逆变器

Multilevel Inverter For Grid-Connected PV System Employing Digital PI ControllerJeyraj Selvaraj and Nasrudin A.Rahim,Senior Member,IEEEAbstract—This paper presents a single-phasefive-level photo-voltaic(PV)inverter topology for grid-connected PV systems with a novel pulsewidth-modulated(PWM)control scheme.Two refer-ence signals identical to each other with an offset equivalent to the amplitude of the triangular carrier signal were used to generate PWM signals for the switches.A digital proportional–integral current control algorithm is implemented in DSP TMS320F2812 to keep the current injected into the grid sinusoidal and to have high dynamic performance with rapidly changing atmospheric conditions.The inverter offers much less total harmonic distortion and can operate at near-unity power factor.The proposed system is verified through simulation and is implemented in a prototype, and the experimental results are compared with that with the con-ventional single-phase three-level grid-connected PWM inverter.Index Terms—DSP TMS320F2812,grid connected,photovoltaic (PV),proportional–integral(PI)current control,pulsewidth-modulated(PWM)inverter.I.I NTRODUCTIONT HE DEMAND for renewable energy has increased sig-nificantly over the years because of shortage of fossil fuels and greenhouse effect.Among various types of renewable energy sources,solar energy and wind energy have become very popular and demanding due to advancement in power electronics techniques.Photovoltaic(PV)sources are used to-day in many applications as they have the advantages of being maintenance and pollution free.Solar-electric-energy demand has grown consistently by20%–25%per annum over the past 20years,which is mainly due to the decreasing costs and prices.This decline has been driven by the following factors: 1)an increasing efficiency of solar cells;2)manufacturing-technology improvements;and3)economies of scale[1].PV inverter,which is the heart of a PV system,is used to convert dc power obtained from PV modules into ac power to be fed into the grid.Improving the output waveform of the inverter reduces its respective harmonic content and,hence,the size of thefilter used and the level of electromagnetic interference (EMI)generated by switching operation of the inverter[2].In recent years,multilevel inverters have become more attractive for researchers and manufacturers due to their advantages overManuscript received January8,2008;revised June23,2008.First published July9,2008;current version published December30,2008.The authors are with the Center of Research for Power Electronics,Drives, Automation and Control(UMPEDAC),Department of Electrical Engineering, University Malaya,50603Kuala Lumpur,Malaysia(e-mail:jeyraj95@um. edu.my).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TIE.2008.928116Fig.1.Carrier and reference signals.conventional three-level pulsewidth-modulated(PWM)invert-ers.They offer improved output waveforms,smallerfilter size,lower EMI,lower total harmonic distortion(THD),and others[3]–[8].The three common topologies for multilevel inverters are asfollows:1)diode clamped(neutral clamped)[9]–[11];2)ca-pacitor clamped(flying capacitors)[12]–[14];and3)cascadedH-bridge inverter[15]–[17].In addition,several modulationand control strategies have been developed or adopted for mul-tilevel inverters,including the following:multilevel sinusoidal(PWM),multilevel selective harmonic elimination,and space-vector modulation[3],[18].A typical single-phase three-level inverter adopts full-bridgeconfiguration by using approximate sinusoidal modulationtechnique as the power circuits.The output voltage then hasthe following three values:zero,positive(+Vdc),and negative(−Vdc)supply dc voltage(assuming that Vdc is the supplyvoltage).The harmonic components of the output voltage aredetermined by the carrier frequency and switching functions.Therefore,their harmonic reduction is limited to a certaindegree[4].To overcome this limitation,this paper presents afive-levelPWM inverter whose output voltage can be represented inthe followingfive levels:zero,+1/2Vdc,Vdc,−1/2Vdc,and−Vdc.As the number of output levels increases,the harmoniccontent can be reduced.This inverter topology uses two refer-ence signals,instead of one reference signal,to generate PWMsignals for the switches.Both the reference signals V ref1andV ref2are identical to each other,except for an offset valueequivalent to the amplitude of the carrier signal V carrier,asshown in Fig.1.Because the inverter is used in a PV system,a proportional–integral(PI)current control scheme is employed to keep theoutput current sinusoidal and to have high dynamic perfor-mance under rapidly changing atmospheric conditions and tomaintain the power factor at near unity.Simulation and exper-imental results are presented to validate the proposed inverterconfiguration.0278-0046/$25.00©2008IEEEFig.2.Single-phase five-level invertertopology.Fig.3.Sinusoidal PWM signal.II.F IVE -L EVEL I NVERTER T OPOLOGY AND PWM L AW The proposed single-phase five-level inverter topology is shown in Fig.2.The inverter adopts a full-bridge configuration with an auxiliary circuit [4].PV arrays are connected to the inverter via a dc–dc boost converter.Because the proposed inverter is used in a grid-connected PV system,utility grid is used instead of load.The dc–dc boost converter is used to step up inverter output voltage V inv to be more than √2of grid voltage V g to ensure power flow from the PV arrays into the grid [19].A filtering inductance L f is used to filter the current injected into the grid.The injected current must be sinusoidal with low harmonic distortion.In order to generate sinusoidal current,sinusoidal PWM is used because it is one of the most effective methods.Sinusoidal PWM is obtained by comparing a high-frequency carrier with a low-frequency sinusoid,which is the modulating or reference signal.The carrier has a constant period;therefore,the switches have constant switching fre-quency.The switching instant is determined from the crossing of the carrier and the modulating signal.A.Sinusoidal PWM LawA fundamental period in Fig.3consists of p pulses whose widths vary sinusoidally throughout the cycle to give the fun-damental component of frequency.The basis of equivalence between the desired sinusoid and the actual pulsed waveform is taken to be volt–seconds,as shown in Fig.4,i.e.,A s 1=A p 1and A s 2=A p 2.One of these pulses,the general k th pulse,is characterized in detail in Fig.5.Fig.4.Basis of equivalence for sinusoidal PWM:volt–seconds.Fig.5.Characterization of pulse.The switching period Δand the frequency modulation ratio p are,respectively,given byΔ=2π/p (1)p =f s /f 1(2)where f s is the switching frequency and f 1is the fundamental frequency.The quarter period of pulse δ0is given asδ0=Δ/4.(3)αk is the position from the origin of the fundamental period of the midpoint of the period Δ.The angles δ1k and δ2k are the modulating angles which vary throughout the cycle,and it is to calculate these angles that a modulation law must be derived.Consider first the average voltages V 1k and V 2k during the two halves of the modulating pulseV 1k =(V s ){δ1k −(2δ0−δ1k )}/2δ0(4)∴V 1k =(V s )(δ1k −δ0)/δ0(5)=(V s )β1k(6)whereβ1k =(δ1k −δ0)/δ0(7)and,similarlyV 2k =(V s )β2k(8)SELV ARAJ AND RAHIM:MULTILEVEL INVERTER FOR GRID-CONNECTED PV SYSTEM EMPLOYING PI CONTROLLER151whereβ2k=(δ2k−δ0)/δ0.(9)The volt–second A s1is the half-pulsewidth of the sine waveand is given according to Fig.4byA s1=αkαk−2δ0V m sinθdθ(10)=2V m sinδ0sin(αk−δ0).(11) However,sinδ0→δ0whenδ0is small∴A s1=2δ0V m sin(αk−δ0)(12) and,similarly,A s2=2δ0V m sin(αk+δ0).(13) For the corresponding volt–second A p1,in the PWM waveform,A p1=2δ0V1k(14)∴A p1=2δ0β1k(V s)(15) and,similarly,A p2=2δ0β2k(V s).(16) For equivalence of volt–seconds from which the modulation law can be derived,we require thatA s1=A p1(17)A s2=A p2.(18) By equating(12)and(14),and(13)and(16)β1k=M sin(αk−δ0)(19) and,similarly,β2k=M sin(αk+δ0)(20) where M is the“modulation index”andM=V mV s.(21)Equation(21)can be expressed in terms of amplitude of carrier signal V c by replacing V s with V c.Because,in this topology, two identical reference signals are used,V s=2V c and V m= V ref1=V ref2.If M>1,higher harmonics in the phase waveform are obtained.Therefore,M is maintained between zero and one. If the amplitude of the reference signal is increased to be higher than the amplitude of the carrier signal,i.e.,M>1,this will lead to rge values of M in sinusoidal PWM techniques lead to full overmodulation[20].Fig.6shows the carrier and reference signals for different values of M.Equa-tions(19)and(20)define the modulation law,which ismore Fig.6.Carrier and reference signals for different values of modulation index M.(a)M=0.3.(b)M=0.5.(c)M=0.7.(d)M=1.2.commonly expressed in terms ofδ1k andδ2k,by substituting from(7)and(9)to giveδ1k=δ0[1+M sin(αk−δ0)](22)δ2k=δ0[1+M sin(αk+δ0)].(23) Thus,the switching anglesδ1k andδ2k for the k th pulse can be calculated from(22)and(23)in terms of modulation index M and anglesαk andδ0which depend upon the fundamental frequency and frequency ratio.B.Harmonic Spectrum of Sinusoidal PWM WaveformThe voltage harmonics produced by the sinusoidal PWM can be computed byfirst calculating the harmonics due to the k th pulse alone,A nk,and then summating the harmonic contributions of all p pulsesA nk=12παk+2δ0αk−2δ0V(θ)e−jnθdθ(24)152IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.56,NO.1,JANUARY2009Fig.7.Ideal five-level inverter output voltage V inv .where V (θ)is the voltage pulse shown in Fig.5∴A nk =1⎧⎨⎩−αk −δ1k αk −2δ0V s e −jnθdθ+αk +δ2kαk −δ1kV s e −jnθdθ−αk +2δ0 αk +δ2kV s e −jnθdθ⎫⎬⎭(25)=(V s )12π −2jn×{e −jnδ2k −e jnδ1k +j sin 2nδ0}e −jnαk .(26)Equation (25)cannot be readily simplified.Therefore,for the harmonic amplitudes due to all p pulses in a fundamental cycleA n =p k =1A nk .(27)III.O PERATIONAL P RINCIPLE OFTHE P ROPOSED I NVERTERBecause PV arrays are used as input voltage sources,the voltage produced by the arrays is known as V arrays.V arraysis boosted by a dc–dc boost converter to exceed √2V g .The voltage across the dc-bus capacitors is known as V pv .The operational principle of the proposed inverter is to generate five-level output voltage,i.e.,0,+V pv /2,+V pv ,−V pv /2,and −V pv as in Fig.7.As shown in Fig.2,an auxiliary circuit which consists of four diodes and a switch S 1is used between the dc-bus capacitors and the full-bridge inverter.Proper switching control of the auxiliary circuit can generate half level of PV supply voltage,i.e.,+V pv /2and −V pv /2[4].Two reference signals V ref1and V ref2will take turns to be compared with the carrier signal at a time.If V ref1exceeds the peak amplitude of the carrier signal V carrier ,V ref2will be compared with the carrier signal until it reaches zero.At this point onward,V ref1takes over the comparison process until it exceeds V carrier .This will lead to a switching pattern,as shown in Fig.8.Switches S 1–S 3will be switching at the rate of the carrier signal frequency,whereas S 4and S 5will operate at a frequency equivalent to the fundamental frequency.Table I illustrates the level of V inv during S 1–S 5switch on and off.IV .C ONTROL S YSTEM A LGORITHM ANDI MPLEMENTATIONThe feedback controller used in this application utilizes the PI algorithm.As shown in Fig.9,the current injected intotheFig.8.Switching pattern for the single-phase five-level inverter.TABLE II NVERTER O UTPUT V OLTAGE D URING S 1−S 5S WITCH O N AND OFFgrid,also known as grid current I g ,is sensed and fed back to a comparator which compares it with the reference current I ref .I ref is obtained by sensing the grid voltage and converting it to reference current and multiplying it with constant m .This is to ensure that I g is in phase with grid voltage V g and always at near-unity power factor.One of the problems in the PV generation systems is the amount of the electric power generated by solar arrays always changing with weather conditions,i.e.,the intensity of the solar radiation.A maximum power point tracking (MPPT)method or algorithm,which has quick-response characteristics and is able to make good use of the electric power generated in any weather,is needed to solve the aforementioned problem [21].Various MPPT control methods have been discussed in detail in [22].Constant m is derived from the MPPT algorithm.The perturb-and-observe algorithm is used to extract maxi-mum power from PV arrays and deliver it to the inverter [23],[24].The instantaneous current error is fed to a PI controller.The integral term in the PI controller improves the tracking by reducing the instantaneous error between the reference and the actual current.The resulting error signal u which forms V ref1and V ref2is compared with a triangular carrier signal,and intersections are sought to produce PWM signals for the inverter switches.A.Mathematical FormulationThe PI algorithm can be expressed in the continuous time domain asu (t )=K p e (t )+K itτ=0e (τ)dτ(28)SELV ARAJ AND RAHIM:MULTILEVEL INVERTER FOR GRID-CONNECTED PV SYSTEM EMPLOYING PI CONTROLLER153Fig.9.Five-level inverter with control algorithm implemented in DSP TMS320F2812. whereu(t)control signal;e(t)error signal;t continuous-time-domain time variable;τcalculus variable of integration;K p proportional-mode control gain;K i integral-mode control gain.Implementing this algorithm using a DSP requires one to transform it into the discrete-time domain.Trapezoidal sum approximation is used to transform the integral term into the discrete-time domain because it is the most straightforward technique.The proportional term is directly used without ap-proximation.P term:K p e(t)=K p e(k).(29)I term:K itτ=0e(τ)dτ∼=K iki=0h2[e(i)+e(i−1)].(30)Time relationship:t=k∗hwhereh sampling period;k discrete-time index:k=0,1,2,....For simplification,it is convenient to define new controller gains asK i=K i h2(31)from which one can construct the discrete-time PI control law asu(k)=K p e(t)+K iki=0[e(i)+e(i−1)].(32)Fig.10.PI control algorithm implemented in DSP TMS320F2812.To eliminate the need to calculate the full summation at eachtime step(which would require an ever-increasing amount ofcomputation as time goes on),the summation is expressed as arunning sumsum(k)=sum(k−1)+[e(k)+e(k−1)](33)u(k)=K p e(k)+K i sum(k).(34)These two equations,which represent the discrete-time PIcontrol law,are implemented in DSP TMS320F2812to controlthe overall operation of the inverter.B.Algorithm ImplementationControl signal saturation and integral-mode antiwindup lim-iting are easily implemented in software.In this work,thecontrol signal itself takes the form of PWM outputs from theDSP.Therefore,the control signal is saturated at the valuethat corresponds to100%duty cycle for the PWM.An un-desirable side effect of saturating the controller output is theintegral-mode windup.When the control output saturates,theintegral-mode control term(i.e.,the summation)will continueto increase but will not produce a corresponding increase incontroller output(and hence will not produce any additionalincrease in plant response).The integral can become quite large,and it can take a long time before the controller is able to reduceit once the error signal changes sign.The effects of windup154IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.56,NO.1,JANUARY2009Fig.11.PWM switching strategy.Fig.12.Inverter output voltage(V inv)and grid current(I g)for different values of M.(a)V inv for M<0.5.(b)I g for M<0.5.(c)V inv for M>1.0.(d)I g for M>1.0.(e)V inv for0.5≤M≤1.0.(f)I g for0.5≤M≤1.0.SELV ARAJ AND RAHIM:MULTILEVEL INVERTER FOR GRID-CONNECTED PV SYSTEM EMPLOYING PI CONTROLLER 155on the closed-loop output are larger transient overshoot and undershoot and longer settling times.One approach for overcoming the integral-mode windup is to simply limit in software the maximum absolute value allowed for the integral,independent of the controller output saturation [25],as shown in Fig.10.V .S IMULATION AND E XPERIMENTAL R ESULTSA.Simulation ResultsIn order to verify that the proposed inverter can be practically implemented in a PV system,simulations were performed by using MATLAB SIMULINK.It also helps to confirm the PWM switching strategy which then can be implemented in a DSP.Fig.11shows the PWM switching strategy used in this paper.It consists of two reference signals and a triangular carrier signal.Both the reference signals are compared with the triangular carrier signal to produce PWM switching signals for switches S 1−S 5as in Fig.8.Note that one leg of the inverter is operating at a high switching rate equivalent to the frequency of the carrier signal,whereas the other leg is operating at the rate of fundamental frequency (i.e.,50Hz).The switch at the auxiliary circuit S 1also operates at the rate of the carrier signal.As mentioned earlier,the modulation index M will determine the shape of the inverter output voltage V inv and the grid current I g .Fig.12shows V inv and I g for different values of M .The dc-bus voltage is set at 400V (>√2V g ;in this case,V g is 240V)in order to inject current into the grid.Fig.12(a)shows that V inv is less than √2V g due to M being less than 0.5.The inverter should not operate at this condition because the current will be injected from the grid into the inverter,rather than the PV system injecting the current into the grid,as shown in Fig.12(b).Overmodulation condition,which happens when M >1.0,is shown in Fig.12(c).It has a flat top at the peak of the positive and negative cycles because both the reference signals exceed the maximum amplitude of the carrier signal.This will cause I g to have a flat portion at the peak of the sine waveform,as shown in Fig.12(d).To optimize the power transferred from PV arrays to the grid,it is recommended to operate at 0.5≤M ≤1.0.V inv and I g for optimal operating condition are shown in Fig.12(e)and (f),respectively.As I g is almost a pure sinewave,the THD can be reduced compared with that under other values of M .To analyze the performance of the PI current control scheme,a sudden step change is applied to the simulation process.This step change is similar to real-time environment condition (for example,the sun is emerging from the clouds).The step response is monitored,as shown in Fig.13.B.Experimental ResultsThe simulation results are verified experimentally by using a DSP TMS320F2812.The proposed inverter is tested with a PV array of 750W.The module’s ratings are shown in Table II,whereas Table III shows the PV multilevel inverter specifications and its controller parameters.Ten modules are connected in series to produce 750W of peak power.Fig.14Fig.13.Step response of the PI current control scheme.TABLE IIPV M ODULE CHARACTERISTICSTABLE IIIPV M ULTILEVEL I NVERTER S PECIFICATIONS ANDC ONTROLLER PARAMETERSFig.14.Prototype of the five-level PWM inverter.shows the prototype of the five-level PWM inverter.PWM switching signals for the switches are generated by comparing a triangular carrier signal with two reference signals,as shown in Fig.15.Fig.16shows the experimental results for V inv and I g ,whereas Fig.17shows a zoom-in view of both the waveforms.It can be seen that V inv consists of five levels of output voltage,and I g has been filtered to resemble a pure sinewave.The modulation index M is 0.8.For M that is less than 0.5,V inv is156IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.56,NO.1,JANUARY2009Fig.15.PWM switching signals for S1–S5.(a)S1.(b)S2and S3.(c)S4 and S5.less than √2V grid.Therefore,current will be injected from thegrid into the PV system,as shown in Fig.18.This condition should be avoided to protect the PV system from damage.For the case of M being more than1.0,the results are not shown because the PV system is designed to operate at condi-tion of M being less than one.This is done by calculating the input current and voltage corresponding to the output voltage and current.Then,M is varied accordingly for the inverterto Fig.16.Experimental result of V inv and I g for M=0.8.Fig.17.Zoom-in view of Fig.16.Fig.18.Experimental result of V inv and I g for M=0.2.operate at minimum and maximum power conditions.Below the minimum power condition(for example,during heavy clouds or nighttime)or above the maximum power condition (for example,over rating of PV arrays which exceeds the rating of the inverter),the inverter should not operate to ensure the safety of the PV system and the environment.THD and power factor measurements for the proposed in-verter are measured by using FLUKE43B Power QualitySELV ARAJ AND RAHIM:MULTILEVEL INVERTER FOR GRID-CONNECTED PV SYSTEM EMPLOYING PI CONTROLLER157Fig.19.THD result of the proposed multilevel PV inverter voltage waveform shown in Fig.17.Fig.20.Grid voltage V g and grid current I g at near-unity power factor.Analyzer.The THD is shown in Fig.19.This result is mea-sured corresponding to Fig.16where the M value is 0.8.The corresponding power factor is measured,and the result is shown in Fig.20.It is notable that both the grid voltage V g and the current injected into the grid I g are in phase with a power factor of 0.96.The results from the five-level PWM inverter are compared with those from the three-level PWM inverter in terms of THD.Fig.21shows the conventional three-level PWM inverter for grid-connected PV application.The same current control techniques were used to control the overall performance of the inverter.The only difference between Fig.21and Fig.9is the elimination of auxiliary circuit,and therefore,only one dc-bus capacitor is used.The resulting waveform of V inv and I g is shown in Fig.22.The results were taken at almost the same environmental conditions to ensure that I g is similar to the measurement made for the five-level inverter.As shown in Fig.23,THD measurement for the three-level inverter is much higher when compared with that for the five-level inverter.This proves that multilevel inverters can reduce the THD which is an essential criterion for grid-connected PVsystems.Fig.21.Conventional three-level PWM inverter for PVapplication.Fig.22.Experimental result of V inv and I g for the three-level PWMinverter.Fig.23.THD result of the three-level PV inverter.Efficiency measurement has been carried out to compare the efficiency of the three-level PWM inverter with that of the five-level PWM inverter for PV application.The measured158IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.56,NO.1,JANUARY2009efficiency of the three-level PWM inverter is approximately 90%,whereas that of thefive-level PWM inverter is86%.As expected,the efficiency of thefive-level PWM inverter is lower compared with that with the conventional three-level PWM inverter.The main reason is the addition of the auxiliary circuit between the dc–dc boost converter and the full-bridge inverter configuration.Switching losses of switch S1in the aux-iliary circuit have caused the efficiency of thefive-level PWM inverter to be approximately4%less than that of the three-level PWM inverter.However,simulation and experimental results show that the THD of the proposed inverter is lower when compared to that of the conventional three-level PWM inverter, which is an important element for grid-connected PV 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amplifier,”Texas Instruments,Dallas,TX, Appl.Rep.Jeyraj Selvaraj was born in Kedah,Malaysia,in1980.He received the B.Eng.(Hons)degree fromMultimedia University,Cyberjaya,Malaysia,and theM.Sc.degree in power electronics and drives fromthe University of Birmingham,Birmingham,U.K.,and University of Nottingham,Nottingham,U.K.,in2002and2004,respectively.He is currently workingtoward the Ph.D.degree at the Center of Research forPower Electronics,Drives,Automation and Control(UMPEDAC),Department of Electrical Engineer-ing,University Malaya,Kuala Lumpur,Malaysia. His research interests include single-and three-phase multilevel inverters, digital proportional–integral current control techniques,photovoltaic inverters, and dc–dcconverters.Nasrudin A.Rahim(M’89–SM’08)was born inJohor,Malaysia,in1960.He received the B.Sc.(Hons.)and M.Sc.degrees from the Universityof Strathclyde,Glasgow,U.K.,and the Ph.D.de-gree from Heriot–Watt University,Edinburgh,U.K.,in1995.He is currently a Professor in the Department ofElectrical Engineering,University of Malaya,KualaLumpur,Malaysia,and the Director of the Center ofResearch for Power Electronics,Drives,Automationand Control(UMPEDAC).Prof.Rahim is the Chairman of the working group WG-8covering reluc-tance motors of the IEEE Motor Subcommittee under the IEEE-PES Electric Machinery Committee.His research interests include power electronics,real-time control systems,and electrical drives.。