Article

Investigation on the short circuit current increase for PV modules using halved cells

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Abstract

It is well established that using halved silicon wafer solar cells in a photovoltaic (PV) module is an efficient way to reduce cell-to-module resistive losses. In this work we have shown that PV modules using halved cells additionally show an improvement in their optical performance, resulting in a higher current generation. We attribute this increase in current to gains in light reflected from the backsheet area. An optical model is presented that quantitatively determines the influence of the backsheet on the short-circuit current of a PV module. We find that, for an accurate prediction, several factors have to be taken into account, including the geometry of the module, the backscattering properties of the backsheet and the illumination spectrum. Particularly the angularly and spectrally resolved scattering properties of the backsheet are shown to have a large impact on the current generation. Furthermore, light beam induced current (LBIC) measurements are used to test the backscattering properties of the backsheet and also the influence of the illumination spectrum. LBIC measurements are also used to verify the simulation results, giving good agreement. Thus the design of a PV module can be optimized by simulation. A standard full-size cell module and a halved-cell module with optimized cell spacing are fabricated. Compared to the standard module, the half-cell module is shown to have 4.60% more power (315.3 vs. 329.8 W), 1.46% higher fill factor (75.5 vs. 76.6%), and 3.08% more current (9.08 vs. 9.36 A).

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... To evaluate and study the effect of tab width on performance of PV modules, an electrical model in the software tool SPICE is used for simulating the electrical behavior of the PV modules in respect to changes in tab width and insolation levels. The model is a two-diode model of a solar cell by considering the resistance network of the tabs since the electrical losses in spacing tabs are different from the electrical losses of the tabs connected to the top or bottom surface of the cells [6,7]. The electrical parameters used for the electrical model are derived from the measurements of a full-cell monocrystalline solar cell with three busbars which are already applied before mini-modules fabrication (see Experiment). ...
... [5] Since the half-cells are cut from the same full-cells, the electrical parameters assumed to be the same for both halfcells and full-cell mini-modules [6]. The effect of optical gain due to extra spacing between half-cells is not a part of electrical model [7]. The total series resistance of the mini-module is divided to series resistance of the cell and the interconnecting tabs which is dependent to the material and the dimensions of the tab. ...
... Assuming constant tab thickness, the electrical resistance of the tabs is proportional to the inverse of the tab width. Since half-cells generate half currents, the electrical power losses in the tabs are reduced to one quarter compared to full-cells [7]. ...
Article
Full-text available
Modules with half-cell layout show an increased efficiency due to reduced electrical losses and increased optical gains. In this work, we demonstrate that by reducing the tab width, additional benefits can be obtained and the demands for reducing costs of material consumption and higher Cell-To-Module power (CTM) ratios can be met. First, we present simulation results on the optimal tab width under different insolation levels and calculation of the energy yield over a year. Second, an experimental setup based on mini-modules which verifies our findings is described. It can be shown that the reduction of the tab width to about 50% does not lead to any significant loss for standard cells and an increase of efficiency by 0.85% for half-cell modules compared to full-cell modules is measured. Furthermore, the loss mechanisms in locations with different insolation levels for both half-cell and full-cell modules with different size of tab widths are discussed. Finally, energy yield based on optimized tab widths for both modules at desert (Morocco) and moderate (Germany) climates is calculated. We show that half-cell modules with optimized tab width have better performance than standard modules with full-cells in both moderate and desert regions with 1.52% and 2.20% more energy yield respectively.
... This additional area of apparent backsheet results in larger current boosts from the light reflected on the surrounding backsheet for the cells located at the edges (and the corners) of modules. This effect of module edge spaces has been very rarely mentioned in the literature and earlier works [8,10] expressed that the gain would be marginal at module level because of the serial interconnection of the cells. In this work, we evaluate the impact of these module edge spaces on the CTM factors and demonstrate that the non-uniform optical gain is not lost because of the serial interconnection of the cells but results in a boost of FF at the module level. ...
... The recaptured fraction from the spaces between cells is simulated in this work assuming a Lambertian reflection on the backsheet. The angular dependence of actual backsheets may differ from that of a Lambertian scatterer but the angular measurements in [8] indicate that the Lambertian approximation seems reasonable and in any case does not overestimate the light trapping. The recaptured fraction after reflection on the apparent backsheet between the cells is calculated using: ...
... This additional area of apparent backsheet results in larger current boosts from the light reflected on the surrounding backsheet for the cells located at the edges (and the corners) of modules. This effect of module edge spaces has been very rarely mentioned in the literature and earlier works [8,10] expressed that the gain would be marginal at module level because of the serial interconnection of the cells. In the second part of this work, we show by simulation that the loss caused by this additional cell-to-cell mismatch is negligible and thus the module edges provide in fact a significant power boost. ...
Conference Paper
The power produced by a photovoltaic module is not simply the sum of the powers of its constituents cells. The difference stems from a number of so-called “cell-to-module” (CTM) gain or loss mechanisms. These are getting more and more attention as improvements in cell efficiency are becoming harder to achieve. This work focuses on two CTM mechanisms: the gain due to the recapture of light hitting the apparent backsheet in the “empty” spaces around the cells and the loss from the serial connection of “mismatched” cells i.e. with different maximum power points. In general, for insulation purposes, the spaces on the edges of modules are larger than the spacing between cells. This study reveals that, when reflective backsheets are used, these “edge spaces” provide an additional current boost to the cells placed at the edges that can lead to a 0.5% gain in the output power of modules (with 60 or 72 cells). This location-dependent current boost adds to the usual variations in cell characteristics dictated by the binning size and results in larger “cell-to-cell mismatch losses”. However, the simulations reveal that for short-circuit current bin size smaller than 5%, this additional mismatch loss is lower than 0.05%. All considered, this study demonstrates that the spaces at the edges of PV modules have a significant impact on the cell to module ratios (≈+0.5%abs or ≈16% of the CTM gains) when reflective backsheets are used.
... A systematic loss analysis of PV modules can be split into active-area loss analysis, which uses optical simulation models similar to those for solar cells [20,65,66], and the inactive-area loss analysis which requires the fraction of lateral photon harvesting as an input parameter [23,28,62]. The challenge is how to quickly and accurately characterize the fraction of lateral photon harvesting from the inactive area, because most characterisation methods require either a rigorous procedure of sample preparations [39,67,68] or a long measurement time [62,67]. ...
... A systematic loss analysis of PV modules can be split into active-area loss analysis, which uses optical simulation models similar to those for solar cells [20,65,66], and the inactive-area loss analysis which requires the fraction of lateral photon harvesting as an input parameter [23,28,62]. The challenge is how to quickly and accurately characterize the fraction of lateral photon harvesting from the inactive area, because most characterisation methods require either a rigorous procedure of sample preparations [39,67,68] or a long measurement time [62,67]. To facilitate the quick evaluation of the laterally harvested photons in a PV module, a luminescence imaging based analysis method is proposed and discussed in Chapter 4. ...
... The photons that impinge in the inactive areas can be reflected diffusely if the materials in these areas have good optical scattering properties. Some of these photons are scattered beyond the escape cone of the glass-air interface and thus experience total internal reflection which directs them back onto the solar cell, where they can contribute to PV power generation.Instead of improving the solar cell efficiency, reducing the cell-to-module efficiency loss is a viable alternative route towards high-performance Si wafer-based PV modules.Many research efforts, such as utilizing optical scattering materials[56][57][58][59][60] and adopting new module designs[61][62][63], have been made to achieve higher lateral harvesting of photons from the inactive area. For example, Trina Solar demonstrated a 60-cell PV module of 6-inch mono-Si Al-LBSF solar cells producing 335 W power in an aperture area of 1760 mm × 996 mm. ...
Thesis
Full-text available
This thesis presents an extensive investigation of characterisation and simulation methods for optical loss analysis of silicon (Si) wafer based photovoltaic (PV) devices, including Si wafer solar cells, Si wafer based PV modules, and thin-film on Si tandem solar cells. Regarding Si wafer solar cells, the conventional optical loss analysis of Si wafer solar cells is improved. A rigorous approach is proposed to assess the surface morphology of textured Si rear surfaces. With the increasing trend of adapting rear passivation, the proposed methodology enables the optimisation of the saw damage etched textures on the rear surface of aluminium local-back-surface-field (Al-LBSF) solar cells. Regarding Si wafer based PV modules, a fast and contactless optical loss analysis using luminescence imaging is proposed. The characterisation method enables the analysis of the lateral light harvesting from inactive-area components of PV modules. Using this method, the amounts of laterally harvested photons from backsheets and metal fingers can be quickly quantified. Thus, a routine assessment can be established for novel materials that increase light harvesting in PV modules. Regarding thin-film on Si tandem solar cells, a fast and comprehensive optical loss analysis is established. An analytical model is developed for comprehensive optical simulation of tandem solar cells, including the light trapping effect. Benefiting from the short computational time, the optical analytical model is subsequently applied to determine the most effective optimisation steps for a four-terminal tandem of a GaAs top cell and an industrial-type Si bottom cell. All methods and models developed in this thesis are readily available for integrating with already existing frameworks, thereby contributing to comprehensive analysis of optical losses and providing guidelines to further optimisation steps.
... The electrical losses in interconnection have a quadratic relation with the current and thus the irradiation level. This means that reduction of nominal short-circuit current of solar cells by cutting them can decrease the electrical losses and consequently the temperature of the modules [1,2,3]. Although the cutting process decreases the efficiency of the solar cells [4,5] , this loss will be overcompensated after module fabrication due to extra optical gains and reduced electrical losses [1,3]. ...
... This means that reduction of nominal short-circuit current of solar cells by cutting them can decrease the electrical losses and consequently the temperature of the modules [1,2,3]. Although the cutting process decreases the efficiency of the solar cells [4,5] , this loss will be overcompensated after module fabrication due to extra optical gains and reduced electrical losses [1,3]. ...
... The tabs with 1.5 mm and 0.8 mm cover 2.88% and 1.53% of the active area of a full size cell respectively. The extra spacing between partial cells is expected to influence the current generation in the relevant modules [3]. ...
Conference Paper
Full-text available
Modules with partial cells have shown better performance compared to full-cell modules due to reduced electrical losses and increased optical gains. In this paper, we have compared different module concepts of full-cell, half-cell and third-cell with different tab widths of 0.8 mm and 1.5 mm in moderate and desert conditions. First, we present the statistical evaluation of indoor measurements results of the modules. The modules were measured with a mask which limits the spacing of the cells and keeps the total inactive area of the mini-modules constant. The efficiency and fill factor of the modules are evaluated to analyze the electrical and optical losses of the modules. We show that the modules with partial cells show better fill factor and efficiency compared to the similar full-cell modules. The modules were measured under different irradiation levels to evaluate the performance of the modules under different light conditions. Based on the measured data, the energy yields of the modules are simulated in Morocco and Germany as desert and moderate climates. We show that extra energy yield can be harvested by choosing the module concept and optimized tab width for each climate. The optimized half-cell modules benefit of 4.12% and 4.97% extra annual energy yield compared to full-cell modules in moderate and desert climates correspondingly. These values increase respectively by transition to third-cell modules to 5.2% and 5.68% at moderate and desert environments.
... M ODULES in desert regions benefit from high irradiation levels resulting in higher current and power generation and increased energy yield. However, high irradiation and current lead to unwanted joule heating in module interconnection [1], [2]. The electrical losses in the module are a function of series resistance and generated current. ...
... However, cutting solar cells can lead to undesired efficiency drop due to defects at the laser cut edge [5]. It has been shown that this efficiency loss will be overcompensated after module fabrication due to optical gains and reduced electrical losses resulting in better cell-to-module (CTM) power ratios [1], [2]. REC presented the first half-cell modules in the market, which showed 2% increased power due to the reduced electrical losses [6]. ...
... The first part is the equivalent resistance of the interconnection in a spacing area, which has constant electrical losses along the tabs, and the second part is the equivalent effective resistance of the interconnecting tabs, which are positioned on the top of the solar cell. The electrical losses in tabs, which are directly on the top of the solar cell, increase from one side to another due to the collection of the current from all regions of the cell and it can be calculated by [1], [2] (1), tab width influences the total resistance of interconnection, where higher resistance for narrower tab width and better conductivity for wider tab width are expected. The electrical losses in the interconnections depend linearly on the tab resistance and show a square relation to the current passing through the tabs. ...
Article
Modules with partial cells show better performance compared to full-cell modules due to lower electrical losses and increased optical gains. In this paper, we compare photovoltaic (PV) modules made of full, half, and third cells with tab widths of 0.8 and 1.5 mm under moderate and desert conditions, respectively. Initially, a statistical assessment of indoor characterization results of the modules is presented. The efficiency and fill factor of the modules are evaluated to analyze the electrical and optical losses of the modules. It is shown that the modules with partial cells and narrower tab widths show higher efficiencies and implying cell-to-module power ratios over 100%. The modules are characterized under different intensity levels to assess their performance under various illumination conditions. Based on the measured data, the energy yields in Morocco and Germany representing desert and moderate climates, respectively, are calculated. It is demonstrated that increased energy yield can be achieved by selecting appropriate module design and optimized tab width for each climate. The optimized half-cell modules show a yield gain of 3.77% and 4.51% compared to full-cell modules in moderate and desert climates, respectively. These values rise to 4.72% and 5.68% by moving to third-cell modules, respectively.
... Electrical losses in solar cell interconnections increase with the square of the electrical current, as defined by Ohm's law. Cutting the cells in half cuts the current in half, and the electrical losses are reduced to one quarter of the full-cell losses [2,3]. It is important to note that only series resistance losses in the cell tabs are affected. ...
... Although an increase in total cell spacing also leads to a larger module in general and a higher cost of materials, these parameters should be reoptimized when moving to half cells. When the cell spacing between half-cell and full-cell modules is kept constant, an increase in short-circuit current of up to 3% is found [3]. Optimization of the module power and geometry can be nicely carried out using Fraunhofer ISE's Smart.Calc tool [10] (see also www.cell-to-module.com). ...
... The module is aligned in a landscape orientation, and the junction box can be either centralized or decentralized and located on the top side of the module. The twoby-two interconnection of half-cell modules with a landscape layout makes them more resistant than the equivalent full-cell modules under partial shading conditions [3,13,14]. ...
Article
Solar modules with half-size solar cells have the potential for becoming the new standard. The cutting of cells leads to electrical recombination losses at the cell level, which are more than compensated by reduced resistive losses as well as by current gains at the module level. At the same time, the cutting process must be optimized to avoid mechanical damage that could lead to cell breakage in the module. Module design opportunities for hot-spot protection, shading resistance and energy yield optimization are presented in this paper. Module power can be increased by 5–8%, which justifies the investment in additional equipment for cell cutting, stringing, lay-up and bussing. Half-cell technology is highly attractive for new solar module production capacity.
... The gain in module current due to the backsheet is mainly influenced by three factors: 1) the geometry of the backsheet area (cell-gap region), 2) the spectral reflective property of the backsheet, and 3) the angular backscattering property of the backsheet [16]. To analyze and quantify the current contribution due to the backsheet in the cell-gap region, a MATLAB-based numerical model was set up. ...
... To analyze and quantify the current contribution due to the backsheet in the cell-gap region, a MATLAB-based numerical model was set up. The model is based on the method introduced in [12] and our previous work [16] but with modifications applicable to bifacial solar cells. Using this model, the 1) The refractive indexes of the glass and EVA are equal (n = 1.5). ...
... The weighted average reflectance of the backsheet (WAR bs ) was calculated using the AM1.5G spectrum [17]. The backscattering properties of the backsheet are quantified by measuring the angular dependent backscattering luminous intensity and also discussed in our previous work [16]. The angular distribution is calculated by dividing the light intensity at a particular angle by the largest measured light intensity. ...
Article
Bifacial solar cells can be encapsulated in modules with either a glass/glass or a glass/backsheet structure. A glass/backsheet structure provides additional module current under standard test conditions (STC), due to the backsheet scattering effects, whereas a glass/glass structure has the potential to generate additional energy under outdoor conditions. In this study, we quantify the current contributions due to various mechanisms in both module structures under STC. The current contributions due to different mechanisms are calculated by measuring the reflectance and transmittance of mini-modules with both structures, together with a MATLAB-based simulation. Our results show that under STC, glass/backsheet modules provide approximately 2.2% more power, as compared with glass/glass modules using the same bifacial solar cells with a standard cell gap of 2.0 mm. Using module optimization, we demonstrate that the maximum possible cost reduction benefit in $/W _P of glass/backsheet modules over glass/glass modules under STC is limited to 3.3%. Due to the potential outdoor energy yield advantages of glass/glass modules reported in the literature, we recommend a glass/glass module structure for bifacial solar cells. Furthermore, in order to compensate for the lower performance of glass/glass modules under STC, we propose a methodology to measure and fairly rate bifacial glass/glass photovoltaic (PV) modules.
... This is because areas covered with backsheet, ribbon or fingers scatter incident light. A part of the scattered light is then trapped at the glass cover and subsequently absorbed by the solar cells [13][14][15]. ...
... In order to calculate the contributions to current generation by backsheet and ribbons, we use the method described in [15]. This method adopts a ray tracing approach to calculate light trapping using the measured wavelength and angular dependent reflectance data of the backsheet. ...
... For details on the applied measurement technique, please refer to [15]. Using the data shown in Figure 2, the area percentage of the backsheet that does not contribute to current generation has been calculated at 7.7%, compared with an actual area of 9.1%. ...
Article
We present an extended analysis to quantify losses in a module under short-circuit conditions. The presented method includes an analysis of the area-related losses in a full-sized module and introduces the concept of “effective area coverage.” The effective area coverage accounts for the amount of light lost on a certain type of area and is different from the actual area coverage, if light trapping area occurs. An example for this effect is light reflected from the backsheet, trapped in the glass cover and reaching the solar cell. Based on our analysis, the effective solar cell area is increased by 5% absolute by this effect. Furthermore, we used an extension of Basore's model for modules in the loss analysis and used it to quantify losses in one exemplary, encapsulated multicrystalline silicon wafer solar cell. These losses are absorption in the rear reflector (corresponding to a loss of 3.5 mA/cm2 on the active solar cell area), collection losses (3.4 mA/cm2) and free carrier absorption (0.18 mA/cm2). Finally, the presented analysis allowed us to calculate a breakdown of all losses in a full-sized module under short-circuit conditions. A list of all considered losses sorted by the corresponding current is presented at the end. Copyright © 2015 John Wiley & Sons, Ltd.
... The electrical current of a solar cell has a linear dependence on its area [48], and the ohmic losses in conducting parts have a quadratic relationship with the current flowing through them [49,50]. By cutting the solar cells in half, the electrical current is reduced by half, consequently leading to four times lower ohmic losses and a better fill factor [8,[49][50][51][52]. ...
... The electrical current of a solar cell has a linear dependence on its area [48], and the ohmic losses in conducting parts have a quadratic relationship with the current flowing through them [49,50]. By cutting the solar cells in half, the electrical current is reduced by half, consequently leading to four times lower ohmic losses and a better fill factor [8,[49][50][51][52]. This is the one of the best designs for the emerged large-size wafers, which produce a high current and consequently higher ohmic losses. ...
... Furthermore, the back reflection of light rays inside the PV laminates can lead to a slight gain in the short-circuit current by influencing the edges of the solar cells [50,53,54]. The half-cell modules benefit from an increased gain in the short-circuit current due to the increased active area influenced by the back reflections from cell spacing between the half cells [50]. Figure 2 depicts the schematic comparison of the back-reflected light over the edges of the solar cells in both full-cell and half-cell module layouts and highlights the increased active area influenced by the back reflections in the half-cell design compared to the full-cell design. ...
Article
Full-text available
Photovoltaic modules in desert areas benefit from high irradiation levels but suffer from harsh environmental stress factors, which influence the Levelized Cost of Electricity by decreasing the lifetime and performance and increasing the maintenance costs. Using optimized half-cell module designs mounted in the most efficient orientation according to the plant requirements can lead to reduced production costs, increased energy yield and longer service lives for PV modules in desert areas. In this work, we review the technical advantages of half-cell modules in desert regions and discuss the potential gains in levelized costs of electricity due to reduced material consumption, a higher cell-to-module power ratio, lower module temperatures, better yields, reduced cleaning cycles and finally, reduced fatigue in interconnection due to thermal cycling. We show that half-cell modules are the most cost-effective option for desert areas and are expected to have a relevant lower Levelized Cost of Electricity.
... In some literature, assessing the light-recycling effect is limited to the backsheet layer of the PV module which is referred to as the backsheet gain [37,43,47]. ...
... Mittag indicated a 1%-3% increase in the CTM power ratio due to the backsheet gain [37]. It is important to note that this optical gain could be much more in some new high-efficiency cell designs such as half-cut cell or heterojunction [6,47]. Haedrich gained 4.9% and 5.3% increase in the CTM power ratio and annual energy yield for the heterojunction PV module [6]. ...
... The second part of this method was the changing cell design from full-cell to half-cell. This optimization has shown to result in a minimum 3% increase in the CTM power ratio.However, implementing simultaneously these two parts in the conventional c-Si PV modules leads to much more increase in the CTM power ratio than the summation of each increase in the CTM power ratio, such as what has been derived in the experiment for the half-cell solar module with optimized tap width[47] . But it is a good approximation for the CTM power ratio gain to determine the other crucial factors. ...
Preprint
Full-text available
Evaluating the cell-to-module (CTM) ratio is an effective method to optimize the efficiency and power output of crystalline silicon (c-Si) photovoltaic (PV) modules. They are the key components of the PV module performance. They depend on loss and gain effects that occur in the whole process of light-harvesting by PV modules. This needs adopting an analytical and mathematical method to assess the CTM ratio including knowing how to mitigate negative effects and boosting positive effects. To this end, this paper develops universal mathematical formulations for both the CTM power ratio and the CTM efficiency ratio of c-Si PV modules based-on all opto-electrical loss and gain effects that have impacts on them. As the optimization in the mentioned key components, the paper proposes a bipartite method including utilizing half-cut cell/shingle solar cell at the cell-level as well as high UV transmittance and conventional UV cutoff with white color encapsulants for the front and rear encapsulant layers at the module-level. The results demonstrate a minimum 3% increase in the CTM power ratio as compared to the full cell PV module due to the former part of this method and separately around 1.74%-2.35% increase in the CTM power ratio due to the latter part. By adopting this method to conventional c-Si PV modules with the CTM power ratio around 98% , PV module producers can achieve the CTM power ratio well above 100%, higher PPT, a product with higher power output and efficiency, better energy yield, higher PV module production, higher gross income, and eventually higher reliability.
... iii. Consistent with [3,5,[7][8][9][10], the backsheet reflectance varies strongly with wavelength. For example, the reflectance of Backsheet A is only 5% at 350 nm, it rises to a maximum of 95% at 500 nm, and it decreases steadily to ~10% at 2400 nm. ...
... Figure 5 indicates that Backsheet A (UniQoat) yields a significant advantage over Backsheet B. We find, for example, that with a cell spacing of 0.4 cm, the UniQoat backsheet yields about +2.5% in J SC , whereas the less reflective backsheet yields about +2.0%. The relative advantage of Backsheet A over Backsheet B is expected to be greater for modules containing half-cells because their exposed backsheet comprises a greater fraction of the total module area [9]. ...
Conference Paper
Full-text available
We measure and analyze two commercially available backsheets. One of the backsheets (AGFA’s monoblock backsheet, UniQoat) is significantly more reflective than the other (a typical Fluoropolymer/PET/Fluoropolymer backsheet). We measure their hemispherical reflectance before encapsulation in air, from which we calculate their intrinsic reflectance, and hence the reflectance at an EVA–backsheet interface after lamination. This intrinsic reflectance is considerably higher than the reflectance measured in air (e.g., the reflectance of UniQoat at 1000 nm increases from 85% to 92% after lamination), and it is this intrinsic reflectance rather than the measured reflectance that is required to accurately predict how a particular backsheet affects a module’s optical behavior. With a combination of measurements and ray tracing, we demonstrate that the calculated intrinsic reflectance is consistent with the hemispherical reflectance of glass– EVA–backsheet test samples. The ray tracing is then extended to predict how each backsheet affect a module’s short-circuit current density JSC as a function of cell spacing. We find, for example, that with a cell spacing of 4 mm, the UniQoat backsheet yields a 2.5% increase in JSC whereas the less reflective backsheet yields a 2.0% increase.
... Influence from the metallization pattern on the current flow through the ribbons Circuit modelling, which is based on the diode models for PV devices, can be used to solve various problems for solar cells and PV modules (Kawamura et al., 2003; Ikegami et al., 2001; Segev et al., 2012; Lun et al., 2015). 2D circuit simulation is an established method for solar cell modelling, and SPICE related software is commonly used for this purpose (Guo et al., 2012Guo et al., , 2015 Grote, 2010; Zekry and Al-Mazroo, 1996; Peters et al., 2012). The simulator used in this work uses a finite element method to solve the full 2D distributed network representation of the metallized solar cell (Wong). ...
... For mini-modules using bifacial halved cells (shown inTable 4), the open-circuit voltage is still exactly two times that of the full-cell mini-modules, while the short-circuit current is slightly (0.1%) higher than half of that of the full-cell mini-modules. This is most likely due to the wide gap region between the two halved cells, which leads to extra current due to scattering of light from the gap region towards the solar cells (Guo et al., 2015). The simulated fill factor increase is 2.2%, which is also very close to the experimental result (2.0%). ...
Article
In a c-Si wafer based photovoltaic (PV) module, the current generated in each solar cell must flow to the ribbons soldered onto its front and rear surfaces. Conventionally, a simplified current flow pattern is assumed in calculating the resistive power losses in the cell plane and the ribbons. However, it is found in this work that this approach leads to more than 30% overestimation for the resistive loss on the rear-side ribbons for a typical monofacial solar cell. This work uses a detailed two-dimensional network simulation, which accurately solves the current flow patterns in both cell surface planes. It is found from this work that the conventional approach is sufficiently accurate in the case of an H-pattern finger-busbar metallization scheme, but not with a full-area metallization pattern, as commonly used on the rear of silicon wafer solar cells. For a c-Si PV module using 3-busbar monofacial solar cells, the actual resistive loss on the rear metallization plane is only 67% of the value calculated conventionally. Also, 17% of the cell interconnection resistive loss comes from the rear metal sheet, which is often ignored. To correct the results of the conventional approach, we introduce correction factors for c-Si PV modules using monofacial cells. Using the correction factors we achieve a significantly better prediction of the module’s fill factor. We apply this approach to explain why the fill factor gain from replacing full-size solar cells by halved cells in a c-Si PV module is higher for bifacial than for monofacial solar cells. Experimentally, we find a 1.7% relative fill factor increase for monofacial halved-cell PV module, and a 2.0% relative increase for bifacial halved-cell PV module. The simulation results agree quite well with the experimental results. Since the influence from the cell metallization pattern on the cell-to-module resistive loss has not been investigated before, this work can be very useful correction and compensation for established methods analysing the cell-to-module losses. It also offers the guideline for PV module optimization in terms of further reducing the resistive loss.
... As an approach to improve module output power, full wafer-sized solar cells (e.g., with an edge length of 156.75 mm) are separated into smallersized cells (e.g., half cells) prior to module integration [11,12]. Smallersized cells generate lower current in the string leading to decreased electrical resistance losses on the interconnection level. ...
... 12. Description of the method to examine the impact on metallized host cells from (left) the cleave process only (no scribe) in comparison to the (right) ...
Thesis
This dissertation deals with the development and characterization of bifacial p-type shingled passivated edge, emitter, and rear (pSPEER) solar cells. The new cell structure connects the concepts of bifaciality, shingling, and the p-type silicon passivated emitter and rear cell (PERC). To obtain the pSPEER solar cells, full wafer-sized host cells with corresponding metallization layouts are separated into shingle solar cells after contact formation. Recombination at the newly formed cell edges leads to a reduction in pseudo fill factor pFFand thus to losses in energy conversion efficiency. Thermal laser separation (TLS) offers the possibility to obtain smooth cell edges with low surface defect density. In combination with the post-separation passivated edge technology (PET), developed within this work, the TLS technology forms the basis for reducing the surface recombination velocity at the cell edges. The PET process sequence itself encompasses an aluminum oxide (Al2O3) layer formation at low deposition temperatures with a maximum of 130°C by means of thermal atomic layer deposition and a post-deposition annealing (PDA) step that takes place at set temperatures equal or below 200°C. This low temperature processing prevents the damage of already existing metal contacts and passivation layers. Applying TLS and PET on pSPEER solar cells leads to a new cell architecture, called “pSPEERPET”.The TLS process has been optimized throughout the work, such that the impact of the separation process on the electrical performance of the shingle solar cells is minimized. It is found that the pFF losses after TLS are mainly attributed to the formation of the new edges and not to the laser process itself. The applied Al2O3 layers show excellent surface passivation quality after PDA. This is shown, among others, by symmetrically passivated floatzone silicon lifetime samples for which very low effective surface recombination velocities Seff = 4.4 cm/s on p-type silicon and Seff = 5.7 cm/s on n-type silicon are demonstrated. On the cell level, a peak output power density pout = 23.7 mW/cm2 is achieved for a ůSPEERPET solar cell considering 10 mW/cm2 rear side irradiance. A recovery of up to about 80%rel of the separation-related pFF loss by the PET is demonstrated. The progress in the cell separation, the low temperature Al2O3 layer surface passivation, and the edge passivation are also of very high interest for other solar cell types such as silicon heterojunction solar cells and tunnel oxide passivated contacts (TOPCon) solar cells.
... Half-cell design can decrease 50% of module current and reduce the resistance power loss of interconnection ribbons by 75%. The added cell gaps can reflect a part of the incident light back to cells and increase the output power of modules [19]. The cell cutting process will lead to a bit loss in mechanical strength and electrical properties [20], and the loss can be reduced to negligible levels by the thermal laser separation process [21,22]. ...
... In addition, the MBBHC structure achieved with conductive belts can further increase P m in the following ways: (1) The silver paste on the front and back busbar areas is removed, which will reduce the surface recombination and improve the V oc of the cell [29]. (2) The backplane between the gaps of the half cells can reflect the light back to the cell, which can increase the P m of a module with 144 half cells by 10 W [19]. (3) It is difficult for conventional screen printing to further decrease the finger width because of more broken fingers. Modules with 16 busbars can tolerate more broken fingers because P f is reduced sharply. ...
Article
Full-text available
An interconnect electrode called conductive belt was applied to modules instead of interconnection ribbons. The conductive belt has multiple wires and can achieve a multibusbar structure by forming ohmic contacts with the cell electrodes. The following problems were studied with innovative approaches to optimize the multibusbar modules: the shading rate and the contact resistance of the conductive belts, the relationship between the finger series resistance and the wire number, and the influence of the series resistance variation on the maximum power output. Furthermore, the wire number and diameter were optimized according to the following conditions: the cell sizes were full, half, and one-third, and the finger wet weights of a full cell were 80 mg, 40 mg, and 20 mg. The result showed that multibusbar and half-cell structures could achieve the maximum power output, the wire number was 16 and the wire diameter was 200 μ m, and the finger wet weight was reduced to 20 mg. Finally, the reliability of the modules made with conductive belts was tested and was qualified according to International Electrotechnical Commission standards.
... As it can be clearly seen in Table 2, despite having the same electrical simulation results for the short-circuit currents of the modules, the experimental results of the half-cell module shows 3% more short-circuit current than the full-cell module. This increase can be explained by the optical gain due to cell spacing and extra light scattering on the half-cells [12]. The optical gain and less electrical losses due to cutting cells in half increase the fill factor of the half-cell module for about 1.48% under full illumination [4,12]. ...
... This increase can be explained by the optical gain due to cell spacing and extra light scattering on the half-cells [12]. The optical gain and less electrical losses due to cutting cells in half increase the fill factor of the half-cell module for about 1.48% under full illumination [4,12]. ...
Conference Paper
Full-text available
Commercial PV modules consist of series connected solar cells and three bypass diodes to protect the strings against hotspots. The power loss of the module’s strings under partial shading conditions is related to the shading area. In this work, we show that solar module’s behavior under partial shading conditions can be improved and its energy characteristics are raised by using halved cells and changing the module configurations and design. A reference module using full size solar cells and a half-cell module are simulated and fabricated and the results are discussed for different shading scenarios. Both simulation and experiment results agree to a good extent and they show better performance of half-cell modules under partial shading conditions and higher output power due to optical gain and less electrical losses in cell connectors. The short-circuit current of the module increase to about 3% due to the cell spacing and the Fill Factor rises to 1.48%. Finally, the movement direction of shade can affect the half-cell module’s performance significantly.
... In order to measure the active-area current, extra preparation of a reference sample [15,16] or a well-defined aperture [17,18] is usually required. Alternatively, optical simulation has been used to evaluate the light harvesting from the inactive area [19][20][21][22][23][24]. However, for accurate simulation, one has to determine optical constants of encapsulation materials (e.g. ...
... backsheet, ribbon, metal finger etc.). To directly measure the spatially resolved light harvesting of PV modules, local beam induced current (LBIC) or local external quantum efficiency (EQE) mapping has been successfully applied in the previous studies [20,[24][25][26]. However, the LBIC or local-EQE mapping is time-consuming compared to its faster camera-based alternative: luminescence imaging. ...
... Example: Half-cell modules PV modules with half-size cells demonstrate better performance than conventional PV modules because of the higher optical gains and lower electrical losses [16,17]. According to the experiments performed on monocrystalline cells by Hanifi et al. [4] and Eiternick et al. [18], when solar cells are cut in half the efficiency of the cells slightly decreases, by about 1.1% rel , because of the laser-scribed edges. ...
Article
The output power of a solar module is the sum of the powers of all the individual cells in the module multiplied by the cell-to-module (CTM) power ratio. The CTM ratio is determined by interacting optical losses and gains as well as by electrical losses. Higher efficiency and output power at the module level can be achieved by using novel ideas in module technology. This paper reviews methods for reducing different optical and electrical loss mechanisms in PV modules and for increasing the optical gains in order to achieve higher CTM ratios. Various solutions for optimizing PV modules by means of simulations and experimental prototypes are recommended. Finally, it is shown that designing PV modules on the basis of standard test conditions (STC) alone is not adequate, and that, to achieve higher CTM ratios by improving the module designs in respect of environmental conditions, an energy yield analysis is essential. https://store.pv-tech.org/store/investigation-of-celltomodule-ctm-ratios-of-pv-modules-by-analysis-of-loss-and-gain-mechanisms/
... One of the most important types is the solar energy, which is the most daily used, and it captures much research nowadays. The most important renewable energy sources are the solar energy for electricity production [1][2][3][4][5]. In this paper, we studied the solar energy sector in a Palestinian city from the point of view of prediction using neural networks to predict the output power of the solar cell panel located in Jericho city of Palestine. ...
Article
Full-text available
A radial basis function neural network is an effective technique for function approximation and prediction. It has been used in many applications in the real world; one of them is the time series prediction which is a relatively complex problem. In this paper, we propose an enhanced radial basis function neural network (RBFNN) model that depends on the standard RBF built-in MATLAB (newrb). The enhancement on newrb depends on the use of intelligent algorithms like K-means clustering, K-nearest neighbor, and singular value decomposition, to optimize the centers c, radii r, and weights w of the RBFNN. These algorithms replace the mathematical calculation used to find these parameters in newrb. The proposed enhanced model is applied to predict the solar cells energy production in Palestine using already installed solar panels in Jericho city. Solar irradiance and daily temperature are used as an input training data set for the proposed model, with the real output power of (2015) as the training supervisor. The model is applied to predict the output power within 1 month and for 1 year. Finally, a power output equation was optimized to calculate the solar energy depending on the irradiance and temperature with an acceptable accuracy. The experimental results show that the enhanced model performs more precisely than the traditional RBFNN and multilayer perceptron neural network methods, with low mean square error of relatively few neurons on the hidden layer.
... Direct optical coupling gains arising by reducing the reflection losses at the active cell surface are analyzed through simulations in [3]. Also the optical gains which can be achieved by using a reflective backsheet material were investigated in [8]. ...
Conference Paper
Full-text available
A major pathway to maximize module power for any solar cell is to decrease the losses between stand-alone solar cell and module. In this work we investigate the impact of these indirect light coupling effects on module power by determining the effective width values (EW) [1] for different finger distances, shapes and surfaces and for varying cell connector ribbons with reflective surfaces. The purpose of this work is to quantify the amount of light recycled by the finger metallization and by reflective ribbon materials on module level. We found the finger width to have a significant impact on power for a cell surrounded by air but not embedded in a module configuration. Further we find the impact of varying finger pitches on module power to be negligible within measurement accuracies. For a set of finger shapes and surfaces (specular and lambertian) we modelled their impact on module efficiency. We defined a theoretical scope of a minimum decrease of -0.09% and maximum increase +0.25% absolute in module efficiency referred to a reference finger type. Finally we found that the coupling gain generated by various ribbon shapes has a strong impact on the module output.
... 12) Direct optical coupling gain (reduced reflectance) arises because of the increasing refractive indices of the encapsulation layers. In addition, the scattering of light incident on the cell-gap area [13][14][15][16][17] (backsheet) and on the tabbing ribbons of a PV module [18][19][20][21] (Fig. 2) contributes to cell-to-module optical gains. Light scattered at an angle greater than the total internal reflection angle for the glass-air interface (approximately 42°) undergoes total internal reflection at the front glass-air interface and redirects back to the solar cell for absorption as shown in Fig. 2. ...
Article
Reducing levelized cost of electricity (LCOE) is important for solar photovoltaics to compete against other energy sources. Thus, the focus should not only be on improving the solar cell efficiency, but also on continuously reducing the losses (or achieving gain) in the cell-to-module process. This can be achieved by choosing the appropriate module material and design. This paper presents a detailed and systematic characterization of various photovoltaic (PV) module materials (encapsulants, tabbing ribbons, and backsheets) and an evaluation of their impact on the output power of silicon wafer-based PV modules. Various characterization tools/techniques, such as UV–vis (reflectance) measurement, external quantum efficiency (EQE) measurement and EQE line-scan are used. Based on the characterization results, we use module materials with the best-evaluated optical performance to build "optimized modules". Compared to the standard mini-module, an optical gain of more than 5% is achievable for the "optimized module" with selected module materials.
... The ribbon parameters are shown in Table III, along with the bussing ribbon. In order to avoid the impact of ribbon length, cell space, and backsheet diffusivity [14], the length of the cell series was fixed at 1388 mm, the space between strings was fixed at 50 mm, and the EVA used in the modules is transparent. The equipment sets used for the PV modules testing were all the same. ...
Article
Full-text available
The use of half-size silicon (Si) wafer solar cells in photovoltaic (PV) modules can enhance the output power compared to full-size Si wafer solar cells. In this paper, an optimal combination of cutting parameters based on the cutting surface, the cutting repetitive time, and the parameters of the Nd:YAG nanosecond laser is achieved. The optimized method consists of a double cutting process on the aluminum back side of the solar cells. The optimized condition was identified with a laser cutting power of 16 W, a laser repetitive frequency of 40 kHz, and a scribing speed of 110 mm/s. Quarter-size Si wafer solar cells in PV modules were also investigated. We compared the output power of full-size, half-size, and quarter-size cells of a double glass transparent PV module quantitatively, finding cell-to-module values of 96.79%, 98.91%, and 99.73%. The total power gain of the half-size cell module and quarter-size cell module compared to the full-cell large-size PV module is 1.46% and 1.92%, respectively. Finally, electroluminescence measurements were carried out to test unconventional size cell PV modules.
... Many innovations have been seen in PV module technologies lately such as half-cut cells and high-density cell packages. PV modules using half-cut solar cells are reported to have reduced cell-to-module energy yield loss through lower series resistance loss and enhanced optical yield [7][8][9]. The market share of half-cell modules is expected to grow from 5% in 2018 to 40% in 2028 [10]. Figure 1 shows a typical cell wiring design for half-cell modules consisting of series-parallel-series connections. ...
Thesis
This thesis is devoted to model and analyse the reliability of photovoltaic modules impacted by non-uniformity of cell performance. Both the short-term failure and the long-term degradation are discussed for a range of module technologies. This thesis is comprised of two main categories: simulating the hotspot effect in crystalline silicon solar modules with different configurations and the reliability of potential perovskite/silicon tandem modules. First, an electrical-thermal simulation method is established to model the operating conditions and cell temperatures of crystalline silicon photovoltaic modules. Explicit solutions to the diode model for solar cells in the model allow for fast computation and easier implementation into other simulation models. Electroluminescence images of cells at reverse bias are used to characterize the distribution of reverse leakage current and verified to provide good simulation accuracy for ohmic-shunt-free cells. Applying the simulation to both a conventional full-cell module and a newer module design using half-cut cells and series-parallel mixed cell connections, the impact of the new module design on the hotspot risk is studied. Simulated and experimental results show a potential drop in the peak hotspot temperature by using the half-cell module design while also unveils a potential risk for certain cells to experience elevated temperatures even when fully-illuminated. Next, the simulation method is applied to potential perovskite/silicon tandem modules to explore both the hotspot risks and long-term module degradation scenarios. Based on experimentally acquired current and voltage (I-V) characteristics of both perovskite and silicon sample cells, the module and cell operating conditions, as well as cell temperatures are modelled for tandem modules at non-ideal conditions using either two- or four-terminal designs. A unique effect by the reverse bias found at the tested perovskite sample cells that causes temporary short-circuit current reduction is studied. Its impact on module operation during dynamic shading conditions and the potential risk of prolonged hotspots are analysed and tested. Furthermore, this thesis presents a techno-economic analysis of the perovskite/silicon tandem modules accounting for potential perovskite cell degradation scenarios. Three perovskite cell degradation cases and an optical degradation coefficient are established including one representative case based on accelerated degradation experiments. The lifetime energy yield and economic viability of tandem modules using both two- and four-terminal designs are then simulated. The permissible perovskite cell degradation rates and additional cost for tandem technologies are estimated in comparison with reference main-stream crystalline silicon modules in 2025.
... Resistive loss mainly arises from the contact resistance between the cell and interconnection ribbon, the resistivity of the welding ribbon, etc. Using half-cut solar cells in a photovoltaic (PV) module is proposed as an efficient way to reduce cell-to-module resistive losses due to the reduced current level in cell strings [10][11][12]. Cells are cut into halves by a laser cutter, the parameters of which are strongly correlated with the quality of the cut cells and further performance of the half-cell-based modules [13]. ...
... In the photovoltaic (PV) domain, there is a growing demand for high-efficiency and long service lifetime PV modules to reduce the levelized cost of energy [1]. Such reduction can emerge from two aspects: (i) reduction of manufacturing and installation costs and (ii) enhanced power output of solar cells and modules [2]. In general, the power output of PV module can be improved by using bifacial silicon solar cells, which utilize both front and rear surfaces of the solar cells to convert light into energy and which results in an increased energy harvesting potential [3]. ...
Article
The half-size bifacial silicon solar cells have garnered significant research attention in photovoltaic (PV) modules because they render enhanced power output. Herein, the influence of cutting surface and scribing iteration times on electrical characteristics of bifacial silicon solar cells is investigated in detail. The results reveal that the cutting process should be carried out from the rear side and scribing iteration times should be twice. Moreover, we have studied the cutting losses of n-type passivated emitter and rear totally diffused (n-PERT) bifacial solar cells and demonstrated that not mechanical breaking but laser scribing is a major source of losses during the cell separation process. In addition, the damage induced by the cut was systematically investigated and it was observed that the heat-affected zone resulted in negligible damage under optimal cutting conditions. Overall, n-PERT half-cell bifacial modules, sectioned under optimal cutting conditions, can maintain high efficiency and excellent reliability.
... The simulation model is developed based on the two diode model with effective resistors [4,5,6]. The solar cells were previously characterized sun simulator to determine the electrical properties. ...
Conference Paper
Full-text available
Besides common installation of PV systems, more technical complex applications such as vehicle integrated PV modules or Energy Parks (combined solar and wind farms) gain significant market attraction. One of challenges for such applications is fast periodic shadings by obstacles or wind blades. This paper investigates an approach to integrate passive elements in parallel to each individual cell of the module and compares the performance of a standard PV module with a module with integrated capacitors as passive elements and a PV module with bypass diodes for every single cell under fast periodic shading conditions. For this purpose, in the first step, the module is simulated under different moving shading conditions. In the next step a PV module with open terminals for every solar cell is fabricated and measured outdoor as reference module with no attached elements and with bypass diodes or capacitors for cells under partial shading conditions. The results show that modules with additional capacitors or diodes in module level can benefit higher energy yield compared to standard PV modules. The energy performance of a capacitor integrated module is mainly dependent by the shading transient, due to the time dependent compensating currents of the capacitors. This paper proves the concept of functionality of capacitor for compensation of power loss under shading conditions but the feasibility of integration is a challenge. However, the results show a better performance of the module with bypass diodes compared to the capacitor integrated module with 44 mF capacity.
... To achieve the quantitative loss analysis, in-depth characterizations of degraded modules are required. While many analysis frameworks were developed for newly-fabricated modules to ensure quality control or to quantify cell-to-module power factor [9][10][11][12][13][14][15], fewer attempts have been made in quantitative analysis of the degraded module. Several recent works start to shed light in this direction. ...
Article
Quantitative analysis of two 30-year-old PV modules is performed by a combination of the equivalent-circuit model and optoelectronic characterization methods. The two modules under analysis were manufactured in 1984 with the nameplate power of 41.0 W, but degraded under two different conditions; one was operated in the field in Northern California for about 30 years, and the other was stored in a warehouse for the same period. The power outputs of the two modules measured in 2016 are as 28.4W for the field-exposed one and 35.9 W for the warehoused one. We further break down this power difference of 7.5 W ± 0.3 W to specific physical mechanisms. Through the encapsulant transmittance measurements and the circuit modeling of module I–V curves, the power degradation due to encapsulant discoloration is found as 59% ± 4% of the total difference. With the bias-dependent electroluminescence imaging and the dark I–V measurement of solar cells (via the additionally-attached probe wires), the series-resistance increase is attributed to 33% ± 1%, with the split of 13% ± 4% due to interconnection resistance and 20% ± 4% due to cell resistance. In addition, the synergistic effect of all the physical mechanisms makes up the remaining 8% ± 4%. This case study presents an example of analyzing multiple degradation mechanisms of the PV modules. With more characterization data being collected for today's modules, the same analysis framework can be broadly applied, yield great insights module power degradation attributed to multiple loss mechanisms.
... The interest of integrating cells cut into modules is not only limited to resistive gains: It increases the CTM power when using with a backsheet or white EVA (but using a larger module) and it is also a path to reduce the shading and hot spot effect when used in combination of series-parallel electrical architecture of module [129] [130]. It results in efficiency gains at the system level, which are particularly interesting for desert conditions [131]. ...
Thesis
Photovoltaic modules with higher efficiency can be envisaged by limiting the optical and electrical performance losses caused by cell integration. This thesis is mainly dedicated to the modelling of PV modules made up of silicon heterojunction solar cells (SHJ). There are already many tools for modelling the performance of a photovoltaic module, but it is necessary to adapt them to account for specificities of this technology, as well as latest developments in module design and interconnection. An optical and electrical model – mainly analytical – has been developed. A standardized classification of performance losses within the module was defined and enriched on the basis of previous work in the literature. Two loss items are analysed in more detail. The first is electrical: in order to reduce resistive losses, modules made up of cut cells have become the standard. The performance losses associated with cutting silicon heterojunction cells were missing data from the literature. An edge recombination current of 8 nA / cm has been measured before and after cutting, as well as a loss of photo-generated current. The impact on module performance has been modelled for different cutting geometries. The second is optical: new encapsulants material exhibit significant diffusive behaviour. A 4-flux model is developed to characterize its optical constants from spectrophotometric measurements in reflection and transmission, total and diffuse. A new item in performance losses is proposed, caused by backscattering of light. The impact on the photo-generated current of the module was analysed for two diffusive, UV opaque and transparent encapsulants.
... The total series resistance of a single solar cell module is divided into series resistance of the cell R s−cell (Ω), and the tabs R tab (Ω), which depends on the material properties and tab dimensions. The electrical losses in the interconnection have quadratic dependence on the current flowing through the tabs, and since the latter increases linearly along the tab, the total effective ohmic losses in the interconnection can be calculated by (2) as follows [7]: ...
Article
Photovoltaic (PV) modules in desert environments benefit from higher irradiation levels and, therefore, better energy yield. However, higher irradiation leads to higher temperature and higher electrical losses in module interconnections, which could influence the lifetime and energy yield of PV modules. The electrical losses in module interconnection act as heat sources. The interconnections’ electrical properties are also affected by solar cell temperature. In this paper, we simulate and evaluate the performance of the interaction between thermal and electrical losses in module interconnections and the influence of tab on module power and temperature. We compare the impact of tab losses on module power and temperature under different irradiation and ambient temperature levels, as well as compare the module in Qatar and Germany as desert and moderate climates. We show that the thermal influence of tab on module power is maximum 0.8% $_rel$ compared to a module without any thermal influence from tab, which, in this case, are the thermal coefficients of the tab and temperate elevation due to joule heating. This change is 0.2% $_rel$ and 0.6% $_rel$ for Qatar and Germany during one year, respectively. As a solution for desert applications, apart from full-cell layout, we have evaluated modules with half-cell design due to increased optical gains and reduced electrical losses. We determined the optimum tab width for the modules with half-cell and full-cell design and for two to five busbars under normal operating cell temperature (NOCT) conditions. We show that in NOCT conditions, the optimized tab width on half-cell modules is almost half of the tab width for full-cell modules. Furthermore, the temperature of half-cell modules is always less than that of full-cell modules for the similar tab widths. By considering the optimum tab width for half-cell and full-cell modules, an average increase of 0.2 °C is simulated, which is due to the higher active area and narrower tabs and, thus, higher irradiance and thermal loads.
... The predictions of the market share of half cells started in the year of 2015. Due to the advantages of applying separated cells, which is clearly seen on module level, concepts based on half cells [14,15] and shingle cells [16][17][18] are subject of increasing interest in the upcoming years. This is shown by the projected market share of more than 60% by 2030; see Fig. 12. ...
Conference Paper
Full-text available
The International Technology Roadmap for Photovoltaics (ITRPV) is a leading roadmap in the PV community. Ever since its first edition has been published in 2010, the ITRPV has succeeded to provide the technology projections in crystalline silicon PV technology covering a wide scope in the PV value chain. The projection data obtained from contributing experts and institutions are processed and published by the German Mechanical Engineering Industry Association (VDMA). In this paper, the projection accuracy of each of eight frequently reported projected topics is studied. The projected topics include: (a) multicrystalline silicon (mc-Si) wafer thickness, (b) mc-Si ingot mass, (c) bulk recombination current density, (d) emitter sheet resistance, (e) finger width, (f) silver amount per cell, (g) screen printing throughput rate, in addition (h) the market share of half cells is studied. The method includes the calculation of the deviation of each year's projection from the reference value for each of the chosen topics. Projection absolute percentage deviations (PAPD) are calculated as the time-dependent projection accuracy measure. Based on this approach, finger width projections show the highest accuracy by having a PAPD as a function of time accuracy slope of (1.5 ± 0.1) %/year. Half cells' market share is the least accurately projected topic featuring a PAPD accuracy slope as a function of time to be (8.1 ± 0.2) %/year. Results of the accuracy study (results of the "past") provide insights for future expected values.
... A technologically promising path towards higher module efficiencies without increasing the cell efficiencies themselves is based on the concept of a half-cell module. [1,2] The major reason is a reduced series resistance loss which is combined with a better light management as more light reflected from the back-sheet reaches the active cell areas. [3,4] This can lead to an increase in module efficiency of about 3% rel . ...
Article
Full-text available
Half-cell modules are promising candidates for a new generation of PV-modules as the electrical losses can be reduced while the optical gains are increased. This technological approach requires a cell separation process which does not induce any significant electrical or mechanical damages on cell level. Thermal laser separation (TLS) is a damage free and kerfless dicing technology for brittle materials such as silicon. We investigate the applicability of TLS for the solar cell splitting and compare it to a reference cell-splitting process based on laser scribing and subsequent cleavage. It is found that the electrical properties of the TLS-half-cells are slightly better compared to the reference process and that compared to a laser separation there is no mechanical damage due to the TLS process.
... Employing appropriate coatings and enhancing optical properties will significantly contribute to the improvement of PV backsheets, which will boost overall efficiency [193,200]. The optical properties of PV backsheets symbolize important features that influence different aspects in backsheet simulations; e.g. the gain or loss in short circuit current, effective area optimization and connectivity, light harvesting and light recovery, ray tracing simulations, ray optics and reflection at various interfaces, and outdoor characteristics [224][225][226][227][228]. In addition, there is a need to increase compatibility in silicone-based electrically conductive adhesives and different surface finishes, as well as obtaining better performance through (low cell-to-module losses) [229]. ...
Article
Over the last two decades, advancements in photovoltaic (PV) technology have been flourishing due to the continuous flow of valuable findings. Relevant insights on recent improvements, manufacturing approaches, and various applications of PV technology are provided. Both the PV cell structure and conversion efficiency may significantly contribute to the progression of the PV system. Currently, a wide range of advanced materials and smart technologies are employed within the PV cell's architecture, improving its structure; i.e. PERC/PERL, IBC, HIT/HJT, and MWT. The applications of nanoparticles and thin film technology in PV cell structures have successfully opened new research prospects to boost PV efficiency and overcome certain limitations with the use of CdSe, ZnCds, CdTe, a-Si/µc-Si, CIS, and CIGS. Additionally, constant development in the third generation of OSC methods using OE, OM, and COP are conducted. The improvement of PV backsheet structures and their enhanced optical properties yielded promising results in optimizing solar radiation, reflectance, and PV cell competence. The emergence of hybrid technologies (e.g. PVTE and TPV systems) led to effective solutions for reducing excessive heat that cause deficiency to a PV cell's functionality. Overall, modelling and effectively implementing appropriate parameters (such as diode parameters, optical parameters, circuit current, circuit voltage, fill factor (FF), conversion efficiency, IR, and UV spectral parameters) contributed to the total efficiency and performance modelling of the PV system.
... Meanwhile, to further promote the photovoltaic technical upgrading and achieve grid parity, the PV market imposes higher requirements on the module efficiency. Therefore, module manufacturers are continuously making in-depth study to improve cell efficiency, optimize material combination and innovate circuit design, such as black silicon [2,3], passivated emitter and rear cell (PERC) [4,5], reflective ribbons [6], halved cells [7][8][9], shingled cells [10] and multi-busbar technology [11,12]. The shingled module is welcome for its high efficiency by incorporating more cells in a limited module size. ...
Article
Photovoltaic (PV) applications such as in the architectural, automotive, and aerospace industries face design contradictions because they are expected to produce a lot of energy but are constrained by available area, surface shape, incident irradiance, shadows, and other aspects that have a negative influence on the energy produced by the solar panel. Solar competition vehicles are some of these challenging PVapplications. The design of such solar arrays needs to consider efficiency evaluation in order to optimize space; it is difficult not to install solar modules in areas impacted by shadows. A design procedure for a solar array configuration based on shadow analysis for competition vehicles is presented. The principle is that shadows in moving objects can be simulated, since the vehicle, the earth and the sun are are moving in semipredictable patterns, thus net energy collection can be forecast. The case study presented is the solar array design of a vehicle that participated in the World Solar Challenge 2013. The obtained results illustrate how the employment of the procedure gives insights on important aspects to consider and also delivers qualitative and quantitative information for decision making. In addition, the experience in competition highlights some issues to be considered, modified, or improved in further vehicle designs.
Presentation
Full-text available
Mechanical and electrical characterization of two half-cell cutting technologies: - Laser Scribe and Cleavage (LSC) - Thermal Laser Separation (TLS)
Conference Paper
Full-text available
Half-cell modules are gaining an increasing market share due to their potential of increasing the module power without requiring any changes in the cell technology. However, it has turned out that different cell separation technologies can yield a similar electrical performance of the half-cells, yet leading to an entirely different mechanical behavior of the cells. Hence, the mechanical strength on solar cell and module laminate level was evaluated for thermal laser separation (TLS) and laser scribing with cleaving (LSC) cutting technologies on multicrystalline silicon Al-BSF solar cells. It could be systematically shown, that mechanical defects which are found on cell level can also be seen on module level. More precisely, the strength for the LSC batch was decreased by 35 % on cell level and 23 % on module level. The TLS process did not change significantly the strength on cell or module laminate level. Additionally, the origin of fracture was found at the edge for the laser batch and on the back side pads for the full cells and TLS cut cells. The electrical evaluation has shown minor electrical power losses of the half-cells leading to an efficiency reduction of less than 1 %rel.
Article
Interconnection of solar cells by an electrically conductive adhesive (ECA) can replace the use of conventional metal ribbon connections for photovoltaic module fabrication. This technology increases the active area for photocurrent generation because the cells are connected in a busbar-less structure, and high-power, high-efficiency modules can be manufactured. In this study, we investigated the influence of the curing conditions on the characteristics of the ECA film and interconnected cell. In addition, this paper presents a new method for extracting the resistance contribution of the ECA to the interconnected cell. A low sheet resistance of <0.023 Ω/sq was observed when an ECA film on a slide glass substrate was cured for >60 s, regardless of the curing temperature. In addition, the sheet resistance was <0.02 Ω/sq at a curing temperature of 150 °C even for a short curing time of 5 s. At curing temperatures above 120 °C, the ECA resistance component of the interconnected cell was reduced to 0.2 mΩ or less, and the efficiency was increased by 0.4% or more. However, a curing time of >60 s was required for a similar efficiency improvement at lower temperatures. Notably, the characteristics of the interconnected cell simulated using the extracted ECA resistance values were similar to the measurement results.
Thesis
Full-text available
For thirty years the c-Si photovoltaic module industry has not incorporated larger changes in the module design and production process. The c-Si based photovoltaic modules still consist of solar cells connected in series by means of soldering and laminating in between sheets of ethylene-vinyl acetate with glass as front cover and white Tedlar®-Polyester-Tedlar based backsheet as rear cover. Moreover, it is not only that traditional modules look almost identical to the ones from thirty years ago, they are also mostly constructed and adjusted for European environmental conditions. Desert climate zones have high solar irradiation which is desirable for solar power generation, but they also have harsh surrounding conditions such as high environmental temperatures, drastic temperature variations between day and night, and dusty environments, among other conditions. To allow a photovoltaic module to last at least thirty years, a proper set of packing materials and module design must be chosen according to the environmental characteristics of the actual climatic conditions where the module will be installed. In this work, the prominent materials to fabricate commercial photovoltaic modules are investi-gated in terms of reliability and electrical performance at field conditions. Any further improvement in optical transmittance of glass and encapsulant does not directly imply an enhancement of power generation. This is not only due to low efficiencies caused by operating temperatures compared to standard conditions, but to the large ohmic loss produced at high irradiance levels, effects that would not have been seen in measurements under standard test conditions. Making efforts to adjust and improve the optical transmittance of the glass-encapsulant interface makes little sense if the module ohmic losses are not reduced. For this reason, the tabbing ribbons have to be carefully evaluated according to the targeted geographical location and to the current output of the solar cells. The properties of three solar cell types and several encapsulants have been evaluated to withstand ultraviolet doses, demonstrating that n-type solar cells are the suitable alternative for desert applications. In addition, the use of silicone as encapsulant is recommended to permit photons of higher energy to reach the solar cell, which allows an enhancement in module efficiency. Silicone also prevents the premature oxidation of the cell metallization and tabbing ribbons provoked by the creation of acetic acid, as it could be the case of using ethylene-vinyl acetate. For desert applications, it has been demonstrated, up to a certain extent, that due to the significant difference of coefficient of thermal expansion between the glass, encapsulant and backsheet, the proper solution to withstand shear stress caused by the heating of the module packing materials is by using double glass packing design. This also places the solar cells to be in the neutral plane of the module hence the tension, compression and stress applied over the solar cells is lower than in a glass-foil design while the module is bent. Furthermore, the effect of soiling for two different desert locations is also observed and quantified. Modules made out of flat glass coated with anti-reflection layers suffer larger optical losses caused by soiling compared to those with non-coated flat glass. If the rear side of a monofacial module is transparent, the effect of soiling is then slightly mitigated. Nevertheless, the power loss due to soiling is further reduced by using bifacial modules. In addition, it is shown that systems based on vertically mounted bifacial modules allow not only to complement the power generation profile during the day (single peak versus double peak curves), but it can also harvest higher annual energy compared to conventionally mounted monofacial modules due to the lower (or almost zero) dust accumulation. http://nbn-resolving.de/urn:nbn:de:bsz:352-2-l3mvyvipnwzl6
Article
Photovoltaic (PV) modules are commonly tested under standard test conditions. However, the performance of the PV module is highly dependent on the location, climate condition, and sun spectrum. Simulation is one of the inexpensive and practical approaches to estimate the performance of PV modules under different climatic conditions. Modeling of PV modules can be complex because different physical phenomena must be coupled and interact with each other. There are several existing multi-physic models, but they are either complex such as numerical models or highly simplified with a lot of assumptions. In this work, we introduce a thermal-electrical model to evaluate the performance of PV modules under different climate conditions based on a previously developed optical-electrical model. The model calculates the electrical parameters and temperature of the PV module after the module reaches the steady-state condition. The temperature, heat flow of all layers of the module, and the heat transfer thermal resistances can be determined. Comparison of the simulation and experimental results shows a deviation of around 1%, which indicates that the simulation and experimental results are in good agreement.
Article
In recent years, the laser half‐cutting technology for silicon solar cells has gotten much attention from researchers for increasing module power and would become particularly important in the photovoltaic modules domain. Herein, this paper would introduce a kind of new laser cutting process, a thermal laser separation (TLS) cutting technology. In the laser cutting processes, the influence on mechanical and electrical characteristics of bifacial p‐type passivated emitter and rear (PERC) solar cell and module were investigated in considerable detail. We have made a series of research and analyses including the cutting principle, opening length, fracture surface, and hot influence zone. The results reveal that the TLS cutting process could reduce damage more than the regular laser scribing and cleaving (LSC) cutting process. The TLS cutting process would achieve the higher power of a PERC half‐cutting bifacial module and the stronger bending strength of half solar cells than the LSC cutting process.
Technical Report
In order to help keep readers up-to-date in the field, each issue of Progress in Photovoltaics will contain a list of recently published journal articles that are most relevant to its aims and scope. This list is drawn from an extremely wide range of journals, including IEEE Journal of Photovoltaics, Solar Energy Materials and Solar Cells, Renewable Energy, Renewable and Sustainable Energy Reviews, Journal of Applied Physics, and Applied Physics Letters. To assist the reader, the list is separated into broad categories, but please note that these classifications are by no means strict. Also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions please email Ziv Hameiri at ziv.hameiri@unsw.edu.au.
Conference Paper
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Ray-trace simulation is used to quantify the optical losses of photovoltaic modules containing silicon cells. The simulations show that when the module's encapsulant is silicone rather than ethylene vinyl acetate (EVA), the module's short-circuit current density under the AM1-5g spectrum is 0.7-1.1% higher for screen-printed multi-cSi cells, 0.5-1.2% higher for screen-printed mono-cSi cells, and 1.0-1.6% higher for high-efficiency rear-contact cells, depending on the type of silicone. This increase is primarily due to the transmission of short-wavelength light (
Conference Paper
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We study the effect of the white rear sheet located around photocells in photovoltaic modules. This white sheet reflects part of the incident light back to the photocell by means of internal reflections, thus increasing the production of electrical current with a low additional cost. We have developed a software program that simulates a simple module with once cell in order to obtain the improvement of electrical current production as a function of the width of the white strip surrounding the cell. We find that the wider the white sheet around the photocell, the greater the increase of electrical current generated in it. These results will help to the optimization of the design of solar panels. We obtain a good agreement when comparing our simulation results with measurements carried out in a real prototype.
Article
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In a silicon wafer-based photovoltaic (PV) module, significant power is lost due to current transport through the ribbons interconnecting neighbour cells. Using halved cells in PV modules is an effective method to reduce the resistive power loss which has already been applied by some major PV manufacturers (Mitsubishi, BP Solar) in their commercial available PV modules. As a consequence, quantitative analysis of PV modules using halved cells is needed. In this paper we investigate theoretically and experimentally the difference between modules made with halved and full-size solar cells. Theoretically, we find an improvement in fill factor of 1.8% absolute and output power of 90 mW for the halved cell minimodule. Experimentally, we find an improvement in fill factor of 1.3% absolute and output power of 60 mW for the halved cell module. Also, we investigate theoretically how this effect confers to the case of large-size modules. It is found that the performance increment of halved cell PV modules is even higher for high-efficiency solar cells. After that, the resistive loss of large-size modules with different interconnection schemes is analysed. Finally, factors influencing the performance and cost of industrial halved cell PV modules are discussed.
Article
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A calibrated measurement of the short circuit current and the surface reflection coefficient can be directly converted into the internal quantum efficiency (IQE) of a solar cell. The IQE at a wavelength of 833 nm were measured on ingot, EFG and RGS silicon solar cells with a spatial resolution of 6 µm. Ingot solar cells were found to be predominantly influenced by a homogeneous distribution of recombination centers. However, if the dislocation densities exceeded a certain limit the IQE was reduced by recombination at dislocations. This limit varied in different parts of the wafer. EFG solar cells only showed a lifetime reduction by dislocations whereas the investigated solar cells made of RGS silicon were dominated by recombination at grain boundaries. The RGS silicon was further investigated by TEM-measurements, which showed that the extended defects were highly decorated with SiO 2 -and SiC-precipitates.
Article
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The actual silicon crisis in photovoltaic industry forces the whole value chain to realize more installed W<sub>p</sub> photovoltaic power out of every kg silicon. This is approached through thinner wafers by the wafer producers, higher cell efficiencies by the cell manufacturers, and efficiency enhancements via improved encapsulation schemes at module production. Recently, some alternative encapsulation materials came in consideration, e.g. EVA replacements and cover glass with anti-reflective coatings. Cell technologies are changing as well. Some innovations are already adopted in standard products, but need to be tuned to each other. While the number of parameters involved has increased, it became cumbersome to minimize the optical losses experimentally. Modelling and variation of those parameters is performed to understand their interdependence and to propose optimal parameters sets, which can be used as good starting parameters for experimental probing
Article
Full-text available
This paper presents a simulation tool to investigate the optical transmission of any encapsulation of PV modules under real-word conditions in order to test various types of encapsulation materials and front covers, with and without anti-reflective-coatings. While standard test conditions are using a fixed spectrum at perpendicular incidence only, real world performance is more complex to determine. The model developed is consequently linked with a precise simulation of the actual irradiance condition for each moment of a clear day considering incidence angles, spectra, dispersion and multiple internal reflections inside and among the layers. To calculate and compare life-cycle yields, several of those "snapshots" (each 15 minutes) of transmittance, actual irradiance, efficiency and electrical power output. The model is an appropriate tool to optimize the optical layout of the encapsulation, including new materials, not just within the standard test conditions but also for real world applications at different locations
Conference Paper
This paper reports on BP Solar's DOE sponsored Solar America Initiative, Technology Pathways Partnership. The paper presents the goals, the technical approach and progress from the first nine months of the program. The overall goals of the program are to reach grid parity for residential and commercial markets and to increase production volumes. This program is addressing all aspects of the PV product chain from raw materials including silicon through installation of the systems at the customer site. To achieve parity with the grid and growth to gigawatt levels of production requires involvement of this entire product chain. To this end the program involves 16 subcontractors including materials vendors, production equipment manufacturers, balance of system component vendors and research laboratories — both university and industrial. During the first nine months of the program progress has been made in casting, wire sawing, processing of thinner cells, development of additional sources of AR coated glass and cost reduction in the encapsulation package.
Article
An important leverage in reducing the cost of photovoltaic energy generation is increasing the power output of the individual solar modules in an installation. Optimizing the efficiency of the individual cells assembled into the modules is often the main focus. However, additional large optimization potential is present at the module level. In this study, we investigate the influence of different design parameters such as cell spacing and solder ribbon type on the encapsulation losses of a solar module using single-cell modules, as well as large 60-cell modules. Combined with a model for series resistance losses encountered during encapsulation, this allows for the prediction of the power output of different module designs and, thus, for simultaneous optimization of different design parameters. The findings were directly introduced in the design of the latest generation of Q-Cells solar modules. These optimized modules were installed on Q-Cells' test field in order to generate yield data. The data show that the optimized design increases not only the modules' performance under standard test conditions but translates into an equivalent gain in energy yield in the field as well.
Article
We present a top-down method to quantify optical losses due to encapsulation of textured multicrystalline silicon wafer solar cells in a photovoltaic module. The approach is based on a combination of measurements and mathematical procedures. Seven different loss mechanisms are considered: 1) reflection at the glass front surface, 2) reflection at the metal fingers, 3) reflection at the textured solar cell surface, 4) absorption in the antireflection coating, 5) absorption in the glass pane and the encapsulation layer, 6) front surface escape, and 7) losses due to a non-perfect solar cell internal quantum efficiency. Losses for each of these mechanisms are obtained as a function of wavelength, and the corresponding current loss for each loss mechanism is calculated. Comparing simulated and measured results, the method predicts the module quantum efficiency with an error of less than 2% and the collected current with an error of less than 1%. In the presented example, the biggest loss (7.4 mA/cm$^{2}$) is due to the nonperfect quantum efficiency, followed by reflection losses at the glass front (2.2 mA/cm$^{2}$ ) and absorption in the glass and encapsulation layer (1.1 mA/cm $^{2}$).
Article
In the cell to complete module process, the cell to module (CTM) loss is inevitable. In typical process, the CTM power loss is larger than 3%. In this letter, we tried to reduce the CTM loss by studying the backsheet reflectance and the string inter space effect. The conclusion was carried out basing on the both simulation and experiment results. It shows if the reflectance of backsheet is from 70% to 90%, the power gain will be improved ∼0.3%. We also show the CTM loss decreases with the increasing string inter space. Around 0.3% less CTM loss can be achieved by changing the string inter space. In the end, we conclude that the CTM loss can be reduced from 3% to 2.28% by combining these two beneficial effects.
Article
In a conventional photovoltaic module, some light that falls between the solar cells is internally reflected onto the cells via the backsheet and the glass–air interface of the module; thus, a module can be considered a static concentrator. We present a simple ray tracer that computes a module's optical concentration as a function of cell separation, cell geometry, and the optical properties of the encapsulants. The ray tracer's primary simplification is to divide the module's backsheet into small pixels and, since the reflection from the backsheet is approximately Lambertian and independent of the incident angle, to sum the intensity of all rays that enter a pixel and treat them as one. The advantage of this pixel approximation is that it makes it simple to simulate curved surfaces—such as the corners of a pseudo-square solar cell—within short computation times. The results of the simple ray tracer are shown to be consistent with those of a conventional ray tracer and an LBIC experiment. We also apply the ray tracer to a present-day SunPower module and find that 25% of the photons that fall between the cells are internally reflected onto the cells, which results in an optical concentration of 1·024. Copyright © 2005 John Wiley & Sons, Ltd.
Article
Non-destructive spatial characterisation tools are essential for the evaluation of thin film photovoltaic modules; as such distributed variations have a significant effect on the overall device performance. A combination of several techniques (solar simulator, LBIC and thermography) is used in conjunction to identify and investigate performance problems and locate possible defects in thin film silicon photovoltaic modules of different structures. An excellent agreement between the different spatial analysis tools is demonstrated. The LBIC system used here is unusual in that it analyses modules where the cells are interconnected and the signal strength does not give as clear a feedback on the defects as in the case of measuring each cell separately. The choice of lasers used in the system allows the investigation of separate junctions in the most common multi-junction devices. The system characterisation is demonstrated here in order to warranty reliability and repeatability of this tool. A special test module is investigated where all techniques are compared and good agreement is demonstrated. Furthermore, the problem of reducing signal strength with increasing junction number is demonstrated and discussed.
Article
An advanced light beam-induced current measurement for solar cell local characterization, called CELLO, has been developed and tested on mono- and multi-crystalline Si solar cells. A solar cell is illuminated at near 1.5 AM light intensity, and is additionally subjected to intensity modulated scanning local illumination by a focused IR-laser. The linear response (current or potential) of the solar cell is measured for various fixed global conditions (different preset voltage or current values) during scanning. A large number of independent data with high spatial resolution are obtained. Applying an advanced fitting procedure to these data yields a set of local parameters for each point on the solar cell. This gives information on the spatial distribution of the photo current, the series and shunt resistance, the lateral diffusion of minority carriers, the quality of the back surface field, and even allows the calculation of local IV curves. The theoretical and experimental approach to this technique will be discussed, and the applicability of this new solar cell characterization tool will be demonstrated.
Article
A 3D distributed model is developed and implemented based on circuit analysis software for the investigation of spatial variation in performance due to the distributed nature and non-uniformity of solar cell properties. This is applied to LBIC measurements where it is used for sensitivity analysis of the measurements with respect to certain parameters in series connected thin film PV modules.The model is used to explain the differences in dark and illuminated measurements, which clearly shows the illuminated LBIC signal is largely dependent on the homogeneity of the background illumination. The dark LBIC is largely affected by the shunt resistance of the neighbouring cells rather than by the signal strength of the cell under test. It is required to bring the cell into limiting conditions, which then gives a signal one order of magnitude stronger than that in the non-limiting case. The simulations are validated against measurements taken in these regimes.
Optimized module design: a study of encapsulation losses and the influence of design parameters on module performance
  • M B Koentopp
  • M Schutze
  • D Buss
  • R Seguin
M.B. Koentopp, M. Schutze, D. Buss, R. Seguin, Optimized module design: a study of encapsulation losses and the influence of design parameters on module performance, in: Proceedings of the 2012 38th IEEE Photovoltaic Specialists Conference (PVSC), 2012, pp. 3178-3182.
Optimization of the output power by effect of backsheet reflectance and spacing between cell strings
  • W.-S Su
  • Y.-C C W Liao
  • C.-H Huang
  • D.-C Liu
  • M.-Y Huang
  • Z.-C Wu
  • S.-J Ho
W.-S. Su, Y.-C.C.W.-H. Liao, C.-H. Huang, D.-C. Liu, M.-Y. Huang, Z.-C. Wu, S.-J. Ho, Optimization of the output power by effect of backsheet reflectance and spacing between cell strings, in: Proceedings of the 37th IEEE Photovoltaic Specialists Conference, Seattle, Wash, USA, 2011, pp. 3218-3220.