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I-V curve of a solar panel. The three characteristic points (short circuit, maximum power, and open circuit points) are indicated on the curve.
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Due to the high dependence of the photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis just focusing on the photovoltaic device characteristics in order to optimize the energy production, even in case of small-scale users. The use of equivalent circuits is the prefe...
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Context 1
... the increasing use of renewable energy sources is not only a fact, but it also represents a great concern of modern society, as the effects of global warming are more and more evident and have spread to almost every corner of planet Earth. Some of these renewable energy sources such as wind energy [1] or both solar photovoltaic [2] and solar thermal [3], had an enormous development in the recent decades. Focusing on the solar photovoltaic energy current users, there is not a clear and defined user profile, those users ranging from the industrial sector, represented by big power plants, to the private sector represented by citizens who invest in solar panels systems to save costs in terms of electricity consumption. Also, the space sector demands photovoltaic technology, and although it is not as massive as the aforementioned ones, it should be said that it leads the technological advances related to solar cells. Despite the wide diversity between users, there is a common need among them: to have a better understanding of their photovoltaic systems in order to get the best efficiency from them in terms of costs and revenue. On the other hand, photovoltaic energy is highly dependent on the environmental conditions (temperature, irradiation...) and that complicates its optimization, making the modeling of the panel a necessary tool. The modeling of solar panels is traditionally achieved through numerical fitting to extensive experimental results. However, this is not affordable for small users and it is not practical when a decision among different commercial solar panels/systems has to be made and only the information included in the manufacturers’ datasheets is available. Analytical methods represent a solution for this problem, as they are simpler and only require a small amount of data (frequently included in the datasheet) to model the solar panel behavior. In the present work an analytical methodology to model the behavior (output current, I , and output voltage, V ) of a photovoltaic device (cell or solar panel) is presented. It is based on the use of an equivalent circuit, which is an extended and accurate way to model solar panels. The present work is part of a larger research related to the UPMSat-2 satellite mission. In previous studies some analytical methods for parameter calculation were successfully developed, the aim now being to simplify the equations (with more sophisticated mathematical tools such as the Lambert function [4,5]), and show how these algorithms can be used in a practical application: to modeling a commercial solar panel at different levels of irradiation and temperature. This is a necessity for a correct power optimization or to include the solar panel in bigger electrical simulations (e.g. MPPT models), but with current methods it is not possible to do it with a small amount of information, and in a way accurate and simple at the same time. This method aims to solve this problem and enhance analysis capabilities to any user of solar energy. As it is well known, ideal solar cells behave like a current source connected in parallel with a diode [6 – 8]. This ideal model is completed with resistors to represent the losses and sometimes with additional diodes that takes into account other phenomena [9,10]. The most popular circuit equivalent to a solar cell/panel is shown in Figure 1, it includes a current source, one diode and two resistors: one in series and one in parallel [11 – 18]. Each element included in the equivalent circuit implies one parameter that has to be determined (two in the case of the diode whose behavior is represented by the Shockley equation [19]). Therefore, five parameters need to be calculated when using this method [20 – 32]. The current-voltage curve of a solar cell or panel, hereinafter the I - V curve (see Figure 2), is quite well reproduced by this simple equivalent circuit. Three points of the I - V curve are also indicated in this Figure 2: short circuit, maximum power, and open circuit points. These representative points are, together with their variation as a function of the temperature, the normal information included in manufacturers’ datasheets. The circuit model formed by one diode and two resistors (Figure 1) is defined by the following expression ...
Context 2
... the increasing use of renewable energy sources is not only a fact, but it also represents a great concern of modern society, as the effects of global warming are more and more evident and have spread to almost every corner of planet Earth. Some of these renewable energy sources such as wind energy [1] or both solar photovoltaic [2] and solar thermal [3], had an enormous development in the recent decades. Focusing on the solar photovoltaic energy current users, there is not a clear and defined user profile, those users ranging from the industrial sector, represented by big power plants, to the private sector represented by citizens who invest in solar panels systems to save costs in terms of electricity consumption. Also, the space sector demands photovoltaic technology, and although it is not as massive as the aforementioned ones, it should be said that it leads the technological advances related to solar cells. Despite the wide diversity between users, there is a common need among them: to have a better understanding of their photovoltaic systems in order to get the best efficiency from them in terms of costs and revenue. On the other hand, photovoltaic energy is highly dependent on the environmental conditions (temperature, irradiation...) and that complicates its optimization, making the modeling of the panel a necessary tool. The modeling of solar panels is traditionally achieved through numerical fitting to extensive experimental results. However, this is not affordable for small users and it is not practical when a decision among different commercial solar panels/systems has to be made and only the information included in the manufacturers’ datasheets is available. Analytical methods represent a solution for this problem, as they are simpler and only require a small amount of data (frequently included in the datasheet) to model the solar panel behavior. In the present work an analytical methodology to model the behavior (output current, I , and output voltage, V ) of a photovoltaic device (cell or solar panel) is presented. It is based on the use of an equivalent circuit, which is an extended and accurate way to model solar panels. The present work is part of a larger research related to the UPMSat-2 satellite mission. In previous studies some analytical methods for parameter calculation were successfully developed, the aim now being to simplify the equations (with more sophisticated mathematical tools such as the Lambert function [4,5]), and show how these algorithms can be used in a practical application: to modeling a commercial solar panel at different levels of irradiation and temperature. This is a necessity for a correct power optimization or to include the solar panel in bigger electrical simulations (e.g. MPPT models), but with current methods it is not possible to do it with a small amount of information, and in a way accurate and simple at the same time. This method aims to solve this problem and enhance analysis capabilities to any user of solar energy. As it is well known, ideal solar cells behave like a current source connected in parallel with a diode [6 – 8]. This ideal model is completed with resistors to represent the losses and sometimes with additional diodes that takes into account other phenomena [9,10]. The most popular circuit equivalent to a solar cell/panel is shown in Figure 1, it includes a current source, one diode and two resistors: one in series and one in parallel [11 – 18]. Each element included in the equivalent circuit implies one parameter that has to be determined (two in the case of the diode whose behavior is represented by the Shockley equation [19]). Therefore, five parameters need to be calculated when using this method [20 – 32]. The current-voltage curve of a solar cell or panel, hereinafter the I - V curve (see Figure 2), is quite well reproduced by this simple equivalent circuit. Three points of the I - V curve are also indicated in this Figure 2: short circuit, maximum power, and open circuit points. These representative points are, together with their variation as a function of the temperature, the normal information included in manufacturers’ datasheets. The circuit model formed by one diode and two resistors (Figure 1) is defined by the following expression ...
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Citations
... So, the ideal model for solar cell consists of a constant current source and a single diode connected in parallel, the configuration is shown in Figure 2.9. The addition of two resistors to this model, one in parallel and the other in series to represent the losses indicate the most popular equivalent circuit to a solar cell [18,19]. Where, I pv is the photocurrent delivered by the constant current source, I D is the reverse saturation current corresponding to the diode Whereas nothing is ideal, so in the case of equivalent circuit of solar panels the integration of the shunt resistance current I sh becomes necessary. ...
... In fitting the illumination I-V characteristic, the ideality factors of the diodes in the model are often initially set at a constant value and not further adjusted [5,[28][29][30]. The ideality factor indicates how closely the properties of the diode match the ideal properties, and it approaches n = 2 if the recombination process dominates. ...
A novel method to extract the seven parameters of the double-diode model of solar cells using the current-voltage (I-V) characteristics under illumination and in the dark is presented. The algorithm consists of two subroutines which are alternatively run to adjust all the parameters of the cell in an iterative process. Curve fitting of the light I-V characteristics ensures accuracy in the prediction of the maximum power point, whereas simultaneously fitting the dark I-V characteristics results in a set of physically meaningful parameters that provide information about the physical performance of the photovoltaic devices. Experimental I-V curves of in-house solar cells are used to validate the proposed parameter extraction method, which can be furthermore applied to other types of p-n junction-based photovoltaic devices.
... Lambert W based optimization [19][20][21][22][23][24] ...
The design of a solar PV system and its performance evaluation is an important aspect before going for a mass-scale installation and integration with the grid. The parameter evaluation of a solar PV model helps in accurate modeling and consequently efficient designing of the system. The parameters appear in the mathematical equations of the solar PV cell. A Chaos Induced Coyote Algorithm (CICA) to obtain the parameters in a single, double, and three diode model of a mono-crystalline, polycrystalline, and a thin-film solar PV cell has been proposed in this work. The Chaos Induced Coyote Algorithm for extracting the parameters incorporates the advantages of the conventional Coyote Algorithm by employing only two control parameters, making it easier to include the unique strategy that balances the exploration and exploitation in the search space. A comparison of the Chaos Induced Coyote Algorithm with some recently proposed solar photovoltaic cell parameter extraction algorithms has been presented. Analysis shows superior curve fitting and lesser Root Mean Square Error with the Chaos Induced Coyote Algorithm compared to other algorithms in a practical solar photovoltaic cell.
... Among them, the 1-Diode/2-Resistor equivalent circuit model was selected, see Figure 6B. It is basically composed of a current source connected in parallel with a diode, together with a shunt resistance Rsh, and a series resistance Rs [16][17][18][19]. Using the Shockley model for the diode, the output current, I, and the output voltage, V, at the terminals of the photodiode are related implicitly by the following equation: ...
This paper presents the development of the UPMSat-2 sun sensor, from the design to on-orbit operation. It also includes the testing of the instrument, one of the most important tasks that needs to be performed to operate a sensor with precision. The UPMSat-2 solar sensor has been designed , tested, and manufactured at the Universidad Politécnica de Madrid (UPM) using 3D printing and COTS (photodiodes). The work described in this paper was carried out by students and teachers of the Master in Space Systems (Máster Universitario en Sistemas Espaciales-MUSE). The solar sensor is composed of six photodiodes that are divided into two sets; each set is held and oriented on the satellite by its corresponding support printed in Delrin. The paper describes the choice of components , the electrical diagram, and the manufacture of the supports. The methodology followed to obtain the response curve of each photodiode is simple and inexpensive, as it requires a limited number of instruments and tools. The selected irradiance source was a set of red LEDs and halogen instead of an AM0 spectrum irradiance simulator. Some early results from the UPMSat-2 mission have been analyzed in the present paper. Data from magnetometers and the attitude control system have been used to validate the data obtained from the sun sensor. The results indicate a good performance of the sensors during flight, in accordance with the data from the ground tests.
... These parameters are estimated from multiple approaches, such as the iterative mathematical techniques that estimate five parameters by assuming the value of the ideality factor [18]. Also, the Lambert W-function method was applied to estimate these parameters from the datasheet of PV cells [19], [20]. The least squares method and the Gauss-Seidel method were used as an iterative approach in the parameter's extraction [21]- [24]. ...
Solar radiation is increasingly used as a clean energy source, and photovoltaic (PV) panels that contain solar cells (SCs) transform solar energy into electricity. The current-voltage characteristics for PV models is nonlinear. Due to a lack of data on the manufacturer’s datasheet for PV models, there are several unknown parameters. It is necessary to accurately design the PV systems by defining the intrinsic parameters of the SCs. Various methods have been proposed to estimate the unknown parameters of PV cells. However, their results are often inaccurate. In this article, a gradient-based optimizer (GBO) was applied as an efficient and accurate methodology to estimate the parameters of SCs and PV modules. Three common SC models, namely, single-diode models (SDMs), double-diode models (DDMs), and three-diode models (TDMs) were used to demonstrate the capacity of the GBO to estimate the parameters of SCs. The proposed GBO algorithm for estimating the optimal values of the parameters for various SCs models are applied on the real data of a 55 mm diameter commercial R.T.C-France SC. Comparison between the GBO and other algorithms are performed for the same data set. The smallest value of the error between the experimental and the simulated data is achieved by the proposed GBO. Also, high closeness between the simulated P-V and I-V curves is achieved by the proposed GBO compared with the experimental.
... To specify the most popular and practical functioning of a solar cell, authors [12] denoted the representation of losses by the resistors as shown in Fig. 1, having a current source connected in parallel with a diode and two resistors, one in series and other in parallel. Authors [13][14][15] noted the importance of the five-parameter approach to an equivalent solar circuit. ...
... To use the Lambert W-function, it is necessary to get equation (14) to the form exp( ) = . For this, we multiply both sides of (14) by the exponent of the right side of equation (15). Next, the reverse replacement is introduced (14) instead of b in (15). ...
... For this, we multiply both sides of (14) by the exponent of the right side of equation (15). Next, the reverse replacement is introduced (14) instead of b in (15). After further simplification of the expression for V, we obtain the requesting formula for finding the solar cell voltage depending on the current I: ...
The main goal of this research is to find and to analyze qualitatively, the current/voltage characteristics of the photovoltaic (PV) array. The proposed mathematical model is based on the single diode equivalent circuit; the analytical relationship between the electrical characteristics of the PV module and external environmental factors such as the intensity of solar radiation and temperature are taken into account. Mathematical and computer modeling are of the particular importance under the conditions of a significant spread in the values of external factors which occur in the mountain and remote desert areas in Central Asia. A mathematical analysis of the resulting transcendental equation is carried out using a Lambert W-function which has been the subject of a large number of publications.
... To specify the most popular and practical functioning of a solar cell, authors [12] denoted the representation of losses by the resistors as shown in Fig. 1, having a current source connected in parallel with a diode and two resistors, one in series and other in parallel. Authors [13][14][15] noted the importance of the five-parameter approach to an equivalent solar circuit. ...
... To use the Lambert W-function, it is necessary to get equation (14) to the form exp( ) = . For this, we multiply both sides of (14) by the exponent of the right side of equation (15). Next, the reverse replacement is introduced (14) instead of b in (15). ...
... For this, we multiply both sides of (14) by the exponent of the right side of equation (15). Next, the reverse replacement is introduced (14) instead of b in (15). After further simplification of the expression for V, we obtain the requesting formula for finding the solar cell voltage depending on the current I: ...
The main goal of this research is to find and to analyze qualitatively, the current/voltage characteristics of the photovoltaic (PV) array. The proposed mathematical model is based on the single diode equivalent circuit; the analytical relationship between the electrical characteristics of the PV module and external environmental factors such as the intensity of solar radiation and temperature are taken into account. Mathematical and computer modeling are of the particular importance under the conditions of a significant spread in the values of external factors which occur in the mountain and remote desert areas in Central Asia. A mathematical analysis of the resulting transcendental equation is carried out using a Lambert W-function which has been the subject of a large number of publications.
... Chatterjee [2] approximated the PV module characteristics by neglecting the term (-1) in the reverse saturation current equation, then form five equations and solve it simultaneously, which is tedious effort. Carlos de Manuel [3], represented estimation of the parameters based on the lambert W-function. Mokhtar et al. [4] estimated the five parameters based on iteration method. ...
... Where, 3 is the dark saturation current of the third diode, 3 is the ideality factor of the third diode. The nine parameters should be estimated according to Equation (7), are( ℎ , 1 , ...
... Where, 3 is the dark saturation current of the third diode, 3 is the ideality factor of the third diode. The nine parameters should be estimated according to Equation (7), are( ℎ , 1 , ...
... The I-V characteristics are nonlinear attributed to its diode properties in PV cells. The one diode equivalent circuit is defined in modelling by the following expression [CUBAS et al, 2014b]: Equation for a is given by: ...
Bypass diodes (BPDs) widely used in the installation of photovoltaic (PV) module are exposed and may sustain failures caused by lightning flash, etc. Such a failure of BPDs can cause the given cluster to enter various conditions. In the case of semi-conductive condition of BPD, power consumption of the given BPD dissipates the Joule heat, followed by various kinds of faults of PV modules. In this paper, numerical results regarding the effects of the resistance of semi-conductive BPD on the electrical and thermal characteristics of PV strings are demonstrated and discussed. It is found that those characteristics such as current-voltage characteristics of string greatly depend on the resistance of failure BPD. It is shown that the maximum power consumption by the failure BPD largely depends on load conditions, and that the thermal impact is more severe under the open-circuit load condition than under the Maximum Power Point load condition.
... So, the ideal model for solar cell consists of a constant current source and a single diode connected in parallel, the configuration is shown in Figure 2.9. The addition of two resistors to this model, one in parallel and the other in series to represent the losses indicate the most popular equivalent circuit to a solar cell [18,19]. Where, I pv is the photocurrent delivered by the constant current source, I D is the reverse saturation current corresponding to the diode Whereas nothing is ideal, so in the case of equivalent circuit of solar panels the integration of the shunt resistance current I sh becomes necessary. ...
https://riunet.upv.es/handle/10251/118802
