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High concentrator photovoltaic module simulation by neuronal networks using spectrally corrected direct normal irradiance and cell temperature F. Almonacid a, * , E.F. Fern andez a, b, ** , T.K. Mallick b , P.J. P erez-Higueras a a Centre of Advanced Studies in Energy and Environment, University of Jaen, Jaen 23071, Spain b Environment and Sustainability Institute, University of Exeter, Penryn, Cornwall TR10 9EZ, United Kingdom article info Article history: Received 2 December 2014 Received in revised form 21 January 2015 Accepted 28 February 2015 Available online 21 March 2015 Keywords: HCPV (high concentrator photovoltaic) modelling Neural networks IeV curve Atmospheric parameters Outdoor characterization abstract The electrical modelling of HCPV (high concentrator photovoltaic) modules is a key issue for systems design and energy prediction. However, the electrical modelling of HCPV modules shows a signicantly level of complexity than conventional photovoltaic technology because of the use of multi-junction solar cells and optical devices. In this paper, a method for the simulation of the IeV curves of a HCPV module at any operating condition is introduced. The method is based on three different ANN (articial neural networks)-based models: one to spectrally correct the direct normal irradiance, one to predict the cell temperature and one to generate the IeV curve of the HCPV module. The method has the advantage that is fully based on atmospheric parameter and outdoor measurements. The analysis of results shows that the method accurately predicts the IeV curve of a HCPV module for a wide range of atmospheric operating conditions with a RMSE (root mean square error) ranging from 0.19% to 1.66% and a MBE (mean bias error) ranging from 0.38% to 0.40%. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction 7HCPV (high concentrator photovoltaic) technology uses cheap optical devices to decrease the solar cell area with the aim of reducing the cost of electricity [1]. HCPV technology is widely based on the use of high efciency IIIeV MJ (multi-junction) solar cells in which each junction (usually three) responds to a particular band of the spec- trum in order to increase the efciency of the device [2]. The optical devices usually consist of a primary optical element (usually a Fresnel lens) which concentrates the light and a secondary optical element that receives the light from the primary ones to homogenize light and improve the angular acceptance angle [3]. A HCPV module is made up of several MJ solar cells and optical devices, and the rest of the components to generate electricity and dissipate the heat produced on the solar cell surface. MJ solar cells and HCPV modules have already reached high efciencies which are expected to continue growing next few years [4e8]. Because of this, HCPV technology could play an important role in the energy generation market within next few years with a cumulative installed capacity that could pass from 358 MWp in 2014 to more than 1 GWp in 2020 [9]. Bearing this in mind, the electrical modelling of HCPV modules is crucial for systems design and energy prediction, and therefore to promote the market expansion of HCPV technology [10e14]. However, due to its special features, the electrical modelling of HCPV modules shows a signicantly great level of complexity than conventional photovoltaic technology. Because of this, in recent years, the scientic community has devoted considerable efforts in developing models that reproduce the electrical performance of HCPV modules, for instance, [15e21]. These models are mainly focused in the estimation of the maximum power since allows the energy yield to be estimated and other crucial parameters for the electrical characterization of HCPV modules such as short-circuit current, open-circuit voltage, maximum power current and voltage are not addressed. The models proposed in Refs. [19,20] allow other parameters than the maximum power to be extracted since the maximum power is obtained by solving the complete IeV curve of the module. These methods offer a valuable tool for the electrical characterization of HCPV modules since a detailed * Corresponding author. ** Corresponding author. Centre of Advanced Studies in Energy and Environment, University of Jaen, Jaen 23071, Spain. E-mail addresses: [email protected] (F. Almonacid), [email protected], e. [email protected] (E.F. Fern andez). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy http://dx.doi.org/10.1016/j.energy.2015.02.105 0360-5442/© 2015 Elsevier Ltd. All rights reserved. Energy 84 (2015) 336e343
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Energy 84 (2015) 336e343

Contents lists avai

Energy

journal homepage: www.elsevier .com/locate/energy

High concentrator photovoltaic module simulation by neuronalnetworks using spectrally corrected direct normal irradiance and celltemperature

F. Almonacid a, *, E.F. Fern�andez a, b, **, T.K. Mallick b, P.J. P�erez-Higueras a

a Centre of Advanced Studies in Energy and Environment, University of Jaen, Jaen 23071, Spainb Environment and Sustainability Institute, University of Exeter, Penryn, Cornwall TR10 9EZ, United Kingdom

a r t i c l e i n f o

Article history:Received 2 December 2014Received in revised form21 January 2015Accepted 28 February 2015Available online 21 March 2015

Keywords:HCPV (high concentrator photovoltaic)modellingNeural networksIeV curveAtmospheric parametersOutdoor characterization

* Corresponding author.** Corresponding author. Centre of Advanced StudieUniversity of Jaen, Jaen 23071, Spain.

E-mail addresses: [email protected] (F. [email protected] (E.F. Fern�andez).

http://dx.doi.org/10.1016/j.energy.2015.02.1050360-5442/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

The electrical modelling of HCPV (high concentrator photovoltaic) modules is a key issue for systemsdesign and energy prediction. However, the electrical modelling of HCPV modules shows a significantlylevel of complexity than conventional photovoltaic technology because of the use of multi-junction solarcells and optical devices. In this paper, a method for the simulation of the IeV curves of a HCPV module atany operating condition is introduced. The method is based on three different ANN (artificial neuralnetworks)-based models: one to spectrally correct the direct normal irradiance, one to predict the celltemperature and one to generate the IeV curve of the HCPV module. The method has the advantage thatis fully based on atmospheric parameter and outdoor measurements. The analysis of results shows thatthe method accurately predicts the IeV curve of a HCPV module for a wide range of atmosphericoperating conditions with a RMSE (root mean square error) ranging from 0.19% to 1.66% and a MBE(mean bias error) ranging from �0.38% to 0.40%.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

7HCPV (high concentrator photovoltaic) technology uses cheapoptical devices todecrease the solar cell areawith the aimof reducingthe cost of electricity [1]. HCPV technology iswidely based on theuseof high efficiency IIIeV MJ (multi-junction) solar cells in which eachjunction (usually three) responds to a particular band of the spec-trum in order to increase the efficiency of the device [2]. The opticaldevices usuallyconsist of a primaryoptical element (usuallya Fresnellens) which concentrates the light and a secondary optical elementthat receives the light fromtheprimaryones tohomogenize light andimprove theangularacceptanceangle [3]. AHCPVmodule ismadeupof several MJ solar cells and optical devices, and the rest of thecomponents to generate electricity and dissipate the heat producedon the solar cell surface. MJ solar cells and HCPV modules havealready reached high efficiencies which are expected to continue

s in Energy and Environment,

cid), [email protected], e.

growing next few years [4e8]. Because of this, HCPV technologycould play an important role in the energy generationmarketwithinnext few years with a cumulative installed capacity that could passfrom 358 MWp in 2014 to more than 1 GWp in 2020 [9].

Bearing this in mind, the electrical modelling of HCPV modulesis crucial for systems design and energy prediction, and therefore topromote the market expansion of HCPV technology [10e14].However, due to its special features, the electrical modelling ofHCPV modules shows a significantly great level of complexity thanconventional photovoltaic technology. Because of this, in recentyears, the scientific community has devoted considerable efforts indeveloping models that reproduce the electrical performance ofHCPV modules, for instance, [15e21]. These models are mainlyfocused in the estimation of the maximum power since allows theenergy yield to be estimated and other crucial parameters for theelectrical characterization of HCPV modules such as short-circuitcurrent, open-circuit voltage, maximum power current andvoltage are not addressed. The models proposed in Refs. [19,20]allow other parameters than the maximum power to be extractedsince the maximum power is obtained by solving the complete IeVcurve of the module. These methods offer a valuable tool for theelectrical characterization of HCPV modules since a detailed

Table 1Characteristics of the high concentrator photovoltaic module used in the study.

Geometric concentration 700Primary optics SOG squared flat Fresnel lensSecondary optics Reflexive truncated pyramidOptical efficiency 0.80Type of solar cells Lattice-matched GaInP/GaInAs/GeSolar cells area 0.763 cm2

Number of solar cells 20Cooling Passive

F. Almonacid et al. / Energy 84 (2015) 336e343 337

modelling of each of the components of modules are taken intoaccount. In both methods the spectral distribution of the incidentdirect normal solar irradiance is obtained with the SMARTS (simplemodel of the atmospheric radiative transfer of sunshine) (SMARTS[22]). Once the spectral distribution is obtained, the incidentspectrum that strikes the solar cell surface is obtained taking intoaccount the optical properties of the modules. After that, the IeVcurve of each MJ solar cell is obtained from the external quantumefficiency of each junction and from different semiconductorproperties of the solar cells. Finally, the IeV curves of each cell areassociated in order to obtain the complete IeV curve of the HCPVmodule. One possible disadvantage of thesemethods is the fact thatrequire detailed information of the materials of the modules whichare not always available and advanced knowledge of semi-conductor physics, optics and different specific software. In anycase, the estimation of the IeV curve of a HCPV module and itsvalidation with long-term measurements in outdoors has not beenaddressed yet.

The simulation of the IeV curve of a module is a key factor forthe electrical characterization and design of systems and powerplants. The modelling of the IeV curve of a module allows the as-sociation in series and in parallel of modules to be done andtherefore the simulation of the IeV curve of the generator underthe time-varying atmospheric parameters. This is important forenergy prediction issues, but also to estimate the current andvoltage at a desire point of the IeV curve of the generator. This iscrucial for the design of the electrical requirements and protectionsof a system or power plant, and also because the generator works indifferent regions of its IeV curve depending on the regulation andcontrol devices used in each installation. Besides, the simulation ofthe IeV curve allows the maximum power current and voltage ofthe generator to be obtained. This is valuable information inchoosing and sizing the inverter of a grid-connected systemdepending on its module electrical configuration and the solarresource and atmospheric parameters of each specific location.Furthermore, in an off-grid-connected system, the battery voltageor charge regulator may determines the working point of thegenerator and therefore the complete IeV curve is fundamentalsince the generator works in different points of its IeV curve.

The main reason of the complexity of the electrical modelling ofHCPV modules lies in the use of MJ solar cells and optical devices.The internal series connection of several cells with different bandgap energies and the use of optical devices which modify thespectral distribution of the solar irradiance make these devicesmore sensible to the incident spectrum [23,24]. An interestingapproach for the electrical characterization of HCPV modules ispointed out in Refs. [25,26]. This approach is based on the idea thatthe electrical characteristics of a HCPV module can be estimatedfrom the spectrally corrected DNIc (direct normal irradiance) andthe cell temperature (Tcell). This is interesting since the spectralinfluence of HCPV modules is quantified by adjusting only the DNI(direct normal irradiance). In [25] a procedure to obtain themaximum power as a function of DNIc and Tcell is introduced. Theprocedure to correct DNI is based on measures gathered with iso-type solar cells, so that is more adequate for short-term and powerrating analysis. In [26] a method based on a set of analyticalequations to obtain the short-circuit current, open-circuit voltage,maximum power current, maximum power voltage and maximumpower as a function of DNIc and Tcell is described. This methodcorrects DNI by the use of the so-called “air mass function”. Becauseof this, it has the advantage that can be used in remote sites forlong-term analysis since the air mass can be easily obtained fromthe sun position [27]. This method is widely used in conventionalPV technology and has also demonstrated good results in theelectrical characterization of HCPV devices [8,28].

Based on the approach commented above, in this work weintroduce a method based on ANN (artificial neural networks) andatmospheric parameters for obtaining the IeV curve of a HCPVmodule as a function of DNIc and Tcell. There are several examples inthe application of artificial networks in the generation of the IeVcurve of conventional photovoltaic modules [29e35]. The use ofANNs is appropriate due to their ability in solving complex prob-lems related with photovoltaics and their good results concerningthe electrical characterization of concentrator photovoltaic tech-nology [36e39]. Furthermore, the method is fully based on atmo-spheric parameter and outdoor measurements. The use ofatmospheric parameters has the advantage that allows the elec-trical characterization at a desired location if the atmospheric pa-rameters are available to be done. Also, the method has theadvantage that not required detailed information about the mate-rials and characteristics of the module [21].

2. Experimental set-up

To conduct this study, a HCPV module was monitored from Julyto December 2013 at the Centre of Advanced Studies in Energy andEnvironment (CEAEMA) at the University of Jaen in Southern Spain(N 37�2703600, W 03�2801200). Themain characteristics of themoduleare shown in Table 1. The module was mounted on a high accuracytwo-axis solar tracker designed by the BSQ Company placed on theroof of the research centre (Fig. 1-left). The electrical characteristicsof the HCPV module were measured by the use of a four-wireelectronic load (PVPM 1000C40) located in the laboratory. Thecell temperature was measured with a four-wire PT100 locatedclose to the solar cell. This thermometer was located in a receiverbetween the centre and the border of the module, so that themeasured temperatures should be considered as the average tem-perature of a receiver due to the temperature distribution of a HCPVmodule [40]. This approach has been previously used and has beenconsidered as an adequate procedure for estimating the cell tem-perature of a HCPV module and for its electrical characterization[41]. In order to record the cell temperature, the temperaturesensor was connected to a data logger (Agilent 34970A) located inthe laboratory. In addition, an atmospheric station (MTD 3000 fromGeonica Company) placed on the roof of the centre linked viainternet to a Personal Computer placed in the laboratory (Fig. 1-right) recorded the main atmospheric parameters: direct normalirradiance, air temperature, wind speed or humidity. All the pa-rameters were recorded daily every 5 min. In addition, the dailyaverage values of aerosol optical depth at 550 nm and precipitablewater not provided by the atmospheric station were obtained fromMODIS Daily Level-3 data source [42].

3. Method description

The process followed to predict the IeV curve of a HCPVmodulebased on artificial neural networks is described in Fig. 2. As can beseen, the proposed method is comprised of three blocks. Themodelling approaches and input required parameters are described

Fig. 1. Experimental set-up to carry out the study at the roof of the Centre of AdvancedStudies in Energy and Environment of the University of Jaen.

F. Almonacid et al. / Energy 84 (2015) 336e343338

in more detail in next subsection. The method estimates the IeVcurve following the next three steps:

1) An ANN-based model to spectrally correct the incident directnormal irradiance as a function of AM (air mass), AOD (aerosoloptical depth) at 550 nm and PW (precipitable water).

2) An ANN-based model to estimate the cell temperature asfunction of air temperature (Tair), DNI (direct normal irradiance)and Ws (wind speed).

3) An ANN-based model to estimate the IeV curve of the HCPVmodule as function of DNIc and Tcell previously estimated withthe other two models.

3.1. ANN-based model for estimating the spectrally corrected directnormal irradiance

HCPV modules are strongly affected by the spectral distributionof the incident direct normal irradiance. The spectral distribution isaffected by the time-varying atmospheric parameters and changesduring the course of a day, month and year. The air mass has been

Fig. 2. Scheme of the proposed method for esti

proven to have the highest impact on the electrical output of HCPVmodules [43,44]. However, there are other parameters that shouldbe taken into account in order to accurately quantify the influenceof the incident spectral distribution. In particular, aerosol opticaldepth and precipitable water have demonstrated to play animportant role in the spectral characterization of HCPV modules[45,46].

The spectrally corrected direct normal irradiance is defined asthe portion of the incident spectrum that a HCPV module is able toconvert into electricity expressed as:

DNIc ¼min

�ZEbðlÞhðlÞSRiðlÞdl

min�Z

Eb;ref ðlÞhðlÞSRiðlÞdl�

ZEb;ref ðlÞdl ¼ Isc

I*scDNI*

(1)

where the index i represents the junction considered, l is thewavelength, SR(l)i is the spectral response of the i-junction, Eb(l) isthe spectral distribution of the direct normal irradiance, h(l) is theoptical efficiency of the HCPV module, Eb,ref(l) is the referencespectrum AM1.5d ASTM (American Society of Testing and Mate-rials) G-173-03 provided by the ASTM (American Society of Testingand Materials) at which MJ solar cells and HCPV modules are rated[47], Isc is the short-circuit current of the HCPVmodule at operatingconditions, I*sc is short circuit current of the HCPV module at thereference conditions and DNI* is the integral of the referencespectrum or reference direct normal irradiance.

Bearing this in mind, a model to spectrally correct the directnormal irradiance as a function of AM (as a function of air mass),AOD and PW has been introduced in Ref. [48]. Due to thecomplexity of finding and analytical expression that provides therelationship among these parameters, the model is based on arti-ficial neural networks. The spectral correction function to correctthe direct normal irradiance could be defined as:

fs ¼ IscI*sc

DNI*

DNI¼ f ðAM;AOD; PWÞ (2)

To estimate this function, a feed-forward neural network trainedwith the LM (LevenbergeMarquardt) back-propagation algorithm

mating the IeV curve of an HCPV module.

Table 3RMSE, MAE and MBE between actual data and predicted data by the ANN-basedmodel for estimating the spectral corrected function.

RMSE (%) MAE (W/m2) MBE (%)

2.92 16.49 �0.12

F. Almonacid et al. / Energy 84 (2015) 336e343 339

was developed. The ANN-based model has three nodes in the inputlayer which correspond to AM, AOD and PW, five nodes in thehidden layer and one node in the output layer corresponding to thespectral correction function. The number of hidden layer nodes wasdetermined empirically [49e52]. To find the final architecture(weights and bias and the number of nodes in the hidden layer),several ANNs with different structures were trained in order to findthe ANN that best fitted the network output to the target. The LMtraining algorithm was used to adjust the weights and bias suchthat the neural network produces the required output for the giveninputs data [53e55]. In order to train, validate and test the ANN, aset of outdoor measurements including the spectral correctionfunction and the atmospheric parameters were used for a widerange of operating conditions. Table 2 shows the maximum, mini-mum and averages values of the parameters used as input of theANN-based model for estimating the spectral correction function.

Once the ANN is training, the spectral correction function isobtained for each value of AM, AOD and PW. The spectrally cor-rected direct normal irradiance is calculated using this function andthe DNI values as:

DNIc ¼ DNI fs (3)

Table 3 shows the RMSE (root mean square error), MAE (themean absolute error) and the MBE (mean bias error) betweenactual data and predicted data which demonstrate the low marginof error of the ANN-based model for estimating the spectrallycorrected direct normal irradiance.

3.2. ANN-based model for estimating the cell temperature of aHCPV module

The operating cell temperature of the MJ solar cells of HCPVmodules affects their electrical performance. Thus, knowledge thecell temperature is crucial for their electrical characterization. Un-der real operating conditions, the cell temperature is not constantsince is affected by the direct normal irradiance, air temperatureand wind speed [56]. The methods for estimating the cell tem-perature of a HCPV modules can be classified in methods that arebased on direct measurements on the modules (electrical param-eters, heat-sink temperature) and methods based on atmosphericparameters (direct normal irradiance, air temperature, windspeed). The methods based on atmospheric parameters show theadvantage of allowing the estimation of the cell temperature of aHCPVmodule for a specific locationwithout directly measuring themodule. Because of this, they are a more appropriate approach forthe electrical characterization of HCPV modules at a desired loca-tion [57]. Taking this into account, the cell temperature of a HCPVmodule can be expressed as:

Tcell ¼ f ðTair ;DNI;WsÞ (4)

In order to estimate the cell temperature as a function of theseparameters, an ANN-based model was developed in Ref. [58]. Tofind this function, a feed-forward ANN composed of three layerswas implemented: a three nodes layer (Tair, DNI and WS) as inputlayer, a five nodes layer as hidden layer and a single node layer

Table 2Maximum, minimum and averages values of the parameters used as inputs of theANN-based model for estimating the spectral corrected function.

Parameter Maximum Minimum Average

AM 9.05 1.02 1.92AOD 0.55 0.04 0.19PW (cm) 3.29 0.39 1.71

(Tcell) as output layer. The number of nodes of the hidden layer wasempirically determined. This architecture was trained with the LMback-propagation algorithm. In order to train, validate and test theANN, a set of outdoormeasurements including the cell temperatureand the atmospheric parameters were used for a wide range ofoperating conditions. Table 4 shows the maximum, minimum andaverages values of the parameters used as input of the ANN forestimating the cell temperature. Table 5 shows the RMSE, the MAEand the MBE between actual data and predicted which demon-strate the low margin of error of the ANN-based model for esti-mating the cell temperature.

3.3. ANN-based model for estimating the IeV curve of a HCPVmodule

An ANN-based model for generating the IeV curve of Si-crystalline and thin-film photovoltaic modules has been intro-duced in Refs. [32,33]. The ANN-based model uses as input pa-rameters the global irradiance and the cell temperature. Taking thisinto account, the IeV curve of a HCPV module is generated usingthis ANN-based model and the DNIc and the Tcell previously esti-mated as inputs. As commented, the use of the DNIc allows thespectral effects on the performance of the HCPV module to bequantified. So that, the method takes into account the main pa-rameters which affect the output of a HCPV module: DNI, spectrumand Tcell.

The architecture of the ANN-based model has two neurons inthe input layers (DNIc and Tcell), three nodes in the hidden layer andfinally the output layer has the points of the IeV curve of the HCPVmodule. This architecture was trained with the LM back-propagation algorithm. For training the ANN, ten IeV curves havebeen selected following the same procedure introduced in Ref. [32].This training set has to be representative enough of the moduleperformance so the ANN trains wells. Thus, to select the operatingrange of the HCPV module, an analysis of the data distribution as afunction of the measured DNIc and Tcell was conducted, as shown inFig. 3. Based on this distribution, ten IeV curves have been selectedfor made up the training set, as shown in Table 6. In this table,curves 1, 4, 6 and 9 represent IeV curves from low to high DNIclevels with low Tcell values. Curves 2, 3, 5 and 10 represent IeVcurves from low to high DNIc levels with high Tcell values. Finally,curves 7 and 8 represent IeV curves around the maximum of thedata distribution which correspond with the average workingconditions of the HCPV module. So that, the training set is repre-sentative of the performance of the HCPVmodule in awide range ofoperating conditions. Table 6 also shows the RMSE and the MBEbetween actual and predicted IeV curves estimated as:

Table 4Maximum, minimum and averages values of the parameters used as inputs of theANN-based model for estimating the cell temperature.

Parameter Maximum Minimum Average

Tair (�C) 40.36 3.74 26.12

DNI (W/m2) 978.42 235.27 763.00Ws (m/s) 9.76 0.00 1.34

Table 5RMSE, MAE and MBE between actual data and predicted data by the ANN-basedmodel for estimating the cell temperature.

RMSE (%) MAE (�C) MBE (%)

4.68 2.51 �0.01

F. Almonacid et al. / Energy 84 (2015) 336e343340

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNi¼1

REðVÞ2i

vuut (5)

MBE ¼ 1N

XNi¼1

REðVÞi (6)

where N is the number of samples on the curve taken at smallvoltage steps and RE (V)i is the relative error between the modelledand the measured current at a voltage V. This relative error iscalculated for each value of voltage as:

REðVÞ ¼ ImodelledðVÞ � ImeasuredðVÞIsc;measured

(7)

As can be seen, the ANN-based model shows an adequate per-formance in the generation of IeV curves of the HCPV module witha RMSE ranging from 0.47% to 1.40% and a MBE rangingfrom �0.34% to 0.46%.

Fig. 3. Normalised data distribution as function of the measured spe

Table 6Reference curves for the training set of the ANN-based model for generating the IeV cu

Curve DNIc (W/m2) Tcell (�C) Isc (A) Voc (V

1 314.95 38.17 1.85 60.62 315.77 63.62 1.86 57.73 515.01 64.35 3.03 57.644 550.33 36.84 3.24 60.795 623.67 70.77 3.67 57.386 725.82 43.84 4.27 59.977 727.18 71.46 4.28 56.848 799.27 72.55 4.71 56.869 935.00 46.10 5.51 59.7810 936.59 89.18 5.52 54.80

As a summary, Table 7 shows the configuration and main fea-tures of each of the ANN-based model used to estimate the com-plete IeV curve of the HCPV module. As can be seen, the procedurefor designing the ANNs has been developed under the Matlab2011bT ANN-toolbox, so all the functions used in this study areavailable in this toolbox in order to allow the design and applicationof the method developed.

4. Analysis of results

In this section, an analysis of the results obtained using themethod outlined above for the electrical stimulation of the HCPVmodule is conducted. First, the IeV curves generated for differentoperating conditions are analysed and compared with the actualIeV curves. Second, the main electrical parameters of the HCPVmodule are extracted from the IeV curves and compared with theactual parameters for the whole period of measurement.

4.1. Estimating the IeV curve

Once the ANN-based models are trained, the IeV curves of theHCPV module can be generated for any operating condition.Figs. 4e6 show some examples of simulated versus actual IeVcurves for different operating conditions: Fig. 4 shows some ex-amples of IeV curves from different DNIc levels with low Tcell, Fig. 5shows some examples of IeV curves from different DNIc levels withhigh Tcell and finally, Fig. 6 shows some examples of IeV curves ofthe average working conditions of the HCPV module. This allows

ctrally corrected direct normal irradiance and cell temperature.

rves of the HCPV module.

) Imax (A) Vmax (V) MBE (%) RMSE (%)

1.65 54.5 0.24 0.591.63 52.5 �0.34 1.402.77 51.1 0.38 0.722.92 53.7 �0.16 1.083.40 49.9 �0.31 0.673.99 51.5 0.12 0.623.93 49.3 �0.09 0.614.32 48.4 0.46 0.925.04 49.6 �0.27 0.474.98 46.3 �0.06 0.48

Table 7Configuration and training performance of ANNs developed for generating thespectrally corrected direct normal irradiance, the cell temperature and the IeVcurves of the HCPV module.

Programing Language Matlab 2011bT

ANN-DNIcNeurons inputs 3Neurons output layer 1Neuron hidden layer 5

ANN-TcellNeurons inputs 3Neurons output layer 1Neuron hidden layer 5

ANN-IV CurveNeurons inputs 2Neurons output layer 202Neuron hidden layer 3

Maximum iteration limits 500Training function LevenbergeMarquardtPerformance function Mean Square ErrorPerformance goal 1.00e�010

Minimum gradient 1.00e�05

Fig. 5. Several examples of simulated IeV curves versus actual IeV curves of the HPCVmodule at different spectrally corrected direct normal irradiance levels with high celltemperatures.

F. Almonacid et al. / Energy 84 (2015) 336e343 341

the analysis of the method in awide range of conditions to be done.It is important to remark that these IeV curves are not used duringthe training of the ANN-based model for generating the IeV curves.As can be seen, there is a good fit between actual and generated IeVcurves for all the operating conditions considered with a RMSEranging from 0.19% to 1.66% and a MBE ranging from �0.38% to0.40%. Also, the method shows similar results for all the operatingconditions.

4.2. Estimating the electrical parameters

In order to study the accuracy of the method, the analysis in theestimation of the four characteristics points of the IeV curve iscarried out: the short-circuit current (Isc), open-circuit voltage(Voc), maximum power current (Imax) and maximum power voltage(Vmax). First, a linear regression analysis between the actual andpredicted data is performed, as shown in Fig. 7. In this figure, thesolid red line represents the perfect results and the solid green linerepresents the best fit regression line. As can be seen, there is not

Fig. 4. Several examples of simulated IeV curves versus actual IeV curves of the HPCVmodule at different spectrally corrected direct normal irradiance levels with low celltemperatures.

significantly different between two lines for all the parameters andalso the determination coefficient (R2) values are close to 1 whichindicates the good performance of the proposed method. However,it is important to note that the method yields poorest results in theestimation of Isc and Imax. This can be explained since these twoparameters are more sensible to the irradiance and spectralchanges than the others [23,59,60].

The RMSE, the MAE and the MBE between actual and predicteddata for each electrical parameter have been also calculated toanalysis the quality of the method in more detail, as shown inTable 8. As can be seen the method presents a high accuracy with amaximum RMSE of 2.49% and a MBE around 0% which indicates thesmall variation of estimated data around actual data and that themethod neither overestimates nor underestimates the electricalparameters. As in the previous analysis, the method shows the bestresults in the estimation of Voc and Vmax while the poorest resultsare given in the estimation of Isc and Imax

Fig. 6. Several examples of simulated IeV curves versus actual IeV curves of the HPCVmodule at average spectrally corrected direct normal irradiance levels and cell tem-peratures values.

Fig. 7. Linear regression analysis between actual and predicted data for the short-circuit current, open-circuit voltage, maximum power current and maximum power voltage.

F. Almonacid et al. / Energy 84 (2015) 336e343342

5. Conclusions

In this paper a method for the simulation of the IeV curve of aHCPV module is presented. The method estimates the IeV curvefrom three different ANN-based models: one to spectrally correctthe direct normal irradiance, one to predict the cell temperatureand one to generate the IeV curve of the HCPV module, so that,takes into account the main parameters that affect the output of aHCPV module: direct normal irradiance, spectrum and cell tem-perature. The method is also fully based on atmospheric parameterand outdoor measurements so has the advantage that the electricalparameters of a HCPV module can be estimated without detailedinformation about the materials and characteristics of the module.Furthermore, the use of atmospheric parameters allows the simu-lation of the complete IeV curve at a desired site if the atmosphericparameters are available to be done. In addition, the proposedmethod has the advantage that avoids using several specificssoftware for modelling each component of the HCPV module toobtain its electrical characteristics.

A complete analysis based on long-term measurements of theIeV curves of a HCPV module has been done. The analysis showsthat the method accurately predicts de IeV curve of a HCPVmodulewith a RMSE ranging from 0.19% to 1.66% and a MBE rangingfrom �0.38% to 0.40% for a wide range of operating conditions.Thus, the proposed method will allow the IeV curve of a HCPVgenerator to be simulated under the time-varying atmospheric

Table 8Root mean square error, mean absolute error and mean bias error for the short-circuit current, open-circuit voltage, maximum power current and maximum po-wer voltage.

Parameter RMSE (%) MAE MBE (%)

Isc 2.49 0.10 A 0.52Voc 0.18 0.10 V 0.13Imax 2.89 0.12 A �0.33Vmax 0.58 0.26 V 0.02

parameters with a low margin of error. This is crucial for energyyield assessments and for the design of the electrical requirementsand/or protections of a system or power plant. This is also impor-tant since the generator works in different regions of its IeV curvedepending on the regulation and control devices used in eachinstallation and therefore, the complete IeV curve needs to beknown in order to accurately predict its electrical performance. Themethod also shows a high accuracy in the estimation of the short-circuit current, the open-circuit voltage, the maximum powercurrent and the maximum power voltage with a RMSE rangingfrom 0.18% to 2.89% and a MBE ranging from �0.33% to 0.52%. Thisis valuable information in choosing and sizing the inverter of a grid-connected system and the battery voltage or charge regulator in anoff-grid-connected system. Taking this into account, the proposedmethod can be considered as a new useful tool for the electricalcharacterization of HCPV technology.

Acknowledgements

Partial funding for this study provided through EPSRC fundedBioCPV (EP/J000345/1) project. Also, this work is part of the project“Desenvolvemento de novos conceptos baseados en tecnoloxía deconcentraci�on fotovoltaica para a produci�on de enerxía el�ectricaadaptados a distintas zonas clim�aticas”, through the program“formaci�on posdoutoral do Plan galego de investigaci�on,innovaci�on e crecemento 2011-2015 (Plan I2C)” funded by theXunta de Galicia and by the European Social Fund.

References

[1] Luque A, Sala G, Luque-Heredia I. Photovoltaic concentration at the onset of itscommercial deployment. Prog Photovoltaics: Res Appl 2006;14(5):413e28.

[2] Cotal H, Fetzer C, Boisvert J, Kinsey G, King R, Hebert P, et al. IIIeV multi-junction solar cells for concentrating photovoltaics. Energy Environ Sci2009;2(2):174e92.

[3] Xie W, Dai Y, Wang R, Sumathy K. Concentrated solar energy applicationsusing fresnel lenses: a review. Renew Sustain Energy Rev 2011;15(6):2588e606.

F. Almonacid et al. / Energy 84 (2015) 336e343 343

[4] Yamaguchi M, Takamoto TAK, Ekins-Daukes N. Multi-junction IIIeV solarcells: current status and future potential. Sol Energy 2005;79(1):78e85.

[5] P�erez-Higueras P, Mu~noz E, Almonacid G, Vidal P. High concentrator photo-voltaics efficiencies: present status and forecast. Renew Sustain Energy Rev2011;15(4):1810e5. vol. 15, no. 4, pp. 1810e1815.

[6] Dimroth F, Grave M, Beutel P, et al. Wafer bonded four-junction GaInP/GaAs//GaInAsP/GaInAs concentrator solar cells with 44.7% efficiency. Prog Photo-voltaics: Res Appl 2014;22(3):277e82.

[7] Ghosal K, Burroughs S, Heuser K, Setz D, Garralaga-Rojas E. Performance re-sults from micro-cell based high concentration photovoltaic research devel-opment and demonstration systems. Prog Photovoltaics: Res Appl 2013;21(6):1370e6.

[8] Ghosal K, Lilly D, Gabriel J, Whitehead M, Seel S, Fisher B, et al. Semprius fieldresults and progress in system development. IEEE J Photovoltaics 2014;4(2):703e8.

[9] Globaldata. Concentrated photovoltaics (CPV) e global market size, compet-itive landscape and key country analysis to 2020. 2014. UK.

[10] Singh G. Solar power generation by PV (photovoltaic) technology: a review.Energy 2013;53:1e13.

[11] Nishimura A, Hayashi Y, Tanaka K, Hirota M, Kato S, Ito M, et al. Life cycleassessment and evaluation of energy payback time on high-concentrationphotovoltaic power generation system. Appl Energy 2010;87(9):2797e807.

[12] Menoufi K, Chemisana D, Rosell J. Life cycle assessment of a building inte-grated concentrated photovoltaic scheme. Appl Energy 2013;111:505e14.

[13] Fthenakis V, Kim H. Life cycle assessment of high-concentration photovoltaicsystems. Prog Photovoltaics: Res Appl 2013;21(3):379e88.

[14] Leloux J, Lorenzo E, Garcia-Domingo B, Aguilera J, Gueymard CA. A bankablemethod of assessing the performance of a CPV plant. Appl Energy 2014;118:1e11.

[15] American society for testing and materials. ASTM E 2527. Standard tet methodfor electrical performance of concentrator photovoltaic modules and systemsunder natural sunlight. 2009.

[16] Peharz G, Ferrer Rodríguez J, Siefer G, Bett A. A method for using CPV modulesas temperature sensors and its application to rating procedures. Sol EnergyMater Sol Cells 2011;95:2734e44.

[17] Fern�andez EF, Almonacid F, Rodrigo P, P�erez-Higueras P. Model for predictionof the maximum power point of a high concentrator photovoltaic module. SolEnergy 2013;97:12e8.

[18] García-Domingo B, Aguilera J, de la Casa J, Fuentes M. Modelling the influenceof atmospheric conditions on the outdoor real performance of a CPV(concentrated photovoltaic) module. Energy 2014;70:239e50.

[19] Chan N, Young TB, Brindley HE, Ekins-Daukes N, Araki K, Kemmoku YY. Vali-dation of energy prediction method for a concentrator photovoltaic module inToyohashi Japan. Prog Photovoltaics: Reserch Appl 2013;21(8):1589e610.

[20] Steinner M, Siefer G, Hornung T, Peharz G, Bett A. YieldOpt, a model to predictthe power output and energy yield for concentrating photovoltaic modules.Prog Photovoltaics: Res Appl 2015;23(3):385e97.

[21] Rodrigo P, Fern�andez E, Almonacid F, P�erez-Higueras P. Models for the elec-trical characterization of high concentration photovoltaic cells and modules: areview. Renew Sustain Energy Rev 2013;26:752e60.

[22] Gueymard C. Parameterized transmittance model for direct beam and cir-cumsolar spectral irradiance. Sol Energy 2001;71(5):325e46.

[23] Fern�andez E, Siefer G, Almonacid F, Loureiro A, P�erez-Higueras P. A twosubcell equivalent solar cell model for IIIeV triple junction solar cells underspectrum and temperature variations. Sol Energy 2013;92:221e9.

[24] McMahon W, Emery K, Friedman D, Ottoson L, Young M, Ward J, et al. Fillfactor as a probe of current-matching for GaInP2/GaAs tandem cells in aconcentrator system during outdoor operation. Prog Photovoltaics: Res Appl2008;16(3):213e24.

[25] Ant�on I, Martinez M, Rubio F, Nú~nez R, Herrero R, Dominguez C, et al. Powerrating of CPV systems based on spectrally corrected DNI. AIP Conf Proc2012;1477:331e5.

[26] King DL, Boyson WE, Kratochvil JA. Photovoltaic array performance modelSAND2004-3535. Albuquerque, New Mexico, USA: Sandia National Labora-tories; 2004.

[27] Kasten F, Young AT. Revised optical air mass tables an approximation formula.Appl Opt 1989;28(22):4735e8.

[28] Rodrigo P, Fern�andez E, Almonacid F, P�erez-Higueras P. Outdoor measure-ment of high concentration photovoltaic receivers operating with partialshading on the primary optics. Energy 2013;61:583e8.

[29] Piliougine M, Elizondo D, Mora-L�opez L, Sidrach-De-Cardona M. Photovoltaicmodule simulation by neural networks using solar spectral distribution. ProgPhotovoltaics: Res Appl 2013;21(5):1222e35.

[30] Piliougine M, Elizondo D, Mora-L�opez L S-d-C M. Multilayer perceptronapplied to the estimation of the influence of the solar spectral distribution onthin-film photovoltaic modules. Appl Energy 2013;112:610e7.

[31] Piliougine M, Elizondo D, Mora-L�opez L, Sidrach-de-Cardona M. Modellingphotovoltaic modules with neural networks using angle of incidence andclearness index. Prog Photovoltaics: Res Appl 2015;23(4):513e23.

[32] Almonacid F, Rus C, Hontoria L, Fuentes M, Nofuentes G. Characterisation ofSi-crystalline PV modules by artificial neural networks. Renew Energy2009;34(4):941e9.

[33] Almonacid F, Rus C, Hontoria L, Mu~noz F. Characterisation of PV CIS module byartificial neural networks. A comparative study with other methods. RenewEnergy 2009;35(5):973e80.

[34] Almonacid F, Rus C, P�erez P, Hontoria L. Estimation of the energy of a PVgenerator using artificial neural network. Renew Energy 2009;34(2):2743e50.

[35] Almonacid F, Rus C, P�erez-Higueras P, Hontoria L. Calculation of the energyprovided by a PV generator. Comparative study: conventional methods vs.artificial neural networks. Energy 2011;36(1):375e84.

[36] Rivera A, García-Domingo B, del Jesús M, Aguilera J. Characterization ofconcentrating photovoltaic modules by cooperative competitive radial basisfunction networks. Expert Syst Appl 2013;40:1599e608.

[37] Almonacid F, Fern�andez EF, Rodrigo P, P�erez-Higueras P, Rus-Casas C. Esti-mating the maximum power of a high concentrator photovoltaic (HCPV)module using an artificial neural network. Energy 2013;53:165e72.

[38] Fern�andez E, Almonacid F, Sarmah N, Rodrigo P, Mallick T, P�erez-Higueras P.A model based on artificial neuronal network for the prediction of themaximum power of a low concentration photovoltaic module for buildingintegration. Sol Energy 2014;100:148e58.

[39] Patra J. Neural network-based model for dual-junction solar cells. Prog Pho-tovoltaics: Res Appl 2011;19(1):33e44.

[40] Ota Y, Nagai H, Araki K, Nishioka K. Temperature distribution in 820X CPVmodule during outdoor operation. AIP Conf Proc 2012;364e367:1477. 1477,pp. 364-367.

[41] Fern�andez E, Rodrigo P, Almonacid F, P�erez-Higueras P. A method for esti-mating cell temperature at the maximum power point of a HCPV moduleunder actual operating conditions. Sol Energy Mater Sol Cells 2014;124:159e65.

[42] “MODIS Daily Level-3 data,” [Online] Available: ttp://gdata1.sci.gsfc.nasa.gov/daac-bin/G3/gui.cgi?instance_id¼MODIS_DAILY_L3. [Accessed 2014].

[43] Fern�andez E, P�erez-Higueras P, Garcia Loureiro A, Vidal P. Outdoor evaluationof concentrator photovoltaic systems modules from different manufacturers:first results and steps. Prog Photovoltaics: Res Appl 2013;21(4):693e701.

[44] Fern�andez E, Rodrigo P, Fern�andez J, Almonacid F, P�erez-Higueras P, García-Loureiro A, et al. Analysis of high concentrator photovoltaic modules in out-door conditions: influence of direct normal irradiance, air temperature, andair mass. J Renew Sustain Energy 2014;6(1).

[45] Chan N, Brindley H, Ekins-Daukes N. Impact of individual atmospheric pa-rameters on CPV system power, energy yield and cost of energy. Prog Pho-tovoltaics: Res Appl 2014;22(10):1080e95.

[46] Fern�andez E, Almonacid F, Ruiz-Arias J, Soria-Moya A. Analysis of the spectralvariations on the performance of high concentrator photovoltaic modulesoperating under different real climate conditions. Sol Energy Mater Sol Cells2014;127:179e87. vol. 127, pp. 179e187.

[47] ASTM G 173-03e1 standar tables for reference solar spectral irradiance: directnormal and hemispherical on 37 tilted surface. American society for testingand materials; 2003. p. 1e20.

[48] Fernandez EF, Almonacid F. Spectrally corrected direct normal irradiancebased on artificial neural networks for high concentrator photovoltaic appli-cations. Energy 2014;74:941e9.

[49] Reed R. Pruning algorithms e a survey. IEEE Trans Neural Netw 1993;4(5):740e7.

[50] Ghosh A, Lubkeman D. The classification of power system disturbancewaveforms using a neural network approach. IEEE Trans Power Deliv1995;10(1):109e15.

[51] Zurada J. Introduction to artificial neural systems. West Publishing Company;1992.

[52] Curry B, Morgan P. Model selection in neural networks: some difficulties. Eur JOperational Res 2004.

[53] Levenberg K. A method for the solution of certain problems in least squares.Q Appl Math 1944;2:164e8.

[54] Marquardt D. An algorithm for least-squares estimation of nonlinear param-eters. SIAM J Appl Math 1963;11:431e41.

[55] Funahashi K. On the approximate realisation of continuous mappings byneural networks. Neural Netw 1989;2:183e92.

[56] Almonacid F, P�erez-Higueras P, Fern�andez E, Rodrigo P. Relation between thecell temperature of a HCPV module and atmospheric parameters. Sol EnergyMater Sol Cells 2012;105:322e7.

[57] Rodrigo P, Fern�andez E, Almonacid F, P�erez-Higueras P. Review of methods forthe calculation of cell temperature in high concentration photovoltaic mod-ules for electrical characterization. Renew Sustain Energy Rev 2014;38:478e88.

[58] Fern�andez E, Almonacid F, Rodrigo P, P�erez-Higueras P. Calculation of the celltemperature of a high concentrator photovoltaic (HCPV) module: a study andcomparison of different methods. Sol Energy Mater Sol Cells 2014;121:144e51.

[59] Domínguez C, Ant�on I, Sala G. Multijunction solar cell model for translating I-V characteristics as a function of irradiance, spectrum, and cell temperature.Prog Photovoltaics: Res Appl 2010;18(4):272e84.

[60] Siefer G, Bett A. Analysis of temperature coefficients for III-V multijunctionconcentrator cells. Prog Photovoltaics: Res Appl 2014;22(5):515e24.


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