in amplitude and oppositein phase to the harmonic currents which is injected intothe load current circuit to offset the harmonic componentof original load current so that the source current (119894119904) justcontains the fundamental active current and a small amountof harmonic components that is the purpose of eliminatingharmonic and compensating reactive power is achieved

3 The Harmonic Extraction Method Based onthe Instantaneous Reactive Power Theory

In this paper we choose the 119894119901-119894119902 method [11ndash13] based oninstantaneous reactive power theory to detect the harmonic

current components compared with the 119901-119902 method whichcannot effectively separate the fundamental current com-ponent and harmonic current components when the gridcurrent distorts The diagram of harmonic current detectionis shown in Figure 2 Consider

1198940 =

119894119886 + 119894119887 + 119894119888

3

(1)

1198941198861015840 = 119894119886 minus 1198940

1198941198871015840 = 119894119887 minus 1198940

1198941198881015840 = 119894119888 minus 1198940

(2)

In Figure 2 119894119886 119894119887 and 119894119888 are the load currents whichcontain zero-sequence component And the zero-sequencecomponent is given in (1)The 1198941198861015840 1198941198871015840 and 1198941198881015840 are calculated by(2) which just contain the positive-sequence and negative-sequence components Then 1198941198861015840 1198941198871015840 and 1198941198881015840 are transferred tothe instantaneous active current 119894119901 and instantaneous reactivecurrent 119894119902 through the following coordinate transformations

(

119894120572

119894120573

) = radic2

3

(

1 minus

1

2

minus

1

2

0

radic3

2

minus

radic3

2

)(

1198941198861015840

1198941198871015840

1198941198881015840

)

(

119894119901

119894119902

) = (

sin120596119905 minus cos120596119905minus cos120596119905 minus sin120596119905

) sdot (

119894120572

119894120573

)

(3)


Nonlinear load

C

Udc

C1

SaSb

ScSn

i1k i2k

iCk

uCk

Oc

ia ib ic in

L1 L2

Rd

C2

+





119894119886ℎ = 119894119886 minus 119894119886119891

119894119887ℎ = 119894119887 minus 119894119887119891

119894119888ℎ = 119894119888 minus 119894119888119891

(4)






(

119880120572

119880120573

119880120574

) = radic2

3

(

(

1 minus

1

2

minus

1

2

0

radic3

2

minus

radic3

2

1

2

1

2

1

2

)

)

(

119880119886

119880119887

119880119888

) (5)






119878119886 119878119887 119878119888 119878119899 119880119886119899 119880119887119899 119880119888119899 119880120572 119880120573 119880120574






1198816









11988114 1 1 1 0 119880dc 119880dc 119880dc 0 0 radic62119880dc

11988115 1 1 1 1 0 0 0 0 0 0

120572

120573

120574

V6

V2

V7

V5

V3

V4

V12

V10

V8

V13

V14

V0V15

V11

V9

V1

U120574 =radic6

2Udc

U120574 =radic6

3Udc

U120574 =radic6

6Udc

U 0120574 =


6Udc


3Udc


2Udc



T

N

Judge the sectorXYZ


PI

PI

PI

abc

+ +

+

+

+

+

minus

minus

minus minus

minus

minustimes

times

times

times

times

times

ibhila

ilb

Udc

T1Tcm1

Tcm2

Tcm3

T2ilc

ich

iah

U120572

U120573120572120573

S1simS6

USa

USb

USc


PILogicalcontrol

Add

++

+ +minus


ilailb

iln

S7

S8

ilc

+


dc_refV and Vdc

a ah_refI and IAPF_

30 AlphaBlock

Pulse0

uaubuc

I_load

I_Sabc



NABC

A

B

C

A

B

C C

AB

gABC

abc

ab

c

a bn

c

a

b

c

+

Discrete

U source_I source_

I source_I load_

I load_

abcIabcIabcV

i i+minus +minus

+

+

+minus

Ts = 2e minus 06 s







004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln


2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn






6 Conclusion


0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)



0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)











References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Nonlinear load

C

Udc

C1

SaSb

ScSn

i1k i2k

iCk

uCk

Oc

ia ib ic in

L1 L2

Rd

C2

+





119894119886ℎ = 119894119886 minus 119894119886119891

119894119887ℎ = 119894119887 minus 119894119887119891

119894119888ℎ = 119894119888 minus 119894119888119891

(4)






(

119880120572

119880120573

119880120574

) = radic2

3

(

(

1 minus

1

2

minus

1

2

0

radic3

2

minus

radic3

2

1

2

1

2

1

2

)

)

(

119880119886

119880119887

119880119888

) (5)






119878119886 119878119887 119878119888 119878119899 119880119886119899 119880119887119899 119880119888119899 119880120572 119880120573 119880120574






1198816









11988114 1 1 1 0 119880dc 119880dc 119880dc 0 0 radic62119880dc

11988115 1 1 1 1 0 0 0 0 0 0

120572

120573

120574

V6

V2

V7

V5

V3

V4

V12

V10

V8

V13

V14

V0V15

V11

V9

V1

U120574 =radic6

2Udc

U120574 =radic6

3Udc

U120574 =radic6

6Udc

U 0120574 =


6Udc


3Udc


2Udc



T

N

Judge the sectorXYZ


PI

PI

PI

abc

+ +

+

+

+

+

minus

minus

minus minus

minus

minustimes

times

times

times

times

times

ibhila

ilb

Udc

T1Tcm1

Tcm2

Tcm3

T2ilc

ich

iah

U120572

U120573120572120573

S1simS6

USa

USb

USc


PILogicalcontrol

Add

++

+ +minus


ilailb

iln

S7

S8

ilc

+


dc_refV and Vdc

a ah_refI and IAPF_

30 AlphaBlock

Pulse0

uaubuc

I_load

I_Sabc



NABC

A

B

C

A

B

C C

AB

gABC

abc

ab

c

a bn

c

a

b

c

+

Discrete

U source_I source_

I source_I load_

I load_

abcIabcIabcV

i i+minus +minus

+

+

+minus

Ts = 2e minus 06 s







004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln


2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn






6 Conclusion


0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)



0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)











References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119878119886 119878119887 119878119888 119878119899 119880119886119899 119880119887119899 119880119888119899 119880120572 119880120573 119880120574






1198816









11988114 1 1 1 0 119880dc 119880dc 119880dc 0 0 radic62119880dc

11988115 1 1 1 1 0 0 0 0 0 0

120572

120573

120574

V6

V2

V7

V5

V3

V4

V12

V10

V8

V13

V14

V0V15

V11

V9

V1

U120574 =radic6

2Udc

U120574 =radic6

3Udc

U120574 =radic6

6Udc

U 0120574 =


6Udc


3Udc


2Udc



T

N

Judge the sectorXYZ


PI

PI

PI

abc

+ +

+

+

+

+

minus

minus

minus minus

minus

minustimes

times

times

times

times

times

ibhila

ilb

Udc

T1Tcm1

Tcm2

Tcm3

T2ilc

ich

iah

U120572

U120573120572120573

S1simS6

USa

USb

USc


PILogicalcontrol

Add

++

+ +minus


ilailb

iln

S7

S8

ilc

+


dc_refV and Vdc

a ah_refI and IAPF_

30 AlphaBlock

Pulse0

uaubuc

I_load

I_Sabc



NABC

A

B

C

A

B

C C

AB

gABC

abc

ab

c

a bn

c

a

b

c

+

Discrete

U source_I source_

I source_I load_

I load_

abcIabcIabcV

i i+minus +minus

+

+

+minus

Ts = 2e minus 06 s







004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln


2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn






6 Conclusion


0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)



0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)











References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










T

N

Judge the sectorXYZ


PI

PI

PI

abc

+ +

+

+

+

+

minus

minus

minus minus

minus

minustimes

times

times

times

times

times

ibhila

ilb

Udc

T1Tcm1

Tcm2

Tcm3

T2ilc

ich

iah

U120572

U120573120572120573

S1simS6

USa

USb

USc


PILogicalcontrol

Add

++

+ +minus


ilailb

iln

S7

S8

ilc

+


dc_refV and Vdc

a ah_refI and IAPF_

30 AlphaBlock

Pulse0

uaubuc

I_load

I_Sabc



NABC

A

B

C

A

B

C C

AB

gABC

abc

ab

c

a bn

c

a

b

c

+

Discrete

U source_I source_

I source_I load_

I load_

abcIabcIabcV

i i+minus +minus

+

+

+minus

Ts = 2e minus 06 s







004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln


2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn






6 Conclusion


0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)



0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)











References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










004

1000

006 008 01 012 014 016 018 02

minus100

1000

minus100

1000

minus100

1000

minus100

i lai lb

i lci ln


2000

minus2002000

minus2002000

minus200100

minus10004 006 008 01 012 014 016 018 02

i Sa

i Sb

i Sc

i Sn






6 Conclusion


0 2 4 6 8 10 12 14 160

5

10

15

20

25

Harmonic order

Mag

( o

f fun

dam

enta

l)



0 2 4 6 8 10 12 14 160

02040608

112141618

2

Harmonic order

Mag

( o

f fun

dam

enta

l)











References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Control for the Three-Phase Four-Wire...

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Transcript of Research Article Control for the Three-Phase Four-Wire...