Keywords

1 Introduction

High-concentrator photovoltaic (HCPV) technology is based on the use of optical devices that focus the light received from the Sun on the solar cell surface. The aim of these systems is to decrease the cost of the electricity by decreasing the semiconductor material by mounting less expensive optical devices [1]. HCPV technology is widely based on the use of high efficiency multijunction (MJ) solar cells; a primary optical element (usually a Fresnel lens), which concentrates the light; and a secondary optical element, which receives the light from the primary one to homogenize light and improve the angular acceptance angle [2]. An HCPV module is made up of MJ solar cells, an optical system for each cell, and the rest of the components required to generate electricity and dissipate the heat produced on the solar cell surface. MJ solar cells and HCPV modules have already reached high efficiencies, which are expected to continue growing in the next few years [3–5]. Thus, HCPV could play an important role in the energy generation market in the coming years [6]. However, due to the use of MJ solar cells and optical elements, the electrical modelling of HCPV devices shows a significant level of complexity than for conventional photovoltaic (PV) technology.

Artificial neural networks (ANNs) have proven to be helpful in solving complex problems and studying nonlinear systems. In the field of PVs, ANNs have been successfully applied to solve different issues [7–9]. For instance, ANNs have been used to:

  • estimate and predict solar radiation data [10–14],

  • estimate the maximum power (P m) and normal operating power of a flat PV module [15, 16],

  • size, model, and simulate both stand-alone PV systems [17, 18] and PV systems with a maximum power-point tracking controller [19, 20],

  • predict the equivalent circuits parameters of a flat PV module [21],

  • select a suitable model for characterising PV devices [22],

  • obtain the current–voltage (I–V) curves of different flat-plane panels [23, 24],

  • or to estimate the energy production of grid-connected PV systems [25, 26].

Due to the advantages of the ANNs to solve complex and nonlinear problems related with the field of PVs and the great level of complexity of electrical modelling of HCPV devices, in the recent years several authors have applied different ANNs to solve various problems related with this new technology. In this chapter, a review of the ANNs developed to address various issues related with the HCPV is presented, and examples of the application of ANNs in this field are given. In particular, the results obtained in the application of some of these ANNs to estimate the main electrical parameters of an HCPV module—including Pm, short-circuit current (I sc), and open-circuit voltage (V oc)—are presented.

2 Application of ANNs to Estimate of Direct Solar Irradiation

Due to the use of lenses that concentrate light on the solar cell, the HCPV devices operate only with direct normal irradiance (DNI). So the DNI is especially important for the characterization, management, and operation of HCPV modules, systems, and power plants. DNI is affected by phenomena that are difficult to forecast such as cirrus clouds, wildfires, dust storms, and episodic air pollution events, which can decrease DNI by ≤30 % on otherwise cloud-free days [27]. Because of this, the modelling and prediction of the DNI is a difficult task, and several authors have used ANN-based models to address this issue. A complete review about the solar data forecast by using artificial intelligence methods including DNI and neural network can be found in [28].

A Bayesian neural network was developed to model direct solar irradiance by Lopez et al. [29]. A relevance-determination method was also employed to obtain the relative relevance of a large set of meteorological and radiometric variables. Results show that the more relevant parameters are the clearness index (K t) and air mass (AM).

In [30], the authors developed an ANN model to estimate beam solar radiation. A new parameter known as the “reference clearness index” was introduced, which is defined as the ratio of the measured beam solar radiation at normal incidence to the beam solar radiation as computed by Hottel’s clear-day model. Results show that root mean square error (RMSE) in the ANN model varies 1.65–2.79 % for Indian regions.

Mishra et al. [31] developed a self-consistent model for the estimation of direct solar radiation in the Indian zone. An ANN-based model was used for the estimation of the Kt. The model predictions for the Indian region were found to be in good agreement with the measurements.

An adaptive model for predicting hourly global, diffuse, and direct solar irradiance was developed in [32]. A comparison between a Feed-Forward Neural Network (FFNN) and the proposed adaptive model was also presented. It was shown that the FFNN was able to predict the DNI with acceptable accuracy at Jeddah, King of Saudi Arabia (KSA). They observed that ANN performed better than the designed adaptive alpha-model with a correlation coefficient of 98 %.

In [33], the author developed an ANN model for estimating of monthly average daily direct solar radiation. According to the author, a correlation coefficient of 0.998 was obtained with mean bias error (MBE) of 0.005 MJ/m2 and an RSME of 0.197  MJ/m2.

In [34], the authors developed forecasting models for hourly solar irradiation using ANNs for lead times of ≤6 days. Model inputs included current and forecasted meteorological data obtained from the United States National Weather Service’s forecasting database and solar geotemporal variables. The gamma test was combined with a genetic algorithm to select the more relevant inputs. According to the authors, the estimation of DNI is much more difficult to predict reliably; the RMSE values obtained on same-day forecasts are in the range of 28–35 %.

Several ANNs were developed by Rodrigo et al. [35] for the generation of DNI hourly time series for some Spanish locations. In particular, different architectures of multiple linear perceptron (MLP) neural networks were used with three different configurations. The designed model could be used for the estimation of the energy that will be produced by concentrating PV systems, to perform economic analysis, and to supervise plant operation. The developed models were tested in different locations. The RMSE among real data and synthetic data for the three configurations and for the different locations considered are in the range 0.01–0.27. Results show that the ANNs yield better results for locations in the south of Spain.

Rehman and Mohandes [36] used a radial basis function (RBF) network for modelling the diffuse and direct normal solar radiation for sites in KSA based on input data such as day number, global solar radiation, ambient temperature, and relative humidity. The results indicate that the RBF (with 50 hidden neurons and 0.1 spread constant) predicts direct normal solar radiation with mean absolute percentage error of 0.016 and 0.41 for diffuse solar radiation.

A regionally based ANN model to retrieve the DNI at the surface of the United Arab Emirates (UAE) was developed by Marpu et al. [37]. The results are promising when estimating the solar irradiance at a 15-minute temporal resolution and a 3-km spatial resolution. The inputs of the designed model were six SEVIRI (on-board Meteosat Second Generation satellite) thermal channels along with several time- and season-dependent parameters, namely the solar zenith angle, solar time, day number, and eccentricity correction.

Recently, Chu et al. [38] designed a novel smart forecasting model for intra-hour DNI. The authors combined sky image processing with ANN optimization schemes. The hybrid forecast models achieved statistically robust forecasting skills in excess of 20 % over persistence both for forecasts 5 and 10 min ahead, respectively. Table 1 lists the applications of ANNs for modelling and prediction of DNI and lists the type of ANN employed in each case.

Table 1 Summary of the applications of ANNs for predicting the DNI
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3 Application of ANNs for the Electrical Modelling of HCPV Devices

As in any kind of energy system, modelling the electrical output of a PV device is crucial for the system design and energy prediction. However, the electrical modelling of HCPV modules and systems shows a significantly greater level of complexity than conventional PV technology. Due to the use of MJ solar cells and optical devices, HCPV modules and systems show a strong spectral dependence. To quantify the spectral changes and to evaluate how these affect the behaviour of an HCPV device is not a trivial issue [39, 40]. In addition, as in conventional PV technology, the cell temperature (T c) is an important input in models used for the electrical characterization of HCPV devices because the temperature at which cells are working in an HCPV module affects its performance. However, one of the problems in HCPV technology is that the direct measurement of this temperature is a complex task because it requires access inside the module [41].

Because of this difficulty, in recent years the scientific community has devoted efforts in developing ANN-based models which try to solve some of these issues.

3.1 Application of ANNs to Modelling Multi-junction Solar Cells

The PV solar cells used in HCPV technology are made of several p-n junctions (usually three junctions) of III–V semiconductor materials of the periodic table. Each p-n junction has a different band gap and is interconnected in series with the others to optimize the absorption of the solar spectrum and increase the efficiency of the solar cell electricity conversion [42]. Thus, although single-junction (SJ) solar cells are mainly influenced by changes in irradiance and temperature, MJ solar cells show complex behaviour because their performance is also strongly influenced by changes in solar spectrum. Due to this, Patra et al. [43–46] proposed approaches based on ANN to characterize these devices.

In [43] and [44], an ANN based-model was proposed to characterize dual-junction (DJ) GaInP/GaAs solar cells. The authors used four multilayer perceptrons: one for estimating the tunnelling effects of a solar cell and the other three for estimating the external quantum efficiency (EQE) and the I–V characteristic, both under 1 sun and in dark, for the DJ solar cell. The inputs for ANNs are the voltage for estimating the tunnelling effects and the I–V characteristic as well as the irradiation wavelength (λ) for estimating the EQE. The results were compared with experimental and simulated data through Silvaco ATLAS software [47]. The results showed that compared with the results obtained through ATLAS, the MLP-based model was able to predict DJ solar cell parameters more closely to that of experimental ones.

In [45], a novel Chebyshev neural network-based model for a DJ GaInP/GaAs solar cell was developed to predict the EQE and the I–V characteristics, both at one sun and dark levels. The inputs of the model are the same as those in the previous case.

In [46], an ANN-based model was used to estimate the EQE and the performance of triple-junction InGaP/GaAs/Ge solar cells under the influence of a wide range of charged particles. The inputs of the models are the wavelength (λ), the proton energy (η), and the fluence (f). The results show that the ANN-based models perform quite well in the estimation of EQE of the solar cell under the influence of proton energy ranging from 30 keV to 10 MeV with fluence levels ranging from 1010 to 1014 ion/cm2.

3.2 Application of ANNs to Modelling HCPV Modules

3.2.1 Application of ANNs to Estimate the Maximum Power of a HCPV Module

Due to the use of MJ solar cells and lenses, HCPV modules are mainly influenced by changes in irradiance, spectrum, temperature, and wind speed (W s). Taking this into account, the output of HCPV modules could be expressed as a function of these parameters:

$$ P_{m} = f\left( {B, S, T, W_{s} } \right) $$
(1)

The relation between these parameters and the output of an HCPV module is complex and nonlinear, so the use of ANN-based models has been proposed by several authors to try to find this relation.

Almonacid et al. [48] developed an ANN-based model, in particular an MLP, to find the relation between the output of an HCPV and the main parameters that affected its performance. The input parameters used by the model are as follows:

  • the DNI to evaluate how the changes in the irradiance affect the performance of an HCPV module

  • AM and precipitable water (PW) to evaluate the spectrum because these are, together with clouds and aerosol optical depth (AOD), the parameters with the largest impact on spectral changes [49, 50] and are also easy to obtain from the data provided by a meteorological station [51–54]

  • air temperature (T air) to evaluate the temperature of the HCPV module; and

  • the wind speed (W s).

Coefficients of neural networks are obtained from outdoor monitored data. The results show that the ANN based-model could be used to estimate successfully the output of an HCPV module with a MBE of 0.07 %, an RMSE of 2.91 %, and an R 2 of 0.99.

This approach has also been followed by Rivera et al. [55]. In this case, a cooperative‒competitive hybrid algorithm for RBF networks was implemented. This model uses as input the average photon energy [56, 57] to quantify the spectral influences on the P m of an HCPV module. This is a single value in eV that characterizes the shape of the spectrum. A spectroradiometer is required for obtaining this input. The rest of the inputs of the model are DNI to evaluate how the changes in the irradiance affect the performance of an HCPV module, T air to evaluate the temperature, and Ws. The coefficients of the neural network are obtained from outdoor monitored data. The model obtained gives an error of approximately 3.3 %.

3.3 Application of ANNs to Estimate the Electrical Characteristics of an HCPV Module

As already indicated, the output of an HCPV module is significantly affected by changes in irradiance, spectrum, and temperature. A different approach for electrical modelling of these devices is based on the premise that the electrical parameters of an HCPV module can be estimated by applying models and equations used for conventional PV technology from the DNI, corrected spectrally, and the T c [58, 59]. According to this approach, two ANNs for estimating these parameters have been proposed in [41, 60].

Application of ANNs to estimate the spectrally corrected direct normal irradiance

The spectrally corrected DNI (DNIc) is defined as the portion of the incident spectrum that an HCPV module is able to convert into electricity expressed here as:

$$ {\text{DNI}}_{c} = \frac{{{ \hbox{min} }\left( {\int {E_{b} \left(\uplambda \right)\eta \left(\uplambda \right)SR_{i} \left(\uplambda \right){\text{d}}\uplambda} } \right)}}{{{ \hbox{min} }\left( {\int {E_{b,{\text{ref}}} \left(\uplambda \right)\eta \left(\uplambda \right)SR_{i} \left(\uplambda \right){\text{d}}\uplambda} } \right)}}\int {E_{b,{\text{ref}}} \left(\uplambda \right){\text{d}}\uplambda} $$
(2)

where the index i represents the junction considered, λ is the wavelength, SRi(λ) is the spectral response of the i-junction, Eb(λ) is the spectral distribution of the DNI, and η(λ) is the optical efficiency of the HCPV module.

The advantage of this approach is that the spectral effects of an HCPV device are quantified by adjusting only the incident DNI [58].

Taking this into account, an ANN-based model for DNIc was presented in [60]. The inputs of the model are the main meteorological parameters that influence the spectral distribution of the DNI and the performance of an HCPV module: AM, AOD, and PW. Results show that the method is able to predict spectrally corrected normal irradiance with an RMSE of 2.92 %, an MBE of −0.12 %, and a R 2 of 0.98.

Application of ANNs to estimate the cell temperature of a HCPV module

The operating temperature of the solar cell is a crucial issue to characterize the electrical behaviour of a PV device. However, the measurement of this temperature in an HCPV module is a complex task due to its special features that do not allow one to access the cell. To solve this problem, several authors have attempted different approaches [41, 61]. One of these is based on the premise that the T c can be obtained from the main meteorological parameters that have an influence in this temperature: DNI, T air, and W s. Using a linear expression [62]:

$$ T_{c} = T_{{\text{air}}} + a{\text{DNI}} + bW_{s} $$
(3)

where a and b are empirical parameters obtained from outdoor monitored data.

According to this approach, an ANN-based model was presented in [41]. This model attempts to characterise the relationship between the T c and the main meteorological parameters that affect it. The input parameters are DNI, T air, and W s. Results show that the ANN-based model significantly improves the results of the method based on a linear expression with an R 2 of 0.95, a relative RMSE of 4.80 %, and an absolute RMSE of 3.24 °C. Table 2 lists the applications of ANNs for modelling HCPV devices and also indicates the type of ANN employed in each case.

Table 2 Summary of applications of artificial neural networks for modelling HCPV devices
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4 Examples of Applications

In this section, some examples of the applications of the ANNs for the characterization of HCPV modules are presented. The first example concerns the P m of an HCPV estimated using the ANN developed by Almonacid et al. in [48]. In the second part, the V oc and the I sc of an HCPV module will be calculated from the DNIc and the T c according to the approach presented in [58, 59]. The ANNs developed in [41, 60] have been used to estimate the spectrally corrected normal irradiance and the T c for an HCPV module.

4.1 Experimental Campaign

To conduct this study, an HCPV module was measured for 6 months in the Centro de Estudios Avanzados en Energía y Medio Ambiente at the University of Jaén. The module is made up of 20 lattice-matched MJ solar cells connected in series (Ns) with a silicon-on-glass Fresnel lens on each cell (Fig. 1, top left). Figure 1 shows the EQE of the MJ solar cells and the transmittance of the lens of the HCPV module used in this study. Table 3 shows the main electrical parameter of the HCPV module.

Fig. 1
figure 1

Top left Photograph of the HCPV module considered in the study. Top right Scheme of the experimental set-up to measure the electrical parameters of the HCPV module and the main parameters necessary to train the ANN. Bottom left EQE of the MJ solar cells of the HCPV module. Bottom right Transmittance of the Fresnel lenses used in the HCPV module considered

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Table 3 Electrical characteristics of the module under study measured at outdoor reference conditions: DNI = 900 W/m2, T air = 20 °C, and AM = 1.5, for wind speed lower than 1 m/s
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The experimental set-up (Fig. 1, top right) used to measure the electrical characteristic of the HCPV module and the main parameters necessary to train the ANNs for estimating Pm, DNIc and the T c, is made up of the following:

  • a high-accuracy two-axis solar tracker to keep the HCPV module always pointing toward the solar rays so lenses are able to focus the radiation on the small solar cell area;

  • a four-wire electronic load to measure the electrical parameters of the module;

  • a four-wire PT100 placed close to the solar cell to measure the T c; and

  • a meteorological station placed at the roof of the centre to record the main atmospheric parameters such as DNI, T air, W s, or humidity.

  • the values of AOD and PW, which were not provided by the meteorological station, were obtained from MODIS Daily Level-3 data source [63].

Table 4 shows the maximum, minimum, and average values of the parameters used as inputs of the different ANNs used in the study.

Table 4 Maximum, minimum, and average values of the parameters used as inputs of the ANNs for estimating P m, DNIc, and T c
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4.2 Estimation of the Maximum Power of a HCPV Module

The ANN developed in [48] has been applied to estimate the Pm of the HCPV module. The inputs of the ANN-based model are DNI, AM, PW, T air, and W s. The structure of the ANN consists of tree layers: the input layer, which has five nodes; the hidden layer, which has seven nodes; and the output layer, which has one node that corresponds to the P m of the HCPV module. This architecture was trained with the Levenberg–Marquardt back-propagation algorithm to determine the coefficients of the ANN. To train and test the ANN, a set of outdoor measurements, including the output of the HCPV module and the meteorological parameters, were used for a wide range of operating conditions (Table 4). Table 5 shows the coefficient of multiple determination (R 2), the RMSE, the mean absolute error (MAE), and the MBE between actual data and data predicted by the ANN-based model.

Table 5 Values of the parameters R 2, RMSE, MAE, and MBE between actual data and predicted data by the ANN-based model for estimating the maximum power of the HCPV module considered
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Figure 2 shows an example in the estimation of the P m of the HCPV module using the ANN based-model for two different days (summer and winter days). Table 6 shows the maximum, minimum, and average values of the parameters used as input of the ANN for the two example days.

Fig. 2
figure 2

Left Actual maximum power of the HCPV module considered versus predicted maximum power by the ANN-based model for a summer day (07 July 2013). Right Actual maximum power of the HCPV module considered versus predicted maximum power by the ANN-based model for a winter day (01 December 2013)

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Table 6 Maximum, minimum, and average values of the parameters used as inputs for the two examples days (summer and winter day)
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4.3 Estimation of the Electrical Parameters of a HCPV Module

According to the approach that the electrical performance of an HCPV device can be quantified from the DNIc and T c [58, 59], the V oc, and the I sc of the HCPV module considered can be estimated from equations used in conventional PVs:

$$ I_{sc} = \frac{{I_{sc}^{ * } }}{{G^{ * } }}G\left( {1 + \gamma \left( {T_{c}^{ * } - T_{c} } \right)} \right) $$
(4)
$$ V_{oc} = V_{oc}^{ * } \left( {1 + \beta \left( {T_{c}^{ * } - T_{c} } \right)} \right) + N_{s}\frac{{mkT_{c} }}{q}\ln \left({\frac{G}{{G^{ * } }}} \right) $$
(5)

where I *sc , G*, T *c , and V *oc are the I sc , solar global irradiance, T c, and V oc at reference conditions; γ and β are the T c coefficient of the I sc and the V oc, respectively; m is the effective ideality factor of the cell; k is the Boltzmann constant; and q is the electron charge.

Equations (4) and (5) must be adapted to HCPV as follows:

$$ I_{sc} = \frac{{I_{sc}^{ * } }}{{{\text{DNI}}^{ * } }}{\text{DNI}}_{c} \left( {1 + \gamma \left( {T_{c}^{ * } - T_{c} } \right)} \right) $$
(6)
$$ V_{oc} = V_{oc}^{ * } \left( {1 + \beta \left( {T_{c}^{ * } - T_{c} } \right)} \right) + N_{s}\frac{{mkT_{c} }}{q}\ln \left( {\frac{{{\text{DNI}}_{c} }}{{{\text{DNI}}^{ * } }}} \right) $$
(7)

where DNI* is the DNI at reference conditions and DNIc is the spectrally corrected DNI. The various parameters for the module considered are m = 3, γ = 0.002 °C−1 and β = 0.0015 °C−1 for the HCPV.

4.4 Estimation of the Spectrally Corrected Direct Normal Irradiance

To estimate the DNIc of the HCPV module considered, the ANN developed in [60] was applied. The inputs of the ANN are AM, AOD, and PW, and the ANN has five nodes in the hidden layer and one node in the output layer corresponding to the spectral correction function. This architecture was trained with the Levenberg–Marquardt back-propagation algorithm to determine the coefficients of the ANN. To train and test the ANN, a set of outdoor measurements were used for a wide range of operating conditions listed in Table 4. Table 7 lists the R 2, the RMSE, the MAE, and the MBE—all of which are considered very adequate—between actual and predicted data using the ANN-based model.

Table 7 Values of the parameters R 2, RMSE, MAE, and MBE between actual data and predicted data by the ANN-based model for estimating the spectrally corrected direct normal irradiance
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Figure 3 shows an example of the DNI measured during 2 days (summer and winter) versus the DNIc predicted by the ANN based-model for the HCPV module. Table 6 shows the maximum, minimum, and average values of the parameters used as input to the ANN for the 2 example days.

Fig. 3
figure 3

Left Actual direct normal irradiance versus spectrally corrected direct normal irradiance predicted by the ANN-based model for a summer day (07 July 2013). Right Actual direct normal irradiance versus spectrally corrected direct normal irradiance predicted by the ANN-based model for a winter day (01 December 2013)

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As can be seen from Fig. 3, although the maximum level of DNI reached on winter and summer is similar (approximately 900 W/m2), the DNIc is lower in winter. This could be mainly explained because the AM values are significantly greater in the winter than in summer, so the portion of the incident spectrum that an HCPV module is able to convert into electricity is lower due to spectral losses. This also can be observed at the sunrise and sunset (both in winter and summer) when the AM values are greater and the DNIc is lower than DNI.

4.5 Estimation of the Cell Temperature

To estimate the T c of the HCPV module considered, the ANN developed in [41] has been used. The inputs of the ANN are: T air, DNI and Ws, and the ANN has five nodes in the hidden layer and one node in the output layer corresponding to the T c of the HCPV module. This architecture was trained with the Levenberg–Marquardt back-propagation algorithm, to determine the coefficients of the ANN. To train and test the ANN, a set of outdoor measurements including the T c of the HCPV module and the meteorological parameters were used for a wide range of operating conditions, listed in Table 4. Table 8 shows the R 2, RMSE, MAE and the MBE between actual data and predicted data using the ANN-based model.

Table 8 Values of the parameters R 2, RMSE, MAE, and MBE between actual data and predicted data by the ANN-based model for estimating the cell temperature of the HCPV module considered
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Figure 4 shows an example of the T c of the HCPV module measured during 2 days (summer and winter day) versus the T c predicted by the ANN based-model. Table 6 shows the maximum, minimum, and averages values of the parameters used as input of ANN for the two example days.

Fig. 4
figure 4

Left Actual cell temperature versus predicted cell temperature by the ANN-based model for a summer day (07 July 2013). Right Actual cell temperature versus predicted cell temperature by ANN-based model for a winter day (01 December 2013)

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4.5.1 Estimation of the Short-Circuit Current and the Open-Circuit Voltage

Once the values of the DNIc and T c are available, it is possible to estimate the I sc and the V oc using Eqs. (6) and (7). Table 9 shows the R 2, RMSE, MAE, and MBE between actual and predicted data using Eqs. (6) and (7).

Table 9 Values of the parameters R 2, RMSE, MAE, and MBE between actual and predicted data using Eqs. (6) and (7) for estimating the short-circuit current and the open-circuit voltage of the HCPV module considered
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Figures 5 and 6 bottom-left show the actual versus the predicted Isc for the HCPV module considered for 2 example day. Figures 5 and 6 bottom-right show the actual versus the predicted V oc for the HCPV module considered for 2 example days.

Fig. 5
figure 5

Top left Direct normal irradiance measured during a summer day versus the spectrally corrected direct normal predicted by the ANN presented in [60]. Top right cell temperature measured during a summer day versus cell temperature predicted by the ANN presented in [41]. Bottom left Actual short-circuit current versus estimated short-circuit current using Eq. (6) for the HCPV module considered during a summer day. Bottom right Actual open-circuit voltage versus open-circuit voltage using Eq. (7) for the HCPV module considered during a summer day

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Fig. 6
figure 6

Top left Direct normal irradiance measured during a winter day versus the direct normal predicted by the ANN presented in [60]. Top right cell temperature measured during a winter day versus cell temperature predicted by the ANN presented in [41]. Bottom left Actual short-circuit current versus estimated short-circuit current using Eq. (6) for the HCPV module considered during a winter day. Bottom right Actual open-circuit voltage versus open-circuit voltage using Eq. (7) for the HCPV module considered during a winter day

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5 Conclusions

In this chapter, a review of ANN-based models developed for solving some problems related with HCPV technology is presented. In addition, several examples of the application of some of these models for estimating the main electrical parameters of an HCPV module—such as the P m, the I sc, and the V oc—are presented.

The ANN based-model developed in [48] was applied to estimate the P m of an HCPV. This model takes into account the main meteorological parameters that affect the output of an HCPV module. The approach presented in [58, 59] was followed to estimate the Isc and the V oc. In this case, these electrical parameters were estimated from the DNIc, the Tc, and use of the equations of conventional PVs. The values of the DNIc and the Tc were obtained by applying the ANNs developed in [25, 60].

From the analysis of results, it can be concluded that ANNs are a useful tool for the electrical characterization of HPCV devices.