R.S. Heemskerk Supervisors: Dr. ir . M. Langelaar , Prof.dr.ir A. van Keulen
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Transcript of R.S. Heemskerk Supervisors: Dr. ir . M. Langelaar , Prof.dr.ir A. van Keulen
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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