三电平逆变器

A DQ Synchronous Reference Frame Control for Single-Phase ConvertersU.A.Miranda and M.AredesFederal University of Rio de Janeiro COPPE/Electrical Engineering Programm 21945-970Rio de Janeiro,RJ-BRASIL Email:ulisses@coe.ufrj.brL.G.B.RolimFederal University of Rio de Janeiro Polytechnic School/Department of Electrical Engineering 21945-970Rio de Janeiro,RJ-BRASILEmail:rolim@dee.ufrj.brAbstract—This paper presents a current control using the DQ synchronous reference frame for single-phase converters. This control method consists in transforming an orthogonal pair composed by the actual single-phase input current and afictitious current,from a stationary to a rotating frame.The steady state current components in DQ frame become DC instead of AC values so a zero error current control can be implemented.A single-phase PFC boost rectifier is used as an example application of this control.To validate the control method simulation and experimental results are presented.I.I NTRODUCTIONSingle-phase converters with input current regulation are widely used in several applications such as Active Power Filters,Power Factor Control(PFC)Rectifiers,Uninterrupted Power Supplies(UPS),Photo-V oltaic Generation,etc.[1]. The current regulation is based on current control loops, however for AC power converters it is not simple to design this controllers,due their time variant currents and voltages. For DC converters it is quite simple to design linear current controllers with no steady state error,but if the AC controllers are designed the same way as DC controllers,a significant steady state error in both amplitude and phase may occur.In three-phase systems the steady-state AC quantities be-come DC by means of the transformation from ABC static frame to dq synchronous frame.To perform this transformation in a single-phase system it is necessary to create a second quantity in quadrature with the real one so as to apply the transformation from the static to the synchronous frame.In the technical literature this second quantity is obtained either using the capacitor current feedback[2],delaying the real oneby14of the line period or by means of notchfilters tuned attwice the line frequency[3],[4].Figure1shows some of this methods.The control presented in this paper is based on the detection of the frequency and phase of the input voltage by a PLL and then generates afictitious input current.The proposed method neither requires tunedfilters nor store samples to produces a quarter cycle ing this method the current control can also be made unsusceptible to switching noise with a proper PLL design.A proper choice for the current peak value also make possible the reduction of the computational requirements in a digital implementation.II.T HE B OOST R ECTIFIERFigure2shows the rectifier topology.This is a well known circuit and there are many papers describing it[5],[6],[7]. The circuit control must be able to regulate the voltage Vdc(a)Real input delayed by14of the lineperiod(b)Notchfilters tuned at twice the line frequencyFig.1.Reference and real currentsacross the capacitor at the reference value and also drain a sinusoidal current with unitary powerfactor.Fig.2.Boost RectifierThe block diagram of the control is showed in Figure3.Thereference value V∗dcis compared with the measured voltage V dc.The error signal is applied to a PI controller and its output is the amplitudeˆI∗of the reference current i∗s.The frequency and phase of the i∗s current are the same of the input voltage v s.They are determined applying v s in a PLL circuit.Once calculated the reference current i∗s it must be synthesized by a current controller.III.DQ S INGLE-P HASE C URRENT C ONTROLLERA.DQ TransformationThe transformation to the synchronous frame DQ requires two orthogonal components.In three-phase systems the ABCFig.3.Rectifier Control Block Diagramcomponents are transformed to the orthogonal and stationaryαβframe system and then to the synchronous frame DQ as shown in Figure 4and equation (1).The inverse transformation is showed in(2).Fig.4.Framesd q =cos(θ)sin(θ)−sin(θ)cos(θ) ·αβ(1)αβ=cos(θ)−sin(θ)sin(θ)cos(θ) ·dq(2)However this transformation cannot be applied directly inthe single-phase systems,because there is only one variable.This drawback can be solved creating a fictitious input current.B.Reference ValuesAs showed in the previous section,the desired current i ∗shas phase and frequency obteined from the ωt signal of the PLL circuit.It is also possible to create a second reference current in quadrature and delayed in relation with i ∗s ,using the same ωt signal.These reference currents are equivalents to the currents in the αβframe,as show in equations (3)and (4).i ∗α=i ∗s =ˆI ∗cos(ωt )(3)i ∗β=ˆI ∗sin(ωt )(4)Performing the DQ transformation taking to the inputvoltage v s as reference,it is equivalent to make θ=ωt in equation (1),leads to equations (5)and (6).I ∗d =ˆI ∗(5)I ∗q =0(6)C.Input currents DQ transformationThe input current i s is defined as i α(7)and the fictitiousinput current i βis defined as the reference current i ∗β(8).This choice for the fictitious input current will result in a simplification,as will be shown.i α=i s =ˆIcos(ωt )(7)i β=i ∗β=ˆ∗sin(ωt )(8)The values of I d and I q are obtained using equation (1)where αis the input current (7)and βthe fictitious current (8).D.Control circuitThe purpose of this control is to regulate the inductor current i s .Considering no losses in the circuit of Figure 2,its average equation through a switching period is given by (9).L dI sdt=V s −V pwm (9)This equation is converted to dq frame substituting the variables for its values in equations (10),(11)and (12).V s (t )=ˆVcos ωt (10)I s =I d cos(ωt )−I q sin(ωt )(11)V pwm =V pwm d cos(ωt )−V pwm q sin(ωt )(12)Splitting the resulting equation in the cosine and sine terms,leads to the circuit equations for the d (13)and q (14)axis.dI d dt =−ωI q −V pwm d L +ˆVL(13)dI qdt =ωI d −V pwm q L(14)The equilibrium point (15),(16)is reached when the deriva-tives terms are equal to zero.V pwm d =−ωLI q +ˆV (15)V pwm q =ωLI d(16)Now the references and the control variables are DC quan-tities and the controller can be implemented the same way asin the DC converters.Note that were added coupling terms between the d and q axis but these terms can be decoupled with a proper controller design.The block diagram of the control is showed in Figure 5.I d and I q currents are compared with their references values and the PI controllers guarantee no steady state current error.The gain ωL provide the decoupling terms and the addition of the peak voltage V is intend to compensate the countereffect of the supply voltage,with respect to the converter output voltage v pwm ,which has the same behavior as a disturbance signal.When transformed to the stationary reference frame (2)the βterm is discarded and the αterm is the signal v pwm that is applied to the single-phase unipolar SPWM.Fig.5.Single-Phase dq Current Control Block DiagramE.Simplified Control CircuitAs the main concern is the real implementation of thiscontrol,it is useful to reduce the number of mathematicaloperations.A simplification in the current control loop ispossible due the value attributed to thefictitious input currenti β(8),as follow.The steady state current error in dq frame in Figure5isgiven by equations(17)and(18).error d=I∗d−I derror d=[i∗αcos(ωt)+i∗βsin(ωt)]−[iαcos(ωt)+i βsin(ωt)]error d=(i∗α−iα)cos(ωt)+(i∗β−i β)sin(ωt)(17)error q=I∗q−I qerror q=[−i∗αsin(ωt)−i∗βcos(ωt)]−[−iαsin(ωt)−i βcos(ωt)]error q=(iα−i∗α)sin(ωt)+(i∗β−i β)cos(ωt)(18) Using equation(8)in equations(17)and(18)results in the simplified equations(19),(20)for the steady-state errors.error d=(i∗α−iα)cos(ωt)(19)error q=−(i∗α−iα)sin(ωt)(20) The decoupling terms have the objective to improve the controller dynamic and can be neglect without committing its operation.The input voltage feed-forward is added directly to the v pwm signal.It has exactly the same effect of adding thepeak value in the v pwmd component and has the advantagethat is no more necessary the voltage peak detector.As result,Figure6shows the simplified current control blockdiagram.Fig.6.Simplified Single-Phase dq Current Control Block DiagramIV.R ESULTSA.Simulation ResultsSimulations of the simplified dq current control have been made by using EMTDC/PSCAD software.The simulated circuit is shown in Figure2and its parameters in Table I.Switching frequency f s5kHzInput V oltage v s220VBoost inductor L5mHRated Direct V oltage V dc425VLoad R L50ΩTABLE IS IMULATED CIRCUIT PARAMETERSAt the simulation instant of0.5s the rectifier is turned on and the load at1.5s.The reference and the real currents in the synchronous dq and in the static reference frames at this instants are shown in Figures7to10.Figure11shows the input voltage and current.B.Experimental ResultsThe experimental implementation of the simplified dq cur-rent control was done using the Texas Instruments DSP TMS320F2812.Figure12shows the turn on transition mo-ment.Once the capacitor voltage was regulated,as Figure13 shows,the load was applied,this instant is showed in Figure14.The steady state input voltage ande current are showed in Figure15.Fig.7.I d and I q :RectifieronFig.8.I d and I q :LoadonFig.9.i s :RectifieronFig.10.i s :Load onV.C ONCLUSIONA single-phase synchronous reference frame current control based on the PLL circuit was presented.The calculation of the fictitious input current using the frequency and phase detected by the PLL was successful.It has the advantage that it is not necessary the use of filters and does not require digital memory to allocate samples.And also,the proper choice for the peak value of this current has made possible a simplification in thecontrolFig.11.Input voltage andcurrentFig.12.Input voltage and current at the beginning of the rectifierswitchingFig.13.Capacitor V oltagewithout compromising its operation.After this simplification the control become very simple to be implemented in a digitalFig.14.Input voltage and current when the load isappliedFig.15.Steady state Input voltage and currentcontroller.The control was able to achieve zero steady state current error.It was validated by the simulation and experimental results presented.A CKNOWLEDGMENTThis project was supported by CAPES/CNPq.R EFERENCES[1]B Singh, B.N.Singh, A.Chandra,K.Al-Haddad, A.Pandey,andD.P.Kothari.A review of single-phase improved power quality ac-dc converters.IEEE Transactions on Industrial Electronics ,50(5):962–981,October 2003.[2]M.J.Ryan and R.D.Lorenz.A synchronous-frame controller for a single-phase sine wave inverter.Conference Proceedings of Applied Power Electronics Conference ,2:813–819,February 1997.[3]Richard Zhang,Makr Cardinal,Paul Szczesny,and Mark Dame.A gridsimulator with control of single-phase power converters in d-q rotating frame.Power Electronics 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