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Topology optimization of Metallisation Patterns in Photo Voltaic applicationsMaster Thesis ProjectR.S. HeemskerkSupervisors: Dr. ir. M. Langelaar, Prof.dr.ir A. van Keulen

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Introduction

• Renewable energy sources / Reduce amount of CO2

• Increasing amount of solar power

• Optimise the efficiency of solar cells

• 0.1% improvement has an effect of 1.6 GW

• Topology optimization of Metallisation Patterns in Photo Voltaic applications

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Contents

• Solar Cell – Working Principle • Solar Cell – Optimal Design• Optimisation• Modelling

• Finite element formulation• Non linear behaviour• Design Objective

• Results• Conclusions and Recommendations

source: www.eere.energy.gov

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Solar Cell – Working Principle

• Based on photovoltaic effect• Stacked layers of silicon typical size 100 cm2)• Transparent coating• Metal grid to catch electrons• Busbar voltage

Source: http://www.solarserver.com/

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Solar Cell – Optimal Design

• Change materials• Reducing losses

• Full electrode / no electrode• Optimizing the amount of busbars• Optimizing the distance between the grid lines

source: www.eere.energy.gov

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Solar Cell – Optimal Design

• How to achieve an optimal design• Goal: use topology optimisation

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Optimisation Techniques

• Optimisation is about finding an optimal solution from a set of alternatives

• General formulation:

• Objective functions• Constraints• Sensitivity information

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Topology Optimisation

• In general: Optimises a material layout within a given design space

• Material density as a variable

• Proven to be successful in mechanics

• Strength lies in the complete design freedom

• Never tried on solar cell electrode design

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Topology Optimisation

Design Area

Initial Conditio

n Design

Compute objective

Convergence check?

Compute sensitivity

information

Update design

Iteration 1 c = 100Iteration 2

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Topology Optimisation

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Finite element formulation

• 2D view of the solar cell• Grid vs transparent layer

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Challenges

• Shading• Non-Linear behavior• Current computations• Objective function• Sensitivity Analysis

• How to achieve an optimal electrode design in order to get a higher efficient solar cell?

• What is the best way of include the non linear behaviour?

• What is the best way of defining an objective?

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Non Linear Behaviour

• Dark current / Illuminated current density

• P = U I 145.5 W/m2 0.13095W 30x30mm

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Computing Currents

• 3 different methods• Averaged Voltage• Nodal voltage• Sample Points / Shape functions

• Compared to integral of current density

Averaged voltage current current Averaged current Sample voltage current

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Computing Currents

Vint

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Design Objective

• Standard objective : • New objective needed -> power• Kirchoffs law: Conservation of charge and currents

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Results

30x30mmP = 121.99 W/m2121.99/ 145.5 =83.8%Area fraction = 6.69%

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Results

• Parameters:• Shading• Density correction• Penalty factor for shading• Method of computing the current density• Position of the busbar• Busbar voltage• Size of the design area• Amount of incoming light• Objective function• Solver

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Results – single busbar 15x15mm

15x15mmP = 130.43 W/m2Area fraction = 3.2%

3.4x15mmP = 135.6371 W/m2Area fraction = 2.94 %

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Results – Point Connection

30x30mmP = 120.73 W/m2Area fraction = 6.65%

30x30mmP = 124.60 W/m2Area fraction = 5.55%

30x30mmP = 121.60 W/m2Area fraction = 4.57%

Initial electrode Obj: Power Obj:

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Results – busvoltage 30x30mm

0.48V 0.485V 0.49V

0.495V 0.505V 0.51V

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Results - Busvoltage

Power as a function of the busbar voltage

Optimised designs

Power as a function of the busbar voltage

For 7 different designs

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Results – 4 points

source: http://www.pv-tech.org

60x60mmP = 124.60 W/m2Area fraction = 5.56 %

120x120mm

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Conclusions

• Topology optimisation can be used to find electrode patterns.

• Voltage dependent current can be modelled in three ways

• Total power as objective gives the highest output power

• A lot of different parameters

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Recommendations

• Model• Verify model, compare the design using other FEM

software• Fabricate one of the designs obtained and compare

• Further additions• Use finer meshes to describe the electrodes in more

detail• Include busbar in the design• Price per kWh• Design robustness

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Thank you

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Results – Illumination

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Include Shading

• Using electrodes decreases amount of incoming light

• Transparent electrodes

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Computing Currents

• Exact current

• 3 different methods• Averaged Voltage• Nodal voltage• Sample Points

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Exponential functions

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Research Questions

• What is the best way of defining the currents?• What is the best way of defining an objective?

• Voltage dependent current can be modelled in three ways

• Total power as objective gives the highest output power

• How to achieve an optimal electrode design in order to get a higher efficient solar cell?

• Topology optimisation can be used

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Current density / increments

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efficiency

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Increase