用于三相PWM并网逆变器的改进型幅相控制方法_英文_

J Shanghai Univ(Engl Ed),2008,12(6):560–564Digital Object Identifier(DOI):10.1007/s11741-008-0617-1The improved PAC method for a three-phase PWMgrid-connected inverterLI Jie( ),MA Yi-wei( ),CHEN Guo-cheng( ),WANG De-li( ),YU Jun-jie( )Shanghai Key Laboratory of Power Station Automation Technology,Shanghai University,Shanghai200072,P.R.China Abstract In this paper,a vector regulating principle of the phase and amplitude control PAC method for three-phase grid-connected inverters is presented.To solve the problem of heavy inrush current and slow dynamic response when system starts up,the starting voltage prediction control and the current feed-forward control are proposed and used,which improve the dynamic performance of the system in the PAC.The experimental results carried out on a three-phase grid-connected inverter proved the validity of the proposed method.Keywords three-phase pulse width modulation(PWM)grid-connected inverter,phase and amplitude control(PAC),starting voltage prediction control,current feed-forward controlIntroductionThree-phase pulse width modulation(PWM)grid-connected inverters can realize feeding electric energy to grid with unity power factor without harmonious pollution.Therefore,it can be applied to many situa-tions,such as solar photovoltaic generation,wind power generation and the energy-regeneration application[1−2]. The current control methods of three-phase PWM grid-connected inverters can be divided into two sorts,the direct current control and the indirect current control.The direct current control includes the hysteresis cur-rent control,the space-vector control,etc.[3−4]These methods can obtain faster current response,but the con-trol structure and algorithm are comparatively complex. The indirect current control is also called the phase and amplitude control(PAC).It has advantages that thecontrol is simple without current feedback and its cost is low[5−6].However,comparing with the direct current control,its current dynamic response is not very fast. Recent research about PAC mainly involved in improv-ing the dynamic performance of the system in operationand design of system parameters[2,7].None of them re-fer to improving startup the dynamic performance of the system.However,in some situations(such as eleva-tors and port machines),grid-connected inverters have to start and stop frequently.The dynamic performance of the system in startup makes an important impact on the quality of electric power fed into grid.In this paper,based on the research concerned[7−8], a15kW three-phase PWM grid-connected inverter us-ing PAC is designed.Moreover,to solve the problem ofheavy inrush current and slow dynamic response when system starts up,the starting voltage prediction controland the current feed-forward control are presented.The experimental results proved the validity of the proposed methods.1Structure of main circuit and operat-ing principle1.1Structure of main circuitThe main circuit structure of a three-phase PWM grid-connected inverter consists of a bridge rectifier made up of six IGBTs with anti-parallel diodes,DC linkcapacitance and series inductances.As shown in Fig.1,The AC output ports of the sys-tem are directly connected to the gird,while the DC in-put ports are connected to E G(E G is a renewable power supply)in series with an isolation diodes V D which en-sure the energy can onlyflow into the grid.Before the system runs,all the IGBTs(V1∼V6)are blocked.En-ergy can’t be fed into the grid and the supply-side cur-rent is zero.After the system runs,the DC link voltage is held on the set voltage by controller and all the IGBTs are switched on or offby the given PWM rule.Then en-ergy is fed into the grid.Received Nov.21,2007;Revised Apr.15,2008Project supported by the Shanghai Education Committee Scientific Research Subsidization(Grant No.05AZ30),and the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20060280018)Corresponding author CHEN Guo-cheng,Prof.,E-mail:gchchen@J Shanghai Univ (Engl Ed),2008,12(6):560–564561Fig.1Main circuit of a three-phase PWM grid-connected inverter1.2Summary of PACOne of the control requirements of the three-phase PWM grid-connected inverter is that energy can be fed into grid with unity power factor,which means the angle between phase current and phase voltage must always be kept 180◦as well as possible.The other is controlling the DC link voltage availably and making it follow the set voltage closely.In order to reach these requirements,PAC is used in this paper.In the PAC,the amplitude and the phase of PWM modulation wave are controlled members.Therefore,the voltage on crunode R ,S ,T are controlled directly and phase current I r ,I s ,I t are changed indirectly to keep their phase opposite to grid voltage.Fig.2shows the equivalent circuit of phase R.In the figure,phasor E R represents grid voltage of phase R,phasor U R is the fundamental wave component of voltage on R ,R R is the distributed resistance,and L is the phase R inductance between grid andIGBTs.E R 'Fig.2Equivalent circuit of phase RAssuming that the current direction from grid to IG-BTs is positive and the distributed resistance R is omit-ted since it is very small,we can get the voltage pha-sor diagram of the three-phase PWM grid-connected in-verter shown in Fig.3.(a) Q < 0(b) Q = 0xFig.3Vector diagram of the three-phase grid-connected in-verterIn Fig.3,αis the control angle,ϕis the factor angle,and U x is the voltage on inductance.Fig.3(a)shows theenergy feedback status while Q <0(Q denotes reactive power).If U R is adjusted,the system operation status will change as well.As shown in Fig.3(b),when U R is in a suitable value,Q will be equal to 0.Unity power factor energy feedback is realized.In order to raise DC link voltage utilities,the three-phase PWM grid-connected inverter uses an optimum sine modulation waveform.When the modulation index M =1[9],the peak value of the R ,S ,T line voltage is E d .Therefore,we can getu R =(ME d /√3)sin(ωt −α).(1)Supposee R =√2E R sin ωt,(2)where,e R is the phase R grid voltage and E R is its root mean square (RMS)value.According to the law of conservation of energy,the input power and output power of the system are balanceable.Therefore,it can be obtained that 3E R I R cos ϕ+E d I d =0,(3)where I R is the RMS value of current of phase R.When cos ϕ=−1,we can get I R =E d I d3E R.(4)The RMS value of voltage on the inductance is U x =ωLI R =ωLE d I d3E R.(5)According to (1),(2)and (5),the amplitudes of U R ,E R and U x are ME d √3,√2E R and √2ωLE d I d /(3E R ).When the renewable power supply changes,DC link voltage E d and current I d will change as well.How-ever the voltage phasor triangle can be kept right-angle,unity power factor feedback can be realized and the DC link voltage can be controlled availably through adjust-ing the modulation index M and the control angle α.2Improvement of startup dynamic per-formanceThe PAC strategy has a simple structure and good static performance.But when we apply the strategy to some situations,in which the system starts and stops frequently,the dynamic performance of the system must be improved.Therefore starting the voltage prediction control and the current feed forward control based on the PAC strategy is proposed and used in the three-phase PWM grid-connected inverter.562J Shanghai Univ(Engl Ed),2008,12(6):560–564 2.1Starting voltage prediction controlBefore the system starts up,the switchs V1∼V6are blocked and the phase current equals to zero.Whenthe system starts up,the amplitude of phasor U R andthe phase angle between it and E R decide the magni-tude of inrush current and the length of regulation time.Therefore,the set value ofαand M at the starting timeis extremely important.The unity power factor start-ing can be realized if the initial value is set correctly.Ifit is unsuitable,the system is unable to enter the sta-ble state quickly and will produce inrush current,whichis several times larger than rating current and can de-stroy the power components.The starting voltage pre-diction control is a method that utilizes the parametersdetected before starting to calculate the ideal referencevalue which is used as the initial set value.Assume the set start voltage is E∗d.According to thephase relationship of right-triangle in Fig.3(b),we canget⎧⎪⎪⎪⎨⎪⎪⎪⎩tanα=√2ωLE∗d I d3E R1√2E R,cosα=√2E R√3ME∗d.(6) At the time the system has not started up,all of thecurrent on DC link is infused into the capacitance and the current is in proportion to the change rate of DC link voltage.I d can be expressed asI d=C d E dd t.(7) Substituting(7)into(8)yields⎧⎪⎪⎪⎨⎪⎪⎪⎩tanα=ωLCE∗d d E d d t3E2R,M=√6E RE∗d cosα.(8)Suppose thatαis small,we get tanα≈k1α,cosα≈1−k2αafter linear approximation,where k1,k2are lin-ear coefficients.Then(8)can be expressed as⎧⎪⎪⎨⎪⎪⎩α=k3d E dd t,M=√6E RE∗d(1−k2α),(9)where k3≈ωLCE∗d3E2R k1.Based on(9)we can get the set value of the initial control angleαand the modulation depth M for keeping unity factor when system starting.2.2Current feed-forward controlDuring the course of the system starting up,only when the operating point moves near the vertical line in Fig.3(b),can the dynamic response time be shortest.As shown in Fig.4,the ideal operating point A of the system is gained through calculating(9).When the system starts up,the supply-side current gradu-ally increases from zero.The system doesn’t operate at the ideal operating point A but produces overshoot, because the dynamic response of current in PAC is com-paratively slow.At that moment,the added current is provided by capacitance C,which results in the falling of DC link voltage.Operating point of the system also moves from A to B.In order to make the system op-erating point come back to A,the current should be decreased.The output DC link current of the system at the next controllable state is expressed asΔI d=Cd E dd t.(10)Fig.4Voltage phasor diagram of regulation processIt can be known from tangent relation of triangle in Fig.3(b)that the variety of R phase current isΔI R=E RωL[tan(α+Δα)−tanα].(11) SinceΔαis small,(11)is linearized asΔI R≈E RωLm1Δα,(12) where m1is the linear co-efficient.Considering energy balance between AC side and DC side of the converter, we have3E RΔI R=E dΔI d.(13) Substituting(10)and(12)into(13)yieldsΔα=ωLCE d3E2R m1d E dd t,(14)based on the triangle illustrated in Fig.3(b),we can getI R=ME d√6ωLsinα.(15)In the new static state,the output phase current I R+ΔI R isI R+ΔI R=(M+ΔM)E d√6ωLsin(α+Δα),(16)J Shanghai Univ(Engl Ed),2008,12(6):560–564563 so that the increasing powers in both sides areE dΔI d=3E RΔI R=3E R E d√6ωL[(M+ΔM)·sin(α+Δα)−M sinα].(17) Substituting(10)into(17),we can getΔM=−M[sin(α+Δα)−sinα] sin(α+Δα)+√6ωL3E R sin(α+Δα)C d E dd t.(18)SinceΔαis small,(19)can derive from(18)by lin-earizing and omiting the second portion of(18)for its smallness.ΔM≈−m2MΔαsin(α+Δα),(19)where m2is the linear coefficient.It can be known from (14)and(19)that the changes of DC link voltage can be transformed intoΔαandΔM,which are added tothe outputs of PI regulators in the next step to improve the dynamic response.3Control system configurationFig.5shows the control system configuration of thethree-phase grid-connected inverter.In order to de-crease the dependence of control angleαand modulation depth M on system parameters and increase stabilityand anti-disturbance ability of the system,two closed loops are used.The control algorithm is implementedusing a TMS320LF2407A DSP of TI.By detecting line voltage u ST and phase current i R,power factor angleϕcan be obtained after phase discrimination.It is usedin PI regulator and transformed into control angleαfor phase control.By detecting DC link voltage E d,the voltage offsetΔE d used in PI regulator is obtained and transformed into the modulation depth M for voltage control.When the system has not started,(9)is used to predict the starting voltage.After the system stars up,the feed-forward values calculated by(14)and(19) are added to the output of PI regulators to improve the dynamic response.4Experimental resultFig.6shows the waveforms of the output voltage and the current in the experiment.The experimental param-eters are that the set start DC link voltage is670V,DC link voltage in static status is620V,and carry wave fre-quency is5.3kHz.DC link voltage has not yet achieved 670V in initial several periods in Fig.6and the sys-tem hasn’t started to work,so the output current is0. When the voltage achieved the set start value,the sys-tem starts to operate.Fig.5Control system configuration of a three-phase grid-connected inverterFig.6Experimental results when system startingFig.6(a)shows the waveform of the supply-side volt-age and the current without starting voltage prediction control and current feed-forward control.It can be seen that there is biggish inrush current and time of current regulation upwards of2s.Fig.6(b)shows the waveform of the supply-side voltage and the current with starting voltage prediction control.There is no biggish inrush current,but the time of current regulation is long all the same(upwards of300ms).Fig.6(c)shows the waveform of the supply-side voltage and the current with starting564J Shanghai Univ (Engl Ed),2008,12(6):560–564voltage prediction control and current-feed forward con-trol.Obviously,the inrush current is very small and the time of current regulation is short (less than 50ms).Fig.7shows the waveforms of grid phase R voltage and the current when the system goes into the stable state.It can be seen that the phase angle between the output current and the grid voltage is very close to 180◦.The current waveform approaches sine wave.The power factor is larger than 0.99.The voltage shown in Fig.7has a distortion nearby the peak of the waveform.It is caused by grid voltage with lots of harmonic instead of the controlstrategy.Fig.7Experimental results in stable state (10ms/div)5ConclusionTraditional three-phase grid-connected inverters based on the PAC generally have heavy inrush current and slow dynamic current response when starting up.This paper presents a starting voltage prediction control and current feed-forward control method to improve the dynamic performance of the system.The experimental results demonstrated that the system has got the fea-tures of the unity power factor energy feedback,DC-link voltage controllability,no inrush current and stable performance.References[1]Wang H N,Su J H,Zhang G R, et al .Unitivecontrol of PV grid-connected generation and reactivecompensation [J].Transactions of China Electrotechni-cal Society,2005,20(9):114–118.[2]Zhang C H, Li K, Du C S, et al.An energy-feedback control system of inverter based on phase and amplitude control [J].Transactions of China Elec-trotechnical Society,2005,20(2):41–45.[3]Wu R,Dewan S B,Slemon G B.A PWM AC-to-DC converter with fixed switching frequency [J].IEEE Transactons on Industry Applications,1990,26:880–885.[4]Kazmierkowski M P,Malesani L.Current controltechniques for three-phase voltage-source PWM con-verters:a survey [J].IEEE Transactions on Industry Electronics,1998,45(5):691–703.[5]Tokuo O.Three-phase voltage fed type PWM powerconverter by means of power factor control [J].The Transactions of the Institute of Electrical Engineering of Japan,1990,110(7):821–830.[6]Dixon J W,Ooi B T.Indirect current control of aunity power factor sinusoidal current boost type three-phase rectifier [J].IEEE Transactions on Industrial Electronics,1988,35(4):508–515.[7]Qu K Q,Chen G C,Sun C B.A PAC based currentfeed forward control for three-phase PWM voltage type converter [J].Journal of Shanghai University (English Edition),2004,8(1):90–95.[8]Qu K Q,Chen G C,Sun C B.A PAC based three-phase zero-voltage soft-switching PWM converter [J].Transactions of China Electrotechnical Society,2005,20(2):41–45.[9]Chen G C,Jin D H.Inverter output characteristic bymeans of optimum PWM modecontrol [C]//Proceed-ing of the 1st Chinese Academic Conference on Variable Speed AC Drives,1989:204–207.(Editor CHEN Hai-qing)。