Energy is very important for the development of the modern world. However, sustainable energy is even more important for the survival of our environment (Bailek et al., 2018; Cho et al., 2019; Chen et al., 2020). Global emissions have increased by more than 20% since the last decade (Shahzad et al., 2017). Many renewable energy resources can be utilized to achieve the sustainability goal (Burhan et al., 2016a; Burhan et al., 2017a; Peng et al., 2020). Solar energy is the only capable renewable energy resource that can meet the current global energy needs (Burhan et al., 2018a; Hakimi et al., 2020). The solar photovoltaic system is the simplest technology to produce sustainable electricity. The most efficient photovoltaic system is the concentrated photovoltaic (CPV) system, using multi-junction solar cells (MJCs), as they offer the highest energy efficiency of 47.1% (NREL, 2022). However, the multi-junction solar cell has a more complex principle of operation compared to conventional single-junction solar cells (Oh et al., 2015; Burhan et al., 2016b; Muhammad et al., 2016). To lower the system cost, MJCs are operated under high irradiance concentrations (assets, 2020), and as a result, under high temperatures (Burhan et al., 2019a), low-cost solar concentrators replace the expensive solar cell material (Cherucheril et al., 2011; Burhan et al., 2019b). The response and the resultant I–V curve of the solar cell change immediately with even minor changes in temperature or irradiance concentration (Burhan et al., 2017b; Burhan et al., 2018b).

The manufacturers of photovoltaic panels rate their performance at certain conditions of radiation and temperature which are not achievable most of the time in real-field operations. Standard testing conditions (STCs) (IEC 60904-3) or nominal operating cell temperature (NOCT) (IEC 61215 and IEC 61646) are two IEC standards that are used to rate the performance of photovoltaic panels as per the defined laboratory conditions, AM 1.5 spectrum, 1,000 W/m² irradiance, and 25°C cell temperature (Burhan et al., 2017c). To analyze the real-field potential of the photovoltaic system, it is very important to understand and analyze its behavior with changing conditions. By only knowing the standard efficiency of PV panels, one cannot predict the actual energy production from photovoltaic panels under realistic changing weather conditions. There are well-developed empirical and analytical expressions for the performance analysis of conventional single-junction photovoltaic cells under sunlight. However, there are limited studies related to performance models of concentrated photovoltaic systems, which are only empirical relations (Burhan et al., 2018c; Burhan et al., 2021). In addition, the structure and operation of concentrated photovoltaic systems make the performance modeling of the CPV system complex due to many factors affecting its performance (Burhan et al., 2018d). The two main parameters dictating the output of the MJC-based CPV system are the irradiance concentration and cell temperature, assuming accurate solar tracking and maximum power point tracking during the operation. These are the two operational parameters varying throughout the operation as the rest of the system parameters related to optics and cell materials remain unchanged. A small change in the irradiance concentration generates a new set of temperature gradients of the MJC (Burhan et al., 2016c; Burhan et al., 2018e).

Due to multi-parameter dependency, the relationship between the input parameters of MJCs, such as concentration and temperature, and the output parameters such as efficiency, current, voltage, power, and temperature gradient is not linear. The irradiance concentration at the MJC area largely affects their temperature characteristics and electrical outputs (Theristis et al., 2016). The analytical expression is not able to easily define the performance characteristics of MJCs with such multi-parameter dependency. On the other hand, empirical expressions require some post-processing of input parameters to define the performance characteristics of the MJC-based CPV system. The artificial neural network (ANN) is an alternative approach to complex expressions and finds the link between input and output parameters in such non-linear cases of photovoltaic systems (Kalogirou, 2000). A set of hidden neurons and their corresponding layers are arranged such that their values and structures define the complex interaction between input and output parameters (Ghritlahre et al., 2020; Zeynali et al., 2020). This ANN approach provides a simple solution for such a complex task. However, extensive effort is needed to get a set of experimental data with a broad range of input parameters as the ANN is trained on such a set of experimental data (Burhan et al., 2019c; Motahar and Bagheri-Esfeh, 2020). An ANN is a very promising tool for complex and multivariable problems in the field of photovoltaics. It can be applied for the prediction and estimation of solar irradiance (Mellit et al., 2005a; Mellit et al., 2006), system capacity for both standalone and grid-connected applications (Mellit et al., 2005b; Mellit et al., 2007), electrical characteristics of the solar cell including I–V curves (Almonacid et al., 2010), and the overall production of the field installed system (Almonacid et al., 2011).

Due to the complexities of the MJC’s electrical and thermal characteristics and structure of the CPV module, the ANN has the advantage over conventional performance models that require an understanding and simulations of the complex physical phenomena involved in the CPV performance. In addition, they do not require detailed information on the material and manufacturing of the system. Also, there is no need for specific modeling software (Almonacid et al., 2017). There are many commercial tools available to simulate the performance of conventional photovoltaic systems, i.e., HOMER (HOMER, 2015), RAPSIM, TRNSYS + HYDROGEMS, ARES, SOMES, HYBRIDS2, SOLSIM, INSEL (Bernal-Agustin and Dufo-Lopez, 2009), and iHOGA (iHOGA, 2004). However, none of these tools can handle MJC-based CPV systems. Therefore, in our previous study (Burhan et al., 2017b), an empirical correlation was proposed for the performance prediction of the MJC-based CPV system. However, it requires complex processing of experimental data to determine the temperature gradients of open-circuit voltage and short-circuit current, although carrying out such an approach is not simple. Although the CPV system can only respond to the direct normal irradiance of solar energy, it is also a difficult parameter to predict and analyze. However, there are many studies on ANNs to predict the normal irradiance for concentrated photovoltaic (CPV) applications. In this paper, the focus is on the development of a performance model of the MJC-based CPV system using an artificial neural network, equivalent to an empirical model (Burhan et al., 2017b), with a higher accuracy and a simple set of input–output parameters. The ANN is developed for triple-junction InGaP/InGaAs/Ge MJCs, which was successfully able to provide cell efficiency up to a concentration factor of ×550 and a temperature range of 25–90°C. A detailed comparison of the proposed ANN configuration with our previously presented model is provided showing a great improvement in the accuracy with very less required information and computational effort/programming.

In this paper, the materials and methodology are discussed first, in which, first, the comparison of the ANN with empirical models is presented. Second, there is a detailed discussion on the collection of experimental data for the training and testing of the ANN. Lastly, the methodology is presented, in which the use of MJC data obtained from a trained ANN is discussed to calculate the performance of the CPV module. The constant parameters and algorithm used to train the ANN are also discussed in Section 2. In Section 3, the training accuracy of the ANN is presented first with mean squared error (MSE) and regression plots. The MJC performance data obtained from the trained ANN are compared against empirical models and experimental data. Lastly, the MJC performance data from the trained ANN are used to predict the real-field power output of the CPV system against the actual available weather data.

By using the Bayesian regularization algorithm, the ANN was trained with the backpropagation technique to minimize the mean squared error of targeted and output values. The training was initially started for 1,000 epochs. However, the algorithm converged at 824 epochs, where the MSE was the lowest, as shown in Figure 4. The plot for the mean squared error of target and output values during the training and testing phase of the ANN is shown in Figure 4. On the other hand, the plot fit for target and output values against input data is shown in Figure 5. It can be seen that the error value is almost zero throughout the input range. This can also be verified by regression plots of the training and testing phases of the ANN as the regression value appears as 1 for both the cases, Figure 6. This shows that the current methodology is perfectly used to train and test the ANN for the performance prediction of MJCs. Due to the high accuracy, the algorithm did not need to validate the ANN. It is important to mention here that such a high accuracy was obtained using the Bayesian regularization algorithm. However, while using the scaled conjugate gradient and Levenberg–Marquardt, the regression accuracy dropped significantly (R < 1).

To verify the accuracy of the trained ANN, a comparison of the output data of the ANN is compared against the experimental data and the data obtained from the conventional empirical model, as shown in Figure 7. First of all, it can be seen that although the empirical model (Burhan et al., 2017b) is trying to follow the efficiency trend of the experimental data, there is still a significant contradiction between actual and calculated values. Although the empirical model is within the 2% error range of the experimental data, the efficiency points obtained through the trained ANN are showing a perfect agreement with the experimental data at various conditions of the concentration and temperature. The ANN prediction is 99.9%, matching the targeted experimental value, as depicted by the regression coefficient “R” in Figure 6. This shows that the ANN is not only simplifying the conventional approach of empirical models but the accuracy of the predicted data is also increased significantly, even when compared with ANN–CPV-based models available in the literature with 2.91% (Rivera et al., 2013) and 3.3% (Almonacid et al., 2013) error ranges, respectively. This will not only simplify the problems but also reduce the computational time. One of the key points of the high accuracy of the ANN is identifying and selecting the key input parameters, which are directly impacting the system performance.

To utilize the trained ANN in the real-field performance prediction of the CPV system performance, the power output of the CPV module consisting a single MJC is presented in Figure 8, against the actual direct normal irradiance (DNI) profile, measured using a pyrheliometer mounted on a two-axis solar tracker, along with the ambient temperature. It is important to mention here that the CPV power output shown here is based on the performance of MJCs obtained through the trained ANN. The DNI is defining the irradiance concentration at the area of MJCs with a concentrator area of 12 cm × 12 cm and an optical efficiency of 75%. On the other hand, the ambient temperature is defining the cell temperature, which is approximated at 40°C higher than the ambient temperature (Burhan et al., 2016d). This shows that with the proposed trained ANN of MJCs, one can easily predict the real production potential of the CPV system if the solar potential and weather conditions are known, which are mostly available through data centers of weather stations. Therefore, instead of relying on the maximum rated performance of the photovoltaic system, the real energy/power output of the CPV system can be easily predicted with ANN-based techniques, with a need for complex non-linear expressions and correlations.

An artificial neural network-based performance model is successfully trained and tested for the performance prediction of the multi-junction solar cell. In comparison to the conventional empirical model, with a 2% error range, the ANN-based model showed a high level of 99.9% accuracy in the solar cell efficiency prediction by knowing the cell temperature and the concentration at the cell area. The use of the Bayesian regularization algorithm for the ANN training increased the regression factor R from 0.97 to 1, as compared to conjugate gradient and Levenberg–Marquardt algorithms. The trained ANN model was extended to predict the real-field performance prediction of a full-scale CPV system of any size capacity, instead of just a single MJC. Due to the complex and non-linear behavior of MJCs, especially in the concentrated photovoltaic (CPV) configuration, the ANN-based approach has simplified the link between input and output parameters. Instead of going through time-extensive evaluations of thermal gradients for different irradiance concentration levels, the ANN model can simplify the prediction with the use of raw input values of the irradiance concentration and cell temperature. By knowing the solar potential and weather data of a certain location, the long-term field production of the CPV system can be easily predicted with the proposed ANN model.