# FlybackInverterControlledbySensorlessCurrentMPPTforPhotovoltaicPowerSystem

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005 1145Flyback Inverter Controlled by SensorlessCurrentMPPT for Photovoltaic Power SystemNobuyuki Kasa, Member, IEEE , Takahiko Iida, and Liang ChenAbstract — This paper presents a ?yback inverter controlled bysensorless current maximum power point tracking (MPPT) fora small photovoltaic (PV) power system. Although the proposedsystem has small output power such as 300 W, a few sets of smallPV power systems can be easily connected in parallel to yieldhigher output power. When a PV power system is constructed witha number of small power systems, the total system cost will in-creaseand will be a matter of concern. To overcome this dif?culty,this paper proposes a PV system that usesno expensive dc currentsensor but utilizes the method of estimating the PV current fromthe PV voltage. The paper shows that the application of this novelsensorless current ?yback inverter to an MPPT-operated PVsystem exhibits satisfactory MPPT performance similar to theone exhibited by the system with a dc current sensor as well. Thispaper also deals with the design method and the operation of theunique ?yback inverter with center-tapped secondary winding.Index Terms— Digital signal processors, photovoltaic (PV) powersystems, pulsewidth-modulated (PWM) inverters.I. INTRODUCTIONPHOTOVOLTAIC (PV) systems have been developed toovercome an energy crisis in terms of ecology. The PVsystem consists of the PV array and the PV power conditioner,and the PV power conditioner usually can be subdividedinto both a dc – dcconverter to control the dc voltage and avoltage-source inverter to connect to the ac utility grid line.Since a PV or a solar cell module can generate rather smallelectric power of approximately 100 W per unit square meterunder ?ne weather conditions, the PV power conditioner adoptsthe maximum power point tracking (MPPT) technique to utilizethe PV array ef?ciently. The PV voltage and PV current arerequired to calculate the PV output power for the MPPT oper-ation. Therefore, an expensive dc current sensor is absolutelyrequired, thereby introducing the problem of high expense forthe PV small power system. As listed in the literature [1] – [10],there are a number of main circuit con?gurations for the PVpower conditioners suitable for a rating less than 1 kW, and wealso had proposed a kind of buck – boost-typeinverter that hadtwo sets of ac semiconductor switches to convert dc power toac power [4]. However, this proposed inverter required two setsof the dc sources of PV arrays, which, respectively, suppliedthe positive and negative half-cycle current to the ac utility gridline. This proposed inverter circuit has been improved to “ onedc-source-type inverter ”as reported in the literature [11] – [13].Manuscript received May 19, 2004; revised October 11, 2004. Abstract pub-lished on the Internet April 28, 2005.The authors are with the Department of Electronic Engineering, OkayamaUniversity of Science, Okayama 700-0005, Japan (e-mail: kasa@ee.ous.ac.jp).Digital Object Identi?er 10.1109/TIE.2005.851602One of the improved main circuit con?gurations is named the“ ?ybackinverter with center-tapped secondary winding ” [13].In this paper, the “ ?ybackinverter with center-tapped sec-ondary winding ” is used to improve the operating performanceof the newly proposed “ sensorlesscurrent ?yback inverter. ”The “ ?ybackinverter with center-tapped secondary winding ” isalready presentedin the literature [12] – [14];however, since themethod still does not have widespread familiarity, the featuresare summarized here asfollows. No dc – dcconverter is required,as the ?yback inverter can directly convert the speci?ed dcpower to ac power, where the dc voltage is not related to theoperation. The main circuit con?guration becomes very simpleand the number of power semiconductor switches used is lessthan that of a conventional one; these features contribute tothe cost reduction of the total system. As the electric potentialof the PV array can be ?xed at the ground potential, there isno possibility of any static capacity between the PV array andthe ground to generate any troublesome discharge current. Onthe other hand, this discharge current becomes an inevitableone when the conventional bridge inverter circuit con?gurationis applied. The control algorithm is very simple and of openloop and is found to be equipped enough to run the PV powerconditioner.The detailed design method of the ?yback inverter is dis-cussed in Section II of this paper. For the MPPT operation, thePV voltage and the PV current are required to calculate the PVoutput power. Using a digital signal processor (DSP), the PVcurrent is calculated from the voltage across the capacitor con-nected to the PV array. Section III treats in detail the algorithmfor the calculation including the ?owchart. The experimental re-sults show that the sensorlesscurrent system has a performancesimilar to that of a system with the current sensors. The detailsare provided in Section IV.II. FLYBACK INVERTER W ITH CENTER -T APPEDSECONDARY W INDINGA. Operation of Flyback Inverter With Center-TappedSecondary WindingFig. 1 shows the main circuit con?guration of a prototypedPV power conditioner. The ?yback inverter consists of three in-sulated gate bipolar transistors (IGBTs), two diodes, and a ?y-back transformer with center-tapped secondary winding. The?yback transformer has the functions to not only generate theac power but also to isolate between the PV array and the acutility grid line to protect against any electric accident. The pri-mary winding is connected to the PV array and IGBT1, wherethe DSP-driven IGBT1 has width-modulated gate pulses. Two0278-0046/$20.00 ? 2005 IEEE1146 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005Fig. 1. Circuit con? guration and operation modes of ?yback inverter withcenter-tapped secondary winding.sets of ac semiconductor switches, one composed of IGBT2and Diode in series and another, IGBT3 and Diode inseries, are, respectively, connected to each terminal of the sec-ondary winding of the ?yback transformer. They can switch re-ciprocally and synchronously with the polarity of the ac utilitygrid line. The switching sequences and waveforms are shownin Fig. 2. Fig. 1 shows the operating modes of the ?yback in-verter with center-tapped secondary winding. Mode I is de?nedfor the situation where IGBT1 is at on-statewith all other IGBTsin off and the stored energy in is discharged to the ac utilitygrid line with the polarity of synchronized with that of theac utility grid line. Mode II is de?ned for the duration whereIGBT2 is at on-state with all the rest in off, implying the storedenergies in and being released to the ac utility grid line andgiving the positive polarity. Modes I and II are switched alter-nately at high switching frequency during thepositive half cycle.The envelope of the peak current through the primary windingof the ?yback transformer is modulated by the pulsewidth mod-ulated (PWM) gate pulse of IGBT1 to a sinusoidal form andis in phase with the ac utility grid line voltage. Mode III is forthe negative half-cycle polarity. Mode I and III are switched al-ternately at high switching frequency during the negative halfcycle. The current ? owing through IGBT1 is controlled in theFig. 2. Switching sequences.Fig. 3. Circuit con?guration applying transformer model.same manner in the negative half cycles as it is controlled in thepositive half cycles.B. Design of InductanceThe strong effect of the winding inductances of the ?ybacktransformer on the performance of the inverter calls for a verycareful design. In the following analysis, it is assumed that thetransformer is an ideal one and has the equivalent magnetizinginductance of in the primary side as shown in Fig. 3. Asthe turns ratio between the primary and secondary winding ofthe ? yback transformer is only two, the mutual inductances be-tween primary and secondary and also between primaryand secondary become . Fig. 4(a) shows how the cur-rent in the magnetizing inductance of ?ows in the discon-tinuous current mode (DCM). “ ” is de? ned as the crest valueof the enveloped peak current in when the inverter operatesat the rated full power of and the summation of andis just equal to the duration at the crest pointof the current. Here, is the ac utility grid line frequency andis the total number of the switching periods during the halfcycle . Using these symbols as de?ned above, theand of IGBT1 can be expressed as(1)(2)KASA et al.: FLYBACK INVERTER CONTROLLED BY SENSORLESS CURRENT MPPT FOR PV POWER SYSTEM 1147Fig. 4. Inductor current mode in DCM. (a) Waveforms of inductor current inL during half cycle of ac utility grid line. (b) Waveforms of switch current,inductor current in L , and capacitor voltage during the kth switching period.where is the root-mean-square value of ac utility grid linevoltage and is the capacitor voltage of . Using (1) and (2),the is expressed as(3)On the other hand, the rated maximum output poweris expressed as(4)where is given by . Substituting (4) into (3), the in-ductance is ?nally given by(5)C. Calculation of Switch-On PeriodAs shown in Fig. 4(b), the enveloped peak current in the mag-netizing inductance during the arbitrary th switching pe-riod is expressed as(6)where is the time from the starting point of the th switchingperiod in seconds.Equation (6) can be written using the sine angle addition for-mula. Therefore, as is a small value, is approx-imated as(7)As the ? yback inverter is operated in DCM, the IGBTswitch current is started from zero initial current at everyswitching as shown in Fig. 4(b); the switch current during theth switching period is expressed as(8)where is the threshold voltage of IGBT1, and is theon-resistance of IGBT1.As is a small value, can be approximated as(9)When the intersection of and is set to theswitch-on period, we obtain the pulsewidth of the thswitching pulse by solving from (7) and (9) as(10)III. M AXIMUM POWER POINT TRACKING W ITHOUTCURRENT SENSORAs the PV array has the nonlinear characteristics on thepower versus voltage chart asshown in Fig. 5, the linear controltheory cannot be applied to extract the maximum electric powerfrom the PV array. The perturbation-and-observation method isoften used for the MPPT in many PV systems [15], [16]. In thismethod, the periodically controlled increase or decrease of thePV voltage moves the operating points toward the maximumpower point. Usually, the maximum point is tracked by varyingthe duty ratio of the switching device switched to its on-state.In the conventional system, it is required to calculate the PVoutput power, which is given by the product of the PV voltageand PV current. The PV current is usually detected by usingan expensive dc current sensor and, therefore, demands analternative means to achieve cost reduction in measuring the dccurrent. In this paper, it is proposed to calculate the PV current1148 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 4, AUGUST 2005Fig. 5. PV characteristics.Fig. 6. Equivalent circuit of ? yback inverter (primary side only).from the PV voltage as described below by the aid of a digitalsignal processor (DSP) in real time. It is considered that the PVcurrent consists of the summation of the capacitor currentand the switch current as shown in Fig. 6(11)When (11) is integrated in the interval of the switchingperiod shown in Fig. 4(b), we get(12)is de? ned as the averaged current of in theinterval , and the total amount of the electric charge which?ows out from the PV array during the th switching period isde?ned as and expressed as(13)In the same way(14)(15)where and are de?ned as the total amount ofelectric charges stored in the capacitor and ? owing throughthe switch of IGBT1 during interval , respectively. Fig. 4(b)shows the capacitor voltage and the switch current waveformsduring the th switching period. When andare de?ned as the capacitor voltages at the endsof the thand the th switching periods, respectively, the relation betweenthese capacitor voltages and the electric charge is ex-pressed as(16)The averaged capacitor current during the th switching pe-riod is given by(17)where . The average capacitor currentis expressed as(18)A it can be assumed that the switch current is composed of themagnetizing current in the ?yback transformer andthe capacitoris so large that the ?uctuation of the capacitor voltage during theswitching period can be neglected, then the switch current canbe expressed as(19)(20)The relation between the electric charge and the switch cur-rent is expressed as(21)From (15), the averaged switch current during the thswitching period is expressed as(22)The averageswitch current is obtained as(23)Finally, the average PV current can be estimated as(24)KASA et al.: FLYBACK INVERTER CONTROLLED BY SENSORLESS CURRENT MPPT FOR PV POWER SYSTEM 1149Fig. 7. Flowchart of interrupt routine for t ( k) including I calculation and MPPT.Fig. 7 shows an outline of the ?owchart of the interrupt rou-tine for including the PV current estimation and MPPT.The main program is not shown in Fig. 7. The examples of theparameters and their values listed below can be set in the mainprogram as their respective initial conditions: ,, , , , and, . Moreover, all pulsewidth data forthe rated full-load condition are stored in the ROM table of themain program in the entries from to .The “ ” is reset to zero by the interrupt routine program whichis started by the external interrupt signal at every zero-crossingelectrical angle of the ac utility grid line voltage in order tosynchronize the generated inverter voltage with the ac utilitygrid line voltage. This interrupt routine is repeated continuouslyat the repetition rate of 9.6 kHz after which “ ” is reset tozero again. When “ ” is less than “ ,” is calculated by(24). When “ ” coincides with “ ,” is renamed to .The repetitive frequency controller is used for smoothing ofthe output power. We make the repetitive frequency controllerswitch to the MPPT routine every six times of the interruptroutine, and so the repetitive frequency is Hz inour experimental system. The MPPT routine or the process ofso-called “ perturbation-and-observation method ” is started andis calculated as(25)Then, the PV power is given asthe product ofand . is compared to the last PV powerand the sign of is given by the process as shown in Fig. 7.Then, the new duty ratio is decided by the summation ofthe last duty ratio and the newly decided differentiationas expressed by(26)where (27)Each is given by the product of andas(28)The data of is derived from the parallel I/O port of theDSP board. As mentioned in Section I, it will be found that thecontrol algorithm is open loop and a very simple one.IV. EXPERIMENTAL RESULTSFig. 8 shows the experimental system con?guration. ThreePV modules with the electrical output rating of 109 W permodule are used in our system. The DSP, type TMS320C31,is used to