A cell-to-module-to-array detailed model for photovoltaic panels

This paper presents a modified current–voltage relationship for the single-diode model. The single-diode model has been derived from the well-known equivalent circuit for a single photovoltaic (PV) cell. A cell is defined as the semiconductor device that converts sunlight into electricity. A PV module refers to a number of cells connected in series and in a PV array, modules are connected in series and in parallel. The modification presented in this paper accounts for both parallel and series connections in an array. Derivation of the modified current–voltage relationships begins with a single solar cell and is expanded to a PV module and finally an array. Development of the modified current–voltage relationship was based on a five-parameter model, which requires data typically available from the manufacturer. The model accurately predicts voltage–current (V–I) curves, power–voltage (P–V) curves, maximum power point values, short-circuit current and open-circuit voltage across a range of irradiation levels and cell temperatures. The versatility of the model lies in its accurate prediction of the aforementioned criteria for panels of different types, including monocrystalline and polycrystalline silicon. The model is flexible in the sense that it can be applied to PV arrays of any size, as well as in simulation programs such as EMTDC/PSCAD and MatLab/Simulink. Accuracy of the model was validated through a series of experiments performed outdoors for different configurations of a PV array.     

Catalytic activity of infiltrated La0.3Sr0.7Ti0.3Fe0.7O3−δ–CeO2 as a composite SOFC anode material for H2 and CO oxidation

Finding cost-effective and efficient anode materials for solid oxide fuel cells (SOFCs) is of prime importance to develop renewable energy technologies. In this paper, La and Fe co-doped SrTiO₃ perovskite oxide, La_0.3Sr_0.7Ti_0.3Fe_0.7O_3?δ (LSTF0.7) composited with CeO₂ is prepared as a composite anode by solution infiltration method. The H₂ and CO oxidation behavior and the electrochemical performance (electrochemical impedance spectra, I–V and I–P curves) of the scandia-stabilized zirconia (ScSZ) electrolyte supported cells fabricated by tape casting with the LSTF0.7–CeO₂ composite anode are subsequently measured at various temperatures (700–850 °C). Electrochemical impedance spectra (EIS) of the prepared cells with the LSTF0.7–CeO₂|ScSZ|La_0.8Sr_0.2MnO₃ (LSM)–ScSZ configuration illustrate that the anode polarization resistance distinguished from the whole cell is 0.072 Ω cm² in H₂, whereas 0.151 Ω cm² in CO at 850 °C. The maximal power densities (MPDs) of the cell at 700, 750, 800 and 850 °C are 217, 462, 612, 815 mW cm^?2 in H₂ and 145, 349, 508, 721 mW cm^?2 in CO, respectively. Moreover, a significant decrease of anode activation energy towards H₂ oxidation is clearly demonstrated, indicating a better electrochemical performance in H₂ than in CO. These results demonstrate an alternative composite anode with high electrocatalytic activity for SOFC practical applications.     

A novel parameter extraction method for the one-diode solar cell model

With the increase in the capacity of photovoltaic generation systems, studies are being actively conducted to improve system efficiency. To develop precise solar cell simulators or design a high-performance photovoltaic generation system, it is important to accurately understand the physical properties of solar cells. However, solar cell models have a non-linear form with numerous parameters. To obtain accurate parameter values, assumptions that differ from real operating conditions must be made to avoid computational complexity. In this paper, a new method for extracting parameter values is proposed. The proposed method deduces the characteristic curve of an ideal solar cell without resistance using the I-V characteristic curve measured and reported by solar cell manufacturers and calculates the difference between the deduced and actual measured curves. In addition, the precision of the proposed method is demonstrated by calculating the correlation between the I-V characteristic curve based on modeling parameters and the I-V curve actually measured employing the least-squares method.     

Exact analytical solution of a two diode circuit model for organic solar cells showing S-shape using Lambert W-functions

Organic solar cells (OSCs) often show a kink, also called S-shape, in the current–voltage (I–V) characteristics, that has been attributed to different physical phenomena such as poor quality of cathode-active layer interface or unbalance charge carrier mobilities. This non-ideal behaviour can be electrically modelled including a second diode, in reverse bias, together with an extra shunt resistance (R_P2) in the traditional solar cell equivalent circuit. In this paper, we solve without approximations the transcendental equation system derived from this modified circuit. We have obtained an analytical expression for I–V curves decoupling the voltage drop in each diode using Lambert W function. This expression has been fitted to experimental data in order to obtain circuital parameters. Simulations varying saturation current of reverse diode (I₀₂) and R_P2 have been performed in order to study the dependence of S-shape with these parameters.     

Quantum-efficiency measurements on carbon–hydrogen-alloy-based solar cells

Solar cell devices have been fabricated with amorphous, hydrogenated carbon (a-C : H) as the primary semiconducting material. These devices clearly demonstrate photovoltaic behavior as determined by their I–V curves. To identify photon energies that contribute to the photogenerated current, quantum efficiency measurements have been performed. The fabricated solar cells exhibit a maximum quantum efficiency response in the ultraviolet region. Using the measured quantum efficiency curves, the short-circuit currents for a global AM1.5 spectrum at an irradiance of 1000 W/m² have been calculated. These values are comparable to the actually measured short-circuit currents.     

Modeling of the I–V curves of the PV modules using linear interpolation/extrapolation

Translation of the I–V curves of solar cells and modules for irradiance G and device temperature T is investigated. A new translation procedure based on the linear interpolation/extrapolation is proposed, in order to translate the I–V curves to target conditions of G and T. The accuracy of the method is investigated based on the indoor and outdoor experimental I–V curves of various kinds of photovoltaic (PV) cells and modules. The calculated the I–V curves over a wide range of G and T well agree with experimental results for various kinds of PV cells and modules. These results indicate that the translation of the I–V curve based on the method is effective for estimating the performance of the PV devices under various climatic conditions.     

Relevance vector-machine-based solar cell model

This paper proposes an advanced machine learning method, relevance vector machines (RVMs), to model photovoltaic (PV) cells with a few measured data, over a range of expected operating conditions. RVMs are established on a Bayesian formulation which results in usage of less number of relevance vectors leading to much more sparse representation than the support vector machine. The RVM model can be used to predict short-circuit current and open-circuit voltage and thereby maximum power point for any unknown temperature and irradiation. Coordinate translation technique is used to plot the nonlinear I–V characteristics of PV cells. The proposed method matches the measured data more accurately than the pure neural network model and the neuro-fuzzy model.     

An analytical-numerical approach for parameter determination of a five-parameter single-diode model of photovoltaic cells and modules

Parameter extraction of the five-parameter single-diode model of solar cells and modules from experimental data is a challenging problem. These parameters are evaluated from a set of nonlinear equations that cannot be solved analytically. On the other hand, a numerical solution of such equations needs a suitable initial guess to converge to a solution. This paper presents a new set of approximate analytical solutions for the parameters of a five-parameter single-diode model of photovoltaic (PV) cells and modules. The proposed solutions provide a good initial point which guarantees numerical analysis convergence. The proposed technique needs only a few data from the PV current-voltage characteristics, i.e. open circuit voltage V_oc, short circuit current I_sc and maximum power point current and voltage I_m; V_m making it a fast and low cost parameter determination technique. The accuracy of the presented theoretical I–V curves is verified by experimental data.     

Electrical modeling of CIGS thin-film solar cells working in natural conditions

In the paper, results of electrical modeling of Cu(In_xGa_1−x)Se₂ (CIGS) thin-film photovoltaic (PV) modules are presented. Whether the equivalent double diode model—DEM (Double diode Equivalent Model) is appropriate to model CIGS PV modules was investigated. Modeling was based on large amount of data (including current-voltage (I-V) curves) collected during long-term outdoor monitoring of PV systems. The process of applying baseline physical parameters to two of five DEM parameters: diffusion I_S1 and recombination I_S2 related components of dark diode saturation current was carried out. Modeled I_S1 and I_S2 values were used to replace previously approximated DEM parameters and then to predict measured I-V curves in order to determine electrical parameters of the PV modules. The parameters are used to predict energy yield in natural operating conditions. Results of modeling are presented and compared with measured data.     

Investigation of cloudless solar radiation with PV module employing Matlab-Simulink

This paper focuses on a novel approach to the prediction of Voltage-Current (V-I) characteristics of a Photovoltaic panel under varying weather conditions and also the modelling of hourly cloudless solar radiation to provide the insolation on a PV module of any orientation, located at any site. The empirical model developed in this study uses standard specifications together with the actual solar radiation and cell temperature. This proposed work develops a Matlab-Simulink model to generate solar radiation at any location and for any time of the year. A new model for V-I characteristics and maximum power operation of a Photovoltaic (PV) module is also presented, which aims to model the effect on V-I and P-V curves of varying climatic conditions. Moreover, this model has been implemented using the Matlab-Simulink and is used to investigate the effect of meteorological conditions on the performance of a PV module generator. Thus the combined model of cloudless solar radiation and the photovoltaic module provides a tool that may be loaded in the library for analysis purpose. It is found that the predicted solar radiation strongly agrees with the experimental data.     

DC conduction mechanism in polyvinyl alcohol films doped with potassium thiocyanate

The current–voltage characteristics of pure polyvinyl alcohol (PVA) films and those doped with potassium thiocyanate (KSCN) are studied as a function of film temperature and dopant concentration. The conduction mechanisms operative in the films in different temperature and voltage ranges are estimated from the behaviour of log I versus V^1/2 plots (I=current, V=voltage). For undoped (pure) films, the conduction mechanism appears to be essentially a Schottky type. On doping, there is considerable influence on the type of conduction mechanism, especially at lower temperatures. At higher temperatures, however, there is no significant effect of doping on the conduction mechanism.     

Application of plasma spray deposited coatings for seawater activated batteries

Seawater activated batteries based on Mg and Ni/Al electrodes were constructed and investigated at different electrolyte temperatures. The Ni/Al coatings which were applied as the cathodes for seawater activated batteries were produced by plasma spray deposition. Voltage–time (U=E−IR(t)) dependence was measured for the galvanic pair Mg–Ni/Al, where I was constant current, E the electromotive force of the galvanic pair and R(t) the variable resistance. It was found that U(t) inclination depends on the anode corrosion rate, and the mass of the anode is the only parameter that restricts the life time of the seawater activated cell. The current density of this cell was found to be a linear function of the temperature of the seawater. Output power density dependence on the spacing between electrodes and number of cells was investigated for cells with different electrode area. A maximum output power density of 3×10⁴ W/m³ was obtained for these cells.     

A linear method to extract diode model parameters of solar panels from a single I–V curve

The I–V characteristic curve is very important for solar cells/modules being a direct indicator of performance. But the reverse derivation of the diode model parameters from the I–V curve is a big challenge due to the strong nonlinear relationship between the model parameters. It seems impossible to solve such a nonlinear problem accurately using linear identification methods, which is proved wrong in this paper. By changing the viewpoint from conventional static curve fitting to dynamic system identification, the integral-based linear least square identification method is proposed to extract all diode model parameters simultaneously from a single I–V curve. No iterative searching or approximation is required in the proposed method. Examples illustrating the accuracy and effectiveness of the proposed method, as compared to the existing approaches, are presented in this paper. The possibility of real-time monitoring of model parameters versus environmental factors (irradiance and/or temperatures) is also discussed.     

Equivalent electrical model for a proton exchange membrane (PEM) electrolyser

In this work, an electrical equivalent model for a proton exchange membrane (PEM) electrolyser has been developed. Through experimental analysis, the input current–voltage (I–V) characteristic for a single PEM electrolyser cell has been modelled under steady-state conditions. It has been developed by using electrical equivalent circuit topology in which the useful power conversion and losses have been taken into account. Electrolytic hydrogen production rates of PEM electrolyser cell have been calculated with respect to the input current and power. The developed model has been tested with experiments results at the nominal operating temperature. The experimental results have been verified with the developed model results and the relative errors between them are around 1–2%. It has been observed that the electrolytic hydrogen production rate increases with the input current in a linear fashion. But the variation of electrolytic hydrogen production rate with the input electrical power is non-linear (i.e. logarithmic). These characteristics are verified by using the developed electrical equivalent model of PEM electrolyser cell. The parameters of the developed model can also be defined by taking into account of temperature and pressure effects. The equivalent electrical model of PEM electrolyser is very useful for analysing the electrical energy system behaviour in which the energy is stored in the form of electrolytic hydrogen.     

Analysis of the polarization of a direct methanol fuel cell using a pseudo-reversible hydrogen reference electrode

In order to observe the performance of the anode and cathode during actual direct methanol fuel cell (DMFC) operating conditions and to minimize the polarization of the reference electrode, we used a reversible hydrogen reference electrode (RHE) with its instability minimized. For analysis of the I–V polarization curve of each electrode, Tafel plots were used as the diagnostic tool. According to the slopes in the Tafel plot, the I–V polarization curves of each electrode were divided into the several regions. The effects of operating parameters on the performance of each electrode were interpreted in terms of mass transfer and electrode activation. The methanol and oxygen crossover through the membrane significantly affected the performance of the cell.     

Separation of solar cell current into its constituent parallel currents under illumination

A method is presented which suggests the sharing out of total cell short circuit current among the constituent parallel branches of the equivalent circuit, allowing for the identification of their contributions to the total current–voltage (I–V) characteristics under illumination in solar cells described through two parallel diodes. The method is based on the fact that all parallel branches are always under the same voltage; in particular, the open circuit voltage is the same for the cell as a whole as well as for each of the two diodes. With the help of the parameters of each diode and its share in the cell short circuit current, its light I–V characteristic can be drawn, and its individual fill factor calculated. Furthermore, the method suggests a way to estimate the cell fill factor with the help of the individual fill factors. The application of the method is carried out on experimental data of a ZnO/CdS/CuGaSe₂ single crystal solar cell.     

Synergistic effects and optimization of photo-fermentative hydrogen production of Rhodobacter sphaeroides DSM 158

The synergistic effects and optimization of pH, carbon-to-nitrogen ratio (C/N), and light intensity (I) on the photo-fermentative hydrogen production of Rhodobacter sphaeroides 158 DSM and light conversion efficiency have been investigated under different conditions of pH (6.5–8); C/N (15–35); and light intensity (35–185 W m^?2). Response surface methodology (RSM) and Box-Behnken experimental design (BBD) were used to identify the optimum values of the three key parameters of pH, C/N, and I, based on the impact on hydrogen production potential (HPP), hydrogen production rate (HPR), and light conversion efficiency $\eta$. With desirability value of 0.91, the optimum values of 7.4, 27.5, and 126 W m^?2 were identified for pH, C/N, and I respectively, with HPP, HPR and $\eta$ reaching 960 mL L^?1, 41.74 mL L^?1 h^?1, and 0.31 respectively. Regression analysis indicated a good fit between experimental and model data. The study showed that both C/N ratio and I have crucial and significant effect on the HPP, HPR and $\eta$, followed by pH, the synergistic effect of pH–I and C/NI on the light conversion efficiency ($\eta$) was significant while pH C/N was insignificant. The results and analysis obtained could be very useful for better optimizing the photo-fermentative hydrogen production.     

CPV module electric characterisation by artificial neural networks

Concentrating photovoltaic (CPV) is a relatively new technology with promising future expectations. However, it is at an early stage of development and it has much room for improvement. In order to gain knowledge about CPV technology, outdoor measurements are necessary to adjust models and to study the influence of the atmospheric conditions on the modules performance. In this work, multilayer perceptron models are applied to generate I–V characteristic curves of one of the most extended commercial module of concentrating photovoltaic technology, using the influential atmospheric variables as inputs to the networks. To train these networks an experiment with real measurements was carried out in Jaén, Spain, from July 2011 to June 2012. In addition to a model based on I–V curves expressed as a list of points in Cartesian coordinates, we present an alternative model trained with curves represented in polar coordinates. A previous selection of the most representative samples from the initial dataset was performed using a Kohonen self-organising map. This procedure allows the simulation of the curves even under non-frequent atmospheric conditions. Using the proposed models, it is possible to obtain the characteristic curve of other CPV modules under different meteorological conditions, with high accuracy and fidelity.     

The comparison of direct borohydride-hydrogen peroxide fuel cell performance with membrane electrode assembly prepared by catalyst coated membrane method and catalyst coated gas diffusion layer method using Ni@Pt/C as anodic catalyst

Carbon supported Ni@Pt nanoparticles are synthesized using sodium dodecyl sulphate (SDS) and sodium borohydride (NaBH₄) as a structure-directing and reducing agents, respectively. The metal loading in synthesized nanocatalyst is 20 wt% and the ratio of Ni:Pt in the nanocatalyst is 1:1. The structural characterizations and morphologies of Ni@Pt/C nanocatalyst are investigated by field emission scanning electron microscopy (FE-SEM), energy-dispersive X-ray spectroscopy (EDX), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HR-TEM) and X-ray diffraction (XRD). The electrocatalytic activity of Ni@Pt/C catalyst toward borohydride $\left({\text{BH}}_4^{?}\right)$ oxidation in alkaline medium is studied by means of cyclic voltammetry (CV), chronopotentiometry (CP) and chronoamperometry (CA). The results show that Ni@Pt/C catalyst has superior catalytic activity toward borohydride oxidation (8825.38 mA mg Pt^?1). The Membrane Electrode Assembly (MEA) used in fuel cell set-up is fabricated with catalyst-coated membrane (CCM) and catalyst coated gas diffusion medium (CCG) techniques. The effect of two MEA performances on current–voltage (I–V) and current–power density (I–P) curves in the direct borohydride-hydrogen peroxide fuel cell was investigated using Pt/C 0.5 mg cm^?2 as cathode catalyst and Ni@Pt/C 1 mg cm^?2 as anode catalyst. The influence of cell temperature, sodium borohydride and hydrogen peroxide concentration on the I–V and I–P is determined. The results show that the maximum power density in MEA prepared using CCM method (CCM-MEA) is 68.64 mW cm^?2 at 60 °C, 1 M sodium borohydride and 2 M hydrogen peroxide (H₂O₂) that is higher than MEA prepared using CCG method (CCG-MEA). The impedance results show that with increasing temperature and discharging current, the overall anodic and cathodic charge transfer resistances reduce.     

Fabrication of cost-effective non-noble metal supported on conducting polymer composite such as copper/polypyrrole graphene oxide (Cu2O/PPy–GO) as an anode catalyst for methanol oxidation in DMFC

Cost-effective non-noble metal catalysts are of key significance to the successful use of direct methanol fuel cells (DMFCs) for electricity generation. Herein, cuprous oxide nanoparticles (Cu₂O NPs) supported graphene oxide (GO), polypyrrole (PPy) and polypyrrole–graphene oxide (PPy–GO) matrices were prepared using borohydride reduction method. The prepared catalysts were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), UV–Vis spectra, Zeta potential and transmission electron microscopy (TEM). The elemental analysis of the composites was done by energy dispersive X-ray spectroscopy (EDX). Cu₂O NPs were homogeneously dispersed and strongly anchored on the PPy grafted GO matrix and this was examined through morphological analysis. The Cu₂O/PPy–GO (80:10:10) NPs exhibited noticeable improvement in electrochemical performance in comparison to pure graphene oxide (GO) and pure PPy supported Cu₂O NPs catalyst and revealed the peak current density of 300 μA cm^?2 at +0.68 V. The Cu₂O/PPy–GO system demonstrated higher current density and also exhibited greater stability in comparison to the commercial Pt–Ru/C catalyst as characterized by chronoamperometry (CA) analysis. This prospective nano-catalyst showed higher I_F/I_B ratio (26%, 8.6% and 19%) compared to the corresponding catalyst systems of Cu₂O/GO, Cu₂O/PPy and Pt–Ru/C. In direct methanol fuel cell (DMFC), the efficiency of Cu₂O/PPy–GO nano-catalyst system as an anode catalyst for methanol oxidation reaction (MOR) was investigated and the result revealed a maximum current density of 155 mA cm^?2 at +0.2 V and power density of 31 mW cm^?2. Hence, Cu₂O/PPy–GO NPs are a cost-effective alternative for Pt–Ru/C system to execute practical application in DMFC.