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Topology optimization of the front electrode patterns of solar cells based on moving wide Bezier curves with constrained end

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Abstract

The front electrode pattern of the solar cell has an important influence on the performance of the solar cell. This paper proposed an explicit topology optimization method for the design of the front electrode patterns of solar cells. The explicit topology optimization method is based on moving wide Bezier curves with a constrained end. The front electrode pattern is composed of a set of wide Bezier curves. The control points and width of the wide Bezier curve are regarded as design variables. The validity of the proposed method is tested on side-contact and pin-up module solar cells. Compared with traditional shape and size optimization, the proposed topology optimization method has greater design freedom, which makes it possible to generate novel and potentially superior front electrode patterns. Compared with the topology optimization method based on the solid isotropic material with penalization (SIMP) method, the proposed topology optimization method can obtain a clear and smooth boundary and easily achieve the minimum width scale control. In addition, the effects of the initial topology, number of control points, number of the components, mesh resolution, and solar cell size on the optimization results are studied. The results suggest that using the proposed method to optimize the front electrode pattern can probably improve the performance of solar cells.

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References

  • Antonini A, Stefancich M, Vincenzi D, Malagù C, Bizzi F, Ronzoni A, Martinelli G (2003) Contact grid optimization methodology for front contact concentration solar cells. Solar Energy Mater Solar Cells 80(2):155–166

    Article  Google Scholar 

  • Burgers AR (1999) How to design optimal metallization patterns for solar cells. Prog Photovolt: Res Appl 7(6):457–461

    Article  Google Scholar 

  • Burgers AR, Bultman JH, Tip AC, Sinke WC (2001) Metallisation patterns for interconnection through holes. Solar Energy Mater Solar Cells 65(1):347–353

    Article  Google Scholar 

  • Djeffal F, Bendib T, Arar D, Dibi Z (2013) An optimized metal grid design to improve the solar cell performance under solar concentration using multiobjective computation. Mater Sci Eng: B 178(9):574–579

    Article  Google Scholar 

  • Du Z, Chen H, Huang G (2020) Optimal quantum valley hall insulators by rationally engineering berry curvature and band structure. J Mech Phys Solids 135:103784

    Article  MathSciNet  Google Scholar 

  • Flat A, Milnes AG (1979) Optimization of multi-layer front-contact grid patterns for solar cells. Solar Energy 23(4):289–299

    Article  Google Scholar 

  • Galiana B, Algora C, Rey-Stolle I, Vara IG (2005) A 3-d model for concentrator solar cells based on distributed circuit units. IEEE Trans Electron Devices 52(12):2552–2558

    Article  Google Scholar 

  • Green MA (1982) Solar cells: operating principles, technology, and system applications. Prentice-Hall Inc, Englewood Cliffs

    Google Scholar 

  • Guo X, Ni C, Cheng G, Du Z (2012) Some symmetry results for optimal solutions in structural optimization. Struct Multidisc Optim 46(5):631–645

    Article  MathSciNet  MATH  Google Scholar 

  • Guo X, Du Z, Cheng G, Ni C (2013) Symmetry properties in structural optimization: some extensions. Struct Multidisc Optim 47(6):783–794

    Article  MATH  Google Scholar 

  • Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically-a new moving morphable components based framework. J Appl Mech 81(8):081009

    Article  Google Scholar 

  • Guo X, Zhang W, Zhang J, Yuan J (2016) Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Methods Appl Mech Eng 310:711–748

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta DK, Langelaar M, Barink M, van Keulen F (2015) Topology optimization of front metallization patterns for solar cells. Struct Multidisc Optim 51(4):941–955

    Article  Google Scholar 

  • Gupta DK, Langelaar M, Barink M, van Keulen F (2016) Optimizing front metallization patterns: efficiency with aesthetics in free-form solar cells. Renew Energy 86:1332–1339

    Article  Google Scholar 

  • Gupta DK, Barink M, Galagan Y, Langelaar M (2017) Integrated front-rear-grid optimization of free-form solar cells. IEEE J Photovolt 7(1):294–302

    Article  Google Scholar 

  • Gupta DK, Barink M, Langelaar M (2018) Cpv solar cell modeling and metallization optimization. Solar Energy 159:868–881

    Article  Google Scholar 

  • Han A, Wang X, Liu X, Huang Y, Meng F, Liu Z (2018) Improvement of ga distribution in Cu(In, Ga)(S, Se)2 film by pretreated mo back contact. Solar Energy 162:109–116

    Article  Google Scholar 

  • Han H, Wu Y, Ma C (2018) Optimization design of a multibusbar structure: the using of a conductive belt. Int J Photoenergy 2018:7630390

    Article  Google Scholar 

  • Khan J, Arsalan MH (2016) Solar power technologies for sustainable electricity generation—a review. Renew Sustain Energy Rev 55:414–425

    Article  Google Scholar 

  • Kulushich G, Zapf-Gottwick R, Bazer-Bachi B, Werner JH (2013) 18.4% efficient grid optimized cells with 100-Ω/sq emitter. IEEE J Photovolt 3(1):254–260

    Article  Google Scholar 

  • Li B, Xuan C, Liu G, Hong J (2019) Generating constructal networks for area-to-point conduction problems via moving morphable components approach. J Mech Des 141(5):051401

    Article  Google Scholar 

  • Li K, Yang Z, Zhang X (2021) Size optimization of the front electrode and solar cell using a combined finite-element-genetic algorithm method. J Photonics Energy 11(3):034502

    Article  Google Scholar 

  • Liang J, Zhang X, Zhu B (2019) Nonlinear topology optimization of parallel-grasping microgripper. Precis Eng 60:152–159

    Article  Google Scholar 

  • Malm U, Edoff M (2008) Influence from front contact sheet resistance on extracted diode parameters in cigs solar cells. Prog Photovolt: Res Appl 16(2):113–121

    Article  Google Scholar 

  • Nong D, Simshauser P, Nguyen DB (2021) Greenhouse gas emissions vs Co2 emissions: comparative analysis of a global carbon tax. Appl Energy 298:117223

    Article  Google Scholar 

  • Raponi E, Bujny M, Olhofer M, Aulig N, Boria S, Duddeck F (2019) Kriging-assisted topology optimization of crash structures. Comput Methods Appl Mech Eng 348:730–752

    Article  MathSciNet  MATH  Google Scholar 

  • Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37(3):217–237

    Article  MathSciNet  MATH  Google Scholar 

  • Shan Y, Zhang X, Chen G, Li H (2019) Laser direct printing of solder paste. AIP Adv 9(12):125306

    Article  Google Scholar 

  • Shan Y, Zhang X, Li H, Zhan Z (2021) Single-step printing of high-resolution, high-aspect ratio silver lines through laser-induced forward transfer. Opt Laser Technol 133:106514

    Article  Google Scholar 

  • Shockley W (1949) The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Syst Tech J 28(3):435–489

    Article  Google Scholar 

  • Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75

    Article  Google Scholar 

  • Song Z, Liu J, Yang H (2021) Air pollution and soiling implications for solar photovoltaic power generation: a comprehensive review. Appl Energy 298:117247

    Article  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24:359–373

    Article  MathSciNet  MATH  Google Scholar 

  • van Deelen J, Frijters C (2017) Cigs cells with metallized front contact: longer cells and higher efficiency. Solar Energy 143:93–99

    Article  Google Scholar 

  • van Deelen J, Klerk L, Barink M (2014) Optimized grid design for thin film solar panels. Solar Energy 107:135–144

    Article  Google Scholar 

  • van Deelen J, Klerk LA, Barink M, Rendering H, Voorthuijzen P, Hovestad A (2014) Improvement of transparent conducting materials by metallic grids on transparent conductive oxides. Thin Solid Films 555:159–162

    Article  Google Scholar 

  • van Deelen J, Barink M, Klerk L, Voorthuijzen P, Hovestad A (2015) Efficiency loss prevention in monolithically integrated thin film solar cells by improved front contact. Prog Photovolt: Res Appl 23(4):498–506

    Article  Google Scholar 

  • van Keulen F, Haftka RT, Kim NH (2005) Review of options for structural design sensitivity analysis. part 1: linear systems. Comput Methods Appl Mech Eng 194(30):3213–3243

    Article  MATH  Google Scholar 

  • Wan L, Zhang C, Ge K, Yang X, Li F, Yan W, Xu Z, Yang L, Xu Y, Song D, Chen J (2020) Conductive hole-selective passivating contacts for crystalline silicon solar cells. Adv Energy Mater 10(16):1903851

    Article  Google Scholar 

  • Wang H, Ma S, Zhang M, Lan F, Wang H, Bai J (2017) Effects of screen printing and sintering processing of front side silver grid line on the electrical performances of multi-crystalline silicon solar cells. J Mater Sci: Mater Electron 28(16):11934–11949

    Google Scholar 

  • Wang R, Zhang X, Zhu B (2019) Imposing minimum length scale in moving morphable component (MMC)-based topology optimization using an effective connection status (ecs) control method. Comput Methods Appl Mech Eng 351:667–693

    Article  MathSciNet  MATH  Google Scholar 

  • Wang R, Zhang X, Zhu B (2021) A projective transformation-based topology optimization using moving morphable components. Comput Methods Appl Mech Eng 376:113646

    Article  MathSciNet  MATH  Google Scholar 

  • Weeber AW, Kinderman R, Tool CJJ, Granek F, De Jong PC (2006) How to achieve 17% cell efficiencies on large back-contacted mc-si solar cells. In: 2006 IEEE 4th world conference on photovoltaic energy conference vol 1, pp 1048–1051

  • Xia L, Xia Q, Huang X, Xie YM (2018) Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch Comput Methods Eng 25:437–478

    Article  MathSciNet  MATH  Google Scholar 

  • Yang H, Huang J (2020) An explicit structural topology optimization method based on the descriptions of areas. Struct Multidisc Optim 61(3):1123–1156

    Article  MathSciNet  Google Scholar 

  • Yang Y, Altermatt PP, Zhu W, Liang X, Shen H (2012) Analysis of industrial c-si solar cell’s front metallization by advanced numerical simulation. Prog Photovolt: Res Appl 20(4):490–500

    Article  Google Scholar 

  • Yu M, Ruan S, Wang X, Li Z, Shen C (2019) Topology optimization of thermal-fluid problem using the MMC-based approach. Struct Multidisc Optim 60(1):151–165

    Article  MathSciNet  Google Scholar 

  • Zhang W, Yuan J, Zhang J, Guo X (2016) A new topology optimization approach based on moving morphable components (MMC) and the ersatz material model. Struct Multidisc Optim 53(6):1243–1260

    Article  MathSciNet  Google Scholar 

  • Zhang W, Song J, Zhou J, Du Z, Zhu Y, Sun Z, Guo X (2018) Topology optimization with multiple materials via moving morphable component (MMC) method. Int J Numer Methods Eng 113(11):1653–1675

    Article  MathSciNet  Google Scholar 

  • Zhou H, Ting KL (2005) Shape and size synthesis of compliant mechanisms using wide curve theory. J Mech Des 128(3):551–558

    Article  Google Scholar 

  • Zhou YP, He YL, Tong ZX, Liu ZB (2019) Multi-physics coupling effects of nanostructure characteristics on the all-back-contact silicon solar cell performances. Appl Energy 236:127–136

    Article  Google Scholar 

  • Zhu B, Zhang X, Wang N (2013) Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method. Struct Multidisc Optim 47(5):659–672

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu B, Chen Q, Wang R, Zhang X (2018) Structural topology optimization using a moving morphable component-based method considering geometrical nonlinearity. J Mech Des 140(8):081403

    Article  Google Scholar 

  • Zhu B, Wang R, Wang N, Li H, Zhang X, Nishiwaki S (2021) Explicit structural topology optimization using moving wide Bezier components with constrained ends. Struct Multidisc Optim 64(1):53–70

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 51820105007), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021B1515020053). This support is greatly acknowledged. We are grateful to Deepak K. Gupta for the discussion.

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Correspondence to Benliang Zhu.

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All the datasets in this study are generated using our homemade MATLAB codes. The full datasets, as well as the source codes, can be available from the corresponding author with a reasonable request.

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Li, K., Wang, R., Zhang, X. et al. Topology optimization of the front electrode patterns of solar cells based on moving wide Bezier curves with constrained end. Struct Multidisc Optim 65, 57 (2022). https://doi.org/10.1007/s00158-021-03162-0

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