Guerrero, Josep M.

Guo, Xiaoqiang

Wei, Baoze

The parallel architecture is very popular for power inverters to increase the power level. This paper presents a method for the parallel operation of inverters in an ac-distributed system, to suppress the cross-circulating current based on virtual impedance without current-sharing bus and communication bus. Simulation and experimental results verify the effectiveness of the control method

    Aalborg UniversitetCross-Circulating Current Suppression Method for Parallel Three-Phase Two-LevelInvertersWei, Baoze; Guerrero, Josep M.; Guo, XiaoqiangPublished in:Proceedings of the 5th IEEE International Conference on Consumer Electronics (IEEE ICCE-Berlin 2015)DOI (link to publication from Publisher):10.1109/ICCE-Berlin.2015.7391297Publication date:2015Document VersionEarly version, also known as pre-printLink to publication from Aalborg UniversityCitation for published version (APA):Wei, B., Guerrero, J. M., & Guo, X. (2015). Cross-Circulating Current Suppression Method for Parallel Three-Phase Two-Level Inverters. In Proceedings of the 5th IEEE International Conference on Consumer Electronics(IEEE ICCE-Berlin 2015) (pp. 423-427). IEEE Press. DOI: 10.1109/ICCE-Berlin.2015.7391297General 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.Downloaded from vbn.aau.dk on: April 29, 2017Cross-Circulating Current Suppression Method forParallel Three-Phase Two-Level InvertersBaoze Wei, Josep M. GuerreroDepartment of Energy TechnologyAalborg UniversityAalborg, Denmarkbao@et.aau.dk, joz@et.aau.dkXiaoqiang GuoDepartment of Electrical EngineeringYanshan UniversityQinhuangdao, Chinagxq@ysu.edu.cnAbstract The parallel architecture is very popular forpower inverters to increase the power level. This paper presents amethod  for  the  parallel  operation  of  inverters  in  an  ac-distributed system, to suppress the cross-circulating currentbased on virtual impedance without current-sharing bus andcommunication bus. Simulation and experimental results verifythe effectiveness of the control method.Index Terms Parallel, distributed, virtual impedance,circulating current, current-sharing.I. INTRODUCTIONRenewable or nonconventional energy resources, such asphotovoltaic arrays, fuel cells, or small wind turbines can beconnected to a common AC line to supply the distributed loadsworking as a microgrid. The diagram of a microgird is shownin Fig.1. And the microgrids are requiring new controlstrategies and power architectures to deal with high powerdemand. Iinverters in parallel is a well-known solution [1-5]. But acirculating current problem must be considered in parallelinverters system because of the different parameters of theparallel inverters [6-7]. The existence of the circulating currentcan increase the power loss of the system, cause distortion ofthe output current of inverters and so on [8-9]. So measuresshould be taken to suppress the circulating current.The three-phase two-level voltage source inverters (VSI)are widely used in microgrids [10]. Figure 2 shows a parallelinverters system consisting a number of n inverters in whicheach of the inverter has individual DC source. The DC sourcescan be photovoltaic arrays, fuel cells, or small wind turbines.The cross-circulating current should be considered for theinverters which have individual DC links [3, 8, 11].In order to avoid the circulating current, traditionalapproach is to use a multiwinding transformer-isolated-ac sidefor the parallel system. However, because of additional ac line-frequency transformer, the whole system becomes bulky and itis not desirable for an efficiency perspective [12-14].Alternative way for avoiding circulating current is to designa current-sharing bus in the system to reduce the circulatingcurrent, all the inverters current information should be knownto calculate the average current as the reference current foreach of the inverter. And a communication bus is always builtFuel cellsPV panelsWind turbineDistributed loadsAC busVSIFig.1. The diagram of a microgrid.to exchange the information between the inverters and thecontrol unit [14-16]. Strategies based on instantaneous current-sharing with communication bus will increase the complexityof the control system, and it is not suitable for the case of longdistance between parallel inverters [17]. A well-knownwireless control method is the frequency and voltage droopcontrol [18-20]. But the performance of droop-method issensitive to the output impedance of the inverters [7].The output impedances of the inverters can be changed byparallel reactors to suppress the circulating current. However,they are removed in most of parallel-inverter systems becauseof their large volume and cost [7]. With proper control strategy,parallel reactors can be replaced by virtual impedances tosuppress the circulating current because of the differentparameters of inverter modules and the line impedances [7, 21-23].Literature [6-7] shows that the circulating current dependson current sharing impedances and the difference in the outputvoltages of parallel inverters, while being independent of theload impedance. This paper presents a control method based onvirtual impedance without current-sharing and communicationbus. The virtual impedance is used to modify the outputimpedance of the inverters.This paper is organized as follows: In Section II, thecirculating current analysis for paralleled inverters is discussed.Then a control method based on virtual impedance is presentedin Section III.  In Section IV, simulation and experimentalresults are implemented. Both the simulation and experimentalresults verify the effectiveness of the presented method. Theconclusions are given in Section V.2015 IEEE 5th International Conference on Consumer Electronics Berlin (ICCE-Berlin)978-1-4799-8748-1/15/$31.00©2015IEEE 423Udc1 LoadLf1Cf1VSI1Udc2Lf2Cf2VSI2Fig. 2.  Parallel three-phase two-level inverters.II. THE CROSS-CIRCULATING CURRENT ANALYSISThis paper takes a system of two parallel-connectedinverters for an example to analyze the cross-circulatingcurrent. Figure 3 shows the cross-circulating current path. Thecross-circulating current will flow from one inverter to anotherthrough the common AC bus.The parallel three-phase inverters considering the outputimpedances can be simplified as Fig.4 because of the similarprinciple of three-phase and single-phase inverters. In Fig.4, Z1and Z2 are the output impedances of the two parallel invertersrespectively, ZL is the load impedance, E1 and E2 are  theoutputs voltage of the two inverters, I1 and I2 are the outputcurrents, Eo is the load voltage and Io is the load current.  In apractical system, Z1 and Z2 will be different because of thedifferent parameters of filters and line impedances or strayparameters. According to literature [6], the circulating currentcan be defined as1 2cirI - II =2                              (1)As shown in Fig.4, the following equations can be written:1 o11E - EI =Z                              (2)2 o22E - EI =Z                             (3)Assuming that the output impedances of the parallelinverters are equal to each other, Z1=Z2=Z, then substituting(2)-(3) into (1) gives us:1 2cirE - EI =2Z                           (4)Based on the former analysis, if the output voltages and theoutput impedances of the parallel inverters are equal to eachother respectively, the circulating current can be eliminated.But  in  a  real  system,  it  is  difficult  to  guarantee  that  differentinverters have exactly the same parameters. In  this  case,  theoutput impedances of the parallel inverters can be regulated byusing  proper  virtual  impedances, to offset the  parametersdifferences   of  the  parallel  inverters   and   to  eliminate  thecirculating current.The equivalent circuit of two parallel-connected inverterswith virtual impedances is shown in Fig.5. And Zvir1 and Zvir2are the virtual impedances. Equation (5) expresses thecomponents of the virtual impedance.Udc1Lf1Cf1VSI1Udc2Lf2Cf2VSI2 IcirFig. 3.  The cross-circulating current path in two parallel inverters.VSI1 VSI2E1 E2I1 I2Z1 Z2EoZLIoIcirFig.4. Equivalent circuit of two parallel inverters.I1 I2Z1 Zvir2EoZLIoIcirE1 E2Zvir1 Z2Fig. 5. Equivalent circuit of two parallel inverters with virtual impedances.,virk virk virkZ = R + jwL (k = 1 2)                    (5)The virtual impedance can be purely resistance orinductance, or combined with two of them based on theparameters differences between parallel inverters.III. THE PRESENTED CONTROL METHODFigure 6 shows the block diagram of the presented controlmethod for parallel three-phase two-level inverters. Thecorresponding schematic for number of n parallel inverters isshown in Fig.7. The main control loops includes the outervoltage control loop and the inner current control loop. Theouter loop regulates the output voltage of the inverter with nosteady-state errors. Zvirk (k=1~n) is the virtual impedance toregulate the output impedances of parallel inverters that locatedin the filter inductor current feedback control loop. Asecondary control loop is added to compensate the voltage dropon the virtual impedance.Figure  7  shows  that  each  of  the  inverters  has  its  owncontrol loops. It can be noticed that there is no current-sharingbus in the control loop. All the inverters in the system only useone common voltage feedback, the load voltage, it is like thevoltage reference bus in literature [13], but there is nocommunication bus in the presented control method. GIoi, Guojare the current controller and the voltage controller respectively,(i=1~n, j=1~n).In practical applications, a soft start of the inverters isneeded. In the presented method, when one inverter is started,the other feedbacks the load voltage from the AC bus as thereference voltage, if the open circuit output voltagesynchronizes with the load voltage, this inverter will beconnected to the load through a static switch.978-1-4799-8748-1/15/$31.00©2015IEEE 424pwmG111ff LL s R 11fC s1LfIuo1G Io1GorefUvir1Zdc1UorefU(s)PIoUo1dUSecondary controlFig.6. Block diagram of the presented control method.Udc1 LoadLf1Cf1UoIabc1PISecondarycontrolGIo1SPWM1UorefVSI1VSInGUo1Zvir1Udc2Lf2Cf2Iabc2PISecondarycontrolGIo2SPWM2UorefVSI2GUo2Zvir2AC busStaticswitchFig. 7.  The schematic of presented control method.IV. SIMULATION AND EXPERIMENTAL RESULTSIn order to verify the effectiveness of the presented method,simulation and experiments has been done.A. Simulation ResultsA simulation model consists of two parallel-connectedinverters was built in Matlab/Simulink, using the presentedcontrol method, and the parameters are listed in TABLE I.Both of the linear and nonlinear loads were considered in thesimulation. The nonlinear load was a rectifier connected with aresistor (57.5 ) and a capacitor (22uF). The maximum phasecurrent of each inverter will be 4.85A with the linear load.  Thecross-circulating current can be effectively suppressed withboth linear and nonlinear load as shown in Fig. 8(a) and Fig.9(a), and the maximum value of the cross-circulating current isabout 200 mA. From Fig. 8(c) and Fig. 9(b), it can be noticedthat the phase currents of two inverters almost overlap eachother.B. Experimental ResultsExperiments has been done on a prototype which is shownin Fig.13. It consists four three-phase two-level inverters fromDanfoss and one dSPACE 1006 control unit in one cabinet.VSI1  and  VSI2  were  used  in  the  experments  to  verify  theeffectiveness of the presented control method. Two DCsuppliers from Delta were connected in series for VSI1, andanother DC source from GSS was used for VSI2. Each inverterwas connected with an L-C output filter, using the parameterslisted in Table I. The experimental results under the conditionof supplying both linear and nonlinear load with the sameparameters of simulation are shown below.Figure 10 shows the results with linear load. From Fig.10(a), it can be seen that the peak value of the cross-circulatingcurrent  is  about  200mA  just  as  the  simulation  results  in  Fig.3(a), Iea, Ieb, Iec are the differences of three phase currents ofVSI1 and VSI2. Figure 10(b) shows single phase currents ofthe two inverters, the  maximum value is near 4.85A asrequired. And the waveform of load voltage is shown in Fig.10(c).Experimental results by supplying a nonlinear load areshown in Fig. 11.  Figure 11(a) shows the cross-circulatingcurrent, and the single phase output currents of the twoinverters are shown in Fig. 11(b). It can be seen that good load-sharing capability is obtained when nonlinear loads aresupplied. Figure 11(c) and (d) depicts the load current, the loadvoltage respectively.The dynamic performance of the parallel system was alsoexperimentally evaluated with respect to the case of suddeninverter connection. Initially, VSI1 was working alone tosupply a linear load. At time Ta , VSI2 was connected to thecommon AC bus. Figure 12 shows the transient response of thesingle phase output currents of both inverters. It can be seenthat the load current was almost average-sharing in twoinverters.0.2 0.3 0.4 0.5-0.4-0.200.20.4Time (s)Current(A)(a)0.2 0.22 0.24 0.26 0.28 0.3-10-50510IaIbIcTime (s)Current(A)(b)0.2 0.3 0.4 0.5-505 Ia1Ia2Time (s)Current(A)(c)0.2 0.22 0.24 0.26 0.28 0.3-400-2000200400UaUbUcTime (s)Voltage(V)(d)Fig. 8. Simulation results with linear load. (a) Cross-circulating current.(b) Load current. (c) Single phase current of VSI1 and VSI2.  (d) Load voltage.978-1-4799-8748-1/15/$31.00©2015IEEE 425TABLE I. Simulation and experimental parametersParameters ValueDC source voltage Udc1=Udc2=600VLinear Load 28.75Switching frequency 10kHZOutput voltage 280VOutput current 9.7AFiltering inductances Cf1=Cf2=27uF (Y)Filtering capacitances Lf1=Lf2=3.6mHDead band of the PWM signals 2 s0.2 0.3 0.4 0.5-0.4-0.200.20.4Time (s)Current(A)(a)0.2 0.3 0.4 0.5-505 Ia1Ia2Time (s)Current(A)(b)Fig. 9. Simulation results with nonlinear load. (a) Cross-circulating current.(b) Single phase current of VSI1 and VSI2.IecIebIeaTime (s)Current(A)(a)Ia1 Ia2Time (s)Current(A)(b)Time (s)Voltage(V)0.00 0.05 0.10-400-2000200400 Ea Eb Ec(c)Fig. 10. Experimental results with linear load. (a) Cross-circulating current. (b)Single phase current of VSI1 and VSI2. (c) Load voltage.Time (s)Current(A)(a)Ia1 Ia2Time (s)Current(A)(b)Ia Ib IcTime (s)Current(A)(c)Ea Eb EcVoltage(V)Time (s)(d)Fig. 11. Experimental results with nonlinear load. (a) Cross-circulating current.(b) Single phase current of VSI1 and VSI2. (c) Load current. (d) Load voltage.Ia1 Ia2TaTime (s)Current(A)Fig. 12. Single phase current of VSI1 and VSI2 when VSI2 suddenlyconnected.978-1-4799-8748-1/15/$31.00©2015IEEE 426VSI1VSI2dSPACE1006DCsource forVSI1DCsource forVSI2Fig.13. The experiment prototype.V. CONCLUSIONParallel inverters are widely used in the microgridapplications for high power demand, and the current-sharingscheme is necessary. A control method without current-sharingbus based on virtual impedance is presented in this paper.Simulation and experiments has been done when parallel-connected inverters were sharing linear or nonlinear load. Theresults demonstrate that, the cross-circulating current betweenthe parallel inverters can be effectively suppressed, and theaverage current-sharing is realized.REFERENCES[1]current distortion in parallel-connected converters through Trans. Ind. Electron., vol. 61, no. 1,pp. 76 91, Jan. 2014.[2] -mode circulating current control of paralleled interleaved three-phase two-level voltage-source converters with discontinuousspace vecto  IEEE Trans. Power Electron., vol. 26,no. 12, pp. 3925 3935, Dec. 2011.[3]conversion system composed of two parallel-connectedh Int.Conf. ICEMS, 2012, pp. 1-4.[4] T.   B.   Lazzarin,  G.   A.   T.   Bauer and Istrategy  for parallel  operation  of  single-phase  voltage  sourceTrans. Ind. 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Cross-Circulating Current Suppression Method for Parallel Three-Phase Two-Level Inverters

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Cross-Circulating Current Suppression Method for Parallel Three-Phase Two-Level Inverters

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