Employing genetic programming to find the best correlation to predict temperature of solar photovoltaic panels
Introduction
The popularity of solar panels has been increasingly grown; they are becoming cost-effective and energy-efficient more and more thanks to making suitable economic plans by policymakers and developing the technology by scientists [1]. Solar panels are not only utilized to provide electricity for the residential use [2] but also employed to generate power for other sectors such as industrial applications [3]. Moreover, they have the significant advantage of being easily used for both grid-connected and off-grid power generation purposes [4].
Among the different kinds of solar panels, the silicon-based type is a favorite item in the market since silicon (Si) is one of the most available elements on the Earth’s crust [5], which leads to having lower prices for this type compared to the other ones [6]. For the commercial solar panels, including the silicon-based type, according to the points mentioned in Section 3.1, there have been two approaches to predict the performance of a solar photovoltaic panel:
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One of the ways to predict the performance has been modeling the electrical characteristics of a panel. In that way, current and voltage of the panel have been the outputs of modeling, and the efficiency has been obtained from dividing the power, which is multiplication of the current by voltage, by the received solar radiation.
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Another approach has been providing a model to describe the thermal performance in which temperature of the solar panel has been found as the output. Having known temperature of the solar panel, the efficiency of that can be determined using a correlation the most famous of which is the one presented in [7].
The ways to obtain the electrical characteristics of a solar panel are categorized into two categories, namely white box and black box methods [8]. In the white box approach, the electric circuit of the photovoltaic panel is considered, and using the governing equations for that, models to estimate voltage and current are developed. The studies of Gu et al. [9], Ma et al. [10], Ogbonnaya et al. [11], Arias-García and Pérez Abril [12], Ayang et al. [13], Beniysa et al. [14], and Abe et al. [15] have been some example of such investigations.
On the other hand, the data-driven black box method refers to the investigations in which machine learning approaches have been employed to predict the electrical parameters of a solar panel. Using the techniques belongs to this approach, especially artificial neural network (ANN) has been increasing at a rapid pace. Some examples of the recent studies from this group have been carried out by López-Guede et al. [16], Ridha et al. [17], Chen et al. [18], Hao et al. [19], Taghezouit et al. [20], and Ahmad et al. [21].
Moreover, modeling the thermal behavior of a photovoltaic solar panel has been done using either writing and solving governing equations or data-driven statistical methods, especially ANN. The studies have been done by Tomar et al. [22], Babu and Ponnambalam [23], Hu et al. [24], Osma-Pinto and Ordóñez-Plata [25], Singh et al. [26], and Boumaaraf et al. [27] are the examples of the ones in which governing equations have been written and solved. Furthermore, the references like Motahar and Bagheri-Esfeh [28], Huerta Herraiz et al. [29], Gowid and Massoud [30], Alnaqi et al. [31], Qiu et al. [32], and Dimri et al. [33] have been some examples of developing data-driven statistical models. In addition to them, having the advantages such as not complexity of the two aforementioned ways, as well as being straightforward and used by all the scientist, employing correlations is another method, which has been very popular during these years. In that approach, having a precise value of the temperature of the solar panel () is necessary and plays a vital role [34]. Considering this point, several studies have tried to introduce an accurate correlation for . Table 1 presents a list of such investigations.
Having reviewed the literature, two substantial gaps are identified:
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Relative humidity, which is a crucial effective parameter on the panel performance, has not been considered as an argument (input) of the correlation to predict . When all other meteorological effective parameters (ambient temperature, wind velocity, and irradiance) stay constant, increasing the relative humidity leads to having more vapor in the air, which makes the heat transfer process weaker, and causes an increase in the temperature of solar panel. In several studies, such as [56], [57], it has been reported that relative humidity has impacts on the performance of a solar panel. However, as reviewing them showed, in none of them, a model in which relative humidity was an input, was developed.
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For obtaining each equation indicated in Table 1, the function form for the correlation to predict has been chosen by researchers. In other words, if the correlation for prediction of is expressed as:
The formula for function has been selected by authors, and then, the coefficients have been determined by them. It means that a way by which the best formula for is determined automatically has not been employed.
As a result, the current study is done, in which the following items are taken into account as the novelties:
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The best function form to predict the temperature of a solar panel () is found for a product family of Si-based solar panels. Genetic programming (GP), as the systematic way for this purpose, is employed. By employing GP, different function forms, including polynomial, power, logarithmic, exponential, and their combinations, are taken into account to obtain the most accurate function form to predict based on the recorded experimental data during a year. As an essential point, it should be noted that according to what discussed in Section 3.2, GP is quite different from the genetic algorithm (GA), which is used for optimization.
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The relative humidity of ambinet air (briefly called relative humidity) is taken into account as one of the inputs for the correlation to predict . Therefore, the proposed correlation predicts as a function of the ambient temperature, irradiance, wind speed, and relative humidity.
According to the previously done investigations by the research team, including [58], [59], artificial neural network (ANN), group method of data handling type neural network (GMDH), genetic programming (GP), multiple linear regression (MLR), and stepwise regression method (SRM) have been the most common methods to find a correlation to predict an output based on the effective inputs. Among the methods, as completely discussed in [58], ANN provides a complex matrix structure, which is very hard to use and is not suitable for engineering applications. On the other hand, GP is able to introduce a simple but accurate equation for prediction. In contrast to other methods, like GMDH, MLR, and SRM in which a fixed function form is considered (usually one or a group of polynomials), by employing GP, as mentioned, a variety of the function forms, including polynomial, power, logarithmic, exponential, and their combinations, are taken into account. It enhances the accuracy of prediction significantly. The higher effectiveness of GP compared to the other methods have been proven in several studies like [58], [60], [61], [62] for different energy systems. Therefore, by considering all the mentioned points, GP was selected in this study for modeling.
The best function form to estimate is found and verified for a 40 W polycrystalline solar panel by GP. Then, the prediction ability of the foremost function form is examined for 20, 30, 50, 60, 80, 120, 150, 200, 250, 300, and 320 W panels from the same product family. It is done to see whether the same function form as the one found for 40 W solar panels with different coefficient values is able to estimate for other panels precisely or not. For both finding the best function form for the 40 W panel and examining the prediction ability of the foremost obtained function form for other panels, the experimental data recorded throughout a year are employed. Finally, the found function form is compared to NMOT and NOCT models, as the most common previously introduced correlations to obtain in the literature, to evaluate the potential of improvement in efficiency prediction.
This paper is organized as follows. After this part, i.e., introduction, the details about the experiments are introduced. Then, the information about the methodology is given. Next, the results are presented and discussed, and in the end, the drawn conclusions are proposed.
Section snippets
Experiments
The experiments were being done during the period of January to December of 2019. The days 5, 10, 15, 20, 25, and 30 in each month were selected as the ones on which experiments were carried out. The only exception was February, which has 28 days, and February 28 was selected as the sixth experiment day on that month. Gathering experimental data began at 8:00 on each day and ended at 16:00, with the time resolution of ten minutes. It means that recording data was performed at 8:00, 8:10, 8:20,
Methodology
This part provides details about genetic programming (GP), by which the best function to predict is found. Moreover, the concept of the panel’s equivalent temperature is also introduced. As will be seen, the value of the panel’s equivalent temperature is used as the experimental value of to develop GP and obtain the best function for this parameter. In addition, NMOT and NOCT models are introduced briefly while the way to obtain produced power and generated energy are also
Results and discussion
This part presents the results of this study and discusses them. Initially, the best-obtained function to predict for the 40 W solar panel is introduced and verified. After that, the generalization capability of the best found function form to predict is checked for other investigated panels. Next, the prediction ability of the best found function form compared to NOCT and NMOT models is evaluated by comparing the profiles for , efficiency, generated power, and produced
Conclusion
By employing genetic programming (GP), the best function form to predict panel’s temperature () was found for a product family of polycrystalline solar panels, which had the panels with the nominal capacities of 20, 30, 40, 50, 60, 80, 120, 150, 200, 250, 300, and 320 W. The experiments were conducted during a year to record the performance, and then, the experimental data was used to find the best function form. After finding the best function form and validation of that, its prediction
CRediT authorship contribution statement
Ali Sohani: Conceptualization, Methodology, Software, Investigation, Writing - original draft, Writing - review & editing, Visualization, Project administration. Hoseyn Sayyaadi: Conceptualization, Methodology, Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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