One-diode Model Research Articles

A more accurate Co-Content function calculation, using alternative integration methods, for Current–Voltage curves measured in the zero volt to open-circuit voltage range

AbstractIn this article, the application of the Newton–Cotes quadrature formula, the 3/8 rule, the Boole’s rule, and order 5 and 6 integration techniques, are explored to more accurately calculate the Co-Content function, of Current–Voltage (IV) measurements done between 0 V and the open circuit voltage, which include a percentage noise of the short circuit current. Their impact on the extraction of the five photovoltaic devices’ parameters (within the one-diode model) is investigated and reported. The shunt resistance, series resistance, ideality factor, and photocurrent can be obtained with less than 10% error, using these integration techniques and 101 measured points per volt, when the percentage noise is 0.05% or less, of the short circuit current. It is not possible to obtain the saturation current with less than 10% error. These integration techniques are implemented in photovoltaic devices, such as solar cells and single-crystalline silicon, CdTe, CIGS, and heterojunction with intrinsic thin-layer solar panels IV curves, to extract the five solar cell parameters.

Electrical power output potential of different solar photovoltaic systems in Tanzania

This study examines the photovoltaic (PV) energy output and levelized cost of energy (LCOE) in seven regions of Tanzania across five different tilt adjustments of 1 MW PV systems. The one-diode model equations and the PVsyst 7.2 software were used in the simulation. The results reveal variations in energy output and LCOE among the regions and tilt adjustments indicating a strong correlation between PV energy output and solar irradiance incident on the PV panel. For horizontal mounting, the annual energy output ranges from 1229 MWh/year in Kilimanjaro to 1977 MWh/year in Iringa. Among the three optimal tilt adjustments, annually, monthly and seasonal, the last two are predicted to yield larger energy outputs, whereas the two axis tracking configuration consistently provides the maximal energy output in all regions, ranging from 1533 MWh/year in Kilimanjaro to 2762 MWh/year in Iringa. The LCOE analysis demonstrates the cost-effectiveness of solar PV systems compared to grid-connected and isolated mini-grid tariffs. The LCOE values across the regions and tilt adjustments range from $0.07/kWh to $0.16/kWh. In comparison, the tariff for grid-connected solar PV is $0.165/kWh, while for isolated mini-grids; it is $0.181/kWh. The monthly optimal tilt configuration proves to be the most cost-effective option for energy generation in multiple regions, as it consistently exhibits the lowest energy cost compared to the other four configurations. The results provide valuable insights into the performance and economic feasibility of various system setups. Through meticulous simulation and data analysis, we have gained a comprehensive understanding of the factors influencing energy generation and costs in the context of solar photovoltaic systems.

Identifying and estimating solar cell parameters using an enhanced slime mould algorithm

This study proposed an enhanced slime mould algorithm (ESMA) for identifying the solar cells’ parameters for five photovoltaic (PV) models, making two modifications to the original slime mould algorithm (SMA). The first modification was an arbitrary average position among the new individual position of slime and the best individual position of the slime mound currently found to resolve the issue of local optimum. Second, the tangent hyperbolical function of the formula p in the original SMA was replaced with an exponential function to create more variations for selecting the updated equation. The proposed ESMA was used to resolve the problem of estimating PV parameters based on the empirical current-voltage (I-V) data. Specifically, ESMA was evaluated on the parameter estimation in several photovoltaic models, i.e., the one-diode model (ODM), dual-diode model (DDM), and PV-module model (PMM). In general, ESMA outperformed the original SMA and other recent algorithms. Also, in order to provide a close approximation of the empirical I-V data of the real PV modules and cells, ESMA was able to determine the optimal parameter values for photovoltaic models.

Evaluating Outdoor Performance of PV Modules Using an Innovative Explicit One-Diode Model

Due to its simplicity, the one-diode model is commonly used for modeling the operation of photovoltaic (PV) modules at standard test conditions (STC). However, its inherent implicit nature often presents challenges in modeling PV energy production. In this paper, the innovative explicit one-diode model developed by us over time is adapted for estimating PV power production under real weather conditions. Simple yet accurate equations for calculating the energy output of a PV generator equipped with a maximum power point tracking (MPPT) system are proposed. The model’s performance is assessed under various normal and harsh operating conditions against measured data collected from the experimental setup located at the Solar Platform at West University of Timisoara, Romania. As an application of the new equation for maximum power, this paper presents a case study where the energy loss in the absence of an MPPT system is evaluated based on atmospheric and sky conditions.

Modified Rime-Ice Growth Optimizer with Polynomial Differential Learning Operator for Single- and Double-Diode PV Parameter Estimation Problem

A recent optimization algorithm, the Rime Optimization Algorithm (RIME), was developed to efficiently utilize the physical phenomenon of rime-ice growth. It simulates the hard-rime and soft-rime processes, constructing the mechanisms of hard-rime puncture and soft-rime search. In this study, an enhanced version, termed Modified RIME (MRIME), is introduced, integrating a Polynomial Differential Learning Operator (PDLO). The incorporation of PDLO introduces non-linearities to the RIME algorithm, enhancing its adaptability, convergence speed, and global search capability compared to the conventional RIME approach. The proposed MRIME algorithm is designed to identify photovoltaic (PV) module characteristics by considering diverse equivalent circuits, including the One-Diode Model (ONE-DM) and Two-Diode Model TWO-DM, to determine the unspecified parameters of the PV. The MRIME approach is compared to the conventional RIME method using two commercial PV modules, namely the STM6-40/36 module and R.T.C. France cell. The simulation results are juxtaposed with those from contemporary algorithms based on published research. The outcomes related to recent algorithms are also compared with those of the MRIME algorithm in relation to various existing studies. The simulation results indicate that the MRIME algorithm demonstrates substantial improvement rates for the STM6-40/36 module and R.T.C. France cell, achieving 1.16% and 18.45% improvement for the ONE-DM, respectively. For the TWO-DM, it shows significant improvement rates for the two modules, reaching 1.14% and 50.42%, respectively. The MRIME algorithm, in comparison to previously published results, establishes substantial superiority and robustness.

Photovoltaic module performance: Modeling, parameter estimation, and environmental effects

This research addresses the pressing need for clean energy solutions by focusing on the increasing adoption of photovoltaic (PV) modules as alternatives to fossil fuel-based energy sources. Despite their promise, PV modules face challenges in maintaining efficiency under varying environmental conditions. To tackle this, the study develops a one-diode model of PV modules using the Gravitational Search Algorithm (GSA) to obtain the optimal PV parameters so that the performance of the PV modules across diverse weather conditions can be obtained. The integration of a microcontroller and sensors in the experimental setup allows for real-time monitoring of critical environmental variables such as irradiance, temperature, and humidity, alongside voltage and current measurements. While there are certain constraints, such as the sensitivity of sensor data to weather conditions and the significant dependency of estimated parameters on measurements. However, by analyzing the performance of three specific PV modules SOLTECH215, PHOTOWATT220, and KC200GT under varying conditions, this research provides invaluable insights into optimizing energy production and efficiency in practical applications. By bridging theoretical modeling with experimental validation, it lays the groundwork for more efficient and reliable solar energy systems, thus driving the transition towards a cleaner and more sustainable energy future.

Solar cell parameter extraction, with less than 10% percentage error, integrating the Co-Content function, using up to order 6 Simpson integration method, and 51 measured points per volt or less, in the case of a percentage noise of the maximum current

In this article, the solar cell parameters (within the one-diode solar cell model) are obtained with less than 10% error, integrating the Co-Content function using up to order 6 Simpson integration method, and as a function of the number of measured points per volt and a percentage noise of the maximum current. It is shown, that less than 10% error (in some cases around 1%) can be obtained, in case the percentage noise is as larger as 0.1%, using higher order Simpson integration than 1, the usually used trapezoidal integration method.

Faults detection and diagnosis of PV systems based on machine learning approach using random forest classifier

Accurate and reliable fault detection procedures are crucial for optimizing photovoltaic (PV) system performance. Establishing a trustworthy PV array model is the primary step and a vital tool for monitoring and diagnosing PV systems. This paper outlines a two-step approach for creating a reliable PV array model and implementing a fault detection procedure using Random Forest Classifiers (RFCs).Firstly, we extracted the five unknown parameters of the one-diode model (ODM) by combining the current–voltage translation method to predict the reference curve and employing the modified grey wolf optimization (MGWO) algorithm. In the second step, we simulated the PV array to obtain maximum power point (MPP) coordinates and construct operational databases through co-simulations in PSIM/MATLAB. We developed two RFCs: one for fault detection (a binary classifier) and another for fault diagnosis (a multiclass classifier).Our results confirmed the accuracy of the PV array modeling approach. We achieved a root mean square error (RMSE) value of 0.0122 for the ODM parameter extraction and RMSEs lower than 0.3 in dynamic PV array output current simulations under cloudy conditions. Regarding the fault detection procedure, our results demonstrate exceptional classification accuracy rates of 99.4% for both fault detection and diagnosis, surpassing other tested models like Support Vector Machines (SVM), K-Nearest Neighbors (KNN), Neural Networks (MLP Classifier), Decision Trees (DT), and Stochastic Gradient Descent (SGDC).

Indoor PV Modeling Based on the One-Diode Model

The use of photovoltaic (PV) panels in interior spaces is expected to increase due to the proliferation of low-power sensor devices in the IoT domain. PV models are critical for estimating the I–V curves that define their performance at various light intensities. These models and the extraction of their parameters have been extensively studied under outdoor conditions, but their indoor illumination performance is less studied. With respect to the latter, several studies have used the parameter-scaling technique. However, the model’s accuracy degrades when the light level decreases. In this study, we propose a simple PV modeling technique that can be applied at various illuminance levels by only using characteristic points (short-circuit current, open-circuit voltage, and maximum-power voltage points) at a reference illumination level. The model uses the characteristic point translation technique to translate the reference characteristic points to other operating conditions. Then, parameter extraction technique is used to extract the model’s parameters. The proposed model’s accuracy is verified using two commercial PV panels and different indoor lighting technologies. The results indicate that the proposed model outperforms the other examined works in terms of accuracy, with an average improvement of 15.75%.

Chaos inspired invasive weed optimization algorithm for parameter estimation of solar PV models

High performance solar photovoltaic models require precise knowledge of solar PV cell parameters. Numerous methods based on both deterministic and meta-heuristics have been developed for identifying solar cell parameters. However, the presented methods in the literature have a heavy computational load and limited ability to extract crucial parameters due to nonlinear dynamics of solar PV systems. In addition, because they rely on approximations to determine the objective function, the preceding state-of-the-art parameter estimation techniques do not provide accurate results. Thus, a novel chaos-inspired invasive weed optimization (CIIWO) has been developed for accurate solar PV system parameter estimation. Adding a chaotic map to IWO improves the performance of suggested method by expanding the search space globally. Moreover, to cope with the inadequacy in state-of-art objective functions, Newton Raphson approach has been combined with proposed CIIWO algorithm. The suggested approach for solar cell parametric identification has been tested on one-diode, two-diode, and three-diode models. By contrasting the outcomes with nine contemporary optimization strategies for parameter estimation, the superiority of the suggested algorithm has been demonstrated. Commercial PV cell RTC France has been used for the experimental validation. Comprehensive study of experimental data validates the efficacy and stability of the suggested algorithm.

Luminescence coupling in 28.4%-efficient tandem solar cell utilizing 20.8%-efficient perovskite minimodule stacked on silicon cell

The total power conversion efficiency (PCE) of 28.4% with an aperture area of 64 cm2 on a four-terminal (4T) tandem solar cell with a 20.8% efficiency-semitransparent perovskite module (SPM) with a series interconnection structure and a conventional passivated emitter and rear cell type crystalline silicon solar cell is independently confirmed. This is the independently confirmed record PCE of a 4T perovskite and crystalline silicon tandem solar cell with a structure having the same active area for both top and bottom cells. The impact of the luminescence coupling monitored by the silicon solar cell in the 4T tandem solar cell was investigated based on electrical properties of the top SPM analyzed by a simple one-diode equivalent circuit model.

An Advanced Bio-Inspired Mantis Search Algorithm for Characterization of PV Panel and Global Optimization of Its Model Parameters.

Correct modelling and estimation of solar cell characteristics are crucial for effective performance simulations of PV panels, necessitating the development of creative approaches to improve solar energy conversion. When handling this complex problem, traditional optimisation algorithms have significant disadvantages, including a predisposition to get trapped in certain local optima. This paper develops the Mantis Search Algorithm (MSA), which draws inspiration from the unique foraging behaviours and sexual cannibalism of praying mantises. The suggested MSA includes three stages of optimisation: prey pursuit, prey assault, and sexual cannibalism. It is created for the R.TC France PV cell and the Ultra 85-P PV panel related to Shell PowerMax for calculating PV parameters and examining six case studies utilising the one-diode model (1DM), two-diode model (1DM), and three-diode model (3DM). Its performance is assessed in contrast to recently developed optimisers of the neural network optimisation algorithm (NNA), dwarf mongoose optimisation (DMO), and zebra optimisation algorithm (ZOA). In light of the adopted MSA approach, simulation findings improve the electrical characteristics of solar power systems. The developed MSA methodology improves the 1DM, 2DM, and 3DM by 12.4%, 44.05%, and 48.88%, 28.96%, 43.19%, and 55.81%, 37.71%, 32.71%, and 60.13% relative to the DMO, NNA, and ZOA approaches, respectively. For the Ultra 85-P PV panel, the designed MSA technique achieves improvements for the 1DM, 2DM, and 3DM of 62.05%, 67.14%, and 84.25%, 49.05%, 53.57%, and 74.95%, 37.03%, 37.4%, and 59.57% compared to the DMO, NNA, and ZOA techniques, respectively.

Parameter identification of solar cells using improved Archimedes Optimization Algorithm

The parameters of solar cells for five PV models are identified using an Improved Archimedes Optimization Algorithm (IAOA) in this paper. Two modifications are made to the original Archimedes Optimization Algorithm (AOA). To control the unequal exploration and exploitation phases, the initial adjustment is to incorporate an augmented density decreasing factor. A random average calculation between the current object position and the best object position is implemented for the second modification to solve the local optima issue. The proposed IAOA is then used to tackle the problem of identifying PV model parameters from experimental I-V data. Different PV models, such as the one-diode model (ODM), the two-diode model (TDM), and the PV module model (PMM), have been distinguished using the suggested IAOA. The proposed IAOA outperforms other present algorithms and even outperforms the original AOA based on the revealed results. As closely as feasible to the experimental I-V data of real PV solar cells and module models, the proposed IAOA can choose the best parameter values for PV models.

Estimation of Solar Cell Equivalent Circuit Parameters for Photovoltaic Module Using Differential Evolution Algorithm

The accurate estimation of solar module parameters is crucial for predicting the energy production of photovoltaic modules under different environmental conditions. In this paper, we present an approach for estimating the optimum parameters of a one-diode model using the Differential Evolution (DE) algorithm implemented in MATLAB. Our system enables the determination of these parameters at any solar irradiance and module temperature conditions, making it easy to apply the model for predicting the energy production of a photovoltaic module. The results demonstrate that the DE algorithm can estimate the parameters accurately. The numerical estimation technique based on a mathematical algorithm approximately fits all the points on the I-V curve at various environmental conditions. This work is a valuable tool for improving solar cells’ performance and efficiency and applies to many photovoltaic applications.

Parameter Estimation Techniques for Photovoltaic System Modeling

In improving PV system performance, the parameters associated with electrical photovoltaic equivalent models play a pivotal role. However, due to the increased mathematical complexities and non-linear traits of PV cells, the precise prediction of these parameters is a challenging task. To estimate the parameters associated with PV models, a reliable, robust, and accurate optimization technique is needed. This paper introduces a new algorithm, Rat Swarm Optimizer (RSO), for obtaining the optimum PV cell and module parameters. The proposed method maintains an adequate balance between the exploration and exploitation phases to overcome premature particle issues. The results obtained using RSO are compared with those of other algorithms, i.e., Particle Swarm Optimization (PSO), Ant Lion Optimizer (ALO), Salp Swarm Algorithm (SSA), Harris Hawks Optimization (HHO), and Grasshopper Optimization (GOA), in this work. The modified one-diode model (MODM) and modified two-diode model (MTDM) are used to analyze the parameters of the mono-crystalline PV cell using the suggested RSO. The obtained findings imply that the parameters estimated by the suggested RSO are more accurate than those calculated by the other algorithms taken into consideration in the paper. The statistical results are compared, and it is clear that RSO is a very accurate, fast, and dependable approach for the parameter estimation of PV cells.

Development of the estimation model for the maximum power point of building-applied photovoltaic systems based on machine learning

With increased photovoltaic (PV) applications in buildings, operational and maintenance (O&M) is crucial to preserving initial performance. Faults detection and diagnostics (FDD) methods, such as current and voltage measurement, are used to identify system errors by comparing measured values with calculated maximum power point (MPP) outputs. This method typically uses the One-Diode model to calculate MPP values and considers them as optimal performance outputs. However, the accuracy can inevitably vary based on PV installation conditions and types of solar cells. Data-driven models have been developed to address these complexities but require further exploration for practical building applications. This study developed a data-driven model using an artificial neural network (ANN) to estimate MPP in the context of FDD for various building-applied PV systems. Initial training was conducted with hourly-based simulated data, and the model was validated using real-world building-applied PV system data, including building-attached PV (BAPV) and building-integrated PV (BIPV) types. To improve the performance of the initial MPP estimation model, additional training and re-validation processes were conducted using the measured data of the BIPV system. Initial results showed acceptable performance for power, current, and voltage estimation with less than 30% CvRMSE for building-attached PV systems. Building-integrated PV systems, affected by external factors like shading, yielded less accuracy with over 30% CvRMSE. After additional training, the model showed improved performance, including around 11% CvRMSE for all parameters. This study indicates that the ANN-based MPP estimation model can be practically applied to FDD with acceptable accuracy.

Active observer-based T-S fuzzy control scheme for maximum power point tracking in PV systems

This paper addresses the problem of maximum power point tracking of photovoltaic (PV) systems in the presence of model uncertainty as well as varying load and atmospheric conditions using techniques based on a Takagi–Sugeno fuzzy model. The proposed approach relies on the linear matrix inequality tool, Lambert W function, and the Newton–Raphson method. First, adopting a quadratic Lyapunov function, an active observer-based fuzzy non-parallel distributed compensation (non-PDC) controller is designed for asymptotic tracking of the desired reference input. Next, to subdue the impact of uncertainty on the PV system, the closed-loop nominal system is regarded as a reference model, and then the main control law is developed using an online lumped uncertainty estimator and keeping the nominal control law within the staple controller. This control law does not require that the bounds on uncertainties be known. The reference voltage is determined by a novel maximum power point-seeking algorithm that is organized based on the one-diode model of PV panel, Lambert W function, and Newton–Raphson method. Finally, simulations are performed for three scenarios to point out the merits and effectiveness of the proposed methodology in the presence of system uncertainties, environmental changes, and load variations.

Estimation of Parameters of One-diode and Two-diode Photovoltaic Models: A Chaotic Gravitational Search Algorithm based Approach

ABSTRACT Photovoltaic (PV) module is one of the major sources of clean energy to substantially reduce the global carbon footprint. Researchers are keen on developing an equivalent PV mathematical model to acquire insights regarding its monitoring and operations. This is a stimulating task as these modules are sensitive to operational conditions. In this work, a chaotic gravitational search algorithm (CGSA) based method is proposed for estimating the PV parameters of the one-diode and the two-diode PV models. The proposed method includes an update to confine the decision variables within the appropriate ranges. It is tested on the RTC France cell and the Photowatt-PWP-201 PV module. The suitability is highlighted considering the mean absolute error (MAE) and the root mean square error (RMSE) between the experimental and the estimated currents. For example, the errors are in the orders of 10 − 4 and 10 − 3 (one-diode model) and 10 − 5 and 10 − 4 (two-diode model), respectively, for the Photowatt-PWP-201 PV module. A comparative analysis of the proposed method with several popular algorithms (e.g. equilibrium optimizer (EO), whale optimization algorithm (WOA), Harris hawks optimization (HHO), variants of particle swarm optimization (PSO) etc.) is presented. Results and the comparative analysis confirm the effectiveness of the suggested approach.

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.

Explicit three-piece quadratic model for accurate analytic representation of S-shaped solar cell current–voltage characteristics

Some interest has been recently directed towards analytic mathematical models for reproducing the current–voltage (I–V) characteristics of solar cells, mainly due to their convenient property of expressing current as an explicit function of voltage (which is not true for the traditional one-diode model). However, as is the case with the one-diode model itself, existing analytic models do not yield a good fit in the case of S-shaped I–V characteristics. In this brief paper, an analytic explicit model based on a three-piece quadratic curve is proposed that surpasses such difficulty and enables accurate representation of S-shaped curves. To evaluate the proposed model, validation was carried out against three empirical solar cell I–V characteristics. In all cases, simulation results show that the proposed approach is more accurate than other closed-form models in the literature.