Solar cell array parameters using Lambert W-function (original) (raw)
Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve) at different levels OPEN ACCESS Energies 2014, 7 4099 of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer's datasheet.
Lambert W-function simplified expressions for photovoltaic current-voltage modelling
2020 IEEE International Conference on Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe), 2020
In this paper, the first work carried out at the IDR/UPM Institute within the frame of the educational innovation project PIRAMIDE is presented. This work is related to photovoltaic behavior modeling simplification. The aim is to derive simplified and easy-to-work-with equations for the Lambert W-function. This mathematical function represents a quite useful tool when modeling solar cells/panels performance (that is, the current-voltage curve) by analytical approaches. However, the Lambert W-function has a complex solving process which might represent an unaffordable mathematical challenge for a great number of professionals/technicians from the photovoltaic industrial sector. Simple approximations for the Lambert W-function on both of its branches (positive and negative), are proposed in this work. The results of the present work show a simple but accurate way of photovoltaic systems modeling, even when working with the implicit equation of the 1-Diode/2-Resistor equivalent circuit model (whose solution is given in the present work by an explicit equation).
Sensors
There are three standard equivalent circuit models of solar cells in the literature—single-diode, double-diode, and triple-diode models. In this paper, first, a modified version of the single diode model, called the Improved Single Diode Model (ISDM), is presented. This modification is realized by adding resistance in series with the diode to enable better power loss dissipation representation. Second, the mathematical expression for the current–voltage relation of this circuit is derived in terms of Lambert’s W function and solved by using the special trans function theory. Third, a novel hybrid algorithm for solar cell parameters estimation is proposed. The proposed algorithm, called SA-MRFO, is used for the parameter estimation of the standard single diode and improved single diode models. The proposed model’s accuracy and the proposed algorithm’s efficiency are tested on a standard RTC France solar cell and SOLAREX module MSX 60. Furthermore, the experimental verification of the...
Solar Energy, 2013
The values of series and shunt resistances play an important role in the modelling behaviour of a photovoltaic cell. The authors proposed in earlier work a new method to determine these values numerically at maximum power point using the Newton-Raphson method and equations based on the Lambert W-function. Here, an experimental investigation has been carried out to further validate this method and observe its behaviour over the entire current-voltage curve. Current-voltage curves from a single multi-crystalline cell were obtained under outdoor testing in Hamilton, New Zealand under three levels of illumination (800, 900, and 1000 W/m 2). In addition to the method of Ghani and Duke (2011), two other methods were also used to calculate series and shunt resistances based on the parameters extracted from the experimental data. A comparative study of each methods output current vector using a root mean square error analysis revealed that greatest accuracy was achieved with the proposed approach.
Energy Conversion and Management, 2018
Accurate modeling plays an important role in solar cell simulation. In order to reveal the applicability and superiority of Special Trans function based single diode model (SBSDM), this paper presents a comprehensive comparison of SBSDM, Lambert W function based single diode model (LBSDM) and exponential-type single diode model (SDM). The performance difference of SBSDM, LBSDM and SDM is verified and compared in two aspects: (1) different fitness to the measured I-V data of solar cells and (2) different parameter extraction performance. To be objective and reproducible, the reported parameter values of standard datasets and measured datasets are employed to validate the fitness difference of the three models. The comparison results indicate that SBSDM always exhibits better fitness than LBSDM and SDM in representing the I-V characteristics of various solar cells and can provide a closer prediction to actual maximum power points. With the help of a ranking based branch selection strategy, a modified Nelder-Mead simplex (MNMS) algorithm is proposed to test the parameter extraction performance of SBSDM, LBSDM and SDM. The comparison results reveal that the time computational efficiency of SBSDM is inferior to SDM but superior to LBSDM. SBSDM always achieves superior accuracy and convergence speed than LBSDM and SDM, although lacking enough statistical robustness. Due to these superiorities, SBSDM is quite promising and envisaged to be the most valuable model for solar cell parameter extraction and PV system simulation.
Simplified Lambert W-Function Math Equations When Applied to Photovoltaic Systems Modeling
IEEE Transactions on Industry Applications, 2021
In this article, simplified and easy-to-work-with equa-Q1 5 tions for the Lambert W-function are derived. This function is 6 widely used to solve equations related to photovoltaic systems. More 7 specifically, this mathematical function represents a useful tool 8 when modeling solar cells/panels performance (that is, the current-9 voltage curve) by analytical approaches. However, the Lambert 10 W-function has a complex solving process which might represent 11 an unaffordable mathematical challenge for a great number of pro-12 fessionals/technicians in the photovoltaic industrial sector. Simple 13 approximations for the Lambert W-function on both of its branches 14 (positive and negative) are proposed in this article. The results of 15 the present article show a simple but accurate way for photovoltaic 16 systems modeling, even when these systems comprise a maximum 17 power point tracking subsystem.
2014
Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage-I-V-curve) at different levels OPEN ACCESS Energies 2014, 7 4099 of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer's datasheet.
Energy Conversion and Management, 2016
Accurate modeling and parameter extraction of solar cells play an important role in the simulation and optimization of PV systems. This paper presents a Lambert W-function based exact representation (LBER) for traditional double diode model (DDM) of solar cells, and then compares their fitness and parameter extraction performance. Unlike existing works, the proposed LBER is rigorously derived from DDM, and in LBER the coefficients of Lambert W-function are not extra parameters to be extracted or arbitrary scalars but the vectors of terminal voltage and current of solar cells. The fitness difference between LBER and DDM is objectively validated by the reported parameter values and experimental I-V data of a solar cell and four solar modules from different technologies. The comparison results indicate that under the same parameter values, the proposed LBER can better represent the I-V and P-V characteristics of solar cells and provide a closer representation to actual maximum power points of all module types. Two different algorithms are used to compare the parameter extraction performance of LBER and DDM. One is our restart-based bound constrained Nelder-Mead (rbcNM) algorithm implemented in Matlab, and the other is the reported R cr-IJADE algorithm executed in Visual Studio. The comparison results reveal that, the parameter values extracted from LBER using two algorithms are always more accurate and robust than those from DDM despite more time consuming. As an improved version of DDM, the proposed LBER is quite promising for PV simulation and thus deserves serious attention.
Investigation of methods used in calculations of solar cell parameters
Radioelectronics and Communications Systems, 2009
Analytical expressions have been obtained for extracting the electrical parameters and characteristics of solar cells, including series and shunt resistances, and the saturation current. The method of Lagrange multipliers was used for computing the shape factor of the current-voltage characteristic (CVC) of solar cell. The calculation results demonstrated a satisfactory agreement with experimental data.
International Journal of Renewable Energy Research, 2013
An exact analytical method using special trans function theory (STFT) is presented to calculate the parameters of a real solar cell. Calculated values are compared with other methods. Various characteristic curves are also drawn using the analytical expressions to validate this approach. The effect of the parasitic resistances in the fill factor is studied in detail. Relative percentage accuracy of STFT method is also calculated to show the significance of the method over other methods.
Applied Sciences, 2021
In this paper, we propose very simple analytical methodologies for modeling the behavior of photovoltaic (solar cells/panels) using a one-diode/two-resistor (1-D/2-R) equivalent circuit. A value of a = 1 for the ideality factor is shown to be very reasonable for the different photovoltaic technologies studied here. The solutions to the analytical equations of this model are simplified using easy mathematical expressions defined for the Lambert W-function. The definition of these mathematical expressions was based on a large dataset related to solar cells and panels obtained from the available academic literature. These simplified approaches were successfully used to extract the parameters from explicit methods for analyzing the behavior of solar cells/panels, where the exact solutions depend on the Lambert W-function. Finally, a case study was carried out that consisted of fitting the aforementioned models to the behavior (that is, the I-V curve) of two solar panels from the UPMSat-...
Solar cells parameters evaluation considering the series and shunt resistance
Solar Energy Materials and Solar Cells, 2007
This paper presents a new technique for the evaluation of the parameters of illuminated solar cell with a single diode lumped circuit model and considering the series and shunt resistances. This method includes the presentation of the standard I ¼ f(V) function as V ¼ f(I) and the determination of the factors C 0 , C 1 , C 2 of this function that provide the calculation of the illuminated solar cell parameters. These parameters are usually the saturation current (I s ), the series resistance (R s ), the ideality factor (n), the shunt conductance (G sh ¼ 1/R sh ) and the photocurrent (I ph ).
Solar Energy Materials and Solar Cells, 2006
We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current-voltage (I-V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I-V characteristics and an analysis of the errors is presented. r
Modeling of solar cell under different conditions by Ant Lion Optimizer with LambertW function
The performance of a solar cell is studied by estimating the internal parameters using single diode model (SDM). The environmental operating conditions like temperature and solar irradiance also influence the electrical I-V curves that characterize the photovoltaic cell. In this paper, the parameters of the solar cell are extracted using the desired single diode model equations, expressed using LambertW function under the influence of temperature and irradiance through the experimental I-V data using Ant Lion Optimizer implemented in IPython. The simulated results are validated by the obtained low Root Mean Squared Error. The different internal parameters under varied environmental conditions, obtained by the LambertW-based Ant Lion Optimizer are in good agreement with the literature reports and proves to be an effective technique.
International Journal of Innovation and Applied Studies, 2016
A new approach is presented in this work, to extract electrical parameters of a photovoltaic cell, using the double exponential model. The equivalent circuit parameters of this model are the photocurrent (Iph), ideality factor (?), diffusion current (Iod), recombination current (Ior), series resistance (Rs) and the shunt resistance (Rsh). Several research studies have been performed to extract these parameters. The majority of these developed methods are limited on several levels. In this work the proposed technique is based on the equalization of the electric model of photovoltaic cells, and a polynomial model equivalent. The comparison of these two models at I=0, allows representing the electrical parameters with the polynomial model coefficients. This method is tested on a monocrystalline solar panel and obtained results show the advantage of this technique in level of speed, convergence and precision.
An Improved Mathematical Model for Computing Power Output of Solar Photovoltaic Modules
International Journal of Photoenergy, 2014
It is difficult to determine the input parameters values for equivalent circuit models of photovoltaic modules through analytical methods. Thus, the previous researchers preferred to use numerical methods. Since, the numerical methods are time consuming and need long term time series data which is not available in most developing countries, an improved mathematical model was formulated by combination of analytical and numerical methods to overcome the limitations of existing methods. The values of required model input parameters were computed analytically. The expression for output current of photovoltaic module was determined explicitly by Lambert W function and voltage was determined numerically by Newton-Raphson method. Moreover, the algebraic equations were derived for the shape factor which involves the ideality factor and the series resistance of a single diode photovoltaic module power output model. The formulated model results were validated with rated power output of a phot...
Journal of Computational Electronics
Finding the equivalent circuit parameters for photovoltaic (PV) cells is crucial as they are used in the modeling and analysis of PV arrays. PV cells are made of silicon. These materials have a nonlinear characteristic. This distorts the sinusoidal waveform of the current and voltage. As a result, harmonic components are formed in the system. The PV cell is the smallest building block of the PV system and produces voltages between 0.5 V and 0.7 V. It serves as a source of current. The amount of radiation hitting the cell determines how much current it produces. In an ideal case, a diode and a parallel current source make up the equivalent circuit of the PV cell. In practice, the addition of a series and parallel resistor is made to the ideal equivalent circuit. There are many equivalent circuits in the literature on modeling the equivalent circuit of a PV cell. The PV cell single-diode model is the most used model due to its ease of analysis. In this study, the iterative method by Newton-Raphson was used to find the equivalent circuit parameters of a PV cell. This method is one of the most widely used methods for determining the roots of nonlinear equations in numerical analysis. In this study, five unknown parameters (Iph, Io, Rs, Rsh and m) of the PV cell equivalent circuit were quickly discovered with the software program prepared based on the Newton-Raphson method in MATLAB.
Finding the equivalent circuit parameters for photovoltaic (PV) cells is crucial as they are used in the modeling and analysis of PV arrays. PV cells are made of silicon semiconductor materials. These materials have a nonlinear characteristic. This distorts the sinusoidal waveform of the current and voltage. As a result, harmonic components are formed in the solar system. The PV cell is the smallest building block of the PV system and produces voltages between 0.5V and 0.7V. It serves as a source of current in the solar system. The amount of radiation hitting the cell determines how much current it produces. In an ideal case, a diode and a parallel current source make up the equivalent circuit of the PV cell. In practice, the addition of a series and parallel resistor is made to the ideal equivalent circuit. There are many equivalent circuits in the literature on modeling the equivalent circuit of a PV cell. The PV cell single diode model is the most used model due to its ease of an...
2012
The electrical behavior of organic solar cell (OSC) has been analyzed using a simple circuital model consisting on an ideal diode together with a series and parallel resistances (R S and R P respectively). Applying Kirchhoff's Laws to the circuit leads to a transcendental equation that can be solved numerically without approximations using the Lambert W function. Theoretical expression has been fitted to experimental current-voltage (I-V) curves under forward bias, obtaining fairly accurate values for the electrical parameters. This model has been validated comparing the extracted parameters for dark and illumination conditions of different devices. Results show good agreement for R S , and ideality factor ( ).
Analytical model of mismatched photovoltaic fields by means of Lambert W-function
Solar Energy Materials and Solar Cells, 2007
A new model of photovoltaic (PV) fields is introduced in this paper. It allows the simulation of a PV generator whose subsections, e.g. cells, groups of cells, panels or group of panels, work under different solar irradiation values and/or at different temperatures. Moreover, different nominal characteristics, rated power, production technology, shape and area can be settled for different subsections. Consequently, the proposed model is able to describe the behaviour of matched as well as mismatched PV fields. It results into a non linear system of equations, which includes bypass and blocking diodes models and is characterized by a sparse Jacobian matrix. The numerical model is reliable and requires a moderate computational burdensome, both in terms of memory use and processor speed. Numeric simulations confirm the accuracy and cheapness of the approach. The proposed model is used to simulate the drawbacks associated to mismatching during maximum power point tracking (MPPT) of the PV generator. r