05416284

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 2, FEBRUARY 2011 403

Cascaded DC–DC Converter PhotovoltaicSystems: Power Optimization Issues

Antoneta Iuliana Bratcu, Member, IEEE, Iulian Munteanu, Member, IEEE,Seddik Bacha, Member, IEEE, Damien Picault, and Bertrand Raison, Member, IEEE

Abstract—This paper investigates the issues of ensuring globalpower optimization for cascaded dc–dc converter architecturesof photovoltaic (PV) generators irrespective of the irradianceconditions. The global optimum of such connections of PV mod-ules is generally equivalent with performing the maximum powerpoint tracking (MPPT) on all the modules. The most importantdisturbance occurs when the irradiance levels of modules happento be sensibly different from a module to another—in this case,voltage-limitation requirements may be broken. The proposedsupervisory algorithm then attempts to establish the best subop-timal power regime. Validation has been achieved by MATLAB/Simulink numerical simulation in the case of a single-phase grid-connected PV system, where individual MPPTs have beenimplemented by an extremum-seeking control, a robust and less-knowledge-demanding perturb-and-observe method.

Index Terms—Extremum-seeking control (ESC), maximumpower point tracking (MPPT), photovoltaic (PV) power systems,supervisory algorithms.

I. INTRODUCTION

NOWADAYS, the world pays growing attention to renew-able energy sources, clean and practically inexhaustible,

and interdisciplinary research is continuously developed inorder to sustain the improvement of existing conversion tech-nologies and the development of new ones [1], [2]. Photovoltaic(PV) installations are an already familiar landscape, either assmall (less than 5 kW) residential stand-alone or even gridconnected, or as larger (hundreds of kilowatts) building inte-grated or not [3], as well as parts of hybrid power systems,also containing other renewable energy sources [4], [5]. Interestis focused on rendering the PV systems more adequately tothe wide use in terms of power, efficiency, grid compliancyand communication capacity for those grid-connected ones,

Manuscript received June 30, 2009; revised October 28, 2009 andDecember 11, 2009; accepted January 27, 2010. Date of publicationFebruary 18, 2010; date of current version January 12, 2011.

A. I. Bratcu and I. Munteanu are with the Grenoble Electrical EngineeringLaboratory (G2ELab), Grenoble National Institute of Technology, 38402,Grenoble France, and also with the Department of Electronics and Telecom-munications, “Dunarea de Jos” University of Galati, 800008 Galati, Romania(e-mail: [email protected]; [email protected]).

S. Bacha is with the Grenoble Electrical Engineering Laboratory (G2ELab),Grenoble National Institute of Technology, 38402 Grenoble, France, andalso with Joseph Fourier University, 38041 Grenoble, France (e-mail:[email protected]).

D. Picault is with Grenoble Electrical Engineering Laboratory (G2ELab),Grenoble National Institute of Technology, 38402 Grenoble, France (e-mail:[email protected]).

B. Raison is with Joseph Fourier University, 38041 Grenoble, France (e-mail:[email protected]).

Digital Object Identifier 10.1109/TIE.2010.2043041

reliability and service time, safety and security, etc. [6]–[9]. APV system usually undergoes an optimization procedure guidedby various and often contradictory criteria, in order for it toresult as the best tradeoff within a specific application [10].

Exploitation of PV systems has proved the necessity ofmethods of automatic control and information processing foroptimizing dynamic performance, reactivity to the variabilityof the primary energy source, i.e., the light, and robustness toas various as possible kinds of disturbances. In the specific caseof grid applications, one of the most important aspects is themaximum power point tracking (MPPT), aiming at maximizingthe extracted energy irrespective of the irradiance conditions[11]. An important research effort has been devoted to findingsimple, efficient, and minimal-knowledge-demanding methodsof MPPT [12]–[14]. Among them, the so-called perturb-and-observe (P&O) class of methods, based upon injecting high-frequency small-amplitude (usually harmonic) perturbations inthe system in order to detect the sign of the power gradient, hasproved as one of the most successful [15], [16].

One can say that the MPPT is practically solved in the caseof a PV system whose cells receive the same irradiance level.Such a system has a unimodal power characteristic, which maynot be the case of large spatially distributed systems, withhigh probability of undertaking partial shading. Indeed, specificconfigurations of PV modules may have global power charac-teristics that exhibit multiple maxima [17]. Recent works reflectthe interest of designing MPPT methods able to track multiplepeaks under rapidly changing irradiance conditions [18], [19].

One such particular topology is the object of this paper.Several PV generators, with each coupled to its dc–dc boostconverter, are cascaded on the same dc bus and interfaced tothe grid by means of a dc–ac inverter. The problem is to find arobust control strategy of extracting the maximum power avail-able from this architecture, given that the PV generators mayundertake supplementary constraints—expressed mainly asoutput-voltage-limitation (OVL) requirements—when exposedto strongly variable irradiance conditions. This problem wasfirst addressed in [20]—here, more extended discussion of theresults and comparison with other configurations are provided.

This paper is organized as follows. In Section II, thestructure, operation, and steady-state analysis of the consideredcascaded dc–dc converter PV topology are presented, with em-phasis on advantages versus some other more usual cases. Somesimulation results suggest the problems that can occur when op-erating all the PV generators at MPPT but under quite differentlevels of irradiance. Hence, a more complex control structure,called a supervisor, is necessary in order to achieve the global

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404 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 2, FEBRUARY 2011

Fig. 1. Block diagram of the considered cascaded PV architecture.

power optimization in the cascaded case, according to how itis detailed in Section III. Numerical simulation results of thesupervised PV system, including the comparison with a paralleldc–dc converter configuration, are presented in Section IV.This paper ends with the conclusions and future work.

II. CASCADED DC–DC CONVERTER PV ARCHITECTURE

A. Structure, Operation, and Steady-State Analysis

The analyzed PV system consists of a series topology ofper-panel dc–dc converters. A high-voltage string connectedto a single dc–ac inverter results, having the advantages ofa “converter-per-panel” approach, obviously cheaper but alsomore efficient than individual dc–ac grid-connected inverters[21]. The buck and boost converters are the most efficienttopologies for a given cost, as shown in [21]. Here, boost dc–dcconverters have been employed (Fig. 1).

The considered structure has some intuitive advantages overthe parallel-connection case. Thus, for a given dc-bus volt-age, the series connection allows individual boost converterswith relatively small step-up ratio being used (usually threeto four), which ensures good efficiency along with low cost.Unlikely, the parallel case would require higher step-up ratios(more than four), which leads either to poorer efficiency or tohigher cost due to eventually using two-stage dc–dc conversion.Constraints regarding current limitation may also be involved.Both of these drawbacks may however be avoided if stepping-up the PV output voltage by series connections of many panelsbefore the dc–dc conversion stage. However, series connectionsof PV panels are disadvantageous from the viewpoint of thepossibility of harvesting the maximum power because they arelimited by the power given by the worst irradiated panel. Thus,the total power provided risks to diminish in the case of, e.g.,partial shading on some panels. A numerical-simulation-basedcomparison between the cascaded case and a parallel case ofthe same power can be found in Section IV.

Fig. 1 shows n dc–dc converter modules supposed identicalconnected in series to a single dc–ac inverter in charge withtransferring the power to the grid. Each converter module i is

based on the PV generator PVi, consisting of either a singlepanel or a connection of panels, supposed to receive all thesame irradiance, such that the power characteristic remainsunimodal. To this, the boost chopper i is associated. Such aPV generator can independently control and thus optimize thepower flow from its source of irradiance Irri: The pulsewidthmodulation (PWM) signal uchi ∈ {0, 1} of chopper i can becontrolled in order to impose the operating point of PVi, i.e.,(IPVi , VPVi), independently from the operation of the othergenerators.

In grid applications, each chopper performs MPPT for its PVgenerator, while the grid inverter regulates the dc-bus voltage.At steady state, the same current Idc passes through all thechoppers, with the sum of their output voltages being the dc-busvoltage

∑ni=1 Voi = Vdc. Let V ∗

dc denote the desired dc-busvoltage value and (I∗PVi , V

∗PVi), i = 1, 2, . . . , n, be the n op-

erating points. The steady-state values of all variables in Fig. 1can be deduced [20]. Thus, the chopper output voltages are

Voi = V ∗dc · I∗PVi · V ∗

PVi

/n∑

i=1

I∗PVi · V ∗PVi︸︷︷︸

wi

(1)

showing that the dc-bus voltage distribution on the convertermodules depends on the weights of the individual PV powersin the global power provided wi, i = 1, 2, . . . , n.

The PV power varies directly with the irradiance level [22].Hence, as long as the irradiance levels are almost the same forall PV generators, one can impose practically the same oper-ating point—in particular, the maximum power one—ensuringthat the dc-bus voltage be almost equally supported by the ndc–dc converters and the total power be maximized. However,when the irradiance levels are sensibly different for some time,then the weights wi become unbalanced, and some dc–dcconverters will undergo overvoltages, as shown next.

B. Simultaneous MPPT for All PV Generators

As widely known, the power curve of a PV module versus themodule voltage PPV(VPV) is unimodal [9], [22]. Let the locusof MPPs corresponding to various irradiance levels be called themaximum power regime (MPR) curve. MPPT operation meansto track the MPR irrespective of the irradiance level. In thispaper, the MPPT on each PV generator is implemented by anextremum-seeking control (ESC), a P&O method that is able tofind the extremum of some difficult-to-model and not preciselyknown unimodal dynamics by feeding the plant with sinusoidalprobing signals [23].

Fig. 2 shows how the ESC can be applied to PV modules.When feeding a PV module with a ω-frequency sinusoidal volt-age variation having a sufficiently small amplitude a, a powervariation is induced, which is generally nonsinusoidal due to thecharacteristic’s nonlinearity and has a ω-first-order harmonic.This latter can be extracted—e.g., by means of a high-passfilter called washout filter—and it is in phase with the voltagevariation if the operating point is on the ascending part of thevoltage–power curve and with a phase lag of π for the descend-ing part. The product of the two signals has two components:

BRATCU et al.: CASCADED DC–DC CONVERTER PHOTOVOLTAIC SYSTEMS: POWER OPTIMIZATION ISSUES 405

Fig. 2. ESC principle applied for the PV modules.

a small-amplitude 2ω-frequency component, which can be ne-glected, and a continuous component, which will toggle its signas the operating point moves from a side to the other of the PPV

curve’s maximum. This latter component is then passed throughan integrator of gain k in order to provide the voltage step VPV

that is necessary to move the operating point to the optimalposition with a convergence speed depending proportionally onk, a, and 1/ω [23]. The voltage reference applied to the PVmodule results as VPV = VPV + a sin(ωt).

As regards how an ESC controller must be tuned, somegeneral considerations can be applied as follows. Thus, theexcitation frequency ω must be sufficiently large, i.e., outsidethe plant’s bandwidth, in order to ensure stability of the closed-loop system. On the other hand, in systems having powerelectronics devices, this frequency is upper limited by thepower electronics switching frequency. The amplitude a mustbe sufficiently small such that the plant’s behavior remainslinear and the induced output variations are as sinusoidal aspossible; therefore, a must be chosen depending on the slopeof the plant’s VPV−PPV characteristic. The integrator gain kresults from upper limiting the reference gradient to the valueof the plant’s main dynamic such that the plant can followthe reference. Note that the VPV−PPV characteristic is timevarying; therefore, the controller can either be tuned on a mosttypical curve, or one can attempt using adaptive laws of controlparameter computation.

MATLAB/Simulink numerical simulations have been per-formed for a three-generator PV topology as in Fig. 1, whereeach PV generator is independently set in MPPT by ESC,under strongly and rapidly variable irradiance conditions. ThePWM signal uchi results within a voltage control loop, whosereference V ∗

PVi comes from an ESC-based MPP tracker usingthe measured PV generator power PPVi . Each PV generator isa series connection of two (125 × 125)-mm-cell PV modules,each of 150-W peak power, 5.3-A short-circuit current, 59-Vopen-circuit voltage, and 40-V typical voltage at typical power.The well-known PV-cell five-parameter diode model has beenused [24]

IPV = Iph − I0

(e(VPV+RsIPV)/Vt − 1

)− (VPV + RsIPV) /Rsh (2)

Fig. 3. Performance of the analyzed PV architecture when all the genera-tors are simultaneously operated in MPPT under rapidly variable irradianceconditions.

where Iph is the current due to the PV effect, I0 is the diodesaturation current, Vt is the thermic voltage, and Rs and Rsh

are the series and shunt resistances, respectively.A requirement imposed when sizing the PV system is that the

ratio between the ideal value of the dc-bus voltage and the ratedvalue of the output chopper voltage Vr to approach the numberof PV generators. In this case, V ∗ideal

dc = 450 V in order to allowinterfacing to a 220-V/50-Hz grid; provided that n = 3, Vr canbe chosen around V ∗ideal

dc /n, i.e., 150 V.The irradiance signals are delayed from a PV generator to

the next one by a time interval, thus simulating a cloud passingover. A two-spectral-component dynamic model of the irradi-ance in analogy with the modeling of another irregular renew-able energy source, the wind speed, has been used [20], [25].Here, the variation speed has been set around 1 s, representingfaster variations than habitually occurring [see Fig. 3(a)]. EachESC controller has been tuned thus: the integrator constant isk = 100; the sinusoidal disturbance has amplitude a = 0.1 andfrequency ω = 100 Hz.

Initially, to all the PV generators, the same voltage referenceis imposed (in this case, V ∗

PV = 65 V, which is a value arbi-trarily chosen somewhere in the middle of the voltage variationrange); then, the control is switched to MPPT. The results of thesimultaneous MPPT operation of all generators can be notedin Fig. 3(b). When the irradiance values became maximallyunbalanced, then the output chopper voltages of the first andthe third generator, i.e., Vo1 and Vo3, have gone well beyondthe rated value Vr = 150 V.

The values of the capacitors have been chosen as CPV =4700 μF and Cdc = 22 000 μF. These quite high values aremotivated by control reasons, i.e., for smoothing the voltagevariations due to fast changes of the primary resource. Thus,the CPV capacitors ensure a reasonably smoothed PV outputvoltage variation. The value of Cdc prevents a sudden imbal-ance of the individual irradiation levels from propagating toofast in the choppers’ output voltage. In this way, enough time iseventually given to a supervisory structure for taking decisions,as shown in the next section. The cost of capacitors may also


be involved in defining the best tradeoff in order to choose thecapacitors’ values, but this is beyond the scope of this paper.

More details on both the ESC design and simulation resultscan be found in [20]. In conclusion, the simultaneous MPPToperation of all generators within a grid-connected cascadedPV topology is effective only when the PV generators areilluminated almost equally. Otherwise, constraints of voltage-limitation type can be violated. The global power optimizationrequires a supervisor that detects a sufficient degree of degrad-ing the initial optimal strategy in order to meet the constraints.

III. SUPERVISORY ALGORITHM PROPOSED FOR

GLOBAL POWER OPTIMIZATION

The maximum power capture irrespective of the irradi-ance conditions, meanwhile meeting the voltage-limitation con-straints, may be ensured if each PV generator is equipped withtwo control laws instead of a single one, the MPPT. The maincontrol law remains the MPPT, with the second one being anOVL control law. A control system, which is able to globallymanage the different events and then to take decisions of en-abling one of the two control ways for each PV generator, mustbe designed. Such a system—called a supervisor—does notneed to run continuously, as it looks rather at variation trendsin a relevant time window than at instantaneous variations.Thus, the supervising algorithm runs every Tsv s, where Tsv

is suitably chosen depending on the fastest dynamic of thesupervised system.

Assuming that the normal operation is MPPT on all thegenerators, the supervisor must be able to detect OVL violationsdue to unbalance between the power weights of generators and,thus, between their output voltages Voi , i = 1, 2, . . . , n, as in(1). The admissible threshold is here set to 1.2Vr. When at leastone such limitation is detected, then a new possible value of thedc-bus voltage reference is first sought for, which results suchthat to reestablish the balance between voltages, meanwhileneeding to lay in between ±20% from V ∗ideal

dc . If such avalue could not be found out, then the supervisor switchesfrom MPPT to OVL for the generators having surpassed theadmissible threshold voltage—the other generators remain inMPPT. If the power weight of a generator operating in OVLdecreases, this means that the global power has increased. Thiscan only be due to the increasing of the power provided bythe generators still operating in MPPT. Furthermore, this meansthat the irradiance balance is going to be reestablished, and theMPPT is again possible. The control of the concerned generatorcan then be switched back to MPPT based on estimating thegradient of the power weight.

The block diagram of the supervisor, together with its con-nection with the choppers’ and inverter’s control blocks, isshown in Fig. 4 (see also [20]). The PV power measures andthe output voltage measures PPVi and Voi , i = 1, 2, . . . , n, aswell as the dc-bus voltage measure Vdc, are conveniently low-pass filtered to reflect the trend on the desired time window.The power weights wi, i = 1, 2, . . . , n, and their gradientsare computed inside the supervisor. The supervisor outputs nbinary decisions referring to the operating modes of the n PVgenerators: Output i is 1 for MPPT and 0 for OVL. Switching

Fig. 4. Block diagram of the supervisor that implements the proposed globalpower optimization strategy and its connections with the choppers’ and in-verter’s control blocks.

between the two controls means, in fact, only changing thevoltage reference.

These outputs feed block 1 in Fig. 4, which genericallydenotes the n chopper control structures; these latter furtherprovide the PWM signals uchi , i = 1, 2, . . . , n, to the choppers.The supervisor also computes a new value of the dc-link voltagereference V ∗new

dc , which is further provided to the invertercontrol block (block 2 in Fig. 4). The PWM signal uinv is finallysent to the inverter. The V ∗new

dc computation block also outputs abinary variable noted “V ∗new

dc found” in Fig. 4, which, togetherwith wi and dwi/dt, i = 1, 2, . . . , n, is used within a finite-state automaton in order to provide the operating modes of thePV generators.

The value of V ∗newdc is computed as follows. If at least one

PV generator has surpassed the maximum voltage threshold,this means that the power available from another generator (ormaybe from many others) has decreased. A new reduced dc-bus voltage reference V ∗new

dc is sought for, which allows for allthe generators to remain in MPPT, meanwhile meeting all thenew constraints V new

oi ≤ 1.2 · Vr, i = 1, 2, . . . , n. Taking intoaccount (1), it is sufficient to reduce the dc-bus reference to

V ∗newdc = 1.2 · Vr

/max

i=1,2,...,n{wi}. (3)

Note that (3) is valuable in steady state, where the PVpower generators reflect exactly the irradiance levels. Thus, theweights wi are the weights of Irri in the sum of Irri. Thevalue (3) can be declared the new dc-bus voltage referencefor the inverter control loop if it is larger than 0.8 · V ∗ideal

dc .If not, the supervisor degrades the MPPT of the generatorshaving surpassed the limit by switching their control to OVL at1.2Vr. This is a suboptimal regime from the energy viewpoint;however, it is the less restrictive degradation as it still ensuresthe constraints to be met at the limit.

In Fig. 4, it is also depicted that the supervisor is a cyclictask, executed every Tsv s.


Fig. 5. Performance of the supervised cascaded PV system under step changes of the irradiance levels. (a) Irradiance scenario. (b) Output voltages of the threechoppers. (c) Time evolutions of the dc-bus voltage and grid current. (d)–(f) Time evolutions of the power provided by the three PV generators.

The steps of the supervising algorithm are listed as follows.

For all PV generatorsCompute their power weights wi, i = 1, 2, . . . , n.Estimate the gradients of their power weights gi, i =1, 2, . . . , n.

If there is at least one generator that has surpassed 1.2Vr, thenCompute a new dc-bus voltage reference, as to (3).If V ∗new

dc �∈ [0.8 · V ∗idealdc ; 1.2 · V ∗ideal

dc ], thenFor those PV generators having surpassed 1.2Vr

Set their control to OVL.Otherwise, send V ∗new

dc as reference to the inverter control.Otherwise

For all generators operating in OVL that have negativegradients of power weights

(Re)set their control to MPPT.

IV. VALIDATION BY NUMERICAL SIMULATION

A. Cascaded Case With Supervisor

The supervised cascaded dc–dc converter PV system de-scribed in Section II has been numerically simulated underthe irradiance scenario shown in Fig. 5(a), with all the PVgenerators initially operating at MPPT, under equal irradiancelevels, i.e., Irr1 = Irr2 = Irr3 = 900 W/m2. The most un-favorable case has been considered, with step variations ofirradiance, which are seldom encountered in nature. After Irr1

decreased from 900 to 400 W/m2, the output voltages Vo2 andVo3 reach the maximum threshold of 1.2Vr = 180 V [Fig. 5(a)].According to (3), a new value of the dc-bus voltage referenceV ∗new

dc results around 1.2 · 150/(900/2200) = 440 V, which isacceptable as it is larger than 0.8 · V ∗ideal

dc = 360 V [Fig. 5(c)].Relation wi = Irri/(Irr1 + Irr2 + Irr3), i = 1, 2, 3, has

been used for computing the weights wi. One must note that

(3) provides a theoretical level of the new dc voltage, as themeasured PV powers and, therefore, their weights wi are sup-posed to be at their steady-state values. The abrupt variations ofthe irradiations on the concerned PV generators determine thatthe optimal power levels change; therefore, the MPPTs needsome time to readjust; moreover, the PV power signals willalways exhibit ripples due to the MPPT algorithms. It is veryprobable that this time cannot be waited, so the supervisor mustdecide the change of V ∗

dc faster than the MPPTs reach their newsteady state. Thus, the weights wi will intervene in (3) withsome transient values; therefore, the computation will give aslightly different value of V ∗new

dc in relation to the theoreticalone. This difference can be noted on the zoom in Fig. 5(c).This new reference must be low-pass filtered and then imposedto the inverter in order to prevent too large values of the gridcurrent. Between t2 and t3, all the PV generators operate inMPPT [Fig. 5(d)–(f)]. The zooms in Fig. 5(e) and (f) show that,once the dc-bus voltage decreased, the searching noise due toMPPT has slightly increased. At time t3, Irr1 comes back to itsinitial level, and the generators remain in MPPT until t4, whenboth Irr1 and Irr2 decrease abruptly and significantly, from900 to 400 and to 500 W/m2, respectively. Shortly after, onlyVo3 reaches the threshold of 180 V, but a new dc-bus voltagereference cannot be found anymore. Consequently, the controlof the third PV generator is switched from MPPT to OVL—theevolution of Vo3 and of the power provided by this generatorcan be seen in Fig. 5(b) and (f), respectively. The other twogenerators continue to operate in MPPT, obviously at reducedpower levels [Fig. 5(d) and (e)].

One can note that this latter case corresponds to a particularsituation. The new dc voltage value computed according to (3)would be 1.2 · 150/(900/1800) = 360 V if using the steady-state values of wi. On the other hand, 360 V is exactly the loweradmissible threshold for Vdc, i.e., 360 V = 0.8 · V ∗ideal

dc .


Therefore, the supervisor would theoretically allow theMPPT operation of all PV generators. However, the valuesof wi effectively used by the supervisor are not the steady-state ones, for reasons already mentioned. Moreover, the abruptdecreases of irradiance on generators 1 and 2 at t4 makePPV1 and PPV2 used for computing wi in (3) to be smallerthan the steady-state ones [Fig. 5(d) and (e)]. Therefore, themaximum of wi results are larger than 900/1800, and V ∗new

dc

results are strictly smaller than 360 V. Thus, the supervisor’sactual decision in this particular case is to degrade the MPPTon PV generator 3, making sure that voltage constraints aremet. Note that slower-than-step variations of irradiance andsmaller transients are more probable in nature; in this case, thesupervisor is more likely to decide keeping the MPPT operationby reducing the dc-bus voltage.

One can note that the dynamic performance of the MPPTcontrol law is better at negative than at positive variationsof irradiance, due to the fact that the VPV–PPV curve is notsymmetric in relation with its maximum, so the dynamics onthe rising side are different from the ones on the falling side.Note also that the MPPT can be speeded up/slowed down bysetting the integrator constant k larger/smaller.

B. Comparison With Parallel Configuration

Numerical simulation can be used in order to perform a com-parison between the supervised cascaded case and a parallelconfiguration, in which the individual choppers are connectedin parallel on a common dc link. The simulations will aim atcomparing the energy efficiencies of the two PV systems underboth balanced and imbalanced individual irradiance levels. Tothis end, modeling of losses is necessary.

A correct comparison is ensured if the two PV systemshave the same power, each PV generator can be individuallycontrolled by means of similar choppers, and the grid inverteris the same. Taking into account the size and ratings of the pre-viously described cascaded PV system, a parallel configurationallowing the same power to be provided, independent controlsof PV generators and power injection into the grid by meansof the same inverter must embed a two-stage dc–dc conversion.The block diagram of such a grid-connected PV architecturecan be seen in Fig. 6. Boost choppers 1–n are controlled tomaintain the PV generators in MPPT; they are connected inparallel on the first common dc link, denoted by dc-link 1.Its voltage must be maintained constant at V0 by the commonchopper. The voltage of the second dc link Vdc is maintainedconstant by the grid inverter, which is also in charge with thepower injection at the grid’s parameters.

The numerical simulation setup has been established asfollows. Both the cascaded and the parallel PV systems containthree PV generators. The PV choppers are the same like thosein the cascaded case and the same as the common chopper;moreover, their control parameters are the same (for details,see the Appendix). The final dc-link voltage is the same asthat in the cascaded case, i.e., Vdc = 450 V, for reasons ofgrid coupling and of using the same grid inverter, whereas theintermediary dc-link voltage can be set to V0 = 150 V in orderto make use of the choppers’ step-up ratios around three. Onlythe losses in choppers have been modeled such as to vary with

Fig. 6. Block diagram of a parallel dc–dc converter PV architecture with twodc–dc conversion stages.

the operating point [26]—because the two architectures use thesame grid inverter—and thus, the comparison will refer to thefinal dc-link power as the output power.

The irradiance scenario used in the simulation is shown inFig. 7(a), where, initially, all irradiances take the reference val-ues Irr1 = Irr2 = Irr3 = 1000 W/m2. On a 25-s time hori-zon, three events take place: at time 5 s, Irr1 decreases abruptlyto 400 W/m2; at time 10 s, the irradiances become again equaland maximum; and finally, at time 17 s, both Irr1 and Irr2

exhibit sudden decreases to 400 and 500 W/m2, respectively.In Fig. 7(b), one can see the time evolutions of the power ofinterest, namely, the optimal power totally delivered by the PVgenerators and the final dc-link power in the two cases.

The chosen parallel configuration can deliver the maximumof power irrespectively of the irradiance conditions becausethere are no supplementary constraints to meet; each PV gener-ator injects the current corresponding to its maximum power inthe dc link. As regards the cascaded case, this one can operateunder imbalanced irradiance levels with all the PV generatorsin MPPT as long as the supervisor can find a reduced dc-linkvoltage in order to allow the voltage constraints being met. Onecan see such evolution between moments 5 and 10 s in Fig. 7(b)and zoom 1). The optimal power level is around 840 W. Thedc-link power of the cascaded case is larger—around 790 W—than that provided by the parallel case—around 760 W—obviously because the latter one has two stages of losses. Onecan also identify the moment when the dc-link voltage referencehas been reduced, as the variations of the dc-link power haveincreased due to the increase of the MPPT search noise. Theefficiency of the cascaded configuration is, in this case, superiorto that of the parallel case (0.94 versus 0.9).

In conditions of equal and maximum irradiance levels, theefficiencies of the two PV architectures are even more clearlydistinguished (0.95 versus 0.89, see zoom 2) in Fig. 7).

The global efficiency of the cascaded case becomes inferiorto that of the parallel case when the irradiances are stronglyimbalanced and the simultaneous MPPT operation of all PVgenerators is not possible anymore. Such a situation is shownafter moment 17 s in Fig. 7(b) and zoom 3). The total optimal


Fig. 7. Comparison between the cascaded case and the parallel case under the same irradiance scenario from the point of view of the energy efficiency.

power is around 655 W. In this case, the supervisor of thecascaded system could not find a suitable reduced value of thedc voltage, and thus, one of the MPPTs had to be degraded.Consequently, the global efficiency has diminished to about0.76 versus 0.93 of the parallel configuration, in which the PVgenerators remain all in MPPT.

Some generalizations can be attempted at the end of thisanalysis. The two PV configurations are comparable from thepoint of view of the energy efficiency under relatively normalirradiance conditions, with a more obvious advantage of thecascaded configuration as the number of dc–dc conversionstages in the parallel one is larger. When the individual irradi-ance levels are sensibly different, the supervisor still potentiallyensures a superior efficiency of the cascaded case versus theparallel one. If the degradation of MPPT operation on somePV generators is absolutely necessary, then the order relationbetween the two efficiencies is likely to change, the cleareras the number of MPPT degradations is larger. A constantadvantage of the cascaded configuration versus the parallelone is its lower cost due to using a smaller number of powerelectronics devices and a relatively cheap digital structure tosupport the supervisor implementation.

V. CONCLUSION

This paper has investigated how the power optimization canbe achieved for cascaded dc–dc converter PV architectures.Such kinds of systems ensure good efficiency, along with quitelow cost, when compared to parallel configurations, mainlybecause the individual choppers are not required to have highboost ratios. Conversely, the simultaneous operation of all PVgenerators at MPPT, in order to maximize the global power,

supposes supplementary constraints that are met as long as thegenerators receive almost the same irradiance level. When thisis not the case anymore, dc-bus overvoltage may arise, as shownby the steady-state analysis and numerical simulations. A con-trol strategy ensuring robustness to rapidly variable irradianceconditions and respect of the voltage-limitation constraints wasproposed. Thus, each PV generator was equipped with a secondcontrol law, aiming at limiting the chopper’s output voltage.A supervisor was designed, which, for each PV generator,switches between the two control laws in order to establishthe best power regime possible under the given constraints.MATLAB/Simulink numerical simulations were performed inthe case of a single-phase grid-connected PV system, whereindividual MPPTs were implemented by a simple and robustESC method.

The main points of interest in the future concern the real-timevalidation on dedicated experimental rigs and, as theoreticaldevelopment, possible generalizations envisaging global poweroptimization by coordinated control strategies.

APPENDIX A

PV generator features:Two series-connected modules of 8 × 9 cellsCell parameters: (125 × 125)-mm 5.3-A short-circuit

currentModule open-circuit voltage 59 VTypical voltage 40 V at typical power 150 W

Power electronics switching frequency: f0 = 10 kHzChoppers’ features:

PV capacitor: capacity CPV = 4700 μF, resistanceRPV = 100 kΩ


Chopper circuit parameters: Lch = 8 mH, Rch = 320 mΩPower MOSFETs: rising time tr = 100 ns, falling time

tf = 50 ns, Rds_on = 200 mΩSchottky diodes: Vd = 0.47 V

Grid inverter features:Grid voltage: 230 V/50 HzGrid parameters: Lgrid = 1 mH, Rgrid = 170 mΩTwo-leg power MOSFETs and Schottky diodesFinal dc-link voltage: Vdc = 450 VFinal dc-link capacitor: cascaded: three series-connected

Cdc = 22 000 μF; parallel: Cdc = 4700 μFIntermediary dc-link features (dc-link 2 parallel case):

Voltage V0 = 150 VCapacitor C0 = 4700 μFResistance R0 = 100 kΩ

Choppers’ control parameters:Nonlinear current controller: gain = 10, hysteresis

width = 0.25PI voltage controller: proportional gain Kp = 10, integral

gain Ki = 250ESC MPPT control parameters:

a = 1, k = 100, ω = 100 Hz, filter bandwidth 50 HzGrid inverter control parameters:

Nonlinear current controller: gain = 10, hysteresiswidth = 0.25

PI voltage controller: proportional gain Kp = 10, integralgain Ki = 75

Supervisor: Tsv = 0.1 ms

ACKNOWLEDGMENT

This work has been partially developed within the frameworkof the Solution PV Project, financed by the French NationalResearch Agency (ANR), to whom the authors are kindlygrateful.

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Antoneta Iuliana Bratcu (M’07) received the M.S.degree in electrical engineering from “Dunareade Jos” University of Galati, Galati, Romania, in1996 and the Ph.D. degree in automatic controland informatics from Université de Franche-Comté,Besançon, France, in 2001.

Between 2007 and 2009, she was a PostdoctoralResearcher with the Grenoble Electrical EngineeringLaboratory (G2ELab), Grenoble National Institute ofTechnology, Grenoble, France. She is currently anAssociate Professor with the Department of Elec-

tronics and Telecommunications, “Dunarea de Jos” University of Galati. Hermajor fields of study include discrete and continuous optimization and hybriddynamical systems with application to energy conversion systems and manage-ment of industrial systems.


Iulian Munteanu (M’07) received the M.S. degreein instrumentation and control from Université duHavre, Le Havre, France, in 1997 and the Ph.D.degree in automatic control from “Dunarea de Jos”University of Galati, Galati, Romania, in 2006.

In 2002, he was a Fellow with the MarieCurie European Framework Program, Laboratoired’Électrotechnique de Grenoble, France, whichbecame the Grenoble Electrical Engineering Labo-ratory (G2ELab), where he was a Postdoctoral Re-searcher between 2007 and 2009. He is currently

a Lecturer with the Department of Electronics and Telecommunications,“Dunarea de Jos” University of Galati. His research work is oriented towardoptimal control of renewable energy systems.

Seddik Bacha (M’08) received the B.E. and M.S.degrees from École Nationale Polytechnique de Al-giers, Algiers, Algeria, in 1982 and 1990, respec-tively, and the Ph.D. degree from the GrenobleNational Institute of Technology, Grenoble, France,in 1993.

In 1990, he joined the Laboratoired’Électrotechnique de Grenoble. In 1998, he washabilitated to conduct research. He is currently theManager of the Power Systems Group, GrenobleElectrical Engineering Laboratory (G2ELab),

Grenoble National Institute of Technology, and is also a Professor withJoseph Fourier University of Grenoble. His research interests include powerelectronics system modeling and control, power quality, and renewable energyintegration.

Damien Picault was born in Vitry-sur-Seine, France,in 1984. He received the M.S. degree in electricalengineering from the Grenoble National Instituteof Technology, Grenoble, France, in 2007, wherehe is currently working toward the Ph.D. degreeon maximizing energy production of grid-connectedphotovoltaic systems.

His main research interests are photovoltaic plantsand power electronics modeling.

Bertrand Raison (M’03) was born in Béthune,France, in 1972. He received the M.S. and Ph.D.degrees in electrical engineering from the GrenobleNational Institute of Technology, Grenoble, France,in 1996 and 2000, respectively.

From 2001 to 2009, he was an Associate Professorwith the Grenoble National Institute of Technology.Since 2009, he has been a Professor with JosephFourier University of Grenoble. His general researchinterests are fault detection and localization in elec-trical systems and distribution network planning with

respect to fault management.

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