Parameters Of Single-diode Model Research Articles

An efficient, fast, and robust algorithm for single diode model parameters estimation of photovoltaic solar cells

AbstractParameter estimation of photovoltaic (PV) solar cells and module models pays attention to researchers owing to their importance in practical considerations. The single diode model (SDM) circuit with five unknown parameters is widely used to model PV solar cells and modules. In this paper, a novel approach called alternate optimization (AO) algorithm based on a discrete search is proposed to estimate the SDM parameters. The proposed algorithm provides efficient and robust performance, considering a limited set of discrete values and increasing the convergence speed. Two practical case studies with actual measurements are considered to assess the proposed AO algorithm: the RTC France solar cell and monocrystalline PV modules with different irradiations and temperatures. The numerical findings underscore the superior performance of the proposed AO algorithm across various metrics. Notably, it achieves an exceptional Root Mean Square Error (RMSE) of 7.7426 × 10−04 for the RTC France PV cell and approximately 1 × 10−03 RMSE for monocrystalline PV modules. Additionally, the algorithm exhibits unparalleled speed, showcasing the fastest convergence with an elapsed time of 1.66 × 10−05—markedly 4.45 times quicker than the fastest method documented in the literature for SDM parameter estimation. Furthermore, the proposed AO algorithm stands out for its efficiency, requiring a maximum of five iterations for parameter estimation, a substantial improvement compared to the more than 10 iterations typically needed by algorithms in the existing literature. Its robustness is also commendable, as evidenced by the stability of final RMSE values across a variety of experiments, distinguishing it from less robust algorithms found in the literature.

Mathematical models to forecast temporal variations of power law shape parameters of a PV module working in real weather conditions: Prediction of maximum power and comparison with single-diode model

In this study, an innovative approach has been proposed to generate real time current–voltage characteristics and forecast peak power of photovoltaic (PV) modules working outdoors beneath real meteorological conditions. Power-Law Model (PLM) including four unknown parameters, two PV metrics (ISC, VOC), and two profile parameters (γ, m), has been used for fast, accurate and reliable modelling of PV modules. Explicit expressions giving γ and m parameters as functions of cardinal point coordinates (IMPP,VMPP, ISC and VOC) have been established. A daily monitoring of PV quantities, throughout one reference day, has been used to derive novel mathematical models of γ and m depending on module temperature and solar irradiance. To describe PV module behavior under changing meteorological conditions during an arbitrary day, mathematical models have been called to reproduce dynamical values of PLM shape parameters γ and m. Reliability of the approach has been assessed by comparing current–voltage characteristics and maximum power coming from PLM and Single-Diode Model (SDM) to experimental data of twenty-two PV modules measured at NREL. Comparison also reveals that I-V characteristics generated and predicted separately by PLM and SDM parameters are very close. In some cases, I-V characteristics generated by PLM parameters are more accurate. Furthermore, NRMSE values for generated and predicted I-V characteristics for all kinds of PV modules evaluated for different working conditions do not exceed 4% for both PLM and SDM, and determination coefficient values for long-term prediction of maximum power are close to one and annual average value is greater than 0,95.

Comparesion the electrical parameters of photovoltaic cell using numerical methods

For a research problem: as a single-diode model (electrical circuit) is difficult to discover the precise answer to employing analytical approaches, develop and compute the electrical parameters of the PV cell roughly using numerical algorithms. Therefore, the goal of this work is to create an algorithm that aids in the approximate solution of the electrical parameters of solar cells. Three methods have been proposed for these calculations, each of which has a quicker calculation time and a higher level of accuracy.
 By streamlining the calculation process, the proposed method solves the problems of complexity and precision. The I-V and P-V characteristic curves of solar cells can then be utilized to compare the efficacy of the tested methods. In addition, the analysis of root mean square error indicates that the proposed method is more applicable than alternative methods. In fact, this extraction procedure can be regarded as an efficient and precise method for estimating the single diode model parameters of solar cells.
 The results indicate that this precise and effective strategy can play an important role in the retrieval of single diode model parameters. In fact, the method proposed in this paper makes numerically implementing parameter models in technology simpler. In addition, it provides an optimization suggestion for the production of solar cells

Extraction of Single Diode Model Parameters of Solar Cells and PV Modules by Combining an Intelligent Optimization Algorithm with Simplified Explicit Equation Based on Lambert W Function

In this paper, the explicit equation of the single diode model (SDM) expressed by the Lambert W function was reduced to its simplified form through variable replacement; then the simplified explicit equation was combined with an intelligent optimization algorithm to estimate the SDM parameters of solar cells and PV modules. To evaluate the parameter extraction performance of the new method, eight typical intelligent optimization algorithms were combined with the implicit, explicit, and simplified explicit equation to extract the SDM parameters of a solar cell and three types of PV modules. The results show that the new method not only improves the accuracy of parameter extraction but also enhances the robustness and convergence speed. Most importantly, the new method can nearly improve the parameter extraction accuracy of a poor-performing algorithm in traditional methods to the level of other well-performing algorithms without enhancing the algorithm itself. In a word, this study offers a new choice for a more accurate and reliable extraction of SDM parameters from both solar cells and PV modules.

A reliable optimization framework for parameter identification of single‐diode solar photovoltaic model using weighted velocity‐guided grey wolf optimization algorithm and Lambert‐W function

AbstractIn estimating the parameters of the five unknown parameters Single‐Diode Model (SDM) of the solar photovoltaic (PV) model, a non‐linear equation for the PV cell current is typically utilized. Then, the error between the estimated current and measured current is computed using the objective function called Root‐Mean‐Square‐Error (RMSE). In order to compute the PV cell current in SDM, an iterative method built on the Lambert‐W function is presented in this study. Along with the Lamber‐W function, an optimization algorithm called Weighted Velocity‐Guided Grey Wolf Optimizer (WVGGWO) is used to identify the unknown lumped parameters of SDM of the cell and the module. The proposed WVGGWO is an updated version of the original Grey Wolf Optimizer (GWO). The position update of the GWO has been modified, and the weightage has been provided for the wolf hierarchy. Additionally, by emphasizing the lengthening of each leading wolf's steps towards the others in the earlier search while emphasizing the shortening of the steps while reaching the later iterations, WVGGWO improves both the exploration and exploitation of the original GWO. Four case studies are considered for testing the validity of the proposed algorithm along with the Lambert‐W function. The performance of the proposed approach is compared with seven other well‐known algorithms. The results demonstrate that the suggested approach produces better outcomes than many optimization algorithms.

Numerical procedure for accurate simulation of photovoltaic modules performance based on the identification of the single-diode model parameters

The current work proposes a novel method for photovoltaic (PV) modules’ performance estimation at various weather conditions based on the extraction of the single-diode model’s five parameters. The new modeling technique is not built on any approximations or iterative processes, and this makes the approach combining two substantial benefits in the PV simulation field which are the accuracy of prediction and the rapidity of convergence. Moreover, the method is founded on the resolution of matrix equations based on reduced forms, and that assures its simplicity by avoiding tedious calculations. Indeed, only the mean points of the current–voltage characteristic are employed to get the values of the five parameters by calculating two of them using a numerical resolution of a two non-linear equations’ system. Then, the expressions giving the three last parameters are determined as functions of the two first parameters and regrouped in a matrix equation, which is solved analytically to get the values of these remaining parameters. The productiveness of the proposed method is tested using PV modules of various technologies and proved using eight well-known simulating methods for the one-diode model. Furthermore, the root mean squared errors matching the new method have not exceeded 0.093 A and the obtained convergence time is less than 0.27 s. The results attest to the relevance of the new method for dynamic applications and for PV designers requiring simple modeling techniques.

Parameters extraction of photovoltaic cells using swarm intelligence based optimization technique: research on single diode model and double diode model

Solar-energy is a clean source of energy and photovoltaic (PV) panels are constructed from solar cells (SC) which convert energy of light into electricity without any environmental effect. The researchers and policy makers focus on the huge scale adoption of solar panels due to its cleaner production. However, there is non-linear behavior in current-voltage characteristics of solar panels and shortage of data in manufacturer’s datasheet. In order to enhance the efficiency of solar panels it is mandatory to develop the PV panels scheme accurately by extracting the basic parameters. In this research study a mathematical model of two different solar cell models is used such as Single Diode Model (SDM) and Double Diode Model (DDM). The Particle Swarm Optimization (PSO) is used to extract the five and seven unknown parameters of SDM and DDM. The algorithm runs with one thousand iterations to minimize the Root Mean Square Error (RMSE) where the RMSE is the vector of five unknown parameters for SDM and seven for DDM. The superiority of proposed PSO algorithm is proved by the optimized results of unrevealed parameters with minimized RMSE of up to 10-3. Optimum parameter values for the solar cell models are applied on the real time data of a 55 mm diameter commercial RTC-France SC. Finally, the results reveal that P-V and I-V curves exhibit smallest deviation between estimated and real time values. The results reveal that the proposed PSO converges to optimal solution with least number of iterations compared to the existing metaheuristic algorithms.

Determining circuit model parameters from operation data for PV system degradation analysis: PVPRO

Physics-based circuit parameters like series and shunt resistance are essential to provide insights into the degradation status of photovoltaic (PV) arrays. However, calculating these parameters typically requires a full current–voltage characteristic (I-V curve), the acquisition of which involves specific measurement devices and costly methods. Thus, I-V curves of the PV system level are often not available. This paper proposes a methodology (PVPRO) to estimate these I-V curve parameters using only operation (string-level DC voltage and current) and weather data (irradiance and temperature). PVPRO first performs multi-stage data pre-processing to remove noisy data. Next, the time-series DC data are used to fit an equivalent circuit single-diode model (SDM) to estimate the circuit parameters by minimizing the differences between the measured and estimated values. In this way, the time evolutions of the SDM parameters are obtained. We evaluate PVPRO on synthetic datasets and find an excellent estimation of both SDM and the key I-V parameters (e.g., open-circuit voltage, short-circuit current, maximum power, etc.) with an average relative error of 0.55%. The performance, especially the extracted degradation rate of parameters, is robust to various measurement noises and the presence of faults. In addition, PVPRO is applied to a 271 kW PV field system. The relative error between the real and estimated operation voltage and current is less than 1%, suggesting that degradation trends are well captured. PVPRO represents a promising open-source tool to extract the time-series degradation trends of key PV parameters from routine operation data.

A novel hybrid analytical/iterative method to extract the single-diode model's parameters using Lambert's W-function

The evaluation of photovoltaic device performance is based on the I-V characteristic curve. Unfortunately, the data sheets provided by the manufacturers only include data at standard test conditions, which requires the construction of a model capable of simulating the electrical behavior of these devices at different conditions. The identification of the model from the I-V curve is a challenging task due to the strong nonlinear relationship between the model parameters. This paper proposes a hybrid analytical/iterative method to extract the parameters of the single diode model. In this method, the four parametersa, Rsh, Io and Ipv are calculated directly by their explicit expressions. The properties of the Lambert function are still used to untie the coupling between the parameters. The parameter Rs is determined using an iterative process based on the minimization of the error between the theoretical and experimental data. Accuracy criteria have been introduced to demonstrate the reliability of the proposed method and its accuracy compared to other methods in the literature. The robustness of the proposed mathematical model in the face of variations in the initial conditions chosen has also been demonstrated.

Photovoltaic single-diode model parametrization. An application to the calculus of the Euclidean distance to an [formula omitted]–[formula omitted] curve

In this paper we provide a new parametrization of the characteristic curve (I-V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I-V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I-V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I-V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I-V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster.

Feasibility of Photovoltaic Module Single-Diode Model Fitting to the Current–Voltage Curves Measured in the Vicinity of the Maximum Power Point for Online Condition Monitoring Purposes

Photovoltaic system condition monitoring can be performed via single-diode model fitting to measured current–voltage curves. Model parameters can reveal cell aging and degradation. Conventional parameter identification methods require the measurement of entire current–voltage curves, causing interruptions in energy production. Instead, partial curves measured near the maximum power point offer a promising option for online condition monitoring. Unfortunately, measurement data reduction affects fitting and diagnosis accuracy. Thus, the optimal selection of maximum power point neighbourhoods used for fitting requires a systematic analysis of the effect of data selection on the fitted parameters. To date, only one published article has addressed this issue with a small number of measured curves using symmetrically chosen neighbourhoods with respect to the maximum power. Moreover, no study has determined single-diode fit quality to partial curves constructed via other principles, e.g., as a percentage of the maximum power point voltage. Such investigation is justified since the voltage is typically the inverter reference quantity. Our work takes the study of this topic to a whole new scientific level by systematically examining how limiting the current–voltage curve measuring range to maximum power point proximity based on both power and voltage affects single-diode model parameters. An extensive dataset with 2400 measured curves was analysed, and statistically credible results were obtained for the first time. We fitted the single-diode model directly to experimental curves without measuring outdoor conditions or using approximations. Our results provide clear guidance on how the choices of partial curves affect the fitting accuracy. A significant finding is that the correct selection of maximum power point neighbourhoods provides promising real-case online aging detection opportunities.

Determining solar cell parameters and degradation rates from power production data

• Power production data can be used to infer solar cell parameters. • Heuristic algorithms can extract these parameters from a few data points. • This method can be used to understand photovoltaic degradation remotely. • This approach is scalable and not very sensitive to environmental data. Practical but accurate methods that can assess the performance of photovoltaic (PV) systems are essential to all stakeholders in the field. This study proposes a simple approach to extract the solar cell parameters and degradation rates of a PV system from commoditized power generation and weather data. Specifically, the teaching-learning-based optimization algorithm was used to estimate the single-diode model parameters of a monocrystalline silicon PV module from a handful of power production data points that capture the operating current and voltage under real working temperatures and irradiance levels. These parameters can reproduce the solar panel’s actual behavior under all operating conditions and provide insights into its underlying degradation mechanisms. The results were validated by site measurements as well as a sensitivity analysis, thus offering exciting possibilities for the future of PV performance analysis, power forecasting, and remote fault detection for real-life applications.

A novel procedure for identifying the parameters of the single-diode model and the operating conditions of a photovoltaic module from measured current–voltage curves

Photovoltaic (PV) module measured current–voltage curves together with the mathematical single-diode model are potential tools for PV system condition monitoring. Changes in model parameters can reveal module degradation and aging. However, all the parameter values change with varying operating irradiance and temperature, so they should also be identified. Unfortunately, useful operating condition measurements are rarely available in PV power plants. Thus, it is necessary to identify both operating conditions and model parameters directly from measured current–voltage curves. Only one such method has been reported in literature, however, using approximate explicit equations. The present work proposes a novel fitting procedure that identifies both single-diode model parameters and PV module temperature and irradiance utilizing an iterative method instead of approximate equations, which guarantees accurate results. The procedure enables degradation and aging analyses using only the internal electrical current–voltage curve measurements of the inverter. The results showed that the identified irradiance and temperature accurately reproduced the measured ones in all outdoor conditions. The stable identification of other single-diode model parameters, of which series resistance is especially suitable for detecting aging, confirmed the functionality of the procedure for condition monitoring.

Analytical extraction of the single-diode model parameters for macro-porous silicon-based dye-sensitized solar cells using Lambert W-function

Analytical extraction of the single-diode model parameters for macro-porous silicon-based dye-sensitized solar cells using Lambert W-function

Estimation of Photovoltaic Cell Parameters Using Measurement Data of Photovoltaic Module String Currents and Voltages

Photovoltaic (PV) models play an important role in the simulation analysis and fault diagnosis of PV systems. The single diode model (SDM) is the most frequently used model in research and applications. There are numerous proposed methods to identify the SDM parameters. However, the characteristics of PV cells alter during the lifetime in normal operating environments; these variations may be due to degradation, faults, dust, weed, and so on. Therefore, it is crucial to estimate the actual parameters of the PV cells that represent those present state. The contribution of this article is to propose a method to estimate PV cell parameters on the basis of the measurement data regarding the currents and voltages of the PV module strings. A PV string model is described on the basis of the adaptive SDM for the PV cells in the system, and the parameters of each cell model are obtained by minimizing the difference between the measured string voltages and the string voltages computed by the model. The application of the proposed method to real data measured in a PV power plant is also presented to evaluate the proposed method.

Modelling and estimating performance for PV module under varying operating conditions independent of reference condition

Existing methods for parameter identification and performance estimation under varying operating conditions are accomplished in two steps: first, the model parameters are extracted under the prescribed reference condition; second, the model parameters under varying operating conditions are calculated based on the dependence of parameters on environmental conditions. There are two disadvantages for existing methods: the results are affected by the selection of reference condition, and the irradiance and temperature dependence of parameters are non-uniform for different types PV modules. This paper studies the effect of the reference condition selection and proposes a novel method for parameter identification and performance estimation under varying operating conditions. In the proposed method, a set of improved transformation equations are modified by considering both irradiance and temperature dependence for all parameters in single-diode model (SDM). Since the improved transformation equations are independent of reference condition, the effect of the selection of reference condition is eliminated. The coefficients of the improved transformation equations are extracted through guaranteed convergence particle swarm optimization technology from measured I-V curves under different operating conditions. The efficiency and accuracy of proposed method is validated by amount of experimental data under different irradiance and temperature conditions for different types of PV modules. The variations of SDM’s parameters by the proposed method have been investigated thoroughly and shown to be in accordance with the physical behavior of the PV devices. The proposed method can be further employed to simulate the performance of a PV module under real operating conditions and exhibits great accuracy and suitability.

A modified stochastic fractal search algorithm for parameter estimation of solar cells and PV modules

In this work, a modified stochastic fractal search algorithm is proposed for effectively estimate the unknown model parameters of the single diode model and the double diode model of solar cells and photovoltaic modules. This algorithm modifies the diffusion process and the update processes of the original stochastic fractal search algorithm and employs a population size reduction mechanism and thus simplifies the implementation of the original algorithm and achieves better performance for the parameter estimation of solar cells and PV modules. Firstly, the algorithm is tested on three widely used estimation benchmark cases and compared with other seven state-of-the-art algorithms. The proposed algorithm shows its advantages in the aspects of accuracy, convergence speed, and stability over the other studied algorithms. In 100 independent runs with the maximum number of fitness function evaluations equal to 50000, the proposed algorithm achieved the best known solutions with 100% probability and the standard deviation of the 100 RMSE values is of the order of 10−17. Then, the proposed algorithm is used to estimate the unknown single diode model parameters and double diode model parameters of three different types of PV modules, i.e. Multi-crystalline S75, Mono-crystalline SM55, and Thin-film ST40 under different irradiance and temperature conditions, and the algorithm also achieves sufficiently accurate models. The root mean square of the error (RMSE) values between the obtained models and the actual current data are of the order of 10−2 or 10−3. In view of its effectiveness and practicability, the proposed algorithm can be used as a new tool for the parameter estimation of solar cells and PV modules.

Nature inspired evolutionary algorithm integrated performance assessment of floating solar photovoltaic module for low-carbon clean energy generation

Development and deployment of FSPV systems are still in the nascent stages hence long-term performance, control and feasibility study of FSPV systems are not well addressed. Precise and robust estimation of FSPV panel parameters will play an important role in determining the actual performance, carbon savings and long-term feasibility studies of FSPV systems. Here, hybrid stochastic firefly algorithm (HSFA) is used for parameter estimation and optimization. The hybrid algorithm is used to find out the parameters of single diode model, double diode model and FSPV module. An experiment is also performed using FSPV modules under varying irradiance conditions. The accuracy of model is evaluated by comparing the simulated results with the experimental results and computing the relative error and root mean square error (RMSE). The parameters extracted using the proposed method has a very low RMSE value of 9.83002E-04. Assessment of the experimental and estimated results show that the relative error for measured electricity on a sunny day is 0.57% while for an overcast day it is 0.89%. For partial shading condition, the relative error and RMSE was 0.79% and 6.5%, respectively. The results which are in well agreement with the experimental values demonstrate the superior performance of the model in determining the FSPV parameters. Proper estimation of the FSPV parameters will help researchers, scientists, engineers and all actors associated with solar PV systems in making sound judgements towards the deployment of FSPV systems and help the society in developing a sustainable ecosystem towards implementation of industry 4.0 by adapting to low-carbon power generation methods.

An Improved Method for Parameter Identification and Performance Estimation of PV Modules From Manufacturer Datasheet Based On Temperature-Dependent Single-Diode Model

The single-diode model (SDM) is widely used in photovoltaic (PV) system modeling and output power estimation because of its simplicity and accuracy. This article proposed an improved and comprehensive method for parameter identification and performance estimation by using manufacturer datasheet information for PV module. The temperature dependence of all physical parameters in SDM of PV module is comprehensively considered and investigated for varying operating conditions. In the proposed method, all physical parameters under reference condition and their temperature coefficients are calculated from information in manufacturer datasheet, which can be used for parameter calculation and output power estimation under varying operating conditions. To improve the accuracy and efficiency, the analytical and optimization methods are combined in calculation procedure of parameter extraction. By using analytical derivation from I–V equations at key operating points and their temperature coefficients, it reduces the dimensions of the search space and save computational cost for parameter optimization. The accuracy and effectiveness of the proposed method are validated by massive experimental data under varying operating conditions for different type PV modules. The proposed processes are simple and especially useful to calculate the actual performances of PV modules under operating conditions, making it scalable for direct online application.

An Effective Method to Accurately Extract the Parameters of Single Diode Model of Solar Cells.

A non-iterative method is presented to accurately extract the five parameters of single diode model of solar cells in this paper. This method overcomes the problems of complexity and accuracy by simplifying the calculation process. Key parts of the equation are to be adjusted dynamically so that the desired five parameters can be obtained from the I-V curve. Then, the I-V and P-V characteristic curves of solar cells are used to compare the effectiveness of this method with other methods. Furthermore, the root mean square error analysis shows that this method is more applicable than other methods. Finally, the I-V and P-V characteristics simulated by using the extracted parameters in this method are compared and discussed with the experimental data of solar cells under different conditions. In fact, this extraction process can be regarded as an effective and accurate method to estimate solar cells’ single diode model parameters.