multiphysics simulation of pv modules

82 Pages·2016·4.45 MB·English

by  Pankaj Arora

MULTIPHYSICS SIMULATION OF PV MODULES

Pankaj Arora

Thesis to obtain the Master of Science Degree in
Energy Engineering and Management

Supervisors: M.Sc. Matthieu Ebert
Prof. Susana Isabel Pinheiro Cardoso de Freitas

Examination Committee
Chaiperson: Prof. Luís Filipe Moreira Mendes
Supervisor: Prof. Susana Isabel Pinheiro Cardoso de Freitas
Member of the Committee: Dr. Vânia Cristina Henriques Silvério

October 2016

ABSTRACT
Modeling and simulation of Photovoltaic (PV) modules play an important role for the development of the
technology and evaluation of new designs. A Finite Element Method (FEM) based multiphysics simulation
software package is used in this work to study and analyze optical, thermal and electrical behavior of PV
modules. An increase in transmittance by 10-15% at low elevation angles and reduction in busbar/ribbon
shadow loss by almost 3% of cell irradiance is calculated from optical simulations of structured glass
models. To determine the temperature distribution in a PV module, a novel thermal model based on the
optical properties of module components is presented. Electrical (ohmic) loss in the emitter for
homogeneous and inhomogeneous cell illumination is studied. Using coupled optical and electrical
simulations, performance of grid models is investigated. Validation of the multiphysics study comprising of
ray-tracing and heat transfer tools is done by outdoor experiments. Experiment and simulation results lay
within an average absolute temperature difference of 0.6 2⁰C for three different illumination cases
investigated.

Keywords- Photovoltaic (PV) modules; Finite Element Method; Multiphysics Simulation; Structured glass

RESUMO
A modelação e simulação de módulos fotovoltaicos são etapas importantes no desenvolvimento de
tecnologias e qualificação de novos desenhos. Nesta tese aplicamos códigos de simulação baseados em
métodos de elementos finitos para estudar e analizar as caracteristicas ópticas, térmicas e eléctricas de
módulos fotovoltaicos. De acordo com os cálculos realizados com modelos baseados em vidro
estruturado, é possível obter aumentos de transmitância na ordem de 10-15% em baixos ângulos e
diminuição do efeito de sombra em quase 3% da célula. Apresentamos um modelo inovador para a
distribuição de temperatura no módulo fotovoltaico, baseado nas propriedades ópticas dos componentes
do módulo. Os efeitos dissipativos por condução de corrente eléctrica (perdas resistivas) são considerados
no modelo, para perfis de iluminação homogénea e inhomogénea. Neste trabalho investigamos o
desempenho dos modelos em rede, acoplando simulações ópticas e eléctricas. Finalmente, a validação
dos modelos baseados em raios de luz e transferência de calor é feita com experiências no exterior. Os
resultados experimentais estão concordantes com as simulações, indicando diferenças de temperatura de
0.6 2⁰C, para as três situações estudadas.
Palavras-Chave- Módulos fotovoltaicos; Método de elementos finitos; Simulação Multiphysics; vidro
estruturado
1
CONTENTS

NOMENCLATURE .................................................................................................................. iii
ABBREVIATIONS ................................................................................................................... v
LIST OF FIGURES ................................................................................................................. vi
LIST OF TABLES.................................................................................................................. viii
1 INTRODUCTION ............................................................................................................. 1
2 THEORETICAL BACKGROUND ........................................................................................ 5
2.1 Photovoltaic modules ............................................................................................................ 5
2.1.1 Standard modules: ........................................................................................................ 5
2.1.2 Relation between cell temperature and electrical efficiency .............................................. 8
2.2 Finite Element Method (FEM) ................................................................................................ 8
2.3 Ray optics .......................................................................................................................... 13
2.3.1 Reflection of light ........................................................................................................ 14
2.3.2 Refraction of light........................................................................................................ 14
2.3.3 Fresnel equations ........................................................................................................ 15
2.3.4 Absorption of light in a medium ................................................................................... 17
2.4 Heat transfer ...................................................................................................................... 18
2.4.1 Heat conduction .......................................................................................................... 18
2.4.2 Heat convection .......................................................................................................... 19
2.4.3 Radiation .................................................................................................................... 19
2.4.4 Heat balance equation ................................................................................................. 20
2.5 Electric (ohmic) losses ........................................................................................................ 21
Emitter power loss ..................................................................................................................... 22
3 OPTICAL MODEL .......................................................................................................... 25
3.1 Assumptions of the optical simulation: ................................................................................. 27
3.2 Boundary conditions ........................................................................................................... 27
3.3 Results and discussion ........................................................................................................ 28
3.4 Improvement in transmittance ............................................................................................ 30
3.4.1 Model designs (structure development) ........................................................................ 31
3.4.2 Assumptions and boundary conditions .......................................................................... 33
3.4.3 Results and discussion ................................................................................................. 33
3.5 Optical study to compute ribbon shadow loss ....................................................................... 37

i
4 THERMAL MODEL ......................................................................................................... 39
4.1 Model description and nomenclature:................................................................................... 39
4.2 Assumptions of the simulation ............................................................................................. 40
4.3 Results and discussion ........................................................................................................ 41
4.4 Thermal modeling for inhomogeneous irradiance .................................................................. 44
5 ELECTRICAL MODEL ..................................................................................................... 47
5.1 Simulation of a simple 3-D model ........................................................................................ 47
5.1.1 Model description and nomenclature: ........................................................................... 47
5.1.2 Assumptions and boundary conditions for the simulation: .............................................. 48
5.1.3 Simulation results for the simple 3-D model .................................................................. 48
5.2 Simulation of cells with inhomogeneous illumination ............................................................. 49
5.2.1 Model design .............................................................................................................. 50
5.2.2 Assumptions of the simulations .................................................................................... 53
5.2.3 Results and discussion ................................................................................................. 53
5.3 Coupled optical and electrical study of structured-glass modules ........................................... 55
6 EXPERIMENTAL VERIFICATION ................................................................................... 57
6.1 Experimental set-up ............................................................................................................ 57
6.2 Experiment results .............................................................................................................. 59
6.3 Multiphysics simulation ....................................................................................................... 60
6.3.1 Assumptions of the simulation: .................................................................................... 60
6.3.2 Boundary conditions of the simulation: ......................................................................... 61
6.4 Results and discussion ........................................................................................................ 61
7 CONCLUSIONS ............................................................................................................. 65
APPENDIX ........................................................................................................................... 67
REFERENCES ....................................................................................................................... 67

ii
NOMENCLATURE
Symbol Definition Unit
Absorption coefficient 1/m
Volumetric temperature coefficient 1/K
Emissivity -
Stefan-Boltzmann constant W/(m2K4)
Standard deviation m

Volumetric mass density kg/m3
Emitter sheet resistivity Ω/square

λ Wavelength m
Cell efficiency -

Efficiency at reference temperature -

Angle of incidence degree

Angle of reflection degree

Angle of refraction degree

Temperature gradient K/m
ΔT Temperature difference K
c Speed of light in medium m/s
c Speed of light in vacuum m/s
0
Specific heat capacity J/(kg K)

d Distance travelled by light ray m
Distance between alternate fingers m

ds Differential length element m
h Convective heat-transfer coefficient W/(m2K)
Current A
Irradiance intensity W/m2

Incident light intensity W/m2

Maximum power point current A

Peak Irradiance intensity of distribution W/m2

Photocurrent A

Diode saturation current A

Short-circuit current A

light intensity entering the loss material W/m2

J Current density A/m2
k Imaginary part of refractive Index -
iii
Thermal conductivity W/(mK)

l Finger length m
m Ideality factor -
n Real part of refractive Index -
N Complex representation of refractive index -
oc Open-circuit -
Emitter power loss W

Maximum power W

Conductive heat flux W/m2

Convective heat flux W/m2

Radiative heat flux W/m2

Useful heat energy W/m2

Q Internal heat generation W/m2
r Position vector m
P-type reflection coefficient -

S-type reflection coefficient -

Emitter resistance Ω

Shunt resistance Ω

P-type reflection power coefficient -

Series resistance Ω

S-type reflection power coefficient -

sc Short-circuit -
P-type transmission coefficient -

S-type transmission coefficient -

T Temperature K
T Ambient temperature K
amb
Cell temperature K

P-type transmission power coefficient -

Reference temperature K

S-type transmission power coefficient -

v Wind velocity m/s
Maximum power point voltage V

Open circuit voltage V

Thermal voltage V

y Distance of element from cell-center m
iv
ABBREVIATIONS
AM Air Mass ratio
AR Anti-Reflecting
CPV Concentrated Photovoltaic
CTM Cell-To-Module
DNI Direct Normal Irradiance
EVA Ethylene Vinyl Acetate
FEA Finite Element Analysis
FEM Finite Element Method
FF Fill Factor
GHI Global Horizontal Irradiance
HPC High Performance Computing
IEC International Electrotechnical Commission
IR Infrared
ISE Institute for Solar Energy Systems
NOCT Nominal Operating Cell Temperature
PDE Partial Differential Equations
PV Photovoltaic
STC Standard Testing Conditions
UV Ultraviolet

v
LIST OF FIGURES
Figure 1.1 Light trapping in a structured glass; ray undergoes multiple reflection due to 2
the pyramid-like glass structures, thereby reducing the solar energy finally lost
in reflection
Figure 2.1 Cut-section of a standard PV module showing the different components 5
Figure 2.2 Equivalent circuit of a solar cell as a double-diode model 6
Figure 2.3 Different steps involved to perform a Finite Element Analysis 9
Figure 2.2 Mesh of a model for FEM study; level of discretization in a specific part 11
depends on the importance of the part on the particular study
Figure 2.5 Mesh convergence study for a numerical solution; increasing mesh density 12
reduces difference between numerical solution and exact solution
Figure 2.6 Reflection and refraction of light on a plane surface when an incident ray 14
strikes an interface between two media of different refractive indices
Figure 2.7 Relation of reflection and transmission power coefficients to Incidence angle 16
for media with refractive indices n=1 and n=1.5
1 2
Figure 2.8 Cross-section of a solar cell showing different series resistance contributors 21
Figure 2.9 A small cross-section of a solar cell. A relation of power loss due to lateral 22
current flow in the emitter layer of the cross-section is evaluated based on this
figure
Figure 3.1 Solar spectrum (AM 1.5) and silicon absorption spectrum 25
Figure 3.2 Transmittance of a 3.2 mm thick low-iron soda lime glass against wavelength 26
Figure 3.3 Depiction of incidence, elevation and azimuth angles 27
Figure 3.4 Comparison of glass transmittance values obtained from simulation and 28
analytical methods
Figure 3.5 Simulation result showing rays incident on the glass medium from air at 29
elevation angle of 30⁰; rays undergo reflection and refraction at the media
interface according to Fresnel’s equations
Figure 3.6 Different glass models studied. An isometric view and top view for each model 30
type is shown
Figure 3.7 Transmittance computed in the 5 different structured glass models at different 33
elevation and azimuth angles and their comparison to transmittance of flat
glass
Figure 3.8 Tracing of rays falling on the type 5 glass design at elevation angle of 60⁰ and 34
azimuth angle of 60⁰ at (a) flat plateau of the pyramids, (b) sides of the
pyramids
Figure 3.9 Simulation results showing irradiance profile at the base of type 5 glass when 35
(a) 3000 rays, (b) 12000 rays, and (c) 30000 rays are incident on the glass
surface at (I) Elevation angle=0⁰, Azimuth angle=0⁰ and (II) Elevation
angle=30⁰, Azimuth angle=60⁰
Figure 3.10 Module with busbar/ribbons placed under the groove of glass pyramid 36
structures (a) isometric view of the model (b) side view of the structure
showing location of busbar
vi