2684 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Maximum Power Point Tracking in aOne-Cycle-Controlled Single-Stage

Photovoltaic InverterMario Fortunato, Alessandro Giustiniani, Giovanni Petrone, Giovanni Spagnuolo, Member, IEEE,

and Massimo Vitelli

Abstract—In this paper, the design of the one-cycle controllerof a single-stage inverter for photovoltaic applications is carriedout by means of a multiobjective strategy to optimize inverterperformance at both high and low insolation levels. Design con-straints that account for different weather conditions are adopted.The optimization algorithm also provides useful information con-cerning the system sensitivity with respect to each of the con-troller parameters. This allows the design of a maximum powerpoint tracking perturb and observe controller that significantlyimproves inverter performance. Experimental measurements con-firm the predictions of theoretical and simulation results.

Index Terms—Maximum power point tracking (MPPT) tech-niques, one-cycle control (OCC), photovoltaic (PV) inverter.

I. INTRODUCTION

PHOTOVOLTAIC (PV) single-stage inverters are becomingmore attractive with respect to double stage models due

to their compactness, low cost and reliability [1]–[7]. Trans-formerless topologies are especially deserving of attention[7]–[9], even with new techniques for avoiding dc currentinjected into the grid and safety protections without the use oftransformers [10]. A single-stage inverter, controlled by usingthe one-cycle control (OCC) technique, has been presented inthe literature [1]. The theoretical analysis of such an inverter, re-ported in [1], is not in-depth. Thus, it does not allow satisfactoryperformance both in terms of power extracted from the PV arrayand quality of the current injected into the grid. This aspect hasbeen included in evidence by the authors of this paper in [6],wherein a significant improvement of the theoretical model hasbeen proposed and used to increase the power extracted fromthe PV array and to reduce the distortion of the current injectedinto the grid. Simulation results have demonstrated that theset of variables influencing the operation of the controller canbe optimized to get nearly maximum power at one assignedinsolation level or the highest average power in a given inso-lation range. In [6] the effectiveness of the changes made to the

Manuscript received October 1, 2007; revised January 11, 2008. This workwas supported by grants from the Università di Salerno and MUR.

M. Fortunato, A. Giustiniani, G. Petrone, and G. Spagnuolo are with the Di-partimento di Ingegneria dell’Informazione ed Ingegneria Elettrica, Universitàdi Salerno, 84084 Salerno, Italy (e-mail: gspagnuolo@unisa.it).

M. Vitelli is with the Department of Information Engineering, SecondaUniversità di Napoli, 81100 Caserta, Italy (e-mail: vitelli@unina.it).

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

Digital Object Identifier 10.1109/TIE.2008.918463

model proposed in [1] has been also discussed, especially interms of design constraints expressing the quality and distortionof the inverter output current, to fulfill international standardsconcerning the power factor (PF) correction in PV applications.Moreover, it has also been highlighted that the inverter pro-posed in [1] is lacking a true maximum power point tracking(MPPT) controller. After values of the parameters of the analogcircuitry implementing the OCC are fixed, power extractedfrom the PV array is maximized at only one specific irradiationlevel. Therefore, under time varying atmospheric conditions,a consistent decrease in efficiency of PV power extraction isobserved. To overcome such a limitation, [6] proposed theidea of matching a digital MPPT controller with analog OCCcircuitry, and some preliminary simulation results have beenpresented.

Nonetheless, some aspects discussed in [6] deserve fur-ther investigation. Moreover, experimental measurements areneeded to confirm the quality of the results presented therein. Inparticular, the optimization process was carried out on a contin-uous search space, without accounting for the discretization ofthe design variables, as required by the use of commercial elec-tronic components. Moreover, in [6] two user-defined constantsα and γ were introduced in a design constraint related to thePF correction at the inverter output. Although such constantspossess a clear physical meaning, the selection of their optimalvalue is not straightforward, but depends on the designer’sexperience and skill. Since their correct setting also affects theperformance of the MPPT algorithm, an in-depth investigationabout their effects on the system behavior is needed.

This paper does not merely report an examination of theresearch activity discussed in [6], but presents an in-depthinvestigation of the aspects discussed above and the results ofsome experimental measurements on a prototype system.

In particular, the aim of this paper is not the introduction of anew MPPT algorithm, but rather the multiobjective optimiza-tion (MOP)-based design of a single stage inverter adoptingjointly the OCC control technique and the perturb and observe(P&O) MPPT approach. The goal of this paper is representedby the significant improvement of the inverter’s performancewith respect to those obtained by adopting the same single stageinverter designed on the basis of the trial-and-error procedure[1] or designed by using the approach described in [6], whichis strongly dependent on the designer’s skill in choosing αand γ. Moreover, a significant result is represented by the

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FORTUNATO et al.: MPPT IN A ONE-CYCLE-CONTROLLED SINGLE-STAGE PHOTOVOLTAIC INVERTER 2685

Fig. 1. Schematic of the whole system.

individualization of the most suitable variable to be perturbedto apply the P&O MPPT.

In Section II, the inverter model is reproposed to highlightsome limitations of the earlier one and to introduce the mul-tiobjective design approach discussed in detail in Section III.Section IV is devoted to the discussion of the simulation resultsand explanation of the need for a real MPPT strategy. Section Vreports the experimental measurements corresponding to simu-lation examples discussed in this paper.

II. INVERTER MODEL

Fig. 1 shows the schematic of the whole system under study,including the PV generator, the dc bus buffer capacitor, theH-bridge inverter, the utility grid and the OCC circuitry [1],[6]. In this paper, a low power/voltage version of the inverteris analyzed. The experimental measurements presented inSection V refer to a prototype realized in the laboratory byusing the parameters listed in Table I. The PV array is realizedby means of two Kyocera KC120 panels; to match the PVarray voltage level with the grid voltage, the inverter outputis connected to a step-up transformer, so that the sinusoidalvoltage at the output of the inverter has a 12 V rms value.

It is worth noting that current sensing was realized by meansof a Hall sensor LEM LA25-NP. Such a device introducesa fixed, small resistance Rs in the inverter output loop andprovides, at its output terminals, a voltage vs proportional tothe sensed current. The gain, in the sequel named Ki = vs/io,can be modulated by means of a trimmer. Resistance ROL inthe inverter output current loop includes input resistance of theLEM device, the equivalent series resistance of the inductor andthe ON resistances of the switching devices during conduction,and its value is reported in Table I.

OCC is a nonlinear control technique based on the integrationof a switched variable (voltage or current) to force its averagevalue to be equal to some control reference [1]. Hardware

TABLE ICIRCUIT PARAMETERS

implementation of the OCC, which works at a constant switch-ing frequency, does not require any digital signal processor oranalog multiplier. In Fig. 2 details of the circuitry implementingthe OCC function are shown.

Inequalities (1)–(5) have been introduced in [6] to guaranteeregular operation of the system

Ts−τ >0 (1)

Vc−KgVg−(2Vo,max−Vg)Kiτ

2L≥0 (2)

Vc−Kg(Vg+∆Vg)>0 (3)

Vg − ∆Vg−(

1+K

KiROL

)· Vo,max >0 (4)

Vm

Vg

∣∣∣∣∣min

−K

(1− Po(S)

α · Pg,MPP(Smax)

)· (1−γ) ≥ 0 (5.a)

K

(1− Po(S)

α · Pg,MPP(Smax)

)· (1+γ) − Vm

Vg

∣∣∣∣∣max

≥0 (5.b)

where τ = R1C1 is the time constant of the resetable integrator,Ts is the switching period, Vc is a control voltage, Vg is thePV field voltage, Vo,max is the maximum value of the outputvoltage, Po is the average power injected into the grid, Pg isthe power extracted from the PV field, K and Kg are suitablegains, Smax is the maximum considered value of the irradiancelevel, Pg,MPP(Smax) is the peak power of the PV field at Smax,α and γ are suitable design parameters and, finally

Vm = (Vc − KgVg)Ts/τ. (6)

The reader is addressed to [1] and [6] wherein a detaileddescription of the meaning of all the different parameters, gainsand variables involved in the inverter model can be found.

Inequalities (1) and (2) have been introduced in [1] andtheir solution ensures a stable operation of the OCC technique.Inequality (3) allows an explanation of the effect of 100 Hzoscillations appearing in the PV voltage and due to the connec-tion of the inverter output to the grid. An estimate of the peak-to-peak amplitude ∆Vg of the 100 Hz oscillations is given asfollows [6]:

∆Vg = Pi/(ωgridVgC) (7)

where ωgrid is the grid frequency in radians per second, C is thecapacitance of the dc bus buffer capacitor and Pi is the averagepower at the inverter’s input.

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2686 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Fig. 2. Circuitry implementing the OCC.

The average power values at the inverter’s output and inputare calculated as follows:

Po =(V 2

0 /Ki

)· (K − Vm/Vg) (8)

Pi =Po · [1 + (ROL/Ki)(K − Vm/Vg)] . (9)

The evaluation of the PV array operating voltage Vg requiresthe solution of the following nonlinear equation:

Pi(Vg) = Pg(Vg) (10)

where Pi is given in (9) and the PV power Pg is evaluated bymeans of the nonlinear model proposed in [11]. This modelprovides the current versus voltage characteristic of a PV fieldas a function of the voltage Vg, the panels’ temperature T,the solar irradiance S and the number of series-connected andparallel-connected panels that make up the PV field.

Solving inequality (3) ensures that the integrator input volt-age is always positive. If such a constraint was violated, theconsequent phase inversion at the output of the resetable inte-grator of Fig. 2 would produce a control fault.

Fulfillment of inequality (4) allows the behavior of theH-bridge as a double-buck converter, where input voltage ofthe power stage is always higher than the output voltage.

Condition (5) has been formulated by the authors in [6] todefine a set of design constraints to preserve the quality of PFcorrection at the inverter’s output. The minimum and maximumvalues of the ratio Vm/Vg are given as

(Vm/Vg)∣∣min

= [Vc/(Vg + ∆Vg) − Kg] · Ts/τ (11.a)

(Vm/Vg)∣∣max

= [Vc/(Vg − ∆Vg) − Kg] · Ts/τ. (11.b)

The value of the constant α is chosen by the designerto set the inverter’s overloading capacity with respect to themaximum power the PV field is able to provide, while thevalue of γ is chosen to bound the excursion of the ratio Vm/Vg

produced by ∆Vg .Since such values strongly affect PF correction performance

of the inverter, they must be tuned carefully. In [6], settingthe values of α and γ is left to the designer’s experience.Nevertheless, instead of assigning a priori the value of α andγ as in [6], it is possible to select the values of such variablesas part of the set of design variables, so that the output power ismaximized. This innovation is discussed in Section III, togetherwith the possibility of improving inverter performance at highand low irradiation levels by using a MOP approach.

III. MOP PROCEDURE

A. Formalization of a General MOP Procedure

The adopted optimization procedure is based on the use ofthe NSGA-II algorithm [12]. This is a nondominated sortingmultiobjective evolutionary algorithm that is able to find morespread solutions in the decision space and is characterized by abetter convergence to the true Pareto-optimal front compared tosimilar approaches [13], [14].

Conflicting objectives encountered during the inverter designprocedure are resolved using MOP. The generic deterministicMOP (e.g., maximization) problem formulation is given asfollows:

MAXx

µ1(x, p), µ2(x, p), . . . , µn(x, p) , n ≥ 2 (12)

subject to

gq(x, p) ≥ 0, q = 1, . . . , r (13)

hj(x, p) = 0, j = 1, . . . , v (14)

xil ≤ xi ≤ xiu, i = 1, . . . , nx (15)

where µi denotes the ith generic design objective; g is a vectorof inequality constraints; h is a vector of equality constraints;x is a vector of design variables; and p is a vector of designparameters. The design variables are bound by their lower (l)and upper (u) limits. An important class of solutions to theMOP are said to belong to the Pareto frontier. Each solutioncomprising the frontier is said to be Pareto optimal, whichmeans there are no other vectors of design variables for whichall objectives are better. More specifically: a design objectivevector µ∗ is Pareto optimal if any other design objective vectorµ in the feasible design space is such that µi ≤ µ∗i for alli ∈ 1, 2, . . . , n, and µj < µ∗j for at least one index of j,j ∈ 1, 2, . . . , n.

B. MOP Scheme for the Inverter

The optimization of the one cycle-controlled single stageinverter involves seven design variables, so that nx = 7

x = K,Kg, Vc,Ki, τ, α, γ. (16)

The search space has been defined in Table II.Upper and lower limits, as well as the number of discretiza-

tion levels, have been identified after a careful analysis andcarried out on the hardware implementation of the circuitry

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FORTUNATO et al.: MPPT IN A ONE-CYCLE-CONTROLLED SINGLE-STAGE PHOTOVOLTAIC INVERTER 2687

TABLE IIDISCRETIZATION OF THE SEARCH SPACE

TABLE IIIPARAMETERS USED FOR THE NSGA-II RUNS

Fig. 3. Pareto front. Right-side scale = values of the variable K.

Fig. 4. Pareto front. Right-side scale = values of the variable Kg .

shown in Fig. 2. The process runs on the basis of charac-teristics of the hardware devices and components used in theimplemented prototype to, for example, avoid op-amp and com-parator saturation, allow operation of the adopted componentswithin their corresponding voltage/current ratings and accountfor the allowed trimmer discretization.

Fig. 5. Pareto front. Right-side scale = values of the variable Vc (in volts).

Fig. 6. Pareto front. Right-side scale = values of the variable Ki (in ohms).

Fig. 7. Pareto front. Right-side scale = values of the variable τ (inmicroseconds).

With the considered discretization level, which can bechanged if different components and devices are adopted, thenumber of possible design solutions runs into billions.

To overcome another limitation of the approach presented in[6], which allows maximization of the inverter output poweronly at a specific irradiation level or at most its averagevalue in a given insolation range, a constrained multiobjec-tive approach has been chosen. In particular, in (12) n = 2

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2688 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Fig. 8. Pareto front. Right-side scale = values of the variable α.

Fig. 9. Pareto front. Right-side scale = values of the variable γ.

TABLE IVEXTREME BEST SOLUTIONS IN THE PARETO FRONT

has been fixed, so that the two concurrent functions are bothmaximized

µ1(x, p) =Po(Smax) Smax = 1 kW/m2 (17.a)µ2(x, p) =Po(Smin) Smin = 100 W/m2. (17.b)

Po(Smax) represents the inverter output power at the maximuminsolation level (Smax), while Po(Smin) represents the inverteroutput power at the minimum insolation level (Smin). Param-eters p and variables x are listed in Tables I and II, respectively.

Design constraints (1)–(5) are checked for any set of designvariables x: inequality (1) does not depend on the insolationlevel, while constraints (2)–(5) are checked for ten values ofthe irradiation level which are linearly spaced in the range[Smin, Smax]: this means that the check for feasibility of a

Fig. 10. PV array power versus voltage characteristics for ten insolations fromSmin = 100 W/m2 to Smax = 1 kW/m2. Thick line = inverter characteristiccorresponding to the set xM; thin line = inverter characteristic correspondingto the set xm.

Fig. 11. PV Power obtained by using the design set xM in Table IV. Upperplot = power at S = 1 kW/m2, lower plot = power at S = 100 W/m2.

Fig. 12. Grid voltage (black line) and inverter output current (gray line)obtained by using the design set xM. Upper plots: PF = 0.999, THD =0.78%, grid voltage scaled by 2 and S = 1 kW/m2, lower plots: PF = 0.998,THD = 5.6%, grid voltage scaled by 20 and S = 100 W/m2.

design set x needs the evaluation of r = 41 [see (13)] constraintfunctions. The number of equality constraints in (14) is v = 0.

It is worth noting that the model proposed in [11] andadopted in this paper either in the optimization algorithm, or insimulation results presented in Section IV, correctly accountsfor the effects of module temperature Tm. In particular, a fixed

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FORTUNATO et al.: MPPT IN A ONE-CYCLE-CONTROLLED SINGLE-STAGE PHOTOVOLTAIC INVERTER 2689

Fig. 13. Single-stage inverter with the MPPT control block.

ambient temperature Ta = 310 K was considered in this paper,but this does not mean that Tm is fixed. In fact, as shown in[11], Tm depends on both Ta and the irradiance level S, so thateven if Ta is fixed, Tm changes according to S. It is obviouslypossible to consider different values of Ta in the optimizationprocess together with different values of S without altering thegeneral validity of the results discussed in this paper. Resultsof the optimization procedure are presented and discussed inSection IV.

IV. SIMULATION RESULTS

A. Optimization Results

The NSGA-II based algorithm was run using the set ofparameters listed in Table III.

Parameters listed in Table III were chosen according to theguidelines given in [12]. In particular, the population size andthe distribution indices for the crossover and mutation functionswere chosen to get an almost uniformly distributed populationalong the Pareto front.

As shown in Figs. 3–9, the Pareto front clearly shows theconflict between the two objectives, namely the power at the in-verter output at the minimum (in abscissa) and at the maximum(vertical axis) insolation level [see (17)]. The designer is freeto choose the desired solution according to weather conditionsat the place of installation. It is worth noting that the solutionslying on the Pareto front represent the best tradeoff betweenthe two conflicting objectives. Consequently, if the productionat high (low) insolation is prioritized, the left-high (right-low)design set in the plot must be chosen.

In Table IV, solutions corresponding to extremes of thePareto front, namely the set xM that guarantees maximumpower at the highest insolation level and the set xm which

provides maximum power at the minimum insolation level, areshown. One of the other sets of the front must be chosen if atradeoff between the two objectives must be achieved.

The solution xm does not seem to be of practical interest,since the power produced at Smax by adopting xm is too lowwith respect to that obtained by adopting xM and even with re-spect to the theoretical value. Nevertheless, Po(Smin) obtainedby adopting set xm is about 50% greater than Po(Smin) ob-tained by adopting set xM. Such remarks become much clearerby looking at Fig. 10, which shows the ten power versus voltagecharacteristics of the PV array made of two Kyocera KC120panels, and the Pi(Vg) inverter characteristics corresponding tothe two design sets xm and xM listed in Table IV.

The PV array characteristics were obtained using data takenfrom the experimental measurements and the model [11]. It isworth noting that both inverter characteristics (especially thosecorresponding to the set xm) exhibit significantly small slopesfar from the peak powers for insolations higher than 500 W/m2.Such slopes are lower with respect to those resulting from thedesign examples shown in [6]; this is due to the introduction ofthe effect of the equivalent resistance ROL of the inverter outputloop, to the fact that the system under testing is different fromthat presented in [6] (in terms of the number of PV modulescomposing the source and the ratio between input and outputvoltages) and to the effect of design constraints in the range[Smin, Smax].

B. OCC Without P&O MPPT Control

Figs. 11 and 12 report simulation results obtained in a PSIMenvironment (PSIM is a software tool designed for powerelectronics, motor control, and dynamic system simulationby Powersim, Inc.) where an inverter designed by using set

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2690 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Fig. 14. Transient of the PV power by using the MPPT P&O control on Vc.Upper plot = power transient, lower plot stairwise waveform of Vc imposed bythe MPPT P&O controller.

Fig. 15. Constraints fulfillment. From the upper to the lower plot constraints(2)–(5.b).

xM was analyzed. For clarity, the inverter output current inFig. 12 is compared with a suitable scaled version of the gridvoltage. Simulation results validate the optimization procedure,especially in terms of the average power extracted by the PVarray. In terms of the quality of the current injected into the grid,the current waveform at S = Smax exhibits a high PF and alow harmonic distortion. As expected, because of its lower rmsvalue, the output current at S = Smin exhibits a more evidentfrequency content, but with a PF that remains high.

The Pareto front was proposed in Figs. 3–9 to highlightwhat values are assumed by the seven design variables (16)for each solution of the front. Such graphs allow us to analyzethe sensitivity of the different solutions with respect to theparameters. All the optimal solutions exhibit almost the samefew values of the current and voltage sensing gain Ki and Kand only a few values of gain Kg . On the other hand, plotsconcerning the time constant τ , the design variables α andγ but, especially, the voltage Vc, allow us to predict that thesystem performance might be changed, even according to atime varying irradiation level, by trimming the values of suchvariables. Such a result confirms the choice made in [6], wherethe concept of a runtime modulation of the value of Vc toimprove inverter performance has been introduced.

Fig. 16. Output current (black line-PF = 0.999, THD = 0.69%) and gridvoltage (gray line) scaled by two.

Fig. 17. Reference voltage and current fed into a resistive load.

It is worth noting that each solution of the Pareto frontcomplies with the design constraints (1)–(5) calculated in cor-respondence with all ten linearly spaced values of insolationlevels in the range [100, 1000] W/m2. Therefore, such designsolutions are obviously characterized by worse performanceswith respect to other design solutions complying with theconstraints calculated at, for example, the maximum insolationlevel only. Consequently, every solution of the Pareto front isa robust starting point for a real implementation of the system,whichever is the actual insolation level Sact. Nevertheless, thesolution set that maximizes Po(Sact) and, at the same time,allows us to fulfill constraints (1)–(5) at S = Sact is generallydifferent from any solution belonging to the Pareto front. Thus,to improve inverter performance in terms of PV power withoutworsening the quality of the current fed into the ac grid,it is possible to trim an operating variable of the controllerimplementing the OCC [6]. The high inverter performancesensitivity with respect to the voltage Vc, which is highlightedby the results of the improved MOP shown in Fig. 5, stronglysuggests that its reduction is helpful in improving runtimesystem performance. In addition to the considerations reportedabove, it is worth noting that reducing the voltage Vc is easierthan varying any other of the first five variables in (5).

C. OCC With P&O MPPT Control

The modified version of the inverter, with the MPPT con-troller that senses the current and voltage values at the PV fieldterminals and accordingly modulates the voltage Vc, is shown

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FORTUNATO et al.: MPPT IN A ONE-CYCLE-CONTROLLED SINGLE-STAGE PHOTOVOLTAIC INVERTER 2691

Fig. 18. From top to bottom: output current (PF = 0.996, THD = 8.13%), grid voltage (THD = 3.89%), PV current, PV voltage.

Fig. 19. Circuit waveforms for a reduced Vc. For the output current it is PF = 0.999, THD = 4.91%; for the grid voltage THD = 3.81%.

in Fig. 13. The MPPT is carried out by means of a classicalP&O approach [15], [16].

The inverter in Fig. 13 was simulated in a PSIM environmentby setting all the control parameters at the values given by theset xM; the value of the control voltage Vc was left free to evolveaccording to the P&O strategy. An insolation step from 0 to S =1000 W/m2 was imposed. Perturbations of Vc were imposedevery 0.1 s and their amplitude was equal to 0.2 V. In Fig. 14 itis shown that the PV power, before the first P&O perturbationoccurring at t = 0.1 s, was nearly equal to about 80 W, in goodagreement with data listed in the second column of Table IV,and evolved toward 140 W with a 75% increase. It is worthnoting that in Fig. 14 the startup transient waveform was alsoincluded to illustrate the dynamic behavior of the controller. Inall the other figures, only the steady-state waveforms have beenreported.

Such an increase stops after a stairwise variation of Vc from11.7 to 5.3 V at almost 3.5 s, as demonstrated in Fig. 14. Thisis due to the violation of constraints (2), (3) and (5.b), as shownin Fig. 15. The P&O algorithm checks if constraints violationsoccur and stop the perturbations of Vc to save the inverterfunctionality and preserve the quality of the output currentwaveform. The simulation result shown in Fig. 16 and referringto the system of Fig. 13 confirms that inverter performancecan be significantly improved by means of the MPPT P&Otechnique with respect to those guaranteed by an optimizedfixed design set x belonging to the Pareto front (see upper plotsof Fig. 12).

Fig. 20. PV array characteristics obtained by a manual trimming of Vc.

V. EXPERIMENTAL MEASUREMENTS

A prototype has been realized in the laboratory to confirm,by means of suitable experimental measurements, results ofthe optimization procedure and of the numerical simulations. A220-V/12-V transformer was used to scale down the sinusoidalvoltage at the inverter output. To highlight the quality of thecurrent waveform produced by the inverter, the system was firstanalyzed by using a signal produced by a waveform generatoras a sinusoidal reference and by connecting the inverter ter-minals to a resistive load of 3 Ω instead of the grid, i.e., thegrid was initially replaced by a resistive load. It is observed

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2692 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Fig. 21. From top to bottom: PV power, Vc.

in Fig. 17 that for a resistive load, the proposed configurationfeeds a nearly sinusoidal current.

A. OCC Without P&O MPPT Control

Graphs shown in Fig. 18 refer to the design set xM. The ir-radiance level is S = 1040 W/m2 and the ambient temperature22 C. Experimental results are in good agreement with simula-tion and, as can be deduced from results of the voltage–currentproducts given in the oscilloscope screenshot, the inverter effi-ciency is equal to 85.61 W/95.95 W, or about 89%.

In Fig. 19 the same waveforms are reported for a lower Vc

value, i.e., Vc = 7.3 V instead of Vc = 11.7 V. The resulting in-crease in power level confirms the simulation prediction that thedesign set xM ensures a good current waveform and fulfillmentof all design constraints in the range [Smin, Smax]. However, itis not able to ensure the maximum allowable PV power.

The effect of Vc on the PV power production is adequatelydescribed by the experimental plots of Fig. 20. They wereobtained by manually trimming Vc and plotting PV current andvoltage in a xy plane by means of the digital oscilloscope. ThePV array characteristic is described only in the region whereinthe maximum power point is placed, and even during insolationvariations (see the small graph in Fig. 20).

B. OCC With P&O MPPT Control

The P&O MPPT strategy was implemented on a NationalInstruments Compact RIO 9004 system. It has not been possibleto settle the starting value of Vc at 11.7 V, as required by xM

in Table IV, since the analog output control module NI 9263of the NI-CRio system has a maximum voltage equal to 10 V.Consequently, the starting value of Vc was equal to 10 V, whileall the other parameters values listed in Table IV were adopted.The design constraints were implemented in a program runningon the NI-CRio, so that all are checked any time a new Vc

perturbation is imposed.

In Fig. 21 the transient behavior of the PV power and ofvariable Vc is shown: this voltage is adjusted by the controllertoward the value Vc = 5.45 V. The PV power is consequentlyincreased by 34 W, i.e., more than 30% of its starting value. Aspredicted by the PSIM simulations, the value of Vc eventuallysettles at a constant rate by the controller due to the constraintsviolation.

VI. CONCLUSION

In this paper, the optimal design of a single-stage inverter forPV applications, controlled by means of the OCC technique,was presented. The advantages offered by the combined use ofa multiobjective design approach and a suitable MPPT P&Ocontrol were illustrated by means of numerical simulations andexperimental results.

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Mario Fortunato was born in Salerno, Italy, in1975. He received the Electronic Engineering degree(cum laude) from the Università di Salerno, Salerno,Italy, in 2005, where he is currently working towardthe Ph.D. degree in the Dipartimento di Ingegneriadell’Informazione ed Ingegneria Elettrica.

His main research interests are in power elec-tronics, modeling, and control techniques for energyconversion systems from renewable sources.

Alessandro Giustiniani was born in Torre del Greco(NA), Italy, in 1980. He received the ElectronicEngineering degree from the University of Naples“Federico II”, Naples, Italy, in 2005. He is currentlyworking toward the Ph.D. degree in the Dipartimentodi Ingegneria dell’Informazione ed Ingegneria Elet-trica, Università di Salerno, Salerno, Italy.

His main research interests are in modeling andembedded control techniques for energy conversionsystems from renewable sources.

Giovanni Petrone was born in Salerno, Italy, in1975. He received the “Laurea” degree in electronicengineering from the Università di Salerno, Salerno,in 2001, and the Ph.D. degree in electrical engi-neering from the University of Napoli “Federico II”,Naples, Italy, in 2004.

Since January 2005, he has been an AssistantProfessor of electrotechnics with the Università diSalerno. His main research interests are in the analy-sis and design of switching converters for telecom-munication applications, renewable energy sources

in distributed power systems, and tolerance analysis of electronic circuits.

Giovanni Spagnuolo (M’98) was born in Salerno,Italy, in 1967. He received the “Laurea” degreein electronic engineering from the Università diSalerno, Salerno, in 1993, and the Ph.D. degree inelectrical engineering from the University of Napoli“Federico II”, Naples, Italy, in 1997.

In 1993, he was with the Dipartimento di In-gegneria dell’Informazione ed Ingegneria Elettrica,Università di Salerno, where he was a PostdoctoralFellow (1998–1999), an Assistant Professor of elec-trotechnics (1999–2003) and, since January 2004, he

has been an Associate Professor. His main research interests are in the analysisand simulation of switching converters, in circuits and systems for renewableenergy sources, and in tolerance analysis and design of electronic circuits.

Dr. Spagnuolo is an Associate Editor of the IEEE TRANSACTIONS ON

INDUSTRIAL ELECTRONICS.

Massimo Vitelli was born in Caserta, Italy, in 1967.He received the “Laurea” degree (with honors) inelectrical engineering from the University of Naples“Federico II”, Naples, Italy, in 1992.

In 1994, he was with the Department of Informa-tion Engineering, Seconda Università di Napoli, asa Researcher. In 2001, he was appointed AssociateProfessor and in 2007 Full Professor in the Fac-ulty of Engineering, Seconda Università di Napoli,where he teaches courses on electrotechnics. Hismain research interests concern the electromagnetic

characterization of new insulating and semiconducting materials for electricalapplications, electromagnetic compatibility and the analysis and simulation ofpower electronic circuits.

Prof. Vitelli is an Associate Editor of IEEE TRANSACTIONS ON POWER

ELECTRONICS.

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