Single-diode Solar Cell Model Research Articles

Iterative Root-Finding Algorithm for Accurate Parameter Extraction of Solar Photovoltaic Cells

The performance of photovoltaic models depends significantly on the accuracy of their parameters, which are determined by the chosen method and objective function. Extracting these parameters accurately under different environmental conditions is essential to enhance reliability, accuracy, and minimize system costs. In this research, a novel technique is proposed for extracting the electrical parameters of the solar cell single diode model, including saturation current, serial resistance, parallel resistance, and ideality factor. To overcome the challenges posed by the chaotic behavior of the I-V curve equation, an improved Iterative Root-Finding algorithm is introduced. This algorithm acts as an optimization tool, increasing the likelihood of obtaining highly accurate solutions by minimizing the quadratic error between experimental and theoretical characteristics in a shorter time frame. The numerical and experimental results demonstrate the effectiveness of this approach in solar module modeling, showing squared errors approaching zero. This study opens new possibilities for improving the accuracy and reliability of photovoltaic models, leading to more efficient solar energy systems.

A novel artificial hummingbird algorithm improved by natural survivor method

The artificial hummingbird algorithm (AHA) has been applied in various fields of science and provided promising solutions. Although the algorithm has demonstrated merits in the optimization area, it suffers from local optimum stagnation and poor exploration of the search space. To overcome these drawbacks, this study redesigns the update mechanism of the original AHA algorithm with the natural survivor method (NSM) and proposes a novel metaheuristic called NSM-AHA. The strength of the developed algorithm is that it performs population management not only according to the fitness function value but also according to the NSM score value. The adopted strategy contributes to NSM-AHA exhibiting powerful local optimum avoidance and unique exploration ability. The optimization ability of the proposed NSM-AHA algorithm was compared with 21 state-of-the-art algorithms over CEC 2017 and CEC 2020 benchmark functions with dimensions of 30, 50, and 100, respectively. Based on the Friedman test results, it was observed that NSM-AHA ranked 1st out of 22 competitive algorithms, while the original AHA ranked 8th. This result highlights that the NSM update mechanism provides a remarkable evolution in the convergence performance of the original AHA algorithm. Furthermore, two constrained engineering problems including the optimization of single-diode solar cell model (SDSCM) parameters and the design of a power system stabilizer (PSS) are solved with the proposed algorithm. The NSM-AHA algorithm provided better results compared to other algorithms with a value of 9.86E − 04 root mean square error for SDSCM and 1.43E − 03 integral time square error for PSS. The experimental results showed that the proposed NSM-AHA is a competitive optimizer for solving global and engineering problems.

An Accurate Explicit Six-Parameter Solar Cell Model Based on Single-Diode and Its Parameter Extraction for Seven Photovoltaic Technologies

Abstract The mathematical modeling of solar cells and panels is critical in many photovoltaic applications. However, the standard single-diode solar cell model, commonly selected to model these devices, is implicit and difficult to integrate into simulation software. Therefore, exact explicit solutions of this model, more suitable for computing purposes, have been proposed based on the Lambert W-function. This work introduces an explicit single-diode, easy-to-use six-parameter solar cell model. The proposed model is formulated with elementary functions. The model is developed and tested over seven photovoltaic technologies as an alternative to traditional approaches. Results of the extensive comparison of the three models (implicit, explicit Lambert W, and explicit six-parameter) show that the proposed approach is more accurate (14.81% relative improvement on average compared to the traditional methods), almost as fast as the Lambert W approach and much faster than the implicit approach. Due to its simplicity and accuracy, the proposed model will become an alternative in photovoltaic applications such as energy prediction and maximum power point tracking.

Comparative performance analysis of metaheuristic search algorithms in parameter extraction for various solar cell models

In today's technology, solar energy continues to be one of the leading renewable energy sources in electricity production methods due to its abundance on the Earth's surface and its non-polluting nature. In solar photovoltaic (PV) systems, it is relatively easy to produce electricity from the sun, and their efficiency can be enhanced by accurately estimating the electrical parameters of solar cells. From this point of view, this paper has focused on solar cell design to improve the performance of solar PV systems. To achieve this target, fitness-distance balance-based stochastic fractal search (FDB-SFS), particle swarm optimization (PSO), student psychology-based optimization (SPBO), and adaptive guided differential evolution (AGDE) algorithms are employed. The experimental analysis is performed on single-diode solar cell, double-diode solar cell, and three PV modules. Considering the experimental results, it is observed that the best estimation accuracy is reached by the FDB-SFS algorithm. Accordingly, root mean square error (RMSE) values between measured and estimated data were calculated to be 9.86E-04 for the single-diode solar cell model, 9.84E-04 for the double-diode solar cell model, 2.42E-03 for the Photowatt-PWP201 module, 1.72E-03 for STM6–40/36 module, and 1.67E-02 for STP6–120/36 module. Consequently, the present paper reports that FDB-SFS is an efficient and powerful method for parameter extraction of solar photovoltaic models.

Enhancement of Power Conversion Efficiency of Non-Fullerene Organic Solar Cells Using Green Synthesized Au-Ag Nanoparticles.

Organic-based photovoltaics are excellent candidates for renewable energy alternatives to fossil fuels due to their low weight, low manufacturing cost, and, in recent years, high efficiency, which is now above 18%. However, one cannot ignore the environmental price of the fabrication procedure due to the usage of toxic solvents and high-energy input equipment. In this work, we report on the enhancement of the power conversion efficiency non-fullerene organic solar cells by incorporating green synthesised Au-Ag nanoparticles, using onion bulb extract, into the hole transport layer poly (3,4-ethylene dioxythiophene)-poly (styrene sulfonate) (PEDOT: PSS) of Poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b;4,5-b']dithiophene-2,6-diyl-alt-(4-(2-ethylhexyl)-3 fluorothieno[3,4-b]thiophene-)-2-carboxylate-2-6-diyl)]: 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2',3'-d']-s-indaceno[1,2-b:5,6-b']dithiophene (PTB7-Th: ITIC) bulk-heterojunction organic solar cells. Red onion has been reported to contain quercetin, which serves as a capping agent that covers bare metal nanoparticles, thus reducing exciton quenching. We found that the optimized volume ratio of NPs to PEDOT: PSS is 0.06:1. At this ratio, a 24.7% enhancement in power conversion efficiency of the cell is observed, corresponding to a 9.11% power conversion efficiency (PCE). This enhancement is due to an increase in the generated photocurrent and a decrease in the serial resistance and recombination, as extracted from the fitting of the experimental data to a non-ideal single diode solar cell model. It is expected that the same procedure can be applied to other non-fullerene acceptor-based organic solar cells, leading to an even higher efficiency with minimal effect on the environment.

An analysis on the performance of metaheuristic algorithms for the estimation of parameters in solar cell models

Alternative energies will be the engine that moves the world in the future; therefore, researchers focus their attention on the problems related to designing and properly exploiting this type of energy. Artificial intelligence methods are explored as tools to improve different branches of alternative energies. In this context, metaheuristic algorithms (MA) are optimization techniques that have been explored in the field of solar cell design. This article analyses the performance of different MAs for modeling solar cells by estimating the parameters of photovoltaic (PV) diode models. The MA used are part of a recent generation of techniques that include innovative processes that permits a proper selection of the optimization operators in the iterative search; such algorithms are the Artificial Hummingbird Algorithm (AHA), Aquila Optimizer (AO), African Vulture Optimization Algorithm (AVOA), Equilibrium Optimizer (EO), Golden Eagle Optimizer (GEO), Side Blotched Lizard Algorithm (SBLA), Social Network Search (SNS), and Reptile Search Algorithm (RSA). We implemented them to optimize the parameters of different models of solar cells with arrays of one, two, and three diodes. The experimental analysis performed on an R.T.C. France solar cell demonstrates which methods are the most suitable for the identification of unknown parameters in three PV models named single diode solar cell model (SDSCM), double diode solar cell model (DDSCM), and triple diode solar cell model (TDSCM). The results were statistically analyzed with Voltage–Current and Voltage–Power tests, comparisons of the best-optimized parameters, convergence plots, four error types such as Root Mean Square Error (RMSE), Absolute Error (AE), Mean Absolute Error (MAE), and Normalized Root Mean Square Error (NRMSE), a run-time analysis and non-parametric tests. The study converges in comparing and defining which of the implemented MA’s is the best alternative for the design of solar cells, concluding that some tested methods, such as AHA, can improve the efficiency of this class of devices; with RMSE values of 0.000986 for SDSCM, 0.00098353 for DDSCM, and 0.0009855 for TDSCM and the fourth-best average execution time according to the overall ranking.

Probabilistic screening and behavior of solar cells under Gaussian parametric uncertainty using polynomial chaos representation model

The paper presents a hierarchical polynomial chaos expansion-based probabilistic approach to analyze the single diode solar cell model under Gaussian parametric uncertainty. It is important to analyze single diode solar cell model response under random events or factors due to uncertainty propagation. The optimal values of five electrical parameters associated with the single diode model are estimated using six deterministic optimization techniques through the root-mean-square minimization approach. Values corresponding to the best objective function response are further utilized to describe the probabilistic design space of each random electrical parameter under uncertainty. Adequate samples of each parameter corresponding Gaussian uncertain distribution are generated using Latin hypercube sampling. Furthermore, a multistage probabilistic approach is adopted to evaluate the model response using low-cost polynomial chaos series expansion and perform global sensitivity analysis under specified Gaussian distribution. Coefficients of polynomial basis functions are calculated using least square and least angle regression techniques. Unlike the highly non-linear and complex single diode representation of solar cells, the polynomial chaos expansion model provides a low computational burden and reduced complexity. To ensure reproducibility, probabilistic output response computed using proposed polynomial chaos expansion model is compared with the true model response. Finally, a multidimensional sensitivity analysis is performed through Sobol decomposition of polynomial chaos series representation to quantify the contribution of each parameter to the variance of the probabilistic response. The validation and assessment result shows that the output probabilistic response of the solar cell under Gaussian parametric uncertainty correlates to a Rayleigh probability distribution function. Output response is characterized by a mean value of 0.0060 and 0.0760 for RTC France and Solarex MSX83 solar cells, respectively. The standard deviation of pm 0.0034 and pm 0.0052 was observed in the probabilistic response for RTC France and Solarex MSX83 solar cells, respectively.

Some Step Methods Applied to Nonlinear Equation

In the present work, we exhibit a third order family of a new iteration method Dekker's and Classic Chord methods for solving nonlinear equations of single diode solar cell model. These methods have free from computation of second order derivatives of the functions and per iteration, one estimation of the function; while just two evaluations involving it is first derivative. Analysis of this family of these numerical methods investigates that it is iterative solution is convergence. Some numerical examples are introduced to show the accuracy, efficiency and good performance of the proposed method.

Evaluation and Determination of the Parameters of a Photovoltaic Cell by an Iterative Method

This paper presents an iterative method Predictor-Corrector Hally Method (HM) for finding the voltage of a solar cell single diode model from the equivalent circuit. The purposes of the obtained results are to reduce the number of iterations. Two numerically methods are applied and compared; newton's and Hally methods. The results showed that the proposed is the most efficient compare with NRM. The goal of the present work; the results obtained of PV parameters by means of various techniques and these results are compared and discussed. The acquired results presented the suggested technique (HM) was a sufficient and effective tool for solving the solar cell's model with a least iterations. All the calculations are achieved using Matlab program

Determination of PV Model Parameters Using Bisection and Secant Methods

The mathematical modeling of solar cell device is used to demonstrate the equivalent circuit of single-diode solar cell model operating under environmental conditions. In this work, bisection (BM) and secant (SM) Methods currently exists to demonstrate the non-linear electrical behavior of this device. The proposed method is tested in order to solve non-linear equation of PV cell with various values of load resistance are characterized. Comparisons between these numerical examples have been compared. The main idea of the present work is to calculate the PV parameters numerically using different methods with the comparison between them. The results showed that secant method is the best because it has least iteration to obtain the optimal values of the PV parameters.

Analysing the effects of solar insolation and temperature on PV cell characteristics

Shortage of power, degradation of the environment, and high cost associated with fossil-fuels like coal, natural gas, oil, etc. compel us to find some economical, sustainable and eco-friendly energy sources. Presently, solar energy is gaining worldwide acceptance fora long and is gathering people’s attention as it is not only clean, pollution-free but also available on earth without any cost. The usage of solar energy in an efficient way is a big challenge for all researchers. The most commonly used materials for the fabrication of solar cells are mono-crystalline silicon, thin-film technology, polycrystalline silicon and nano-materials. These materials have selected because they are all either in production or have the expectancy of being in production over the next few years. In the present scenario, silicon material based PV cells are dominating the power industry. But in the coming time, nanomaterials such as graphene, carbon nanotubes and many others will be dominating the systems due to their small size and high electrical conductivity. Studying the PV cell characteristics is an important way to know that how a solar cell works and responding to various parameters. This study can be done either through fabrication or mathematical modeling. Hence, in this paper, a single diode solar cell model is chosen and the effect of intensity of solar insolation and temperature is seen. Further, the simulations are being performed to understand the IV and PV characteristics. Finally, the effect of variations in temperature and solar irradiance on electrical parameters such as s/c current, Fill-Factor, o/c voltage, and conversion efficiency have been also discussed.

Turbulent Flow of Water-Based Optimization Using New Objective Function for Parameter Extraction of Six Photovoltaic Models

With the development of new energy power systems, the estimation of the parameters of photovoltaic (PV) models has become increasingly important. Weather changes are random; therefore, the changes in the PV output power are periodic and nonlinear. Traditional power prediction methods are based on linearity, and relying only on a time series is not feasible. Consequently, metaheuristic algorithms have received considerable attention to extract the parameters of solar cell models and achieve excellent performance. In this study, the Turbulent Flow of Water-based Optimization (TFWO) is used to estimate the parameters of three traditional solar cell models, namely, Single-Diode Solar Cell Model (SDSCM), Double-Diode Solar Cell Model (DDSCM), and Three-Diode Solar Cell Model (TDSCM), in addition to three modified solar cell models, namely, modified SDSCM (MSDSCM), modified DDSCM (MDDSCM), and modified TDSCM (MTDSCM). Moreover, a polynomial equation of five degrees for the sum of squared errors (PE5DSSE) between the measured and calculated currents was used as a new objective function for extracting the parameters of the solar cell models. The proposed objective function delivered improved prediction accuracy than common objective functions. Experimental results revealed the effectiveness of TFWO compared with six counterparts, namely, “Tunicate Swarm Algorithm (TSA), Grey wolf optimizer (GWO), modified particle swarm optimization (MPSO), Cuckoo Search algorithm (CSA), Moth flame optimizer (MFO) and Teaching Learning based optimization algorithm (TLBO),) for all the traditional and modified solar cell models based on the optimal parameters extracted using best PE5DSSE values.

Evolution of the physical parameters of photovoltaic generators as a function of temperature and irradiance: New method of prediction based on the manufacturer’s datasheet

The characterization of photovoltaic generators with acceptable accuracy require the use of suitable experimental devices and appropriate methods. In this study, the used I-V curve tracer (Amiry et al. 2018) [1] allows to collect a current- voltage characteristic of a hundred (I, V) points under real operating conditions. Each (I, V) point is taking in one millisecond. A new method for extracting physical parameters of solar cell single diode model is presented. It allows for the prediction of an I-V characteristic without recourse to any approximation. It is based on considering the current-voltage values (I, V) at short-circuit point (ISC, 0), maximum power point (Im, Vm) and open circuit point (0, VOC) provided by the manufacturer. In addition, the current and voltage temperature coefficients KIm and KVm respectively at maximum power point are estimated independently using two explicit equations associated with two simplified models. The simulation of I-V curves built based on extracted physical parameters depending on temperature allows for making equations that introduce coefficients and allow for approximate description of their behavior depending on temperature. These coefficients form a new basis for technical datasheets to predict the performance of photovoltaic generators according to their operating temperatures. The irradiance effect has been taken into account by introducing specific terms depending on G in these equations. The accuracy of this developed approach is assessed by comparing the experimental characteristics with those plotted using extracted physical parameters values by implemented method and those obtained by other extraction methods reported in the literature.

Reliability analysis and design of a single diode solar cell model using polynomial chaos and active subspace

In recent times, photovoltaic power systems are being used worldwide with a high rate of adoption as a source of clean energy. It is therefore important to study the impact of environmental uncertainties on the yielding power of these solar cells. This paper considers the problem of reliability analysis/design for the yield power in a single diode solar cell when there are uncertainties in the outdoor conditions (e.g. temperature, irradiance) with polynomial chaos and active subspace methods. With the polynomial chaos based surrogate modeling of the yield power, one can accurately and efficiently compute the mean and variance of the yielding power. Following this, reliability design is formulated as a bi-objective optimization problem involving (A) maximization of the mean power yield and (B) minimization of the power yield variation under temperature and irradiance uncertainties. The active subspace method is used to simplify the bi-objective formulation. It is found that utilizing the active subspace method can simplify the bi-objective nonlinear design problem to a bi-objective linear optimization one. Our simulation result shows that the bi-objective linear optimization problem results in a higher mean and lower variance in the maximum power point (MPP) than the direct non-linear design approach.

Diagnostics of Solar Cells

The paper represents the mathematical model for diagnostics of solar cell. The research objectives are the problem of determining a solar cell technical condition during its operation. The solar cell diagnostics is based on the mathematical model of solar cells. The single-diode solar cell model is characterized by a slight deviation of the theoretically calculated characteristics from the characteristics of the real solar cell, one of the reasons being the complexity of the accurate measurement of the series resistance. The single-diode solar cell model uses the current and voltage ratio in the form of an implicit function and it cannot be solved directly. For its solution it is necessary to use numerical methods. This is main disadvantage of the single-diode solar cell model. The methodological approach to increasing the reliability of the solar cell diagnostic has been proposed, in terms of multi-parameter the solar cell diagnostic by applying the solar cell impedance model.

RESISTANCE, TEMPERATURE AND IRRADIANCE PARAMETER ANALYSIS OF A SINGLE DIODE PHOTOVOLTAIC CELL MODEL

This paper presents an analysis of parameter variations of a single-diode solar cell model. The parameters analyzed are the series resistance, shunt resistance, temperature and radiation change. Model equations are derived and simulated. All simulations were performed in MatLab using looping iterative method. Results obtained show that an increase in series resistance causes a decrease in short-circuit current and output power. A decrease in shunt resistance also causes a decrease in short circuit current and output power. An increase in temperature above the nominal value of 25oC causes a significant decrease in the open circuit voltage. An increase in irradiance above a nominal value of 1000 W/m2 causes the short circuit current to increase from 8.21A at 1000 W/m2 to 10.67A at 1300W/m2. It can be seen that parameter variations have a net effect on the current-voltage (I-V) and power-voltage (P – V) characteristics.

Numerical Analysis of an Industrial Polycrystalline Silicon Photovoltaic Module Based on the Single-Diode Model Using Lambert W Function

It is adopted the single-diode solar cell model and extended for a PV module. The current vs. voltage (I-V) characteristic based on the Lambert W-function was used. The estimation parameters for the simulation approach of the photovoltaic (PV) module make use of Levenberg-Marquardt method. It was considered an industrial polycrystalline silicon photovoltaic (PV) module and the simulated results were compared with the experimental ones extracted from a specific datasheet. The I-V characteristic for the analysed PV module and its maximum output power are investigated for different operating conditions of incident solar radiation flux and temperature, as well as parameters related to the solar cells material and technology (series resistance, shunt resistance and gamma factor). The analysis gives indications and limitations for design and optimization of the performance for industrial PV modules. This study can be implemented in any type of PV module.

Non-approximated series resistance evaluation by considering high ideality factor in organic solar cell

The quality performance analysis of any solar cell can only be predicted through the parameters extracted from its current-voltage characteristics. Herein, we demonstrate an efficient analytical method to calculate the series resistance of organic solar cells without any pre approximation. It has been shown that the inaccuracy in series resistance takes place due to the high ideality factor of the organic based solar cells, usually ranging from 2-5. Using a systemic approach, we solved the single diode solar cell model to determine the series resistance expression. The dependence of series resistance on ideality factor of the device and the reverse saturation current calculation through the illuminated current-voltage characteristics has been presented here for the first time. The entire method has been programmatically realized in MATLAB. The extracted parameters values have been compared to the other methods for the proof of validation and it shows good agreement where as some outputs are better resolved. Additionally, the effectiveness of the present method is also matched with NREL certified silicon solar cell (reference cell model 60623) parameter extracted from K24XX cell software provided with PET cell tester model, CT200AAA solar simulators. The present proposed method is not restricted to the organic solar cell only but it can also be applied for the other type of solar cell as well. Therefore, the proposed method shows the relevance in the present scenario of solar cell research and development.

Effects of Mechanical Damage and Temperature on the Electrical Performance of CIGS Thin-Film Solar Cells

In this paper, we investigate the effect of mechanical damage and temperature on copper indium gallium diselenide (CIGS) thin-film solar cells through experiments and modeling. After generating mechanical damage on CIGS solar cell with 20% increments, the electrical performance was measured (current–voltage curve) while temperature was varying from 10 to 70 °C at 20° increments. Other measured values are open-circuit voltage ( V oc), fill factor (ff), maximum power ( P max). Those electrical values ( V oc, ff, P max) are found as a function of temperature and percent damage. Moreover, the parameters of the single diode solar cell model were obtained as a function of temperature and percentage damage: light generation current ( IL ), saturation current ( I0 ), shunt resistance ( R sh), and series resistance ( R s ). Our paper contributes to the deeper understanding of the concurrent effect of temperature and mechanical damage to solar cells.

Review of Parameter extraction methods for single-diode model of solar cell

In recent years, the parameter extraction methods of solar cell have attracted a lot of research attention. The reason is that the matching solar cell parameters can effectively reduce the influences of internal and external factors on photovoltaic efficiencies. In this paper, the five-parameter extraction methods of solar cell single-diode model are discussed in detail. The five parameters are the photocurrent, the reverse diode saturation current, the ideality factor of diode, the series resistance, and the shunt resistance. In fact, the existing research methods are classified as four categories, namely, analytically extracting parameter methods, extracting parameter methods with the help of Lambert W function, constructing or using special functions to extract parameter methods, and using intelligent algorithm to extract parameter methods. In this article, we not only elaborate their main theories and approaches, but also discuss their advantages and disadvantages. The main conclusion is that the analytical method for the extraction of solar cell model parameters requires some assumptions. Therefore, this method is fast but less accurate due to various approximations. In addition, the parameter extraction using the analytical method needs a thorough calculation, and deducing the actual values of (dI/dV)|V=Voc and (dI/dV)|I=Isc and peak power point is also challenging. When the five parameters of solar cell are calculated using the Lambert W-function method, the results show that the extraction process is easier when using the consecrated software such as MATLAB, but the larger computational time is needed. Generally, the Lambert-W function provides the exact explicit expression for parameter extraction. As a result, the accuracy of approximate solution using Lambert-W function is much higher than that of the above method. It is obvious that the accuracy of using special functions to extract cell parameters is limited by those function characteristics. Of course, those special functions, such as Green's function, seem to be complex approaches. The accuracy of the extracting cell parameters by using intelligent algorithm strongly depends on the type of fitting algorithm, the fitting criterion, objective function and the starting values of the parameters. Finally, based on the conducted review, the future research trend of parameter extraction is also predicted