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Application of the full thermal model for PV devices
Abstract
Efficiency limits of solar cells have been studied since a long time ago giving the maximal theoretical efficiency and capacity current generation for different solar photovoltaic (PV) devices, and at the same time, real solar cells are becoming more efficient. However, some gaps are still remaining to be further improved and get closer to the desired theoretical limit. Therefore, the optimization of the PV efficiency is possible only if the intrinsic and extrinsic losses are well defined, identified, quantified and then mitigated. In this paper, a brief overview of the research evolution of thermal losses is presented. A physical-driven model is used to quantify internal heat sources, optical losses and the actual performance of a PV device. The Full Thermal Model for thermal assessment is presented in detail and applied to a bifacial heterojunction solar cell.
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A full thermal model for photovoltaic devices is presented. It consists of describing the physics of the conversion losses that come with heat dissipation together with giving analytical expressions of the associated heat sources. The consistency of the model is demonstrated by its application to a crystalline silicon solar cell. The modeling is completed by the balance equation which drives the equilibrium temperature of the cell. The impact of considering a full thermal model for designing photovoltaic devices is illustrated with two examples related to solar cells. First, the dependence of the heat source on the applied bias suggests that the Nominal Operating Cell Temperature should be defined at the Maximum Power Point instead of at open circuit and also could be function of representative climate conditions and mounting configurations. Second, a simple combined analysis of the heat source and the dependence of output electrical power with temperature – i.e. temperature coefficient – suggests that taking into consideration a full thermal modeling of solar cells has an impact on choosing the semiconductor material that maximizes the efficiency in real operating conditions.
Evaluation of GaAs laser power converters (LPC) is reported in light of theoretical maximum limits calculated with detailed balance method as proposed by Shockley and Queisser (SQ). Calculations were done for three different theoretical structures of LPCs homogeneously illuminated by monochromatic light. Effects of LPC thickness, central wavelength of a monochromatic light source and various irradiance levels are discussed. Reflection of incident light from the interface between air and GaAs is calculated and countermeasures in the form of single and double layer anti reflection coatings are theoretically studied. Measurements of single junction, single segment GaAs LPC illuminated by monochromatic light with central wavelength λ 0 = 808 nm are presented and compared with the theoretical maximum values. The conversion efficiency η meas = 54,4 % was measured for GaAs LPC illuminated with power density of monochromatic light p illum = 14,3 W/cm 2 at the temperature of the LPC casing T = 302 K. For the same parameters conversion efficiency η SQ = 76,6 % was calculated resulting in utilization ratio η meas /η SQ =0,71. Measured J sc and V oc achieve 88,5 % and 89,2 % of theoretically calculated SQ limit values.
The conversion efficiency of solar energy into electrical energy is the most important parameter when discussing solar cells, photovoltaic (PV) modules or PV power plants. So far many papers have been written to address the limiting efficiency of solar cells, the theoretical maximum conversion efficiency an ideal solar cell could achieve. However, most of the researches modelled sun's spectrum as a blackbody which does not represent a realistic case. In this paper we have calculated the limiting efficiency as a function of absorbers band gap at standard test conditions using the solar spectrum AM1.5. In addition, the other key solar cells performance parameters (open-circuit voltage, short-circuit current density and fill factor) are evaluated while the intrinsic losses in the solar cells are also explained and presented in light of a cell temperature.
Physics ruling the temperature sensitivity of photovoltaic (PV) cells is discussed. Dependences with temperature of the fundamental losses for single junction solar cells are examined and fundamental temperature coefficients (TCs) are calculated. Impacts on TCs of the incident spectrum and of variations of the bandgap with temperature are highlighted. It is shown that the unusual behavior of the bandgaps of perovskite semiconductor compounds such as CH3NH3PbI3-xClx and CsSnI3 will ultimately, in the radiative limit, give PV cells made of these materials peculiar temperature sensitivities. The different losses limiting the efficiency of present commercial cells are depicted on a p-n junction diagram. This representation provides valuable information on the energy transfer mechanisms within PV cells. In particular, it is shown that an important fraction of the heat generation occurs at the junction. A review of the loss mechanisms driving the temperature coefficients of the different cell parameters (open circuit voltage Voc, short circuit current density Jsc, fill factor FF) is proposed. The temperature sensitivity of open circuit voltage is connected to the balance between generation and recombination of carriers and its variation with temperature. A general expression that relates the temperature sensitivity of Voc to the External Radiative Efficiency (ERE) of a solar cell is provided. Comparisons with experimental data are discussed. The impacts of bandgap temperature dependence and incident spectrum on the temperature sensitivity of short circuit current are demonstrated. Finally, it is argued that if the fill factor temperature sensitivity is ideally closely related to the open circuit voltage temperature sensitivity of the cell, it depends for some cells strongly on technological issues linked to carrier transport such as contact resistances.
Recently, several parameters relevant for modeling crystalline silicon solar cells were improved or revised, e.g., the international standard solar spectrum or properties of silicon such as the intrinsic recombination rate and the intrinsic carrier concentration. In this study, we analyzed the influence of these improved state-of-the-art parameters on the limiting efficiency for crystalline silicon solar cells under 1-sun illumination at 25 °C, by following the narrow-base approximation to model ideal solar cells. We also considered bandgap narrowing, which was not addressed so far with respect to efficiency limitation. The new calculations that are presented in this study result in a maximum theoretical efficiency of 29.43% for a 110-μm-thick solar cell made of undoped silicon. A systematic calculation of the I--V parameters as a function of the doping concentration and the cell thickness together with an analysis of the loss current at maximum power point provides further insight into the intrinsic limitations of silicon solar cells.
The radiative recombination coefficient B(T) of intrinsic crystalline silicon is determined as a function of temperature over the temperature range 77–300 K. We observe that B(T) decreases as a function of temperature and we compare our results to previously published contradictory data from the literature. The radiative recombination coefficient is calculated from the absorption coefficient for band-to-band transitions, which we determine at different temperatures from photoluminescence spectra measured on planar high resistivity float zone silicon wafers. Photoluminescence spectra could be detected over a large range of more than five orders of magnitude, which allowed us to determine extremely low values of the absorption coefficient in the spectral range where absorption processes are accompanied by the simultaneous absorption of up to four phonons. © 2003 American Institute of Physics.
An accurate quantitative description of the Auger recombination rate in silicon as a function of the dopant density and the carrier injection level is important to understand the physics of this fundamental mechanism and to predict the physical limits to the performance of silicon based devices. Technological progress has permitted a near suppression of competing recombination mechanisms, both in the bulk of the silicon crystal and at the surfaces. This, coupled with advanced characterization techniques, has led to an improved determination of the Auger recombination rate, which is lower than previously thought. In this contribution we present a systematic study of the injection-dependent carrier recombination for a broad range of dopant concentrations of high-purity n-type and p-type silicon wafers passivated with state-of-the-art dielectric layers of aluminum oxide or silicon nitride. Based on these measurements, we develop a general parametrization for intrinsic recombination in crystalline silicon at 300 K consistent with the theory of Coulomb-enhanced Auger and radiative recombination. Based on this improved description we are able to analyze physical aspects of the Auger recombination mechanism such as the Coulomb enhancement.
The detailed balance method for calculating the radiative recombination limit to the performance of solar cells has been extended to include free carrier absorption and Auger recombination in addition to radiative losses. This method has been applied to crystalline silicon solar cells where the limiting efficiency is found to be 29.8 percent under AM1.5, based on the measured optical absorption spectrum and published values of the Auger and free carrier absorption coefficients. The silicon is assumed to be textured for maximum benefit from light-trapping effects.
Consolidated tables showing an extensive listing of the highest independently confirmed efficiencies for solar cells and modules are presented. Guidelines for inclusion of results into these tables are outlined, and new entries since January 2019 are reviewed.
Only a small part of the incident solar energy converts to the electrical power in photovoltaic devices. The majority of the energy loss contributes to the heat generation in devices and thus leads to a temperature rise, causing an inevitable impact on the performance of photovoltaic devices. Hence, loss processes in solar cells play very important roles in solar-electric conversion process. This paper systematically studies both the intrinsic and extrinsic losses in solar cells. Energy distributions of solar cells with different kinds of parameters are presented to characterize the different kinds of loss processes in detail. The sensitivities of loss processes to the structural and operating parameters of solar cells such as external radiative efficiency, solid angle of absorption and operating temperature are discussed, for the parameters have significant impact on the loss processes. The external radiative efficiency, solid angle of absorption (e.g., the concentrator photovoltaic system), series resistance and operating temperature are demonstrated to greatly affect the loss processes. Furthermore, based on the calculated thermal equilibrium states, the temperature coefficients of solar cells versus the bandgap Eg are plotted.
A back contact of bifacial silicon heterojunction solar cells was investigated and sensitivity of design studied by means of optical and electrical simulations. With 3-D optical simulations the realistic bifacial silicon heterojunction solar cell with metal fingers at the front and back was simulated. Specular illumination was applied at the front and Lambertian diffuse illumination at the back side. The advanced multiscale approach to combine 3-D optical simulations with 2-D electrical simulations is shown. The complete solar cell was simulated and the results were verified on fabricated test samples. The spacing of back finger contacts was optimized in order to improve the electrical performance of the bifacial silicon heterojunction solar cell with respect to albedo and bulk charge carrier lifetime. Furthermore, an outlook of front finger spacing and the finger width on series resistance is shown, while keeping the ratio of finger width and spacing fixed. The study shows the front finger spacing of 1 mm is the most reasonable spacing. By means of simulations the 24% apparent efficiency of the encapsulated cells with charge carrier lifetime in bulk higher than 7 ms is demonstrated and an outlook for the further optimization is discussed.
Maximum possible photovoltaic performance is reached when solar cells are 100% radiatively efficient, with different photovoltaic technologies at different stages in their evolution towards this ideal. An external radiative efficiency is defined, which can be unambiguously determined from standard cell efficiency measurements. Comparisons between state-of-the-art devices from the representative cell technologies produce some interesting conclusions. Copyright © 2011 John Wiley & Sons, Ltd.
A rigorous proof for a reciprocity theorem that relates the spectral and
angular dependences of the electroluminescence of solar cells and light
emitting diodes to the spectral and angular quantum efficiency of
photocarrier collection is given. An additional relation is derived that
connects the open circuit voltage of a solar cell and its
electroluminescence quantum efficiency.
Excitonic effects are known to enhance the rate of intrinsic recombination processes in crystalline silicon. New calculations for the limiting efficiency of silicon solar cells are presented here, based on a recent parameterization for the Coulomb-enhanced Auger recombination rate, which accounts for its dopant type and dopant density dependence at an arbitrary injection level. Radiative recombination has been included along with photon recycling effects modeled by three-dimensional ray tracing. A maximum cell efficiency of 29.05% has been calculated for a 90-μm-thick cell made from high resistivity silicon at 25°C. For 1 Ω cm p-type silicon, the maximum efficiency reduces from 28.6% for a 55-μm-thick cell in the absence of surface recombination, down to 27.0% for a thickness in the range 300–500 μm when surface recombination limits the open-circuit voltage to 720 mV. Copyright © 2002 John Wiley & Sons, Ltd.
This paper considers intrinsic loss processes that lead to fundamental limits in solar cell efficiency. Five intrinsic loss processes are quantified, accounting for all incident solar radiation. An analytical approach is taken to highlight physical mechanisms, obscured in previous numerical studies. It is found that the free energy available per carrier is limited by a Carnot factor resulting from the conversion of thermal energy into entropy free work, a Boltzmann factor arising from the mismatch between absorption and emission angles and also carrier thermalisation. It is shown that in a degenerate band absorber, a free energy advantage is achieved over a discrete energy level absorber due to entropy transfer during carrier cooling. The non-absorption of photons with energy below the bandgap and photon emission from the device are shown to be current limiting processes. All losses are evaluated using the same approach providing a complete mathematical and graphical description of intrinsic mechanisms leading to limiting efficiency. Intrinsic losses in concentrator cells and spectrum splitting devices are considered and it is shown that dominant intrinsic losses are theoretically avoidable with novel device designs. Copyright © 2010 John Wiley & Sons, Ltd.
Solar cell performance generally decreases with increasing temperature, fundamentally owing to increased internal carrier recombination rates, caused by increased carrier concentrations. The temperature dependence of a general solar cell is investigated on the basis of internal device physics, producing general results for the temperature dependence of open-circuit voltage and short-circuit current, as well as recommendations for generic modelling. Copyright © 2003 John Wiley & Sons, Ltd.
In order to find an upper theoretical limit for the efficiency of p‐n junction solar energy converters, a limiting efficiency, called the detailed balance limit of efficiency, has been calculated for an ideal case in which the only recombination mechanism of hole‐electron pairs is radiative as required by the principle of detailed balance. The efficiency is also calculated for the case in which radiative recombination is only a fixed fraction f c of the total recombination, the rest being nonradiative. Efficiencies at the matched loads have been calculated with band gap and f c as parameters, the sun and cell being assumed to be blackbodies with temperatures of 6000°K and 300°K, respectively. The maximum efficiency is found to be 30% for an energy gap of 1.1 ev and f c = 1. Actual junctions do not obey the predicted current‐voltage relationship, and reasons for the difference and its relevance to efficiency are discussed.
The maximum efficiencies of ideal solar cells are calculated for both single and multiple energy gap cells using a standard air mass 1.5 terrestrial solar spectrum. The calculations of efficiency are made by a simple graphical method, which clearly exhibits the contributions of the various intrinsic losses. The maximum efficiency, at a concentration of 1 sun, is 31%. At a concentration of 1000 suns with the cell at 300 K, the maximum efficiencies are 37, 50, 56, and 72% for cells with 1, 2, 3, and 36 energy gaps, respectively. The value of 72% is less than the limit of 93% imposed by thermodynamics for the conversion of direct solar radiation into work. Ideal multiple energy gap solar cells fall below the thermodynamic limit because of emission of light from the forward‐biased p‐n junctions. The light is radiated at all angles and causes an entropy increase as well as an energy loss.
Auger recombination processes are shown to impose the most severe intrinsic bounds on the open-circuit voltage and efficiency of silicon solar cells. This applies for both heavily doped and lightly doped material. The upper bound on the open-circuit voltage of a 300- µm-thick silicon cell is 750 mV (AMO, 25°C) irrespective of substrate resistivity. This bound increases to 800 mV for a 20 µm thick cell but decreases to a maximum value of 720 mV for cells thicker than the corresponding minority carrier diffusion length. The corresponding practical bound on cell efficiency is estimated as 25 percent (AM1.5, 100 mW/cm<sup>2</sup>, 28°C).
The efficiency of the conversion of solar energy into electrical energy by solar cells is improved if the incident solar radiation is first absorbed by an intermediate absorber. The reemitted radiation is directed onto the solar cell. This mode of operation is known as thermophotovoltaic energy conversion. A black-body intermediate absorber is advantageous for small-bandgap solar cells. An even higher improvement is, however, achieved by a selective intermediate absorber with an absorption edge at the energy of the bandgap of the solar cell. Furthermore, if only a narrow spectral interval of radiation near the absorption edge is transmitted through a filter from the intermediate absorber to the solar cell, a maximum efficiency of 65 percent is obtained for a solar cell and absorber with a bandgap of 0.8 eV.
Standard Tables for References Solar Spectral Irradiance at Air Mass 1.5: Direct Normal and Hemispherical for a 37° Tilted Surface
- Astm International
ASTM International, "Standard Tables for
References Solar Spectral Irradiance at Air Mass 1.5: Direct
Normal and Hemispherical for a 37° Tilted Surface," G 159
-98, 1999.