Number Of Subcells Research Articles

Energy production advantage of independent subcell connection for multijunction photovoltaics

AbstractIncreasing the number of subcells in a multijunction or “spectrum splitting” photovoltaic improves efficiency under the standard AM1.5D design spectrum, but it can lower efficiency under spectra that differ from the standard if the subcells are connected electrically in series. Using atmospheric data and the SMARTS multiple scattering and absorption model, we simulated sunny day spectra over 1 year for five locations in the United States and determined the annual energy production of spectrum splitting ensembles with 2–20 subcells connected electrically in series or independently. While electrically independent subcells have a small efficiency advantage over series‐connected ensembles under the AM1.5D design spectrum, they have a pronounced energy production advantage under realistic spectra over 1 year. Simulated energy production increased with subcell number for the electrically independent ensembles, but it peaked at 8–10 subcells for those connected in series. Electrically independent ensembles with 20 subcells produce up to 27% more energy annually than the series‐connected 20‐subcell ensemble. This energy production advantage persists when clouds are accounted for.

Optimum band gap combinations to make best use of new photovoltaic materials

The detailed balance approach has been used to analyze the optimum use of band gaps in a multi-junction device of up to 6 sub-cells. Results for the AM1.5G spectrum suggest that as the number of sub-cells increases the importance of the bottom sub-cell band gap becomes less critical, assuming the optimum band gap combination for that value can be obtained. Given this greater freedom in choice, the potential for the use of silicon as an active substrate is investigated along with a cell thinning ‘current sharing’ approach to improve current mismatch in the device. Results show a more robust design space of multi-junctions with active silicon substrates when the current sharing approach is used, with performances close to the optimum for a completely free choice of band gaps. The use of the AM1.5D spectrum for a concentration ratio of 100, shows similar results for the substrate and a slight increase in band gap sensitivity for the upper band gaps in the stack. Inclusion of optical coupling between the sub-cells lowers limiting efficiency, with luminescent coupling mitigating the band gap sensitivity. The results and approach outlined are useful for determining how best to deploy new photovoltaic materials in multi-junction solar cells.

A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions

This paper deals with a subcell finite volume strategy for a discontinuous Galerkin (DG) scheme discretizing the shallow water equations with non-constant bottom topography. Using finite volume subcells within the DG scheme is a recent shock capturing strategy decomposing elements marked by a shock indicator into a specific number of subcells on which a robust FV scheme is applied. This work newly considers the subcell approach in the context of wetting and drying shallow water flows. Here, finite volume subcells are introduced for almost dry cells in order to enable an improved resolution of the wet/dry front. Furthermore, in this work, the theory for positivity preserving and well-balanced DG schemes is extended to the DG scheme using finite volume subcells. The performance of the resulting novel approach both in the context of preserving lake at rest stationary states and for wetting and drying computations is then numerically demonstrated for challenging standard test cases in two space dimensions on unstructured triangular grids.

Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting

In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order a posteriori sub-cell ADER-WENO finite volume limiter. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in [53], the discrete solution within the troubled cells is recomputed by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space–time adaptive AMR framework in two and three space dimensions, after assuring the proper averaging and projection between sub-cells that belong to different levels of refinement. The combination of the sub-cell resolution with the advantages of AMR allows for an unprecedented ability in resolving even the finest details in the dynamics of the fluid. The spectacular resolution properties of the new scheme have been shown through a wide number of test cases performed in two and in three space dimensions, both for the Euler equations of compressible gas dynamics and for the magnetohydrodynamics (MHD) equations.

Multijunction solar cell efficiencies: effect of spectral window, optical environment and radiative coupling

Solar cell efficiency is maximized through multijunction architectures that minimize carrier thermalization and increase absorption. Previous proposals suggest that the maximum efficiency for a finite number of subcells is achieved for designs that optimize for light trapping over radiative coupling. We instead show that structures with radiative coupling and back reflectors for light trapping, e.g. spectrum-splitting cells, can achieve higher conversion efficiencies. We model a compatible geometry, the polyhedral specular reflector. We analyze and experimentally verify the effects of spectral window and radiative coupling on voltage and power. Our results indicate that radiative coupling with back reflectors leads to higher efficiencies than previously studied architectures for practical multijunction architectures (i.e., ≤20 subcells).

Optimization of absorption bands of dye-sensitized and perovskite tandem solar cells based on loss-in-potential values.

A numerical study of optimal bandgaps of light absorbers in tandem solar cell configurations is presented with the main focus on dye-sensitized solar cells (DSSCs) and perovskite solar cells (PSCs). The limits in efficiency and the expected improvements of tandem structures are investigated as a function of total loss-in-potential (V(L)), incident photon to current efficiency (IPCE) and fill factor (FF) of individual components. It is shown that the optimal absorption onsets are significantly smaller than those derived for multi-junction devices. For example, for double-cell devices the onsets are at around 660 nm and 930 nm for DSSCs with iodide based electrolytes and at around 720 nm and 1100 nm for both DSSCs with cobalt based electrolytes and PSCs. Such configurations can increase the total sunlight conversion efficiency by about 35% in comparison to single-cell devices of the same VL, IPCE and FF. The relevance of such studies for tandem n-p DSSCs and for a proposed new configuration for PSCs is discussed. In particular, it is shown that maximum total losses of 1.7 V for DSSCs and 1.4 V for tandem PSCs are necessary to give any efficiency improvement with respect to the single bandgap device. This means, for example, a tandem n-p DSSC with TiO2 and NiO porous electrodes will hardly work better than the champion single DSSC. A source code of the program used for calculations is also provided.

Understanding tandem organic photovoltaic cell performance

We develop a framework to understand the performance of tandem organic photovoltaic (OPV) cells consisting of a series-connected stack of an arbitrary number of sub-cells. The power conversion efficiency penalty, Δη, is defined as the loss incurred when the tandem cell is at its maximum power point (MPP) but one or more sub-cells are not operating at their individual MPPs. To minimize Δη, the current at the MPP for each sub-cell must be equal. We also develop a method to calculate the tandem cell spectral mismatch factor and fill factor, showing that they are related to both the fill factors and short circuit currents of all the constituent sub-cells. By including the current generated in the dark, exciton dissociation at the donor-acceptor heterojunction, and photoconductivity, along with current losses due to polaron-pair and bimolecular recombination, we simulate the operation of small molecule bilayer and mixed-layer sub-cells used in the tandem, and from these results derive the behavior of the integrated device. This analysis is used to understand and optimize tandem OPV cell performance.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM-LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very “tight” lower and upper bound solutions can be obtained using PIM-LS2.

Addressing volumetric locking and instabilities by selective integration in smoothed finite elements

AbstractThis paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain.This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM.The one‐subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi‐equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses.The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one‐subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency.Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd.

Smooth finite element methods: Convergence, accuracy and properties

AbstractA stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu–Washizu assumed strain variational form is developed.We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi‐equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one‐subcell element with a quasi‐equilibrium finite element, leading to a global a posteriori error estimate.We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost.It is shown numerically that the one‐cell smoothed four‐noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd.

Local and overall flow in composites predicted by micromechanics

Abstract Rate-dependent inelastic flow in metal matrix composites subjected to multiaxial stress states is quantified by flow surfaces, which are geometrically analogous to yield surfaces. The definition of flow is important because the most meaningful definition from a theoretical viewpoint, dissipation, is not measurable in the laboratory. Inelastic power is measurable, but differs from the dissipation due to residual stresses and evolution of the material state. Since experiments are necessary for development and validation of models, both definitions are important and considered here. The relationship between local flow in the matrix and overall flow of the composite is explored using finite element and generalized method of cells micromechanical analyses. The loci of flow surfaces in the axial–transverse and transverse–transverse stress planes are plotted. At the threshold, the overall flow surface is the intersection of all the local flow surfaces. Beyond the threshold, the intersection of all the local flow surfaces is smaller than the overall flow surface and differences between the dissipation and inelastic power are notable. Most importantly, the directions of the overall inelastic strain rate vectors are generally not normal to the overall surface of constant dissipation after the material state has begun to evolve. Thus, an associative macroscale continuum model will be, at best, approximate. Interestingly, local flow surfaces beyond the threshold are not necessarily convex when plotted in the overall stress plane. This is due to the existence of residual stresses. In addition, the generalized method of cells was found to accurately estimate the inner and outer envelopes of the local flow surface cluster with a surprisingly small number of subcells.

High power metal hydride bipolar battery

Nickel/metal hydride batteries in a bipolar design offer some advantages for an application as a power storage system for electric and hybrid vehicles. The paper deals with some aspects of combining a number of sub-cells in a common vessel design.

Computational aspects of modeling complex microstructure composites using GMC

A computationally efficient implementation of the generalized method of cells (GMC) is presented and tested in connection with problems that require large numbers of subcells. The new implementation is found to be substantially faster in predicting the elastic properties of unidirectional composites. Furthermore, the new implementation makes it possible to solve problems with complex microstructures and a degree of refinement that was not possible before. Cell discretizations with up to 10,000 subcells were employed in the numerical experiments. The modeling capabilities of GMC and the new implementation are tested in the context of predicting the effective elastic behavior of composites with randomly distributed fiber inclusions. It is shown that GMC accurately predicts the asymptotic behavior of the engineering properties of the composites studied. This is demonstrated by examining the limiting values of the effective engineering properties of the composites studied when the number of subcells is large.

Micromechanical analysis of composites by the generalized cells model

In the original formulation of the micromechanical method of cells, designated for the analysis of fibrous composites with periodic structure, the repeating volume element consists of four interacting subcells. The various capabilities and reability of the micromechanical model were verified in a recent review paper and a monograph. The present investigation offers a generalization of the method to an arbitrary number of subcells for the modeling of multiphase periodic composites. Such a generalization is particularly advantageous when dealing with elastic-plastic composites, since yielding and plastic flow of a metallic phase may take place at different locations. Effective constitutive laws that govern overall behavior of the elastic-viscoplastic composite material are established. These laws are given in terms of relationships between the average stress-rate and strain-rate of the inelastic multiphase composite. Comparisons between the response of boron/aluminum composite obtained by the present model and a finite element solution are given.

Die Kristallstrukturen von Cr11G19, Mo13Ge23und V17Ge31*

The crystal structures of the compounds Cr 11 Ge 19 (isotypic with Mn 11 Si 19 ), Mo 13 Ge 23 and V 17 Ge 31 have been determined by means of Fourier synthesis. The crystal structures are characterized by a tetragonal subcell forming a diamond-like arrangement similar to that of the titanium atoms in the TiSi 2 structure. The germanium deficiency according to the composition of a digermanide is correlated with the number of subcells along the c axis (11-, 13- and 17-fold subcell).