Aalborg Universitet Step By Step Design Of A High Order Power Filter .
Aalborg UniversitetStep by Step Design of a High Order Power Filter for Three-Phase Three-Wire Gridconnected Inverter in Renewable Energy SystemHuang, Min; Blaabjerg, Frede; Yang, Yongheng; Wu, WeiminPublished in:Proceedings of the 4th IEEE International Symposium on Power Electronics for Distributed Generation Systems,PEDG 2013DOI (link to publication from Publisher):10.1109/PEDG.2013.6785603Publication date:2013Document VersionEarly version, also known as pre-printLink to publication from Aalborg UniversityCitation for published version (APA):Huang, M., Blaabjerg, F., Yang, Y., & Wu, W. (2013). Step by Step Design of a High Order Power Filter forThree-Phase Three-Wire Grid-connected Inverter in Renewable Energy System. In Proceedings of the 4th IEEEInternational Symposium on Power Electronics for Distributed Generation Systems, PEDG 2013 (pp. 1-8). IEEEPress. https://doi.org/10.1109/PEDG.2013.6785603General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.- Users may download and print one copy of any publication from the public portal for the purpose of private study or research.- You may not further distribute the material or use it for any profit-making activity or commercial gain- You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.
Step by Step Design of a High Order Power Filterfor Three-Phase Three-Wire Grid-connectedInverter in Renewable Energy SystemMin Huang, Frede Blaabjerg, Yongheng YangDepartment of Energy TechnologyAalborg UniversityAalborg, Denmarkhmi@et.aau.dk, fbl@et.aau.dk, yoy@et.aau.dkAbstract— Traditionally, when designing an LCL-filter, athree-phase inverter is simplified as a single-phase inverter foranalysis and the output phase voltage is used to calculate theinverter-side current harmonics and to design inverter-sideinductor. However, for a three-phase three-wire grid-tiedsystem, the output current harmonics of inverter are directlyaffected by the output line to line voltage. Hence, this paperproposes a new method to analyze the inverter output currentharmonics by using the equivalent phase voltage of the threephase inverter. Based on this, a step by step design method of thehigh order power filter is introduced. Simulations are carriedout to verify the accuracy and the validity of the proposedmethods through a 6 kW, 380V/50 Hz grid-connected invertermodel with three different types of high order power filters.Keywords—LLCL-filter; LCL-filter; current harmonics;voltage harmonics; equivalent phase voltage; design procedure;three-phase grid-tied inverter; SPWMI.INTRODUCTIONRecently, due to the energy crisis, the distributedgeneration (DG) systems using clean renewable energy suchas solar energy, wind energy, etc., have become an importantissue in technical research. However, the use of pulse widthmodulation (PWM) introduces undesirable harmonics thatmay disturb other sensitive loads/equipment on the grid andalso result in extra power losses [1]. Hence, a low-pass powerfilter is inserted between the voltage source inverter (VSI) andthe grid to attenuate the high-frequency PWM harmonics to adesirable limit. Fig. 1 shows the structure of three-phasethree-wire grid-connected inverter with different high orderfilters: LCL-filter, LLCL-filter with one trap [2] and LLCLfilter with two traps [3].Typically, a simple series inductor L is used as the filterinterface between power converters in the renewable energysystem. But a high value of inductance needs to be adopted toreduce the current harmonics around the switching frequency,which would leads to a poor dynamic response of the systemand a high power loss. In contrast to the typical L-filter, theLCL-filter can achieve a high harmonic attenuationperformance with less total inductance (L1 L2), significantlysmaller size and cost, especially for applications above severalWeimin WuElectrical EngineeringShanghai Maritime UniversityShanghai, Chinawmwu@cle.shmtu.edu.cnkilowatts [4]. In order to further reduce the total inductanceeven more, the LLCL-filter was proposed [2] and theapplication of the LLCL-filter on the three-phase three-wireShunt Active Power Filter (SAPF) was analyzed [5].Compared with the LCL-filter, the total inductance andvolume of the LLCL-filter can be reduced which has beenexemplified in a single-phase inverter. Since the voltageharmonics spectrums caused by modulation of three-phaseinverter are different from that of single-phase inverter, thestructure and the parameters of three-phase LLCL-filtershould be redesigned.Ref [3] has analyzed the character of multiple shunt RLCtrap filters, but the detail design procedure is not given. Ref[6] presented a design procedure using the trial and errormethod. Some other LCL-filter design guidelines, criteria andoptimizing processes were also proposed in [7]-[9]. However,the design principle and method of the three-phase three-wirepower filter need to be further described in detail.In this paper, the analysis on the output current harmonicof the three phase inverter using SPWM modulation methodsis first presented. Secondly, a design procedure of the highorder power filter is proposed and the related analysis iscarried out. Finally, simulations on the designed inverter caseswith three different type of high-order power filter areillustrated to verify the theoretical analysis.L1L2CL1icig Lg U gL2LfCfL1L2Lf 1Lf 2Cf1Cf 2Fig. 1. Structure of three-phase three-wire inverter with differenthigh order filters
II.INVERTER-SIDE CURRENT HARMONIC ANALYSIS FORA THREE-PHASE INVERTERThe lower limit of the filter inductance is determined by theharmonic requirement of grid-injected current according toIEEE 519-1992[10], as specified in Table I. Ig is the nominalgrid-side fundamental current. ISC is the short circuit currentof power system. The harmonic currents can be calculated bythe corresponding harmonic voltage amplitudes at differentharmonic frequencies.TABLE IMaximum Harmonic Current Distortion in Percent of IgMaximum Harmonic Current Distortion in Percent of IgIndividual Harmonic Order (Odd Harmonics)ISC /IL 11 204.011 h 172.017 h 2323 h 351.50.635 h0.3(1)where L1 is the inverter-side inductor. ω is the frequency inradians per second.ia1La1uaN (n, m ) amplitude of the phase voltage harmonic;Mthe modulation index;the DC link voltage;Udcmcarrier band number [1, );nside band number ( , ).When calculating the amplitude of the inverter currentharmonics a three-phase three-line inverter is divided intothree same single phase circuits to analyze. Usually, theamplitude of the inverter phase voltage harmonics uaN is used,as shown in (3),I a1ω ωo uaN ( n, m)(3)Z o ( jω )Fig. 3 shows the main harmonic current spectrum of theinverter output current under the condition that the gridvoltage (phase to phase) is 50 Hz/ 380 V, the DC-link voltageof Udc is 700V, the modulation index M is 0.9, converter-sideinductance L1 is 2.4 mH and the switching frequency fs is 10kHz.11 1100.1 20.01101 1010 33 41 1010 4200100400600η700Fig. 3. Inverter output phase voltage spectrumubNib1Lb1 nucNic1Lc1N(2)where5.0A. Traditional MethodFor an LLCL-filter or LCL-filter, within the low-frequency,the equivalent output impedance of the filter is approximatedas the sum of the overall main inductance, while in the highfrequency range, since the capacitor bypasses the high ordercurrent harmonics, the output impedance (Zo) of inverter isapproximated as the inverter-side inductor alone [2], [7], asderived in function (1).uaN2U dc 1 π (m n )π J m M sin ,π m n 2 2 THDIn this paper, only asymmetrical regular sampledSinusoidal Pulse Width Modulation (SPWM) will bediscussed, but the method presented can also be applied toother modulation techniques with slight modificationsaccording to the voltage output characteristics.Z o ( jω ) L1 jωuaN (n, m) Fig. 2. Simplified three-phase voltage source inverter with phasevoltage in high frequencyTraditionally, when designing a high order filter, a threephase inverter is simplified to analyze, as shown in Fig. 2,where uaN, ubN and ucN are three phase voltages; La1, Lb1 andLc1 are converter-side inductors; ia1, ib1 and ic1 are inverter-sidecurrents in three-phase respectively. Note that the neutralpoint of “N” is the same as that labeled in Fig. 1.In the SPWM mode, the amplitude of the inverter phasevoltage harmonics based on the Bessel functions is given asfollows [11],[12]:It can be seen output voltage harmonics around switchingfrequency are most significant. Then the output phase voltageharmonics can be used to obtain the current harmonics for thedesign of inductors. This design method is suitable for athree- phase four-wire system. But, for a three-phase threewire system, since inverter-side point “N” (in Fig.1) is notconnected to the grid neutral point “n” , the calculatedharmonics of the line current using phase voltage is not soaccurate.B. Proposed MethodConsidering the high-order current harmonics, Fig. 1 can besimplified as shown in Fig. 4, where uab, ubc and uca are threephase line voltages, respectively.
ia 1ucauabubcLa1ib 1Lb1ic 1Lc1u 'c nFig. 4. Simplified three-phase voltage source inverter with line toline voltage in high frequencyAccording to the inverter three phase voltage functions[12], the output line to line voltage uab, ubc and uca can bederived as (4):uab Note that the neutral point of “N’” is the equivalent neutralpoint which is obtained from balanced three inverter-side lineto line voltages and it is different from the neutral point of“N” as labeled in Fig. 1and Fig. 2.According to (4), the main harmonics spectrum magnitudes(p.u.) of line to line inverter output voltage by the sinusoidalpulse-width modulated waveform (SPWM) from the voltagesource inverter are shown as an example in Fig. 6 under thecondition that the modulation index M is 0.9 and Udc is 700V.113π 4U 1 π U dc M cos(ω0t ) dc J n m M 26π m 1 n 1 m 2 1100.1ππ π (m n)π sin n cos mωst n(ωot ) sin 233 2 ubc 20.01103π 4U 1 π U dc M cos(ω0t ) dc J n m M 22π m 1 n 1 m 2 (4)1 1010 332ππ (m n)π sin ncos mωct nωot sin 232 uca 41 1010 4 'N'harmonicsLa1ib1Lb1u' cic1Lc1The equivalent phase voltage can be derived as (5):uab 30 3u 'b ubc 30 3converter-side current harmonicI AMcan be derived as in(6):π π π 4Udc J n m M sin (m n) sin n 2 3 2 U A (n, m) 3 mπω ωo U A ( n, m )Z1 ( jω )(6)Since the angle does not change the spectrum of amplitude,the voltage spectrum of the equivalent phase voltage based on(5), u ' a , can also be depicted in Fig. 6.nFig. 5. Simplified voltage source inverter with equivalent outputvoltage sourcesu 'a 700U A ( n , m ) and the ideal amplitudes ofI AMub600ηThe amplitudes of the equivalent inverter output voltagewhere ωs and ωo are the switching frequency and fundamentalswitching frequency in radians per second respectively. For asymmetrical three-phase circuit, three-phase line to linevoltage can be converted into three-phase phase voltage, asshown in Fig. 5.ia1400Fig. 6. Line to line output switched voltage spectrumππ (m n)π sin n cos mωct n(ωot ) π sin 233 u'a20010035π 4U1 π Udc M cos(ω0t ) dc J n m M 26π m 1 n 1 m 2 uca 30 3(5)
Fig. 7. The calculated harmonic spectrum of output current ofinverterWith (6), the calculated harmonic spectrum of outputcurrent of inverter is shown in Fig. 7 under the condition thatconverter-side inductance L1 is 2.4mH, rated power is 6 kWand switching frequency fs is 10 kHz.C. Simulation results of Converter-side Current HarmonicsFig. 8 shows the simulated harmonics spectrum of theinverter-side current under the same conditions forcalculation. Compared Fig. 7 with Fig. 8, it can be seen thatthe calculated current harmonics spectrum is almost same asthe simulated current harmonics spectrum. Hence, theproposed method of equivalent output phase voltage based online to line voltage spectrum is accurate for designing theoutput high order filter. It can also be seen from Fig. 8. Thatinverter-side current harmonics are dominant around theswitching frequency and the double of the switchingfrequency.Fig. 9. Equivalent single-phase circuit of the LLCL filter with twotrapsRf1 and Rf2 is the equivalent resistor of the inductor Lf1 andLf2, respectively. Neglecting the influence of the gridimpedance and equivalent series resistances (ESRs) of theinductors and capacitors, then a grid current control blockdiagram of the inverter with LLCL filter could be obtained asFig.10.igucui*1 i1L1sigugZ c (s)uc1L2igFig. 10. Block diagram of grid current control structure with outputfilterThe transfer function ig (s) / ui (s) of LLCL-filter withtwo traps can be derived as given in (7).Z1 ( s ) L1sZ 2 ( s ) L2 sZ c ( s) (Lig (s)ui (s) u (s) 0gFig. 8. Inverter-side current harmonics spectrumIII.CHARACTERISTICS OF THREE TYPICAL HIGH ORDERFILTERSAccording to the converter-side current spectrum, differentfrom single-phase inverter, the current harmonics of threephase inverter at the double of switching are also dominant.Reference [3] makes use of multiple (n) RLC shunt trap filters,but many traps will increase the size of the filter and bring theextra cost. The LLCL-filter topology with two resonantcircuits between the ripple inductor and the grid-side inductorto attenuate the two dominant harmonic currents around theswitching frequency and the double of switching frequencycan be used, as shown in Fig. 9.i1uiL1igC f 1s 2 1)( L f 2C f 2 s 2 1)f1( L f 1C f 1C f 2 L f 2C f 1C f 2 ) s 3 (C f 1 C f 2 ) sGui ig (s) (b) Simulation result(7) Zc (s)Z1(s)Z2(s) Z1(s)Zc (s) Z2(s)Zc (s)While all the other parameters of LCL-filter, LLCL-filter withone trap and LLCL-filter with two traps are the same exceptfor resonant circuits.Fig. 11 shows the transfer functions ig (s)/ui (s) of LCLfilter, LLCL-filter with one resonant circuit and LLCL-filterwith two resonant circuits when L1, L2 and the totalcapacitance are the same and the high order resonantfrequencies are set at the switching frequency and the doubleof switching frequency.L2Cf1Cf 2Lf 1Rf 1Lf 2Rf 2Fig. 11. Bode plots of transfer functions ig (s) / ui (s) forugdifferent filtersFrom Fig. 11, it can be seen that magnitude response andphase response of the LCL-filter and the LLCL-filter in thehalf of the switching frequency range are similar, so there areno obvious differences during the design of the controller forLCL-filter and LLCL-filter based systems. The resonant peak
of the LCL-filter and LLCL-filter can be attenuated by sameactive and passive damping methods [13] - [14] and [15].IV.PARAMETERS DESIGN OF A THREE PHASED HIGHORDER POWER FILTERA.Constraints on the Design of a High Order Power FilterWhen designing a power filter, the base impedance of thesystem should be known. Then the base values of the totalimpedance, inductance, and capacitance are define as (8)Zb U n2PrateLb Zbω0Cb 1ω0 Z b(8)wherethe line-to-line RMS voltage;Unω 0 the grid frequency;Pratethe active power absorbed by the converter in ratedconditions.The following aspects of the design limitation must beaddressed [2] and [6]:1) Constrain of the total inductor (L1 L2): The maximumvalue of the total inductance should be less than 0.1pu to limitthe ac voltage drop during operation and thereby limit the dclink voltage.2) Resonance frequency of the filter: The resonance frequencyis assumed to be in a range between ten times the linefrequency and one-half of the switching frequency to avoidresonance problems.3) Design of the filter capacitance: It is considered that themaximum power factor variation at rated power is less than5%, as it is multiplied by the value of base impedance of thesystem Cf 5%Cb (Cf Cf1 Cf2).4) The value of the inverter–side inductor (L1): It is decidedby the maximum ripple current.B. Design Procedure of the High Order Filter in a ThreePhase InverterBased on constrains addressed above, then, the currentharmonics attenuation around the triple of the switchingfrequency should be concentrated in the design of the threephase three-line LLCL-filter design procedures can be derivedas:1) In order to meet a specific current ripple requirement, theinductance can be calculated from the equation [16]:L1 U dc8 f s (α I ref )(9)where, Iref is the rated reference peak current, α is theinverter-side current ripple ratio, which generally is lowerthan 40% [2];2) Select the total capacitance to achieve maximum reactivepower absorbed at rated conditions.(Cf1 C f 2 ) 0.05Cb(10)3) Decide the resonant circuit. Since Lf1-Cf1 and Lf2-Cf2circuit resonate at the switching frequency and the doubleof the switching frequency, then, Lf1 and Lf2 can becalculated as:11 ωs , ωs 2L f 1C f 1L f 2C f 2where,ωs 2(11)is twice of the switching frequency in radiansper second.4) Selection of L2.For, an LCL-filter L2 mainly depends on the objective toattenuate each harmonic around the switching frequencydown to 0.3%. Then it can be described in (12): π 4Udc π max J2 M , J4 M Gui ig ( jωs )Lf 1,2 03 3π 2 2 0.3% (12)Irefwhere J2 (1/2πM) and J4 (1/2πM) are the Bessel functionscorresponding to the 2nd and 4th and the sidebandharmonics at the switching frequency.For an LLCL-filter with one trap based three-phaseinverter, the uppermost harmonics will appear around thedouble of the switching frequencies.4Udc max J1 (π M ) , J5 (π M ) Gui ig ( j2ωs )Lf 2 03 3π 0.3% (13)Iref()where J1 (πM) and J5 (πM) are the Bessel functionscorresponding to the 1st and 5th sideband harmonics at thedouble of the switching frequency.For an LLCL-filter with two traps based three-phaseinverter, the uppermost ones will appear around the tripleof the switching frequency. 34Udc 3 3 max J2 π M , J4 π M , J8 π M Gui ig ( j3ωs )3 3π 2 2 2Iref 0.3%(14)where J2 (3/2πM), J4 (3/2πM) and J8 (3/2πM) are theBessel functions corresponding to the 2nd, 4th and 8th andthe sideband harmonics at the triple of the switchingfrequency.5) Verify the resonance frequency obtained. Due toinductors Lf1 and Lf2 are small, the resonant frequencyωr can be derived approximately to:ωr 1(15) L1 L2 L L (C f 1 C f 1 ) 12 It is necessary to check resonant frequency to satisfyconstraint 2). If it is not, the parameters should be re-selectedfrom step 2.C. Filter Design ExampleUnder the condition of that fs 10 kHz, Udc 700V, Prated 6kW, Rf1 Rf2 0.1Ω, grid phase to phase voltage is 380 V/50Hz, and the sine-triangle, and asymmetrical regular sampled
TABLE II shows the parameters of the designed filters.Fig.11. shows the value of different inductors in three cases.TABLE IICONVERTER RATINGS USED FOR SIMULATIONSElementsParametersValuesInverterDC link voltage UdcSwitching frequency fsRated power Prate700 V10 kHz6kWGrid phase voltage UgGrid frequency foConverter side inductor L1Grid side inductor L2Resonant circuit inductor Lf1Resonant circuit inductor Lf2Resonant circuit capacitor Cf2Resonant circuit capacitor Cf1Converter side inductorL1Grid side inductorL2Resonant circuit inductor LfResonant circuit capacitor Cf220 V50 Hz2.4 mH0.25 mH128 µH32 µH2 µF2 µF2.4 mH1.2 mH64 µH4 µFConverter side inductorGrid side inductorFilter capacitor2.4 mH2.4 mH4 µFAC GridLLCL-filter(two LCtraps)LLCL-filter(one LC trap)LCL-filterL1L2CV. SIMULATION RESULTSTo verify the design procedure, this paper uses PI controllerwith voltage feed forward control. Fig. 13 shows the controlblock diagram of three-phase inverter system for simulation.VdIdΔI d**ΔVd*Vα *ΔVd *Va *Vb*IdIqVc *Vβ *I q* 0ΔVq*ΔI q*VqΔVq*VdIdIqVqFig. 13. Block diagram of voltage forward control of three-phaseinverterThe effectiveness of the analyses is supported bysimulations conducted in Matlab/Simulink and the parametersof the simulation are based on those shown in Table II.Simulation results of three cases are shown in Fig.14, Fig.15and Fig.16 respectively.151050-5-10-1500.01Mag (% of Fundamental)PWM, design examples of LCL-filter and LLCL-filter aregiven as following:1) Base on the constraint of the total inductor andinverter-side current ripple, a 28% current ripple canbe obtained to design L1. Then the inverter-sideinductor is selected to be 2.4 mH.2) The total capacitor value is designed as 4 μF to limitthe reactive power which should meet the constraint of5%. Then, the capacitance of Cf1 and Cf2 are set to thesame.3) The grid-side inductor value of L2 can be calculated by(13), (14) and (15) for three types of high order filters.In this paper, L2 is selected to be 0.25 mH for theLLCL filter with two traps, 1.2 mH for LLCL-Filterwith one trap and 2.4 mH LCL-filter according tofunctions.4) For the LC resonant circuits, Lf1 and Lf2 can be chosenbased on the chosen capacitors and the 020.030.040.050.060.070.080.09(a)Fundamental (50Hz) 12.91 , THD 1.32%200 300 400 500 600 700Harmonic order(b)Fig. 14. Grid-side currents of LCL-filter based inverter. (a) Currentwaveforms and (b) The current spectrum.Fig. 12 Comparisons of different inductors in three cases0100
9Mag (% of damental (50Hz) 12.91 , THD 1.32%0switching frequency. Fig. 15 shows the simulated grid-sidecurrent waveforms and its spectra of LLCL-filter basedinverter with one trap. It has most significant currentharmonics at the double of the switching frequency. Fig. 16shows that LLCL-filter with two LC traps can reduce the gridside current ripple at the switching frequency and the doubleof the switching frequency.All the design of the three case of high order based systemcan meet the harmonic requirement given in IEEE Standard519-1992. Note that compared with the LCL-filter, the totalinductance of the LLCL-filters with one trap and two traps canbe reduced by a factor of 25% and 40% respectively.100200300400500600700Harmonic order(b)Fig. 15. Grid-side currents of LLCL-filter based inverter with onetrap. (a) Current waveforms and (b) The current spectrum.1510CONCLUSIONThis paper has introduced a harmonic current calculationmethod and a step by step design method of the high orderpower filter in the three-phase three-wire grid-connectedinverter. The following can be concluded:1. Compared with the traditional harmonic currentcalculation based on the phase voltage, the proposed methodbased on the equivalent phase voltage is more accurate.2. The character of LCL filter and LLCL filter in the half ofthe switching frequency are similar, so the additional inductorof LLCL filter brings no extra control difficulty.3. Compared with the LCL-filter, under sine-triangle, andasymmetrical regular sampled PWM, the total inductance ofLLCL-filters with one trap and two traps can be reduced by afactor of 25% and 40% respectively.The accuracy of the proposed calculation on the inverteroutput current harmonics and the step by step parametersdesign method of high order filters have been verified throughthe simulation on a 6 kW inverter model with the currentcontroller.5REFERENCES0-5-100Mag (% of 020.030.040.050.060.070.080.09(a)Fundamental (50Hz) 12.92 , THD 1.17%0100200300400 500600700Harmonic order(b)Fig. 16. Grid-side currents of LLCL-filter based inverter with twotraps. (a) Current waveforms and (b) The current spectrum.Fig. 14 shows the grid-side currents of LCL-filter basedinverter which has the dominant current harmonics at the[1] H.G. Jeong, K. B. Lee, S. Choi, and W. Choi, “Performanceimprovement of LCL-filter-based grid-connected invertersusing PQR power transformation,” IEEE Trans. PowerElectron., vol. 25, no. 5, pp. 1320-1330, May 2010.[2] W. Wu, Y. He, and F. Blaabjerg, “An LLCL power filter forsingle-phase grid-tied inverter,” IEEE Trans. Power Electron.,vol. 27, no. 2, pp. 782-789, Feb. 2012.[3] J. M. Bloemink, T C. Green, “Reducing Passive Filter Sizeswith Tuned Traps for Distribution Level Power Electronics,” inProc. IEEE EPE 2011, Aug. 2011, pp. 1-9.[4] A.A. Rockhill, M. Liserre, R. Teodorescu, P. Rodriguez, "GridFilter Design for a Multimegawatt Medium-Voltage VoltageSource Inverter," IEEE Trans. Ind. Electron, vol.58, no.4,pp.1205-1217, April 2011.[5] K. Dai, K. Duan, X. Wang, “Yong Kang Application of anLLCL Filter on Three-Phase Three-Wire Shunt Active PowerFilter,” in Proc. IEEE INTELEC2012, Sep. 2012, pp. 1-5.[6] M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control ofan LCL filter-based three-phase active rectifier,” IEEE Trans.Ind. Appl., vol. 41, no. 5, pp. 1281–1291, Sep./Oct. 2005.[7] Y. Lang, D. Xu, S. R. Hadianamrei, and H. Ma, “A noveldesign method of LCL type utility interface for three-phasevoltage source rectifier,” in Proc. IEEE 36th Conf. PowerElectron, Jan. 2006, pp. 313–317.[8] P. Channegowda and V. John, “Filter Optimization for GridInteractive Voltage Source Inverters,” IEEE Trans. Ind.Electron., vol. 57, no. 12, pp. 4106–4114, Dec. 2010
[9] Limitations of Voltage-Oriented PI Current Control of GridConnected PWM Rectifiers with LCL Filters[10] IEEE Recommended Practices and Requirements for HarmonicControl in Electrical Power Systems, IEEE Standard 519-1992,1992.[11] K. Jalili and S. Bernet, “Design of LCL Filters of Active-FrontEnd Two-Level Voltage-Source Converters,” IEEE Trans.Power Electron, vol. 56, no. 5, pp.1674-1689, May 2009.[12] D. G. Holmes and T. A. Lipo, Pulse Width Modulation forPower Converters. New York: Wiley, 2003.[13] W. Wu, Y. He, and F. Blaabjerg, “A New Design Method forthe Passive Damped LCL- and LLCL-Filter Based Single-PhaseGrid-tied Inverter,” IEEE Trans. Ind. Electron., vol. 60, no. 10,pp. 4339-4350, Oct. 2013.[14] W. Wu, M. Huang, Y. Sun, X. Wang, F. Blaabjerg, "Acomposite passive damping method of the LLCL-filter basedgrid-tied inverter", In Proc. of PEDG 2012, Aalborg, Denmark,25-28 June 2012,pp: 759 – 766. W.[15] J. Dannehl, M. Liserre, and F. W. Fuchs, “Filter-Based ActiveDamping of Voltage Source Converters with LCL Filter” IEEETrans. Ind. Electron., vol. 58, no. 8, pp. 3623-3633, Aug. 2011.[16] T.C.Y. Wang ; Z. Ye ; G. Sinha ; X. Yuan ,“Output FilterDesign for a Grid-interconnected Three-phase Inverter,” inPESC '03 IEEE 34th Annual, 2003, pp. 779 – 784.
Step by Step Design of a High Order Power Filter for Three-Phase Three-Wire Grid-connected Inverter in Renewable Energy System Min Huang, Frede Blaabjerg, Yongheng Yang Department of Energy Technology Aalborg University Aalborg, Denmark hmi@et.aau.dk, fbl@et.aau.dk, yoy@et.aau.dk Weimin Wu Electrical Engineering Shanghai Maritime University
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