Transcript PPTX - TU Delft Repositories

Topology optimization of Metallisation Patterns in
Photo Voltaic applications
Master Thesis Project
R.S. Heemskerk
Supervisors: Dr. ir. M. Langelaar, Prof.dr.ir A. van Keulen
08/04/2013
Topology optimization in PVCells
1
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
08/04/2013
Topology optimization in PVCells
2
Contents
•
•
•
•
Solar Cell – Working Principle
Solar Cell – Optimal Design
Optimisation
Modelling
source: www.eere.energy.gov
• Finite element formulation
• Non linear behaviour
• Design Objective
• Results
• Conclusions and Recommendations
08/04/2013
Topology optimization in PVCells
3
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/
08/04/2013
Topology optimization in PVCells
4
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
08/04/2013
Topology optimization in PVCells
5
Solar Cell – Optimal Design
• How to achieve an optimal design
• Goal: use topology optimisation
08/04/2013
Topology optimization in PVCells
6
Optimisation Techniques
• Optimisation is about finding an optimal solution from a set
of alternatives
• General formulation:
• Objective functions
• Constraints
• Sensitivity information
08/04/2013
Topology optimization in PVCells
7
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
08/04/2013
Topology optimization in PVCells
8
Topology Optimisation
1
Iteration 2
Design
Area
Initial
Condition
Update
design
Compute
sensitivity
information
08/04/2013
c = 100
Design
Compute
objective
Convergence
check?
Topology optimization in PVCells
9
Topology Optimisation
08/04/2013
Topology optimization in PVCells
10
Finite element formulation
• 2D view of the solar cell
• Grid vs transparent layer
08/04/2013
Topology optimization in PVCells
11
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?
08/04/2013
Topology optimization in PVCells
12
Non Linear Behaviour
• Dark current / Illuminated current density
•P=UI
08/04/2013
145.5 W/m2
0.13095W
30x30mm
Topology optimization in PVCells
13
Computing Currents
• 3 different methods
• Averaged Voltage
• Nodal voltage
• Sample Points / Shape functions
Averaged voltage  current
current  Averaged current
Sample voltage current
• Compared to integral of current density
08/04/2013
Topology optimization in PVCells
14
Computing Currents
Vint
08/04/2013
Topology optimization in PVCells
15
Design Objective
• Standard objective :
• New objective needed -> power
• Kirchoffs law: Conservation of charge and currents
08/04/2013
Topology optimization in PVCells
16
Results
30x30mm
P = 121.99 W/m2
121.99/ 145.5 =83.8%
Area fraction = 6.69%
08/04/2013
Topology optimization in PVCells
17
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
08/04/2013
Topology optimization in PVCells
18
Results – single busbar 15x15mm
15x15mm
P = 130.43 W/m2
Area fraction = 3.2%
08/04/2013
3.4x15mm
P = 135.6371 W/m2
Area fraction = 2.94 %
Topology optimization in PVCells
19
Results – Point Connection
Initial electrode
30x30mm
P = 120.73 W/m2
Area fraction = 6.65%
08/04/2013
Obj: Power
30x30mm
P = 124.60 W/m2
Area fraction = 5.55%
Obj:
30x30mm
P = 121.60 W/m2
Area fraction = 4.57%
Topology optimization in PVCells
20
Results – busvoltage 30x30mm
0.48V
0.485V
0.495V
0.505V
08/04/2013
0.49V
0.51V
Topology optimization in PVCells
21
Results - Busvoltage
Power as a function of the busbar voltage
Optimised designs
08/04/2013
Power as a function of the busbar voltage
For 7 different designs
Topology optimization in PVCells
22
Results – 4 points
60x60mm
P = 124.60 W/m2
Area fraction = 5.56 %
08/04/2013
source: http://www.pv-tech.org
120x120mm
Topology optimization in PVCells
23
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
08/04/2013
Topology optimization in PVCells
24
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
08/04/2013
Topology optimization in PVCells
25
Thank you
08/04/2013
Topology optimization in PVCells
26
Results – Illumination
08/04/2013
Topology optimization in PVCells
27
Include Shading
• Using electrodes decreases amount of incoming light
• Transparent electrodes
08/04/2013
Topology optimization in PVCells
28
Computing Currents
• Exact current
• 3 different methods
• Averaged Voltage
• Nodal voltage
• Sample Points
08/04/2013
Topology optimization in PVCells
29
Exponential functions
08/04/2013
Topology optimization in PVCells
30
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
08/04/2013
Topology optimization in PVCells
31
Current density / increments
08/04/2013
Topology optimization in PVCells
32
efficiency
08/04/2013
Topology optimization in PVCells
33
Increase
08/04/2013
Topology optimization in PVCells
34