Solar cell array parameters using Lambert W-function

Exact closed-form solution based on Lambert W-function are presented to express the transcendental current–voltage characteristic containing parasitic power consuming parameters like series and shunt resistances for solar cell array. Maple software was used to solve the transcendental equation of solar cell array.     

A new method to determine the diode ideality factor of real solar cell using Lambert W-function

A new method using Lambert W-function is presented to determine the diode ideality factor of real solar cell.     

Numerical determination of parasitic resistances of a solar cell using the Lambert W-function

Several methods are currently available to determine the values of series and shunt resistance of a solar cell. A new method is presented here to numerically locate these values using the popular Newton-Raphson technique at maximum power point. Equations based on the Lambert W-function and their partial derivatives are provided so that all calculations may be performed in a Matlab or similar environment. The results of this new method are presented and compared with two published methods and the analytically obtained for a blue and grey type solar cell in earlier work (Charles et al., 1981). Additionally, three modules of various type (single, poly, and amorphous crystalline) were investigated. Values determined agreed with experimentally verified results and were obtained with quadratic convergence in all instances provided initial estimates of the roots were within vicinity of the actual roots.     

A new approach to study organic solar cell using Lambert W-function

Organic photovoltaic solar cells bear an important potential of development in the search for low-cost modules for the production of domestic electricity. One of the main differences between inorganic and organic solar cells is that photo-excitation in these materials does not automatically lead to the generation of free charge carriers, but to bind electron–hole pairs (exciton) with a binding energy of about 0.4 eV. Till now various numerical methods using approximations have been reported to study different aspects of organic solar cells. For the first time an accurate method using Lambert W-function is presented to study different parameters of organic solar cells.     

Study of CdS/Cu(In,Ga)Se2 interface by using n values extracted analytically from experimental data

This paper presents that an analytical method based on Lambert W-function can be applied to estimate the value of the diode ideality factor n, of a ZnO/CdS/Cu(In,Ga)Se₂ (CIGS) solar cell by using its dark current-voltage characteristics. The method is tested at different temperatures in the dark and found that the resulting n(T) values are in good agreement with those estimated experimentally from the slopes of the straight-line regions of Log I-V plots. The suggested values of n(T) under illumination are also determined using the exact explicit analytic solutions for the current-voltage relation expressed in terms of Lambert W-functions and experimentally estimated parasitic series and shunt resistances (R_s, R_sh), diode saturation current (I_o), open circuit voltage (V_oc) and short circuit current (I_sc) values at various temperatures. Temperature dependence of the diode ideality factor revealed that after illumination still tunnelling enhanced interface recombination mechanism dominates the current transport with relatively low tunnelling energy as compared to the dark case.     

Nondestructive diagnostics of solar cells in modules and batteries by means of modulated optical beam-induced photovoltaic signal

An alternative signal appearing at the photovoltaic module output under chopped illumination has been shown to have an information allowing to recover both dark and illuminated I–V characteristics of the individual cells, provided the module circuit is in the Galvanostatic mode. The important cell parameters such as voltage drop, open circuit voltage, short circuit current and ideality factor are evaluated experimentally without the disassembly of the module. The approach may be useful for the control of the quality of cells in the already encapsulated or single-substrate integrated modules.     

Exact analytical solutions of the parameters of real solar cells using Lambert W-function

Exact closed-form solution based on Lambert W-function are presented to express the transcendental current–voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. The W-function expressions are derived using Maple software. Different parameters of solar cell are calculated using W-function method and compared with experimental data of Charles et al. for two solar cells (blue and grey). Percentage accuracy of W-function method is also calculated to prove the significance of the method.     

Explicit model of photovoltaic panels to determine voltages and currents at the maximum power point

A simple explicit photovoltaic formulation for characterizing and dimensioning cell-arrays is presented. The method permits the short-circuit current, the open-circuit voltage, the maximum cell power and the optimum cell-operation conditions to be determined. Further, the model also allows quantifying the effects of panel temperature and solar irradiance on key cell parameters. Based on several datasheets, the methodology is validated by covering a wide range of operation conditions. The proposed approach can thus, be very useful for design engineers to quickly and easily determine the performance of any photovoltaic array without performing tedious numerical calculations.     

A new method to determine the optimum load of a real solar cell using the Lambert W-function

An exact explicit solution based on the Lambert W-function is presented to express the optimum load of an illuminated solar cell containing a parasitic series resistance and a shunt resistance. The W-function expressions are derived using Matlab software. The method is validated by comparing the model-predicted results to the experimental data for three real solar cells. The impacts of the series resistance and shunt resistance on the optimum load are also studied and the results show a good consistency with the data reported in the literature.     

Study for improvement of solar cell efficiency by impurity photovoltaic effect

This paper is to study for efficiency improvement of solar cells by utilizing impurity traps introduced in the band gap of semiconductor, that is, impurity photovoltaic (IPV) effect. It is revealed theoretically that there is a certain energy range where impurity-traps act as stepping stones in two-step excitation of electrons from the valence band to the conduction band under suppression of carrier recombination through such traps. Indium is selected as one of proper impurities that satisfy this condition in crystalline silicon, and theoretical prediction is experimentally verified. A good agreement between theory and experiment is obtained concerned with photoconductive properties. It is concluded that the IPV effect is useful to improve the cell efficiency.     

A two dimensional thermal network model for a photovoltaic solar wall

A two dimensional thermal network model is proposed to predict the temperature distribution for a section of photovoltaic solar wall installed in an outdoor room laboratory in Concordia University, Montréal, Canada. The photovoltaic solar wall is constructed with a pair of glass coated photovoltaic modules and a polystyrene filled plywood board as back panel. The active solar ventilation through a photovoltaic solar wall is achieved with an exhaust fan fixed in the outdoor room laboratory. The steady state thermal network nodal equations are developed for conjugate heat exchange and heat transport for a section of a photovoltaic solar wall. The matrix solution procedure is adopted for formulation of conductance and heat source matrices for obtaining numerical solution of one dimensional heat conduction and heat transport equations by performing two dimensional thermal network analyses. The temperature distribution is predicted by the model with measurement data obtained from the section of a photovoltaic solar wall. The effect of conduction heat flow and multi-node radiation heat exchange between composite surfaces is useful for predicting a ventilation rate through a solar ventilation system.     

Analytical and quasi-explicit four arbitrary point method for extraction of solar cell single-diode model parameters

In this paper, the five parameters of the solar cell single-diode model are analytical and quasi-explicitly extracted for the first time, just using the coordinates of four arbitrary points of the characteristic I–V curve and the slopes of the curve in these points. The new method presented, called Analytical and Quasi-Explicit (AQE) method, is exact because no simplifications of the model nor a priori approximations of the parameters are used and, it is quasi-explicit in the sense that all the parameters except one are explicitly given. The unique parameter not explicitly computed is easily obtained by solving a five-degree polynomial equation. Accurate and practical conditions are provided to select which solution of the previous equation is the desired parameter.It is also introduced a very easy method to obtain, directly from real data measurements, the needed four points of the I–V curve as well as the slopes in these points, without using any kind of sophisticated techniques.Finally, some experimental results are presented to demonstrate the high accuracy and simplicity of the new method. The results are compared with the well-known analytical five-point method and the recent oblique asymptote method.     

Interpretation of light-induced cell performance degradation by means of spectroscopic light illumination

Light-induced cell performance and lifetime degradation are investigated using blue and red light illuminations in order to clarify the responsible factor for the metastable defect activation. The evaluation of the cell-performance decay curves with exponential decay fittings results in the same decay time constants for the degradation. Spectral response degradation is investigated under blue-light illumination. Only the decrease in red response indicates deep distribution of the activated metastable defect into the bulk. Injected carriers are responsible for the defect activation. Carrier diffusion lengths of more than 100 μm in a cell at a degraded state is considered to make blue light possible to degrade the bulk.     

Modelling the light absorption in organic photovoltaic devices

Electromagnetic reflection, transmission and absorption properties are basically important for the optical characterization of multilayers used in optoelectronic and photovoltaic devices. They describe the interaction of incident light with the layers of the system. Depending on the thicknesses and optical constants of the individual layers, the interaction of a light source with a multilayer causes distinct distributions of the electric field and energy absorption density. Consequently the optical modelling of an organic bilayer photovoltaic device, in which the incident sunlight must be absorbed in a very narrow region near the active interface, has to take into account the influence of the optical parameters and the thicknesses of the device layers in order to gain optimal energy conversion. We focussed on the electrodynamic behavior of organic photovoltaic bilayer devices with varied layer thicknesses. We found a sensitive response of the maxima of the absorption density inside the solar cell to even fine changes in the thicknesses of the active layers. We also investigated the electrodynamic behavior of a photovoltaic device in dependence on the incident light wavelength. As a new and interesting result, our investigations showed a good correlation between measured photo current and calculated absorption density and no good correlation between measured photo current and calculated square of the electric field.     

Optimizing Gallium Arsenide multiple quantum wells as high-performance photovoltaic devices

We examine the possibility of using gallium arsenide (GaAs) quantum wells, which have significantly high absorption coefficient for photon energies near the energy band gap, as high-performance solar cells. Using a semi-empirical model of the absorption spectrum, we determine the critical well widths at which the efficiencies of solar cells based on the GaAs/Al_xGa_1−xAs quantum well structure can be optimized.     

Analytical model of solar pond with heat exchanger

This paper presents an analytical model of a three zone solar pond with heat exchange pipes laid in its bottom convective zone. Explicit expressions for the transient rate of heat extraction and the temperature at which heat can be extracted are derived as a function of geometrical and operational parameters of the system. The transfer of heat from the pond bottom convective zone to the heat exchange fluid is expressed in terms of a heat removal factor, F_R. Analytical results, characteristic of the optimum performance of the pond, are presented and the criteria for the size and heat transfer characteristics of the heat exchanger are investigated. The annual average efficiency of heat extraction exhibits the asymptotic increase with the increase of length per unit pond area of heat exchange pipe.     

Estimation of global radiation using clearness index model for sizing photovoltaic system

A methodology for developing a simple theoretical model for calculating global insolation on a horizontal surface is described in this paper. The input parameters to the model are the latitude of the desired location and the amount of total precipitable water content in the vertical column at that location. Both the parameters are easily measurable with inexpensive instrument such as global positioning system (GPS). The principal idea behind the paper is to have a model that could be used for designing a photovoltaic system quickly and within reasonable accuracy. The model in this paper has been developed using measured data from 12 locations in India covering length and breadth of the country over a period of 9–22 years. The model is validated by calculating theoretical global insolation for five locations, one in north (New Delhi), one in south (Thiruvanandapuram), one in east (Kolkata), one in west (Mumbai) and one in central (Nagpur) part of India and comparing them with the measured insolation values for these five locations. The measured values of all these locations had been considered for developing the model. The model is further validated for a location (Goa) whose measured data is not considered for developing the model, by comparing the calculated and measured values of the insolation. Over the range of latitudes covering most parts of India, the error is within 20% of the measured value. This gives the credibility of the model and the methodology used for developing the model for any region in the world.     

Thermographic sampling technique applied to microelectronics and photovoltaic devices

We investigated the energy turnover due to current flow across microelectronic devices and the energy loss during the light into current conversion by solar cells by use of a sampling technique of a space resolved infrared thermographic video imaging system. The change of temperature is correlated with current induced heating or cooling. The sampling technique increases the signal to noise ratio, the sensitivity of the system and suppresses misleading temperature drifts and effects due to infrared reflection of the surrounding or inhomogeneous composition of the sample. This video technique provides space resolved information about the maximum power point and of the efficiencies of solar cells, and may also be applied to macroscopic power systems such as the entire fields of photovoltaic panels.     

Semiconductor septum electrochemical photovoltaic cell with electrodeposited CdSe thin films

The performance of a semiconductor septum electrochemical photovoltaic (SC-SEP) cell based on electrodeposited CdSe thin films is reported. Photovoltages and photocurrent densities of 1.06 V and 15 mA/cm², respectively, were obtained. The proper selection of the electrolyte/electrode combination in the back compartment is a key factor better performance. A low fill factor causes a relatively low conversion efficiency of about 3.5%.     

Effect of solar photovoltaic and various photovoltaic air thermal systems on hydrogen generation by water electrolysis

A novel photovoltaic thermal air (PVTa) system with semi length fins in the downstream portion of the air channel was tested experimentally for its performance capability for the generation of hydrogen in the present work. Fins are passive devices used to overcome the main detrimental effect of reduced power output due to photovoltaic panel heating. For this purpose, 2 semi length fin configurations namely longitudinal fin and wavy fin were placed in second half length of the channel in the direction of air flow. To compare the impact of PVTa systems with semi lengthened fins in hydrogen generation, the performance study of PV and PVTa system assisted hydrogen generation were also conducted. The experiments were conducted at the site of Tiruchirappalli district, Tamilnadu state, India having latitude and longitude of 10.82 and 78.70 respectively during March–June 2019 from 9 a.m. to 4 p.m. on clear and sunny days. The results indicated PVTa system with semi length wavy fins yielded maximum generation of hydrogen among the 4 cases of PV assisted hydrogen generation techniques considered. It was observed that downstream located longitudinal and wavy fins provided enhanced PV panel cooling which increased the current supply to the electrolyzer unit. The hydrogen generation rate was 13.5, 12.1, 9.5 and 7.8 ml/min for PVT with wavy fins, longitudinal fins, PVT and PV respectively. Keywords: Solar PV, fins, hydrogen, heat transfer.