Using a novel optimization algorithm for parameter extraction of photovoltaic cells and modules

Among all renewable energy sources, solar cells are considered the most popular solution for a clean source of energy and have a wide range of applications from few watts to Megawatt industrial and domestic loads. Building a precise mathematical model based on nonlinear equations for solar cells as well as photovoltaic (PV) modules is an essential issue for reasonable performance assessment, control and optimal operation of PV energy systems. In the current study, a novel optimization algorithm, Tree Growth Algorithm (TGA), is applied for accurate and efficient extraction of the unknown solar cell and PV module parameters. TGA is applied for estimating the unidentified parameters of PV models. Single diode model (SDM), double diode model (DDM) and three diode model (TDM) are investigated in the mathematical models of both solar cells and PV modules. The obtained results from the application of TGA to achieve this objective are compared with different algorithms reported in the literature. Moreover, the results demonstrated that the proposed algorithm of TGA superior to other reported methods. The good matching of the I-V characteristic curve of the computed parameters with those of the measured data from the manufacturer’s PV modules/cells datasheet proved that the proposed TGA may function as a competitor to the methods provided in literature for parameters’ identification of PV of solar cells.

As countries attach importance to environmental protection, clean energy has become a hot topic. Among them, solar energy, as one of the efficient and easily accessible clean energy sources, has received widespread attention. An essential component in converting solar energy into electricity are solar cells. However, a major optimization difficulty remains in precisely and effectively calculating the parameters of photovoltaic (PV) models. In this regard, this study introduces an improved rime optimization algorithm (RIME), namely ERINMRIME, which integrates the Nelder-Mead simplex (NMs) with the environment random interaction (ERI) strategy. In the later phases of ERINMRIME, the ERI strategy serves as a complementary mechanism for augmenting the solution space exploration ability of the agent. By facilitating external interactions, this method improves the algorithm’s efficacy in conducting a global search by keeping it from becoming stuck in local optima. Moreover, by incorporating NMs, ERINMRIME enhances its ability to do local searches, leading to improved space exploration. To evaluate ERINMRIME's optimization performance on PV models, this study conducted experiments on four different models: the single diode model (SDM), the double diode model (DDM), the three-diode model (TDM), and the photovoltaic (PV) module model. The experimental results show that ERINMRIME reduces root mean square error for SDM, DDM, TDM, and PV module models by 46.23%, 59.32%, 61.49%, and 23.95%, respectively, compared with the original RIME. Furthermore, this study compared ERINMRIME with nine improved classical algorithms. The results show that ERINMRIME is a remarkable competitor. Ultimately, this study evaluated the performance of ERINMRIME across three distinct commercial PV models, while considering varying irradiation and temperature conditions. The performance of ERINMRIME is superior to existing similar algorithms in different irradiation and temperature conditions. Therefore, ERINMRIME is an algorithm with great potential in identifying and recognizing unknown parameters of PV models.

the important issue in the extraction of the unknown parameters in the photovoltaic model is the mathematical models.Therefore, a five equivalent circuit is analyzed in this work.The unknown parameters are five for single diode model, seven for double-diode model, eight for modified double-diode, and nine for three-diode model and ten for modified three-diode parameters.The performance of the modified three-diode model and three-diode model after estimate all parameters without assumption for any variable are compared with the performance of the both single diode model, double-diode model and also the modified double-diode of the same solar cell.Cuckoo search optimization algorithm (CSOA) is proposed for the estimation of the unknown parameters for the five solar cell equivalent models.The root mean square error, the absolute error for current and power, and the maximum power point absolute error are analyzed to the performance of the five solar cell models.

This paper presents a critical analysis of the meta-heuristic techniques used in various researches on the optimisation of photovoltaic (PV) parameters, which involves the use of different algorithms in order to extract and improve these parameters from the single diode model (SDM), double diode model (DDM) and three diode model (TDM) respectively. The modelling parameters such as the photon current, saturation current, the series and parallel resistances are investigated to understand the optimum value. It will also equate the results of datasheet values from PV manufactures with experiment values obtained from PV module measurements. The meta-heuristics techniques to be considered include genetic algorithm (GA), particle swarm optimisation (PSO), harmony search (HS), flower pollination algorithm (FPA), simulated annealing (SA), teaching learning based optimisation (TLBO), and other different hybrid solutions to optimize the convergence speed. Root mean square error (RMSE) is used as a performance indicator of each meta-heuristic technique. These optimisation techniques are utilised in extracting the parameters of a 5 W polycrystalline panel at standard testing conditions. The results presented in this paper compared the performances of the mentioned meta-heuristics on the single, double and triple diode models respectively.

Photovoltaic technology, which converts the sun’s light energy directly into electricity, can be used to make photovoltaic cells. The use of photovoltaic cells is centered on the idea of a low-carbon economy and green environmental protection, which effectively addresses the pollution problem in smart cities. Accurate identification of photovoltaic cell parameters is critical for battery life cycle and energy utilization. To accurately identify the single diode model (SDM), dual diode model (DDM), and three diode model (TDM) parameters of solar photovoltaic cells, and an improved honey badger algorithm (IHBA) is proposed in this paper. In the early stages of iteration, the IHBA uses the spiral exploration mechanism to improve the population’s global exploration ability. Furthermore, a density update factor that varies according to the quasi-cosine law is introduced to speed up the algorithm’s convergence speed and prevent the algorithm from falling into the local optimal value. Simultaneously, the pinhole imaging strategy is utilized to disturb the present optimal position to improve the algorithm’s optimization accuracy. The experimental comparison results of 18 benchmark test functions, Wilcoxon rank sum statistical test, and 30 CEC2014 test functions reveal that an IHBA shows remarkable performance in convergence speed, optimization accuracy, and robustness. Finally, the IHBA is used to identify the parameters of three kinds of commercial silicon R.T.C French solar photovoltaic cell models with a 57 mm diameter. In comparison to other algorithms, the IHBA can minimize the root mean square error (RMSE) between the measured current and estimated current at the fastest speed, demonstrating the practicality and superiority of the IHBA in tackling this problem.

Photovoltaic parameter estimation using honey badger algorithm and African vulture optimization algorithm

A photovoltaic (PV) module is an equipment that converts solar energy to electrical energy. A mathematical model should be presented to show the behavior of this device. The well-known single-diode and double-diode models are utilized to demonstrate the electrical behavior of the PV module. “Matlab/Simulink” is used to model and simulate the PV models because it is considered a major software for modeling, analyzing, and solving dynamic system real problems. In this work, a new modeling method based on the “Multiplexer and Functions blocks” in the "Matlab/Simulink Library" is presented. The mathematical analysis of single and double diodes is conducted on the basis of their equivalent circuits with simple modification. The corresponding equations are built in Matlab by using the proposed method. The unknown internal parameters of the PV panel circuit are extracted by using the PV array tool in Simulink, which is a simple method to obtain the PV parameters at certain weather conditions. Double-diode model results are compared with the single-diode model under various irradiances and temperatures to verify the performance and accuracy of the proposed method. The proposed method shows good agreement in terms of the I–V and P–V characteristics. A monocrystalline NST-120 W PV module is used to validate the proposed method. This module is connected to a variable load and tested for one summer day. The experimental voltage, current, and power are obtained under various irradiances and temperatures, and the I–V and P–V characteristics are obtained.

Solar cell/module modeling involves the formulation of the non-linear current versus voltage (I-V) curve. Determination of parameters plays an important role in solar cell/module modeling. This paper presents an application of the improved PSO search method and Particle Swarm Optimization technique for identifying the unknown parameters of solar cell and photovoltaic module models, namely, the series resistance, shunt resistance, generated photocurrent, saturation current, and ideality factor that govern the current-voltage relationship of a solar cell/module. For the confirmation of accuracy of the proposed method, a measurement data of 57 mm diameter commercial (R.T.C. France) silicon solar cell and a module consisting of 36 polycrystalline silicon cells (Photowatt-PWP 201) has been selected and the best optimal value of each parameter has been obtained using Improved PSO. Comparative study among different parameter estimation techniques is presented to demonstrate to verify the accurateness and the effectiveness of the proposed approach.

The operation of Photovoltaic (PV) system mainly rely on appropriate modeling of solar cells and optimum approximation of parameters associated with them. Recently, various hybrid, numerical and analytical techniques were proposed to extract optimal parameters of PV cell. This paper presents an efficient approach, A Simulated Annealing Inertia Weight Particle Swarm Optimization (SAIW-PSO) for optimal estimation of PV parameters for double and single diode models. In addition, fitness indicator is guided using the Newton Raphson Method (NRM) that supports SAIW -PSO to explore the optimal solution. The premature convergence problem of typical PSO is resolved by the proposed framework. The strength of proposed approach is validated under standard test conditions (STC) on RTC France Silicon Solar cell. The SAIW-PSO is capable to explore optimum solution in smaller number of iterations and less computation time. The obtained results clearly depict that the proposed framework is fast, efficient and much accurate for PV cells parameters approximation.

Parameters identification of photovoltaic models by using an enhanced adaptive butterfly optimization algorithm

The modeling and control of photovoltaic and other engineering systems highly depend on the accuracy of parameter identification. However, parameter extraction for photovoltaic equivalent models typically presents a high-dimensional, strongly nonlinear, and multimodal global optimization problem. Traditional analytical or gradient-based methods are sensitive to initial values and easily fall into local optima. To address this issue, this paper proposes a multi-strategy improvement teaching–learning-based optimization algorithm (SNTLBO). A social learning network structure with symmetric interaction topology is introduced into the classical TLBO framework to characterize the knowledge propagation relationships among individuals. Through this symmetric and balanced information exchange mechanism, learners can be guided not only by the teacher but also by multiple neighbors within the network, enabling more diverse and symmetric exploration of the search space and enhancing population diversity and global search capability. Furthermore, a teacher reputation mechanism is constructed, where historical performance is used to weight teacher influence, strengthening the guidance of high-quality solutions and accelerating convergence. Meanwhile, an adaptive teaching factor is designed to dynamically adjust the teaching intensity based on the distance between the teacher and students in the solution space, maintaining a dynamic balance (symmetry) between exploration and exploitation. To evaluate the performance of the proposed algorithm, SNTLBO is systematically compared with 11 advanced optimization algorithms on two benchmark test suites, CEC2017 (30D, 50D) and CEC2022 (10D, 20D). Non-parametric statistical tests are conducted to assess significance. The results demonstrate that SNTLBO shows competitive advantages in terms of convergence speed, solution accuracy, and stability. Finally, SNTLBO is applied to the parameter estimation of single-diode, double-diode, triple-diode, quadruple-diode, and photovoltaic module models. Experimental results show that the proposed algorithm achieves higher identification accuracy and robustness in terms of RMSE, IAE, and I–V/P–V curve fitting, verifying its effectiveness and practical value for complex global optimization and practical engineering applications.

This paper compares two methods for extraction of photovoltaic (PV) module parameters. The numerical method called Gauss-Seidel, used on the single diode model, and the analytical method applied on the double diode model. Both methods are based on the manufacturer’s datasheets to extract the five parameters. These methods are validated using monocrystalline PV module. The modified mathematical modeling equations are classified into models 1 to 5. Only model 2 and model 4 are used for the analytical method. Each model is based on the different combinations of the ideality factor, the series resistance, photocurrent and saturation current plotted under varying temperature and irradiance. The accuracy of PV module based on both methods is evaluated by Absolute Error (AE). In order to evaluate the effectiveness and accuracy of the proposed methods, the equations were implemented in the MATLAB/Simulink environment and the results obtained are compared with extracted experimental data.

Lately, there has been a notable interest among researchers in constructing a precise mathematical representation using experimentally gathered data from solar cells and photovoltaic (PV) modules. This representation serves as a means to simulate and assess the performance of PV systems. In this study, the Walrus Optimization Algorithm (WaOA) and Cheetah optimizer (CO) were employed to deduce the unknown parameters inherent in various modes of solar cells and PV modules, specifically the single-diode model (SDM) and double-diode model (DDM). Furthermore, the evaluation criterion for this work involved measuring the route mean square error (RMSE) between the simulated outcomes generated using identified parameters for each mathematical model and the actual voltage derived from measurements of solar cells and PV modules. Notably, a comprehensive statistical analysis was carried out to validate the efficacy and stability of the WaOA and CO algorithms. These algorithms were compared against other optimization techniques for their effectiveness in solving the optimization challenge of accurately estimating the design parameters of PV systems. The outcomes of simulations and the extensive statistical assessment substantiate the superior performance and reliability of the Walrus Optimization Algorithm in effectively extracting parameter values from diverse PV modules under various operational scenarios.

Clean energy resources have become a worldwide concern, especially photovoltaic (PV) energy. Solar cell modeling is considered one of the most important issues in this field. In this article, an improvement for the search steps of the bald eagle search algorithm is proposed. The improved bald eagle search (IBES) was applied to estimate more accurate PV model parameters. The IBES algorithm was applied for conventional single, double, and triple PV models, in addition to modified single, double, and triple PV models. The IBES was evaluated by comparing its results with the original BES through 15 benchmark functions. For a more comprehensive analysis, two evaluation tasks were performed. In the first task, the IBES results were compared with the original BES for parameter estimation of original and modified tribe diode models. In the second task, the IBES results were compared with different recent algorithms for parameter estimation of original and modified single and double diode models. All tasks were performed using the real data for a commercial silicon solar cell (R.T.C. France). From the results, it can be concluded that the results of the modified models were more accurate than the conventional PV models, and the IBES behavior was better than the original BES and other compared algorithms.

It is important to investigate the long-term performances of an accurate modeling of photovoltaic (PV) systems, especially in the prediction of output power, with single and double diode models as the configurations mainly applied for this purpose. However, the use of one configuration to model PV panel limits the accuracy of its predicted performances. This paper proposes a new hybrid approach based on classification algorithms in the machine learning framework that combines both single and double models in accordance with the climatic condition in order to predict the output PV power with higher accuracy. Classification trees, k-nearest neighbor, discriminant analysis, Naïve Bayes, support vector machines (SVMs), and classification ensembles algorithms are investigated to estimate the PV power under different conditions of the Mediterranean climate. The examined classification algorithms demonstrate that the double diode model seems more relevant for low and medium levels of solar irradiance and temperature. Accuracy between 86% and 87.5% demonstrates the high potential of the classification techniques in the PV power predicting. The normalized mean absolute error up to 1.5% ensures errors less than those obtained from both single-diode and double-diode equivalent-circuit models with a reduction up to 0.15%. The proposed hybrid approach using machine learning (ML) algorithms could be a key solution for photovoltaic and industrial software to predict more accurate performances.