Online Recording a PV Module Fingerprint

IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014 659

Online Recording a PV Module FingerprintP. L. Carotenuto, P. Manganiello, G. Petrone, and G. Spagnuolo

Abstract—In many applications, the current versus voltagecurve of a photovoltaic cell, module, string, or field is acquired.A high number of samples are usually acquired, but the curve con-tains the main information in the open- and short-circuit points,as well as where it has a strong change in the slope. In this paper,these parts are called “the fingerprint” of the photovoltaic genera-tor. The fingerprint allows us to recognize the working conditionsof the photovoltaic generator, e.g., if it is affected by a partial shad-owing or not. Saving the fingerprint and discarding the other pointsof the original curve allows us to minimize the memory needs forstoring the curve without losing the main information content. Inthis paper, a numerical technique for selecting, from among thesamples of the acquired current versus voltage curve of any pho-tovoltaic generator, the ones to be included in the fingerprint isproposed. The processing steps and the memory needed to achievethe result are minimized in order to allow an implementation ofthe algorithm also in a low-cost processor for on-field real-timeapplications. The technique is validated through curves generatedby using analytical models as well as by means of some curvesacquired experimentally in outdoor conditions.

Index Terms—Diagnostic, photovoltaic (PV), photovoltaic arrayreconfiguration.

I. INTRODUCTION

THE acquisition of the current versus voltage (I–V) or powerversus voltage (P–V) curve of the generator is an opera-

tion performed in many photovoltaic (PV) applications. The I–Vcurves of cells, modules, strings, and PV fields are measured formany different purposes. They are acquired by means of a cur-rent, voltage, or load sweep through dedicated instrumentation,or by using the power-processing systems whose main functionis maximum power point tracking (MPPT) of the PV sourceitself. A good example is represented by many of the PV invert-ers in the market: they acquire the P–V curve of the string or ofthe whole field in order to drive the inverter’s MPPT algorithmtoward the absolute maximum power point. This function is runperiodically but, to the best of the authors’ knowledge, the P–Vcurve is not stored at all for any post processing purpose.

Moreover, many commercial products, performing the MPPTfunction at a string level or employing distributed MPPT(DMPPT) technologies, propose monitoring software tools

Manuscript received October 3, 2013; accepted December 3, 2013. Date ofpublication January 2, 2014; date of current version February 17, 2014.

P. L. Carotenuto, G. Petrone, and G. Spagnuolo are with the Department of In-formation Engineering, Electrical Engineering and Applied Mathematics, Uni-versity of Salerno, Fisciano Salerno 84084, Italy (e-mail: [email protected];[email protected]; [email protected]).

P. Manganiello is with the Department of Industrial and Information Engi-neering, Second University of Napoli, Aversa 81031, Italy, and also with theDepartment of Information Engineering, Electrical Engineering and AppliedMathematics, University of Salerno, Fisciano Salerno 84084, Italy (e-mail:[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/JPHOTOV.2013.2294759

aimed at visualizing the I–V curves of the PV sources, at differ-ent levels of granularity, for diagnostic purposes. In particular,in DMPPT architectures, one dc/dc converter, known as the“power optimizer,” or “microinverter” is dedicated to each PVmodule. Such devices often interact with a central unit that col-lects data concerning the modules operation and gives the useran idea of the produced power and energy. The availability ofmore detailed information, which is the whole I–V curve ofall the PV modules in the field, acquired with a predeterminedperiodicity and processed properly, would give the user fur-ther information about the sources of unexpected drops in thepower and energy productivity of the PV field (e.g., see [1], [2],and [3]).

Some data about the actual operating conditions of the sourceare mandatory in those systems that reconfigure the PV modulesof a field in some strings in order to increase the electricalpower produced in the presence of mismatching. They acquirethe I–V curve of each module periodically and perform somecalculations on these data in order to determine the best electricalconnection among the modules that maximizes the producedpower [4], [5]. Also, the curves are, or might be, processed fordiagnostic and prognostic purposes.

In all the aforementioned cases, the I–V curve of the PV gen-erator must be acquired through suitable hardware, at a suitablerate, in order to avoid undesired dynamical effects [6], and witha proper number of samples, in order to detect all the maxi-mum power points, and the voltage and current levels at whichthey occur. At the end of the acquisition process, it is evidentthat a high number of samples are useful where the knees ofthe I–V curve occur, but a very low number of samples wouldbe enough to describe the almost-constant-current and almost-constant-voltage branches of the curve itself. Many samples inthese parts of the curve are useless and increase the memoryrequirements for curve storage, e.g., aimed at the creation of adatabase that the diagnostic/prognostic function would be basedon. Moreover, the transmission of a large number of samplesfrom a module-dedicated unit to a central monitoring systemrequires a lot of time and expensive resources. The problem es-pecially arises when the I–V curves must be temporarily stored,thus, processed and transmitted by low-cost digital controllers,as in the case of reconfiguration systems or module-dedicatedpower processing units for DMPPT applications.

The problem described previously is trivial, if an I–V curvegenerated by a numerical PV model is analyzed by using a per-sonal computer: the P–V curve is obtained by doing as manymultiplications as the number of the curve samples. Afterward,one of the many numerical procedures aimed at detecting thecurve’s maxima can be used. Unfortunately, in the real applica-tions mentioned previously, the I–V curve is affected by the noise(e.g., due to quantization effects). Moreover, the implementa-tion into a digital controller requires algorithms performing the

2156-3381 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

660 IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 4, NO. 2, MARCH 2014

Fig. 1. Simulated I–V curve used for explaining the procedure. (a) Uniformconditions. (b) Mismatched conditions.

minimum number of simple operations with the lowest memoryusage.

In this paper, an approach to the digital processing of thesampled I–V curve of a PV source is proposed. The numericaltechnique is designed for requiring a very low computationalpower and memory, thus, it is suitable for a microcontrollerimplementation. The method records the fingerprints of theI–V curve: it keeps the short-circuit current and the-open cir-cuit voltage, and it especially preserves the information acrossthe knees of the curve. In this way it reduces the number ofuseless samples in the regions that are characterized by an al-most constant voltage or current. The technique is also ableto give synthetic information about the number of maximumpower points in the corresponding P–V curve; thus, if the PVgenerator is working in mismatched conditions or not. In Sec-tion II, the method is explained by referring to a PV module,but it will be evident that it can be applied to any PV source,from the cell level up to the field level, as well as to other non-linear systems, like batteries or fuel cells. In Section III, someexamples referring to experimental outdoor I–V curves are pro-posed in order to show that, even if in Section II the method hasbeen described by referring to curves generated by a numericalmodel, the proposed technique is also robust in real cases. Somedata about the execution times obtained by means of a commer-cial microcontroller are also given. In Section IV, some furtherimprovements to the algorithm are discussed. Conclusions areprovided in Section V.

II. NUMERICAL PROCEDURE

The procedure is explained by using two I–V curves obtainedby means of a numerical model widely validated in the liter-ature [7]. In the following, the procedure is explained step bystep by referring to a PV module with an open-circuit voltageVoc = 41.5 V and a short-circuit current Isc = 7 A, in STC. Thecurves, which are not obtained in STC conditions, are gener-ated by sampling the range [0,Voc] into n = 100 equally spacedvoltage values. Fig. 1 shows both the case of uniform operat-ing conditions and the mismatched case with the PV modulereceiving two different irradiance levels.

As stated in Section I, the proposed procedure allows us todetect Isc , Voc , and the knee regions of the I–V curve. The first

two values are achieved by examining the first and the lastsamples of the curve, i.e., the samples closer to the two axes sothat the paper is dedicated to the description of the procedure todetect the curve’s knees.

A. Histograms Generation

The first step involves the analysis of the way in which thesamples of the I–V curve form some clusters, with respect toboth the voltage and current axes. The voltage and current axesare divided into a suitable number of intervals, whose width ischosen on the basis of a simple analysis based on the module’sSTC data available from the datasheet and on the Voc and Iscvalues detected on the curve of Fig. 1.

As is evident from Fig. 1(a), for the range [0,Voc], an interval[VMPP , Voc] would include a large number of samples that in-tervals of the same amplitude in the range [0,VMPP ] would notbe able to collect.

Similarly, by referring to the current axis, [IMPP , Isc] wouldinclude a large number of samples that intervals of the sameamplitude in the range [0,IMPP ] would not be able to collect.

Thus, a reference value for the width of the intervals, thevoltage axis is divided into is dV = 0.2Voc , because usuallyVMPP = 0.8Voc [7].

The interval current width is smaller, because of the factthat the parallel resistance Rp is many orders of magnitudehigher than the series one. The interval current width is dI =Isc − IMPP and, according to well-known relationships [7], itis

dI

VMPP=

1Rp

=Isc

Rp,STCIsc,STC(1)

so that

dI =VMPPIsc

Rp,STCIsc,STC=

0.8VocIsc

Rp,STCIsc,STC(2)

where it has been assumed that a standard procedure [7] tocalculate the value of the parallel resistance in STC has beenapplied on the basis of the values taken from the module’sdatasheet. Alternative, Rp,STC = 200 Ω can be considered asan indicative average value [8].

Once divided, the two ranges [0,Voc] and [0,Isc] into NV andNI intervals, respectively, whose width is chosen according tothe guidelines discussed previously, two histograms per axis arecreated, thus, four histograms in total. One, in the sequel nameddensity histogram (DH) is obtained by counting the numberof samples falling in each interval. Thus, one DH is createdby referring to the voltage axis and one by referring to thecurrent axis. The second histogram, in the sequel named widthhistogram (WH) shows for each voltage (current) interval, thevalue of the current (voltage) interval covered by the samplesfalling in that voltage (current) interval itself. Fig. 2 shows thishistogram construction by referring to an interval on the voltageaxis. Eleven points fall in the interval of width dV, this givingthe bar value of such an interval for the DH. On the other side,the samples falling in the voltage interval shown in Fig. 2 covera current interval of value δI, this being the value of the bar ofthe WH related to that interval of the voltage axis.

CAROTENUTO et al.: ONLINE RECORDING A PV MODULE FINGERPRINT 661

Fig. 2. Construction of the WHs.

Figs. 3 and 4 show the WH and DH histograms referring toboth the cases shown in Fig. 1. The axes scales refer to theI–V curve, which has been left to give a correlation between thesamples distribution and the bars heights.

The histograms in the case of a uniform operation modeshown in Fig. 3 reveal clearly that one plateau in the currentexists; thus, the PV module works with only one irradiationlevel. This result is confirmed by the WH referred to the voltageaxis, which indicates a clustering of the samples only close tothe open-circuit voltage.

The histograms shown in Fig. 4 refer to the mismatched case.They clearly show the presence of two plateaus in the current.This indication is confirmed by the histogram referred to thevoltage axis, because it shows that the samples do not onlyaggregate close to the Voc , as in the uniform case, but also at anintermediate voltage value. It is worth noting that, if two or morecurrent plateaus fall within the same interval of width dI, theycannot be distinguished so that too large a dI does not allow us todetect the presence of light shadowing affecting a part of the PVsource, because in this case, the difference between the currentplateaus is smaller than dI. This aspect will be discussed muchmore in depth in the final part of this paper. The curves usedfor the analysis are generated through a model with a uniformvoltage sampling. This is the reason why the DHs do not giveany useful information. As shown after in this paper, their rolebecomes important when real I–V curves are considered.

Once the histograms are generated, the next step is aimed atdetecting where the points of curvature, thus the knees, of theI–V curve are, namely the regions where the maximum and theminimum power points in the P–V curve occur. This operationmust be done with the lowest possible computational burden. Apossible approach is described in the section that follows.

B. Histograms Processing

The simplest way of obtaining an indication of the regionswhere the knees in the I–V curve occur, is to calculate thedifference between the voltage and the current WHs. In order tohave comparable values, one of the two WHs is suitably scaledup in order to have bars with comparable values in both theWHs.

(a)

(b)

(c)

(b)

Fig. 3. Histograms for the uniform case. (a) and (b) are the WHs. (c) and(d) are the DHs.


(a)

(b)

(c)

(d)

Fig. 4. Histograms for the mismatched case. (a) and (b) are the WHs. (c) and(d) are the DHs.

The first step of the scaling procedure consists in taking themaximum values of the bars appearing in the two WHs, namedWHV and WHI in the following:

MV = MAX {WHV (1) ,WHV (2),WHV (3), ...}MI = MAX {WHI (1) ,WHI (2),WHI (3), ...} .

Afterward, the absolute maximum is taken

M= max{MV ,MI }

so that the following scaled values and the corresponding his-tograms are obtained:{

WHV (1) · M

MV, WHV (2) · M

MV, WHV (3) · M

MV, ...

}(3)

{WHI (1) · M

MI, WHI (2) · M

MI, WHI (3) · M

MI, ...

}. (4)

At the end of this scaling process, the largest bars in the twoWHs have the same height. It is worth noting that the scalingrequires only one division and as many multiplications as thenumber of bars of the WH that needs to be scaled up; thus, anumber which is significantly lower than the number of samplesin the I–V curve.

After the WHs scaling, each sample of the original I–V curvefalls into one current interval and one voltage interval. Thus, ithas two values associated with it: the values of the normalizedbar heights of the current and voltage intervals it belongs to. Forinstance, if one sample of the I–V curve falls into the secondvoltage interval and into the 27th current interval, the valuesassociated with it are{

WHV (2) · M

MV, WHI (27) · M

MI

}. (5)

These values are shown, with blue and red bars, respectively,in the same plot, in Fig. 5 for the both the homogeneous and forthe mismatched cases.

Because of the fact that, in general, the ranges [0,Voc] and[0,Isc] are divided into different numbers of intervals of widthdV and dI, respectively, the two normalized WHs (3) and (4)have a different number of bars; thus, the difference betweenthe two histograms is not possible because there is not a directcorrespondence between the two WHs. Therefore, the differenceis done for every sample of the I–V curve, because each sam-ple belongs to only one interval of the voltage axis and to onlyone interval of the current axis. The difference between thesetwo values, calculated for every point of the I–V characteristic,results in the new bar plot shown in Fig. 5 for both the homo-geneous and for the mismatched cases. This new histogram hasone bar for each sample of the I–V curve. For instance, by re-ferring to the point in (5), the new histogram has for that pointa bar of height equal to

WHV (2) · M

MV− WHI (27) · M

MI.

It is worth noting that this operation, as the creation of thehistogram in the preceding step, is quite cheap in terms of cal-culation time and memory resources needed.


(a)

(b)

Fig. 5. Bar charts for each sample and difference between the bars for the(a) uniform and (b) mismatched cases.

Fig. 5 shows the results for both the cases under analysis. Foreach case, the scaled bars for each sample are reported in blueand red so that the bar chart obtained after the difference betweenthe bar values, sample by sample, is easily interpreted. The plotsof the difference between the bar values shown in Fig. 5 exhibitsome changes in the sign of the bar heights. Negative bars occurin the regions where the samples cover a wide voltage range(highest bars in the WH referred to the current axis) and a smallcurrent range (lowest bars in the WH referred to the voltageaxis), thus, in the almost horizontal parts of the I–V curve. Onthe contrary, positive bars occur in the regions where the samplescover a small voltage range (lowest bars in the WH referred tothe current axis) and a large current range (highest bars in theWH referred to the voltage axis), thus in the almost verticalparts of the I–V curve. It is evident that the transition regions,from positive to negative values and vice versa, of the bar plotare those ones where neither a high slope nor a low slope of theI–V curve is detected so that they are close to the knees of thecurves. Fig. 5 shows that a point close to each knee is picked thisway. This is a good starting point for a refinement of the kneebounding. In particular, in Fig. 5, the red crosses are the startingpoints for the maxima and the blue crosses are the guess pointsfor the valleys bounds search, respectively. Both are passed tothe procedure described in the section that follows.

In the next section, a procedure for determining the initial andthe final sample bounding the regions of the I–V curve where achange in the slope occurs is explained. It is almost similar tothat procedure, well known as Perturb and Observe, used in theMPPT of PV systems.

C. Knees Bounding

The points marked by crosses in Fig. 5 are used as guesssolutions for a local search, performed by means of a perturba-tive algorithm that starts from each cross and moves toward thepeak (valley) of the P–V curve until the latter is bounded. Forinstance, by referring to a peak in the P–V curve, starting fromthe crossed point, the analysis of the samples is done by mov-ing by a suitable step ΔV toward the closest maximum powerpoint. When the first sequence of two samples, whose voltagediffers by ΔV at least, for which a power decrease is detected,then, the last sample and the one considered two steps beforeare taken. These are the initial and final points of the region inwhich one knee of the I–V curve occurs. Thus, the maximumpower point belongs to the detected interval and it can be storedas well. Similarly, the valleys, each one of them belonging toa region including a minimum power point between two con-secutive maximum power points in the P–V curve are detected.Nevertheless, the valleys are sharper than the maximum powerpoints so that three samples for their description are too much.Thus, the perturbative approach is used to detect the valley,and only the sample in the center of the detected valley, thusplaced a step before a power increase is detected, is stored inthe fingerprint.


(a)

(b)

(c)

Fig. 6. Description of the procedure for the knee bounding. (a) General case.(b) Final result for the case of Fig. 1(a). (c) Final result for the case of Fig. 1(b).

The operation described previously, clearly inspired by a per-turbative approach to tracking the maximum power point, isdescribed in Fig. 6. In this example, the procedure starts fromthe sample on the left side, picked by means of the precedingstep of the procedure [see Fig. 5(a)]. By moving toward the rightside with a step ΔV = 1 V, in three steps, the peak is climbedand detected so that the last sample and the two before it arestored as the left and right samples bounding the peak as wellas the central sample of the bound.

Fig. 6 shows the points analyzed by the climbing procedurefor both the curves considered up to now. No more than threesteps are needed to bound each maximum power point or valley.

It is worth noting that the product between the current andthe voltage value of every sample analyzed by the perturbative

approach, thus for a very small fraction of the samples in thewhole I–V curve, is calculated. It is well known that this opera-tion is quite expensive for many digital devices, but it is done asmany few times as the initial point detected by the histogramsdifference is more close to the knee. A small ΔV value wouldrequire many steps, thus an increased number of multiplications,but it would allow a narrower bounding of the knee. Moreover, asmall ΔV allows us to detect small differences of the irradiancelevel affecting different sections of the PV source. Indeed, inthis case, a small knee of the I–V curve corresponds to a slightlyprominent peak in the P–V curve, which can be detected onlyby analyzing the curve by moving with a small step ΔV [9].

Unfortunately, in real applications, when the I–V curve isacquired on the field, the noise affecting some consecutive sam-ples might worsen the result of the perturbative algorithm usedto bound the knee region. As a consequence, a too small ΔVvalue cannot be used for the analysis of real curves.

At the end of this final step of the algorithm, the number ofpeaks of the P–V curve is known so that it’s working conditions,i.e., uniform or mismatched, are available. On the basis of thenumber of peaks, it is also known the number of the irradiancelevel the PV source is subjected to.

For each I–V curve, knee corresponding to a maximum of theP–V curve, three points are stored: the two at the boundariesand the central one, close to the maximum itself. For each kneecorresponding to a minimum in the P–V curve, one point justplaced close this minimum is stored. Consequently, a compres-sion ratio (CR), defined as the ratio between the number of thepoints detected by the proposed algorithm; thus, the PV sourcefingerprint and the initial number of samples in the I–V curveare calculated as

CR =3 · Npeaks + Nvalleys + 2

Ns

where Npeaks and Nvalleys are the number of knees, peaks, andvalleys of the P–V curve, respectively, detected by the proposedalgorithm, Ns is the initial number of samples, and the value 2at the numerator is added because the algorithm also stores thesamples in short-circuit and open-circuit conditions.

The total number of operations required by the algorithmdeserves a final comment. A sample-by-sample analysis of theP–V curve to extract the fingerprint would require 2Ns currentby voltage multiplications; the detection of the peaks and valleysbeing strongly influenced by the noise affecting the acquireddata.

Instead, by neglecting the number of sums and subtractions,which have a low computational impact in digital controllers,the proposed algorithm requires a very low number of multi-plications and divisions. Two divisions are needed to calculatethe DHs mean values (see Section II-D). One division and anumber of multiplications not bigger than the maximum valuebetween NI and NV is required by the scaling-up process of theWHs already described in Section II-B. Finally, the proceduredescribed in Section II-C requires further multiplications, butthe guess solution ensured by the previous steps of the algo-rithm allows us to keep the number of multiplications very lowwith respect to Ns .


D. Further Actions in Case of Heterogeneous Sampling

Two further steps are needed if the algorithm is used to an-alyze real I–V curves, which are not generated by a model butacquired on the field. Indeed, in this case, the curve samplingmight be irregular and/or it might be affected by the quantiza-tion effect introduced by the A/D converters. For instance, ifthe A/D converter is settled to acquire samples at the maximumresolution at high irradiation levels; for low irradiances, a poorresolution results in few I–V samples.

The coarsely sampled regions, and especially, the heteroge-neous sampling of the I–V curve, might worsen the quality ofthe WHs. As a consequence, the histogram obtained by the dif-ference between the two WHs, shown in Fig. 5 for the two casesanalyzed previously, might show a large number of inversionpoints. Thus, the procedure described in the previous sectionmust be launched many times, one for each inversion point, thisresulting in long calculation times. These fakes do not result inreal knees of the I–V curve so that a high percentage of the cal-culation time becomes useless. Thus, the procedure describedin Section II-C is not applied to the inversion points falling intothe coarsely sampled regions, the latter being detected by usingthe DHs, which have been shown in Figs. 3 and 4 for the twoexamples considered previously. In particular, for each DH, theaverage value of the number of samples included in each bar isfirst calculated. This operation also requires one division, thusalso in this case the number of nonlinear operations is very lowwith respect to the number of samples in the I–V curve. Theaverage value of the DHs is indicated in Fig. 3, and in Fig. 4by means of a dashed line. The samples falling in the voltageand current intervals whose bars heights are both lower than therespective average values are representative of a coarsely sam-pled region. Such samples are included in the fingerprint andadded to those ones selected by means of the procedure stepsdescribed up to now. It is worth noting that the points savedat this stage must belong to a portion of the curve where boththe DHs indicate a coarse sampling. Indeed, the samples havingonly one of their own DH bars height below the average belongto portions of the curve that are under sampled, but owing to analmost constant current or to an almost constant voltage region.

In Section III, some cases are discussed. They do not refer toI–V curves numerically generated by means of a model, but tocurves experimentally acquired in outdoor conditions.

III. EXPERIMENTAL EXAMPLES

I–V curve sampling has been done at a fixed current stepthrough an A/D converter with voltage and current LSB equalto 161 mV and 14 mA, respectively. The A/D converter coversa 0–10 A current range and a 0–120 V voltage range, which aresuitable for acquiring the PV curves of the most common PVmodules available in the market. In both examples, dV = 4 Vand dI = 100 mA.

A. Three Levels of Irradiance on the Same Module

The curves used in the examples that follow refer to a SunoweSF125 × 125–72-M(L) monocrystalline module, with 180-W

(a)

(b)

Fig. 7. WHs for the first experimental example.

peak power, equipped with three bypass diodes, and thus ableto show up to three knees in its I–V curve.

The I–V curve refers to the PV module working in a deepmismatched condition, with three different irradiance levels af-fecting the three sections it is made of. As shown in Fig. 7, themodule works at a low irradiance level so that its short-circuitcurrent is almost low. The third knee, at a high voltage, appearsat a current level that is about 200 mA; thus, the constant valueof the quantization level gives a coarse sampling of the curve inthat voltage range.

Moreover, the series and parallel resistances of the module,which might also be influenced by the measurement systemand/or cabling, are far from being close to their ideal values, thus,zero and infinite, respectively. Therefore, the almost constantcurrent and voltage regions are far to be almost horizontal andvertical, respectively.

The WHs shown in Fig. 7 clearly put into evidence wherethe slope changes occur in the I–V curve. Both the DHs, shownin Fig. 8, have small bars in the region belonging to the high-voltage knee, which is really described by very few samples.

The difference between the WHs, shown in Fig. 9, revealssome points of inversion so that the crosses are close to themaximum power points and to the valleys.

Fig. 10 shows the final fingerprint of the module in the P–Vplane. The red dots at the left and right extremes of the voltage


Fig. 8. DHs for the first experimental example.

Fig. 9. Bar chart obtained by calculating the difference of the normalizedWHs for the first experimental example.

Fig. 10. Module fingerprint in the P–V plane.

Fig. 11. Experimental evaluation of the calculation time (220 μs).

range in the bottom part of the plot are the samples at the open-circuit voltage and the short-circuit current, respectively. Thelight blue, red, and green sequence of dots characterizes themaximum power points. The valleys are marked with a bluedot, the one at about 30 V being coincident with the left-sidepoint of the third maximum power point at the highest voltage.On the right side of the figure some points are evidenced by redcrosses and they are included in the final fingerprint of Fig. 10.These points fall within the intervals where the DHs are bothbelow their respective average values (see Fig. 8) so that theyare taken in order to improve the reconstruction of the curvewithout increasing the size of the fingerprint significantly.

The experimental evaluation of the calculation time neededby the algorithm has been conducted on a Renesas V850ES/FJ332-bit single-chip microcontroller. As shown in Fig. 11, thecalculation time is few hundreds of microseconds for the con-sidered I–V curve. Such a time is significantly lower in the caseof a PV generator working in homogeneous conditions, thusexhibiting one maximum power point only.

This gives a realistic idea of the execution times in PVmodule-dedicated applications. In string dedicated applications,with more than three peaks occurring in the I–V curve, the exe-cution time can be longer, but a much more powerful hardware,whose cost is negligible with respect to the electronics involvedin that case, can be employed. In those applications in whichthe I–V curve of many modules is acquired and they have tobe processed by the proposed algorithm running on a central


Fig. 12. WHs for the second experimental example.

unit, a simple evaluation can be done by referring to a domesticPV plant consisting of ten modules. According to the EN50530standard, the maximum typical rate of change of the irradiancelevel is 100 W/m2 /s. If the same digital device has to processten I–V curves (by supposing that a suitable hardware has al-lowed the acquisition of the I–V curves of the ten modules),even if the processing of each curve should need a time fivetimes longer than the one obtained for the application examplereported in the manuscript, the irradiance level would changeby almost 1 W/m2 , which is a negligible quantity that allowsus to conclude that all the curves are processed while the irra-diance level keeps more or less constant. The upper bound ofthe computation time for the proposed method depends on theapplication, but the typical, and even worst if referred to a singlePV module, case shows a calculation time that is significantlyshorter than the time during which the irradiance can have arelevant variation.

B. Slightly Shadowed Module

The second example concerns a slightly shadowed STP245–20/Wd Suntech module showing an I–V curve with two currentplateaus differing by a few tens of milliamperes.

It is evident that, if the difference between the current plateausis smaller than the width of the current interval dI, the two differ-ent irradiance levels cannot be recognized. Instead, in the casepresented in this section, the two plateaus are clearly detectedby means of the current WH shown in Fig. 12.

Fig. 13. Bar chart obtained by calculating the difference of the normalizedWHs for the second experimental example.

Fig. 14. Module fingerprint in the P–V plane.

The difference between the two WHs shown in Fig. 13 con-firms that the current step occurring at about 10 V is correctlydetected: the red cross at about 20 V will allow us to detect theabsolute maximum power point. The red and blue crosses atabout 10 V suggest that there is another maximum power point,and the consequent valley, whose position has to be refined bymeans of the procedure described in Section II-C.

Fig. 13 also reveals that the visible current step at about 10 Vin the I–V curve does not give rise to a maximum power pointin the P–V curve. This is due to the fact that the modules inthe same panel are subjected to two different irradiance levelswhich are only slightly different, but the peculiarity is in thefact that the short-circuit current of the one receiving the lowerirradiation is higher than the maximum power point current ofthe one receiving the highest irradiation. This effect is amplifiedby the low slope of the I–V curve at its right-hand side.

In these conditions, the procedure described in Section II-Cis not able to find neither the maximum power point nor thevalley at low voltages, merely because they do not occur in theP–V curve. Indeed, the fingerprint shown in Fig. 14 includes theshort-circuit and open-circuit samples, at the two extremes ofthe figure, and a point close to the maximum power point, inred, and its bounds, in light blue and green.


IV. CONCLUSION

In this paper, a numerical method, which allows us to givethe fingerprint of a PV source, is introduced. The fingerprint in-cludes the main points of the curve, that are the open-circuit andthe short-circuit points, the maximum and the minimum powerpoints, as well as two points bounding each region including amaximum power point. The method is useful for extracting themain operating features of the source, by eliminating the pointswhere the information content is lower, which are those pointsin the linear parts of the curve itself. The main applications arein the field of monitoring and diagnostics as well as dynamicalreconfiguration of PV strings. The procedure is explained bymeans of two numerical examples and its robustness is shownalso on experimentally acquired I–V curves. An experimentalmeasurement of the time needed by the online application ofthe procedure reveals that, in this worst case, it only needs a fewhundreds of microseconds on a low cost microcontroller.

The proposed algorithm is especially focused on the locationand the number of maximum power points shown by a P–V curveof a PV array. From this point of view, it would be useful alsofor diagnostic purposes, e.g., in conjunction with approachesaimed to identify the actual value of the series resistance of thePV module, which is an indicator of its state of health.

The algorithm is robust with respect to the type of samplingused in acquiring the I–V curve. It gives the PV generator finger-print provided that the parameters of the algorithm are suitablydesigned.

Some events leading to an inaccurate result of the proposedalgorithm are described here below.

In the presence of more than one current plateau in the I–Vcurve, due to the fact that the module is subjected to a partialshading, the proposed method misses one knee if the differencebetween two consecutive plateaus is smaller than dI. Neverthe-less, depending on the Rs value, two current plateaus differingfor a small current value might not give rise to an MPP in theP–V curve so that a minimum dI value can be designed, as afunction of Rs , in order to avoid detection of those I–V curveknees that do not lead to MPPs in the P–V curve.

As for the voltage, the dV value is obviously smaller than thevoltage difference between two consecutive constant-voltageregions of the I–V curve, because this distance is usually equalto Voc /N, depending on the number N of bypass diodes includedin the PV module.

Intermediate values of the I–V curve slope, e.g., due to toosmall a value of the parallel resistance and due to too big a valueof the series resistance, can cause a missed change in the sign

of the bar plot whose calculation is described in Section II-B.In this case, the knee is missed. Furthermore, checks can beintroduced in the algorithm in order to detect conditions thatmight be due to module malfunctioning.

Too large a step size ΔV , used in the part of the proceduredescribed in Section II-C, might lead to missing of an MPP. Thismight happen if two consecutive current plateaus are quite close;thus, two modules are subjected to similar irradiance levels. Inthis case, the MPP in the P–V curve is slightly pronounced anda large ΔV hides the presence of the MPP. This occurs also inperturbative MPPT methods using too large a perturbation step.

Last, but not least, failures in the procedure acquiring the I–Vcurve samples, e.g., due to the switching converter performingthe electrical sweep, to noise or to the bad control or settingof the A/D converters, might worsen the performances of theproposed procedure as of any other postprocessing tool.

REFERENCES

[1] http://www.solaredge.com/groups/monitoring/module-monitoring, Dec.2013.

[2] E. Drury, T. Jenkin, D. Jordan, and R. Margolis, “Photovoltaic investmentrisk and uncertainty for residential customers,” IEEE J. Photovoltaics,vol. 4, no. 1, pp. 278–284, Jan. 2014.

[3] D. C. Jordan and S. R. Kurtz, “The dark horse of evaluating long-termfield performance—Data filtering,” IEEE J. Photovoltaics, vol. 4, no. 1,pp. 317–323, Jan. 2014.

[4] www.bitronenergy.com, Dec. 2013.[5] P. L. Carotenuto, S. Curcio, P. Manganiello, G. Petrone, G. Spagnuolo, and

M. Vitelli, “Algorithms and devices for the dynamical reconfiguration ofPV arrays,” presented at the Int. Exhib. Conf. Power Electron., Intell.Motion, Renewable Energy Energy Manage., Nuremberg, Germany, May14–16, 2013.

[6] M. Seapan, C. Limsakul, T. Chayavanich, K. Kirtikara, N. Chayavanich,and D. Chenvidhya, “Effects of dynamic parameters on measurementsof IV curve,” in Proc. IEEE 33rd Photovoltaic Spec. Conf., May 11–16,2008, pp. 1–3.

[7] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, Power Electronicsand Control Techniques for Maximum Energy Harvesting in PhotovoltaicSystems, 1st ed. Boca Raton, FL: CRC, 2012.

[8] A. Orioli and A. Di Gangi, “A procedure to calculate the five-parametermodel of crystalline silicon photovoltaic modules on the basis of thetabular performance data,” Appl. Energy, vol. 102, pp. 1160–1177, Feb.2013.

[9] A. Maki, S. Valkealahti, and J. Leppaaho, “Operation of series-connectedsilicon-based photovoltaic modules under partial shading conditions,”Progress Photovoltaics: Res. Appl., no. 20, pp. 298–309, 2012.

Authors’ photographs and biographies not available at the time of publication.

Documents

Online Recording a PV Module Fingerprint