Design and Implementation of Three-Phase Two-Stage Grid-Connected Module Integrated Converter

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 3881

Design and Implementation of Three-PhaseTwo-Stage Grid-Connected Module

Integrated ConverterLin Chen, Member, IEEE, Ahmadreza Amirahmadi, Student Member, IEEE, Qian Zhang, Student Member, IEEE,

Nasser Kutkut, Senior Member, IEEE, and Issa Batarseh, Fellow, IEEE

Abstract—Module integrated converters (MICs) in single phasehave witnessed recent market success due to unique features suchas improved energy harvest, improved system efficiency, lower in-stallation costs, plug-and-play operation, and enhanced flexibilityand modularity. The MIC sector has grown from a niche market tomainstream, especially in the United States. Assuming further ex-pansion of the MIC market, this paper presents the microinverterconcept incorporated in large size photovoltaic (PV) installationssuch as megawatts (MW)-class solar farms where a three-phase acconnection is employed. A high-efficiency three-phase MIC withtwo-stage zero voltage switching (ZVS) operation for the grid-tiedPV system is proposed which will reduce cost per watt, improve re-liability, and increase scalability of MW-class solar farms throughthe development of new solar farm system architectures. The firststage consists of a high-efficiency full-bridge LLC resonant dc–dcconverter which interfaces to the PV panel and produces a dc-linkvoltage. A center points iteration algorithm developed specificallyfor LLC resonant topologies is used to track the maximum powerpoint of the PV panel. The second stage is comprised of a three-phase dc–ac inverter circuit which employs a simple soft-switchingscheme without adding auxiliary components. The modeling andcontrol strategy of this three-phase dc–ac inverter is described.Because the dc-link capacitor plays such an important role fordual-stage MIC, the capacitance calculation is given under type Dvoltage dip conditions. A 400-W prototype was built and tested. Theoverall peak efficiency of the prototype was measured and found tobe 96% with 98.2% in the first stage and 98.3% in the second stage.

Index Terms—Center points iteration (CPI), maximum powerpoint tracking (MPPT), module integrated converter (MIC), threephase, two stage.

I. INTRODUCTION

W ITH ever dwindling natural resources and increasingdemands for power, the need to seek out viable alter-

native sources of renewable energy is not just acute but urgent.Due to the fact that solar energy offers extraordinary merits in-cluding environmentally neutral, unlimited availability and low

Manuscript received June 29, 2013; revised September 9, 2013 and November12, 2013; accepted December 5, 2013. Date of current version March 26, 2014.This work was supported in part by DoE Award EE0003176, the NSF Award1156633, and the FESC project. Recommended for publication by AssociateEditor B. Ozpineci.

L. Chen, A. Amirahmadi, Q. Zhang, and I. Batarseh are with the Departmentof Electrical Engineering and Computer Science, Florida Power Electronic Cen-ter, University of Central Florida, Orlando, FL 32826 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

N. Kutkut is with the College of Business, University of Central Florida,Orlando, FL 32826 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/TPEL.2013.2294933

cost capable of competing with conventional sources with tech-nology advances and mass production in the coming few years.The photovoltaic (PV) industry has seen over 25% growth onan average over the last 10 years [1]. Other than the PV panelitself, the inverter is the most critical device in a PV system bothfor off-grid or grid-connection applications. Currently, the PVsystem architectures can be categorized into three basic classeswith respect to the types of grid-tied inverter: central inverter,string or multistring inverter, and module integrated converter(MIC) (also called microinverter) [2]–[4]. Although the centralinverter can operate at high efficiency with only one dc/ac powerconversion stage, this structure has some disadvantages: 1) eachPV module may not operate at its maximum power point whichresults in less energy harvested; 2) additional losses are intro-duced by string diodes and junction box; and 3) single point offailure and mismatch of each string or PV panel affects the PVarray efficiency greatly.

The string inverter is a modified version of the central inverter.It partially overcomes the issues arising in central inverters;however, it still suffers some of the disadvantages of the centralinverter. In an effort to maximize the power from each PV panel,a new approach was recently proposed which can be applied toeither central or string inverter architectures. A power maximizer(usually in the form of a dc/dc converter) is attached to each PVpanel to implement maximum power tracking. Although thearchitecture maximizes power from each PV panel at the costof additional dc/dc module, it still suffers from drawbacks suchas high-voltage hazard, single-point failure, and difficulty inmaintenance.

The MIC typically used in distributed PV systems is a smallgrid-tie inverter of 150–400 W that converts the output of a sin-gle PV panel to ac. The MIC ac outputs are connected in paralleland routed to a common ac coupling point. No series or paralleldc connections are made leaving all dc wiring at a relatively lowvoltage level of a single panel (typically < 60 Vdc). The MICcan be further integrated into PV modules to realize a true plug-and-play solar ac PV generation system. Thus, ac PV moduleswith integrated MIC have significant advantages over traditionalPV systems since they allow maximum peak power tracking oneach solar panel to maximize energy harvesting, and offer dis-tributed and redundant system architecture. In addition, MICand ac PV systems greatly simplify system design, eliminatesafety hazards, and reduce installation costs [3], [5], [6]. Withthese advantages, the ac module has become the trend for futurePV system development. Although MIC and ac PV modules

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3882 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

have witnessed recent market success, MIC still has many tech-nical challenges remaining such as high efficiency, high relia-bility at module level, low-cost and high-level control issues. Todate, research of the MIC has mainly focused on isolated topolo-gies for the following two reasons: 1) from reported literature,most topologies with a few exceptions cannot meet the dualgrounding requirement without transformer isolation accordingto the UL1741 standard; and 2) using transformer is the bestway to boost the low input voltage to high output voltage forac grid with high efficiency. Since line transformers are bulkyand costly, this architecture is not practical for MIC. This papermainly focuses on the architecture employing a high-frequencytransformer.

The MIC with its high-frequency transformer can be groupedinto three architectures based on the dc-link configurations: dc-link, pseudo-dc-link, and high-frequency ac [3]–[5]. Usually theMIC just pumps the power from PV to ac grid with unidirectionalpower flow. However, with the presence of the power decouplingcapacitor, MIC can support the ac grid not only as an ac powersource, but as a VAR and possibly a harmonics compensatoras well [5]. For the latter two cases, bidirectional power flowis needed between ac grid and the power decoupling capacitorrequiring MIC with bidirectional power flow capability.

For applications with power levels under several kilowatts,the single-phase connection is commonly used. However, thesingle-phase connection has the disadvantage that the powerflow to the grid is time varying, while the power of the PVpanel must be constant for maximizing energy harvest, whichresults in instantaneous input power mismatch with the outputinstantaneous ac power to the grid. Therefore, energy storageelements must be placed between the input and output to bal-ance (decouple the unbalance) the different instantaneous inputand output power. Usually, a capacitor is used to serve as apower decoupling element [2]. However, the lifetime of differ-ent types of capacitors varies greatly. For example, electrolyticcapacitors typically have a limited lifetime of 1000–12 000 h at105 ◦C operating temperature [7]. Although some researchershave developed various methods of reducing the required ca-pacitance in single-phase MICs in order to allow use of longerlifespan film capacitors [9], [40]–[44], these approaches havethe drawbacks of either complicating the inverter topology andcontrol or reducing the overall efficiency. Most presently avail-able commercial MICs still use electrolytic capacitors as powerdecoupling storage elements due to their large capacitance, lowcost, and volumetric efficiency. This tends to limit the lifespanof these MICs [7], [8].

The distributed PV system [10], whether used in large-scalesolar farms, tens of kilowatt installations, or even down to a sin-gle PV panel, will be a trend for future solar PV deployment dueto its remarkable merits: 1) easy modularization and scalabil-ity; 2) elimination of single-point failure; 3) simple installationand maintenance; and 4) high efficiency and low cost. Floridapower electronics center (FPEC) which is a research arm of theUniversity of Central Florida has first developed system archi-tecture for a PV solar farm based on three-phase MICs with filmcapacitor shown in Fig. 1. A three-phase MIC is attached orintegrated directly into each PV panel. The outputs of each MIC

Fig. 1. Three-phase microinverter-based architecture for solar farm.

are directly connected to low-voltage three-phase grid and thenthrough medium-voltage transformer boost the low three-phasevoltage to high voltage at power transmission line side. EachMIC operates independently regardless of the failure of otherMICs. This architecture will reduce the cost per watt, improvesystem reliability, and provide more cost effective and efficientpower distribution. FPEC also commissioned market researchthat confirmed the viability of this PV system architecture.

II. PROPOSED ARCHITECTURE OF TWO-STAGE THREE-PHASE

GRID-TIE INVERTER SYSTEM

In order to provide galvanic isolation, various isolated con-verters for high step up applications have been proposed. In gen-eral, the topologies with galvanic isolation suitable for this appli-cation can be categorized into two groups: single-switch topolo-gies and multiswitch topologies. Recently, the LLC resonanttopology has become attractive due to its desirable characteris-tics such as high efficiency and natural zero voltage switching(ZVS)/zero current switching (ZCS) commutation [11]–[16].Therefore, a full-bridge LLC resonant converter is employed inthe first stage to achieve high efficiency and track the maximumpower point of each PV panel.

For the three-phase dc/ac converter in the second stage,a variety of active soft-switching topologies have been pro-posed in last three decades [17]–[30]. Most of them can bedivided into three groups: auxiliary resonant commutated pole(ARCP) group [19]–[22], resonant dc-link inverter (RDCLI)group [23]–[28], and resonant ac-link converter (RACLC) [29],[30]. The ARCP can be applied broadly for the voltage-source-type single-phase or three-phase inverters but it requires a largenumber of auxiliary components. Compared to the ARCP, theRDCLI has the advantages of fewer auxiliary switches and asimpler circuit. Several soft-switching topologies in [27], [28],and [29] were proposed to achieve the minimum number of ex-tra components. However, the driving signals of the auxiliaryswitches are very sensitive to the noise from the main circuit.Since the RACLC can achieve voltage boosting and electricalisolation at the same time, it is highly preferred for renewableenergy power generation. Unfortunately, the control circuit forthe RACLC is complex and bidirectional switches are required.In fact, auxiliary components are unavoidable for all of the soft-switching topologies mentioned earlier.

CHEN et al.: DESIGN AND IMPLEMENTATION OF THREE-PHASE TWO-STAGE GRID-CONNECTED MODULE INTEGRATED CONVERTER 3883

Fig. 2. Two-stage three-phase four-wire grid-tie inverter system.

The proposed soft-switching technique shown in Fig. 2 sim-plifies the inverter topology and reduces the cost since it doesnot require any auxiliary components. The body capacitors ofthe main MOSFETs and the output inductor L1 are combined toform a resonant circuit. The inductor current is intentionallybidirectional within a switching cycle to generate ZVS con-ditions during commutation. Meanwhile the average inductorcurrent is controlled to produce a sinusoidal current in L1 . Theproposed soft-switching technique is suitable for MIC applica-tions where the switching losses are usually dominant. Basedon the above, Fig. 2 shows the proposed high-efficiency MICarchitecture with both-stage zero-voltage switching consistingof a full-bridge LLC resonant dc–dc step up converter and three-phase four-wire soft-switching dc–ac converter. The detail op-erating modes in the three-phase four-wire dc/ac converter willbe presented in the following sections.

III. OPERATION MODE OF THE PROPOSED ZVS THREE-PHASE

FOUR-WIRE DC/AC CONVERTER

Because many articles about LLC resonant converters havebeen published over the last decade [11]–[16], this paper doesnot discuss it in great detail. The operating modes of the pro-posed ZVS three-phase four-wire dc/ac converter are presentedin this section. As shown in Fig. 2, the three phases of the dc/acsecond stage are symmetrical around the neutral point; there-fore, the analysis can be performed on a single phase as shownin Fig. 3 and described below.

Interval 1 [t0 − t1]: Prior to t0 , S7 is off and S8 is still turnedON. Assume that the current direction through L1 , as shown inFig. 3, is already from right to left at t0 . Then S8 is turned OFF

and the voltage across the parasitic capacitor CS8 of low sideMOSFET S8 starts increasing due to the inductor current. As CS8charges the voltage across S7 decreases. This interval ends oncethe voltage across S7 reaches zero.

Interval 2 [t1 − t2]: The body diode of S7 will be conductingat t1 and S7 can be turned ON with ZVS. The current flow decayslinearly from right to left due to the fact that Ubus /2 minus thevoltage across L1 . This mode ends when the inductor currentdecays to zero.

Interval 3 [t2 − t3]: S7 is conducting and the current directionthrough L1 is now changed from left to right and increasinglinearly. This is the power delivery interval.

Interval 4 [t3 − t4]: At t3 , S7 is turned OFF and its parasiticcapacitor CS7 is charged by the inductor current while CS8 isdischarging. Once the voltage across CS8 drops to zero, the

parasitic body diode of MOSFET S8 conducts since the currentdirection through L1 does not change.

Interval 5 [t4 − t5]: Continuing from the previous interval 4,the body diode of S8 continues conducting which creates a ZVScondition when S8 is turned ON. The length of this interval istypically quite short and ends once S8 is turned ON.

Interval 6 [t5 − t6]: S8 is turned ON under ZVS condition att5 . The current through S8 is gradually decreasing due to the factthat Ubus /2 plus the output voltage appears across the inductorL1 . During this interval the energy stored in the inductor istransferred to the load and the current that was flowing in thebody diode of S8 now flows through the MOSFET on resistancethus reducing conduction losses.

Interval 7 [t6 − t0]: The current through S8 continues to flowand the current direction will change once the current decays tozero at t6 . Once the current through S8 changes direction fromtop to bottom as shown in Fig. 3, a ZVS condition is created forS7 . When the current through S8 reaches the negative thresholdcurrent, the cycle repeats.

IV. SYSTEM CONTROL DESCRIPTION

An overall control diagram for two-stage three-phase four-wire MIC PV system is shown in Fig. 4. The voltage (Upv)and current (Ipv) of PV panel are both sensed continuouslyto calculate the instantaneous power. The MPPT algorithm isbased on variation of the instantaneous power of PV panel thatchanges the switching frequency of the LLC resonant dc–dcconverter to track the maximum power output. In order to keeppower balanced between the generator (PV panel) and the gridfor two-stage MIC system, a bus voltage regulator is used to keepthe voltage constant. The bus voltage is regulated by controllingthe amount of current injected into the grid. For example, if theirradiance is increasing, the bus voltage increases because thedc–dc stage is running with MPPT. When Ubus is greater thanU ∗

bus , the output value of the dc-link regulator (I∗d) increases andthe inverter stage injects more current into the grid. Conversely,if the irradiance is decreasing, the inverter stage reduces theamount of current injected into the grid. Low total harmonicdistortion (THD) is achieved by sensing the injected grid currentvia d/q transformation and causing it to follow the referencecurrent I∗d . If the power factor is assumed to be unity, the reactivecurrent will be zero after d/q transformation (no phase shift). Asdescribed in Section III, the bidirectional current through thehigh-frequency inductor (L1) is also sensed as a part of theinternal current loop to achieve ZVS and improve the dynamicresponse of dc/ac stage. This will be discussed in more detail inSection V which follows.

V. MODELING AND CONTROL OF THREE-PHASE FOUR-WIRE

GRID-CONNECTED INVERTER

A. Average Model of Three-Phase Four-Wire InverterWith LCL Filter

The schematic of a three-phase four-wire voltage source in-verter (VSI) connected to the grid through an LCL filter isshown in Fig. 5. The series resistances of the inductors (L1 and


Fig. 3. Theoretic waveforms and operating intervals of a single-phase dc/ac converter. Interval 1: [t0 − t1 ], interval 2: [t1 − t2 ], interval 3: [t2 − t3 ], interval4: [t3 − t4 ], interval 5: [t4 − t5 ], interval 6: [t5 − t6 ], and interval 7: [t6 − t0 ].

Fig. 4. Overall control diagram of a two-stage three-phase grid-tie invertersystem.

Fig. 5. Three-phase four-wire grid-connected inverter.

L2) have been neglected in order to simplify the derivation ofaverage model. Fig. 6 shows an average model of three-phasefour-wire dc/ac converter which may be obtained by neglectingthe high-frequency components of both the dc voltage and theac phase currents. According to Kirchhoff’s current and voltagelaw, the differential equation to illustrate current and voltage as

Fig. 6. Average model in the synchronous three-phase frame.

shown in Fig. 5 can be expressed as follows:

I1 = −Rd

L1I1 +

Rd

L1I2 −

1L1

Ucf +Ubus

L1D − Ubus

2 · L1Γ

(1)

I2 =Rd

L2I1 −

Rd

L2I2 +

1L2

Ucf − 1L2

Ug (2)

Ucf =1

CfI1 −

1Cf

I2 (3)

UBus =ibus − idc

C12

=2C1

ibus −2C1

DT I1 (4)

where I1 = [i1a i1b i1c ]T I2 = [i2a i2b i2c ]

T

Ucf = [Uca Ucb Ucc ]T Ug = [Uga Ugb Ugc ]

T

D = [da db dc ] Γ = [1 1 1]T .

In the steady state, the grid phase currents i2a , i2b , and i2c arecontrolled to be sinusoidal and in phase with the correspondinggrid phase voltages Uga , Ugb , and Ugc which can be expressed


as follows:

⎡⎣

Uga

Ugb

Ugc

⎤⎦ =

⎡⎢⎢⎢⎢⎢⎣

Um cos (ωt)

Um cos

(ωt − 2π

3

)

Um cos

(ωt +

2π

3

)

⎤⎥⎥⎥⎥⎥⎦

(5)

where Um and ω are the amplitude of the phase voltage andthe angular frequency of the power source, respectively. Themodel in the stationary coordinates can be transformed into asynchronous reference frame by the transformation matrix T(Park’s transformation) as follows:

T =23

⎡⎢⎢⎢⎢⎢⎢⎣

cos(ωt) cos(

ωt − 2π

3

)cos

(ωt+

2π

3

)

− sin(ωt) − sin(

ωt − 2π

3

)− sin

(ωt+

2π

3

)

12

12

12

⎤⎥⎥⎥⎥⎥⎥⎦

.

(6)Fig. 6 shows the whole averaged model of the inverter af-

ter transformation into the synchronous three-phase referenceframe. The equations of the averaged model are expressed asfollows [31]:

I1dq = −WI1dq −Rd

L1I1dq +

Rd

L1I2dq −

1L1

Ucf dq

+UBus

L1Ddq (7)

I2dq =Rd

L2I1dq − WI2dq −

Rd

L2I2dq +

1L1

Ucf dq

− 1L2

Ugdq (8)

Ucf dq = ωUcf dq +1

Cf(i1dq − i2dq ) (9)

Ubus = − 2C1

DTdq I1dq +

2C1

ibus (10)

where W =[

0 −ωω 0

].

B. Hybrid Control Scheme for Three-Phase Four-WireDC/AC Converter

Peak current control is usually implemented using analog cir-cuits to turn on and off the inverter switches when the currentreaches the expected boundaries. It is well known that digi-tal control offers advantages over analog control such as pro-grammability, better noise immunity, and low susceptibility toage and environmental factors [32]. Another method to imple-ment the peak current control is to predict the required switchingtime using the calculation inside the controller. The required Tonand Toff of the switches can be predicted in order to change thecurrent between the desired boundaries. The problem with theprediction method is accumulated error caused by the change inthe inverter parameters. In order to eliminate the accumulated

Fig. 7. Hybrid boundary conduction mode (BCM) current control.

Fig. 8. Reset boundary of hybrid BCM current control.

error, two methods are applied from the control side: 1) combi-nation of hardware reset and predictive control which is referredto as hybrid control; and 2) sensing the grid current and causingit to follow the reference which determines how much currentis injected into the grid as shown in Fig. 4. Hybrid control doesnot require external components and can be completely imple-mented using the advanced features of digital signal processors(DSPs) designed for power electronics applications. By takingadvantage of the DSP’s internal comparator, the pulse widthmodulation (PWM) period can be reset whenever the inductorcurrent reaches the required boundary. Turn-on or Turn-off du-ration can be predicted using the calculation inside the DSP.Fig. 7 shows this hybrid control method.

As shown in Fig. 8, turn-on time is defined as the time requiredto keep the upper switch on and make the inductor currenttraverse from the lower limit to the upper limit. The lower limitand the upper limit are determined by (11) and (12) accordingto the polarity of grid voltage. Ton is calculated according to(13). Turn-off time is defined as the required time which lowerswitch should stay on to make the inductor current traverse fromthe upper limit to the lower limit. Toff is calculated according to(14). The switching frequency is derived using the Ton and Toffexpressions according to (15). Generally, efficiency is closelyrelated to switching frequency. Based on the parameters shownin Table II, the switching frequency versus output power during aline period is plotted in Fig. 9 at California Energy Commission(CEC) weighted power levels [33]. The switching frequencyrange at rated output power (400 W) is from 20 to 185 kHz.The switching frequency range is only 45–185 kHz even at 10%rated output power (40 W). Experimental results in Section VIIIverify the range of the switching frequency that is reasonable.

{iupper = 2

√2 ∗ Im ∗ sin (ωt) + B0 , if sin (ωt) > 0

ilower = −B0(11)

{iupper = B0 , if sin (ωt) < 0

ilower = 2√

2 ∗ Im ∗ sin (ωt) − B0(12)

where


Fig. 9. Switching frequency versus load range variation at a line period ofoutput current.

Fig. 10. DSP implementation of hybrid BCM current control.

Im : output root-mean square (RMS) current of three-phasedc/ac stage.

B0 is a comparator value at lower limit or upper limit asshown in Fig. 8, B0 equals to 1A

ton = Liupper − ilower12 UBus − Um

(13)

toff = Liupper − ilower12 UBus + Um

(14)

fs =(UB u s

2 )2 − U 2m

LUBus (iupper − ilower). (15)

The implementation of hybrid BCM current control is shownin Fig. 10. This control method requires accurate sensing ofthe inductor peak current. Since the inductor current includesboth the switching frequency and the line frequency, it is bulkyto measure it with a single current transformer. However, itcan easily be sensed with a high-frequency current transformerand a low-frequency current sensor chip. This current sens-ing approach reduces the size of current measurement compo-nent. These high- and low-frequency components are separatelysensed from the capacitor and the output line and then addedtogether to produce the inductor current. For each phase, onlyone comparator and a PWM generator are needed to producethe switching signals. Since all the controller parts are locatedinside the DSP chip, the propagation delay is very short for thiscontrol method.

Fig. 11. Normalized gain versus frequency with various loads for LLC.

VI. CENTER POINTS ITERATION (CPI) MPPT ALGORITHM FOR

LLC RESONANT STAGE

The topology of the LLC converter is illustrated in Fig. 2 asthe first stage of the whole system. The input voltage of theresonant tank is a square-wave E generated by switches S1–S4and UPV provided by the PV panel. Although state functions canbe provided to calculate an accurate voltage gain of Ubus /UPV , itis usually cumbersome due to the complex interaction betweenthe resonant components. Fourier analysis can be used to convertthe square-wave signal into a set of odd harmonic componentswith the expression is as follows:

E = UPV4π

∞∑k=1,3...

[sin(kωst)/k]. (16)

Thus, classical ac-circuit analysis can be applied for eachharmonic component in (17) as follows [14]:

Mk =UBus (k)

UP V

=2n

k

[(kfn )2 (m − 1)

m (kfn )2 − 1 + jQ (m − 1) ((kfn )2 − 1)kfn

]

(17)

where m= Lr +Lm

Lr; fr = 1

2π√

Lr Cr; fn = fs

fr; Q=

√Lr /Cr

Ra c

Rac = 2UB u sn2 π 2 IB u s

with the relative parameters listed in Table II.Ubus(k) refers to the kth order harmonic components of the busvoltage. fs refers to switching frequency of the full bridge. Racrefers to the equivalent load resistance at the primary side of thetransformer and n refers to the turns ratio of the transformer.Thus, the voltage gain M can be calculated as follows [14]:

M =UBus

UPV=

√√√√∞∑

k=1,3···M 2

k . (18)

Based on (18), the normalized gain (Mn = M /2n) versusfrequency (fn = fs /fr ) waveforms with varying loads for theLLC can be calculated and illustrated in Fig. 11 where Pn refersto normalized output power.

To ensure the ZVS of LLC converter, the operating fre-quency should be constrained in the inductive zone as shownin Fig. 11 [13], [15], [16]. Due to the complex interaction


Fig. 12. P–F curves of LLC MIC connected to a PV panel with varyingirradiance.

Fig. 13. P–F curves of LLC MIC connected to a PV panel with varyingirradiance and CPI MPPT algorithm.

between the LLC resonant components, the relationship be-tween UPV and fn is nonlinear and nonexplicit. Moreover, thenonlinearity in PV module characteristics exacerbates the com-plexity of power control with the frequency parameter. Thus,simulation instead of direct calculation of the LLC MIC wasused to demonstrate the power curves as shown in Fig. 12 (withsimulation fr = 140 kHz). The initial frequency of the LLCMIC is generally—three to four times resonant frequency fr

due to the soft start function. Fig. 12 illustrates P–F curves withvarying PV Panel irradiance and an initial frequency of 280 kHz.As shown in Fig. 12, the power difference near the initial fre-quency is almost constant. Therefore, the conventional P&O orINC MPPT algorithm is difficult to apply for an LLC resonantconverter [14], [34]–[36]. In order to solve this problem, a cen-ter point iteration algorithm is proposed. The control parameteris the switching frequency. As shown in Fig. 13, the whole fre-quency region is first divided into four parts: part 1: F(1)–F(4),part 2: F(4)–F(3), part 3: F(3)–F(5), and part 4: F(5)–F(2). Con-sidering the inductive zone of LLC converter as illustrated inFig. 11, the initial boundary frequencies are set as: F(1) = 0.5Fr ,F(2) = 2Fr , where fr refers to the LLC resonant frequency andcan be calculated by fr = 1

2π√

Lr Cr.

As illustrated by Fig. 14(a), if the maximum power is P3,the search range can be reduced by reassignment: F(1) = F(4),F(2) = F(5), and F(3) = F(3). If the maximum power is P5,the search range can be reduced by reassignment: F(1) = F(3),F(2) = F(2), and F(3) = F(5). If the maximum power is P4,the search range can be reduced by reassignment: F(1) = F(1),F(2) = F(3), and F(3) = F(4). The next iteration dividing cen-ter points are calculated by: F(4) = [F(3)+F(1)]/2 and F(5) =[F(2)+F(3)]/2. The interval is divided into four parts again for

Fig. 14. Application of the proposed MPPT on the LLC MIC. (a) ProposedMPPT iterations. (b) Detail flowchart of the proposed MPPT.

the next power comparisons. The flowchart of the MPPT tech-nique is illustrated as Fig. 14(b). Iterations are continued untilthe boundary frequencies are close enough to reach the MPPcriterion

Pmax(P3,P4,P5) − Pmin(P3,P4,P5) < ε (19)

where P3, P4, and P5 are the calculated instantaneous powerat Fn (3), Fn (4), and Fn (5), respectively. The threshold ε deter-mines whether the MPP has been reached or not. The value isbased on the current and voltage sensing accuracy. In this paper,it is selected to be 0.5% Pn .

VII. CAPACITANCE CALCULATION OF DC-LINK CAPACITOR

AND INPUT CAPACITOR

The dc/dc stage and dc/ac stage are decoupled due to theaction of the dc-link capacitor, simplifying the controller designfor both stages. Because of the three-phase dc/ac converter in thesecond stage, the value of the dc-link capacitor can be smaller fora given MIC power rating. Thus, the reliability of whole systemwill be significantly improved if the electrolytic capacitors arereplaced by film capacitors. Although the capacitance value


TABLE ITHREE-PHASE UNBALANCED DIPS DUE TO DIFFERENT FAULT TYPES AND

TRANSFORMER CONNECTIONS

of dc-link based on the qualitative analysis is not large in athree-phase balanced system, the grid quality must be taken intoaccount in a grid tied MIC. The dc-link and input capacitancerequirement is determined by many factors such as capacitorvoltage variation, grid voltage dips and surges, and disturbanceresponse time. Generally, these factors can be classified intosteady conditions and dynamic conditions of MIC accordingto the specification. Calculation of the input capacitance in thedc/dc stage is also discussed under severe conditions in thissection.

A. DC-Link Capacitance Calculation

Referring to the small-signal model of the dc-link capacitorshown in [37], the dc-link capacitance is determined by grid dis-turbance and generator disturbance. Because the MPPT iterationtime is relatively slow, the dc-link capacitance is only calculatedbased on grid disturbance of an unbalanced three-phase systemin this paper. Asymmetrical faults lead to drops in one, two,or three phases with not all phases having the same drop. Theresulting voltage drops and phase-angle shifts depend on a num-ber of factors. The different types of voltage sags present in ageneric distribution system are summarized in Table I [38].

The voltage variations on the dc-link capacitor with typeD dips for a three-phase unbalanced system is investigated asfollows: the equation of output voltage and current for eachphase can be expressed as follows:

⎧⎪⎨⎪⎩

Uga (t) =(√

2Um + ΔU)

sin (ωt)

Ugb (t) =√

2Um sin (ωt)

Ugc (t) =√

2Um sin (ωt)

(20)

⎧⎪⎨⎪⎩

I2a (t) =√

2Im sin (ωt)

I2b (t) =√

2Im sin (ωt)

I2c (t) =√

2Im sin (ωt)

(21)

where Um is the RMS ac output voltage, Im is the RMS acoutput current, and ΔU is the voltage dip. From the outputpower of the grid side, we can get the instantaneous power ofthree-phase system

Pac (t) = Uga (t) I2a (t) + Ugb (t) I2b (t) + Ugc (t) I2c (t) .(22)

Substitute (20), (21) into (22), then simplify it

Pac (t) = 3Um Im +√

22

Im ΔU −√

22

Im ΔUcos 2ωt. (23)

Fig. 15. Simplified block diagram of two-stage MIC.

Assuming no power loss in the dc–dc stage, we get the in-stantaneous generated power of PV panel that can be expressedby Ppv = UP V IP V .

Then based on Fig. 15 we get

Ppv = Pdc + Pac . (24)

Combining (23) and (24), the energy stored in dc-link capac-itor can be calculated under type D dip condition

Edc =∫ 1

2 f

0

∣∣∣∣∣Ppv − 3Um Im −√

22

Im ΔU +√

22

Im ΔUcos2ωt

∣∣∣∣∣ dt.

(25)

Alternately, the energy stored in dc-link capacitor can also beexpressed as follows:

Edc =C

(U 2

Bus,max − U 2Bus,min

)

2= CUBusΔUBus . (26)

Substitute (25) into (26), and we find Ppv = 3Um Im for three-phase balanced system, the dc-link capacitance is representedby (27) after simplification

C =

√2

2 Im ΔU

2UBusΔUBusf. (27)

For a maximum output power of 400 W, the power rating ofeach phase is 133 W. The dc-link voltage (UBus) is selectedas 400 V with voltage ripple (ΔUBus = 20 V) and voltagedip (ΔU = 40 V). The capacitance is 35.3 μF based on thecalculation in (27) with a line frequency f = 60 Hz and Im =1.2 A.

B. Input Capacitance Calculation for LLC Resonant Stage

As mentioned previously, the LLC stage is decoupled fromthe inverter stage by the dc-link capacitor; therefore, grid distur-bances have little impact on the calculation of input capacitance.The input capacitance is a function of the steady state and dy-namic characteristics of the PV panel and the LLC resonantconverter. Since the execution of MPPT algorithm is slow, PVpanel irradiance change is not a critical factor when calculatinginput capacitance. For the LLC resonant converter operating atmaximum input current and maximum ripple on the input capac-itor, the basic equation

∫ i

C in=

∫C in

dUC indt is used to calculate

the capacitance. The parameters for the LLC dc/dc stage are asshown in Table II (Lr = 1.9 μH, Lm = 10.3 μH, Cr = 680 nF,and turns ratio of the transformer N = 4.5) and are given accord-ing to Xiang’s numerical model for the LLC resonant converteras referenced in [13]. For demonstration purposes, the current


TABLE IIKEY PARAMETERS OF THE EXPERIMENTAL PROTOTYPE

Fig. 16. Input capacitor current with various switching frequency at 400 Woutput and different input voltage. (a) fs =fr . (b) fs > fr . (c) fs < fr .

ripple of the input capacitor is plotted by Matlab Simulink atthe maximum output power (400 W) as shown in Fig. 16 withthree different input voltage conditions, fs < fr , fs = fr , andfs>fr . Under the severe condition of the maximum power out-put at 35 V (fs <fr ), input capacitor current is higher than twoother conditions as illustrated in Fig. 16(c), where tx ≤ 2.3 μsand the LLC resonant cycling period is 7.14 μs due to the val-ues of Lr and Cr . Thus, input capacitance could be calculatedwith (28). Assuming the voltage ripple on the input capacitor(ΔUC in ) is less than 0.25 V, and Icin,peak equals to 9.2 A asshown in Fig. 16(c), the input capacitance is 83.16 μF when

Fig. 17. Photograph of the 400-W three-phase two-stage grid-tied MICprototype.

Fig. 18. Experimental current waveform of resonant tank in the dc–dc stage.(a) Switching frequency is less than resonant frequency (fs < fr ). (b) Switch-ing frequency equal to resonant frequency (fs =fr ).

those values are substituted into (28). The input capacitance isselected to be 85.8 μF in this prototype using 26 PCS 3.3 μFceramic capacitors in parallel

Cin =

∫ i

C in

ΔUC in=

∫ tx

0 IC in,peak(sin t√Lr Cr

)dt

ΔUC in

=IC in,peak

√LrCr

ΔUC in. (28)

VIII. EXPERIMENTAL RESULTS

A three-phase four-wire MIC prototype with both-stage ZVSwas built as shown in Fig. 17 with the following specifications:maximum output power 400 W and output voltage 120 VACkey parameters are shown in Table II. The renewable source isan ASP-400M PV panel from advanced solar photonics. Theinput voltage range for maximum power tracking is from 35to 55 V. Because the open-circuit voltage of the ASP-400M isless than 60 V, Fairchild MOSFETs with low Rds(on) are usedin the full-bridge LLC resonant dc–dc converter. The secondstage is a three-phase four-wire VSI that connects the dc-bus tothe grid through an inductance of 600 μH. The dc-bus voltagereference is 400 V and the grid voltage peak value is 120

√2V .

The control algorithms for the whole system are implemented bytwo DSPs DSPIC33FJ16GS504 and STM32F103C8 employedin dc–ac stage and dc–dc stage, respectively. The two controllerscommunicate via a standard SPI port.

Fig. 18 shows the measured current waveforms of the reso-nant tank with fs=fr and fs < fr in dc–dc stage. The inductorcurrent waveform and injected grid current in the three-phasedc–ac converter are shown in Fig. 19. Although the inductorcurrent has a high ripple, the THD of the injected grid currentis less than 2.5% and meets the IEEE 1547 standards [39].


Fig. 19. Current waveforms in the dc–ac stage. (a) Each phase inductor cur-rent. (b) Three-phase injected grid current.

Fig. 20. Measured ZVS performance. (a) Measured ZVS waveform of onephase. (b) Measured switching on/off loss at the peak of injected grid current.

The PWM hardware reset is set for Bo = 1.0 A which isthe reverse current through inductor to achieve ZVS. Fig. 20(a)shows the main switch S8 driver signal, the current of the in-ductor L1 and the voltage across the switch S8 . It can be clearlyseen in this figure that the drain source voltage across the corre-sponding mosfet has already reached to zero before the arrivalof the turn-on gate signal. Therefore, the proposed controllercan realize ZVS during turn-on transitions. Fig. 20(b) illustratesthe switching loss for switch S8 close to the peak of the inductorcurrent. Switching loss is measured using the product of mosfetdrain current and drain to source voltage. The figure confirmsthat the turn-on loss is zero.

Fig. 21 shows the CPI MPPT algorithm’s performance inthe LLC resonant dc–dc stage. Fig. 22 shows the experimentalwaveform of overall system when connected to the grid. Thedc-link regulator is employed to keep the bus voltage constantwhile the CPI MPPT algorithm is active. As shown in Fig. 22,the injected current (green channel) to the grid is graduallyincreasing with the MPPT is tracking the maximum power ofthe PV panel.

Fig. 21. CPI MPPT algorithm in the dc–dc stage.

Fig. 22. Experimental waveform of overall system with grid connected.

Fig. 23. Efficiency measurement for each stage without auxiliary power, sep-arately. (a) Efficiency curve in dc/dc stage. (b) Efficiency measurement in dc/acstage.

Efficiency is measured at each stage with different inputpower levels, as shown in Fig. 23. From Fig. 23, it can beseen that the peak efficiency is 98.2% at dc–dc stage and 98.3%at dc–ac stage.

IX. CONCLUSION

A high-efficiency three-phase grid-connected MIC with two-stage ZVS is proposed in this paper and verified by experimentalresults based on a 400-W prototype. The measured peak effi-ciency is 98.2%, in the dc/dc stage and 98.3% in the dc/ac stage.The ZVS operating mode of the three-phase four-wire dc/acconverter is illustrated. Average modeling and hybrid controlin the dc–ac stage are also discussed. Additionally, a dedicatedMPPT algorithm for the LLC resonant topology is analyzedand verified by experimental results. Since the dc-link capacitorplays a key role in the dual-stage system, the capacitor’s valueis calculated under type D voltage dip conditions. It was shown


that based on the dc-link capacitance calculation, film capaci-tors can be used for three-phase MIC systems which will extendtheir life time and improve overall reliability.

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Lin Chen (S’10–M’13) received the B.S. degree inelectrical engineering from Tongji University, Shang-hai, China, in 1999. He is currently working towardthe Ph.D. degree in electrical engineering at the Uni-versity of Central Florida, Orlando, FL, USA.

Between 2001 and 2009, he was with the DeltaPower Electronics Center, and STMicroelectronics-Greater China Region, both in Shanghai, China. Hisresearch interests include the modeling and designof power converters, renewable energy, and soft-switching techniques.

Ahmadreza Amirahmadi (S’09) received the B.S.and M.S. degrees in electrical engineering fromShahrood University of Technology, Shahrood, Iran,in 2007 and 2010, respectively. Since 2010, he hasbeen working toward the Ph.D. degree at the Univer-sity of Central Florida (UCF), Orlando, FL, USA.

Since 2010, he has been a Research Assistantwith FPEC, UCF, where he is focusing on the effi-ciency optimization of dc/ac inverters. He has been aMarketing Engineering Intern from June 2013 at theInternational Rectifier. His research interests include

high-frequency dc–dc converters, soft-switching control of power electronic in-verters, and efficiency optimization.

Qian Zhang (S’08) received the B.S. degree fromHuazhong University of Science and Technology,Hubei, China, in 2006, and the M.S. degree in elec-trical engineering from Wuhan University, Hubei,China, in 2008. She is currently working toward thePh.D. degree at the University of Central Florida, Or-lando, FL, USA.

Her research interests include digital controlin power electronics, single-phase and three-phasepower factor correction, and single-phase and three-phase dc/ac inverter.

Nasser Kutkut (S’90–M’95–SM’02) received theB.Sc. degree in electrical engineering from the JordanUniversity of Science and Technology, Irbid, Jordan,in 1989, the M.Sc. degree in electrical engineeringand computer science from the University of Illi-nois, Chicago, IL, USA, in 1990, the Ph.D. degreein electrical and the M.B.A. degree in managementand entrepreneurship, both from the University ofWisconsin–Madison, Madison, WI, USA, in 1995and 2001, respectively, and the Doctorate in Busi-ness Administration degree in entrepreneurship and

marketing from Grenoble Ecole de Management, Grenoble, France, in 2013.Between 1995 and 1998, he was a Senior Scientist with Soft Switching

Technologies Corporation, Middleton, WI, USA, where he was involved in thedesign and development of power electronic apparatus and systems. Between1998 and 2008, he was Founder and CEO of Power Designers, LLC, Madison,WI, USA, where he successfully developed and commercialized a line of ad-vanced high frequency and high efficiency fast and opportunity chargers andbattery monitors for the industrial motive power battery market. Between 2008and 2010, he was the Director of the Florida Energy Systems Consortium, Uni-versity of Central Florida (UCF), Orlando, FL, USA. Since 2010, he has beenwith the College of Business, UCF where he is currently a Lecturer at the De-partment of Management. He has more than 17 years of technology leadershipand management experience developing and commercializing innovative bat-tery management technologies for motive and stationary power battery markets.He has a wide array of business expertise in the areas business start-ups, salesand marketing strategy development, technology and product development, aswell as extensive technical expertise in the areas of renewable energy powersystems, battery charging and monitoring technologies for motive power appli-cations, energy storage systems, and smart grid technologies. He is a holder of13 issued U.S. and international patents and has published more than 60 papersin leading technical and trade journals.

Issa Batarseh (S’86–M’89–SM’92–F’06) receivedthe B.S. degree in electrical and computer engineer-ing, and the M.S. and Ph.D. degrees in electrical en-gineering, in 1983, 1985, and 1990, respectively, allfrom the University of Illinois at Chicago, IL, USA.

He is currently a Professor of electrical engineer-ing with the Department of Electrical Engineeringand Computer Science, University of Central Florida(UCF), Orlando, FL, USA. From 1989 to 1990, hewas a Visiting Assistant Professor with Purdue Uni-versity, Calumet, IN, USA, before joining UCF in

1991. He is the Author or Coauthor of more than 70 refereed journals and 320conference papers and the holder of 20 U.S. patents. He is also an Author ofa textbook entitled “Power Electronic Circuits” (New York: Wiley, 2003). Hisresearch interests include power electronics, developing high-frequency solarenergy conversion systems to improve power density, efficiency, and perfor-mance, the analysis and design of high-frequency solar and wind energy con-version topologies, and power factor correction techniques. He is a RegisteredProfessional Engineer in the State of Florida. He has served as a Chairman forthe IEEE Power Electronics Specialist Conference in 2007 and was the Chairof the IEEE Power Engineering Chapter and the IEEE Orlando Section.

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Design and Implementation of Three-Phase Two-Stage Grid-Connected Module Integrated Converter