Analysis and Implementation of an Improved Flyback

3428 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 7, JULY 2014

Analysis and Implementation of an Improved FlybackInverter for Photovoltaic AC Module Applications

Mingzhi Gao, Min Chen, Chi Zhang, and Zhaoming Qian, Senior Member, IEEE

AbstractFlyback inverter has the advantages such as compactconformation, simple control loop, electric isolation, high step-upratio, high efficiency, etc., therefore is an attractive solution forphotovoltaic ac module applications. In this topology, BCM is morepreferred compared to DCM and CCM, because of its higher powerlevel, higher efficiency and wider switching frequency bandwidth.However, the control of BCM is more complicated due to its vari-able switching frequency. This also leads to the difficulty to get theaccurate mathematical model between the output current iout andthe reference current iref , which has a great influence on the THDof iout . This paper analyzes and proposes a mathematical modelbetween iout and iref in BCM through theoretical derivation, andproposes a novel control strategy to generate the reference currentthat can decrease THD of output current. Meanwhile the realiza-tion of MPPT based on the mathematical model is also investigated.Finally, simulation and experiment results based on an improvedflyback-inverter prototype are presented, which validates the pro-posed mathematical model and the control strategy.

Index TermsAC module, energy conversion, photovoltaicpower systems, system analysis and design.

NOMENCLATUREACM: Photovoltaic ac module.BCM: Boundary conduction mode.Cin : Input capacitance of ACM.Cf : Filter capacitance.Coss : Equivalent capacitance across the MOSFET.CCM: Continues conduction mode.DCM: Discontinues conduction mode.fo : Frequency of grid voltage.fs : Switching frequency.IA : Amplitude of iout .ic : Input capacitance current.icon : Output current of interleaved flyback converter.iin : Current of PV panel.Iin : RMS value of iin .iout : Output current of PV ACM.Iout : RMS value of iout .ip : Primary current of transformer.Ip : Peak value of ip .

Manuscript received July 28, 2012; revised October 10, 2012, January 16,2013, and May 20, 2013; accepted August 6, 2013. Date of current versionFebruary 18, 2014. This work was supported by China National Science Fundunder Grant 51107116. Recommended for publication by Associate EditorT. Shimizu.

The authors are with the Department of Applied Electronics, ZhejiangUniversity, Hangzhou 310057, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2279266

iref : Reference current.is : Secondary current of transformer.Is : Peak value of is .Lf : Filter inductance.Lp : Primary inductance of transformer.Ls : Secondary inductance of transformer.Lep : Leakage inductance of Lp .Les : Leakage inductance of Ls .Lmp : Magnetizing inductance of Lp .Lms : Magnetizing inductance of Ls .n: Turns-ratio of transformer.pdc : Instantaneous input power of PV panel.Pin : Average input power of ACM.Pout : Average output power of ACM.PR : Rated output power.PV: Photovoltaic.THD: Total harmonic distortion.Ton : Turn-on time of switching cycle.To : Turn-off time of switching cycle.udc : Voltage of PV panel.uds : Drainsource voltage of MOSFET.ug : Grid voltage.Vg : RMS value of ug .Vp : Amplitude of ug .ZCS: Zero-current switching.

I. INTRODUCTION

PHOTOVOLTAIC ac module (PV ACM), also named asmicro-inverter [1], is a compact and modular structure forsmall power PV generation system applications [2]. This con-cept was conceived 30 years ago at Caltechs Jet Propulsion Lab-oratory [3]. However, it is only recently reaching commercialrealization. Nowadays, its recognized as an attractive solutionfor the residential utility-interactive PV systems [4][6].

PV ACM is defined as the integration of a single PV paneland a single-phase grid-tied (GT) inverter [6]. The GT inverteris the direct interface between the PV panel and the residentialutility, which converts the low dc voltage from the PV panel tothe higher ac voltage of the grid. Compared to the conventionalsingle- or multistring inverters in PV applications, advantagesof PV ACM include more flexibility and less installation costin system expansion as a plug and play device, lower manu-facturing cost through mass production, lack of the power mis-match between PV modules, and higher system-level energyharvesting ability under shaded conditions [7].

However, the PV ACM must meet a series of harsh require-ments, such as THD and islanding protection demanded by

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GAO et al.: ANALYSIS AND IMPLEMENTATION OF AN IMPROVED FLYBACK INVERTER FOR PHOTOVOLTAIC AC MODULE APPLICATIONS 3429

standards of GT devices, maximum power point track (MPPT)and minimum power fluctuation demanded by PV panels, highefficiency, high reliability, long lifetime, low cost, and easy in-stallation demanded by users [6], [8].

For satisfying these harsh requirements, many topologies andcontrol methods have been reported in references [6], [9], [10].Nowadays, a single stage flyback-type utility interactive in-verter, which combined a voltage-controlled current-source fly-back and a GT inverter as one single stage [11], is regardedas an attractive solution in PV ACM applications. Its majoradvantages include electric isolation, high power density, highefficiency, and high step-up ratio, which are based on the sim-ple control loop and compact structure [12][14]. But its largeinput capacity and loss of leakage inductance energy are stillthe challenges for designers. At present, more and more workshave been done on the improvement for the flyback inverter,such as control loop [15][21], power decoupling [22][25],soft-switching [26][28], and MPPT control [29], [30].

In [15][20], three operation modes (CCM, DCM, and BCM)of the flyback inverter are investigated in the PV ACM applica-tions. CCM can be realized with average-current control [15].However, the peak-current control of the secondary current isnot appropriate for CCM, since the transformer is incompletelydemagnetized during each switching cycle, and the system willbehave as a load-independent voltage source with peak-currentcontrol [19]. Moreover, the flyback inverter at light load will slipinto DCM operation around the zero crossing of grid voltage,which increases the difficulty of control system design [15].

DCM and BCM can be easily realized with peak-current con-trol [17], which has no phase delay compared to the average-current control. Meanwhile, DCM and BCM have the ZCS fea-ture naturally, so can have higher efficiency in comparison withCCM operation. Furthermore, the power density of BCM isusually higher than DCM [19]. Hence, BCM is more preferredfor PV ACM applications considering all the earlier researchworks.

In the BCM with peak-current control, the output current ioutis directly controlled by the reference current iref during eachevery switching cycle. Since the flyback inverter operates as anac current source, a variable switching frequency (VSF) controlstrategy must be applied [17]. However, the VSF fs leads to thedifficulty to get the accurate mathematical model between ioutand iref . As the THD of iout must comply with the standards ofGT devices, the mathematical model is extremely important inthe design of iref .

The purpose of this paper is to analyze and propose an ac-curate mathematical model between iout and iref through theo-retical derivation. Based on the proposed mathematical model,the relationship between fs and iref is also analyzed. Then, anovel control strategy of iref is proposed to decrease THD ofiout . Moreover, the realization of MPPT based on this controlstrategy is also investigated. Finally, the control strategy is ver-ified based on an improved flyback-inverter topology, which isdescribed in [27]. Both simulation and experiment results onthis topology are shown in this paper.

This paper is organized as follows. In Section II, theresidential utility-interactive PV system and the improved

Fig. 1. Residential utility-interactive PV system.

flyback-inverter topology employed in this paper are described.Section III analyzes and proposes the mathematical model be-tween iout and iref in BCM by theoretical derivation. SectionIV proposes the control strategy of iref and fs for the improvedflyback inverter in BCM operation. Section V analyzes the re-alization of MPPT based on the proposed mathematical model.Simulation and experiment results are then presented in SectionsVI and VII, respectively, which validates the performance of theproposed mathematical model. In Section VIII, the conclusionsof this paper are given.

II. IMPROVED FLYBACK-INVERTER TOPOLOGY

A. Residential Utility-Interactive PV SystemThe residential PV system has great potential of being a sig-

nificant market, due to following advantages [31], [32]: 1) trans-lating the utility value into an allowable system cost using thehomeowner economic parameters and 2) the PV system is ableto utilize the roof for support structure, eliminating the land anddirect structure expenses.

Fig. 1 shows the diagram of the residential utility-interactivePV system based on ACM device [4], [5]. In this system, thePV array is mounted on the customers roof, the consumersload is connected at the ac line terminal, and the ACM can bemounted on each individual PV panel as a modular device [22].The available dc power from the PV panel varies with the solarirradiation and ambient temperature [33], is converted to thesingle-phase 50/60 Hz ac power and fed to the utility line throughACM. In the daytime, the solar power supplies to the consumerand the surplus is fed to the utility line, while in cloudy weatheror after dusk, the utility line feeds the load.

B. Flyback InverterFig. 2 shows the topology of the flyback inverter, which con-

sists of three MOSFETs, two diodes, and a flyback transformerwith center-tapped secondary winding. The two outputs fromthe transformer are connected to the grid, through a commonfilter circuit, which can switch reciprocally and synchronouslywith the polarity of the grid voltage. Hence, the flyback-inverter


Fig. 2. Fundamental flyback-inverter topology.

Fig. 3. Improved flyback-inverter topology.

modulates the secondary current into the folded sinusoidalcurrent by SM 1 , then unfolds it by SM 2 and SM 3 , and finallyinjects the ac current into the grid through the output filter.

C. Improved Flyback-Inverter TopologyFig. 3 shows the topology of the improved flyback in-

verter, which is described in [27]. This topology comprises aninterleaved-flyback converter and a line-frequency GT inverter.Its principle is same as the fundamental flyback inverter. Theinterleaved-flyback converter modulates the secondary currentinto folded sinusoidal current. Then, the current is unfolded andinjected through the output filter by the GT inverter.

In fact, the improved topology is not as compact as the fun-damental flyback inverter, but does have following advantages:

1) The introduced interleaved-flyback converter comprisestwo flybacks, which can improve the power ratingdramatically.

2) Every flyback is phase-shifted 180 in each switching cy-cle, as shown in Fig. 4. This interleaved operation canachieve equivalent double switching frequency and so toreduce the secondary current ripple.

3) The transformer with center-tapped secondary winding isno needed due to the independent GT inverter, which canreduce the difficulty of transformer design. The voltagestress of secondary switches is also decreased because ofthe GT inverter.

Fig. 4. Principle of interleaved-flyback converter.

Fig. 5. Equivalent diagram of a single flyback inverter.

III. MATHEMATICAL MODEL OF THE BCM OPERATINGFLYBACK INVERTER

This section analyzes and proposes the mathematical modelbetween iout and iref in a BCM operating flyback inverter. Be-cause the operation of the improved topology is the same as thefundamental topology, the following analysis is mainly basedon the fundamental flyback inverter for simplification.

A. BCM OperationDue to the polarity switching circuit, the operations of the

flyback inverter are the same during both the positive and neg-ative half cycle of the grid voltage. Therefore, the equivalentdiagram for a single flyback inverter can be shown as Fig. 5.According to this figure, the output current iout is obtained byfiltering secondary current is .

In BCM operation, the peak value Ip of the primary currentip is forced to follow the reference current iref . During eachswitching cycle, when is decreases to zero, SM conducts, andthis process can be realized by quasi-resonant (QR) control.When SM switches on, ip increases gradually in a linear relationwith udc . Once ip equals to iref , SM is off and is decreaseslinearly with ug . Therefore, the relationship between iout andiref in BCM during half one cycle is shown in Fig. 6. In thisfigure, the envelope of ip equals to iref and iout can be regardedas the average current of is during each switching cycle.

According to Fig. 6, the switching frequency varies with irefin BCM operation, which is more complicated than in DCMoperation. The VSF fs leads to the difficulty to get the accuratemathematical model between iout and iref . Meanwhile, due tothe requirements of the GT devices, iout should be a perfect


Fig. 6. Relationship between iout and iref in BCM.

Fig. 7. Primary and secondary currents.

sinusoidal waveform, while have the same frequency and phasewith the utility. That means the accurate mathematical model isextremely important.

B. Proposed Mathematical Model Between iout and irefThe proposed mathematical model between iout and iref in

BCM operation will be analyzed through theoretical derivationwith two fundamental assumptions as:

1) since the flyback inverter operates at high switching fre-quency, udc , ug , and iref can be assumed as constantsduring each switching cycle;

2) all the components in the circuit are ideal, therefore theleakage inductance of transformer, switching loss andother parasitic parameters of the circuit (such as Coss)are not taken into account.

Fig. 7 shows the primary and secondary currents in the switch-ing cycles. According to the volt-second balance of inductance,the turn-on and turn-off times can be expressed as (1). And therelationship of Ip and Is can be shown as (2)

Ton = Lp Ip 1udc

To = Ls Is 1ug

(1)

Ip = iref

Is = n Ip = Ip

LpLs

. (2)

Since iout is obtained by filtering the secondary currentis , iout approximately equals to the average value of is dur-ing each switching cycle. So, the area S1 and S2 can be thoughtas equal, as shown in Fig. 7. Therefore, iout can be expressedas (3)

iout =12 Is To 1

Ton + To(3)

iout =12(iref

Lp/Ls

)(Ls iref

Lp/Ls (1/ug )

)

iref Lp (1/udc) + Ls iref

Lp/Ls (1/ug ).

(4)Substituting (1) and (2) into (3), (4) can be obtained. After

simplification, the ideal mathematical model between iout andiref can be obtained as (5). This is the proposed mathematicalmodel, which can be applied in the single flyback inverter. Ac-cording to this expression, iref is determined by the grid voltageug , the input voltage udc and the turns ratio n of transformer. Inthe PV ACM application, the input voltage is decided by the PVpanel and input capacitor Cin , and there is usually a large inputcapacitor that is used to obtain steady input voltage. So, udccan be regarded as constant in the steady state. Therefore, theproportion of iref and iout varies with ug in the line-frequencycycle according to the following equation:

iref = 2iout

(ugudc

+

LsLp

)

. (5)

C. Analysis of the Output Currents THDAccording to the proposed mathematical model, the output

current iout can be controlled by the reference current iref , andiref can be obtained by substituting the expression of iout into(5). Since PV ACM is a GT device, iout should comply with theTHD requirement. If the mathematical model is inaccurate, ioutwill be distorted. Therefore, the accurate mathematical model isthe key to guarantee the THD of iout meet the standard require-ments.

References [17][19] treated the envelope of peak primarycurrent ip as a sinusoidal waveform in BCM operation, whichis similar to the expression of ip in DCM operation as shown in(6) [34]

iref = 2

Po

Lp fs sint. (6)

Reference [17] and [19] adopted (7) as the control law of iout .According to these references, Tonp is the Ton interval valuereferring to the switching cycle that occurs at the time area oft = /2, and is a constant. The expression of iref in [18] is notclearly presented, but it is similar to (7), which can be provedby the fifth figure of reference [18]

iref =udcLp

Ton,p sint. (7)


Fig. 8. Modified transformer model.

Fig. 9. Waveforms of the QR control.

If these equations are used to calculate the iref in BCM op-eration, it has little influence on the system efficiency, but ioutwill be distorted and THD will increase. It is verified by thesimulation results in Section VI-C.

D. Further Discussions on the Proposed Mathematical ModelAs mentioned earlier, some practical aspects are not consid-

ered in the ideal mathematical model. As an instance, the trans-formers leakage inductance is an important factor consideringthe system power loss [12], while the QR control is a preferredapproach for BCM operation to realize soft-switching [20]. Bothof them have a measure of influence on the accuracy of the pro-posed mathematical model.

Fig. 8 is a more realistic model of the transformer, whichincludes the influnce of the leakage inductances. The leakageinductances can be described in (8). Therefore, the relationshipof Ip and Is should be modified as (9)

{Lp = Lmp + LepLs = Lms + Les

(8)

Is = Ip

LmpLms

= Ip

Lp LepLs Les . (9)

Fig. 9 shows the waveforms of the QR control, and its princi-ple is elaborated in [20]. In this figure, uds is the drainsourcevoltage of MOSFET SM . Compared to the ideal case shown inFig. 7, there are an additional period designated as the QR timeTQR in Fig. 9. Therefore, Equation (3) should be changed intothe following expression:

iout =12 Is To 1

Ton + To + TQR. (10)

According to [20], TQR can be described as (11). Coss is theequivalent capacitance across the MOSFET, as shown in Fig. 5.It is clear as in (11) that TQR is determined by the hardwareparameters. Therefore, it can be regarded as a fixed dead-bandtime in (10). Considering the VSF control technique in BCMoperation, TQR should be designed as small as possible

TQR =

LpCoss . (11)

After substituting (1) and (9) into (10), the modified math-ematical model can be obtained as (12). However, this is toocomplicated and hard to be simplified into a linear function as(5), which is fatal to the realization of reference current calcu-lation in practical application

iout =12

iref

(Lp Lep)/(Ls Lms) (ug/iref )

Coss/Ls + (ug/udc)

Lp/Ls + 1

.

(12)Moreover, the leakage inductance and the QR time are not

dominant in the system, and they can be minimized throughthe hardware optimization. Therefore, this paper employs theideal mathematical model, as shown in (5), in flyback-inverterapplication after taking all factors as a whole. The performanceof the ideal mathematical model is verified by the simulationand experiment results, which are presented in the followingsections.

IV. CONTROL STRATEGY FOR THE IMPROVED TOPOLOGYIn this section, the control strategy of the reference current

iref and the switching frequency fs for the improved topologyin BCM operation is analyzed and designed, which is based onthe proposed mathematical model in Section III.

A. Reference Current AnalysisEquation (5) shows the mathematical model between iout

and iref , thus iref can be obtained by substituting the expressionof iout to (5). Because PV ACM is a GT device, iout shouldcomply with the THD requirement, and the ideal condition is toguarantee iout as a perfect sinusoidal waveform. Moreover, ioutshould have the same frequency and phase with the grid voltageug to make sure ACM supply the maximum active power to thegrid. So, iout and ug can be described as follows:

{iout = IA sin(t)

ug = Vp sin(t). (13)

Substituting (13) into (5), the reference current iref in BCMfor a single flyback inverter can be obtained as follows:

iref = 2IA

(Vpudc

sin2(t) +

LsLp

sin(t)

)

. (14)

In the improved topology, the two flybacks will share theoutput power of ACM equally when they work in the interleavedmode. Therefore, the reference current of each flyback should


be half of iref , which can be shown as follows:

iref1 = iref2 = IA

(Vpudc

sin2(t) +

LsLp

sin(t)

)

. (15)

B. Switching Frequency AnalysisSince the switching frequency varies with iref in BCM op-

eration, the variation range of fs should be considered in theflyback-inverter design. As mentioned in Section III-D, the in-fluence of TQR is ignored in the calculation of iref in order toget a simplified linear mathematical model. This is importantfor the realization of the reference current calculation in digitalcontrol. However, in the analysis of fs, TQR should be consid-ered to get more precise mathematical model after that iref hasbeen defined. Therefore, fs can be described as follows:

fs =1

Ton + To + TQR. (16)

After substituting (1), (2) and (11) into (16), formula (17) canbe obtained, which appears that fs is inversely proportional toiref when ug is stable. However, iref also varies with ug due to(14), so formula (17) is not yet simplified

fs =1

iref (Lp 1ud c + Ls

Lp/Ls (1/ug )

)+

LpCoss

.

(17)Therefore, the final formula (18) can be obtained by substi-

tuting (13) and (14) into (17). Equation (18), as shown at thebottom of the page.

According to (14) and (18), one conclusion is that iref isproportional to IA and fs can be approximately regarded asinversely proportional to IA . Moreover, the maximum and min-imum of fs also can be calculated, as shown in (19). In theseequations, udc is assumed as a constant during each switchingcycle

fs. max =

12IALs/Vp +

LpCoss

, t = 0,

fs. min =1

2IA

(Vp Lpu2d c

+2

Lp Lsud c

+ LsVp

)

+

LpCoss

, t =

2

.

(19)Due to (15), iref1 and iref2 of the improved topology are both

half of iref , when two flybacks work in the interleaved mode. So,the switching frequency of each phase flyback can be obtained

TABLE IVALUES OF CIRCUIT PARAMETERS

by substituting (13) and (15) into (17), shown as (20), at thebottom of the page

C. Parameters DesignA 200 W PV ACM prototype at 220 V/50 Hz utility condition

is designed in this paper. Table I lists the values of the circuitparameters in the improved topology. The PV panel voltage udcis 40 V when PV panel outputs the maximum power, while itsacceptable input range is 30 V-50 V in the design.

The value of IA is related to Pout , shown as (21). When Poutequals to the rated power PR (200 W), IA is 1.286 A. IA will beadjusted by MPPT control method to track the maximum powerpoint, which will be shown in Section V

IA =2PoutVp

. (21)

The relationship of Pout and Pin is shown in (22). The max-imum output power Pout of ACM is 200 W, and the requiredefficiency is above 90% when Pout is 200 W. So, Pin shouldbe less than 222 W at full load

Pout = Pin . (22)The switching frequency variation range of the transformer

for each phase flyback is chosen at first. Because of the vol-ume and weight requirements, the optimal range is between300400 kHz. Meanwhile the minimum should be more than200 kHz, and the maximum should be less than 600 kHz.

1) Transformer Design: In the improved topology, the inter-leaved flyback comprises two current-source flybacks. So, theturns ratio n should be determined by the inverse ratio of the in-put current and output current, which can be calculated by (23).In this equation, Iin and Iout are the root-mean-square (rms)value of iin and iout , respectively

{Iin = P inud c

Iout = Po u tVg. (23)

Therefore, the turns ratio n is designed according to (24). Therequired value is 1:6.11 when udc is 40 V, 1:4.44 when udc is

fs =1

2IA((VpLp sin2(t)/u2dc) + (2

LpLs sin(t)/udc) + (Ls/Vp)

)+

LpCoss

(18)

fs1 = fs2 =1

IA((VpLp sin2(t)/u2dc) + (2

LpLs sin(t)/udc) + (Ls/Vp)

)+

LpCoss

(20)


50 V, and 1:8.15 when udc is 30 V, respectively. Finally, n isselected as 1:6

n =IoutIin

= udc

Vg. (24)

In the improved topology, the reference current of each fly-back should be half of iref , shown as (15), when the two flybackswork in the interleaved mode. This equation can be rewritten as(25), and the maximum primary current Ip.max can be calculatedshown as (26)

iref1 = iref2 = IA

(Vpudc

sin2(t) +1n

sin(t))

(25)

Ip. max = IA

(Vpudc

+1n

)

, t =

2. (26)

Then, the primary inductance Lp can be obtained from (27)according to reference [35]. In the equation, max is the max-imum duty cycle, which is usually 0.5 in the design of thetraditional flyback converter. According to (19), when ip equalsto Ip.max , the switching frequency fs is the minimum, which is200 kHz

Lp =udc. min maxIp. max fs . (27)

Therefore, the required Lp is 3.564 H. Then, the secondaryinductance Ls can be calculated by (28), which is 128.3 H.Subsequently, the primary and secondary inductances are ad-justed according to the experiment results, and finally the mea-sured value is 3.7 and 133.6 H, respectively

Ls =Lpn2

. (28)2) Input Capacitance Design: This topology needs a very

large dc input capacitance Cin to decouple the power pulsationcaused by single-phase power generation to the utility line [22].The value of Cin can be calculated according to (29) in [34].In this formula, udc is 2 V. So, the required capacitanceis 8.83 mF. In this paper, Cin is comprised of four 2.2 mFelectrolytic capacitors in parallel

Cin =Pin

udcudc. (29)

However, the electrolytic capacitor with large capacitancehas a large volume and a relatively short lifespan. Especiallyunder a very high atmospheric temperature, the lifetime of theelectrolytic capacitor is shortened dramatically [22]. In order tosolve this problem, some power decoupling circuits and controlmethods are proposed in [22][25]. In these references, thepower decoupling capacitance is about 2050 F, which can bereplaced by the film capacitors. And this will be the future workof this topology.

3) Output Filter Design: Fig. 10 shows the equivalent dia-gram of CL filter in the topology, and the relationship of is , ioutand ug can be shown as (30). Thus, the expression of the CLfilter can be obtained as shown in (31)

Iout(s) =1

1 + s2Lf CfIs(s) sCf1 + s2Lf Cf Ug (s) (30)

Fig. 10. Equivalent diagram of CL filter.

TABLE IIDESIGNED VALUES OF CIRCUIT PARAMETERS

Fig. 11. iref and fs of single flyback inverter.

Iout(s)Is(s)

Ug (s)=0

=1

1 + s2Lf Cf

Iout(s)Ug (s)

Is (s)=0

=sCf

1 + s2Lf Cf

. (31)

This is a second-order low-pass filter with a resonant fre-quency fr , which can be expressed as (32). In this design, frshould comply with (33) [20]. Therefore, the range is from500 Hz to 20 kHz. Finally, Lf and Cf are selected as 510 Hand 280 nF, respectively, considering the requirement of volumeand cost. And the resonance frequency is 13.3 kHz

fr =1

2

Lf Cf(32)

10fo 12

Lf Cf

110

fs. min . (33)

D. Design of the Reference Current for Improved TopologyTable II lists the designed values of circuit parameters. Ac-

cording to the values of Tables I and II, iref and fs of singleflyback inverter can be shown as in Fig. 11. In this figure, iref(t, IA ) is the reference current for single flyback inverter, andfs (t, IA ) is its switching frequency, iref (t, IA /2) is the


reference current for each flyback converter in the interleavedmode, and fs (t, IA /2) is its switching frequency.

This figure illustrates that iref is very small at the zero cross-ing, which causes fs extremely high at this time. However, theacceptable range of fs is expected as 200600 kHz. Therefore,the principle of the improved topology is designed as followsto comply with the requirement, which is also used in refer-ence [27], [34]:

1) when iref is smaller than a value defined as I1 , both twoflybacks stop working. This period can be called as deadband;

2) when iref is larger than I1 and smaller than I2 , the firstflyback works in stand-alone mode;

3) when iref is larger than I2 , both two flybacks work in theinterleaved mode

{I1 = iref (t1)

I2 = iref (t2). (34)

The expression of I1 and I2 can be described as (34). There-fore, iref1 and iref2 of the two flyback are designed as (35) and(36). Then, fs1 and fs2 of two flyback can be expressed as (39)and (40), as shown at the bottom of the next page, which arecorresponding to (35) and (36)

iref 1(t) =

0 (0 iref (t) < I1)iref (t) (I1 iref (t) < I2)iref (t)/2 (I2 iref (t))

(35)

iref2(t) =

{0 (0 iref (t) < I2)iref (t)/2 (I2 iref (t)) . (36)

The value of I1 is related to the dead band time and fs.max .The larger the I1 is, the smaller the fs.max is. But if I1 istoo large, the dead band time will be increase, which will alsoincrease the THD of iout . Therefore, the value of I1 should becarefully selected to guarantee that fs.max complies with thedesign requirement and the dead band time is the minimum.According to equation (18) and (19), fs.max can be expressedas (37) shown at the bottom of the next page.

Therefore, the value of t1 can be obtained by solving equation(37), and the value of I1 can be obtained by (34). According tothe values in Tables I and II, t1 is 0.077 rad when fs.max is600 kHz, and the required value of I1 is 1.306 A.

The selection of I2 is different from that of I1 because thevariation of I2 wont cause a dramatic change of fsmin . Mean-while, its influence on the THD of iout is weak. Thus its allow-able range is not so limited. Moreover, the time of interleavedmode is controlled by I2 . If Pout is small and the peak of iref issmaller than I2 , the interleaved mode will be disabled, and onlyone flyback works during the whole period. In this design, theboundary is selected as half of the rated output power, which is100 W. Therefore, I2 can be obtained by (38). In this equation,IA is 1.286 A. So, the required value of I2 is 17.729 A, which

Fig. 12. Reference current of flyback 1.

Fig. 13. Reference current of flyback 2.

is half of peak primary current, and t2 is 0.683 rad

I2 = iref(

2

)/2 = IA

(Vpudc

+

LsLp

)

. (38)

After substituting the values of parameters in Table II,iref1 , iref2 , fs1 , and fs2 can be shown as Figs. 1214, respec-tively. In these figures, fs is limited in between 250 and 600 kHz.Meanwhile, when I1 and I2 use different values, the influenceon THD is shown in Section VI-D

V. REALIZATION OF MPPT CONTROL IN THE IMPROVEDTOPOLOGY

Most of the traditional MPPT control methods are appliedto the voltage-source converter, and are usually implementedby adjusting input voltage udc [36][40]. However, PV ACMis a current-source system, and input voltage cant be directlycontrolled, which depends on PV panel characteristics. So, theseMPPT methods should be modified and realized by adjustinginput current iin to apply to the PV ACM application.


Fig. 14. Switching frequencies of two flybacks.

In the flyback inverter, the reference current iref is used tocontrol the output current iout directly. If the input voltage andgrid voltage is stable in line-frequency cycle, the input currentiin can be directly controlled by iref . And the relationship of irefand iin will be investigated as follows.

According to Fig. 5, the input current iin is the sum of ip andic , so the input power Pin can be described as follows:

Pin = T

0udciindt =

T

0udcicdt +

T

0udciP dt. (41)

Because udc is also the voltage across the input capacitor, therelationship of ic and udc can be shown in (42). Therefore, (43)can be obtained from (41) and (42)

ic = Cdudcdt

(42)

Pin =12Cinu

2dc

T

0+

T

0udciP dt. (43)

As mentioned earlier, the input voltage udc can be regardedas a constant in the steady state. So, (41) can be simplified asshown in (44). Therefore, iin can be regarded as the average of

Fig. 15. Primary current and secondary current.

ip during each switching cycle, which is shown in Fig. 15

Pin = T

0udciP dt. (44)

As shown in Fig. 15, iin can be calculated according to thesame assumption as iout in the foregoing analysis, which is thatthe area S3 (blue) and S4 (green) are approximately equal. So,the primary current iin can be expressed as (45), which is similarto (3)

iin =12 Ip Ton 1

Ton + To. (45)

After substituting (1) and (2) into (45), (46) can be obtained,which shows the relationship between iin and iref . When ACMworks at steady state, ug and udc can be regarded as stable inline-frequency cycle. Therefore, the input current can be directlycontrolled by iref . This formula also applies to the improvedtopology, because in the interleaved mode, iin equals to the sumof two primary currents of each flyback, but their references arehalf of iref

iin =12 iref ug

ug + udc

Ls/Lp. (46)

fs. max =1

2IA((VpLp sin2(t1)/u2dc) + (2

LpLs sin(t1)/udc) + (Ls/Vp)

)+

LpCoss

(37)

fs1(t) =

1

2IA(

Vpu2d c

Lp sin2(t) + 2ud c

LpLs sin(t) + LsVp

)+

LpCoss

(I1 iref (t) < I2)

0 (0 iref (t) < I1)1

IA

(Vpu2d c

Lp sin2(t) + 2ud c

LpLs sin(t) + LsVp

)+

LpCoss

(I2 iref (t))

(39)

fs2(t) =

0 (0 iref (t) < I2)1

IA

(Vpu2d c

Lp sin2(t) + 2ud c

LpLs sin(t) + LsVp

)+

LpCoss

(I2 iref (t)) (40)


Fig. 16. Diagram of MPPT control.

Meanwhile, equation (5) shows that iref is a function of iout .After substituting (5) into (46), the relationship of iin and ioutcan be expressed as (47). The equation also proves that, the in-stantaneous input power udc iin equals to instantaneous outputpower ug iout in the ideal state

iin = iout ugudc

(47)

iin =Vpudc

IA sin2(t). (48)

According to the expression of iout and ug as shown in (13),iin can be obtained as (48), which shows that the input cur-rent iin can be adjusted by changing IA proportionally in theflyback inverter. Therefore, the traditional MPPT methods canbe modified and realized by adjusting IA to apply to the PVACM application. For example, Fig. 16 shows the conventionalIncremental conductance algorithm using fixed step-length,which is realized by adjusting IA . This method is verified bythe simulation results in the following section.

VI. SIMULATION RESULTSA simulation platform based on MATLAB integrated with

PLECS is established, in order to verify the mathematical modeland the proposed control strategy of BCM operation on theimproved flyback-inverter topology. Moreover, MPPT controlis implemented by adjusting IA is also verified. The simulationresult is shown as follows.

A. Control Block Diagram of Improved TopologyFig. 17 shows the control block diagram of simulation plat-

form, which is based on the analysis in Section IV. Phase-lockedloop (PLL) is used to detect the phase angle, amplitude and fre-quency of grid voltage accurately and quickly. Islanding protec-tion guarantees the ACM works under normal utility condition.The output of MPPT control is IA , which is used to adjust thereference current iref . The whole diagram of Fig. 17 is estab-lished in MATLAB. And the power circuit, as shown in Fig. 3,is established in PLECS.

Fig. 17. Control block diagram of ACM.

Fig. 18. Primary currents of flyback 1 and 2.

The parameters value on the simulation platform has beenshown in Tables I and II. The amplitude IA of output currentiref is designed as 1.414 A. Only after that simulation resultsmeet the design requirement, the mathematical model and thecontrol strategy can be verified.

B. Simulation Result of Reference Current DesignFig. 18(a) and (b) illustrates the primary currents ip1 and ip2 of

flyback 1 and 2 in interleaved mode, respectively. The envelopesof primary currents are equal to the reference currents iref1and iref2 , respectively. Fig. 19(a) and (b) shows the secondarycurrents is1 and is2 of flyback 1 and 2, respectively. Fig. 19(c)shows the output current icon of the interleaved flyback, whichequals to the sum of two secondary currents.

Fig. 20(a) and (b) shows the details of ip1 and ip2 , respectively.Fig. 21(a) and (b) shows the details of is1 and is2 , respectively.Fig. 21(c) shows the details of icon .

Fig. 22, shows the output current iout of the improved topol-ogy and the sampling voltage of grid for the comparison of ioutand ug . The amplitude of iout meets the design requirements,which is designed as 1.286 A. The THD of iout is 2.286%, cal-culated by MATLAB. Fig. 23 is the peak magnitude spectrum ofiout , which proves the harmonic components are in the acceptedrange.


Fig. 19. Secondary currents of flyback 1 and 2.

Fig. 20. Details of primary currents.

Fig. 21. Details of secondary currents.

C. Comparision With Other ModelsAccording to [17][19], the reference current can be ex-

pressed as (49). Another reference current is shown as (50) forthe comparison. Fig. 24 shows the waveforms of iref , iref .a andiref .b . In these equations, the values of A and B equal to the peak

Fig. 22. Output current of ACM and sampling of grid.

Fig. 23. Spectrum of ACMs output current.

Fig. 24. Waveforms of iref , iref .a , and iref .b .

primary current (35.458 A), which guarantees the amplitude ofiout is close to IA (1.286 A)

iref .a = A sin(t) (49)iref .b = B sin2(t). (50)


Fig. 25. Output current of ACM using (49).

Fig. 26. Spectrum of output current using (49).

Fig. 27. Output current of ACM using (50).

Fig. 25 shows the output current using (49) as the referencecurrent, Fig. 26 illustrates the spectrum of output current, andthe measured THD is 14.84%. Fig. 27 shows the output cur-rent using (50) as the reference current, Fig. 28 illustrates thespectrum of output current, and the measured THD is 13%.

Fig. 28. Spectrum of output current using (50).

Fig. 29. Relationship of I1 , I2 and THD.

According to the earlier results, when (49) or (50) are adoptedas the reference current, THD is much larger than that of the pro-posed mathematical model in this paper. Therefore, the accuracyof the proposed mathematical model is verified.

D. Simulation Result for I1 and I2According to Section IV-D, the values of I1 and I2 will affect

the THD of iout . Fig. 29 shows the relationship of I1 , I2 andTHD. According to this figure, the increase of I1 will cause THDdeteriorate dramatically. Thus, the value of I1 should be the min-imum when fs.max complies with the requirement. Meanwhile,the influence on THD is weak when I2 varies in a large range.Therefore, the allowable range of I2 is wide.

E. Simulation Result of MPPT ControlFig. 30 shows the VI curve of PV panel, of which the max-

imum power is set as 200 W. Fig. 31 illustrates the simulationresult of MPPT control. The steady state starts form 0.18 s, andMPPT control is enabled in 0.24 s. Fig. 31(a) shows the value ofIA , Fig. 31(b) and (c) shows the output voltage udc and currentiin of PV panel, respectively, and Fig. 31(d) show the aver-age output power of PV panel. From Fig. 31, the conventional


Fig. 30. VI curve of PV panel.

Fig. 31. Simulation result of MPPT control.

Incremental conductance algorithm using fixed step-length isrealized by adjusting IA .

VII. EXPERIMENT RESULTS

A 200 W PV ACM prototype at 220 V/50 Hz utility conditionwas implemented to validate the proposed mathematical modeland the control strategy. The control algorithm is the same asFig. 17, in which the light-color blocks are implemented on theFPGA EP3C10E144 from ALTERA and the dark-color onesare implemented by hardware. The power circuit is still the im-proved flyback-inverter topology. Then, the experimental resultsare shown as follows.

A. Experiment Result of Reference Current DesignIn the experiment, the input voltage of ACM is 36 V, which

is supplied by a dc voltage source. The amplitude IA of outputcurrent is designed as 1 A, so the output power should be around156 W. The values of other parameters are same as Tables I andII.

Fig. 32 shows the primary currents ip1 and ip2 of flyback 1and 2 in the interleaved flyback. These currents are measuredby two current transformers, respectively, of which the ratio is

Fig. 32. Primary currents of flyback 1 and 2.

Fig. 33. Secondary currents of flyback 1 and 2.

Fig. 34. Output current of interleaved flyback.

40 A:1 V. The envelopes of primary currents are equal to thereference currents. Fig. 33 shows the secondary currents is1 andis2 of flyback 1 and 2, measured by the current probe. Fig. 34shows the output current icon of the interleaved flyback, whichis equal to the sum of is1 and is2 .

Fig. 35 shows the output current iout of PV ACM and the gridvoltage ug . The output current is a good sinusoidal waveform,but has a little distortion at zero crossing. That is because both


Fig. 35. Output current of ACM and grid voltage.

Fig. 36. Harmonic components of ACM output current.

of the two flybacks do not work in this period and the currentis discontinuous. Moreover, the amplitude of current is 1.06 A,which is close to the theoretical value 1 A.

Fig. 36 shows experimental data about the harmonic compo-nents of iout , measured by WT3000 of Yokogawa. Fig. 37 showsthe percentage spectrum of iout , which is based on the data ofFig. 36. From these figures, there are some high-frequency har-monics (3rd, 11th, 13th, and 15th) in output current, but theirmagnitudes are very small. And the THD of iout is 2.459%shown by Fig. 36, which can also prove the good quality of theoutput current.

According to the experiment results, the proposed mathemat-ical model of BCM operation is validated. Using the proposedcontrol strategy in the experiment, the output current of ACMexhibits good sinusoidal waveform and is very close to the the-oretical value. Moreover, THD and harmonics of iout are in thesatisfying range, which meet IEC61727 [41] and IEEE1547 [42]standards quite well, verifying the excellent performance of thecontrol strategy.

Fig. 37. Percentage spectrum of harmonics.

Fig. 38. Measured efficiency versus output power of ACM.

B. Experiment Result of EfficiencyIn this experiment, the input voltage of ACM is 36 V, which

is supplied by a dc voltage source. Fig. 38 shows the measuredefficiency versus output power of the ACM, which is measuredby WT230 of Yokogawa. When the load is between 60 and140 W, the efficiency is above 93%, and when the load is between140 and 200 W the efficiency is above 94%. The experimentresult shows the proposed control strategy in BCM operationguarantees high efficiency at different load condition.

Moreover, according to the principle of interleaved flyback,only one flyback converter of the ACM works when Pout isless than 100 W, and two flyback converters of the ACM workin the interleaved mode when Pout is more than 100 W. Sincethe output power is shared equally by the two flybacks in theinterleaved mode, the efficiency between 100 and 130 W issmaller than that between 70 and 100 W.

C. Experiment Result of MPPT ControlIn this experiment, the input power of ACM is supplied by

a PV panel, of which the maximum power is around 140 W.


Fig. 39. Voltage, current and power of PV panel.

Fig. 40. Output current of ACM and grid voltage.

The MPPT control strategy is based on the proposed method inSection V.

Figs. 39 and 40 illustrate the dynamic response of the ACMwhen the illumination condition changes form partial occlusionto no occlusion. In these figures, the changing of illuminationcondition happened at the instant of the dash line.

Fig. 39 shows the voltage udc and current iin of the PV panel.In this figure, the product of udc and iin , which is the instanta-neous power pdc of PV panel. Fig. 40 shows the output currentiout of ACM and the grid voltage ug . The dynamic responselasts for about 2 seconds. Finally, the output power is stabilizedaround 138 W according to Fig. 39, which is close to the max-imum power point of the PV panel. Thus, the proposed MPPTcontrol method is implemented by changing IA is validated.

VIII. CONCLUSIONFlyback inverter is an attractive solution for photovoltaic ac

module application. As a grid-connected device, flyback invertershould work as a current source and provides the sinusoidaloutput current that is synchronous with the grid voltage. Mean-

while, the flyback inverter should have high efficiency to satisfyusers demand.

In this topology, BCM is more preferred compared to DCMand CCM, because of its higher power level, higher efficiency,and wider switching frequency bandwidth. However, the controlof BCM is more complicated, due to its VSF. This also leads tothe difficulty to get the accurate mathematical model betweenoutput current iout and reference current iref , which has a greatinfluence on THD of iout .

In this paper, the relationship between ACM output currentiout and reference current iref of flyback inverter in BCM isinvestigated, and an accurate mathematical model is proposedthrough theoretical derivation. Then, a novel control strategy ofiref is proposed to decrease THD of iout . Moreover, the real-ization of MPPT based on this control strategy is also investi-gated. Finally, simulation and experiment results of an improvedflyback-inverter topology are presented, which verifies the pro-posed control strategy.

ACKNOWLEDGMENT

The authors would like to thank Altenergy Power System Inc.of China, for the support of PV ACM power stage during theproject. The authors would also like to thank PLEXIM Inc., forthe support of the powerful system-level simulation tool PLECS.

REFERENCES

[1] W. Bower, R. West, and A. Dickerson, Innovative PV micro-invertertopology eliminates electrolytic capacitors for longer lifetime, in Proc.Conf. Rec. 2006 IEEE 4th World Conf. Photovoltaic Energy Convers.,vol. 2, May 712, 2006, pp. 20382041.

[2] J. J. Bzura, The AC module: An overview and update on self-containedmodular PV systems, in Proc. 2010 IEEE Power Energy Soc. GeneralMeeting, Jul. 2529, 2010, pp. 13.

[3] R. H. Wills, S. Krauthamer, A. Bulawka, and J. P. Posbic, The AC photo-voltaic module concept, in Proc. Proc. 32nd Intersociety Energy Convers.Eng. Conf. (IECEC-97), 27 Jul.1 Aug., 1997, vol. 3, pp. 15621563.

[4] E. Roman, R. Alonso, P. Ibanez, S. Elorduizapatarietxe, and D. Goitia,Intelligent PV module for grid-connected PV systems, IEEE Trans. Ind.Electron., vol. 53, no. 4, pp. 10661073, Jun. 2006.

[5] B. Liu, S. Duan, and T. Cai, Photovoltaic DC-building-module-basedBIPV systemConcept and design considerations, IEEE Trans. PowerElectron., vol. 26, no. 5, pp. 14181429, May 2011.

[6] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, A review of single-phasegrid-connected inverters for photovoltaic modules, IEEE Trans. Ind.Appl., vol. 41, no. 5, pp. 12921306, Sep./Oct. 2005.

[7] W. Yu, C. Hutchens, J.-S. Lai, J. Zhang, G. Lisi, A. Djabbari, G. Smith,and T. Hegarty, High efficiency converter with charge pump and coupledinductor for wide input photovoltaic AC module applications, in Proc.Energy Convers. Congr. Expo., Sep. 2024, 2009, pp. 38953900.

[8] X. Yuan and Y. Zhang, Status and opportunities of photovoltaic invertersin grid-tied and micro-grid systems, in Proc. CES/IEEE 5th Int. PowerElectron. Motion Control Conf. (IPEMC 2006), Aug. 1416, 2006, vol. 1,pp. 14.

[9] S. V. Araujo, P. Zacharias, and R. Mallwitz, Highly efficient single-phasetransformerless inverters for grid-connected photovoltaic systems, IEEETrans. Ind. Electron., vol. 57, no. 9, pp. 31183128, Sep. 2010.

[10] B. Sahan, A. N. Vergara, N. Henze, A. Engler, and P. Zacharias, A single-stage PV module integrated converter based on a low-power current-sourceinverter, IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 26022609, Jul.2008.

[11] N. Papanikolaou, E. Tatakis, A. Ciritsis, and D. Klimis, Simplifiedhigh frequency converters in decentralized grid-connected PV systems:A novel low-cost solution, in Proc. 9th Eur. Conf. Power Electron. Appl.(EPE2003), Toulouse, France, Jun. 1519, 2003, paper on CD.


[12] A. C. Nanakos, E. C. Tatakis, and N. P. Papanikolaou, A weighted-efficiency-oriented design methodology of flyback inverter for AC photo-voltaic modules, IEEE Trans. Power Electron., vol. 27, no. 7, pp. 32213233, Jul. 2012.

[13] T. Shimizu, K. Wada, and N. Nakamura, A flyback-type single phaseutility interactive inverter with low-frequency ripple current reduction onthe DC input for an AC photovoltaic module system, in Proc. 2002IEEE 33rd Annu. Power Electron. Spec. Conf. (PESC02), 2002, vol. 3,pp. 14831488.

[14] S. B. Kjaer and F. Blaabjerg, Design optimization of a single phaseinverter for photovoltaic applications, in Proc. 2003 IEEE 34th Annu.Power Electron. Spec. Conf. (PESC03), Jun. 1519, 2003, vol. 3,pp. 11831190.

[15] Y. Li and R. Oruganti, A low cost flyback CCM inverter for AC moduleapplication, IEEE Trans. Power Electron., vol. 27, no. 3, pp. 12951303,Mar. 2012.

[16] Y. Li and R. Oruganti, A flyback-CCM inverter scheme for photovoltaicAC module application, in Proc. Power Eng. Conf. (AUPEC08), Dec.1417, 2008, pp. 16.

[17] A. Ch. Kyritsis, E. C. Tatakis, and N. P. Papanikolaou, Optimum designof the current-source flyback inverter for decentralized grid-connectedphotovoltaic systems, IEEE Trans. Energy Convers., vol. 23, no. 1,pp. 281293, Mar. 2008.

[18] Y.-H. Ji, D.-Y. Jung, J.-H. Kim, C.-Y. Won, and D.-S. Oh, Dual modeswitching strategy of flyback inverter for photovoltaic AC modules, inProc. 2010 Int. Power Electron. Conf. (IPEC), Jun. 2124, 2010, pp. 29242929.

[19] A. Kyritsis, N. Papanikolaou, E. Tatakis, and J. Kobougias, Designand control of a current source flyback inverter for decentralized grid-connected photovoltaic systems, in Proc. 2005 Eur. Conf. Power Elec-tron. Appl., Jun. 1519, 2005, pp. 110.

[20] Z. Zhang, M. Chen, M. Gao, Q. Mo, and Z. Qian, An optimal controlmethod for grid-connected photovoltaic micro-inverter to improve theefficiency at light-load condition, in Proc. 2011 IEEE Energy Convers.Congr. Expo. (ECCE), Sep. 1722, 2011, pp. 219224.

[21] Z. Zhang, C. Zhang, M. Chen, and Z. Qian, An improved on-time controlmethod to reduce the line-current distortion for BCM-DCM mixed micro-inverter at light load condition, in Proc. 2012 IEEE Int. Symp. Ind.Electron. (ISIE),, May 2830, 2012, pp. 17601764.

[22] T. Shimizu, K. Wada, and N. Nakamura, Flyback-type single-phase utilityinteractive inverter with power pulsation decoupling on the DC input for anAC photovoltaic module system, IEEE Trans. Power Electron., vol. 21,no. 5, pp. 12641272, Sep. 2006.

[23] G. H. Tan, J. Z. Wang, and Y. C. Ji, Soft-switching flyback inverter withenhanced power decoupling for photovoltaic applications, Electric PowerAppl., IET, vol. 1, no. 2, pp. 264274, Mar. 2007.

[24] H. Hu, S. Harb, X. Fang, D. Zhang, Q. Zhang, Z. J. Shen, and I. Batarseh,A three-port flyback for PV microinverter applications with power pulsa-tion decoupling capability, IEEE Trans. Power Electron., vol. 27, no. 9,pp. 39533964, Sep. 2012.

[25] T. Hirao, T. Shimizu, M. Ishikawa, and K. Yasui, A modified modulationcontrol of a single-phase inverter with enhanced power decoupling for aphotovoltaic AC module, in Proc. 2005 Eur. Conf. Power Electron. Appl.,Jun. 1519, 2005, pp. 110.

[26] N. Kasa, T. Iida, and A. K. S. Bhat, Zero-voltage transition flyback in-verter for small scale photovoltaic power system, in Proc. IEEE 36thPower Electron. Spec. Conf. (PESC05), Jun. 16, 2005, pp. 20982103.

[27] J.-Y. Gu, H.-F. Wu, G.-C. Chen, and Y. Xing, Research on photovoltaicgrid-connected inverter based on soft-switching interleaved flyback con-verter, in Proc. 2010 5th IEEE Conf. Ind. Electron. Appl. (ICIEA), Jun.1517, 2010, pp. 12091214.

[28] Q. Mo, M. Chen, Z. Zhang, M. Gao, and Z. Qian, Research on a non-complementary active clamp flyback converter with unfolding DCACinverter for decentralized grid-connected PV systems, in Proc. 2011 IEEEEnergy Convers. Congr. Expo. (ECCE), Sep. 1722, 2011, pp. 24812487.

[29] N. Kasa, T. Iida, and L. Chen, Flyback inverter controlled by sensorlesscurrent MPPT for photovoltaic power system, IEEE Trans. Ind. Electron.,vol. 52, no. 4, pp. 11451152, Aug. 2005.

[30] Y.-H. Kim, J.-G. Kim, Y.-H. Ji, C.-Y. Won, and T.-W. Lee, Flybackinverter using voltage sensorless MPPT for AC module systems, in Proc.2010 Int. Power Electron. Conf. (IPEC), Jun. 2124, 2010, pp. 948953.

[31] S. J. Chiang, K. T. Chang, and C. Y. Yen, Residential photovoltaic energystorage system, IEEE Trans. Ind. Electron., vol. 45, no. 3, pp. 385394,Jun. 1998.

[32] B. K. Bose, P. M. Szczesny, and R. L. Steigerwald, Microcomputer con-trol of a residential photovoltaic power conditioning system, IEEE Trans.Ind. Appl., vol. IA-21, no. 5, pp. 11821191, Sep. 1985.

[33] J.-S. Lai, Power conditioning systems for renewable energies, in Proc.Int. Conf. Electr. Machines Syst. (ICEMS), Oct. 811, 2007, pp. 209218.

[34] Z. Zhang, X.-F. He, and Y.-F. Liu, An optimal control method for photo-voltaic grid-tied interleaved flyback micro-inverters to achieve high effi-ciency in wide load range, IEEE Trans. Power Electron., vol. 28, no. 11,pp. 50745087, Nov. 2013.

[35] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics.Norwell, MA, USA: Kluwer, 1997.

[36] W. Xiao and W. G. Dunford, A modified adaptive hill climbing MPPTmethod for photovoltaic power systems, in Proc. 2004 IEEE 35thAnnu. Power Electron. Spec. Conf. (PESC04), Jun. 2025, 2004, vol. 3,pp. 19571963.

[37] K. H. Hussein, I. Muta, T. Hoshino, and M. Osakada, Maximum pho-tovoltaic power tracking: An algorithm for rapidly changing atmosphericconditions, IEE Proc. Generation, Transmiss. Distrib., vol. 142, no. 1,pp. 5964, Jan. 1995.

[38] F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, A variable step size INCMPPT method for PV systems, IEEE Trans. Ind. Electron., vol. 55, no. 7,pp. 26222628, Jul. 2008.

[39] Y.-C. Kuo, T.-J. Liang, and J.-F. Chen, Novel maximum-power-point-tracking controller for photovoltaic energy conversion system, IEEETrans. Ind. Electron., vol. 48, no. 3, pp. 594601, Jun. 2001.

[40] A. Durgadevi, S. Arulselvi, and S. P. Natarajan, Study and implementa-tion of maximum power point tracking (MPPT) algorithm for Photovoltaicsystems, in Proc. 2011 1st Int. Conf. Electr. Energy Syst. (ICEES), Jan.35, 2011, pp. 240245.

[41] Characteristics of the Utility Interface for Photovoltaic (PV) Systems, IEC61727 CDV, 2002.

[42] IEEE Standard for Interconnecting Distributed Resources with ElectricPower Systems, IEEE Std. 1547, 2003.

Mingzhi Gao received the bachelors degree in elec-tronic and information engineering, in 2007, fromZhejiang University, Hangzhou, China, where he iscurrently working toward the Ph.D. degree in powerelectronics and power driver.

His current research interests include digi-tal control in power electronics, renewable energysystems, wireless-parallel-inverter system, uninter-ruptible power systems, distributed power systems,and smart microgrid system.

Min Chen received the B.S. degree in applied elec-tronics and the Ph.D. degree in electrical engineeringfrom Zhejiang University, Hangzhou, China, in 2000and 2006, respectively.

From 2007 to 2009, he was a PostdoctoralResearcher in the Electrical Engineering College,Zhejiang University, where he is currently a Lecturer.Since 2007, he has been responsible for the LightingResearch and Development Laboratory, National En-gineering Research Center for Applied Power Elec-tronics, Zhejiang University. He has authored or coau-

thored more than 30 technical papers. He holds ten issued and pending patents.His current research interests include regenerative energy systems, distributedgeneration, microgrid, electric vehicle and modern lighting system for HIDlamps and LED.


Chi Zhang received the Bachelor degree in electronicinformation engineering in 2012 from Zhejiang Uni-versity, Hangzhou, China, where he is currently work-ing toward the Ph.D. degree in power electronics.

He is involved in the research on wireless paral-lel control technique based on triple 3-kW-parallel-inverters in cooperation of TDI. His current researchinterests include wireless parallel control, distributedgeneration, and microgrid.

Zhaoming Qian (SM92) received the Graduate de-gree in radio engineering from the College of Elec-trical Engineering, Zhejiang University, Hangzhou,China, in 1961, and the Ph.D. degree in ap-plied science from Catholic University of Leuven,Leuven, Belgium and the Interuniversity Microelec-tronics Center, Leuven, in 1989.

Since 1961, he has been involved in teaching andthe research on electronics and power electronics atZhejiang University. In 1992, he was a Professor inthe College of Electrical Engineering, Zhejiang Uni-

versity. He was the Deputy Director of National Engineering Research Centerfor Applied Power Electronics and the Deputy Director of Scientific Committee,National Key Laboratory of Power Electronics. His current research interestsinclude power electronics and its industrial applications, power electronic sys-tem integration, and electromagnetic compatibility (EMC) in power electronicsystems, etc. He has authored or coauthored more than 200 papers authoredor coauthored in international journals and conferences and one book on EMCdesign.

Dr. Qian has received the Excellent Education Awards from the China Educa-tion Commission and Zhejiang University in 1993, 1997, and 1999, respectively,and the Science and Technology Development Awards from the China Educa-tion Commission in 1999 and 2003, respectively.

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Analysis and Implementation of an Improved Flyback