4116 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 12, DECEMBER 2010genetic algorithms and neural networks, in the control of dcand ac drives and in the tuning of state observers, the latterintroduced in the control loop for enhancing its behavior. Itsuse in power converter control and modulation was mainly inthe ﬁeld of dc/dc converters –. Few papers proposedthe use of FL in the control of ac converters chieﬂy forproportional–integral (PI) or sliding-mode current controllerenhancement through gains adaptation –. Only a fewpapers, such as –, proposed true FL controllers (FLCs).This situation probably depends on the high computationalspeed required by conditional and branch statements, typicalof FLC. This drawback can now be overcome using ﬁeld-programmable gate arrays (FPGA) in replacement of micro-processors.In the authors’ knowledge, until now, only a group of re-searchers previously addressed the use of FL in the ﬁeld ofmultilevel converters, proposing a controller combining optimalPWM switching-angle generator and PI controller , ;nobody proposed a pure FLC.This paper proposes a full FL-based CHB-MLI for stand-alone and grid-connected PV applications. The main noveltiesof the proposed system are the use of a fully FLC (without anyintermediate optimal PWM switching-angle generator and PIcontroller), its practical implementation using a mixed-mode(analog and digital) FPGA, and the use of a power-sharingalgorithm for H-bridge efﬁciency optimization. The proposedcontroller embeds both the modulator and the controller, thusrealizing a new one-step controller.In the following, Section II brieﬂy recalls the main char-acteristics of MLIs; Section III illustrates the proposedFLC/modulator; Section IV contains a simulation analysis,Section V describes the experimental system, reporting someexperimental results and their analysis; Section VI deals withsystem analysis and developments; and, ﬁnally, Section VIIreports some general conclusions.II. MLI FOR PV APPLICATIONSFig. 1 shows the considered system, consisting of k dcgenerators and k cascaded H-bridges arranged in a single-phaseMLI topology.Each dc generator consists of PV cell arrays connected inseries and/or in parallel, thus obtaining the desired outputvoltage and current. H-bridges basically consist of four metal–oxide–semiconductor ﬁeld-effect transistors (MOSFETs) em-bedding an antiparallel diode and a driver circuit.Three-phase systems can be realized by delta or wye connec-tion of three single-phase systems.The number k of H-bridges depends on the number n =2k + 1 of desired levels, which has to be chosen by taking intoaccount both the available PV ﬁelds and design considerations:the higher the number of levels, the better the sinusoidal voltageand the current waveforms. However, the number of levelsincreases the complexity and the cost of the system whilereducing its switching frequency in comparison with two-levelconverters. From the energy point of view, it can be noticed that,even if the amount of switching losses increases proportionallyto the number of devices in series, the transistor [MOSFET orFig. 1. Cascaded n-levels H-bridge inverter.insulated-gate bipolar transistor (IGBT)] conduction resistancedecreases when using devices with lower maximum applicablevoltage. Hence, the total losses can be lower using a multilevelconverter rather than using a two-level converter.Since low-voltage transistors (typically MOSFETs) presentsigniﬁcantly higher switching frequency than high-power tran-sistors (typically IGBT), MLIs can operate at signiﬁcantlyhigher switching frequencies than two-level converters. Thisallows the use of smaller low-pass ﬁlters.Neglecting power component voltage drops, the instan-taneous total output voltage of the n-level cascade in-verter is VAN = ni=1 Vouti, being Voutithe i-stage outputvoltage.Each H-bridge can be driven by a square waveform witha suitable duty cycle or a PWM pattern, thus resulting in astaircase without or with embedded PWM . In the consideredsingle-phase 230-V system, the cells are arranged into fourdistinct arrays, thus resulting in a nine-level converter, whichcan be considered a reasonable tradeoff among complexity,performance, and cost.
CECATI et al.: MULTILEVEL INVERTER FOR PHOTOVOLTAIC SYSTEMS WITH FUZZY LOGIC CONTROL 4117Fig. 2. Block diagram of the developed system.III. INTEGRATED FLC/MODULATORA. OverviewPower quality requirements can be addressed using eithera “PQ” or “PV” control approach . In the ﬁrst case, theinverter is controlled such as to supply the assigned active andreactive powers; in the second case, the inverter supplies theload with ﬁxed voltage and frequency. Both control strategiesare suitable for grid-connected inverters (although the former ispreferred); only voltage/frequency control schemes can be usedwith stand-alone applications. The proposed control systemimplements both strategies.Most MLI includes separate controller and modulator; more-over, they often present relevant computational burdens dueto the large number of operations, such as coordinate trans-formations, trigonometric functions, parameter identiﬁcation,ﬁltering, and so forth (see, e.g., – and the other ref-erenced multilevel papers). Often, they do not guarantee thedesired performance, particularly when occurring large param-eter variations and nonlinearities. An FLC, instead, does notrequire neither detailed knowledge of the process under controlnor its precise description in terms of mathematical model andoften, if well designed, outperforms more complex controllersbecause it adapts its outputs to the actual state of the systemeven without the use of observers.B. Controller/Modulator Design and AnalysisA schematic diagram of the proposed system is shown inFig. 2. It consists of four PV arrays (represented by variablevoltage sources vdc), the nine-level inverter, a low-pass ﬁlter,the load, and the grid. As already pointed out in the previoussection, the system incorporates two distinct and alternativeFLCs for grid-connected or stand-alone operations, respec-tively. In the ﬁrst case, a PQ control strategy is implementedusing a phase-locked loop (PLL) circuit, measuring the phaseangle of the grid voltage and generating a synchronizationsignal between the grid and the inverter; in the second one,this function is substituted by a reference voltage generatorimposing amplitude, frequency, and phase, thus implementinga PV control strategy. Feedback signals are included in theFLC, whose outputs are continuous waveforms applied to theTABLE ISWITCHING STATES FOR THE iTH H-BRIDGEthe MLI “Driver” block which consists of conditional statementfunctions producing the discrete signals for gating the inverterMOSFETs.The input variables to the FLC are as follows:1) Vn, i.e., the inverter output voltage Voutinvdivided by 100,measured after a low-pass ﬁlter (for both PV and PQcontrols);2) the difference between the actual and reference signalsa) AIdiﬀ = Ioutinv− Iref (PQ control);b) AVdiﬀ = Voutinv− Vref (PV control).Both Ioutinvand Voutinvare measured after a low-pass ﬁlterat the load terminals. This choice improves the quality of thecontrol without introducing delays; ﬁlter bandwidth is chosenaround 1 kHz with resistive load. The output of the controller isapplied to the inverter gate drivers.The normalized input Vn is used in order to identify theactual inverter operating state. Both the latter and the FLCoutput may assume nine different states, i.e., integer valuesbounded within the range [−4, 4].Table I summarizes the switching states versus the outputvoltage for each H-bridge. It is worth noting that not all thepossible switching states must be mapped into voltage outputsof the FLC, thus reducing the number of FL rules and of thenecessary FPGA gates.The ﬁrst step during the FLC design was the creation ofa knowledge base, i.e., fuzzy rules, expressed in terms ofstatements, conditions, and actions. Starting from the condition“TRUE” (i.e., the situation is veriﬁed), a set of rules wasdeﬁned for the errors. Then, conditions were deﬁned accord-ingly, obtaining variable reactions. The number and type ofmembership functions (MFs) represent a key point for thecontroller, being a tradeoff among achievable performance,memory space occupation, and execution speed. Their shapedepends on the input data distribution and can inﬂuence boththe tracking accuracy and the execution time , . Al-though any convex shape can be adopted, the most commonare the triangular, trapezoidal, or Gaussian ones. In this paper,the knowledge base was obtained through experimentation withthe system and its dynamics. Triangular shapes were chosen forinput and output MFs because of their satisfactory performanceand simpler implementation using FPGA.The following description deals with the controller designedfor PV control; the one for PQ operation can be quicklyaccomplished.Figs. 3 and 4 show the MFs chosen for the two inputparameters. The labels “NB,” “NS,” “ZE,” “PS,” and “PB” usedfor AVdiﬀ stand as follows: “NB” = negative−big, “NS” =negative−small, “ZE” = zero, and so forth.It is worth noting that, on the basis of simulations andsensitivity analysis, and in order to limit the output voltage
4118 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 12, DECEMBER 2010Fig. 3. MFs of parameter AVdiﬀ .Fig. 4. MFs of parameter Vn.variations below 10%, the input AVdiﬀ was assumed boundedwithin the range [−30, 30] V.The fuzzy sets for both the input and output variables werenine, as the number of levels: IV −, III−, II−, I−, ZE, I+,II+, III+, and IV +. A Mamdani-based system architecturewas realized; Max − Min, composition technique, and thecenter-of-gravity method were used in the inference engineand in the defuzziﬁcation process, respectively. The latter wasadopted because it is a good tradeoff between complexity andperformance.It is worth pointing out that a high number of fuzzy rulesensure both completeness and appropriate resolution of the con-troller and, hence, high control accuracy. Nevertheless, sinceboth their type and quantity inﬂuence the fuzzy approximationerror, a high number of rules may lead to an overparametrizedsystem, thus reducing generalization capability and accuracy,and increasing execution time. The number of fuzzy rulesdepends on the number of input variables, system performance,the execution time, the chosen MFs, the ease of construction,and the adaptability. In this paper, the number and type of thecontrol rules were decided according to a sensitivity analysisTABLE IIINFERENCE RULESFig. 5. 3-D visualization of inference rules.made by varying the number and type of rules. A satisfactorylevel of performance was obtained after a tuning process, i.e.,starting from some initial heuristic rules and progressivelymodifying their number and type. At the end of this process, the45 inference rules summarized in Table II and shown in Fig. 5were selected. In the latter ﬁgure, the x-axis reports the possiblevalues for AVdiﬀ , the y-axis the possible values for Vn, and thez-axis the next state evaluated by the FLC.The following logic was adopted for designing the inferencerules.1) If AVdiﬀ is equal to ZE, the current state is correct, andthe inverter preserves its current state.2) Considering a generic state, if AVdiﬀ is positive Voutinv>Vref , then the inverter state should be reduced; if AVdiﬀis negative Voutinv< Vref , the inverter state should beincreased.The same approach was used for designing the FLC for PQoperation. In this case, the signal AIdiﬀ was used instead ofAVdiﬀ .One problem arises with the power partitioning among thefour H-bridges. In fact, the use of uniform modulation leadsto power unbalances among the H-bridges (highlighted inTable III), which can generate overheating.This situation can be circumvented by introducing a circularshift register, i.e., applying the signal synthesized for one levelsequentially to all H-bridges. The resulting power distributionbecomes well balanced, being close to 25% for all H-bridges.
CECATI et al.: MULTILEVEL INVERTER FOR PHOTOVOLTAIC SYSTEMS WITH FUZZY LOGIC CONTROL 4119TABLE IIIPOWER SHARING AMONG H-BRIDGES WITHOUT CORRECTIONFig. 6. Inverter modulation patterns. (a) With power sharing. (b) Withoutpower sharing.This technique was implemented, sequentially imposing thesignal “rp,” shown at the bottom of Fig. 6, to each H-bridgeevery 10 ms.The modulation patterns with and without power sharing areshown in Fig. 6 (top and bottom, respectively), obtained by Veryhigh speed integrated circuit Hardware Description Languagesimulations and using the MOSFET conﬁguration shown inFig. 1, where each row represents the transistor switching statefor each transistor of a nine-level converter.IV. SIMULATION RESULTSThe proposed system was simulated using Simulink andSimPowerSystems Toolbox. Different tests were carried out,considering the inverter operating either as a voltage source(PV control) or a current source (PQ control).A. Stand-Alone Operation (PV Control)A stand-alone PV system was considered. The inverter gener-ates both active and reactive powers and imposes both referencevoltage and frequency. The extraction of energy from the PVgenerators depends on the load demand. Each PV array wassimulated by a V –I characteristic with open-circuit voltage thatis equal to 90 V, corresponding to an installed power that isequal to 9 kW (4 × 85 V at 26.5 A). An 8-kW resistive loadwas assumed, and an LC ﬁlter was designed with L = 1 mHand C = 1 μF. The top H-bridge (PV1) was obfuscated by aFig. 7. Voltage variations caused by cloud shadowing the top PV array PV1.(a) Input dc voltage variation. (b) Output voltage variation. (c) Magniﬁcation ofthe output voltage variation.moving cloud starting at t = 0.1 s for a time duration that isequal to 0.1 s and with a voltage drop that is equal to 40 V.Fig. 7(a) shows the dc voltage input produced by the PV1array, Fig. 7(b) shows the generated reference voltage, as wellas the obtained output voltages before and after the ﬁlter, andFig. 7(c) shows a magniﬁcation of the output voltage transitionscompared with the reference voltage. It can be noticed that
4120 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 12, DECEMBER 2010Fig. 8. Phase voltage variation due to cloud obscuration.the application of a 50% dc voltage variation modiﬁes themodulation such that the output voltage tracks its reference witha drop below 6%. The maximum percentage voltage and currentTHDs were 1.3% without the cloud and 2.4% during darkeningof the upper H-bridge source.The dynamic behavior and the robustness of the controlsystem were evaluated by considering a moving cloud obfus-cating only one PV array (PV1) and then, sequentially, all PVarrays, but only two per time and according to the followingdynamic sequence: “1, 1 + 2, 2 + 3, 3 + 4, 4.” The perturbationwas simulated by subtracting a semiperiod sinusoidal voltagewith embedded white noise from the PV array output voltage.The obtained results, shown in Fig. 8, demonstrate that, whena single PV array is obscured, the rms output voltage remainsalways above 200 V, becoming less than 200 V if the dc voltagedrop is higher than 60 V during darkening of two panels.B. Grid-Connected Operations (PQ Control)Further tests were carried out, considering a grid-connectedsystem. In this case, a PQ control strategy was adopted. EachPV array was simulated by a V –I characteristic with open-circuit voltage that is equal to 90 V, resulting in an installedpower that is equal to 9 kW (4 × 85 V at 26.5 A). An outputLC ﬁlter was included, choosing L = 1 mH and C = 1 μF.1) Leading and Lagging Loads: The active and reactivepower references in the PQ control were set equal to 4 kWand zero (unity power factor), respectively. Different loads wereconsidered in order to evaluate the performance of the FLC; inparticular, the following ones were considered:1) a series RL load absorbing 8 kW of active power and2 kVAR of reactive inductive power [Fig. 9(a)];2) a series RC load absorbing 8 kW of active power and2 kVAR of reactive capacitive power [Fig. 9(b)].Fig. 9 shows that, whatever the load (leading or lagging), theoutput current follows its reference. It can be noticed that theinverter current was synchronized with the grid voltage; there-fore, the power factor was always higher than 0.99. The reactivepower (either inductive or capacitive) was always supplied bythe grid. In fact, the controller PLL circuit allows both gridvoltage phase angle measurement and the generation of Iref inphase with the grid voltage, thus forcing Ioutinvsynchronizationwith the grid voltage.Fig. 9. Leading and lagging loads. (a) Series RL load. (b) Series RC load.2) Variation of the Active Power Reference: A series RLload absorbing 8 kW and 2 kVAR was assumed. In order totest the PQ control tracking capabilities, different variationsof the active reference power were assumed (Fig. 10). Startingfrom 3-kW PV reference power, 5 kW, and 2 kVAR suppliedby the grid, the active power reference was increased up to4 kW at t = 0.1 s and decreased down to 2 kW at t = 0.2 s.The maximum percentage voltage and current THDs are shownin Table IV. They are below 0.5% and 3.1%, respectively;the lower voltage THD mainly depends on the inverter grid-connected operation.MLI performance was compared with that of a standardPWM converter, consisting of a dc/dc booster and a two-level PI-controlled inverter. During this simulation, the four PVarrays were connected in parallel, feeding the dc/dc converter;the same reference active power variations were providedduring simulations. The obtained voltage and current THDs,summarized in Table IV, demonstrate that the proposed systemgenerates better voltage and current waveforms, particularly atlow power, thus improving output power and its quality, evenwithout a speciﬁc MPTT algorithm.3) Variation of the Active and Reactive Powers Requested bythe Load: The PQ control tracking capability was evaluated
CECATI et al.: MULTILEVEL INVERTER FOR PHOTOVOLTAIC SYSTEMS WITH FUZZY LOGIC CONTROL 4121Fig. 10. Variation of the active power reference of inverter PQ control.(a) Voltages and currents. (b) Detail of the inverter current.TABLE IVVOLTAGE AND CURRENT PERCENTAGE THDs OF THE MLIAND THE TWO-LEVEL CONVERTERin the presence of load variations, too. A 2-kW generatorreference was assumed, and different active and reactive powerrequests were applied. Initially, a series RL load absorbed 3 kWof active power and 1 kVAR of reactive inductive power was as-sumed. The following load variations were considered (shownin Fig. 11):1) a reduction of the active and reactive powers requested bythe load below to 2 kW and 0 kVAR, at t = 0.1 s;2) an increase of the load active and reactive power requestsup to 4 kW and 1 kVAR at t = 0.2 s.Fig. 11 shows that, if the reference active power is keptconstant, the generated power remains constant and the loadFig. 11. Variation of the active and reactive powers requested by the load.Fig. 12. Voltage sag.demand is satisﬁed by the grid. Also, in these cases, the powerfactor was higher than 0.99.4) Symmetrical Voltage Sag: Voltage sags have negative ef-fects on the grid and the inverter, becoming a potential cause ofreliability reduction. Therefore, it is desirable that these distur-bances are bounded within the limits imposed by anti-islandingprotections. Different standards are adopted by different coun-tries; in this paper, the German DIN/VDE 0126, imposinginverter disconnection within 0.2 s for voltage deviations below80% or above 115% of the rated voltage, was considered .A 100-ms-long −20% Vn symmetrical voltage sag starting att = 0.2 was considered. A resistive load absorbing 8 kW andan active power reference of the generator equal to 2 kW wereassumed.Results, shown in Fig. 12, conﬁrmed that, as the active powerreference is unchanged, during the voltage sag, the referencecurrent increased in inverse proportion with the voltage sagamplitude. Accordingly, the current supplied by the PV systemthrough the MLI increased from Irms = 8.7 A up to Irms =10.6 A. Therefore, the MLI can withstand this voltage sag.During the voltage sag, the maximum percentage current THD
4122 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 12, DECEMBER 2010Fig. 13. Experimental system.was lower than 6%, while the maximum percentage voltageTHD did not exceed 1%.In conclusion, this study has demonstrated that the proposedFLC exhibits reduced overshoots during transients and accuratesteady-state conditions even in the presence of load variations,voltage sags, or reference power variations.V. EXPERIMENTAL RESULTSA. Hardware DescriptionThe experimental setup is shown in Fig. 13. The wholecontroller and modulator were implemented using an FPGAActel Fus1on Starter Kit , incorporating a mixed-modeFPGA Actel (AFS600-FG256) embedding both analog anddigital gates in the same chip. This avoids the use of externalA/D converters, operational ampliﬁers, and other analog com-ponents, allowing the realization of a System-on-Chip (SoC)controller. The single-phase four-H-bridge MLI was designedand realized by DigiPower Ltd., a University of L’Aquila spin-off, and it mainly consists of 16 IRF 540N MOSFETs (100 V,33 A, RDS = 44 mΩ)  driven by optically isolated drivers.The chosen power devices allow both high-frequency and high-current operations.B. Software DescriptionThe controller/modulator software was developed using“Actel development system” (Libero v. 8.5) . The mainblocks, already shown in Fig. 2, are as follows:1) Analog System Builder (ASB): includes both analog todigital converters (10 b at 294.118 kb/s) performing datasignal conditioning and data acquisition;2) OPTIMIZATION: ampliﬁes the data provided by theASB (ranging from 0 up to 2.7 V);3) RCO (oscillator) and PLL: deﬁne the internal clocksneeded for synchronization;4) CORE: manages the inputs from ASB, synchronizingthem with the FLC;5) ﬁnite-state machine (FSM): synchronizes ASB dataand FLC;6) FLC: implements real-time fuzziﬁcation and defuzziﬁca-tion algorithms;7) DEADTIME: implements interlock between half-bridgepower devices. Its outputs are the inverter patterns.C. ExperimentsThe proposed system was tested in laboratory duringstand-alone operations. Because of their unavailability, PVarrays were replaced by dc power supplies with variable outputvoltage.Fig. 14 shows (top) the multilevel output voltage, (center) theﬁltered output voltage, and (bottom) a fast Fourier transform(FFT) signal. The voltage signals were scaled down to matchthe FPGA analog input level (vin ≤ 2.7 V). These oscillo-graphs demonstrate the good quality of the obtained voltagewaveforms, conﬁrming simulation results. When operating at50 kHz (as in the case of the experiment), the MOSFETswitching frequency does not exceed 14 kHz, thus achievinglow switching losses while respecting EMI speciﬁcations. Theuse of FPGA allows very high speed control loops, resultingin signiﬁcantly enhanced performance over microprocessorimplementation . If necessary, the computational speed andthe switching frequency can be further increased. It is worthnoting that the output waveforms have very limited harmoniccontent; therefore, a small and light output ﬁlter is sufﬁcient forfulﬁlling EMI rules, thus reducing size and cost.VI. ANALYSIS AND DEVELOPMENTSThe proposed system offers several advantages over thecommon dc/dc converter plus PWM inverter in addition to thebetter THD summarized in Table IV. Because of its modularity,the number of levels and phases can be modiﬁed according todifferent needs and without signiﬁcant burdens. The inverteremploys low-voltage MOSFETs, which are cheaper, faster,and more efﬁcient than IGBTs. They allow high-switching-frequency operations for improved output waveforms and THD;when operating at low frequency, they reduce power losses andcomponent stress.The proposed system is very appealing in the case of largesolar plants with thousands of PV cells because they can bearranged in many separate small generators, reducing darkeningproblems, thus simplifying the farm electric layout, reducingpower losses, and improving the overall efﬁciency. In the caseof medium–high power systems, the output voltage can reachthe desired level without the use of expensive transformers.MPPT can be embedded inside each separate H-bridge con-troller. This solution offers good performance, particularly inlarge systems where input power management is often criti-cal. Possible algorithms are described in  and –.The proposed FLC does not require the exact knowledge of thesystem; therefore, it is intrinsically robust. Moreover, both thealgorithm and the system can be easily modiﬁed or expanded,increasing the number of levels and phases. The use of FPGAeliminates constraints on the number of switching signals andspeeds up the computational speed, signiﬁcantly contributing tothe obtained controller results. It represents an important step
CECATI et al.: MULTILEVEL INVERTER FOR PHOTOVOLTAIC SYSTEMS WITH FUZZY LOGIC CONTROL 4123Fig. 14. Experimental results. (a) Multilevel voltage. (b) Filtered outputvoltage. (c) Voltage FFT.ahead over microprocessor-based FL implementations. Justfor evaluation, while  reports that a 32-b microcontrolleroperating at 40 MHz requires about 400 μs for executing anFLC applied to two-level active rectiﬁer (its computationalcomplexity is similar to that of an inverter), here, the executiontime is about 1 μs. Notice that the chosen FPGA Fus1on offers additional features not exploited in this project. In fact, itcan embed an ARM Cortex M1 microprocessor core operatingindependently by the developed controller/modulator. Hence,additional features and functions can be easily added, includinga real-time operating system (e.g., RT-Linux and WinCE),Internet connectivity, database management capability, and theuse of sophisticated graphical user interfaces and softwarelibraries. These capabilities are very appealing when designingsophisticated PV systems incorporating data logging, Internetconnectivity, and other high-level features.VII. CONCLUSIONA novel single-phase multilevel cascaded H-bridge inverterfor PV applications with FL control and SoC approach has beenproposed. Its performance satisﬁes the demand of ﬂexible andaccurate electric power generation and reduces both the outputﬁlter dimensions and the inﬂuence of perturbations caused bycloud darkening or seasonal variations. Due to its modularity,the proposed system can be improved by increasing the numberof levels, further reducing its THD. Three-phase inverters canbe easily assembled, too. The use of FPGA allows controllerimplementation at very high speed, resulting in signiﬁcantlyenhanced performance over microprocessor-based implemen-tations. Based on these results, it is expected that MLIs for PVsystems will become an effective commercial solution shortly.REFERENCES L. G. Franquelo, J. Rodriguez, J. I. Leon, S. Kouko, R. Portillo, andM. A. M. Prats, “The age of multilevel converters arrives,” IEEE Ind.Electron. Mag., vol. 2, no. 2, pp. 28–39, Jun. 2008. J.-S. Lai and F. Z. Peng, “Multilevel converters—A new breed ofpower converters,” IEEE Trans. Ind. Appl., vol. 32, no. 3, pp. 509–517,May/Jun. 1996. J. R. Rodriguez, J.-S. Lai, and F. Z. Peng, “Multilevel inverters: A sur-vey of topologies, control, and applications,” IEEE Trans. Ind. Electron.,vol. 49, no. 4, pp. 724–738, Aug. 2002. L. M. Tolbert, F. Z. Peng, and T. G. Habetler, “Multilevel converters forlarge electric drives,” IEEE Trans. Ind. Appl., vol. 35, no. 1, pp. 36–44,Jan./Feb. 1999. J. R. Rodriguez, J. W. Dixon, J. R. Espinoza, J. Pontt, and P. Lezana,“PWM regenerative rectiﬁers: State of the art,” IEEE Trans. Ind. Elec-tron., vol. 52, no. 1, pp. 5–22, Feb. 2005. C. Cecati, A. Dell’Aquila, M. Liserre, and V. G. Monopoli, “Design ofH-bridge multilevel active rectiﬁer for traction systems,” IEEE Trans. Ind.Appl., vol. 39, no. 5, pp. 1541–1550, Sep./Oct. 2003. C. Cecati, A. Dell’Aquila, M. Liserre, and V. G. Monopoli, “A passivity-based multilevel active rectiﬁer with adaptive compensation for tractionapplications,” IEEE Trans. Ind. Appl., vol. 39, no. 5, pp. 1404–1413,Sep./Oct. 2003. 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. 1292–1306, Sep./Oct. 2005. M. Calais and V. G. Agelidis, “Multilevel converters for single-phasegrid connected photovoltaic systems—An overview,” in Proc. ISIE, 1998,vol. 1, pp. 224–229. M. Calais, V. G. Agelidis, L. J. Borle, and M. S. Dymond, “A transformer-less ﬁve level cascaded inverter based single phase photovoltaic system,”in Proc. IEEE 31st Annu. Power Electron. Spec. Conf., Galway, Ireland,2000, vol. 3, pp. 1173–1178. H. Ertl, J. W. Kolar, and F. C. Zach, “A novel multicell DC–AC converterfor applications in renewable energy systems,” IEEE Trans. Ind. Electron.,vol. 49, no. 5, pp. 1048–1057, Oct. 2002. O. Alonso, P. Sanchis, E. Gubia, and L. Marroyo, “Cascaded H-bridgemultilevel converter for grid connected photovoltaic generators with
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Electron., vol. 55, no. 7, pp. 2610–2621, Jul. 2008.Carlo Cecati (M’9–SM’03–F’06) received theDr.Ing. degree in electrotechnics from the Universityof L’Aquila, L’Aquila, Italy, in 1983.Since 1983, he has been with the Department ofElectrical and Information Engineering, Universityof L’Aquila, where he is currently a Professor ofindustrial electronics and drives and is a Rector’sDelegate. He is the Founder and the Coordinatorof the Ph.D. courses on management of renewableenergies and sustainable building at the University ofL’Aquila. In 2007, he was the Founder of DigiPowerLtd., L’Aquila, which is a spin-off dealing with industrial electronics andrenewable energies. His research and technical interests cover several aspectsof power electronics and electrical drives.Dr. Cecati is a Co-Editor-in-Chief of the IEEE TRANSACTIONS ON INDUS-TRIAL ELECTRONICS, and he has been a Technical Editor of the IEEE/ASMETRANSACTIONS ON MECHATRONICS. He has been a General Cochair of theIEEE International Symposium on Industrial Electronics (ISIE) 2002, IEEE-ISIE 2004, and IEEE-ISIE 2008; an Honorary Cochair of the IEEE-ISIE 2010;a Technical Program Cochair of the IEEE Industrial Electronics Conference(IECON) 2007; and a Track Cochair or Special Session Chair of IEEE-ISIE andIEEE-IECON conferences. From 2000 to 2004, he was an AdCom member ofthe IEEE Industrial Electronics Society (IES) and, from 2005 to 2006, an IESVice President. Since 2007, he has been an IES senior AdCom member andan IES Region-8 Coordinator. He is a member of IEEE IES Committees onRenewable Energy Systems and on Power Electronics.
CECATI et al.: MULTILEVEL INVERTER FOR PHOTOVOLTAIC SYSTEMS WITH FUZZY LOGIC CONTROL 4125Fabrizio Ciancetta (M’03) was born in Pescara,Italy, in 1977. He received the M.S. degree inelectronic engineering and the Ph.D. degree inelectrical and information engineering from theUniversity of L’Aquila, L’Aquila, Italy, in 2003 and2009, respectively.In 2003, he joined the Department of Electri-cal Engineering, University of L’Aquila, where heworked on the development of digital and distributedmeasurement systems. Since 2009, he has been hold-ing a postdoctoral position at the same university.His research and technical interests cover several aspects related to distributedmeasurement systems, signal processing, and multilevel inverters; in theseﬁelds, he authored about 50 journal and conference papers.Pierluigi Siano received the M.Sc. degree inelectronic engineering and the Ph.D. degree ininformation and electrical engineering from theUniversity of Salerno, Salerno, Italy, in 2001 and2006, respectively.Since 2001, he has been performing researchactivities in the ﬁeld of electrical power systems.Since 2005, he has been an Assistant Professor withthe Department of Information and Electrical Engi-neering, University of Salerno. From 2006 to 2007,he was the Scientiﬁc Coordinator of the researchproject “Integration of New and Renewable Energy Into Urban ElectricalNetworks” supported by the British–Italian partnership program for youngresearchers (2005–2006). His research activities are centered on the integrationof renewable distributed generation into electricity networks and Smart Gridsand on the application of soft-computing methodologies to the analysis andplanning of power systems. In these ﬁelds, he has published more than65 technical papers, including 25 international journal papers and 40 inter-national conference papers. His teaching activities are on the areas of powersystems, technology and economics of energy, automation of power systemsand power plants, and power electronics. He is a member of the Editorial Boardof the International Journal on Power System Optimization.Dr. Siano served as a Reviewer and the session Chairman for many inter-national conferences. He has been the Special Sessions Cochair of the IEEEInternational Symposium on Industrial Electronics (ISIE) 2010 and is theCochair of the Special Session on “Methods and Systems for Smart GridsOptimization” of IEEE-ISIE 2010. He has been a Guest Editor of the SpecialSection of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS on“Methods and Systems for Smart Grids Optimization.” He is a member of the“Technical Committee on Renewable Energy Systems” of the IEEE IndustrialElectronics Society.