Masterthesis Ismail Shoukry Final

Master of Science Thesis
Bifacial Modules-
Simulation and Experiment
Ismail Shoukry
2657503
Supervised by
Prof. J. H. Werner Dr. Eckard Wefringhaus
Dr. Joris Libal
University of Stuttgart International Solar Energy
Institute for Photovoltaic Research Center Konstanz
Pfaﬀenwaldring 47 Rudolph-Diesel-Straße 15
70569 Stuttgart 78467 Konstanz
5. November 2015

Statement
I hereby certify that this research paper has been composed by myself, and describes
my own work, unless otherwise acknowledged in the text. All references and verbatim
extracts have been quoted, and all sources of information have been specifically acknowl-
edged. I confirm that this work is submitted in partial fulfillment for the degree of M.Sc.
in the University of Stuttgart and has not been submitted elsewhere in any other form
for the fulfillment of any other degree or qualification.
Constance, 09.10.2015

Abstract
Bifacial cells, which are locally rear contacted silicon solar cells, enable the absorption
of light by the cell’s rear side, hence increasing the generated current and therewith the
energy yield, with the biggest contribution coming from the ground-reflected irradiance.
A software tool for the simulation of the performance of bifacial modules is therefore
developed in the scope of this thesis and used to predict the bifacial gain BF.
The performed calculations yielded bifacial gains of up to 35 % for a stand-alone module.
By using white reflective plates beneath the modules, BF can be increased to 55 %, while
a bifacial module mounted on a sun-belt tracking system near the Equator, would result
in BF ≥ 60 %. The bifacial gain is decreased in a field installation, where the optimum
distance between module rows is estimated at 3±0.5 m, dropping to circa 32 % and 28 %
for the best and worst performing modules, respectively. The results of the simulation
are verified by a set of short-term and long-term outdoor measurements.

Zusammenfassung
Silizium Solarzellen mit lokalen Rückseitenkontakten, sogenannte bifaziale Zellen, können
Licht auch von der Rückseite absorbieren. Dies erhöht den generierten Strom und damit
den Energieetrag, wobei der größte Beitrag von der bodenreflektierten Strahlung kommt.
Ein Werkzeug für die Simulation der Leistung von bifazialen Modulen wurde im Rahmen
dieser Masterthesis entwickelt und wurde zur Bestimmung des Bifacial Gain BF, benutzt.
Die durchgeführten Simulationen liefern einen BF von bis zu 35 %, für ein alleinstehen-
des Modul. Weiße Reflektionsplatten unter den Modulen könnten BF auf 55 % erhöhen,
während eine ein-achsige Sonnennachführung in Äquatornähe zu BF ≥ 60 % führen
würde. BF sinkt jeweils auf ca. 32 % und 28 % für das leistungsstärkste und leistungs-
schwächste Modul in einem Feld, wobei die Berechnung des optimalen Abstands zwischen
den einzelnen Modulreihen einen Wert von 3±0.5 m ergibt. Die Ergebnisse der Simulation
wurden anhand einer Reihe von Außenmessungen bestätigt.

Contents
1 Introduction 1
2 Background 5
2.1 The Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Solar irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Reflection and albedo . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Basics of photovoltaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Solar cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1.1 Standard chrystalline silicon solar cell . . . . . . . . . . . 11
Cell structure . . . . . . . . . . . . . . . . . . . . . . . 11
Electrical model . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1.2 Shift from p-type to n-type . . . . . . . . . . . . . . . . . 13
2.2.1.3 Bifacial cell . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Cell structure . . . . . . . . . . . . . . . . . . . . . . . 14
Cell efficiency . . . . . . . . . . . . . . . . . . . . . . . 14
Electrical model . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Solar module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Solar park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Existing research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Simulation 23
3.1 Optical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Module installation parameters . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Sun’s position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.3 Direct irradiance Idir . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.4 Diffuse irradiance Idiff . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.5 Reflected irradiance Irefl . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.6 View factor FA1→A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.6.1 Influence of shading . . . . . . . . . . . . . . . . . . . . . 33
3.1.6.2 Influence of blocking . . . . . . . . . . . . . . . . . . . . . 35
3.1.6.3 Influence of white sheet . . . . . . . . . . . . . . . . . . . 36

II Contents
3.2 Electrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1 Module power Pmpp . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2 Annual energy yield Y . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.3 Bifacial gain BF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1.1 Weather and irradiance . . . . . . . . . . . . . . . . . . . 41
3.3.1.2 Module performance . . . . . . . . . . . . . . . . . . . . . 43
3.3.2 Sun’s position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Standard module . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.4 Stand-alone bifacial module . . . . . . . . . . . . . . . . . . . . . . 46
3.3.4.1 Tilt angle γM . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.4.2 Module elevation hM . . . . . . . . . . . . . . . . . . . . . 47
3.3.4.3 Diffuse irradiance factor fD . . . . . . . . . . . . . . . . . 50
3.3.4.4 Ground surface size . . . . . . . . . . . . . . . . . . . . . . 52
3.3.4.5 Ground albedo α . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.4.6 Model complexity . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.4.7 Time and date . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.5 East-west vertically mounted stand-alone bifacial module . . . . . . 58
3.3.6 Stand-alone bifacial module with one-axis tracking . . . . . . . . . 61
3.3.7 Bifacial module field . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.7.1 Adjacent modules . . . . . . . . . . . . . . . . . . . . . . 64
3.3.7.2 Additional module rows . . . . . . . . . . . . . . . . . . . 66
3.3.7.3 Module field . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Validation 73
4.1 Short-term experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.1 Location and setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.2 Experiment I: Reflective surface size . . . . . . . . . . . . . . . . . 74
4.1.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1.3 Experiment II: Blocking effect . . . . . . . . . . . . . . . . . . . . . 78
4.1.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Long-term measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 Location and setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.2 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Conclusions 83
Ismail Shoukry Bifacial Modules: Simulation and Experiment

Contents III
Appendix 87
Figures 97
Tables 101
Abbreviations 103
Symbols 105
References 114
Bifacial Modules: Simulation and Experiment Ismail Shoukry

IV Contents

Chapter 1
Introduction
A nation’s Gross Domestic Product (GDP) and therefore, its economic growth and wel-
fare, are directly connected to its energy consumption and to the constant availability of
electricity and other forms of energy. With the emergence of several developing economies
and the exponential growth of the human population, the rising demand for energy can-
not be sustainably met by burning the ever decreasing reserves of fossil fuels. Hence,
renewable energies, which offer an ecological and economical alternative to fossil fuels,
are already playing a big role in energy production, a role which is only expected to grow
further, as visible in figure 1.1.
SOLAR POWER PLANTS
A SUSTAINABLE INVESTMENT
2
2000
GLOBAL ENERGY MIX UP TO 2100
2010 2020 2030 2040 2050 [EJ/a]
2100
800
400
200
0
Figure 1.1: Global energy mix up to 2100 as forecast by the Scientific Advisory Board of the
German government [1]. Photovoltaic is expected to provide a large portion of the
world’s energy usage in the future.
Harvesting the sun’s energy and directly converting it into electricity using photovoltaic
modules is projected to have the biggest contribution to the future global energy mix.
This can be attributed to the comparably low Levelized Cost Of Energy (LCOE) of

2
photovoltaics, which has been rapidly decreasing, especially since 2008, as the module
prices in figure 1.2 show. The slight price increase before 2008 is caused by the rising
costs of contract poly-silicon material. The relatively constant decrease is linked to the
development of new processing techniques and new technologies which increase the energy
production of a single solar module, reducing the cost of the generated electricityd.
1990 1995 2000 2005 2010 2015
1
2
3
4
5
6
Averagemoduleprice[$/W]
Figure 1.2: Module average selling price trend from 1991 to 2014 in $/W [2]. Notice the increase
in module price in 2008, caused by the rising of raw poly-silicon prices. Prices have
been rapidly decreasing ever since.
One novel concept, which promises to decrease the LCOE even further, is the bifacial
module, which can absorb light from both module sides. With the use of solar cells with
local rear contacts and transparent rear passivation, it is possible for the incident light to
penetrate the cell from both sides, generating a higher current than in standard solar cells,
and hence resulting in a higher power output. Thanks to an innovative cell design, the
production process of bifacial solar cells is highly compatible with existing standard solar
cell production lines, making the integration of the new process in existing production
facilities relativity easy and highly cost effective. This, in addition to the higher annual
energy yield of a stand-alone bifacial module of up to 30 %, adds greatly to the appeal of
bifaciality, explaining the increase in the market share of bifacial crystalline silicon solar
cells as forecast by the International Technology Roadmap for Photovoltaic (ITRPV) in
figure 1.3. The gain in the energy yield is caused mainly by the extra irradiance reflecting
diffusely off the ground and reaching the rear side of the module, thus increasing the
generated current in the cells and enhancing the overall electricity production of the
photovoltaic system by up to 30 %.
In order to determine the LCOE of bifacial modules and therewith their profitability, it is
necessary to determine exactly how high the gain in energy production is. However, still
no commercial tool for calculating the annual energy yield of a bifacial module field exists.
The calculation of the energy production of bifacial modules is more complex, compared

Chapter 1. Introduction 3
2014 2015 2017 2019 2022 2025
0
20
40
60
80
100
Bif.Monofacial
Marketshare[%]
Figure 1.3: Worldwide market shares for monofacial and bifacial monocrystalline solar cells [3].
Market share of bifacial PV is expected to increase in the near future, due to the
higher energy yield, among other advantageous.
to that of a standard module. In addition to the standard dependencies, it also depends
on the module installation height, the ground reflection, the distance between module
rows and between neighbouring modules (of the same row), and the self shadowing of the
modules on the ground, with existing simulation tools only partially tackling the issue,
modelling only installations with one module.
Therefore, in this thesis, a model for simulating the annual energy yield of bifacial modules
is developed and introduced, to determine the exact gain in energy production by bifacial
modules. After an introduction in the required theoretical knowledge in chapter 2, the
methodology and results of the undertaken simulation are described in chapter 3, showing
bifacial gains of a stand-alone module of up to 34 % for an albedo of 0.5, while the worst
performing module in a field with a distance of 2.5 m between the module rows has a
bifacial gain of up to 27 %. Enhancing the ground albedo using white reflective plates
can further increase the bifacial gain to 55 %. Furthermore, it is shown, that a tracked
bifacial module has a 62 % higher energy yield compared to a fixed south-facing monofacial
module. To verify the correctness of the simulation results, a set of short term experiments
are undertaken at the International Solar Energy Research Center (ISC) in Constance, the
results of which are compared to the observations from the simulation, and are described
in chapter 4, showing good correlation between the measured and simulated bifacial gain.
Finally, the results are summarized and interpreted in chapter 5, where additionally,
conclusions on the optimal setup of bifacial modules and the proper standardization of
the measurement and assessment of the performance of bifacial modules are drawn.

4

Chapter 2
Background
In order to fully comprehend the individual steps undertaken in the simulation and the
various occurring eﬀects which are discussed at a later point, a common ground of basic
knowledge in several issues has to be established. Familiarity with the behaviour of
light passing through the atmosphere and the complete process of photovoltaic energy
generation from solar cell to solar park is required. Such knowledge will be attained in
the following sub-chapters, where also the thus far existing research in the simulation and
measurement of bifacial modules is introduced.
2.1 The Sun
The Sun, being the largest (and only) nuclear fusion reactor in our solar system, is the
basis of all life on Earth and the source of virtually all forms of energy utilized by humans,
whether directly or indirectly. Earth’s surface is warmed up by the Sun’s energy causing
transfers of heat and pressure in weather patterns, resulting in air currents that drive
wind turbines to generate electricity. The heat also evaporates water which later falls as
rain and builds up behind dams, and can be utilized via hydro-power. Even burning fossil
fuels is just another way of reclaiming the power of sunlight, which when striking a plant
was trapped through photosynthesis, stored in chemical bonds and turned into fossil
fuels such as coal, oil or natural gas after millions of years of geological and chemical
activity underground. However, the most direct way of utilizing sunlight is through
photovoltaic systems, where sunlight is directly converted to electricity using panels with
cells constructed from semi-conductor materials. The Sun is a predominant source of
primary energy, as visible in ﬁgure 2.1, which visualizes the results of calculations carried
out among others by the German Aerospace Center (DLR), which suggest that the amount
of solar irradiation reaching Earth annually is several thousand times larger than the
annual global electricity consumption.

6 2.1. The Sun
Research Centre (JRC) also collects and publishes
European solar irradiation data from 566 sites1.
Where there is more Sun, more power can be
generated. The sub-tropical areas of the world
offer some of the best locations for solar power
generation. The average energy received in Europe
is about 1,200 kWh/m2 per year. This compares
with 1,800 to 2,300 kWh/m2 per year in the
Middle East.
While only a certain part of solar irradiation can be
used to generate electricity, this ‘efficiency loss’
d t t ll t fi it it d
WIND
SOLAR (CONTINENTS)
BIOMASS
GEOTHERMAL
OCEAN & WAVE
HYDRO
COAL
GAS
OIL
NUCLEAR
PRIMARY ENERGY
CONSUMPTION
FOSSIL FUELS ARE EXPRESSED WITH REGARD
TO THEIR TOTAL RESERVES WHILE RENEWABLE ENERGIES
TO THEIR YEARLY POTENTIAL.
GLOBAL ANNUAL
ENERGY CONSUMP
ANNUAL SOLAR
IRRADIATION
TO THE EARTH
GLOBAL ANNUAL
ENERGY CONSUMPTION
Figure 2.1: Solar irradiation versus established global energy resources and global annual energy
consumption [4]. Notice how the amount of annual solar irradiation is much larger
than the annual global electricity consumption.
Since the electricity generated by photovoltaic systems is directly dependent on the solar
irradiation, it is necessary to know exactly how much solar irradiation reaches Earth’s
surface and fully understand the physics behind sunlight and the effects that take place,
when it passes through the atmosphere.
2.1.1 Solar irradiance
Solar irradiance reaching Earth’s atmosphere is dependent on the time of year or on the
distance of Earth to the Sun, varying by 6.9 % during a year between 1.321 kW/m2
in early
July to 1.412 kW/m2
in early January. The solar constant of 1.367 kW/m2
is defined as
the solar irradiance reaching Earth’s atmosphere at a distance of one Astronomical Unit
AU from the Sun, which is the mean distance from Earth to the Sun [5, 6]. However, only
a fraction of the solar irradiance reaches Earth’s surface. Figure 2.2 shows the spectrum of
the incoming extraterrestrial light, the spectrum of the light that reaches Earth’s surface
and the spectrum that can be utilized by single junction silicon based photovoltaic cells.
As visible in figure 2.2, the intensity of the light at sea level is only a fraction of the
intensity outside Earth’s atmosphere. Sunlight passing through the atmosphere, which
consists mostly of oxygen and nitrogen, experiences several effects. Part of the solar ir-
radiance is absorbed, another part is reflected and another is diffusely scattered by the
gas molecules in the air and by clouds. Light’s ability to pass through the atmosphere
also depends on its wavelength, which explanes the differently strong reductions in the
light intensity at different wavelengths. Hence, the longer light travels through the atmo-
sphere, the more intensity is lost through absorption or reflection by the air molecules.
Consequently, solar irradiance varies spatially, decreasing with increasing latitude, and
varies during the day, decreasing with increasing time difference to the solar noon. The
distance light has to travel through the atmosphere and the therewith connected intensity

Chapter 2. Background 7
Wavelength at which photon energy
equals silicon bandgap
Theoretical single junction solar cell
response (maxumum 31% efficient)
At upper atmosphere
At sea level
Wavelength (nm)
UV Visible Infrared
250 500 750 1000 1250 1500 1750 2000 2250 2500
0
0.5
1.0
1.5
2.0
2.5
SpectralIrradiance(W/m2/nm)
Figure 2.2: The energy spectrum of sunlight at upper atmosphere and at sea level and the
spectrum that can be theoretically utilized by single junction silicon solar cells [7].
Light intensity at sea level lower than at upper atmosphere, due to absorption and
reflectance in the atmosphere.
reduction is quantified by the Air Mass AM coefficient. With the syntax ”AM” followed
by a number, the Air Mass coefficient is the direct optical path length L which light takes
through the atmosphere normalized to the shortest possible path length L0, that is the
distance vertically upwards at the Equator, and is defined as
AM =
L
L0
=
1
cos θz
, (2.1)
where the zenith angle θz is the angle between the Sun’s position to the vertical axis.
Sunlight consists of two main components, direct and diffuse radiation. Direct radiation,
also called beam or direct beam radiation, is used to describe solar radiation travelling
directly in a straight line from the Sun to Earth’s surface. Having a definite direction, it
can be completely blocked by a certain object, which then casts a shadow behind itself.
On the other hand, sunlight that has been scattered by molecules and particles in the
air, but that has still made it down to the surface is called diffuse radiation. It has no
definite direction and therefore does not cause objects to cast shadows, since it cannot be
completely blocked by an object. The direct (or beam) horizontal irradiance BHI and
the diffuse horizontal irradiance DHI quantify the amount of solar irradiation reaching
Earth’s surface on a horizontal plane with an area of 1 m2
for each component. The
global horizontal irradiance GHI is the total solar irradiance reaching Earth’s surface on
a horizontal plane with an area of 1 m2
, and is given by
GHI = BHI + DHI. (2.2)

8 2.1. The Sun
The amount of diffuse irradiance can be given using the diffuse irradiance factor fD, which
is defined as
fD = 100
DHI
GHI
. (2.3)
More important for the electricity generation from solar power is the total solar irradiation
on a tilted plane Itot, which also consists of a third component, namely the irradiance
reflected by the ground. Another difference is that the diffuse component of the solar
radiation is reduced, since when the receiving plane is tilted, radiation from some parts
of the hemisphere can no longer reach the plane’s surface. Itot is then defined as
Itot = Idir + Idiff + Irefl, (2.4)
where Idir, Idiff , and Irefl are the direct, diffuse and reflected components of the solar
irradiation on a tilted plane with an area of 1 m2
. Because of the importance of the
ground reflected component of solar irradiance for the electricity generation using bifacial
photovoltaic modules, it will be described in more detail in chapter 2.1.2.
2.1.2 Reflection and albedo
According to Dobos [8], albedo is defined as ”the fraction of the incident radiation that is
reflected from the surface”. It is a complex feature dependent on the soil characteristics
and other soil independent environmental factors. The soil dependent factors affecting
the albedo the most are the type of the vegetation covering the soil surface, the organic
matter content, the moisture of the soil and the chemical composition of the materials in
the soil [8, 9], where the albedo of a dry surface is higher than that of a moist soil with the
same chemical composition [9]. In addition, albedo varies with changing angle of incident
solar radiation, thus fluctuating seasonally and during the day [6, 5], where generally the
albedo is higher for lower sun height angles.
There are two mechanisms involved in the reflection of incident light by a surface, spectral
and diffuse reflection, which are visualized in figure 2.3, whereby the roughness of the
surface dictates which type predominates. Specular reflection, which occurs on the surface,
describes the mirror-like reflection of light from smooth surfaces like some metals and
water bodies, giving the considered surface a glossy appearance. Light from a single
incoming direction is reflected into a single outgoing direction, where the angle of the
incident ray with respect to the surface normal equals the angle of the reflected ray. Diffuse
reflection, originating beneath the surface, describes the reflection of an incident ray by
rough surfaces like paper or sand such that it is reflected at many angles instead of just
one, giving the surface a matte appearance. In this case, light travels through the body
beneath the surface, reflecting repeatedly off multiple particles until finally exiting the
surface in every direction. Lambertian reflection describes ideal diffuse reflecting surfaces,
which will reflect light equally in all directions, making the surface appear equally bright
regardless of the viewing angle.

surface
body
incident
light
direct
reflection
diffuse
reflection
Figure 2.3: The two reflection mechanisms, spectral and diffuse reflection. While spectral re-
flectance has a definite direction, diffuse reflection is scattered evenly in all directions.
The reflection of surfaces also varies for the different wavelengths of the incident solar
radiation, thus giving the surface its colour. An example of such variation of the albedo
with respect to the wavelength is visualized in figure 2.4 for sand, where the reduction of
the albedo for higher moisture contents is also shown. Because of the aforementioned vari-
ation, it is necessary to differentiate between spectral and total albedo, whereby ”spectral
albedo refers to the reflectance in a given wavelength [and] the albedo is calculated as an
integral of the spectral reflectivity times the radiation, over all wavelengths in the visible
spectrum” [8].
Wavelength (nm)
0
10
PercentReflectance
SAND
20
40
30
50
60
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
0-4% moisture content
5-12%
22-32%
Figure 2.4: Spectral reflectance of sand against wavelength of incident light for different moisture
contents [8]. The albedo decreases with increasing moisture content, due to the soil
moisture absorbing the incident radiation.
The albedo α is therefore an average of the spectral albedo over all wavelengths and over
the whole year, quantifying the average ability of a surface to reflect incident light. It
ranges from 0 to 1, where a value of 0 refers to a blackbody which theoretically absorbs
100 % of the incident radiation, and a value of 1 refers to an absolute white surface with
an ideal reflection, where 100 % of the incident radiation falling on the surface is reflected.

10 2.2. Basics of photovoltaics
Approximate ranges of albedo of various surfaces are summarized in table 2.1.
Table 2.1: Approximate ranges of albedo of various surfaces [8].
Surface type Albedo range
Blackbody 0
Forest 0.05 - 0.2
Grass and crops 0.1 - 0.25
Dark-colored soil 0.1 - 0.2
Sand 0.2 - 0.4
Mean albedo of Earth 0.36
Granite 0.3 - 0.35
Fresh snow 0.9
Water 0.1 - 1
Absolute white surface 1
In this thesis, the ground beneath the modules will be considered an ideal diffuse reflective
surface with Lambertian reflection characteristics. Light is therefore diffusely reflected
equally in every direction. The diurnal and seasonal variations in the albedo, as well as
its dependence on the incoming light’s wavelength, will be neglected. The term albedo
will therefore refer to the average albedo of a given surface over all wavelengths and over
the whole year. Since during most of the day, the variations in the albedo are relatively
small, increasing in the early morning and late evening [10], when the solar radiation
intensity is week and the resulting contribution to the energy production is very low, this
simplification should not cause large errors in the simulation.
2.2 Basics of photovoltaics
Photovoltaics (PV) is defined as a method of converting sunlight to a direct electrical
current using semi-conductor materials, whereby silicon is most widely used in the pho-
tovoltaic industry with a market share of over 90 % [11]. The basic principles of the tech-
nology have been established for years and the step-by-step process of converting sunlight
into direct current electricity has been discussed in detail in several books [12, 13, 14],
explaining all the technical terms involved in the process such as semi-conductors, doping,
p-n junction, band diagram and recombination, among others. The detailed functionality
of a solar cell and the exact chemical and physical processes occurring inside the cell will
therefore not be discussed in this thesis any further. In addition, since the improvement
of the efficiency of solar cells using new or improved processing techniques is not the focus
of this thesis, the specific steps of the production process will also not be explained. The
main purpose of the following chapters is consequently highlighting the major differences

between standard and bifacial solar cells, modules and parks respectively. In chapter
2.2.1, the structure of bifacial solar cells, which enables the absorption of light from both
sides of the cell is explained and compared to the structure of a standard solar cell. The
differences in module designs are introduced in chapter 2.2.2, whereas the influences of a
field installation on bifacial modules are established in chapter 2.2.3.
2.2.1 Solar cell
The solar cell is the core of photovoltaic systems and is the part, in which the electrical
current is generated. Consisting of semi-conductor materials, silicon (Si) in the case of the
devices used for the experiments conducted within the framework of this thesis, photons
from incoming solar radiation with an energy greater than the band-gap of silicon can
excite electrons into higher energy bands, creating an electrical current which can then
flow when connected to an electrical load. Since its market share of currently 90 % is not
expected to decrease significantly, at least during the coming decade, according to [15],
only crystalline silicon cell technology will be described in the following sub-chapters.
2.2.1.1 Standard chrystalline silicon solar cell
Cell structure
There exist numerous different technologies and silicon solar cell designs, originating from
different research centres and universities competing to achieve the highest cell efficiency.
All silicon based solar cells however, are based on a p-n junction and roughly have the
same basic structure, consisting of a base, an emitter, front and rear contacts and an anti
reflective layer, which is visualized in figure 2.5
n+ Si emitter
n++ Si emitter
p-type Si
front contact
AR layer (SiNx)
p+ Si layer
rear contact
Figure 2.5: Structure of a standard industrial p-type Cz-silicon solar cell with a selective emitter
and full surface back contact.
The base layer of the solar cell can be composed of either p-type or n-type silicon, which
is produced using boron or phosphorous doped silicon, respectively. With a share of over
80 % of the Czochralski (Cz) crystal production for PV, the majority of industrial standard

mono-crystalline silicon solar cells are based on boron doped p-type wafers, a phenomenon
which according to Libal and Kopecek [16] is mostly of ”historical background” and is
further driven by the currently 20 % lower costs of p-type wafers. Figure 2.5 visualizes
the structure of a standard solar cell with a p-type base layer, a selective emitter, an anti
reflective (AR) layer made from silicon-nitride (SiNx) and a full aluminium back surface
field (Al-BSF) and aluminium rear contact.
Electrical model
To understand the functionality and behaviour of a solar cell and to be able to predict and
simulate the processes occurring inside the cell from an electrical point of view, several
models were developed over the years, taking into account the various physical effects
taking place inside the cell. With an electrical model, the complex behaviour of a solar
cell can be replicated using basic electrical components, whose behaviour and functionality
are well understood, such as an electrical resistance or a diode. One of the most accurate
and widely used models for simulating solar cells, is the two-diode model, which is a more
advanced version of the single-diode model. Figure 2.6 schematically shows the equivalent
circuit of a monofacial solar cell using two diodes D1 and D2.
J
V
RS
RP
JD1 JD2
Jph
+
-
Figure 2.6: Two-diode model of a standard solar cell with the illumination dependent current
sourve Jph.
Whereas ”D2 is used to model Shockley-Read-Hall recombination currents in the space
charge region, ... D1 represents recombination currents elsewhere” [17], i.e. the Shockley-
Read-Hall and Auger recombination in the base and emitter, or surface recombination in
the front and rear. RP represents the parallel resistance working as a shunt, whereas the
resistance of the entire circuit is consolidated into RS. The codependency of the external
voltage V and current J is given by
J = JPh − JD1 − JD2 −
V + JRS
RP
. (2.5)
The photo current JPh represents the light generated current source and is linearly de-
pendent on the solar irradiance [18]. Due to irrelevance, the exact terms of the currents
JD1 and JD2 flowing through the two diodes, which were explicitly defined and discussed
in several previous works [19, 18, 20, 21, 17], will not be shown in this thesis. The last
component of the external current J is the current flowing through the shunt.

2.2.1.2 Shift from p-type to n-type
The first ever silicon solar cell, the ”Bell solar battery”, was produced on a n-type Cz-Si
wafer in 1954 [22]. In the 1960’s it has been shown that the electronic quality (minority
carrier lifetime) of n-type Si degrades under exposure to cosmic rays [23]. Since the most
important PV application in the 60’s and 70’s was supplying electricity for satellites in
space, the cell processes and materials were optimized for p-type Si wafers. By the time
the terrestrial PV market started to grow in the end of the 70’s, the cell processes and
materials were already established for p-type Si on a small industrial scale. Hence, the
phase of stronger market growth starting in the 90’s was based on p-type PV. However,
in recent years, the PV research community and industry industry are showing increased
interest in n-type c-Si solar cells, believing it to be the more suitable material for high
efficiency solar cells. The ITRPV predicts that the market share of n-type monocrystalline
silicon will increase in the following years, surpassing that of p-type monocrystalline Si
by the year 2020 [3], as represented by the blue bar in figure 2.7.
5.3 Products
Today’s wafer market for c-Si silicon solar cell manufacturing is dominated by casted materials
will achieve a market share in excess of 60% in 2015. However, this market share will eventuall
to below 50%. Simply distinguishing between mono-Si and mc-Si, as was done some years
insufficient. The c-Si materials market is further diversifying, as shown in Fig. 24. High-perfo
(HP) mc-Si material now dominates the casted silicon market. Due to its excellent performan
material is expected to replace conventional mc-Si completely by 2022. Monolike-Si has disap
today but is expected to come back with a market share of up to 8% in 2025.
Mono-Si is expected to make significant gains over casted material and will attain a share
than 47% in 2025. The roadmap confirms the predicted shift from p-type to n-type mono-S
the mono-Si material market, as described in former editions. Considerable volumes of Si
produced by other technologies such as kerfless or ribbon will appear after 2020.
Fig. 25 shows the different technologies that will be used for mono-Si crystallization. CCz w
significant gains in market share over classical Cz due to the former’s cost advantages. Float zo
material for producing cells of the highest efficiency is also expected to appear on the mono S
with a share of nearly 20% by 2025.
Fig. 24
World market sha
different wafer typ
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2014 2015 2017 2019 2022 2025
p-type mc-Si p-type HPmc-Si p-type monolike-Si
p-type mono-Si n-type mono-Si other (e.g. ribbon, ker ess, ...)
ITRPV2015
Figure 2.7: World market shares for different wafer types [3]. The market share of n-type mono-
crystalline silicon is expected to grow strongly.
Since the current 20 % higher price for n-type wafers is only a consequence of the current
respective production capacities and ”there is no technological difference between the
growths of p- and n-type crystals that would explain an increased manufacturing cost for
n-type wafers” [16], the cost of n-type wafers is expected to decrease and meet the cost
of p-type wafers in the near future. The decreasing costs and the physical superiority of
phosphorous doped silicon over boron doped silicon as the base of a solar cell, explain the

current shift to n-type c-Si solar cells. Not only does n-type Si react less sensitively to
diffusion and other high temperature processes, but it also exhibits substantially higher
minority carrier diffusion lengths than p-type Cz-Si, due to its reduced sensitivity to
common metallic impurities [24]. Light induced degradation (LID), which occurs because
of boron in p-type Si wafers, does not exist in the phosphorous doped n-type Si wafers.
2.2.1.3 Bifacial cell
Cell structure
The main difference in cell structure, that allows bifacial solar cells to absorb solar radi-
ation from both sides, is the lack of non-transparent Al-BSF and contacts, which block
incoming light in standard cells. Like the front contact, the back contact in bifacial cells
is local. A layer of SiNx is also applied on the back to reduce reflection and the n+
BSF
repels the majority carriers produced in the base layer, thus passivating the rear side.
This allows for light to penetrate the solar cell from the back side generating majority
carriers mostly close to the rear surface. The minority carriers generated close to the rear
end of the solar cell, whether holes in case of a p-type or electrons in case of a n-type base,
have to travel through the cell to the front contacts, which explains the need for a high
carrier lifetime, in order to reach high bifacial factors. The required carrier lifetime and
diffusion length can be achieved either using very high quality cost intensive p-type wafers
or standard n-type wafers, which explains why cell manufacturers are switching from p- to
n-type wafers for high efficiency, for use in bifacial and interdigitated back contact (IBC)
solar cells. The front side remains unchanged compared to standard solar cells, except
for using boron to dope the emitter instead of phosphorous in case of solar cells with a
n-type base layer, in order to achieve the necessary positive doping of the emitter. The
structure of a bifacial n-type Cz-silicon solar cell, which was explained above, is depicted
in figure 2.8.
p+ emitter
n-type Si
front contact
AR and passivation layer (SiNx)
n+ BSF
rear contact
AR and passivation layer (SiNx)
SiOx or AlOx
Figure 2.8: Structure of a bifacial n-type Cz-silicon solar cell. Notice the light sensitive rear side
with local contacts.

Cell efficiency
Bifacial solar cells have a slightly smaller front power than comparable standard cells with
a full surface rear contact. In standard cells the photons that pass through the cell and
are not absorbed on the first time, are reflected by the rear contact and pass through the
cell again, having another chance of generating an electron-hole pair. Due to the missing
full surface rear contact in bifacial solar cells, less photons are reflected back into the cell
for a second chance to generate an electron and the overall power decreases slightly. This
is however compensated by the comparably large amount of solar irradiation reaching the
cell’s rear side, generating electron-hole pairs, mostly close to the rear side surface. The
rear sides of bifacial solar cells do not perform as well as their front sides, with normal
bifaciality factors reaching values between 85 % and 95 % for n-type wafers, where the
bifaciality factor fB is defined as the ratio of the rear side efficiency ηcell,r to the front side
efficiency ηcell,f and is given by
fB = 100
ηcell,r
ηcell,f
. (2.6)
The main cause of the comparably smaller efficiency of the bifacial cell’s rear side is the
generation of the minority carriers close to the back surface. These have to travel to
the emitter at the front side of the cell, where they can then be transferred to the front
contact. Because of the longer path the minority carriers have to travel through the cell,
the chance for recombination is increased and the efficiency slightly drops. Hence, higher
wafer material quality decreases the recombination rates of the carriers generated by rear
side solar irradiation, thus increasing the rear side efficiency and driving the bifaciality
factor closer to 100 %.
Electrical model
With a small modification to account for the current generated by the rear side irradiance,
bifacial cells can also be characterized using the two-diode model introduced in chapter
2.2.1.1. The linearity of the front side photo current Jph,f and the rear side photo current
Jph,r has been shown [25, 26]. Consequently, the resulting photo current can be calculated
by the summation of the two components. Hence, the new equation for the modified two-
diode model for bifacial cells is given by
J = JPh,f + JPh,r − JD1 − JD2 −
V + JRS
RP
. (2.7)
This implies, that the electrical model of a bifacial solar cell needs to include a second
illumination dependent current source, which is parallel to the existing one, resulting in
the following adjusted schematic drawing of the two-diode model.

J
V
RS
RP
JD1 JD2
Jph,r
+
-
Jph,f
Figure 2.9: Two-diode model of a bifacial solar cell. Notice the second illumination dependent
current source, caused by the bifacial cell’s rear side.
2.2.2 Solar module
The next step in the solar energy generation chain is the production of the solar module,
which is the energy generating unit in a solar system. Solar modules are a packaged
assembly of typically 6x10 interconnected solar cells, with peak powers ranging from 230
W to 320 W. The 60 solar cells are encapsulated from both sides by a transparent ethyl-
vinyl-acetate (EVA) foil with an additional white sheet at the back and a glass panel in
the front, as shown in figure 2.10. The white back-sheet helps reflect back the portion
of the irradiance falling in the space between the solar cells, a part of which is totally
reflected by the front EVA foil into the solar cells, where it can generate additional carriers.
Some modules also have an aluminium frame, mechanically stabilising the module and
facilitating standard mounting methods, such as on the rack. A junction box in the
back serves as the electrical connection to the other modules of the solar system and also
typically contains three bypass-diodes, which in case of strong shading, bypasses a string
of solar cells, to prevent damaging the shaded solar cell.
Tempered glass
EVA
Solar cells
Frame
Back sheet
EVA
Junction box
Figure 2.10: Schematic of the layers in a standard solar module [27]. In bifacial modules, the
backsheet is transparent or replaced by glass and the junction box is redesigned in
order to avoid shading of the rear side of the cells.
Like their solar cells, bifacial modules differ slightly from standard modules, in order to
allow absorption of light from the rear side of the module. The white sheet on the rear side

of solar modules would block the rear side irradiation in bifacial modules and is therefore
removed and replaced by either a transparent backsheet in case of glass-backsheet modules
or another glass panel in case of glass-glass modules, allowing sunlight to reach the rear
side of the bifacial solar cells. In standard modules with a white back-sheet, light shining
on the space between the cells was partly reflected by the white sheet and totally reflected
back on the cells’ front side by the front glass foil, allowing for the portion of light falling
between the cells to be partly utilized. This effect however cannot be utilized in bifacial
modules, which have no reflective white back-sheet. Consequently, the front side power
of a bifacial module is further reduced, compared to a standard module. In addition,
standard junction boxes, as depicted in figure 2.10, would block a portion of the rear side
irradiance from reaching the top solar cells, and thus have to be redesigned to cope with
the light sensitive rear side of bifacial modules. An example of such a redesign is shown
in figure 2.11, which shows the front and rear sides of a bifacial module.
Figure 2.11: Front (left) and rear (right) side of a bifacial module with a redesigned junction
box to reduce shadowing losses.
2.2.3 Solar park
Solar systems typically include several solar modules, whereas installations with a single
module are a rare exception and will therefore not be considered. A field installation of
standard solar modules, that is an installation with several modules per row and possibly
several module rows, poses several electrical and optical considerations. Some of the
difficulties of the electric design of a field installation include the electrical mismatching
of serially connected modules, the number of maximum-power-point (MPP) trackers to
be utilized and several other safety issues resulting from the high currents flowing in the
field. Optically, the mutual shading of the PV modules is one of the major issues, forcing
a certain minimum distance between module rows, thus decreasing the installed power
per given area.
The aforementioned challenges are enhanced when using bifacial modules and become
more complex to calculate. Knowing at what time of day and at which module row
distance modules are no longer shaded by the front module rows is not sufficient when
using bifacial modules. The rear side of bifacial modules utilizes the irradiance diffusely
reflected by the ground, which is reduced by the shadows of the modules on the ground,

which are shown in figure 2.12 for an exemplary bifacial field installation with twelve
modules in three rows. It is therefore vital to calculate, where the module shadows are at
every time during each day of the year, in order to determine the reduction in rear side
irradiance due to the shadows of the modules on the ground. This optical phenomenon
causes increased electrical mismatching within the solar park, since the modules on the
edge of the field have less shadow beneath them than those in the middle and thus higher
rear side irradiance and a higher power output.
Figure 2.12: Schematic of a field with twelve bifacial modules in three rows with their respective
shadows.
The rear side irradiance, in addition to being reduced by the module shadows on the
ground, is further reduced via blocking by other modules rows. Solar irradiation diffusely
reflected by the ground, which would reach the rear side of the bifacial module, is blocked
by the modules in the row behind it, thereby decreasing the solar irradiance reaching its
rear side and reducing its power output. This effect is visualized in figure 2.13, which
shows two module rows and the reflected solar irradiance reaching the module rear side
(green), the irradiance blocked by the additional module row (red) and the irradiance
that would not have reached that module’s rear side, even in the absence of a second row
(yellow).
Figure 2.13: Schematic of blocking of ground reflected irradiance by rear module row, where the
bottom cell rows of a module receive more irradiance than top cell rows.

2.3 Existing research
Multiple scenarios calculated by various institutes predict the increase of the share of
bifacial PV in worldwide markets, as was demonstrated in the sixth edition of the ITRPV
in figure 1.3. The need for estimations of the energy yields of bifacial photovoltaic instal-
lations and the therewith associated costs of the produced electricity are resulting in the
growing importance of simulation tools for bifacial modules, with which the profitability of
planned projects can be determined. The topic is also becoming academically increasingly
interesting, with some research already being conducted on the simulation and measure-
ment of the influence of various installation parameters, the ground albedo and shading
on the annual energy yield of bifacial module installations. Conducted research on the
simulation and measurement of bifacial modules is introduced in this chapter.
One attempt was made by Rosas [28], where two approaches for simulating the perfor-
mance of bifacial modules were considered and consequently compared to data from a
measurement site in El Gouna, Egypt. The first method assumed a constant proportion
of the irradiance reaching the rear side of the bifacial module installed in a sand covered
area, namely 20 %, and then using existing tools, such as the simulation environment
INSEL, to estimate the energy yield of the module. The second approach was simulating
two back-to-back monofacial modules with the second module turned backwards. The
results of the simulation, which are shown in figure 2.14, were comparable with the data
measured on site. However, due to the assumptions and simplifications made, consider-
able deviation from the measured data was observed for some of the tested modules, since
the rear side irradiance Itot,r is variable and not a constant 20 %, and because the rear side
of a bifacial module performs differently than a monofacial module turned backwards.
Module 1 Module 2 Module 3 Module 4
0
100
200
300
400 back-to-back
measured
constant Itot,r
PoweroutputP[W]
Figure 2.14: Results of the two simulated and the measured output powers of several bifacial
modules tested in El Gouna, Egypt [28]. Relatively large deviations between sim-
ulated and measured data.

20 2.3. Existing research
Actual simulations of the yield of bifacial modules were carried out by Yusufoglu et al.
[29], who, borrowing from thermal dynamics used the principle of the view factor (VF) to
estimate the ground reflected irradiance reaching the rear side of an stand-alone bifacial
module. The estimated amount of solar irradiation reaching each cell was used to model
the energy output of the cell using the modified two-diode model introduced in chapter
2.2.1.3. The simulation was run repeatedly for different module installation parameters, to
determine the optimum tilt angle depending on the elevation of the considered module,
the results of which are given in figure 2.15, where the optimum tilt angle is plotted
against the module elevation for two albedo coefficients of α = 0.2 and α = 0.5 and for
two locations, namely Cairo, Egypt and Oslo, Norway.
Figure 2.15: Optimum tilt angle of bifacial modules for maximized yield in Oslo and Cairo de-
pending on the albedo and module elevation [29]. Optimum tilt angle decreases
with increasing module elevation, and is overall larger in Oslo, due to higher lati-
tude.
With increasing albedo and module elevation, the optimum tilt of the module decreases,
allowing for more reflected irradiation to reach the rear side. Additionally, the optimum
module elevation was calculated to be 1.0 m and 0.5 m for Cairo and Oslo respectively.
Yusufoglu et al. [29] also introduced the bifacial gain factor BF, which quantifies the
gain in the specific energy yield (kWh/kWp) when using a bifacial module compared to
a standard module of similar specifications. Using the module elevations 0 m, 0.5 m
and 2 m and their corresponding optimum tilt angles, the bifacial gains of stand-alone
modules installed in Cairo and Oslo with two different albedo coefficients were calculated
and summarized in table 2.2, with stand-alone bifacial modules producing up to 30 %
more energy than comparable standard modules.
Research conducted on the topic of bifaciality and the resulting increase in energy produc-
tion is however not limited to the simulation of such an improved performance. Kreinin
et al. [31] analysed the increase in energy generation of bifacial over monofacial PV mod-
ules experimentally, using a roof-top PV field with both module types in Jerusalem for

Table 2.2: Annual bifacial gain and its dependence on site, module elevation and albedo [30].
Bifacial gain increases for higher albedo coefficient.
Module Cairo Oslo
elevation [m] α = 0.2 α = 0.5 α = 0.2 α = 0.5
0 10.6 % 24.3 % 15.4 % 28.1 %
0.5 12.9 % 28.8 % 15.5 % 28.3 %
2 13.8 % 30.6 % 15.5 % 28.3 %
testing. The measurement was conducted over a whole year with data acquired from both
stand-alone bifacial modules and from ones installed in a field. The results of the mea-
surement campaign are visualized in figure 2.16, where the preveiously defined bifacial
gain of both configurations is given as a monthly average.
Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug
0
5
10
15
20
25
30
in-field
stand-alone
BifacialgainBF[%]
Figure 2.16: Results of measurements of both stand alone bifacial modules and bifacial modules
in a field installation in Jerusalem [31]. Bifacial gain of an in-field bifacial module
drops significantly, compared to a stand-alone module.
The most important observation is the large decrease in the bifacial gain of a bifacial
module installed in a field compared to a stand-alone module. The shading of the other
modules on the ground and the mutual blocking of the reflected solar irradiance signifi-
cantly reduces the rear side irradiance of the module and consequently its energy output.
However, the reduction of the bifacial gain is dependent on various installation param-
eters, weather conditions and location and the results are therefore only valid for that
specific measurement. To be able to predict the bifacial gain of different in-field instal-
lations with bifacial modules, simulation tools with such capabilities are needed. The
major topic of this thesis is therefore, the developing of a software tool, with the ability
to simulate the energy yields of both stand-alone bifacial modules and modules in a field.

22 2.3. Existing research

Chapter 3
Simulation
If used correctly, simulations can be powerful tools with limitless applications including
commonly used ones, such as weather predictions. Imitating the characteristics and key
functions of a system or a process, simulations can be used in various contexts, including
performance optimization, safety testing, visual effects and the functioning of natural
or human systems. Simulations are often used, when the real system or process is not
accessible, whether because the process is dangerous, or it is in the design phase, or it
does not exist and can therefore not be experimentally tested.
In the scope of this thesis, the simulation tool is developed to model the behaviour of
different configurations of bifacial solar systems which are not yet installed or built. The
performance of the system can consequently be optimized and the influence of the various
installation parameters on the energy yield can be determined. The developed optical
and electrical models and the functions used in the simulation will be explained in detail
in chapters 3.1, 3.2, whereas the various results of the performed simulations will be
presented in chapter 3.3.
3.1 Optical model
The optical model used in the simulation is comprised of several equations, each mimicking
one part or process of the considered system, which will be explained in detail in the
following sub-chapters. Due to the geometric complexity of a solar module installation
and the existence of a large number of angles, lengths and other quantities, a unified
definition of such geometric values and what they quantify will be established in chapter
3.1.1, before the functions used in the simulation are explained in chapters 3.1.2 to 3.1.6.
The key purpose of this thesis is to simulate the annual energy yield of both stand-alone
and in-field installations of bifacial modules, with the main focus on the simulation of

24 3.1. Optical model
the optical component of the bifacial solar energy generation process, namely the cal-
culation of how much solar irradiation reaches the rear sides of such modules. This is
possible through a number of steps, starting with the definition of the module setup and
the installation parameter values. Using the Sun’s position, which is dependent on the
time and location of the simulated solar system, the direct, diffuse and reflected irradi-
ances, Idir, Idiff and Irefl, can be calculated for both the module front and rear side, and
consequently summed to determine the total irradiance Itot. Whereas the calculation of
the total front irradiance Itot,f and the direct and diffuse rear irradiances Idir,r and Idiff,r
are relatively straightforward, the estimation of the albedo reflected rear side irradiance
Irefl,r, which contributes the most to the total rear side irradiance Itot,r, can be highly
complex, depending on the module installation to be simulated. Once the front and rear
side irradiances have been calculated, a simple model, which will be introduced in chapter
3.2, is used to estimate the output power of the module, with which the annual energy
yield of monofacial and bifacial modules can be computed and the bifacial gain can be
determined.
3.1.1 Module installation parameters
To avoid confusion about the geometric quantities of a solar module setup, a unified
definition of such quantities will be introduced. In the geographic coordinate system, the
definition of the angle is given in the reverse mathematical direction, namely clockwise,
where North is set at 0◦
, East at 90◦
and South at 180◦
. Figure 3.1 shows a single
solar module with the width wM and the length lM installed at a certain elevation of
the lower edge of the module hM in the direction of the z-axis. The tilt angle of the
module, the angle between the module and the horizontal plane, is given by γM , whereas
North
z
hM
θSM
γM
αM-180°
γS
αS
nM
nS
nS'
lM
wM
Figure 3.1: Stand-alone module setup and definition of the module installation parameters and
the position of the sun.

Chapter 3. Simulation 25
the orientation of the module, or which cardinal direction the module is facing, is given
by αM . The position of the sun, which is dependent on the date, time and location, is
described using two angles, the Sun elevation angle γS and the Sun azimuth angle αS,
which are shown in figure 3.1. The angle of incidence θSM is defined as the angle formed
between the two normal vectors of the Sun and the module, ns and nM respectively.
For the purpose of clarity, further quantities, including ones to describe the installation
of modules in a field, will be visualized in another figure. These include the distance dM
between the modules in the same row and the distance dR between module rows, which is
the distance from the rear edge of the front module to the front edge of the module in the
next row, and can be seen in figure 3.2. Other geometric values describing the size of the
surface reflecting solar irradiation onto the module rear side include LS, the width of the
surface from the module center, L1, the length from the module center to the rear end of
the surface, and L2, the length from the module center to the intersection of the module
plane with the ground plane. In the case of using white reflective plates or sheets beneath
the modules to increase the albedo coefficient and hence the rear side irradiance, the size
of the sheet can be given by wS, w1 and w2, which are the lengths from the module center
to the sides, to the rear end and to the front end of the reflective sheet respectively.
w2
w1
wSL2
L1
LS
dR
dM
Figure 3.2: In field module setup and definition of the field installation parameters and other
input parameters of the simulation.
3.1.2 Sun’s position
The Sun’s position is dependant on the date, time and location and can be described using
the elevation and azimuth angles, γS and αS. The two angles are calculated according
to the DIN 5034 algorithm. The position of the sun is strongly influenced by the angle
between the equatorial plane of the Earth and the Earth’s rotational plane around the
Sun. The so-called declination angle δ varies between +23.5◦
and −23.5◦
over the year

[32]. Using the parameter J , which is described by
J = 360◦ day of the year
number of days in a year
, (3.1)
the solar declination angle δ can be calculated by
δ = 0.3948 − 23.2559 cos(J + 9.1◦
)
− 0.3915 cos(2J + 5.4◦
)
− 0.1764 cos(3J + 26◦
). (3.2)
The solar altitude further depends on the latitude ϕ of the site and on the hour angle ω.
The hour angle ω is calculated using the Solar time, which in turn is dependent on the
equation of time EOT and the mean local time MLT. With the Local time, the longitude
of the standard meridian of the local time zone λSt and the longitude of the site λ, the
MLT is given by
MLT = Local time − 4 (λSt − λ) [min]. (3.3)
The equation of time EOT, which is dependent on the parameter J and diﬀerentiates
the Solar time from MLT, the Solar time and the hour angle ω can be calculated using
the following equations
EOT = 0.0066 + 7.3525 cos(J + 85.9◦
)
+ 9, 9359 cos(2J + 108.9◦
)
+ 0.3387 cos(3J + 105.2◦
), (3.4)
Solar time = MLT + EOT, (3.5)
ω = (12 : 00h − Solar time) 15◦
/h. (3.6)
With the previous equations, the position of the sun can be determined and described by
the values of the Solar altitude γS and Solar azimuth αS, which are given by
γS = arcsin(cos ω cos ϕ cos δ + sin ϕ sin δ), (3.7)
αS =



180◦
− arccos
sin γS sin ϕ − sin δ
cos γS cos ϕ
for Solar time 12:00h (3.8)
180◦
+ arccos
sin γS sin ϕ − sin δ
cos γS cos ϕ
for Solar time > 12:00h. (3.9)
3.1.3 Direct irradiance Idir
Using the position of the Sun and data from measurements of the global, direct (beam) and
diﬀuse horizontal irradiances, GHI, BHI and DHI, the total irradiances on the module
front and rear side can be estimated, which in case of the direct irradiance on the front
surface of a module Idir,f is a straightforward geometrical relationship [32, 33, 34, 35, 36].

AS
Ahor γS
Figure 3.3: Incoming solar irradiance on a horizontal surface Ahor and a surface perpendicular
to the incoming sunlight AS.
A horizontal surface ”with the area Ahor receives the same direct radiant power Φdir as
the smaller area AS, which is normal (perpendicular) to the incoming sunlight” [32], both
of which are shown in figure 3.3. With
Φdir = BHI Ahor = Idir,S AS, (3.10)
where BHI is the solar irradiation on the horizontal surface Ahor and Idir,S is the irradiance
on the normal surface AS. If AS < Ahor, then it follows that Idir,S ≥ BHI, which given
equation 3.10 and the trigonometric relation
AS = Ahor sin γS, (3.11)
can be given as
Idir,S =
BHI
sin γS
≥ BHI. (3.12)
The fact, that the irradiance on a tilted surface is greater than the irradiance on a hori-
zontal surface is used in the planning of PV systems, where inclining the solar modules
increases the energy yield of the system. Using the solar incidence angle θSM , which was
defined in figure 3.1 as the angle between the incoming sunlight nS and the normal vector
of the module nM , the direct irradiance on the front side of a tilted surface Idir,f can be
calculated using
Idir,f = Idir,S cos θSM , (3.13)
where
nS = (cos αS cos γS, sin αS cos γS, sin γS)T
, (3.14)
nM = (cos αM sin γM , sin αM sin γM , cos γM )T
, (3.15)
and
θSM = arccos(nS · nM )
= arccos(− cos γS sin γM cos(αS − αM ) + sin γS cos γM ). (3.16)

Inserting equation 3.13 into equation 3.12 gives
Idir,f = BHI
cos θSM
sin γS
, (3.17)
which in case BHI is known, can be used to calculate the direct irradiance reaching the
module front side Idir,f directly.
To calculate the direct irradiance reaching the rear side of the module Idir,r, the same
equation is used, albeit with one difference, namely that the normal vector of the module
is reversed, so that it is facing backwards. This can be mathematically described by
inverting the sign of the normal vector using
nM,r = −nM,f , (3.18)
where the indices r and f signify the normal vectors of the rear and front side respectively.
The new normal vector is used in equation 3.16 to calculate the incidence angle, which is
then used in equation 3.17 to calculate Idir,r.
3.1.4 Diffuse irradiance Idiff
Unlike the calculation of the direct irradiance on a tilted surface, the calculation of the
diffuse irradiance on a titled surface is not a straightforward geometric computation,
and there exist several different approaches, which can be categorized under isotropic
and anisotropic approaches. A thorough comparison of the different models is given by
Noorian et al. [34]. The simpler of the two models, the isotropic model, assumes a uniform
intensity of the diffuse irradiance over the sky hemisphere. Hence, the diffuse irradiance
reaching a tilted surface depends on the fraction of the sky hemisphere it can see [35].
A tilted surface therefore receives less diffuse irradiance than a horizontal surface, since
it cannot see the diffuse irradiance behind it. However, the assumptions made in the
isotropic models cause imprecision and make them only suitable for rough estimations or
for very overcast skies [32, p. 62].
The more complex anisotropic models, which describe the sky diffuse radiance more accu-
rately, presume the sky diffuse irradiation consists of three factors; the anisotropic diffuse
irradiance in the region near the solar disk, the brightening effect near the horizon and
the isotropically distributed diffuse component from the remaining portion of the sky
hemisphere [35]. Several models consider the aforementioned effects, the most accurate
of which is the Perez model, which, according to Noorian et al. [34], ”shows the best
agreement with the measured tilted data” and is ”used world wide to estimate short time
step (hourly or less) irradiance on tilted surfaces based on global and direct (or diffuse)
irradiance measured on horizontal surfaces”. Despite its relative complexity compared
to the other models, the Perez model will be used in this thesis to estimate the diffuse
irradiance on the module front and rear surface, in order to minimize the sources of error
in the simulation.

To calculate the diffuse irradiance on the front side of a tilted surface Idiff,f , an atmo-
spheric clearness index ε and an atmospheric brightness factor ∆ are defined by the Perez
model [37]. These are determined by
ε =
DHI+BHI arcsin γM
BHI
+ κ θ3
SM
1 + κ θ3
SM
(3.19)
∆ = AM
DHI
E0
, (3.20)
where θSM is the angle of incidence defined in equation 3.16, κ is a constant equalling
1.041, E0 is the solar constant and AM is the Air Mass defined in chapter 2.2.1 and is
given by
AM =
1
sin γS
. (3.21)
To account for the brightening effects around the solar disk and near the horizon, the cir-
cumsolar brightening coefficient F1 and the horizon brightening coefficient F2 are defined
and can be calculated with
F1 = F11(ε) + F12(ε) ∆ + F13(ε) θSM (3.22)
F2 = F21(ε) + F22(ε) ∆ + F23(ε) θSM , (3.23)
where F11 to F23 are the empirically determined constants shown in table 3.1, where the
constants are given according to the corresponding atmospheric clearness index ε, which
is divided into eight different atmospheric clearness classes. The diffuse irradiance on the
front of a tilted surface can then be calculated using
Idiff,f = BHI
1
2
(1 + cos γM ) (1 − F1) +
a
b
F1 + F2 sin γM , (3.24)
where
a = max(0; cos θSM ) (3.25)
b = max(0.087; sin γS). (3.26)
To determine the diffuse irradiance on the rear side of a tilted surface Idiff,r, the module
installation angles αM and γM are changed using
αM,r = 180◦
+ αM,f (3.27)
γM,r = 180◦
− γM,f , (3.28)
so that the considered surface is facing backwards, hence imitating the rear side of a
bifacial module.
3.1.5 Reflected irradiance Irefl
Two different approaches are used to calculate the ground reflected irradiance reaching
the module front and rear sides respectively. To determine the reflected irradiance on the

Table 3.1: Constants for estimating F1 and F2 as a function of ε [37].
ε class 1 2 3 4 5 6 7 8
ε 1.000− 1.065− 1.230− 1.500− 1.950− 2.800− 4.500− 6.200−
−1.065 −1.230 −1.500 −1.950 −2.800 −4.500 −6.200 −∞
F11 −0.008 −0.130 −0.330 −0.568 −0.873 −1.132 −1.060 −0.678
F12 −0.588 −0.683 −0.487 −0.187 −0.392 −1.237 −1.600 −0.327
F13 −0.062 −0.151 −0.221 −0.295 −0.362 −0.412 −0.359 −0.250
F21 −0.060 −0.019 −0.055 −0.109 −0.226 −0.288 −0.264 −0.159
F22 −0.072 −0.066 −0.064 −0.152 −0.462 −0.823 −1.127 −1.377
F23 −0.022 −0.029 −0.026 −0.014 −0.001 −0.056 −0.131 −0.251
front side of the module Irefl,f , an assumption of isotropy is sufficient, because the few
existing anisotropic effects would introduce great complications to the calculation that
are not justified, since they do not significantly improve the the accuracy of the model.
Therefore, ”the isotropic model simply based on a constant mean albedo measured on
site is satisfactory” [38] and is defined as
Irefl,f = GHI
α
2
(1 − cos γM ). (3.29)
However, this approach delivers inaccurate results for the ground reflected irradiance on
the rear side of the module Irefl,r and according to Yusufoglu et al. [29], a more complicated
calculation is required, suggesting using the concept of the view factor known from heat
transfer fundamentals. Also known as shape factor, configuration factor and angle factor,
the view factor FA1→A2 is a purely geometric quantity describing the fraction of the
radiation leaving a random surface A1 that strikes the surface A2 directly [39]. The view
factor is based on the assumption that the surfaces are ideal diffuse reflectors, as described
in chapter 2.1.2. The radiation exchange between surfaces depends on the orientation
of the surfaces relative to each other and is independent of the surface properties and
temperature.
Assuming a mean ground albedo α, an ideal Lambertian character of the ground, and
given horizontal irradiances GHI and DHI, the view factor approach can be used to
calculate the ground reflected irradiance on the rear side of the bifacial module Irefl,r.
The surface beneath and surrounding the module As is divided into the region outside
the shadow, denoted as Ansh, and the shadow region, denoted as Ash. Whereas only DHI
is reflected from the shadow region Ash, because the direct portion of the solar irradiance
is blocked by the module, throwing the shadow on the ground, the reflected portion of
GHI stems only from the region outside the shadow Ansh. Irefl,r is therefore the sum of
the reflected irradiances from the two regions Ansh and Ash, given as
Irefl,r = α GHI FAnsh→AM
+ α DHI FAsh→AM
. (3.30)

In order to account for the inhomogeneity of the irradiance reaching the rear side of the
module, the view factors from the two regions to each cell of the module are calculated
individually. This process is repeated for every time step of the entire simulated period,
allowing for an extensive spatial and temporal distribution of Irefl,r. The basics of the
view factor, how it is calculated and how the different effects of shadowing and blocking
are taken into account, will be explained in detail in the following chapter.
3.1.6 View factor FA1→A2
As mentioned in chapter 3.1.5, the view factor FA1→A2 is a geometric quantity, defining the
fraction of the radiation leaving A1 and reaching A2. It can be computed as the integral
of the portions of radiation leaving the differential areas dA1 that reach the differential
areas dA2,
FA1→A2 =
1
A1
A1 A2
cos θ1 cos θ2
πr2
dA1 dA2, (3.31)
where r is the distance between the differential areas dA1 and dA2. The angles between the
normals of the surfaces and the line that connects dA1 and dA2 are θ1 and θ2 respectively,
and are depicted in figure 3.4.
A1
A2
θ2
θ1
n1
n2
r
dA2
dA1
Figure 3.4: Geometry for determining the view factor between two surfaces.
Assuming the ground has a Lambertian character, the view factor approach can be used
to determine the fraction of irradiance leaving the ground with the area As, the geometry
of which is defined by LS, L1 and L2, which were depicted in figure 3.2, that reach the rear
side of the module with the area AM,r. Such a configuration is visualized in figure 3.5.
For the computation of the view factor, the coordinates of the modules and surface edges
have to be provided in the x-y-ξ-coordinate system. In the case the module coordinates
are given in the N-W-z-coordinate system, they have to be transformed using a rotation
with the angle αM around the z-axis to the appropriate coordinate system. The module
edges are then given by δ1 and δ2 in the δ-axis and ξ1 and ξ2 in the ξ-axis, whereas the
surface edges are given by x1 and x2 in the x-axis and y1 and y2 in the y-axis.
Because the calculation of the view factor can be highly complex, depending on the

N
W
x
y,δ
ξ
αM-180°
γM
ξ2
ξ1
δ2
δ1
x1 x2
y1
y2
AM
,r
As
Figure 3.5: Geometry for determining the view factor between the ground surface As and the
module rear surface AM,r inclined at the angle γM .
considered configuration, the view factors of various configurations were computed and
collected in catalogues [40]. The view factor equation required for the configuration
considered in this thesis, which consists of two differently sized plane rectangular surfaces
with parallel boundaries and arbitrary position, meaning that they are not necessarily
parallel or perpendicular to each other and are randomly inclined, was developed by Gross
et al. [41]. ”Since for parallel rectangular areas the limits of integration are independent
from each other, it is possible to separate the integration and the insertion of the limits
[, which] is advantageous for a numerical treatment of this problem” [41], and will be
explained in the following section. Equation 3.31 is rewritten as
A1 FA1→A2 =
ξ2
ξ1
δ2
δ1
y2
y1
x2
x1
g(x, y, δ, ξ) dx dy dδ dξ, (3.32)
with
g(x, y, δ, ξ) =
cos θ1 cos θ2
πr2
. (3.33)
Applying the separation of the integration and the insertion of limits delivers
G(x, y, δ, ξ) =
ξ δ y x
g(x, y, δ, ξ) dx dy dδ dξ (3.34)
for the integration, and
A1 FA1→A2 = G(x, y, δ, ξ)
x2
x1
y2
y1
δ2
δ1
ξ2
ξ1
(3.35)
for the insertion of limits. Next, the unknown variables θ1, θ2 and r are redefined and
expressed in terms of x, y, δ and ξ, whereby the distance of the points on the areas is
r2
= x2
− 2xξ cos γM + ξ2
+ (y − δ)2
(3.36)

and the direction angles are
cosθ1 =
ξ sin γM
r
(3.37)
cosθ2 =
x sin γM
r
. (3.38)
Substituting the previous three equations into equation 3.34 delivers
G(x, y, δ, ξ) =
ξ δ y x
x ξ
[x2 − 2xξ cos γM + ξ2 + (y − δ)2]2 dx dy dδ dξ, (3.39)
which can be solved by analytically integrating x, y and δ, yielding
G(x, y, δ, ξ) = −
sin2
γM (δ − y)
2π
ξ
cos γM x − ξ cos γM − ξ sin2
γM
sin2
γM (x2 − 2xξ cos γM + ξ2)
1
2
arctan
δ − y
(x2 − 2xξ cos γM + ξ2)
1
2
+
cos γM
sin2
γM (δ − y)
ξ2
sin2
γM + (δ − y)2
1
2
arctan
x − ξ cos γM
ξ2 sin2
γM + (δ − y)2
1
2
− ξ sin γM arctan
x − ξ cos γM
sin γM
+
ξ
2(δ − y)
ln
x2
− 2xξ cos γM + ξ2
+ (δ − y)2
x2 − 2xξ cos γM + ξ2
, (3.40)
where the last integration over ξ has to be carried out numerically, which was realized
using the FORTRAN 77 library QUADPACK [42]. Following the completion of the
integration, the insertion of the limits, or the solving of equation 3.35 can be easily
carried out numerically, by performing the following series of additions
A1 FA1→A2 =
2
l=1
2
k=1
2
j=1
2
i=1
(−1)(i∗j∗k∗l)
G(xi, yj, δj, ξl) . (3.41)
The view factor FAs→AM
from the surface area As to the module rear side AM can conse-
quently be determined for any module installation with one edge parallel to the ground.
For the special cases, where the module is either completely parallel or perpendicular to
the ground, for example for vertically installed modules, equation 3.39 can be simpliﬁed,
allowing for a less complex analytical integration, the results of which will however not
be shown.
3.1.6.1 Inﬂuence of shading
In order to determine the irradiance on the module rear side using equation 3.30, the
ground surface has to be divided into two regions, the shadow region and the one outside
the shadow, and consequently FAsh→AM
and FAnsh→AM
have to be derived from FAs→AM
.

Whereas calculating FAs→AM
once is sufficient, the computation of the view factor from
the shadow area Ash to the module rear side FAsh→AM
is more complex, because since the
shadow area is moving, the calculation of FAsh→AM
needs to be repeated for each time
step. This is the major cause of the large computation times required in the simulation.
The configuration from figure 3.5 was modified with the shadow region and shown in
figure 3.6, where Ansh describes the portion of As outside the shadow region Ash.
N
W
x
y,η
ξ
αM-180°
γM
ξ2
ξ1
δ1
δ2
x1 x2
y1
y2
AM
,r
A
sh
As
Ansh
Figure 3.6: Geometry for determining the view factor between the shadow region Ash and the
module rear surface AM,r inclined at the angle γM .
Furthermore, the area of the shadow is not a rectangle but a parallelogram, and its edges
are not parallel to the modules edges, which is the assumption required in chapter 3.1.6.
Because the integration limits, that is the surface and module limits, were independent
of each other, the separation of the integration process and the insertion of the limits was
possible. Without this simplification, solving the four integrals becomes highly complex
and time consuming. To simplify the computation, the parallelogram area of the module
shadow on the ground was fitted to a rectangle, as depicted in figure 3.6. Due to the
little skewness of the parallelogram during most of the day and the consequently small
difference in the shape of the shadow, the resulting error was presumed to be minimal.
The view factor from the shadow to the module FAsh→AM
can thus be calculated using
the process described in chapter 3.1.6, where the shadow rectangle edges are given by x1
and x2 in the x-axis and y1 and y2 in the y-axis. It is still necessary to determine the view
factor from the region outside the shadow to the module FAnsh→AM
. This calculation
can be done using the two other view factors already calculated and the view factor
superposition rule [39] given by
A2 + A3FA(2,3)→A1 = A2FA2→A1 + A3FA3→A1 . (3.42)
Replacing the index 1 with M, 2 with sh, 3 with nsh and (2, 3) with s, equation 3.42 can

be rewritten as
Ash + AnshFAs→AM
= AshFAsh→AM
+ AnshFAnsh→AM
, (3.43)
where Ash + Ansh = As, and can be rearranged to
AnshFAnsh→AM
= AsFAs→AM
− AshFAsh→AM
(3.44)
to determine the remaining view factor from the region outside the shadow to the mod-
ule. The shadow region on the ground is determined using the equations introduced in
[43]. In case the installation consists of several modules, then the view factors from each
module shadow to the considered module rear side have to be computed separately, sig-
nificantly increasing the run time of the simulation. One approach to limit the increase
in computation time with additional modules in the same row, is to treat the shadows of
neighbouring modules as one large shadow, in case the distance between the modules dM
is zero. Since the numerous shadows are treated as one shadow, the computation duration
is reduced by the number of modules in the considered row, for example five times faster
calculation for an array with five modules.
3.1.6.2 Influence of blocking
Solar module installations usually do not only consist of one module row but several,
hence a further effect has to be considered in the optical model, namely the blocking of
the ground reflected irradiance from reaching the module rear side by the modules in the
back rows, which is schematically visualized in figure 3.7.
L16L15L14L11 L12 L13
1
2
3
4
5
6
Figure 3.7: The different reductions of the reflective surface length L1 by the back module row
for each cell row in the considered module, where the irradiance reaching the top
cell row is decreased the strongest.
The module rear side sees irradiance reflected from an area that has the length L1 from
the module center to its rear edge. To account for the blocking effect, L1 is reduced
depending partially on the module elevation hM , tilt angle γM and module row distance

dR. The amount of blocking also depends on which cell row is being considered, where
cells at the top edge of the module are more strongly blocked off than the cell rows at the
bottom of the module. How strongly the reflective area is reduced by the additional back
row for each cell row, where L11 denotes the length L1 for the top cell row and L16 for
the bottom cell row, is visualized in figure 3.7. The new lengths can be calculated using
simple geometric relations, if the required module installation parameters are available.
3.1.6.3 Influence of white sheet
The ground reflected irradiance reaching the module rear side is directly dependent on
the albedo coefficient of the ground, as given by equation 3.30, where a greater α is
advantageous for the bifacial gain. Consequently, white reflective sheets with αw = 70 −
100 % can be placed beneath the modules to increase Irefl,r and the module’s energy yield.
The additional surface slightly complicates the calculation of the view factor and the rear
side irradiance. To avoid confusion, the indices which will be used in the following figures
and equations are defined in table 3.2. The corresponding areas, those of the ground
surface, the shadow and the white reflective sheet, which are also given in table 3.2, are
depicted in figure 3.8, when viewing the ground beneath the module from above.
Table 3.2: Indices used for the calculation of the view factor and their meaning.
Index Meaning Area
M module AM
s entire reflective surface As
w entire reflective white sheet Aw
sh entire shadow area Ash
ssh part of shadow area outside white reflective sheet Assh
wsh part of shadow area inside white reflective sheet Awsh
wnsh part of white reflective sheet without shadow Awnsh = Aw − Awsh
snsh area outside shadow and white reflective sheet Asnsh = As − Ash − Awnsh
Because the ground beneath the module has two different albedo coefficients when using
a white reflective sheet, equation 3.30, with which the rear side irradiance is determined,
has to be changed to
Irefl,r = α GHI FAsnsh→AM
+ α DHI FAssh→AM
+ αw GHI FAwnsh→AM
+ αw DHI FAwsh→AM
, (3.45)
where the required view factors FAsnsh→AM
, FAssh→AM
and FAwnsh→AM
can be calculated
using the superposition rule given by equation 3.42 and rearranging it to the following

As
Awnsh
Aw
Awsh
Ash
Asnsh
Assh
Figure 3.8: View of the ground beneath the module from the top with the various regions on
the ground with a reflective white sheet used for the calculation of the view factors.
equations
AwnshFAwnsh→AM
= AwFAw→AM
− AwshFAwsh→AM
, (3.46)
AsshFAssh→AM
= AshFAsh→AM
− AwshFAwsh→AM
, (3.47)
AsnshFAsnsh→AM
= AsFAs→AM
− AwnshFAwnsh→AM
− AshFAsh→AM
. (3.48)
Whereas the view factors from the surface and the white reflective sheet to the module
each have to determined once, the view factors from the two shadow regions Awsh and
Assh to the module have to be determined for each time step, doubling the time required
for each simulation, because in this case the shadow consists of two areas.
3.2 Electrical model
The performance of standard monofacial PV modules is assessed based on the output
power of the module given by the manufacturer, where a 300 W module is expected to
produce 20 % more energy than a 250 W module with a similar technology. This com-
parison is however not enough when assessing the performance of bifacial modules, since
a bifacial module with a front side power of 300 W will not produce the same amount
of energy as a 300 W standard module. A model for calculating the output power of a
bifacial module depending on the total irradiance on the front and rear side is explained
in chapter 3.2.1 and an approach for comparing the performances of standard and bifacial
module is introduced in chapters 3.2.2 and 3.2.3. Since the development of the optical
module was the major goal of this thesis, the considered electrical model is a simple one
with various assumptions negatively affecting the simulation results. Therefore, the sim-
ulations are not expected to predict correct absolute values, but serve as a comparison of
the performance of bifacial modules in different configurations relative to the performance
of standard modules.

38 3.2. Electrical model
3.2.1 Module power Pmpp
The output power of PV modules is dependent on the amount of solar irradiation reaching
the light sensitive surface. Several different approaches exist for determining the module
power, most of which are based on an indoor measurement of the open circuit voltage
Voc,0, the short circuit current Isc,0, the maximum power point voltage and current Vmpp,0
and Impp,0, and the fill factor FF of the considered module at standard test conditions
(STC), where a flasher with an intensity of I0 = 1000 W/m2
and an AM 1.5 spectrum is
used for the illumination of the module being measured. These measurements are used to
determine the values of the currents and voltages at arbitrary light intensities reaching the
module in outdoor conditions. The model described by Singh et al. [25], which is a simple
approach for converting the indoor measurements at STC to real conditions. For more
accurate simulations, the electrical model can be extended by determining the required
parameters using the two-diode model, but since the optical modelling was the main focus
of this thesis, the model described by Singh et al. [25] will be used in this these, because it
”gives already a good approximation to the expected efficiency under bifacial operations”
[44]. Table 3.3 summarizes what the indices used in the following equations denote. If an
equation is given without specifying whether it is used for a monofacial module or for the
front or rear side of a bifacial module, then it is therewith implied, that it can be used
for all the mentioned cases.
Table 3.3: Indices used for calculation of the output power of monofacial and bifacial modules.
Index Meaning
m monofacial module
b bifacial module
f front side of bifacial module
r rear side of bifacial module
0 standard test conditions
mpp maximum power point
oc open circuit
sc short circuit
x variable with options m,f,r
The first step of the used electrical model, is the conversion of the short circuit currents
Isc,x,0 and the open circuit voltages Voc,x,0 measured at STC at I0 to the short circuit
currents Isc,x and the open circuit voltages Voc,x at a given irradiance Itot,x, where x =
{m, f, r}. Using the linear dependence of Isc on the light intensity [44], the short circuit
current of a monofacial module or of a front or rear side of a bifacial module can be given
by
Isc,x = Isc,x,0
Itot,x
I0
. (3.49)

Whereas the dependence of Isc on the incident light is linear, Voc is logarithmically depen-
dent on the light intensity on the module surface. The conversion of the Voc,0 measured
at STC to the Voc at a certain incident light intensity is given by
Voc,x = Voc,x,0
ln Itot,x/ ln Im0 + 1
ln I0,x/ ln Im0 + 1
, (3.50)
where Im0 is the saturation current. For standard modules, equations 3.49 and 3.50 have
to be used once for the front side, whereas they have to be repeated to retrieve the
values for both the front and rear side of a bifacial module. From the front and rear side
Isc,f/r and Voc,f/r, the total current and voltage of a bifacial module Isc,b and Voc,b have
to be calculated. With the assumption of a linear current response under different light
intensities, the resultant module current can be calculated as a simple sum of the currents
generated at the front and rear side using
Isc,b = Isc,f + Isc,r. (3.51)
Singh et al. [25] also deduces the relation between the two voltages of the front and rear
side with the total open circuit voltage Voc,b of the bifacial module, which they define as
Voc,b = Voc,f +
(Voc,r − Voc,f ) ln(
Isc,f +Isc,r
Isc,f
)
ln Isc,r
Isc,f
. (3.52)
The output power of a PV module, whether monofacial or bifacial, can then be determined
using
Pmpp,x = FFVoc,xIsc,x (1 + αmpp · (ϑM − 25◦
C)) , (3.53)
where αmpp is the temperature coefficient of the module at the maximum power point, ϑM
the module temperature and ϑamb the ambient temperature. Whereas ϑamb is measured
at the installation site, ϑM can be calculated using the nominal cell temperature (NOCT)
approach [45], given by
ϑM = ϑamb +
TNOCT − 20◦
C
8
Itot, (3.54)
where following the assumptions made by Yusufoglu et al. [29] TNOCT,m = 45◦
C for
monofacial modules and TNOCT,b = 47◦
C for bifacial modules.
3.2.2 Annual energy yield Y
Comparing the performance of mono- and bifacial modules using the output power of their
front sides at STC is unfair for the bifacial modules, which in reality receive a portion
of the incoming irradiance on their rear side, increasing the current and allowing them
to produce more energy than a monofacial module with the same front side power. One
attempt to adequately compare the performances of the two technologies is using the
annual energy yield Y , which quantifies the amount of energy produced in one year in

40 3.3. Results
kWh per installed peak module power in kWp, giving Y a unit of kWh/kWp. Giving
the produced energy relative to the installed peak module power not only allows for the
comparison of bifacial and standard module, but also of different standard modules with
varying peak powers. The annual energy yield of standard modules Ym and of bifacial
modules Yb are given by
Ym/b =
n
i=0
Pmpp,m/b,i
Pmpp,f,0
∆t, (3.55)
where the produced energy is given in reference to the front side module power Pmpp,f,0
measured at STC.
3.2.3 Bifacial gain BF
After establishing that the comparison between the performances of monofacial and bi-
facial modules will be done using the respective annual energy yields, a value is defined,
with which this comparison is quantified. This allows for the reduction of the comparison
between the performances of both technologies to one value, which quantifies the annual
energy yield increase (or decrease) in percent based on Ym. The so called bifacial gain
BF given in % is therewith defined as
BF = 100
Yb − Ym
Ym
. (3.56)
This quantity will be used often in this thesis to assess the various module configurations
with different installation parameters, allowing for the determination of the optimal con-
figuration for a solar PV system with bifacial modules. Using the developed models, the
performance of bifacial PV systems will be determined for various different installations
and optimized for a maximum bifacial gain.
3.3 Results
In order to better understand the behaviour of bifacial modules in different configurations,
simulations will be carried out at varying installation parameters, each time keeping all the
parameters except one constant, and varying one parameter to observe its influence on the
energy production of the bifacial module. Not only the resulting energy yield of a bifacial
module under the different conditions will be considered, but also the bifacial gain and
the amount of solar irradiance reaching each cell on the rear side of the bifacial module.
First, the sources of the weather and module data are explicitly given, following which,
the optimum installation of a standard module is determined. The annual energy yield of
a standard module at the determined optimum configuration is then used as the reference,
when determining the bifacial gain of a certain bifacial module. The effect of the different
installation parameters on a stand-alone bifacial module is then simulated, before then
calculating the bifacial gains of bifacial modules installed in a field. All the simulations

are done for the locations El Gouna, Egypt and Constance, Germany, to compare the
performance of bifacial modules at different latitudes and weather conditions.
3.3.1 Input data
In this chapter, the sources of the input data, which are fed to the simulation tool, are
given. The details of the procurement of the weather and irradiance data are explained and
the electrical data of both the monofacial and bifacial modules chosen for the comparison
are mentioned.
3.3.1.1 Weather and irradiance
The developed simulation tool requires measurement data of the global, diffuse and direct
(beam) horizontal irradiances GHI, DHI and BHI respectively, in order to simulate the
irradiance reaching the front and rear sides of bifacial modules. Since GHI is the sum
of the two other components, measurement data of two components would be sufficient,
since the third can then be calculated. The database used by the software tool is acquired
from SoDa Services [46], a service developed in the framework of the project SoDa and
supported by the European Commission. The database includes among others, measure-
ments of GHI, DHI and BHI with a temporal resolution of 15 minutes. Free irradiance
data is available for any location for the period 01.02.2004-31.12.2005, from which only
the data from 2005 for El Gouna (N27◦
24’8”, E33◦
39’4”) and Constance (N47◦
40’40”,
E9◦
10’23”) is used for all simulations. The GHI data with a 15 minute time step is ac-
quired using a satellite-based method for surface solar radiation estimation, known as the
HelioSat method, and is described in [47, 48, 49]. The DHI is then calculated from the
satellite-measured GHI using the model developed by Ruiz-Arias [50], following which
the two irradiance components can be used to determine the direct horizontal irradiance
using equation 2.2.
The amount of monthly solar irradiance, divided into DHI and BHI, is depicted on the
left y-axis for El Gouna and Constance, in figures 3.9a) and 3.9b) respectively.
It is visible, that El Gouna receives more global solar irradiance than Constance, especially
in the winter months. The diffuse irradiance factor fD, which is also depicted in figures
3.9a) and 3.9b) on the right y-axis is however greater in Constance, due to more cloudy
or foggy weather conditions. In the winter, fD even reaches 80 % as a monthly average,
whereas the annual average of fD in 2005 in El Gouna is circa 20 % and it reaches 55 % in
Constance. Even though the high amount of diffuse irradiance in Constance in the winter
is beneficial for the bifacial gain of a module, since the module casts less shadow beneath
it, the solar irradiance is so low, that a bifacial module will nevertheless produce more
electricity in El Gouna, where fD is lower and the modules cast more shadow, therewith
reducing the rear side irradiance, but where there is more solar radiation, increasing

42 3.3. Results
significantly the electricity production due to the front side irradiance.
To model the reduction of the module output power due to the temperature coefficient αM
using equation 3.54, ambient temperature ϑamb data are also required. These are acquired
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0
50
100
150
200
250
Monthlyirradiance
Imon[kWh/m2]
0
20
40
60
80
100
DHIBHI
Diffuseirradiance
factorfD[%]
0
50
100
150
200
250
b) Constance
Monthlyirradiance
Imon[kWh/m2]
0
20
40
60
80
100
DHIBHI
Diffuseirradiance
factorfD[%]
Figure 3.9: Monthly diffuse and direct horizontal irradiance DHI and BHI, and diffuse irradi-
ance factor fD for a) El Gouna and b) Constance. Itot is higher for El Gouna than
in Constance (but highest for both in summer), fD is higher for Constance than for
El Gouna (but highest for both in winter).
0
10
20
30
40
Constance El Gouna
Ambienttemperature
ϑamb[◦C]
Figure 3.10: Monthly average of the ambient temperature during daytime depending on the
location, where El Gouna has higher temperatures all year long.

Masterthesis Ismail Shoukry Final

Masterthesis Ismail Shoukry Final

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