4. toward the design of control algorithms

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014 1447

Toward the Design of Control Algorithms for aPhotovoltaic Equalizer: Choosing the Optimal

Switching Strategy and the Duty CycleLuiz Fernando Lavado Villa, Xavier Pichon, Farshid Sarrafin-Ardelibi, Bertrand Raison,

Jean Christophe Crebier, and Antoine Labonne

AbstractThe photovoltaic equalizer is a promising response tothe problems of partial shading in photovoltaic modules. Equippedwith a network of transistors, this system can connect itself tothe unshaded cells of the photovoltaic module, gather their ex-cess current, and share it with the shaded cells. Thus, for a givenshadow, the equalizer must always choose the transistors to acti-vate and their associated duty cycle. This paper studies the impactsof these choices over power production in two parts. First, a quasi-exhaustive simulation is used to find the best transistors to activatefor maximizing power production under a given shadow. Second,changes in the duty cycle are applied and its effects evaluated byanalyzing the IV curve of the associated PV module. All simu-lations are validated through measurements. The conclusions aresummarized into behavior laws which can be used to developalgorithms for the equalizer control system.

Index TermsEmbedded systems, partial shading, photovoltaicplants, power electronics, PV mismatch.

I. INTRODUCTION

PHOTOVOLTAIC (PV) systems rate among the mostpromising renewable energy sources commercially avail-able, with a mature auxiliary power electronics technology androbust control algorithms [1]. There are two major challenges tobe addressed in order to disseminate the PV energy throughoutthe world: rising the efficiency of the PV modules and reducingproblems with intermittency [1], [2]. This paper focuses on thelatter.

The intermittency is intimately linked to the occurrence shad-ows. These can completely compromise the power productiononly by covering 10% of the module, depending on the form ofthe shadow [3]. Several authors have proposed many differentsolutions to this problem, ranging from the connections amongPV modules [3], [4] to power electronics systems embedded di-rectly into the PV module [5], [6]. These can be roughly divided

Manuscript received December 12, 2012; revised February 28, 2013;accepted April 11, 2013. Date of current version September 18, 2013. Rec-ommended for publication by Associate Editor V. Agarwal.

The authors are with the G2ELabGrenoble Electrical EngineeringLaboratory, University of Grenoble, 38402 St. Martin dHe`res Cedex,France (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TPEL.2013.2260177

into series and parallel systems [7]. All of these seek to allow thePV cells to have different currents and voltages, effectively de-coupling their power production, ultimately leading to a powerindependence among the cells.

Among the parallel systems is the PV equalizer. Because of itsflexibility, it can connect to any unshaded cells of a PV moduleand share their power with any other shaded cells. Thus, all cellsproduce at their respective optimum and the output current istheir average [8]. Its control must properly choose the transistorsto be activated and their duty cycle. These choices are the focusof this paper.

This paper is divided into six sections. Section II explains theproblems of intermittency in PV systems, the solutions devel-oped so far to solve them and the equalizer system. Section IIIdescribes the implications of the choosing which transistors toactivate and their duty cycle. Section IV proposes their the-oretical study, while Section V confirms the results throughmeasurements. Section VI concludes and comments on futurework perspectives.

II. PV SYSTEMSPartial shading is a complicated phenomenon, involving many

variables. This section introduces them and their associated ter-minology.

A. PV ModulesPV modules are composed of PV cells connected in series

or in parallel, forming groups. They are described by currentvoltage (IV) or powervoltage (PV) curves, such as the onein Fig 1. Under normal conditions, PV modules have one singlemaximum power point (MPP), which changes as the sun movesthrough the sky [2].

In order to maximize power production, the MPP is tracked inreal time during the entire day. This is done by means of a powerelectronics structure, such as a boost converter, controlled by adisturb and observe algorithm [2]. While simple and robust, thisalgorithm is unable to maximize power production if the moduleis partially shaded.

Some authors have proposed versions of this algorithm ac-tually capable of maximizing the global production under anyshadow scenario [9], [10]. However, they do not optimize theproduction of each individual PV cell group, due to the natureof the shading phenomenon [11][13].

0885-8993 2013 IEEE

1448 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 3, MARCH 2014

Fig. 1. (a) IV and (b) PV curves of a shaded and unshaded PV module.

B. Shadows in PV SystemsA shadow is a random phenomenon that filters the light that

shines over a PV module. It can be considered as 2-D, having alength and a depth.

Its length is equivalent to the number of cell groups coveredby the shadow, while its depth, also called shading factor (SF),describes how much power carried by light, or irradiance, hasbeen filtered. An SF of zero means that there is no shadow, whilean SF of one means that the totality of the irradiance is filtered.

Both of these dimensions are random phenomena. They de-pend on the environmental conditions, the shape of the objectssurrounding the PV module, and the seasons of the year.

The impact of a shadow with an SF of 0.5 and a length of 1(one shaded cell group) is illustrated by its IV curves in Fig. 1.

In Fig. 1, at the operation point 35 V and 1.6 A, all cell groupsare producing but their current is limited by those shaded. Atthe operation point 20 V and 3.8 A, only the unshaded cells areproducing. The shaded ones are in reverse bias, protected fromdestruction by bypass diodes. Either way, part of the power islost due to the shaded conditions [14].

To avoid this situation, several authors have proposed dedi-cated power electronics systems, which are embedded in the PVmodule.

C. PV Embedded SystemsEvery PV embedded system (PES) seeks to make the cur-

rent and voltage of the PV cells different while keeping themconnected together. By doing so, they weaken the impact ofthe shadow over the entire module, even though it still has a

Fig. 2. PV equalizer topology.

strong local impact over the PV cells. This is called the powerindependence principle [8].

There are two families of PES: series and parallel.The series PES manipulate the operating point of each cell

group separately. They are called distributed maximum powertracking systems in the current literature [2], [6], [11], [15], [16].

The parallel PES balance the current production by connect-ing the cell groups to one or several inductors, thus erasing localpower points. Return energy architecture [17], [18], generationcontrol circuit [19], or PV equalizer [8] are its three main ex-amples in the current literature.

The advantages and disadvantages of each approach have al-ready been studied in previous work [8]. The PV equalizer hasbeen shown as among the most efficient parallel PESs, depend-ing on the shadow [7].

D. Equalizer SystemThe PV equalizer is a parallel PES inspired from its equivalent

battery equalizer [5]. Its topology is shown in Fig. 2.The diodes (D) impose the current flow, allowing it to be

controlled by the transistors (T). The inductor (L) works as anenergy buffer, instantaneously stocking the surplus current fromthe unshaded cells. The capacitors (C) are used to filter voltagefluctuations on the cell groups (PVI to PVIV ).

The dc/dc converter connected in series with the equalizerimposes the overall current, represented by IOUT . Its value isconstantly changing as to seek the optimum power point of thePV module. To avoid any interferences, the equalizer switchesmust work at a frequency five to ten times higher than its dc/dcconverter counterparts.

Due to its concept, the architecture of this system is scalable.It can be used to design applications for many different voltagelevels ranging from PV cells to entire plants.

The advantages of the equalizer and its improvements in com-parison with other state-of-the-art applications are studied in de-tail in [8]. It is not the objective of this paper to restate what waspreviously explained. However, some details of the principlesof operation of this systems are described below to justify thecontributions of this study.

VILLA et al.: TOWARD THE DESIGN OF CONTROL ALGORITHMS FOR A PHOTOVOLTAIC EQUALIZER 1449

Fig. 3. Circuit legend adopted in this study.

Fig. 4. Bypass mode. (a) One cell group bypass. (b) Security bypass.

Fig. 5. Equalizer mode. (a) Charge phase. (b) Discharge phase.

1) Operating Modes: The equalizer has three distinct opera-tion modes: equalize, bypass, and search. For each one of them,the transistors of the topology are controlled differently. But,as a general rule, for any of the operating modes, the equalizermust choose the transistors to be controlled and their duty cycle.

To understand how the equalizer circuit work, the legend inFig. 3 will be adopted to explain the working modes.

The bypass mode allows the structure to short-circuit shadedcell groups. This is possible by applying a long discharge to theshaded cell groups, as shown in Fig. 4.

In Fig. 4(a), a single cell group is bypassed. In Fig. 4(b), allcell groups are shaded, showing an important security featureof this structure.

The search mode is used by the equalizer to detect the pres-ence of the shadows. It can assume many strategies and is cur-rently under research.

The equalize mode is the main function of the equalizer. Itdraws the excess current from the unshaded cell groups andshares it with the shaded ones. This is done through the succes-sive charging and discharging of an inductor at high frequency.Fig. 5 shows these two phases.

Fig. 6. Results of the equalize mode. (a) IV curve. (b) PV curve.

The result is a compensation in the IV curve of the system,as shown in Fig. 6.

While the equalizer is active, the PV system can produce morepower at higher voltage. Ideally, this makes the PV module morerobust to any shadow. However, the shadow can appear at anycell group, with any shape and any SF. This random behaviorbrings forward the need to properly control the equalizer inorder to constantly maximize its efficiency in redistributing thecurrent.

Thus, an important question must be answered to design acontrol that keeps the equalizer at its best performance: howdoes choosing the transistors to be active and their duty cyclealter the behavior of the PV module itself? This paper proposesan exploratory work that, by answering the question above, willprovide clues that may lead to the development of the equalizercontrol system.

III. DETAILS ON THE EQUALIZER CHOICESThe choice of which transistor to be controlled is closely

linked to the location of the shadow over the PV module. Thechoice of the duty cycle, however, is closely linked to the char-acteristics of the equalizer and its interaction with the MPPT.Each equalizer choice requires a different study methodologyinspired by these inherent differences.

A. Switching Sequence ChoiceThe transistors used during the charge or the discharge periods

constitute what is called a switching sequence and can beclassified into two types: basic and complex.

Basic switching sequences (BSS) have only one charge anddischarge period. Usually, all the cell groups of the PV module


Fig. 7. Example of a CSS. (a) P VI and P VI I charging. (b) P VI V charging.

participate in the equalizing process. An example of BSS isgiven in Fig. 5.

Complex switching sequences (CSS) are those where two ormore periods of charging and discharging are needed to makemost of the cell groups of the PV module participate in the equal-izing process. However, due to the greater number of switchesparticipating in the equalizing, CSS tend to have greater switch-ing losses than BSS. Fig. 7 shows two BSS combined into aCSS.

The switches and diodes painted in two colors participateduring charge and discharge.

Studying the switching sequences involves a large number ofshadow scenarios, all equalized using many different switchingsequences. While not exhaustive, this approach covers manypossibilities, drawing general clues concerning the influence ofthe BSS and the CSS during equalizing. Thus, it is consideredas a quasi-exhaustive study throughout the rest of this paper.

B. Choice of the Duty CycleThe equalizer can work at fixed duty cycle. This is only

possible because the PV module is a voltage-controlled currentsource, adapting itself any operating point imposed from theoutside. However, if the chosen value is not optimal, the modulewill not produce to its full capacity [8].

The role of the duty cycle is to control the amount of energythat will be transferred from the shaded to the unshaded cells.This transfer has losses which are linked to the physical proper-ties of the equalizer and the shadow. A duty cycle of zero meansthat the shaded PV cell group behaves as if it were bypassed.For example, in Fig. 7, only the dashed red path would be active.Thus, IOUT is equal to the current flowing through the inductorplus the current produced by PVIII .

When the duty cycle is optimal, the totality of the currentdrawn from the unshaded cell groups is shared with the shadedone. IOUT is the average between the currents produced by allgroups. If it is equal to 1, then the unshaded PV cell groupbehaves as an open circuit. In Fig. 7, only the solid blue pathswould be active. Thus, the diodes D5 and D2 block the passageof IOUT and all the current produced by PVI and PVII flowsthrough the inductor.

Fig. 8. Simplified equalizer circuit with losses in red. The gray module rep-resents the shaded cells.

Previous work has proposed a simple approach to calculatethe duty cycle [8], based on the following equation:

=nDCH

nCH + nDCH(1)

where n represents the number of cell groups participating inthe charge (CH) or discharge (DCH) phases of the BSS.

Under real operating conditions, the losses of the componentshave an influence over the duty cycle of the equalizer. Fig. 8proposes a simplified circuit to describe them.

By taking into consideration these imperfections, the optimalduty cycle of the equalizer for a given switching sequence andoperating voltage can be described by

=VPVD C H +RDCH IL + VDDCH + VDL

VPVC H + VPVD C H +V(2)

where RDCH , RCH , V , and IL are defined by (3)(6), respec-tively

RDCH = RTDDCH + RTDL + RL (3)RCH = RTDCH + RTDL + RL (4)V = (RCH RDCH) IL + (V DDCH V DCH) (5)IL = IPVC H IPVD C H . (6)

Equation (2) shows that the duty cycle depends on the internalresistances of the transistors and diodes, shown in bold. Thesetend to drift under different temperatures, vary for differenttechnologies, and differ from component to component.

Since there are infinite possible scenarios, the duty cyclecannot be studied with the same quasi-exhaustive approach pro-posed for the switching sequence study. Rather, it requires ageneric approach that gives an overview of its behavior princi-ples and at the same time a more specific one to validate these fora few cases. Their results are then extrapolated and generalizedto other cases.

IV. THEORETICAL STUDIESEven though the switching sequence and its duty cycle are

intertwined, their effects will be studied separately. For each ofthem, a set of variables will be considered fixed, while others


Fig. 9. IV curves of a single PV cell group used in the model.

TABLE IIMPERFECTIONS OF THE PV EQUALIZER

will be allowed to vary. This approach is useful for drawingconclusions from the superposition of the results.

The approach to study the choice of the switching sequences isa quasi-exhaustive set of simulations, all with fixed duty cycles.The idea is to apply a large number of switching sequences tomany different shadows scenarios and rank the results in termsof power. The comparison between the results is expected to giveclues on what is needed to build a switching sequence decisionalgorithm.

As for the duty cycle choice, the switching sequence are fixed,while the duty cycle itself is allowed to vary. A theoretical andgeneric approach is used at first to give the overview of theduty cycle behavior principles. It is followed by simulationsthat shows how the IV curves of a shaded PV module changefor different duty cycles.

A. System ModelThe PV module used in the theoretical study is composed of

72 cells connected in series, composing four groups of 18 cells.Each group of the PV module is modeled by SF-dependent IVcurves extracted in previous work [3], as shown in Fig. 9. Inorder to simplify the simulations, all the cells within a singlecell group are considered to have the same SF and share thesame current.

The imperfections of the PV equalizer have been measuredand are detailed in Table I.

The imperfections are considered identical during the chargeand discharge periods, and the internal resistance of the capaci-tors is considered negligible.

B. Switching Sequence StudyThe most important issue of a quasi-exhaustive study is to

determine how many scenarios are needed to reach plausibleconclusions. For this study, this issue is twofold, as the shadowscenarios and switching sequences must be chosen together.

TABLE IISFS OF THE SHADOW SCENARIOS

Limiting both of them is paramount; otherwise, thousands ofsimulations would be necessary to reach any conclusion at all.

1) Shadow Scenarios: To limit the number of shadow sce-narios, a few simplifying hypothesis are taken into account.

First, not all SFs need to be simulated, since their effect oncurrent is considered as linear [1]. Thus, four SFs were chosento study the shadow: 0.0, 0.2, 0.5, and 0.8. Second, the shadowsare considered binary in occurrence. Thus, for a PV module withfour cell groups, there are only 16 possible shapes: 0000 to 1111.Finally, shadow shapes such as 1000 or 0001 are consideredequivalent since they use similar switching sequences.

After using these hypothesis, 20 shadow cases have beenchosen, as shown in Table II. To facilitate their study, they areregrouped into four blocks, according to their similarities andpurposes.

In the first block, only one cell group is shaded at a time. Thisis especially useful to determine the effectiveness of using theBSS or CSS against local and small shadows. The scenarios inthe second block have two or more shaded cell groups but onlyone SF. Its objective is to study how the effectiveness of the BSSand CSS change with the shadow shape.

The third block is composed of scenarios with two or threeshaded cell groups, each with a different SF. In these cases, theprinciples that work on the shadow shape can be compared tothose used against the shape and SF at the same time. In the lastblock, all four cell groups are shaded, each with a different SF.These scenarios are used to understand if the equalizer can beused to equalize shaded cell groups.

The switching sequences of each shadow scenarios are de-tailed as follows:

2) Switching Sequences: Choosing switching sequences canalso be challenging, as each shadow scenario can be treated inmany different ways. To simplify their number, some hypothesisare also made.

First, no CSS will be composed by more than three BSS.Second, the BSS will try to involve as many cell groups as


Fig. 10. Three examples of the proposed convention. (a) I.II III.IV .(b) IV 4. (c) 4 3.

possible in the equalizing. Third, some BSS will either chargeor discharge using all the cell groups.

All duty cycles will be considered fixed and independent.They will be calculated using (1). This means that a single CSSmay have up to three different duty cycles.

Even with these simplifications, a total of 178 cases havebeen chosen. Representing them can be difficult since each caseuses different groups in different orders. To avoid confusion, aconvention is proposed to address this problem. To explain it,Fig. 10 will be used as an example.

Fig. 10(a) represents a BSS, which charges with groups PVIand PVII , while discharging over groups PVIII and PVIV .The equalizing process is represented by an arrow, going fromthe charging to the discharging cell groups. The groups arerepresented by roman numerals, from I to IV. When they are usedtogether during charge or discharge their numbers are separatedby a point, as in I.II or III.IV.

Fig. 10(b) represents another BSS, but with other character-istics. In it, the discharge over the entire group of cells is notrepresented by I.II.III.IV but rather by a 4, in Arabic. Arabic nu-merals are only used to represent the use of three or four groups,allowing a more compact notation.

Fig. 10(c) shows another example of the use of Arabic nu-merals. It is important to notice that the number 3 is only used torepresent contiguous groups of PV modules. If it is used duringthe charging phase, the three groups are unshaded. Conversely,if it is used during the discharge phase, the three groups areshaded.

Table III shows the result of applying this convention to Figs. 4and 5.

TABLE IIICONVENTION CODE OF FIGS. 4 AND 5

TABLE IVSOME OF THE SWITCHING SEQUENCES USED

IN THE QUASI-EXHAUSTIVE STUDY

The CSS of Fig. 5 is represented by its two BSS, namely,1st and 2nd . In Table III, the third BSS, represented by 3rd , isnot used and expressed by the symbol. Not all the switchingsequences (SwSq) used in the quasi-exhaustive simulation arelisted in Table IV due to restrictions of space.

The results from the simulations are ranked according to theirpower output. The recurring patterns among the best results areused to draw the conclusions.

3) Simulation Results: The important amount of data issuedfrom this quasi-exhaustive study require a statistical approachto mine any information from it. To do so, an indicator of theefficiency of the switching sequence is proposed by

=PProducedn

i=1(SFi Piu n s h a d e d ) Plosses. (7)

The denominator is equivalent to the total available power ofthe PV module. Thus, a of 1 means that the switching sequencedelivers all the power that the PV module can produce minuslosses.

To simplify the analysis, the switching sequences are re-grouped into five categories according to their complexity. Theyare presented in Table V, where ntot represents the total numberof cell groups within the PV module.

The BSS are divided into complete, noncomplete, and univer-sal. The complete BSS are those that involve all of the cell groups


TABLE VFIVE CATEGORIES OF THE SWITCHING SEQUENCES

Fig. 11. Overall efficiency per category.

(3 1). The noncomplete BSS are those in which either notall groups participate (1 1) or some groups participate morethan once (3 2). The universal BSS are those in which all cellgroups either charge (4 1) or discharge (1 4) together .

The CSS is divided into CSS2 and CSS3, composed by twoand three BSS, respectively.

Fig. 11 shows the mean efficiency for each category.The noncomplete BSS are those which deliver more power.

This is largely due to the fact that these strategies are bestfitted for complicated shadows, such as the ones simulated inthis study. This leads to the important conclusion that there isno single switching sequence that works for all of the shadowscenarios.

The CSS2 strategies have an overall efficiency similar to theuniversal strategy. This indicates that for some shadow scenar-ios, it might be more interesting to equalize using all of the cellgroups together instead of looking for more specific switchingsequences.

As for the CSS3 strategy, it has an overall low efficiency,making it a poor choice for equalizing.

To confirm some of these general results, each block ofshadow scenarios will be analyzed separately. Table VI showsthe two best strategies for each shadow scenario of the first blockand their switching sequences.

The first three cases have their best results by using simpleBSS, while the last two have a better performance by usingthe universal one. Thus, if the shaded and unshaded groups arecontiguous, as for the first three cases, simple BSS are a goodchoice. While if the shaded cell group is in the middle of the

TABLE VIBEST RESULTS FOR THE FIRST BLOCK

TABLE VIIBEST RESULTS FOR THE SECOND BLOCK

module or noncontiguous, the universal BSS is a straightforwardanswer to the problem.

The second block of shadow scenarios proposes more in-sight about noncontiguous shadows. Table VII shows the beststrategies.

In these cases, the universal BSS is the overall best solution.Even in cases 7 and 9, we have similar for both strategies. Thus,for the sake of simplicity, it is more interesting to systematicallyuse the universal BSS as an answer to noncontiguous shadowssuch as these.

All of these shadow scenarios above have only one SF. Thismight not be the case under real conditions, making it necessaryto understand the response of the system under nonhomoge-neous shadow shapes and SF. The best answers to these casesare listed in Table VIII.

This group is richer in information than the previous ones, asthere is no simple solution for these shadows.

Cases 10, 12, and 14 show that it might be more interestingnot to involve a mildly shaded cell group in equalizing. In cases11 and 13, such cell groups may serve either during charge anddischarge or not at all. It depends on how many SF are presentover the PV module. As for case 15, it shows that the equalizershould concentrate its efforts in compensating the highly shadedcell groups.

The conclusion from these cases is that the best choice isconditioned not only by the shape but also by the SF of theshadow scenario. The more precise is the information about theshadow, the more efficient the equalizer will be.


TABLE VIIIBEST RESULTS FOR THE THIRD BLOCK

TABLE IXBEST RESULTS FOR THE FOURTH BLOCK

The last block is composed of shadow scenarios where all cellgroups are shaded. This puts forward the challenge of choosingwhich groups charge and which discharge and how to explorethe symmetries of the shadow. The best strategies are listed inTable IX.

Cases 16, 19, and 20 confirm that mildly shaded cell groupseither charge and discharge or do nothing. Case 17 confirmsthat if the shaded and unshaded groups are contiguous, then thecomplete BSS is the answer. Finally, case 18 shows that theCSS2 can work if it profits from the symmetries of the shadowto minimize its switching losses. A total of five transistors andone diode are used in the best switching sequence (T2 , T3 , T5 ,T7 , and D10). However, they only switch four times, becauseT3 , T5 , and T7 are used in both BSS.

Two general rules may be applied to make the best choice,regardless of the properties of the shadow. First, the averagecurrent between the charging and discharging groups should be

TABLE XOPTIMAL SWITCHING SEQUENCES

maximal. This can be used to determine which will charge anddischarge depending on their SF. Second, if a CSS is required,it should minimize switching losses by using the symmetries ofthe shadow.

More specific conclusions are summarized in Table X, whichelaborates the criteria for choosing the optimum switching se-quence further in detail. In it, the shadow is classified by typeand length. There are three types, namely contiguous, noncon-tiguous, and mildly shaded. The length is described by nUSHand nSH , which are the number of unshaded and shaded cells,respectively.

These conclusions will be confirmed in Section V.

C. Duty Cycle StudySeveral parameters have a direct influence over the duty cycle,

as seen in (2). This requires a more elegant and general approachto study the problem, while keeping in mind the need to validateit through examples.

The general approach consists in finding an expression thatdirectly relates the power output and the duty cycle. This willgive an overview of the effects of the duty cycle. The exampleswill consists of PV curves of the system traced for differentduty cycles. The idea is to see how each duty cycle changes thedistribution of current within the PV module. Both results willbe compared in order to draw conclusions.

In this study, the shadow scenarios and switching sequencesare fixed, while the duty cycle is allowed to vary.

As with the previous study, a set of shadow scenarios andswitching sequences needs to be chosen. While not exhaustive,a few examples are necessary to allow some generalization ofthe observed effects. They are detailed in Table XI.

1) General Approach: For complete BSS, like the two de-scribed previously, VPVC H + VPVD C H is equal to VOUT . This


TABLE XIDETAILS OF THE DUTY CYCLE STUDY SCENARIO

Fig. 12. Output power as functions of the duty cycle. Simulation results areindicated by (sim).

helps to simplify (2), allowing its output current to be expressedby the following equation [8]:

IOUT = ICH (1 SF ). (8)Many VPVC H and VPVD C H pairs are used to estimate ICH and

IDCH , based on the IV curve of each cell group. These fourvalues, along with all the imperfections of the equalizer and theSF, are used in (2) and (8) to give the variation of power with theduty cycle. Fig. 12 shows the general results, along with thosesimulated in the next section.

For both BSS, an MPP is visible at a duty cycle value nearly15% higher than the value calculated without taking the lossesinto consideration. Thus, for a given BSS, there is a duty cyclethat compensates the imperfections of the system, thus deliv-ering more power. The simulation results follow the same gen-eral pattern and a single duty cycle for which power output ismaximal.

As for the CSS, expressing (8) is much more complicated.Thus, the results from the BSS will be extrapolated to the CSSand will also be validated directly through examples.

2) Examples Approach: The MPP in Fig. 12 brings forth thequestion: what happens within the PV module while the dutycycle changes? The answer comes from the PV curves of thescenarios from Table XI. They are traced for several duty cycles,yielding Fig. 13.

The duty cycle has a clear impact in the presence of the severallocal MPPs. If it is underestimated, the PV curves show severalMPPs. Since the charge phase is largely underestimated, theequalizer behavior approaches that of the bypass mode, whichwas explained in Section II.

As the duty cycle approaches its optimum, the current fromthe unshaded groups is gradually transferred to the shaded ones.As their currents draw close, their local MPP disappears, leavingthe PV curves with a single MPP. It rises until compensating

Fig. 13. PV curves for the duty cycle study. (a) I.II III.IV .(b) 3 IV . (c) I II.III and IV II.III .

the imperfections, thus reaching a single optimum duty cyclearound 0.6, 0.3, and 0.7 for Fig. 13(a)(c), respectively.

If the duty cycle is overestimated, the current iOUT cannotflow because of the equalizer diodes. Their unidirectional cur-rent sense makes the equalizer become the equivalent of an opencircuit, stopping power production. This explains the voltageloss in the PV curves for 0.70, 0.40, and 0.8.

As a general conclusion, the choice of the duty cycle is seento have a double influence over the output of the PV module. Asit changes the internal distribution of current among unshadedand shaded cells, it also imposes a single voltage, only when allimperfections are compensated that this single voltage reachesits maximum, effectively erasing all local MPP.

In terms of control algorithm, this study reveals a very usefultrait of the equalizer duty cycle. It can be maximized througha disturb and observe algorithm, similar to the one used by the


Fig. 14. Five major components of the test bench, clockwise: The equalizer,the microcontroller, the reference PV cell, the dcdc converter, and the shadedPV module.

MPPT. It should, however, be design as not to interfere withiOUT by constantly changing its own value. Thus, the controlsystem must be designed with these time span differences inmind.

V. EXPERIMENTAL VALIDATION

The series of experiments proposed below have the objectiveof validating the two theoretical studies proposed in this paper.For the switching sequence, the four most important scenarioswill be used to validate the ranking and decision principlesdescribed in Section IV. Each switching sequence will haveits PV curves traced and compared. For the duty cycle, thePV curves traced in Fig. 13 for the duty cycle study will bereproduced.

A. Test BenchThe test bench is composed of a partially shaded PV module,

the equalizer, a reference PV cell, a microcontroller, and a dcdcconverter, as shown in Fig. 14.

The PV module is a PhotoWatt PW1650, equipped with 72polycrystalline silicon cells, forming eight strings of nine cells.It has an open-circuit voltage of 41 V at 45 C. Each cell mea-sures 125 125 mm2 and has a 5.3-A short-circuit current at1000 W/m2 . This module reaches 36 V and 4.04 A at typicalpower (130 W). The module is located at Grenoble, France,facing south with a 35 tilt angle.

The reference PV cell is a monocristallin Phox sensor cellavailable with certain PV IV tracer applications.

The microcontroller is a microchip dsPIC33FJ16G540 em-bedded in an explorer 16 development board. It is configured tocontrol the equalizer and the dcdc converter at the same time.

The equalizer is equipped with 4 IRF9Z34N p-type and 4IRF5540FI n-type MOSFETs. Their internal resistance is of77 m for the n-type and 100 m for the p-type. The diodes areBYW81-PI Schottky diodes with a series resistance of 26 m.The inductor is made of solid wire with 22 turns, having aninductance of 100 H and a resistance 120 m. For each cellgroup, 15 ceramic capacitors of 22 F each were connectedin parallel, reaching nearly 230 F at 100 kHz, their seriesresistance is 75 m, and their parallel resistance is 6.75 m.

TABLE XIICHARACTERIZATION OF THE PLASTIC LAYERS

Fig. 15. Connection scheme for the experimental setup.

TABLE XIIIMEASURED SCENARIOS AND THEIR BSS

The dcdc converter is a buckboost topology. It is connectedto a fixed load of 100 , and equipped with two sensors forreading the input voltage and current. It traces an IV curvethe PV module. To minimize the noise of the measured data, amoving average filter is applied to it during postprocessing.

The shadow is composed of layers of translucent plastic film.Its equivalent SF was characterized through IV curve measure-ments. The results are summarized in Table XII.

The overall connection scheme of the experimental setup isdescribed in Fig. 15.

The dashed lines represent the digital impulses sent fromthe microcontroller to the close control stages. The solid linesrepresent electrical connections.

B. Experimental Validation 1Switching Sequence ChoiceTracing many PV curves in similar weather conditions can

be very difficult. To facilitate this task, only four scenarios willbe measured, one per group studied. Cases 4, 9, 12, and 18were chosen because they regroup all the characteristics neededto reach all the conclusions of the simulation section. Theyare detailed in Tables XIII and XIV, where TM represents themodule temperature, TA represents the ambient temperature,and Irr represents the irradiance during the measurements.

For each scenario, a reference measurement is made withbypass diodes. The total theoretical power of the PV module is


TABLE XIVWEATHER CONDITIONS DURING THE MEASUREMENTS

TABLE XVTOTAL POWER OUTPUT

Fig. 16. IV Curve for Group 1 (Case 4).

calculated by using the current of each PV group and a fixedvoltage of 8 V. Table XV lists the total power of each scenario.

The details of all the results are shown in Figs. 1619.In Fig. 16, the universal BSS is confirmed as the most straight-

forward answer to the problem, having the same power outputas the CSS2 strategy.

The strategies for case 9, shown in Fig. 17, confirm the ideathat the universal BSS is the best solution for noncontiguousshadow shapes.

The strategies in case 12 (see Fig. 18) confirm that a mildlyshaded cell group might be unused during equalizing, as itscurrent value is similar to the average between the unshadedand highly shaded groups.

Fig. 17. IV curve for group 2 (case 9).



Finally, Fig. 19 confirms that complicated shadow situationsrequire a more specific approach, and that the symmetries of theshadow can be used to reduce switching losses.

All results being confirmed, the conclusions summed up inTable X can be considered as accurate and valid for futuredevelopment.

C. Experimental Validation 2Duty Cycle ChoiceThe limited number of cases used during the duty cycle study

allows for a full reproduction of the simulated results. Theswitching sequences can be perfectly reproduced; however, thisis not the case for the shadow. The SF is similar to the one used


TABLE XVIDUTY CYCLE SCENARIOS

TABLE XVIIWEATHER CONDITIONS DURING THE DUTY CYCLE MEASUREMENTS

Fig. 20. Measured PV curve for the first scenario.

during the simulations, as shown in Table XVI. The irradianceand temperature changes are described in Table XVII.

The results are presented in several PV curves per case, onefor each duty cycle.

Fig. 20 validates the duty cycle choice simulation results. Forlow duty cycles, the system behaves as if equipped with bypassdiodes. There is only one duty cycle that maximizes poweroutput, considered optimal. For a higher value of the duty cycle,its open-circuit voltage starts to shrink, showing signs that thesystem becomes an open circuit.

Fig. 21 confirms that the same behavior seen in Fig. 20 canbe reproduced for another BSS. This validates the idea that anyBSS has only one duty cycle that maximizes the power outputof the PV module.

Fig. 22 confirms that the CSS may also have a duty cycle thatmaximizes power production. In this case, the values of bothduty cycles were kept the same to reduce the number of curves

Fig. 21. Measured PV curve for the second scenario.

Fig. 22. Measured PV curve for the third scenario.

and to show that both duty cycles may be controlled together.They are represented by the two numbers in the legend.

The measurements confirm that an algorithm such as a dis-turb and observe may be adapted to control the duty cycle ofthe equalizer. The same solution can also be used for CSS bycontrolling all duty cycles simultaneously. This solution mightnot be optimal, but it is simpler than controlling several dutycycles separately and risk interfering with the MPPT.

VI. CONCLUSIONA PV equalizer system is an extremely flexible power elec-

tronics structure embedded on a PV module. Its main objectiveis to mitigate the effects of partial shading by sharing the excesscurrent of the unshaded cells with the shaded ones. To do so, itmust choose which transistors to activate, called switching se-quence. Once chosen, each needs to be given a duty cycle. Bothchoices are conditioned by the characteristics of the shadow andare bound to change constantly.

The objective of this paper is to study the influence of bothchoices in the power output of the system by simulation andexperimental validation. This was done in two parts.

The first one was a quasi-exhaustive simulation study of theswitching sequence influence over the power production of ashaded PV module. An important effort was put into sim-plifying the number of possible scenarios, while remaining


representative of the phenomena to be observed, still a totalof 178 switching sequences spread over 20 different shadowscenarios were simulated. The results were ranked in terms ofpower output, and the optimal switching sequence was foundto depend on the characteristics of the shadow. Straightforwardsolutions are possible if the shadow shape is contiguous. Oth-erwise, a careful knowledge of the intensity of the shadow isneeded. These and other results are explained in detail, repro-duced through measurements, and can serve as a base for futurealgorithm development.

The second part focused on the impact of the duty cycle inpower production. Since the duty cycle was found to be depen-dent on variables whose values may vary, a different approachto its study was proposed. First, a theoretical expression linkingthe duty cycle and the power output was used to describe theirinterdependence, which was confirmed through a few examples.The equalizer was found to have only one duty cycle for whichthe power output is maximal. If the duty cycle is underestimated,the equalizer behaves like a short circuit. If it is overestimated,then the equalizer behaves like an open circuit. This was proofedby the progressive fading for the local MPPs as the duty cycleapproaches its optimum, whose value is closely linked to systemimperfections.

The results of the two parts can be used to develop a controlsystem for the equalizer. The duty cycle can be corrected by asimple disturb and observe algorithm. The switching strategy,however, needs the precise location of the shadow and its associ-ated SF. Further work will focus on the detection of the shadowand how to use recurrent patterns to predict its movement.

REFERENCES

[1] Y. Wang, X. Lin, Y. Kim, N. Chang, and M. Pedram, Enhancing efficiencyand robustness of a photovoltaic power system under partial shading, inProc. 13th Int. Symp. Quality Electron. Design, Mar. 2012, pp. 592600.

[2] A. Bidram, A. Davoudi, and R. S. Balog, Control and circuit techniquesto mitigate partial shading effects in photovoltaic arrays, IEEE J. Photo-voltaic, vol. 2, no. 4, pp. 532546, Oct. 2012.

[3] L. Villa, D. Picault, S. Bacha, A. Labonne, and B. Raison, Maximizing thepower output of partially shaded photovoltaic plants through optimizationof the interconnections among its modules, IEEE J. Photovoltaic, vol. 2,no. 2, pp. 154163, Apr. 2012.

[4] D. Picault, B. Raison, S. Bacha, J. de la Casa, and J. Aguilera, Forecastingphotovoltaic array power production subject to mismatch losses, SolarEnergy, vol. 84, no. 7, pp. 13011309, 2010.

[5] S.-H. Park, T.-S. Kim, J.-S. Park, G.-W. Moon, and M.-J. Yoon, A newbuck-boost type battery equalizer, in Proc. 24th Annu. IEEE Appl. PowerElectron. Conf. Expo., Feb. 2009, pp. 12461250.

[6] R. Giral, C. Carrejo, M. Vermeersh, A. Saavedra-Montes, and C. Ramos-Paja, PV field distributed maximum power point tracking by means ofan active bypass converter, in Proc. Int. Conf. Clean Electr. Power, Jun.2011, pp. 9498.

[7] L. F. L. Villa, L. Kerachev, J. C. Crebier, Y. Lembeye, and B. Raison,Comparative analysis of power electronics system embedded in photo-voltaic modules, in Proc. Future Power Electron. Conf., Jul. 2012.

[8] L. Villa, T. Ho, J. Crebier, and B. Raison, A power electronics equalizerapplication for partially shaded photovoltaic modules, IEEE Trans. Ind.Electron., vol. 60, no. 3, pp. 11791190, Mar. 2013.

[9] K. Ishaque, Z. Salam, M. Amjad, and S. Mekhilef, An improved particleswarm optimization (PSO)-based MPPT for PV with reduced steady-stateoscillation, IEEE Trans. Power Electron., vol. 27, no. 8, pp. 36273638,Aug. 2012.

[10] C. N.-M. Ho, H. Breuninger, S. Pettersson, G. Escobar, and F. Canales,A comparative performance study of an interleaved boost converter using

commercial Si and SiC diodes for PV applications, IEEE Trans. PowerElectron., vol. 28, no. 1, pp. 289299, Jan. 2013.

[11] C. Ramos-Paja, G. Spagnuolo, G. Petrone, M. Vitelli, and J. Bastidas,A multivariable MPPT algorithm for granular control of photovoltaicsystems, in Proc. IEEE Int. Symp. Ind. Electron., Jul. 2010, pp. 34333437.

[12] A. Safari and S. Mekhilef, Simulation and hardware implementation ofincremental conductance MPPT with direct control method using Cukconverter, IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 11541161,Apr. 2011.

[13] T. L. Nguyen and K.-S. Low, A global maximum power point track-ing scheme employing direct search algorithm for photovoltaic systems,IEEE Trans. Ind. Electron., vol. 57, no. 10, pp. 34563467, Oct. 2010.

[14] B. Patnaik, P. Sharma, E. Trimurthulu, S. Duttagupta, and V. Agarwal, Re-configuration strategy for optimization of solar photovoltaic array undernon-uniform illumination conditions, in Proc. 37th IEEE PhotovoltaicSpec. Conf., Jun. 2011, pp. 001859001864.

[15] I. Abdalla, J. Corda, and L. Zhang, Multilevel dc-link inverter and con-trol algorithm to overcome the PV partial shading, IEEE Trans. PowerElectron., vol. 28, no. 1, pp. 1418, Jan. 2013.

[16] W. Li, X. Xiang, C. Li, W. Li, and X. He, Interleaved high step-up ZVTconverter with built-in transformer voltage doubler cell for distributed PVgeneration system, IEEE Trans. Power Electron., vol. 28, no. 1, pp. 300313, Jan. 2013.

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[18] C. Olalla, M. Rodriguez, D. Clement, J. Wang, and D. Maksimovic, Ar-chitecture and control of PV modules with submodule integrated convert-ers, in Proc. IEEE 13th Workshop Control Model. Power Electron., Jun.2012, pp. 16.

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Luiz Fernando Lavado Villa was born in Foz doIguacu, Brazil, in 1984. He received the Electri-cal Engineer degree from the Federal University ofSanta Catarina, Florianopolis, Brazil, in 2009, andthe M.S. degree from the Grenoble Institute of Tech-nology, Grenoble, France, in 2010. He is currentlyworking toward the Ph.D. degree at the G2ELabGrenoble Electrical Engineering Laboratory, Univer-sity of Grenoble, St. Martin dHe`res Cedex, France.

His research interests include the interface be-tween power electronics and control applications for

shaded photovoltaic systems.

Xavier Pichon was born in Paris, France, in 1989.He received the Graduate degree in electrical powerengineering from the Grenoble Institute of Technol-ogy, Grenoble, France, in 2012. He completed hisfinal training course at the G2ElabGrenoble Elec-trical Engineering Laboratory, University of Greno-ble, St. Martin dHe`res Cedex, France. His masterwork focused on the control of the PV equalizer andon a method for shading diagnostic. He is currentlyworking toward the Ph.D. degree in the energy man-agement optimization of Li-ion storage device at the

G2Elab.


Farshid Sarrafin-Ardebili was born in Mashhad,Iran, in 1983. He received the Electrical Engi-neer degree from the Azad University of Bojnourd,Bojnourd, Iran, in 2008, and the M.S. degree from theUniversity of Grenoble, St. Martin dHe`res Cedex,France, in June 2012. His master work focused onthe study of the characteristics of the PV equalizerand methods for improving its imperfections.

Bertrand Raison was born in Bethune, France, in1972. He received the M.S. and Ph.D. degrees inelectrical engineering from the Grenoble Institute ofTechnology, Grenoble, France, in 1996 and 2000,where he was an Associate Professor from 2001 to2009.

Since 2009, he has been a Professor at the ScienceUniversity Joseph Fourier, Grenoble. His general re-search interests include fault detection and localiza-tion in electrical systems and distribution networkplanning and protection with respect to fault man-

agement.

Jean Christophe Crebier received the Bachelorsdegree in electrical engineering from INP Grenoble,Grenoble, France, in 1995, and the Ph.D. degree inpower electronics, EMC, and power factor correctionfrom the Electrotechnical Laboratory of Grenoble,Grenoble Institute of Technology, Grenoble.

In 1999, he was a Postdoctoral Researcher in theCenter for Power Electronics Systems, Virginia Tech,Blacksburg, USA, doing research in system integra-tion. In 2001, he joined the National Center for Sci-entific Research, Paris, France, as a Full Time Re-

searcher in power electronics. His main research interests include system andfunctional integration, hybrid and monolithic integration, and packaging formedium- to high-voltage active devices. His research interests also include ap-plications to the management of multicell systems such as PV, batteries, anddistributed systems.

Antoine Labonne received the Eng. and Master de-grees from the Blaise Pascal University, Clermont-Ferrand, France, in 2005.

He is currently an Electrical Engineer with theElectric Grid and Systems Team at the Grenoble Elec-trical Engineering Laboratory, University of Greno-ble, Grenoble, France. His main research interestsinclude photovoltaic energy and smart grids.

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