A New Approach for Solar Photovoltaic Parameter Extraction Using Metaheuristic Algorithms From Manufacturer Datasheet

Estimating the parameters of solar photovoltaic (PV) panels is crucial for effectively managing operations in solar-based microgrids. Various techniques have been developed for this purpose, and one accurate approach is solar cell modeling using metaheuristic algorithms from current–voltage ( ${I}$ – ${V}$ ) data of the PV panel. However, this method relies on experimental datasets, which may not be readily available for most industrial PV panels. Hence, this research proposes a new technique for estimating the parameters of different types of PV modules using only manufacturer datasheets. Additionally, three metaheuristic optimization techniques, namely, particle swarm optimization (PSO), artificial bee colony (ABC) optimization, and Harris Hawks optimization (HHO), are investigated for solving this problem. The obtained results using these optimizers indicate that PSO mostly outperforms other algorithms, in terms of accuracy, while demonstrating faster computation. The proposed method is evaluated for three different PV units. Under 1000W/m2 of irradiance and a specified temperature, the method has been validated with available experimental datasets. Furthermore, a comparative analysis with some other existing methods in the literature reveals the model’s competitiveness despite not relying on experimental datasets. Also, an uncertainty analysis for the extracted parameters has shown that the obtained results are reliable enough to predict the actual dynamics of PV units. This study holds significance for other research on the basis of PV panel parameters, managing commercial PV power plant operation with with maximum power point tracking controller, etc.


I. INTRODUCTION
S OLAR technologies have emerged as highly efficient energy resources and have witnessed widespread utilization for power generation worldwide in recent decades.The Earth receives a staggering daily energy potential of approximately 84 TW, which can be harnessed effortlessly through the use of photovoltaic (PV) panels to generate electricity [1].However, prior to the installation of any solar plant, an understanding of its performance and efficiency is necessary.Also, the design of maximum power point tracking (MPPT) controllers holds principal importance for energy generation using PV panels, enabling the maximum utilization of solar energy.Both of these purposes require extraction of module parameters with bare minimum accuracy, reduced complexity, and fast calculation.
The primary objective of this research was to develop a methodology that can easily but accurately replicate the I-V characteristics of solar panels through the application of metaheuristic algorithms, by extracting the PV panel parameters.By combining solar cell modeling with metaheuristic algorithms, the extraction of panel parameters can be achieved with exceptional precision.These algorithms belong to the category commonly employed for solving transcendental equations, encompassing nonlinear optimization functions with multiple unknown variables.As the dynamics of the solar PV units are highly nonlinear, metaheuristics are the best option in related applications for optimization.
A solar cell can be represented by a single-diode model (SDM), a double-diode model (DDM), or a triple-diode model (TDM), each comprising multiple parameters, such as series resistance (R s ), parallel resistance (R sh ), diode reverse saturation currents (I 0 ), diode ideality factors (a), and photo-generated current of PV unit (I ph ).The accuracy of the modeling process is heavily reliant on these solar cell or panel parameters.Nevertheless, not all of these parameters are provided by the manufacturing industry.The modeling process aims to determine the appropriate values for these parameters in order to achieve an accurate estimation of photocurrent, i.e., generation by PV panel.
Accurate modeling of solar cells holds paramount importance across various applications, including power generation estimation [2], MPPT [3], and degradation analysis [4].Hence, precise determination of modeling parameters becomes crucial.
From [8], [9], [10], [11], [12], [13], [14], and [15], the authors presented different techniques for extracting the parameters of SDM of the PV panel.In [8], the parameters of SDM were estimated using the particle swarm optimization (PSO) technique and were compared with other techniques, proving to be highly accurate and promising based on experimental I-V data of PV cell.Firefly algorithm (FA) was proposed for estimation based on SDM in [9] and was compared with other methods from the literature.Bharadwaj et al. [10] proposed the trust region reflective Newton, steepest descent optimization, and Levenberg-Marquardt algorithm (LMA) for identification of SDM parameters.The particle swarm optimization with adaptive elite mutation (PSO-AEM) is used to overcome the problem associated with PSO in case of parameter estimation of SDM [11] and this proposed technique also increases processing speed.In [12], a new circuit model using one diode is developed for the PV panel and identified the parameters of the model by performing some tests.The photovoltaic (PV) string model is used to estimate the parameters of the SDM in [13].The artificial hummingbird algorithm (AHA) [14] and genetic algorithm (GA) [15] are utilized to determine solar cell parameter values and demonstrate the accuracy and efficiency of these methods for the identification of parameters of SDM.Huynh et al. [16] identified the parameters of DDM applying a combination of Artificial bee colony (ABC) optimization and PSO.A three-diode mode was addressed in [17] with hunter-prey optimization (HPO) and wild horse optimization (WHO) techniques.
From the information of the datasheet, the circuit parameters of the PV model is estimated using the Newton-Raphson (N-R) method [30] and hybrid N-R and SA method [31].Application of analytical methods are presented in [32], [33], [34] for modeling of PV panel from manufacture data.A new method for parameter estimation using D.C. power supply is proposed in [35].The optimization techniques like the combination of GA and the interior-point method (IPM) [36], GA [37], improved electromagnetic-like algorithm (IEM) [38], PSO and GA [39], are employed to determine parameters of PV model from datasheet knowledge.In [40], the parameters of SDM and DDM are identified from the open circuit, short circuit, and maximum power points applying an adaptive differential evolution algorithm and analytically.
The performance of solar cells exhibits variations under different solar radiation and temperature conditions.Consequently, analyzing and estimating module performance necessitates drawing the characteristics, typically obtained by varying voltage/current within certain ranges to derive current-voltage (I-V) and power-voltage (P-V) curves.However, this approach demands expensive setups [5], [12], substantial time, resources, and effort in collecting experimental data.Also, available methods using datasheet information are somewhat complex, as they need derivation of abstract equations from original dynamics of the P-V panels or finding slopes of the I-V curves at PV  5) The performance of this proposed approach is compared with the other approaches for the same solar module for the same temperature and irradiation conditions in terms of accuracy, complexity, and data required.

II. METHODS AND PROCEDURES A. MODELING OF SOLAR PANEL OR MODULE
Solar cells are the building blocks of any PV module.In this study, SDM is typically preferred to represent a PV cell due to its simplicity and an analogy from the same is being extended for the representation of PV modules.SDM: The most common equivalent circuit model of the solar cell used for all purposes is shown in Fig. 1 which is known as SDM.
The relationship between I t and V t is given as follows [8]: where I ph = photo-generated current in the cell, I D = diode current, R s = series resistance, I sh = current through shunt resistance, and R sh = shunt resistance of the equivalent SDM of solar cell.As per the Shockley equation, the diode current can be written as where I 0 = diode reverse saturation current, a = diode ideality factor (value is generally between 1 to 2), and V T = thermal voltage = (kT c /q) (where k = Boltzmann's constant = 1.381×10 −23 J/K, q = elementary charge = 1.602×10 −19 C, and T c = temperature of the p-n junction in Kelvin).Thus, the current I t is given by To find the unknown parameters of (3), it is nothing but extracting five indefinite parameters, i.e., SDM-Based Model of PV Panel: A PV panel or module is a combination of several PV cells connected in series and/or parallel.Its equivalent circuit is described in Fig. 2.
The output current of the PV module is formulated as follows [25]: where N s and N p are, respectively, the number of PV cells connected in series and parallel in a PV module.Similar to SDM of the solar cell, the PV module is also having five unknown parameters; these are X Module(SDM) =

B. METHODOLOGY FOR IDENTIFICATION OF SOLAR CELL MODEL PARAMETERS
Proposed Approach for Parameter Extraction: Parameter extraction generally involves the calculation of unknown quantities of a system's dynamic model.This model can replicate the behavior of the original system.In this article, the system under consideration is a PV cell or module.The proposition here is to use the minimum amount of information to find out PV system parameters.The parameters of the equivalent circuit of a solar cell or panel can be determined using only three data points on its I-V curve, which are basically, (V oc , 0), (V m , I m ), and (0, I sc ); where V oc = open-circuit voltage, I sc = short-circuit current, V m = voltage at maximum power, and I m = current at maximum power.These data can easily be obtained from any commercial manufacturer's datasheet for its PV panels.
These estimated parameters can be used to obtain the corresponding output currents for different terminal voltages using ( 1) and ( 4) at different temperatures and irradiances.This process involves fitting a curve through these three points as shown in Fig. 3 and can be considered as an optimization problem.The optimization is carried out by estimating the parameters of the SDM for single cell unit and SDM-based model of PV panels while comparing the output results with the datasheet values of the three mentioned points on the I-V curve.Now for the validation purpose, the whole I-V curve is then reconstructed with the extracted parameters and the values of the estimated currents (I t_estimated ) at different terminal voltages (V t ) are compared with experimental results under the same operating conditions to ensure the credibility of the obtained results.Not only that, the same procedure is applied on three different PV units to ensure the validity of the method applied for parameter extraction of solar panels.PV units under consideration are as follows.
For any kind of optimization, a good objective function is required.Objective functions like absolute error (AE), mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), etc. [41] have been considered for finding the difference between estimated data and experimental data.The objective function needs to be minimized to achieve the goal of finding solutions for unknowns.In this study, RMSE has been used as the objective function, which is given by (6).The expressions of MAE and RMSE are given below.
The datasheet information of considered PV units are readily available from [28] and [39], respectively.Estimated values of current (I t ) are being calculated using (3) for the solar cell represented by SDM and using (4) for the solar panel based on SDM.Now, using (6), to pose the problem as an optimization issue, the exact objective function can be  represented by OBJECTIVE_FUNCTION(X) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where f (V t I t , X SDM ) = I − I ph + I D + I for the SDM solar cell and f (V t , I t , X Module(SDM) ) = I t − N p I ph + N p I D + I sh for SDM-based PV module with N = 3 denoting the total number of available (V t , I t ) datasets from manufacturer's datasheet, X is a vector which contains the parameters to be identified.It is evident from (7), that the smaller the value of the objective function, the more accurate extracted parameters will be obtained.
As it can be seen that ( 3) or ( 4) is a transcendental equation; metaheuristic optimization techniques are most suitable for finding its solution.Thus, in this case, three such well-known optimization algorithms, e.g., PSO and  ABC optimization and HHO are applied, to minimize the objective function.Now, a flowchart is being shown in Fig. 4 which is a good visualization of the workflow for the method of extracting parameters of the solar panel, applied herein.In this case, the objective is to find the unknown PV panel parameters.
Optimization Techniques: Since all of these mentioned optimizations are widely recognized, a detailed discussion about them would be superfluous.Therefore, only the pseudocodes for these algorithms are provided as a ready reference in Tables 1-3, demonstrating their way of execution for the purpose of this article.Now, for all the simulation purposes, MaxIter = 5000 and no. of search agents = 50 have been selected for uniformity and a justified comparison between applied metaheuristics.All these algorithms are developed using MATLAB software and simulations are performed on a computer   with AMD Ryzen 5 4600H CPU @3 GHz and 16-GB RAM.Simulation results are discussed in the subsequent section.

III. RESULTS
As discussed earlier, the proposed three-point (3 pt.) technique has been applied on three different PV units.So, there will be three case studies that will justify this methodology of PV parameter extraction.The input data for different PV units are given in Table 4 [28], [39].
To compare the proposed method with other models in the literature, we adopted the upper and lower limits of the parameters for each PV panel, as quantified on the basis of results of different literature and are presented in Table 5.

Case Study-I (Considering R.T.C. France Silicon Solar Cell):
The Silicon PV cell of R.T.C. France is a 57-mm diameter commercial silicon solar cell.For this, cell data is being obtained at an irradiance G = 1000 W/m 2 and at a temperature T = 306.15K, as shown in Table 4.The measured I-V datasets [25] served as a standard in validating the findings of cell parameters.The datasets contain 26 data points for an R.T.C. France solar cell at predefined irradiance and temperature.

FIGURE 12. Error comparison of different optimizations for finding unknown parameters of Photowatt PWP-201 PV module using three-point technique.
From Fig. 5, it is clearly visible that though ABC and HHO have performed well but PSO has given a very quick optimization and the value of the objective function achieved is of the order of <10 −17 which can be considered to be 0(zero) for all valid practical requirements.In Table 6, we can have a better look at the extracted parameters values with a comparison of values of minimized objective function.Not only that, in Fig. 6, the tracking of PSO-based three-point (3 pt.) technique extracted parameters have given a better tracking of experimental I-V curve of the PV cell under consideration.In this regard, a detailed error analysis at each data point can be found in the bar chart of Fig. 11.Time taken by different algorithms is, respectively, 5.1720 s (PSO), 12.2603 s (ABC), and 14.5389 s (HHO), for their convergence during parameter extraction.
Case Study-II (Considering Photowatt PWP-201 Polycrystalline Solar Panel): For this module with 36 polycrystalline silicon cells in series, the data obtained as per Table 4 is at an irradiance G = 1000 W/m 2 and at a temperature T = 318.15K.The measured I-V datasets [25] have served as a standard in validating the findings regarding PV module parameters.The datasets contain 25 data points for a Photowatt-PWP201 solar panel at the mentioned irradiance and temperature.
Again, from Fig. 7, it can be observed that PSO is the clear winner among its competitors.Also, it is clear with Fig. 8, that the proposed three-point (3 pt.) technique is properly working for a PV module, too.All extracted parameters are within the provided boundaries and can easily be used for the prediction of output currents (I t ) at any given voltage (V t ).Thus, Table 7 gives us the comparison of extracted parameters for the PWP201 module with different metaheuristics.Time taken by different algorithms is, respectively, 4.4111 s (PSO), 10.8508 s (ABC), and 13.2104 s (HHO), for their convergence during parameter extraction.
Case Study-III (Considering Siemens SM55 Mono-Crystalline Solar Panel): For this module with 36 monocrystalline silicon cells in series, the data obtained as per Table 4 is at an irradiance G = 1000 W/m 2 and at a temperature T = 298.15K.The measured I-V datasets [24] have served as a standard in validating the findings regarding PV module parameters.The datasets contain 25 data points for a Siemens SM55 solar panel at the mentioned irradiance and temperature.This is the third panel for which the three-point (3 pt.) technique is applied and the results are worth noting.Minimized objectives have achieved a value in the range of 10 −7 to 10 −9 for ABC and HHO, respectively, whereas PSO has done again a better job to reduce the objective function to 0 (zero as <10 −18 ).Fig. 10. can give the tracking characteristics for different algorithms while establishing the fact that the extracted parameters are efficient in reproducing the I-V curve of the PV panel named SM55.
Time taken by different algorithms is, respectively, 4.5739 s (PSO), 10.8438 s (ABC), and 13.0192 s (HHO), for their convergence during parameter extraction considering SM55 PV module.Now, a detailed error analysis has been shown using Figs.11-13, for each of the PV units under parameter extraction by three different metaheuristic algorithms.In each of the cases, errors in estimated currents using parameters, extracted by the three-point technique have been shown.Results are exclusively pointing toward the capability of the method in finding these unknowns in the light of only the manufacturer's datasheet information; as the MAE and RMSE are always in the range of 10 −2 to 10 −3 while considering all the estimated currents.Table 9 is showing us different uncertainty [42] associated with the extracted PV units' parameters on the basis of PSO-based Three-point Technique.As PSO has given the best results in most of the cases, thus only this method has been considered for the said uncertainty analysis.Similar results can be obtained for other optimizations too.
Also, it is crucial to compare the achieved outcomes with relevant literature to demonstrate its acceptability.Table 10 fulfills this essential requirement by providing a clearer perspective on the usability of the proposed technique, which exhibits significantly lower complexity compared to alternative methods.It can be seen from Table 10 that methods using several data points (found by experimental setups) on the I-V curve of PV units are not producing better results always.Thus, the proposed three-point technique which only relies on three points on the I-V curve of PV units are very easy to apply, less time consuming, and can produce equivalent results or sometimes results better than the conventional methods nullifying the requirement of any experimental data during the analysis of PV units, on the basis of these extracted parameters.

IV. CONCLUSION
The developed method underwent validation using experimental data, investigating PSO, ABC optimization, and HHO to estimate solar cell parameters.It was tested for different PV units, demonstrating its accuracy across PV cell and modules.Based on the study, the following conclusions can be drawn.
1) The results indicated that utilizing the three points from the manufacturer datasheet, PSO, ABC, and HHO, all algorithms have yielded reasonable optimization outcomes, with PSO surpassing others for R.T.C. cell and PWP201, while HHO proved itself for SM55.This is in consideration of the proposed method only.
2) The proposed technique, which only needs three measurements from manufacturer datasheets, offers a highly effective methodology for estimating solar cell parameters in all commercial modules.This eliminates the need for experimental measurements.3) Testing the proposed model on the R.T.C. France solar cell confirmed its ability to perform as accurately as other available techniques.4) The validation using PWP201 and SM55 also demonstrated the model's applicability to all commercial multicell solar modules.5) Uncertainty analysis delves into the unpredictability of decision parameters.The efficacy of the proposed method in consistently yielding the best results among different techniques might appear uncertain.But the results of calculations in Table 9 imply that PSO has shown very good quality in terms of extracted parameters' predictability as the uncertainty is less than 10% for more than 92% cases under consideration.6) Finally, it is important to highlight that even without resorting to external equipment for acquiring real I-V data measurements, the proposed three-point technique, solely reliant on manufacturer datasheets, demonstrates the ability to generate dependable I-V curves for various photovoltaic (PV) modules on the basis of extracted parameters.Notably, this approach offers a straightforward means of parameter extraction and occasionally outperforms existing intricate methodologies.This can be confirmed from the RMSE achieved for the PWP201 module with the PSO-based three-point technique (first row of Table 10).This model can be utilized for various purposes, mostly where experimental data is unavailable.It provides results comparable to standard models which rely on multiple measurement data points.Moreover, this model holds potential for MPPT research and development, as well as facilitating the management of PV-based microgrids.Further discussion on these topics will be presented in a subsequent study.

FIGURE 2 .FIGURE 3 .
FIGURE 2. Equivalent circuit model of the SDM-based PV module.

FIGURE 4 .
FIGURE 4. Workflow for the extraction of PV system parameters using three-point technique with metaheuristic algorithms.

FIGURE 5 .TABLE 6 .
FIGURE 5. Comparison of convergences of simulations for finding unknown parameters of R.T.C. France solar cell with PSO, ABC, and HHO.

FIGURE 6 .
FIGURE 6. I-V Curves of R.T.C. France solar cell with measured current and estimated values of current for PSO, ABC, and HHO.

FIGURE 7 .
FIGURE 7. Comparison of convergences of simulations for finding unknown parameters of Photowatt-PWP201 PV module with PSO, ABC, and HHO.

FIGURE 8 .
FIGURE 8. I-V Curves of Photowatt-PWP201 solar panel with measured current and estimated values of current for PSO, ABC, and HHO.

FIGURE 9 .
FIGURE 9. Comparison of convergences of simulations for finding unknown parameters of Siemens SM55 PV module with PSO, ABC, and HHO.

FIGURE 10 .
FIGURE 10.I-V Curves of Siemens SM55 solar panel with measured current and estimated values of current for PSO, ABC, and HHO.

FIGURE 11 .
FIGURE 11.Error comparison of different optimizations for finding unknown parameters of R.T.C. France PV module using three-point technique.

FIGURE 13 .
FIGURE 13.Error comparison of different optimizations for finding unknown parameters of SM55 PV module using three-point technique.TABLE 9. Uncertainty analysis of extracted parameters using three-point technique by PSO.