Single-diode Equivalent Circuit Research Articles

Development of generalized photovoltaic model using ISIS-PROTEUS

Photovoltaic (PV) energy is a form of renewable energy that generates electricity from sunlight. PV systems consist of solar cells, which convert sunlight into electricity using a process known as the photovoltaic effect. Modeling and simulating PV systems involves using mathematical and computational models to predict the behavior and performance of PV systems under various conditions. This can include modeling the electrical characteristics of solar cells, as well as the interactions between multiple cells in a PV module or system. Following this sense, we present in this work a novel implementation of a generalized PV model using ISIS Proteus software. Proteus is layout software for electronic circuit simulation, schematic capture and PCB design. Some studies have indeed taken this context to model the PV modules either by using a Proteus Spice model of the photovoltaic panel without including the effect of climatic conditions variation, or by using pure mathematical relations that describe all physical and environmental parameters which will lead to a static behavior. The developed model in this paper as it is generalized, can be typically used as a PV cell, module even a generator for a complete simulation of a PV system. PV cell, which is the elementary component of PV system, is modeled using the single diode equivalent circuit (SDM) also known as five-parameter model and its behavior is simulated in details. The most advantage in our study is the fact that the PV output can be obtained wherever what solar radiation and ambient temperature where PV module is operating. Our model gives also the possibility to simulate a dynamic behavior under any climatic conditions. The accuracy between obtained results of simulation and the experimental data confirm the reliability and the high performance of the developed model.

Assessment of photovoltaic I–V curve translation methods in real-world situations

The evaluation of performance of a photovoltaic array is effectively conducted through the analysis of its I–V curves. However, conducting these measurements under real-world field conditions introduces certain shortcomings in subsequent analysis and modeling. Therefore, it becomes imperative to translate the I–V curves from measured data points to conform to the standard test condition (STC). The approach presented in IEC 60891:2021 addresses this requirement. This study focuses on investigating the accuracy of the translation process using Procedure 4 from IEC 60891:2021 across a wide range of irradiance and temperature, and compares it with state-of-the-art alternatives (Hansen and metaheuristic methods). Experimental data and optimization methods were employed to assess errors and determine the optimal conditions utilizing a single-diode equivalent circuit, along with its parameters for temperature and irradiance correction. The results demonstrated that the metaheuristic method achieved the best results in terms of average RMSE, surpassing the IEC in all cases and the Hansen method in approx. 81% of outcomes. Moreover, the outcomes under real outdoor conditions significantly diverge from those observed in indoor measurements conducted using a flash solar simulator.

A generalized mathematical modeling and performance analysis of GaAs, m-Si and Ge single - junction solar PV cells

Earlier theoretical approaches have analyzed the performance of semiconductor materials for the influence of temperature and band gap which is implemented in solar photovoltaic systems. This paper investigates the detailed mathematical analysis of single junction semiconductor materials such as Gallium Arsenide (GaAs), mono-crystalline Silicon (m-Si) and Germanium (Ge) solar cells parameters namely, Band gap (Eg), reverse saturation current (Io), shunt resistance (Rsh), Short circuit current (Isc), open circuit voltage (Voc), Fill factor (FF), Maximum Power (Pmax) and Efficiency (Ƞ) for temperature ranging from 273K (≈0°C) to 373K (≈100°C). The optimized cell parameters values are obtained under Air Mass 1.5 Global spectrum (Area = 100cm2 and Irradiance = 100 mW/cm2 for the semiconductor materials (GaAs, m-Si and Ge)) at 300K (≈25°C) are compared to identify the higher efficiency and open circuit voltage. Among the semiconductor materials, the single junction GaAs compound semiconductor material is identified with better efficiency and optimized open circuit voltage. A generalized mathematical model of semiconductor materials is developed using single diode equivalent circuit model under SIMULINK platform and it is used to observe the effect of different temperature, irradiance levels, series resistance and shunt resistance values on the performance of solar cells. The discussion is extended for a 2KW PV array for the semiconductor materials (GaAs, m-Si and Ge) under different temperature and irradiance levels. Evaluating the performance of a PV array, rather than individual cells, provides a more comprehensive understanding of how the chosen semiconductor materials function as part of a larger solar energy system.

Characterization of a small amorphous photovoltaic panel and derivation of its SPICE model

This paper presents a simple method to resolve the parameters of the single-diode equivalent circuit for small amorphous photovoltaic (PV) panels. It is based on a precise measurement using a test bench that allows the characterization of PV panels at different illumination levels from 10 lx to 3000 lx. The measurement under different illumination conditions allows the calculation of the model parameters using only a standard polynomial, logarithmic and exponential functions - no numerical approach or Lambert W function is required. The solved parameters are later used in LTspice simulations, which are compared with the real measurements. The Spice model presented in this paper is based on the single diode model, but is modified to be more reliable at low illumination levels. The Spice model can be used for the design of MPPT systems or for various indoor IoT applications, where it allows to predict the available energy under different conditions.

Non-Linear Analysis of Novel Equivalent Circuits of Single-Diode Solar Cell Models with Voltage-Dependent Resistance

The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance, and both resistors. Second, analytical relationships between the current and the voltage expressed were derived using the Lambert W function for each proposed model. Third, the paper presents a hybrid algorithm, Chaotic Snake Optimization (Chaotic SO), combining chaotic sequences with the snake optimization algorithm. The application of the proposed models and algorithm was justified on two well-known solar photovoltaic (PV) cells—RTC France solar cell and Photowatt-PWP201 module. The results showed that the root-mean-square-error (RMSE) values calculated by applying the proposed equivalent circuit with voltage dependence of both resistors are reduced by 20% for the RTC France solar cell and 40% for the Photowatt-PWP201 module compared to the standard single-diode equivalent circuit. Finally, an experimental investigation was conducted into the applicability of the proposed models to a solar laboratory module, and the results obtained proved the relevance and effectiveness of the proposed models.

An Analytical Algorithm for Extracting Model Parameters in a Lumped-Parameter Equivalent Circuit of Solar Cells

An analytical algorithm is proposed to extract model parameters in a single-diode lumped-parameter equivalent circuit of solar cells. In the calculation process, six relevant factors in the datasheet are necessary to establish a set of transcendental equations. This set of equations is analyzed and solved to acquire accurate values for the model parameters, by retaining equation items with important physical significance. Furthermore, based on simulations and reconstruction experiments, verifications show the accuracy and universality of the algorithm. Therefore, the proposed algorithm can be regarded as a valid solution for estimating the model parameters of a single-diode lumped-parameter circuit of solar cells.

Finite Element Simulation of Electrical Intradevice Physics of Thin-Film Solar Cells and Its Implications on the Efficiency

One key aspect to further improve thin-film photovoltaic devices is the optimal sizing of the different layers, such as grids, transparent conducting oxides (TCOs), back contacts, and absorber materials, with respect to their mutual electrical influences. This article describes a novel quasi-3-D finite element method (FEM) tool on a digital twin, which is capable of simulating all electrical influences from a holistic perspective from semiconductor materials to device level. It yields a spatially resolved intradevice distribution of electrical potentials and currents, helping to understand the physical processes within solar cell devices. Experimentally inaccessible data, such as the breakdown of different loss mechanisms, can be provided. Moreover, the internal cell properties can be used for forecasting calculations of characteristic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I–V</i> curves. This process can also be reversed in a procedure called reverse engineering fitting. It allows to calculate backward from the external cell properties to the internal loss-exempt semiconductor material characteristics. Our approach is verified by semitransparent cells with a perovskite absorber, a silver rear metalization grid, and indium zinc oxide as a rear TCO. Our simulation predicts characteristic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I–V</i> curves with a coefficient of determination of well above 0.99 with respect to experimentally measured cells. The power conversion efficiency (PCE) can be forecast within a mean error of 0.18% <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{\mathrm{abs}}$</tex-math></inline-formula> at absolute PCEs around 13% for different TCO and grid thicknesses. The advantage of our FEM approach in contrast to a single-diode equivalent circuit model is demonstrated by considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I–V</i> curve predictions for different cell sizes.

Theoretical and experimental evaluation on the electrical properties of multi-junction solar cells in a reflective concentration photovoltaic system

Solar photovoltaic systems represent an important technology for renewable energy utilization and have broad potential for application and development. However, the further development of solar photovoltaic systems is hindered by their higher generation costs. A high-concentration photovoltaic system (HCPVs) can use an inexpensive concentrator to replace solar cells; this, in turn, reduces the cost of electricity generation, because the solar cell requirement decreases for a given power. This study developed a mathematical model for multi-junction solar cell (MJSC) based on single-diode equivalent circuit, furthermore, an HCPVs with hyperboloid mirrors was established. The electrical properties for an MJSC module, including the short-circuit current (Isc), peak power (Pm), open-circuit voltage (Voc), fill factor (FF), and efficiency (η) were investigated at concentration ratios between 650 X and 800 X and direct solar radiation intensities between approximately 400 W/m2 and 730 W/m2. Furthermore, the experimental results and theoretical values were comparatively analyzed. The results demonstrated that Isc, Voc, and Pm of MJSC module increased as the direct solar radiation raised. In contrast, the FF and η of an MJSC module decreased as the direct solar radiation raised. As the direct solar radiation intensity was 700 W/m2 and concentration ratio increased from 650 X to 800 X, Isc, Voc, and Pm increased from 1.002 A to 1.243 A, 11.095 V to 11.158 V, and 9.466 W to 11.358 W, respectively. Conversely, the FF and η of the MJSC module decreased from 32.51 % to 31.33 % and 0.851 to 0.819, respectively. The tallied between the numerical and experimental results was evaluated, which indicated that root-mean-square error between the experimental and calculated values increased as the direct solar radiation increased.

A new model for a photovoltaic panel using Proteus software tool under arbitrary environmental conditions

The photovoltaic (PV) panel generates power based on different parameters, including environmental conditions such as solar irradiance, temperature, and internal electrical parameters of the PV panel. Thus, a PV model should be studied in advance to forecast and evaluate the impact of these factors on the PV performance, and this model should be matched with the PV panel's real behavior. For this reason, this paper developed a new model for a PV panel using the Proteus software. A flexible PV model with possibility of varying the weather conditions has been proposed using mathematical equations of a single-diode equivalent circuit, (i.e., photo-generated current, shunt-resistor current, and diode current). Moreover, these equations were modeled using “Pick Devices” in Proteus software library. To prove the effectiveness of the proposed model, it was applied on two types of monocrystalline, and multi-crystalline silicon cells of PV panel technologies. Subsequently, the corresponding current-voltage (I–V) and power-voltage (P–V) characteristics are obtained and compared with the manufacturer's data, PVsyst software, and other authors' results under arbitrary values of irradiance and temperature. The simulation results identified that the proposed model is flexible, simple, and suitable for different PV panel technologies under diverse weather conditions.

High-Speed Laser Beam Induced Current Imaging: A Complementary Quantitative Diagnostic Tool for Modules

High-resolution imaging techniques based on thermography, luminescence imaging, and laser beam induced current (LBIC) probe and inspect solar cells and correlate the observed inhomogeneities to the cell performance. The imaging methods get increasingly qualitative as the size scales from cell level to module dimensions, where several solar cells are connected in series, as in silicon panels. Electroluminescence (EL) imaging is a standard measure of inspecting solar panels and extensively utilized in the manufacturing assembly line. The complementary method of obtaining images from the LBIC scanning technique, however, is rarely utilized at large panel dimensions. We report strategies to implement LBIC imaging at module levels and procedures to analyze in terms of microscopic and circuit parameters. LBIC is inherently quantitative and well suited to identify microscopic defects, since it involves measuring local photo-current. We demonstrate that the contrast features from LBIC in a specific cell region are directly associated with the shunt resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{\text{sh}}$</tex-math></inline-formula> ) variation of that specific cell. Using a single diode equivalent circuit model, we show that the current contrast of the cell under study is purely a function of its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{\text{sh}}$</tex-math></inline-formula> , and an effective load resistance that includes shunt-resistance of the other series-connected cells. The resulting LBIC-map along with EL then becomes a complete diagnostic tool to quantitatively map and identify the defects prevailing in a solar panel. We overcome the key issue of the slow speed of LBIC based imaging by a modified scan routine for rapid screening of large areas (2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bf m}$</tex-math></inline-formula> by 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bf m}$</tex-math></inline-formula> ) panels under 5 min, at high resolution.

A single-diode model for photovoltaic panels in variable environmental conditions: Investigating dust impacts with experimental evaluation

The current study utilized a single-diode equivalent electrical circuit with a non-iterative parameter extraction approach and innovative modifications to predict the photovoltaic modules' electrical behavior in variable environmental conditions. The model's outputs were validated using both the presented data in the module's datasheet and experimental investigations under more than 500 different real conditions. For the first time, besides irradiation and temperature, dust accumulation effects on the single-diode model's main parameters have been investigated to predict the module's electrical behavior under real environmental conditions. Comparing and simulating more than 13,200 different cases, it was shown that by considering dust effects, respectively, the series resistance, parallel resistance, ideality factor, reverse saturation current, and photocurrent source could be defined with up to 25%, 40%, 9%, 35%, and 40% more accuracy. The trend and dependencies of the prediction improvements for each parameter were also investigated thoroughly. Finally, compared with experimental results in more than 500 different cases showed that, on average, the proposed model improved the prediction of the module's output electrical behavior by 25% to 35%. The proposed model could be easily adjusted and applied to predict photovoltaic modules' output behavior under diverse environmental conditions.

Performance Analysis of Photovoltaic Panels Under the Effect of Electrical and Environmental Parameters in Erbil City

This paper presents the performance analysis of a photovoltaic cell derived from a single diode equivalent circuit under the influence of several kinds of electrical and environmental parameters. The characteristics of a solar cell have been investigated using MATLAB simulation and have been validated experimentally. In this paper the photovoltaic cell is represented by an exact equivalent circuit including all parameters such as a diode saturation current, light generated current, temperature effects, series and shunt resistance values. Also, this paper includes the impacts of clouds, dust, chalk powder, fly ash and bird droppings on the efficiency of the photovoltaic panel. A comparison between the experimental and model simulation results confirmed the reality of results, and indicate the validity of the exact model for photovoltaic performance analysis.

An Accurate and Fast Computational Algorithm Based on Hybrid Methods

The numerical solutions of nonlinear equation for a single diode equivalent circuit of a solar cell are introduced. Four numerically algorithms, which include newton's; Predictor-Corrector Hally and Accelerated Predictor-Corrector Hally methods are described and compared in the present work. These algorithms are applied to calculate the voltage; current; power of a solar cell with the different values of load resistance programmed by Matlab language. The results showed that the proposed algorithm is the most efficient compare with other three algorithms.

Modeling and optimization of organic tandem photovoltaic solar cells using silver nanowires as electrode and interconnecting layer

Much research has been conducted to improve the performance of photovoltaic solar cells. Transparent conductive film and interconnection layers have a significant impact on the performance of photovoltaic cells. In this work, we analyze the experimental results obtained on tandem organic photovoltaic solar cells with simple inverted structures using silver nanowires AgNW as transparent conductive electrode (TE) and as interconnection layer (ICL) between PEDOT: PSS and ZnO. This type of contact leads to a strong ohmic contact in both sub-cells having P3HT: ICBA as the lower active layer and having PTB7: PC71BM (1: 1.5) as the upper active layer with a good complement of the absorption spectrum. To study the advantages of using AgNWs as an interconnection layer (PEDOT: PSS/AgNWs/ZnO) in tandem photovoltaic solar cells and as an anode and its impact on the performance of these organic cells, we have simulated the electrical characteristics obtained by these tandem organic photovoltaic cells using an equivalent circuit model. This model is based on a single diode model with five photovoltaic parameters. We therefore extracted all the physical parameters of the illuminated photovoltaic cell from its experimental characteristics (J–V), such as the diode saturation current density (J0), the series and shunt resistors (RS, RSh), the ideality factor (n) and the photogenerated current density (JPh). For this we have solved the analytical equations of the current density using Newton Raphson's method. The equations are derived from the single diode equivalent circuit proposed to simulate the measured current density as a function of the voltage of the manufactured tandem type organic solar cells. A good agreement was obtained between the theoretical model and the experimental electrical characteristics. This confirms that the use of AgNWs between PEDOT: PSS and ZnO as an interconnection layer in reverse geometry of these tandem devices, has improved the efficiency (PCE = 9.24%) and is proving to be an efficient recombination layer for tandem organic photovoltaic solar cells.

Моделювання роботи фотоелектричних панелей з використанням середовища Matlab/Simulink

Modeling of the photovoltaic panels’ parameters makes it possible to predict in the shortest time the performance of a photovoltaic station in the context of specific days, months and along the year for any area and the method of solar panels arranging. One of powerful tools of computer mathematics, which recently has been widely used to simulate various technical systems, is the MATLAB environment. Due to the built-in Simulink package, MATLAB allows to realize visual-oriented block simulation of dynamic systems, in particular, various devices of functional electronics, solar cells and photovoltaic modules. This paper proposes an approach to modeling the operation of real photovoltaic panels in the MATLAB/Simulink environment using information from the panel technical documentation as input data for the Solar Cell block. The method for determining the input parameters of the Solar Cell block, which are not specified in the technical documentation of the solar panel, is presented. This method is based on the analysis of the light current-voltage characteristic of the panel for standard test conditions in the approximation of a single-diode equivalent circuit of a photovoltaic cell. Proposed method was tested on the example of JAP6(BK) 60-250/3BB, AS-6P30-270W and LG290N1C panels from the world's leading manufacturers. A visual-oriented model based on Solar Cell block was created in the MATLAB/Simulink environment to build the light characteristics of photovoltaic panels. The light characteristics of the JAP6(BK) 60-250/3BB, AS-6P30-270W and LG290N1C panels were simulated using created model, and main parameters of the panels under standard test conditions were calculated. Comparison of the panels parameters determined from the simulated light characteristics with the data presented in the technical documentation showed that for all panels the deviation of the simulation results from the documentation parameters is less than permissible 3%. This indicates the acceptability of the proposed approach to modeling the operation of real photovoltaic panels in the MATLAB / Simulink environment.

Numerical Simulation and Experimental Analysis of Electrical Properties of InGaP/InGaAs/Ge Triple-Junction Solar Cell with Reflective High-Concentration Photovoltaic System

Photovoltaic power systems is one of the most important ways of utilizing solar energy, and high-concentration photovoltaic systems have received much attention due to its high conversion efficiency. This study developed a mathematical model of an InGaP/InGaAs/Ge triple-junction solar cell (TJSC) according to a single-diode equivalent circuit. Moreover, a correlation of the series resistance of TJSC considering the effects of temperature and incident energy density was obtained and further verified by experiments. Based on a reflective high-concentration photovoltaic system, the electrical properties, including the short-circuit current, open-circuit voltage, peak power, and efficiency, were investigated. The results showed that the series resistance increased from 0.0095 Ω to 0.0123 Ω with temperature increased from 298 K to 358 K at the incident of 2×105 W /m2, and it increased from 0.0094 Ω to 0.0196 Ω as the incident energy density increased from 2.0×105 W/m2 to 1.0×106 W/m2 at temperature of 298K. In addition, the relationships between other electrical properties and the incident energy density or temperature were investigated. The simulations were remarkably consistent with the experimental results. The experimental values were slightly less than the theoretical values, which was caused mainly by the temperature instead of the incident energy density.

Parameters extraction of single diode model for degraded photovoltaic modules

The single–diode model is widely used for the analysis of photovoltaic systems and reproducing accurately the I–V curve. Numerical or analytical methods can be employed to estimate the model parameters; among them explicit methods are well assessed providing precise results and low computational complexity, thus suitable to be developed on embedded systems. Due to their approximated nature, the accuracy of such methods may be affected by the operating conditions and by the state of health of the photovoltaic modules that have been characterised. The main contribution of this paper is to analyse a selection of explicit methods with the aim of testing their capability to detect degradation in photovoltaic modules. Since different degradation phenomena are reflected in a variation of the series resistance of the single diode equivalent circuit, the study is mainly focused on the estimation of this parameter. The comparison of different explicit methods has been done by using outdoor experimental I–V curves of a photovoltaic module operating in normal as well as degraded conditions. The analysis shows that only few methods exhibit enough reliability to estimate correctly the model parameters in presence of degradation and are less sensible to the environmental operating conditions.

Parameters estimation of photovoltaic cells using simple and efficient mathematical models

This paper proposes a simple and efficient method to estimate the parameters of the photovoltaic (PV) cells at standard test conditions (STC). The proposed method is based on developing a mathematical model for each parameter of the single-diode equivalent circuit of the PV cell. The models are formulated using Eureqa software based on thousands of training data collected from simulating the equations that represent the equivalent circuit behavior of the PV cell. Only the data provided by the manufacturer’s datasheet are needed to execute the models and evaluate the parameters. The performance of the developed models is then assessed by comparison with simulation data, Simulink library modules, experimental data, and various recent reported algorithms. The assessments have shown an overall efficient performance of the models to evaluate the equivalent circuit parameters for any poly and monocrystalline PV cell/module at STC. In addition, the models are in good agreement and, in some cases, have outperformed various algorithms presented in the literature in terms of the accuracy of predicting the I-V curve characteristics.

SoC-based embedded real-time simulation of mismatched photovoltaic strings

The real time simulation is a key tool for the implementation of monitoring and diagnostic methods as well as of model-based control strategies in modern photovoltaic systems. Under the hypothesis that all the cells of the photovoltaic array operate in the same temperature and irradiance conditions and have the same degradation level, the values of the parameters appearing in the single diode equivalent circuit referred to one cell are scaled up to the whole array, so that the simulation is not computationally demanding at all. Unfortunately, when mismatching effects have to be taken into account, including partial shadowing phenomena and uneven degradation of the cells, the simulation is not as straightforward as in the previous case. A numerical method, which has been recently presented in literature, allows to simulate a large mismatched photovoltaic array with a low computational effort. It exploits a suitable formulation of the non linear system of equations leading to an inverse Jacobian matrix formulated explicitly. In this paper it is shown the process for engineering such a numerical method by using a low cost system-on-chip device available on the market. The analysis presented shows the critical aspects of the implementation, if the computing time has to be minimized for real-time simulation purposes. The advantages offered by the system-on-chip are explored in order to deploy in the best way the algorithm functions on the ARM processor and on the FPGA available therein. Implementation results show the performance of the proposed approach, especially in terms of computation time and use of resources.

Virtual Sensing of Photovoltaic Module Operating Parameters

The single diode equivalent circuit allows describing photovoltaic panels behavior quite accurately. The values of the five parameters appearing in this model are usually identified in standard test conditions, at which irradiance and temperature values are given. Instead, when this identification has to be performed on field, suitable environmental sensors are required. In this article, a procedure for the on-site identification of the single diode model parameters as well as of the working irradiance and temperature conditions is presented. The procedure operates only on the measured panel current versus voltage curve, or on a part of it around the maximum power point, and does not need any other input data. A consolidated identification algorithm, effectively running on any embedded system for on-site application, is used. The proposed procedure is validated through a large number of experimental measurements acquired in two different geographic locations.