Masterthesis Ismail Shoukry Final

Master of Science Thesis

Bifacial Modules-Simulation and Experiment

Ismail Shoukry

2657503

Supervised by

Prof. J. H. Werner Dr. Eckard WefringhausDr. Joris Libal

University of Stuttgart International Solar EnergyInstitute for Photovoltaic Research Center Konstanz

Pfaffenwaldring 47 Rudolph-Diesel-Straße 1570569 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 Ruckseitenkontakten, sogenannte bifaziale Zellen, konnen

Licht auch von der Ruckseite absorbieren. Dies erhoht den generierten Strom und damit

den Energieetrag, wobei der großte Beitrag von der bodenreflektierten Strahlung kommt.

Ein Werkzeug fur die Simulation der Leistung von bifazialen Modulen wurde im Rahmen

dieser Masterthesis entwickelt und wurde zur Bestimmung des Bifacial Gain BF , benutzt.

Die durchgefuhrten Simulationen liefern einen BF von bis zu 35 %, fur ein alleinstehen-

des Modul. Weiße Reflektionsplatten unter den Modulen konnten BF auf 55 % erhohen,

wahrend eine ein-achsige Sonnennachfuhrung in Aquatornahe zu BF ≥ 60 % fuhren

wurde. BF sinkt jeweils auf ca. 32 % und 28 % fur das leistungsstarkste und leistungs-

schwachste 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 bestatigt.

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 PLANTSA 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

Ave

rage

mod

ule

pric

e[$/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 20250

20

40

60

80

100

Bif.

Mon

ofac

ial

Mar

kets

hare

[%]

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 publishesEuropean solar irradiation data from 566 sites1.

Where there is more Sun, more power can begenerated. The sub-tropical areas of the worldoffer some of the best locations for solar powergeneration. The average energy received in Europeis about 1,200 kWh/m2 per year. This compareswith 1,800 to 2,300 kWh/m2 per year in theMiddle East.

While only a certain part of solar irradiation can beused 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 ENERGYCONSUMPTION

FOSSIL FUELS ARE EXPRESSED WITH REGARDTO THEIR TOTAL RESERVES WHILE RENEWABLE ENERGIESTO THEIR YEARLY POTENTIAL.

GLOBAL ANNUALENERGY CONSUMP

ANNUAL SOLARIRRADIATIONTO THE EARTH

GLOBAL ANNUALENERGY 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 25000

0.5

1.0

1.5

2.0

2.5

Sp

ectr

al I

rra

dia

nce

(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 = 100DHI

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

10Pe

rce

nt R

efle

cta

nce

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.

24

5.3 ProductsToday’s wafer market for c-Si silicon solar cell manufacturing is dominated by casted materials, which will achieve a market share in excess of 60% in 2015. However, this market share will eventually shrink to below 50%. Simply distinguishing between mono-Si and mc-Si, as was done some years ago, is insufficient. The c-Si materials market is further diversifying, as shown in Fig. 24. High-performance (HP) mc-Si material now dominates the casted silicon market. Due to its excellent performance, this material is expected to replace conventional mc-Si completely by 2022. Monolike-Si has disappeared 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 of more than 47% in 2025. The roadmap confirms the predicted shift from p-type to n-type mono-Si within the mono-Si material market, as described in former editions. Considerable volumes of Si material 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 will make significant gains in market share over classical Cz due to the former’s cost advantages. Float zone (FZ) material for producing cells of the highest efficiency is also expected to appear on the mono Si market with a share of nearly 20% by 2025.

Fig. 24World market shares for different wafer types.

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-Sip-type mono-Si n-type mono-Si other (e.g. ribbon, kerŇess, ...)

ITRP

V 20

15

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+ emittern-type Si

front contactAR and passivation layer (SiNx)

n+ BSF

rear contactAR 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 = 100ηcell,rηcell,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

EVASolar cells

FrameBack sheetEVAJunction 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 40

100

200

300

400 back-to-backmeasured

constant Itot ,r

Pow

erou

tput

P[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 Aug0

5

10

15

20

25

30

in-field

stand-alone

Bifa

cial

gain

BF

[%]

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 ,rare 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 dMbetween 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 ′ = 360day 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(cosω cosϕ cos δ + sinϕ sin δ), (3.7)

αS =

180 − arccos

sin γS sinϕ− sin δ

cos γS cosϕfor Solar time 6 12:00h (3.8)

180 + arccossin γS sinϕ− sin δ

cos γS cosϕfor 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)

whereBHI is the solar irradiation on the horizontal surfaceAhor 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 = (cosαS cos γS, sinαS cos γS, sin γS)T , (3.14)

nM = (cosαM sin γM , sinαM 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 = BHIcos θSMsin 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 θ3SM

1 + κ θ3SM(3.19)

∆ = AMDHI

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

bF1 + 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 = GHIα

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 θ2πr2

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

A2θ2

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)]x2x1

]y2y1

]δ2δ1

]ξ2ξ1

(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]2dx 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)

12

arctan[ δ − y

(x2 − 2xξ cos γM + ξ2)12

]+

cos γMsin2 γM(δ − y)

[ [ξ2 sin2 γM + (δ − y)2

] 12

arctan[ x− ξ cos γM[ξ2 sin2 γM + (δ − y)2

] 12

]− ξ sin γM arctan

[x− ξ cos γMsin 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→AMfrom 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→AMand FAnsh→AM

have to be derived from FAs→AM.



Whereas calculating FAs→AMonce is sufficient, the computation of the view factor from

the shadow area Ash to the module rear side FAsh→AMis more complex, because since the

shadow area is moving, the calculation of FAsh→AMneeds 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→AMcan thus be calculated using

the process described in chapter 3.1.6, where the shadow rectangle edges are given by x1and 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 dMis 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

12

34

56

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 AMs entire reflective surface Asw entire reflective white sheet Awsh entire shadow area Ashssh part of shadow area outside white reflective sheet Asshwsh part of shadow area inside white reflective sheet Awsh

wnsh part of white reflective sheet without shadow Awnsh = Aw − Awshsnsh 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→AMcan be calculated

using the superposition rule given by equation 3.42 and rearranging it to the following



As

AwnshAw

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,0and 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,0Itot,xI0

. (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,0ln 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,rIsc,f

)

ln Isc,rIsc,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 − 25C)) , (3.53)

where αmpp is the temperature coefficient of the module at the maximum power point, ϑMthe 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 − 20C

8Itot, (3.54)

where following the assumptions made by Yusufoglu et al. [29] TNOCT ,m = 45C for

monofacial modules and TNOCT ,b = 47C 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,iPmpp,f ,0

∆t, (3.55)

where the produced energy is given in reference to the front side module power Pmpp,f ,0measured 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 = 100Yb − YmYm

. (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 (N2724’8”, E3339’4”) and Constance (N4740’40”,

E910’23”) 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 αMusing equation 3.54, ambient temperature ϑamb data are also required. These are acquired

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

50

100

150

200

250

Mon

thly

irrad

ianc

eI m

on[k

Wh/

m2 ]


20

40

60

80

100

DH

IB

HI

Diff

use

irrad

ianc

efa

ctor

f D[%

]


50

100

150

200

250b) Constance

Mon

thly

irrad

ianc

eI m

on[k

Wh/

m2 ]


20

40

60

80

100

DH

IB

HI

Diff

use

irrad

ianc

efa

ctor

f D[%

]

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).


10

20

30

40

Constance El Gouna

Am

bien

ttem

pera

ture

ϑam

b[

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.



in one hour time steps for the desired locations in Egypt and Germany from the software

tool Meteonorm [51], a comprehensive meteorological reference database. The monthly

average of ϑamb measured during daytime is depicted in figure 3.10, where the higher

temperatures all year round in El Gouna compared to Constance are visible. The higher

temperatures result in higher temperature coefficient losses in El Gouna, but the much

higher irradiance there, compensates for these losses, with solar PV modules producing

more energy in El Gouna than in Constance, despite the higher temperatures.

3.3.1.2 Module performance

To estimate the power of either a standard or a bifacial module from the solar irradiance

reaching the module front and rear sides, the developed electrical model, introduced in

chapter 3.2, requires I-V -curve measurements of the considered module, whether standard

or bifacial, at STC. It is necessary to measure the front and rear side of the bifacial module

separately, which can be achieved by covering the side currently not being measured with

black tape. The tape prevents light from reflecting off the walls and reaching the other

side of the bifacial module, consequently contaminating the measurement. The I-V -curve

measurement provides values for the Isc, Voc, FF , Impp, Vmpp, Pmpp, and in case of a

bifacial module, the bifaciality factor fB, defined by equation 2.6. In order to allow for a

fair comparison between the performance of a standard and a bifacial module, modules

with a similar front side I-V -parameters were chosen. The data of the two modules, which

are used in the simulation, are given in table 3.4.

Table 3.4: I-V-curve measurement results of a standard and a bifacial module. Rear and front

side of bifacial module measured separately. Front power of bifacial module higher

than that of monofacial module.

Type Side Voc [V ] Isc [A] FF [%] Pmpp [W ] Vmpp [V ] Impp [A] fB [%]

Monof. front 37.82 8.85 76.40 255.58 30.78 8.30 −

Bif.front 38.98 8.84 74.15 260.40 31.00 8.24

89.80rear 38.80 8.07 74.68 233.85 31.04 7.54

3.3.2 Sun’s position

The first step of the simulation, is the determination of the position of the Sun using

the DIN 5034 algorithm, described in chapter 3.1.2. The position of the sun not only

influences the irradiance reaching the front side of the module, but also determines the

position of the shadow of the module on the ground, hence influencing also the rear side

irradiance. The position of the Sun, given by the elevation angle γS and the azimuth angle

αS, was computed and plotted for the 21st day of each month in figures 3.11a) and 3.11b)


44 3.3. Results

for El Gouna and Constance respectively. Whereas in El Gouna the Sun is higher up in

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 3600

20

40

60

80

100a) El Gouna

6

7

8

9

10

11

12

13

14

15

16

17

18

Solar time

Sun

elev

atio

nan

gleγ

S

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 3600

20

40

60

80

100b) Constance

56

78

910

11 12 1314

1516

1718

19

Solar time

Sun azimuth angle αS

Sun

elev

atio

nan

gleγ

S 21. JunMay/JulApr/AugMar/SepFeb/OctJan/Nov21. Dec

Figure 3.11: The position of the Sun given by the azimuth and elevation angles for a) El Gouna

and b) Constance. Notice that Constance has longer summer days, shorter winter

days and overall lower γS than El Gouna.

the sky all year long than in Constance, Constance shows longer days in June compared

to the Egyptian city with the lower latitude. El Gouna however, has longer days during

December. Since both locations are situated in the northern hemisphere, the movement

of the Sun is always around the south, with the Sun reaching its highest point directly in

direction south, which occurs at noon according to the solar time. The higher elevation

angles in El Gouna will cause the modules to cast smaller shadows at a closer distance to

the modules, than in Constance.

3.3.3 Standard module

To define the reference, to which the bifacial modules are compared, simulations are car-

ried out using standard PV modules. The determined optimal configuration of a standard

module for different locations and albedo coefficients is then used for the comparison with



bifacial module installations. Additionally, the corresponding maximum annual energy

yield of the monofacial module is used as reference in the calculation of the bifacial gain

using equation 3.56. To determine the optimum γM of a monofacial module, the annual

energy yield is calculated for 0 6 γM 6 90 in 1 steps. This prediction was repeated for

α = 0.2 and α = 0.5, both for El Gouna and Constance, the results of which are visualized

in figure 3.12, where the optimums of the different locations and albedo coefficients are

each marked by a triangle. The exact values of the optimum configuration are given in

table 3.5. Since both sites are in the northern hemisphere, the optimum module azimuth

angle αM was presumed to be 180, where the modules would be facing south. The annual

0 10 20 30 40 50 60 70 80 90

500

1,000

1,500

2,000

2,500

α = 0.5

α = 0.2

optimum

El Gouna

Constance

Module tilt angle γM [−]

Ann

uale

nerg

yyi

eld

Ym

[kW

h/kW

p]

Figure 3.12: Tilt angle dependant annual energy yield of monofacial module Ym higher in El

Gouna. Yield decreases on both sides of the optimal tilt angle γM . Difference

between curves with α = 0.2 and α = 0.5 stronger for higher γM .

energy yield of standard modules Ym, varies depending on the location, albedo coefficient

α and tilt angle γM , and is higher in El Gouna than in Constance, due to the stronger

solar irradiance. It decreases with increasing deviation from the optimal tilt angle γM ,opt.

In addition, the deviation between the curves with α = 0.2 and α = 0.5 is larger at a tilt

angle of γM = 90 than at γM = 0. This effect is due to the fact, that a vertically in-

stalled PV module receives more ground-reflected irradiance than a horizontally installed

module, which receives none. The enhancing of Irefl by a greater albedo coefficient is

therefore more visible for steeper installation angles.

Observing the optimum tilt angles, marked by the triangles in figure 3.12 and the exact

values given in table 3.5, it is visible, that γM ,opt increases in Constance, the location with

the higher latitude, compared to El Gouna. Due to the lower sun elevation angles γS in

Constance, PV modules have to be installed at a steeper angle, to maximize the solar

irradiance reaching the module surface. In addition, the increase in γM ,opt for increasing

ground albedo coefficient can be observed. This occurs, because the reduction in the direct

and diffuse irradiances on the module surface, caused by the increasing γM , is smaller than

the enhancement in the ground-reflected irradiance.


46 3.3. Results

Table 3.5: Results of simulation of monofacial module. Optimum tilt angle γM ,opt of monofacial

module increases for locations with higher latitudes. γM ,opt also rises for higher α, to

make better use of the increased ground-reflected irradiance.

El Gouna Constance

α = 0.2 α = 0.5 α = 0.2 α = 0.5

Optimum tilt angle γM ,opt [−] 25 30 35 41

Annual energy yield Ym [kWh/kWp] 1888 1919 1040 1070

3.3.4 Stand-alone bifacial module

Whereas the annual energy yield of a stand-alone monofacial module is only dependant

on a few installation parameters, including γM and αM , the annual energy yield of a

bifacial module Yb and the resulting bifacial gain BF are influenced by other factors,

including the module height hM and the diffuse irradiance factor fD. The influence of the

various installation and site parameters and weather conditions on Yb, BF and the rear

side irradiance of the bifacial module Itot,r are examined separately in the following sub-

chapters. The aim of the optimization of the installation parameters of a bifacial module,

is the maximization of the overall performance of the module, and not the bifacial gain

BF . Other configurations might therefore be beneficial for higher BF .

3.3.4.1 Tilt angle γM

Unlike a standard module, the power output of a bifacial module is more sensitive to

suboptimal tilt angles. Furthermore, γM ,opt of a bifacial module is also dependant on the

module installation height, since the view factor, and therewith the amount of rear side

irradiance, depend on the distance between the two surfaces. Therefore, Yb was calculated

for varying tilt angles in 1 steps for varying module heights with 0.5 m steps, and the

resulting optimum tilt angles γM ,opt, for which the yield is maximized, are depicted in

figure 3.13a) for El Gouna and in figure 3.13b) for Constance for varying module elevations.

Similar to a standard module, the optimum tilt angle of a bifacial module is larger for

Constance, which is located at a higher latitude than El Gouna, regardless of the module

elevation. Due to the lower solar elevation angle at higher latitudes, PV modules are

installed at a greater γM , in order to receive more incident radiation. To receive maximum

reflected irradiance on the rear side, a bifacial module should theoretically be installed very

close to the ground, in order to maximize the view factor, which is inversely proportional

to the distance between the two considered surfaces. However, the closer the modules is

mounted to the ground, the closer it get to its own shadow, where the reflected irradiance

is strongly reduced, due to the diminished incident direct and diffuse irradiances. The



0 0.5 1 1.5 2 2.5

20

25

30

35

40

45

50

α = 0.5

α = 0.2

a) El Gouna

Module height hM [m]

Opt

imum

tilta

ngle

γM

,opt

[−]

0 0.5 1 1.5 2 2.5

α = 0.5

α = 0.2

b) Constance


Figure 3.13: Optimum tilt angle γM ,opt is higher in b) Constance, due to higher latitude, com-

pared to a) El Gouna. Steep inclination at lower module heights hM to increase

distance between module and shadow, and lower inclination at larger hM to de-

crease distance between module and reflective ground.

determination of the optimum tilt angle depending on the module elevation is therefore

about finding a compromise between the two mentioned effects.

Figures 3.14a) and 3.14b) show the total irradiance reaching the rear side of a PV module

with γM = 25 and γM = 60 respectively. The color-bars beneath the graphs allow

for a comparison of the absolute values of the irradiance between the two different con-

figurations. Choosing the same range of 40 W/m2 for both axes makes comparing the

homogeneity of Itot,r of both configurations possible. The reduction of Itot,r caused by the

shadow of the module on the ground is clearly visible in figure 3.14a), identifiable by the

strong color gradient. Because the module surface is further away from the shadow at a

tilt angle of 60, the consequent inhomogeneity shown in figure 3.14b) is less prominent.

However, the module is also further away from the ground, causing the overall smaller

Itot,r. Figure 3.14b) also shows a slight decrease of Itot,r in the top cell row, which is a

consequence of the top section of the module being too far away from the ground and the

resulting reduction of the view factor.

3.3.4.2 Module elevation hM

Determining the optimal module elevation hM is also a process of finding the proper

compromise, at which the module is far enough from its shadow, but not too far from

the irradiance reflecting ground. Higher module mounts also tend to be more costly and

mechanically challenging, forcing project developers to opt for lower sub-optimal heights,

due to lower installation costs. Since the purpose of this thesis is to maximize the en-


48 3.3. Results

a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, γM = 25

Module length lM

Mod

ule

wid

thw

M

350 360 370 380 390

Total rear side irradiance Itot ,r [ Wm2 ]

b) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, γM = 60

Module length lM

290 300 310 320 330


Figure 3.14: A γM of b) 60 causes lower overall irradiance, but also less inhomogeneity, due to

increased distance to the ground, compared to a) 25. Lower Itot,r at the bottom of

figure a) and b) caused by module shadow on the ground. The dashed lines indicate

the subdivision of the module area into an array of 6x10 elements according to the

6x10 solar cells of which the module is composed.

ergy production and bifacial gain of bifacial modules, the higher installation costs are

disregarded. Consequently, the bifacial gain was calculated for various hM with the cor-

responding optimum tilt angle for each module installation height, determined in figures

3.13a) and 3.13b) for different locations and albedo coefficients. The results are visual-

ized in figures 3.15a) and 3.15b), for El Gouna and Constance respectively, where the

dependence of the yearly bifacial gain BF on the module elevation hM is shown.

Regardless of the location of the installation, the yield increase from the additional rear

side irradiance rises significantly for bigger α, due to the higher reflectance of the ground.

The determined BF reaches its maximum at hM = 1.5 m for all configurations, except

in Constance for α = 0.2, where BF is maximized at an elevation of 1 m. For reasons

of consistency, a module height of 1.5 m is used in all the following simulations, unless

stated otherwise. The optimal module heights hM ,opt, the corresponding γM ,opt and the

resulting BF , which are used in the subsequent calculations are further listed in table 3.6

to provide better and quicker visibility.

According to the calculations, bifacial modules mounted in El Gouna at hM = 1.5 m and

the corresponding tilt angle 25, would produce 13.46 % and 33.85 % more electricity than

a comparable standard module, for α = 0.2 and α = 0.5 respectively. In Constance, a

bifacial module would be optimally mounted at hM = 1.5 m and γM = 37, and would

have a bifacial gain of 15.98 % and 35.73 % for α = 0.2 and α = 0.5 respectively, which is



0 0.5 1 1.5 2 2.50

10

20

30

40

α = 0.5

α = 0.2

a) El Gouna


Bifa

cial

gain

BF

[%]

0 0.5 1 1.5 2 2.5

α = 0.5

α = 0.2

b) Constance


Figure 3.15: Elevation dependant yearly bifacial gain BF increases for higher albedos for both

a) El Gouna and b) Constance. Module height optimum is between 1 m and 1.5 m

for all configurations.

Table 3.6: Results of simulation of bifacial module. Bifacial gain BF is higher in Constance

and increases for larger albedo. Module height is constant for all configurations.

Compared to a standard module, γM ,opt is lower.

El Gouna Constance

α = 0.2 α = 0.5 α = 0.2 α = 0.5

Optimum module height hM ,opt [m] 1.5 1.5 1.5 1.5

Optimum tilt angle γM ,opt [−] 25 25 37 37

Bifacial gain BF [%] 13.46 33.85 15.98 35.73

a slightly higher bifacial gain than in El Gouna. This is due to higher portion of diffuse

irradiation in Constance, the effect of which is explained in chapter 3.3.4.3. Compared

to a standard module, γM ,opt declines for bifacial modules, resulting in better viewing

of the ground-reflected irradiance by the module rear side. Figures 3.16a) and 3.16b)

depict the influence of the height on the amount of irradiance reachnig the rear side of

a bifacial module for hM = 1 m and hM = 10 cm respectively. Modules installed at

hM = 1 m receive relatively homogeneous radiation on the rear side, with a deviation of

circa 40 W/m2, compared to modules mounted at hM = 10 cm, where the deviation is

greater than 150 W/m2. Furthermore, Itot,r is overall lower at hM = 10 cm. A bifacial

module mounted at an elevation of 10 cm is very close to the shadow region, where

there is less incident radiation to reflect, due to the complete blocking off of BHI by the

module, causing a strong reduction in Itot,r, more prominently in the bottom cell rows of


50 3.3. Results

a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m

Module length lM

Mod

ule

wid

thw

M

150 200 250 300 350 400


b) El Gouna, 21.06.2005, noon,α = 0.5, hM = 10 cm

Module length lM

Figure 3.16: Total irradiance on module rear side Itot,r is 369 W/m2 and 234 W/m2 for elevations

a) 1 m and b) 10 cm respectively. Lower overall Itot,r and stronger deviation at

10 cm, due to close proximity to shadow.

the module.

3.3.4.3 Diffuse irradiance factor fD

The amount of diffuse irradiance DHI of the total GHI, given by the diffuse irradiance

factor fD, also affects the energy yield of standard modules, the influence however, is

more pronounced for bifacial modules. A PV module blocks off the direct portion of

the irradiance BHI, casting a shadow beneath it. Therefore, only DHI is available for

reflection in the shadow region, and Itot,r is consequently decreased. Increasing fD would

consequently increase the amount of irradiation available for reflection in the shadow

region, the influence of which is attenuated as a result. This increase in fD would also

cause an increase in the bifacial gain of the module, since it would receive more rear

side irradiation, which is shown in figures 3.17a) and 3.17a) for El Gouna and Constance

respectively, where the optimum configurations determined in chapters 3.3.3 and 3.3.4.2

are used in the simulation of the energy yield. Assuming physically impossible weather

conditions with a diffuse irradiance factor of 100 %, a bifacial module would produce 40 %

for α = 0.5 and 15 %−20 % for α = 0.2 more energy than a standard module. The yearly

average of fD under real weather conditions in 2005 is 20 % in El Gouna and 55 % in

Constance, resulting in slightly higher BF in Constance than in El Gouna for simulations

using real irradiance data. The resulting irradiance reaching the rear side at a given

date and time is visualized in figures 3.18a) and 3.18b) for fD = 25 % and fD = 100 %

respectively, using an otherwise identical configuration. Because the module does not cast

a shadow at fD = 100 %, the irradiance available for reflection beneath the module is not



0 20 40 60 80 1000

10

20

30

40

50

α = 0.5

α = 0.2

a) El Gouna

Diffuse irradiance factor fD [%]

Bifa

cial

gain

BF

[%]

0 20 40 60 80 100

α = 0.5

α = 0.2

b) Constance


Figure 3.17: The incident BHI is blocked by the module, reducing the solar irradiation available

for reflection in the shadow region for a) El Gouna and b) Constance. Increasing

fD consequently causes reduction of shadow’s influence and increases Itot,r and BF .

reduced, and the module rear side therefore receives overall more irradiation than under

real weather conditions. The inhomogeneity caused in configuration a) by the shadow

region being closer to the center of the lower cell rows at noon time, is not observed in

configuration b), where the influence of the shadow on the reflection is annulled due to the

a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, fD = 25 % (real)

Module length lM

Mod

ule

wid

thw

M

340 360 380 400


b) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, fD = 100 %

Module length lM

390 410 430 450


Figure 3.18: Total irradiance on module rear side Itot,r for diffuse irradiance factors a) 25 % and

b) 100 %. Figure b) shows higher overall Itot,r and a much better homogeneity, due

to the lack of shadow-casting direct irradiance at fD = 100 %.


52 3.3. Results

lack of shadow-casting direct irradiance at fD = 100 %. At a theoretical fD of 100 %, the

results at α = 0.5 would be BF ≈ 40 % for both cities, whereas at α = 0.2, BF = 15 %

and BF = 19 % for El Gouna and Constance respectively.

3.3.4.4 Ground surface size

The view factor, used in the calculation of the ground-reflected irradiance reaching the

rear side Irefl,r, is a geometric value quantifying the amount of radiation leaving one closed

surface, that reaches a second closed surface. As a consequence, the ground surface has

to be defined by outer limits. The length L2 to the front edge of the surface is defined

by the intersection of the module plane with the ground. The module rear side does not

receive irradiance from the area further away than L2. The lengths LS and L1 to the

side and back edges of the surface are a compromise between two effects. Minimizing

LS and L1 would decrease computation time, but falsify the results, because parts of

the area contributing to Irefl,r would not be considered, and the opposite would be the

effect, in case LS and L1 are maximized. L2, LS and L1 are visually defined in figure

3.2. To determine the optimized surface size, BF calculations were carried out with the

optimum module installation for varying lengths LS and L1 and depicted in figures 3.19a)

and 3.19b) for El Gouna and Constance respectively.

0 10 20 30 40 500

10

20

30

40

α = 0.5

α = 0.2

a) El Gouna

Surface width LS and length L1 [m]

Bifa

cial

gain

BF

[%]

0 10 20 30 40 50

α = 0.5

α = 0.2

b) Constance


Figure 3.19: Reducing the size of the reflective surface too much reduces BF , since a portion of

the area contributing to Irefl,r is excluded. Optimum at LS = L1 = 15 m for a) El

Gouna and b) Constance.

It is visible that the optimum surface size is given for the saturation point LS = L1 = 15m,

which is used for all simulations in this thesis, unless explicitly stated otherwise. Increas-

ing the reflective surface size would only increase computation time, but not accuracy.

Decreasing the lengths below 15 m would exclude a portion of the ground that con-

tributes to Irefl,r, causing the drop in BF for lengths below 15 m visible in figures 3.19a)



and 3.19b).

3.3.4.5 Ground albedo α

Higher ground albedo coefficients result in increasing energy production of bifacial mod-

ules, mainly due to the enhanced contribution of the module rear side. This has led

project developers to consider increasing α by changing the surface beneath the mod-

ules, for example by using white reflective plates or sheets made from different materials.

The albedo of these sheets ranges between 0.7 and 0.9, making them very promising in

terms of increasing energy production of a PV installation. Since the use of such sheets

increases investment and maintenance costs, it is beneficial to minimize their size. Using

an albedo of 0.85 for the white surface, the bifacial gain was calculated at varying white

sheet areas, the edges of which are given by w2, wS and w1, which are visualized in figure

3.2. The results of the simulation are depicted in figures 3.20a) and 3.20b) for El Gouna

and Constance respectively, where w2 was held constant at 0.5L2.

0 2 4 6 80

10

20

30

40

50

60

70

1 3 5 7

α = 0.5

α = 0.2

a) El Gouna

Surface width wS and length w1 [m]

Bifa

cial

gain

BF

[%]

0 2 4 6 81 3 5 7

α = 0.5

α = 0.2

b) Constance


Figure 3.20: Yearly bifacial gain BF increases for bigger white reflective sheets (featuring an

albedo of 0.85), reaching almost a) 55 % in El Gouna and b) 50 % in b) Constance,

where α indicates the albedo of the portion of the ground that is not covered by

the reflective sheet.

The curve with an original albedo of 0.2 exhibits a sharper increase of BF with increasing

white sheet surface size, caused by the larger difference between the original ground albedo

coefficient, and that of the white sheet. The two curves draw nearer to each other until

they meet, when the whole ground surface is covered with the white sheets, and it no longer

makes a difference, what the albedo of the ground is. Theoretically covering the whole

ground white, enables the bifacial module to produce 55 % and 50 % more than a standard

module in El Gouna and Constance respectively. However, depending on the additional


54 3.3. Results

costs project developers and financiers are willing to invest in the white plates, and on the

albedo coefficient of the ground, a length w1 between 3 m and 5 m would already generate

a much higher bifacial gain. The effect of α on the rear side irradiance can be seen in

figures 3.21a) and 3.21b), where, keeping all installation parameters constant, Itot,r was

determined for α = 0.2 and α = 0.5.


Module length lM

Mod

ule

wid

thw

M

350 375 400


b) El Gouna, 21.06.2005, noon,α = 0.2, hM = 1 m

Module length lM

150 175 200


Figure 3.21: Total irradiance on module rear side Itot,r for diffuse irradiance factors a) 0.2 and

b) 0.5. Figure b) shows lower overall Itot,r of 157 W/m2, compared to 369 W/m2

in figure a), and a more homogeneous irradiation, due to the lower reflectance of

the ground.

Figure 3.21b) shows, that the bifacial module rear side receives less than half the irradiance

with a ground albedo of 0.2 compared to the irradiance with α = 0.5. This reduction is

caused by the weaker reflectivity of a ground with α = 0.2. Since the reflectance is low,

inside and outside the shadow region, the reduction of Itot,r, caused by the shadow on the

ground, is not as substantial as with α = 0.5, where the shadow causes the significant

inhomogeneity visible in figure 3.21a).

3.3.4.6 Model complexity

For reasons of accuracy, the view factor from the ground to the rear side of the module

is calculated for each cell separately. The cell with the lowest irradiation then acts as the

limiting factor for the current flowing in the module. Determining the view factor from

the ground to the module as an individual surface, only delivers an estimate of the average

irradiation over the whole module surface, not accounting for the inhomogeneities, caused

by the different distances between each cell and the ground. However, dividing the module

into 60 parts, dramatically increases the computation time. It is therefore beneficial, to



decrease the number of parts, the modules rear side is divided in to, without strongly

affecting the accuracy of the simulation. How many parts the module is divided into, is

given by the number of columns and rows, which for a 60 cell module means 6 rows and 10

columns, if the module is mounted with the longer edge parallel to the ground. The BF is

consequently calculated for different numbers of rows and columns. The deviation of the

resulting BF from the most accurate simulation with 6 rows and 10 columns, which is a

measure of the simulation’s inaccuracy, is given as an intensity graph for varying row and

column numbers in figures 3.22a) and 3.22b) for El Gouna and Constance respectively.

The measure of relative inaccuracy ∆BF is defined as

∆BF = 100BFi −BF60

BF60

, (3.57)

where BFi is the bifacial gain at any given simulation and BF60 is the bifacial gain,

determined when dividing the module into 6 rows and 10 columns.

a) El Gounaα = 0.5

1 2 3 4 5 6 7 8 9 101

2

3

4

5

6

Number of columns

Num

bero

frow

s

0 0.5 1 1.5 2 2.5 3 3.5Relative inaccuracy ∆BF [%]

b) Constanceα = 0.5

1 2 3 4 5 6 7 8 9 10Number of columns

Figure 3.22: Inaccuracy of the simulation increases with decreasing number of parts for both a)

El Gouna and b) Constance. Simulation with four columns and three rows sufficient

for a deviation of less than 1 %.

From the figures it is visible, that dividing the module rear side into less parts, causes

inaccurate simulation results, due to not taking into account the different distances be-

tween each cell and the ground. However, it is also visible, that it is not necessary to

divide the module into ten columns and six rows to achieve the desired accuracy. Already

at four columns and three rows, the deviation from the most accurate simulation is under

1 %. Note that the 1 % is not the absolute difference in BF , but a value relative to

the simulation with 60 parts. This means, that even a simulation only considering the

module rear side as a whole, which delivers the least accurate results, with 3.5 % relative

deviation, is sufficiently accurate for some applications, where the computation time is of

great importance and where a relatively small discrepancy of 3.5 % is tolerable. But even

restricting the division of the module to twelve parts, already reduces the computation

time five fold, without strongly affecting the accuracy of the simulation.


56 3.3. Results

3.3.4.7 Time and date

Solar generated energy varies diurnally and seasonally, fluctuating strongly with the season

and time dependant solar irradiation. The behaviour of bifacial modules is not any

different, except for the additional dependency on the module elevation hM or the ground

albedo α. Since the total energy yield of bifacial modules is dependant on the available

amount of GHI, it varies through the day. The total amount of irradiance reaching the

front side of a PV module and the irradiance reaching the rear at α = 0.2 and α = 0.5

was simulated for the 21.06.2005 and visualized in figure 3.23a) for El Gouna and figure

3.23b) for Constance using the coordinated universal time (UTC).

4 6 8 10 12 14 16 180

200

400

600

800

1,000 a) El Gouna

Itot ,f

Itot ,r , α = 0.2

Itot ,r , α = 0.5

Hour (UTC)

Sol

arirr

adia

nce

I[W m

2]

4 6 8 10 12 14 16 18

b) Constance

Hour (UTC)

Figure 3.23: Notice the time dependant irradiance Itot,r follows the same trend as Itot,f . Whereas

the peak of the irradiance is at solar noon, the amount of Itot,r relative to Itot,f is

higher in the morning and evening hours, in a) El Gouna and b) Constance.

Figures 3.23a) and 3.23b) show again, that the rear side irradiance strongly increases

for higher albedos. Itot,r additionally depends on the time of day, its curve following the

same trend as Itot,f , with its peak at solar noon of a clear day. However, where the total

irradiance on the front and rear is highest at noon, the difference between Itot,f and Itot,ralso is maximized at noon. The contribution of the rear side is therefore stronger in the

morning and in the evening, than at noon. This can be seen in figures 3.24a) and 3.24a),

where the bifacial gain BF was computed at α = 0.2 and α = 0.5 for the 21.06.2005 and

visualized for El Gouna and Constance respectively.

Because Itot,f is more strongly reduced than Itot,r in the morning and evening, a bifacial

module has a higher gain at the beginning and the end of a day. At certain times, the

rear side even has a higher contribution to the energy production than the front side, for

example very early, when the sun is behind the module. BF is further influenced by the

position of the module shadow on the ground, whereby the further away the shadow is,

the less it affects the module rear side irradiance. Consequently, the irradiance on the left



3 6 9 12 15 18 210

100

200

300a) El Gouna

α = 0.2α = 0.5

Hour (UTC)

Bifa

cial

gain

BF

[%]

3 6 9 12 15 18 21

b) Constance

α = 0.2α = 0.5

Hour (UTC)

Figure 3.24: The bifacial gain is at its maximum in the morning and evening, reaching values

higher than 100 %, for example, when the sun is behind the module, and the

contribution of the rear side is very high, in a) El Gouna and b) Constance.

side of the module in the afternoon, receives a larger amount of solar irradiation than at

noon. These effects can be seen in figures 3.25a) and 3.25b), where Itot,r is given as an

intensity graph for a stand-alone module at noon and in the afternoon respectively.


Module length lM

Mod

ule

wid

thw

M

350 360 370 380 390 400 410 420


b) El Gouna, 21.06.2005, 14:00,α = 0.5, hM = 1 m

Module length lM

Figure 3.25: Reduction of Itot,r in the b) afternoon no longer symmetrical like at a) noon, but

more to the west, closer to the module shadow. Itot,r increases on the module west

side, due to larger distance to shadow.

The bifacial gain does not only vary on an hourly basis, but also on a monthly one. BF is

simulated for each month separately at albedo coefficients of 0.2 and 0.5, and the results


58 3.3. Results

are visualized in figure 3.26a) for El Gouna and in figure 3.26b) for Constance. The bifacial

gain reaches its maximum of almost 40 % in both cities during the summer months, while

it decreases to almost 30 % in the winter at an albedo coefficient of α = 0.5, whereas for

α = 0.2 the maximum and minumum are 17 % and 10 % respectively. The reduction of

the bifacial gain during the winter months is also not as sharp as the reduction of the

monthly irradiance shown in figures 3.9a) and 3.9b). Moreover, it is visible from figures

3.26a) and 3.26b), that whereas both cities have comparable bifacial gains in the summer,

BF is slightly higher in Constance than in El Gouna in the winter, especially in February,

due to the much higher portion of diffuse irradiance, given by fD, which is also depicted

in figures 3.9a) and 3.9b).


10

20

30

40 a) El Gouna

α=

0.5

α=

0.2

Bifa

cial

gain

BF

[%]


10

20

30

40 b) Constance

α=

0.5

α=

0.2

Bifa

cial

gain

BF

[%]

Figure 3.26: Monthly bifacial gain in a) El Gouna and b) Constance reaches maximum of circa

40 % in the summer. BF in the winter is higher in Constance, due to higher fD.

3.3.5 East-west vertically mounted stand-alone bifacial module

One of the drawbacks of solar energy, is the production of most of the electricity at noon,

causing an hourly mismatch of demand and production, at least in residential applications.

Whereas the peak of the residential electrical load is in the evening, solar panels produce

most electricity at noon. One approach to spreading the electricity production more



evenly over the day without the utilization of batteries, suggests the use of vertically

mounted bifacial modules (VMBM), with one side facing east and the other facing west

[52, 53]. The theory is, that the east and west sides would produce more energy than

a south-facing module in the morning and in the evening respectively, since they would

be better positioned towards the sun, than a south-facing module. A vertically mounted,

east-west-facing bifacial module is depicted schematically in figure 3.27.

N

ES

W

Figure 3.27: Schematic depiction of a vertically mounted, east-west-facing bifacial module.

In order to examine the behaviour of a VMBM, the developed model was used to deter-

mine the irradiance on both sides, while changing the calculation of the ground-reflected

irradiance reaching the front side Irefl,f from the isotropic model, given by equation 3.29,

to the view factor approach, since the isotropic model would no longer yield accurate

results, because the model would not take into account the effect of the shadows on the

ground. Presuming the module front side is facing east, the module sides are no longer

referred to as the front and rear sides in this chapter, but more precisely as the east- and

west-facing sides. As an initial examination, the amount of irradiance reaching the east-

and west-facing sides of a bifacial module Ieast and Iwest, their sum Isum, and the amount

of irradiance reaching the front side of an optimally installed standard module Istd are

each simulated for a whole day in 15 minute steps at α = 0.5. The results are shown for

El Gouna in figures 3.28a) and 3.28b), and for Constance in figures 3.28c) and 3.28d), for

the summer and winter respectively. As expected, the results show a higher irradiance on

the east-facing side during the first half of the day, and on the west-facing side during the

second half of the day, though both sides still receive a considerable amount of irradiation,

when the Sun is facing the other side, due to the contribution of the ground-reflected ir-

radiance. The drop in the total irradiance reaching the VMBM Isum at noon is caused by

the Sun shining on the side edge of the module, thus no direct irradiance reaches either

side of the module, and Isum drops as a consequence. The amount of solar irradiation

reaching a VMBM on the 21.06.2015, either in El Gouna or in Constance, given by the

area beneath the Isum curve, seems greater than the area beneath the Istd curve. On

the 21.12.2005 however, a VMBM will produce less energy than an optimally installed

standard module, since the area beneath Isum is smaller than the area beneath Istd.

To determine the gain or loss of energy produced by a bifacial module in an east-west


60 3.3. Results

vertical installation compared to an optimally installed monofacial module, simulations

with VMBM at a height of 0.5 m were carried out and compared to an optimally installed

monofacial module. The resulting positive or negative bifacial gains BF are given in table

3.7 for the various albedo coefficients and locations.

Table 3.7: Vertically mounted bifacial module at hM = 0.5 m has a lower yield than an optimally

mounted monofacial module, except in Constance with α = 0.5.

A→BEl Gouna Constance

α = 0.2 α = 0.5 α = 0.2 α = 0.5

BFMonofacial optimum −14.88 % −5.99 % −4.52 % +15.77 %→ Bifacial vertical

0

200

400

600

800

1,000a) El Gouna21.06.2005

IeastIwest

IsumIstd

Sol

arirr

adia

nce

I[W m

2]

c) Constance21.06.2005

4 6 8 10 12 14 16 180

200

400

600

800

1,000b) El Gouna21.12.2005

Hour (UTC)

Sol

arirr

adia

nce

I[W m

2]

4 6 8 10 12 14 16 18

d) Constance21.12.2005

Hour (UTC)

Figure 3.28: Notice the two peaks of the total irradiance Isum reaching a vertical bifacial module,

due to the east- and west-facing sides. Isum experiences a significant drop at noon,

caused by the Sun shining on the module side edge. Energy production due to Isum

(area beneath the curve) higher than Istd in the summer, but lower in the winter.



According to the results in table 3.7, a VMBM produces in El Gouna, less energy than a

standard module, regardless of the albedo, with a loss of−14.88 % and−5.99 % for α = 0.2

and α = 0.5 respectively. Whereas the loss in energy yield is lower in Constance for an

albedo of 0.2 than in El Gouna, with a value of −4.52 %, a VMBM located there would

have a 15.77 % higher annual energy yield than a standard module, in addition to the

initial advantage of a VMBM of not producing most of the electricity at noon. Moreover,

depending on the application and the purpose of the planned solar power plant, a loss in

Y of −5.99 % or −4.52 % might be tolerable, if the desire of the developer is to provide

more electricity in the morning and evening, without the application of batteries. Using

both VMBM and optimally tilted modules in a solar park, whether bifacial or monofacial,

would provide a more homogeneous production curve over the whole day, without the drop

or the peak at noon.

3.3.6 Stand-alone bifacial module with one-axis tracking

Tracking systems for photovoltaic arrays are used to increase the energy production per

module, and hence decrease the cost of the delivered electricity by actively adjusting the

installation angles of the PV module, so that it is optimally facing the Sun. Tracking

systems include two-axis tracking, where both the tilt and azimuth angles of the module,

γM and αM , can be adjusted using electric motors [54, 55]. Whereas this kind of system

delivers the optimum positioning towards the Sun, it also the most expensive, mechanically

challenging and electrically demanding. The use of sophisticated structures and motors,

which require significant amounts of electricity and continuous maintenance, strongly

increase the cost of such systems. The concept of two-axis tracking is schematically

depicted in figure 3.29b). A more cost effective alternative, is the one-axis tracking system,

where at a fixed γM and αM , the module is turned around the rotation axis, facing east

in the morning, and west in the evening [56, 57, 58], as shown in figure 3.29a).

N

ES

W

rotation axis

(a) One-axis tracking

N

ES

W

rotation axis

rotation axis

(b) Two-axis tracking

Figure 3.29: Schematic of a module installation with the rotation axes of a) a one-axis and b)

two-axis tracking system.


62 3.3. Results

Even though one-axis tracking results in a smaller gain in energy production compared

to two-axis tracking, its advantages include a relatively simple structure and a less so-

phisticated and energy demanding motor like the one used in two-axis tracking systems.

Both tracking systems mentioned above cannot be simulated using the developed model.

However, a special case of the one-axis tracking system, where γM = 0, can be handled

using the developed simulation. In the so-called sunbelt-tracking system, a module is ro-

tated around a horizontally fixed north-south-facing axis and tilted towards the east in the

morning, upwards at noon, and towards the west in the evening, which is schematically

shown in figure 3.30.

N

ES

W

rotation axis

Figure 3.30: PV module mounted on a horizontal rotation axis, enabling using an east-west

tracking of the Sun. Module is horizontal and facing upwards at noon.

Since a horizontally mounted and upward-facing module at noon is suboptimal, when

the Sun has low elevation angles, this kind of tracking system is mostly beneficial for

installation at the Equator, where the Sun is at its highest, all year long. Therefore, the

simulation of a bifacial module with sunbelt-tracking will not be carried out for El Gouna

and Constance, but for Kasese, Uganda (N00’58”, E3010’55”), which is located near

the Equator. Figure 3.31 shows the irradiances reaching the front and rear sides of the

tracked bifacial module Itrk,f and Itrk,r, their sum Itrk,sum and the irradiance reaching the

front side of a fixed tilt, horizontally mounted monofacial module Istd, on the 22.01.2005..

Istd follows the same trend of a monofacial module in El Gouna or Constance, with the

peak at noon and a strong decrease in the morning and evening. But because a tracked

module is better positioned towards the Sun in the morning and evening, it receives more

irradiance at these times than a module fixed at an optimum tilt angle, which the more

spread out Itrk,f curve in figure 3.31 shows. If the tracked module is also a bifacial module,

the sum of the irradiation reaching its sides further increases, due to the contribution of

the irradiance on its rear side Itrk,r. A tracked bifacial module would therefore produce

more energy than both a tracked monofacial and a fixed bifacial module.

To determine the exact difference in the energy yields of the different configurations,

simulations are carried out for whole year (2005) in Kasese with various configurations,

which are then compared to each other. Since in this case, the reference of the gain is



4 6 8 10 12 14 16 180

250

500

750

1,000

1,250

1,500 Kasese22.01.2005

Itr k ,r

Itr k ,sum

Itr k ,f

Istd

Hour (UTC)

Sol

arirr

adia

nce

I[W m

2]

Figure 3.31: Due to the better positioning of a tracked module to the Sun all day, it receives more

irradiance than a fixed module, especially in the morning and evening. Adding a

light sensitive rear side, significantly increases Itrk,sum compared to Istd.

not always the energy yield of a fixed tilt monofacial module, the bifacial gain will be

redefined for this comparison as

BFA→B = 100YB − YAYA

, (3.58)

where YA is the energy yield of the reference configuration, and YB is the energy yield of

the configuration being compared to the reference. Table 3.8 shows the resulting gains

from cross comparing fixed and tracked, monofacial and bifacial modules, at different

albedo coefficients and locations.

Table 3.8: Adding tracking to a monofacial module increases yield by up to 18 % (Nr. 1), while

bifaciality increases it by up to 44 % (Nr. 3). Combining bifaciality and tracking

results in a gain of up to 62 % (Nr. 5).

Nr. A → BKasese

α = 0.2 α = 0.5

BFA→B

1 Monofacial fixed → Monofacial tracked 14.71% 17.93%

2 Bifacial fixed → Bifacial tracked 20.30% 12.82%

3 Monofacial fixed → Bifacial fixed 16.47% 43.77%

4 Monofacial tracked → Bifacial tracked 22.12% 37.53%

5 Monofacial fixed → Bifacial tracked 40.10% 62.20%

Whereas adding tracking to a monofacial module increases Ym by up to 18 % (Nr. 1),

using a fixed bifacial module increases the energy yield by a significantly larger amount


64 3.3. Results

than tracking of up to 44 % (Nr. 3). Additionally, while adding tracking to a bifacial

module only increases Yb by 13 % (Nr. 2), using a bifacial instead of a monofacial module

in a tracked installation increases the energy production by 38 % (Nr. 4). As expected, the

highest gain of up to 62 %, compared to a fixed monofacial module (Nr. 5), is achieved

by combining tracking and bifaciality. Using a cost-effective tracking solution like the

sun-belt tracker combined with such a high gain in energy yield will enable a very low

cost of the electricity generated by this type of PV system in low latitude regions.

3.3.7 Bifacial module field

The simulations performed so far on various configurations of stand-alone bifacial mod-

ules have provided an insight on the behaviour of bifacial modules under the influence

of several factors, including installation parameters and weather conditions. The opti-

mum installation parameters for bifacial modules have been determined for El Gouna and

Constance at varying albedo coefficients, and the advantages and disadvantages of special

installations, such as vertical and tracked systems, have been examined. But since PV

modules are rarely installed as stand-alone systems, but rather in a field of several neigh-

bouring modules and module rows, the following chapters are dedicated to the simulation

of the performance of bifacial module fields, starting in chapter 3.3.7.1 with only adjacent

modules in the same row. In chapter 3.3.7.2, the influence of additional module rows

depending on the distance between them is examined, while in chapter 3.3.7.3, a whole

field with bifacial modules is simulated.

3.3.7.1 Adjacent modules

Whereas a monofacial module is not affected by another module mounted in the same

row (at the same height on an even ground), a bifacial module is indeed influenced by

the additional neighbouring module casting a further shadow on the ground. As seen in

figure 3.14a) and other figures, Itot,r is reduced by the shadow on the ground. Since there

is no BHI in the shadow region, because it is blocked by the module surface, there is

less irradiance available for reflection by the shadow region. Hence, increasing the size of

the shadow on the ground, due to lower sun angles, or additional neighbouring modules,

would further decrease Itot,r. The influence of the shadow of the second module can clearly

be seen in figures 3.32a) and 3.32b), where the irradiance on the rear of a bifacial module

is shown for a stand-alone module, and for two adjacent modules in one row.

Whereas the minimum light intensity on the rear side of the module is circa 350 W/m2,

for a single module, it drops to circa 325 W/m2 for two adjacent modules. Furthermore,

the reduction of Itot,r is no longer symmetrical at noon, but is shifted further to the right,

closer to the shadow of the second module. So not only, does the overall intensity decrease,

but the decrease is also shifted towards the edge of the module, where the second module



is mounted. Since adjacent modules in a row are rarely mounted with a great distance

dM between them, the dependency of the bifacial gain of a certain module on the distance

to its neighbouring module will not be investigated. Instead, the influence of the number

of adjacent modules on the bifacial gain will be examined, where the worst case scenario

is considered, when the module is in the middle of the row. In case of an even number of

modules, the bifacial gain of one of the two center modules is considered. The results of

the simulation, where dM = 0 m and α = 0.2 and α = 0.5, are depicted in figure 3.33a)

for El Gouna and figure 3.33b) for Constance.

As expected, BF clearly decreases for a rising number of neighbouring modules in one row.

A saturation point is however reached in all cases at a number of five adjacent modules,

where the bifacial gain is no longer reduced by additional modules. At five modules, the

considered module has two modules on each side, meaning that the influence of the third

module and further on the bifacial gain of a given module, is negligible. It follows that

there is no or very little difference between a module with two neighbouring modules on

each side, and a module with ten modules on each side. A module with an infinite number

of adjacent modules would at α = 0.5 have a BF of circa 29 % in both locations and at

α = 0.2 have a BF of circa 12 % in El Gouna and 14 % in Constance.

a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, 1 module

Module length lM

Mod

ule

wid

thw

M

330 340 350 360 370 380 390


b) El Gouna, 21.06.2005, noon, α = 0.5,hM = 1 m, 1 row with 2 modules

Module length lM

Figure 3.32: Itot,r is lower for a row with two modules b), than for a single module a), due to

the larger shadow region. The reduction is also not symmetrical, but is stronger in

the area of the module adjacent to the neighbouring module.


66 3.3. Results

0 2 4 6 8 10 120

10

20

30

40

α = 0.5

α = 0.2

a) El Gouna

Number of modules nM [−]

Bifa

cial

gain

BF

[%]

0 2 4 6 8 10 12

α = 0.5

α = 0.2

b) Constance


Figure 3.33: BF decreases for increasing number of adjacent modules in both a) El Gouna and in

b) Constance. Saturation point is reached for a row with 5 modules, corresponding

to 2 modules on each side, with the third module no longer influencing BF .

3.3.7.2 Additional module rows

Since a solar park with bifacial modules will rarely consist of one row of modules, but

rather of several, as shown in figure 2.12, simulations of stand-alone modules or of single

module rows are insufficient. For the prediction of the energy yield of a module field

to be precise, the influence of the rows on each other has to be regarded. But since

the focus of this thesis is the optical modelling of the rear side of bifacial modules, the

shadowing of the front sides by other module rows will not be considered, due to the

complexity of the calculation on field level, and its little influence on BF . Since both a

bifacial module’s front side and a monofacial module are affected equally by front side

shadowing, the effect on the bifacial gain is cancelled out and will therefore not be taken

into account. However, additional module rows also have an influence on the rear side

irradiance, caused by their blocking of the reflected irradiance. This behaviour has been

taken into account by reducing the size of the relevant reflective surface for each cell row

on the considered module, according to figure 3.7. The blocking effect can clearly be seen

in figure 3.34a), where Itot,r is shown for one module with another one behind it, compared

to a stand-alone module in figure 3.34b).

Viewed geometrically, the irradiance reaching the top cell row of a module is blocked the

strongest by the additional module row, which is shown in figure 3.7. This effect can be

seen in figure 3.34b), where compared to a stand-alone module, shown in figure 3.34a).

The intensity of the reduction of Itot,r due to blocking is effectively dependent on the

distance between the module rows dR, an important parameter in the development of

any solar park, whatever the module type. To examine the influence of dR on the energy



production of bifacial modules installed in a field, BF is simulated for the center module

in a field with three rows, with eleven modules each, for varying distances between the

individual rows. Because the bifacial gain of a module is only affected by the rows directly

in front of it and behind it, carrying out simulations with more than three rows would be

a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, 1 module

Module length lM

Mod

ule

wid

thw

M

340 350 360 370 380 390


b) El Gouna, 21.06.2005, noon, α = 0.5,hM = 1 m, 2 rows with 1 module each

Module length lM

Figure 3.34: Itot,r drops from a) 369 W/m2 to b) 356 W/m2, due to additional module row.

Reduction of Itot,r for top cell row of configuration b) is caused by blocking effect,

while for bottom cell rows it is caused by the module shadow on the ground.

0 1 2 3 4 5 6 70

10

20

30

α = 0.5 α = 0.2

a) El Gouna

Distance between rows dR [m]

Bifa

cial

gain

BF

[%]

0 1 2 3 4 5 6 7

α = 0.5α = 0.2

b) Constance


Figure 3.35: Yearly bifacial gain BF increases with increasing distance between rows dR, which

each have 11 modules, in both a) El Gouna and in b) Constance. Saturation point

reached for dR ≈ 3 m, further than which, additional module rows have a negligible

influence on BF .


68 3.3. Results

superfluous, only adding to the computation time without increasing the accuracy. The

resulting BF on the center module, which is surrounded the most by other modules, is

shown for α = 0.2 and α = 0.5 in figures 3.35a) and 3.35b) for El Gouna and Constance

respectively.

As expected, placing module rows in close vicinity to each other, reduced the bifacial

gain of the center module, while BF increases the further away the rows are mounted

from each other. To make solar park projects more profitable, especially in cases with

high land costs, developers attempt to place module rows as densely as possible, without

adversely affecting the energy yield of the individual rows. According to the results shown

in figures 3.35a) and 3.35b), a dR of 3 m would be a reasonable distance to keep between

the modules. More than 3 m would reduce the land coverage of the solar park, without

tangibly increasing the energy yield of each module of the rear side of each module. Using

commercially available software the row to row distance can be optimized regarding the

shadowing of the front sides by neighbouring module rows, which is determined at 2.5 m

and 1 m for El Gouna and Constance respectively. Hence, depending on the location, a

field with bifacial modules would require the same dR or more, compared to a monofacial

module field. At dR = 3 m and α = 0.5, the bifacial gain in both cities would still be

27.5 %, whereas at α = 0.2 it would be 11 % and 12 % for El Gouna and Constance

respectively.

3.3.7.3 Module field

Compared to a stand-alone configuration, a bifacial module’s rear side contributes less to

the energy production in a field installation. Surrounded by other modules from every

side, Itot,r is strongly reduced by the additional module shadows, as shown in figure 3.32

and by the blocking effect from additional module rows as shown in figure 3.34. The

combined effect is visible in the comparison between the irradiacne on the rear side of a

stand-alone module, depicted in figure 3.36a), and of the worst case scenario, a module

installed in a field, with other modules surrounding it from each side, shown in figure

3.36b).

As expected, the irradadiance on the rear side of a bifacial module is overall lower in a field

installation than as a stand-alone system. However, the different effects reducing Itot,r are

combined to result in a homogeneous irradiation of the module’s rear side, as can be seen in

figure 3.36b). Since the shadow region is not exclusively beneath the considered module,

but also right and left of the module’s own shadow, due to the adjacent modules, the

reduction of Itot,r due to the shadows on the ground is not more pronounced in the center

of the module like in figure 3.36a), but is spread out evenly to the sides. Comparably,

since there is a complete row of modules behind and not just one, the reduction of Itot,rdue to blocking is not solely in the center of the top cell row like in figure 3.34b), but also

evenly spread out. The overall more homogeneous Itot,r implies that it is not necessary to



a) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, single module

Module length lM

Mod

ule

wid

thw

M

340 365 390


b) El Gouna, 21.06.2005, noon,α = 0.5, hM = 1 m, module field

Module length lM

280 305 330


Figure 3.36: Itot,r drops from a) 369 W/m2 to b) 290 W/m2, due to the additional shadow

regions and the blocking effect in a field installation. However, the irradiance of b)

is reduced over the whole module area evenly, making Itot,r more homogeneous.

perform the calculation of the view factor FA1→A2 for each cell separately, and that the

module surface can be divided into less parts, reducing the high calculation time.

To determine the necessary number of view factor calculations for a tolerable accuracy, the

yield of a bifacial module installed in a field is simulated for varying number of parts the

module is divided into. Figures 3.37a) and 3.37b) show the relative inaccuracy depending

on the number of rows and columns the module rear side is divided into at an albedo of 0.5

for El Gouna and Constance respectively. Because Itot,r of a module installed in a field is

more homogeneous than a stand-alone module, the number of individual computations of

the view factor necessary to achieve an inaccuracy smaller than 1 %, decreases. Whereas

at least twelve parts were needed for an accurate simulation of a stand-alone module, in

the case of a field installation, dividing a module in El Gouna to six parts, consisting

of three columns and two rows, and a module in Constance to nine parts, consisting

of three columns and three rows, is sufficient to achieve the desired level of accuracy.

As a consequence, the computation time can be drastically reduced. The reason for the

higher number of required parts in Constance could be the lower sun angles, casting larger

shadows and producing larger inhomogeneity of Itot,r.

Throughout the previous simulations of the energy yield, the module in the center of the

field was considered, which receives the least rear side irradiance. This provided results

for BF for the worst case scenario, where the module is surrounded by modules from

every side. Since there are discrepancies between the performances of the modules at the

edge and at the center of the field, the bifacial gains of all modules of a field with five


70 3.3. Results

a) El Gounaα = 0.5

1 2 3 4 5 6 7 8 9 101

2

3

4

5

6

Number of columns

Num

bero

frow

s

0 0.5 1 1.5 2 2.5 3 3.5Relative inaccuracy ∆BF [%]

b) Constanceα = 0.5

1 2 3 4 5 6 7 8 9 10Number of columns

Figure 3.37: Inaccuracy of the simulation increases with decreasing number of parts for both a)

El Gouna and b) Constance. Simulation with four columns and three rows sufficient

for a deviation of less than 1 %.

rows, each with eleven modules, and a distance of 2.5 m between the rows, are determined

and shown in figure 3.38 for El Gouna and in figure 3.39 for Constance.

The distance of circa 2.5 m between the module rows, is the distance recommended for a

monofacial module field of five times the height difference between the upper and lower

module edges. Increasing dR would further increase the bifacial gain. The reduction of

the bifacial gain of a module surrounded from both sides by additional module rows, is

only partly caused by the blocking effect by the rear module row. With bifacial modules,

it is not only important to examine when the modules in the front row are casting a

shadow on the front side of the considered module, but also when the front row is casting

a shadow beneath the considered module, therewith reducing the irradiance available for

reflection by the ground. Therefore, both front and rear rows negatively influence BF of

the module in between.

As expected, the modules mounted at the edge of the field have a higher BF , since there

are less objects in their surrounding casting shadows and blocking the ground-reflected

irradiance. However, only the first two modules from the side edge of the field have an

increased BF , and starting from the third inner module, the reduction of BF is constant,

as also shown by the simulation in chapter 3.3.7.1. Both figures also show different module

performances, depending on the placement of the row in the field, whereby only the first

and last row have an increased energy production compared to the inner rows, where the

modules are surrounded from each side by other modules. In El Gouna, the modules in

the first row perform better than those in the last row, implying that the blocking effect

has less influence on BF compared to the additional shadow beneath the last row from

the modules in the rows in front. On the other hand, in Constance the last row has a

higher BF than the front row, implying that in Constance the blocking effect has a more



31.41

31.13

31.20

30.20

28.53

29.90

29.56

27.72

29.31

31.41

31.13

31.20

30.20

28.53

29.90

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

28 29 30 31 32Bifacial gain BF [%]

Figure 3.38: Bifacial gain of all modules in a field in El Gouna with α = 0.5. The outer modules

have a higher BF . Notice how in El Gouna the first row, has a higher BF than

the last row, where the shadow of the front rows decrease Irefl,r strongly reducing

BF .

30.87

29.67

31.53

30.01

28.59

30.64

29.41

27.85

30.12

30.87

29.67

31.53

30.01

28.59

30.64

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

28 29 30 31 32Bifacial gain BF [%]

Figure 3.39: Bifacial gain of all modules in a field in Constance with α = 0.5. The outer modules

have a higher BF . Notice how in Constance the last row, has a higher BF than

the first row, where the blocking of Irefl,r strongly reduces BF .


72 3.3. Results

significant effect on BF , than the shadows on the ground from the front module rows. It

is important to note, that even though the reduction of the bifacial gain of a module in a

field compared to a stand-alone module is relatively high, going in El Gouna from 33.85 %

to 31.41 % and 27.72 %, and in Constance from 35.73 % to 31.53 % and 27.85 %, in the

best and worst case respectively, the remaining BF is still very high. Bifacial modules

are therefore still an attractive option, despite the reductions of BF , when installed in a

field. The results presented in figures 3.38 and 3.39 are for α = 0.5. The results of the

simulation with α = 0.2 show the same behaviour, albeit with an overall lower BF , and

are therefore presented in appendix 5 for reasons of clarity.


Chapter 4

Validation

In order to verify the accuracy of the results of the developed simulation tool, a set of

experiments are carried out, providing insight on the behaviour of the simulated con-

figurations in real life. The goal of the experiments, is to prove the correctness of the

performed calculations, within a tolerable level of deviation. Both short-term experi-

ments, carried out at the ISC Konstanz, and several months long measurements, taken in

the TUB campus in El Gouna, are used for the validation, and are described in chapters

4.1 and 4.2.

4.1 Short-term experiments

4.1.1 Location and setup

The experiments are carried out at the ISC Konstanz (N4740’18”, E99’6”) during Au-

gust 2015. The rooftop installation consists of two adjacent south-facing bifacial modules,

mounted at an elevation of the lower edge of 1.2 m and a tilt angle of 30, whereas only the

left module, when viewed from the front, is examined. The ground beneath the modules

consists of gravel, with an estimated albedo of α = 0.35. A photo of the measurement

setup is shown in figure 4.1, whereby the white reflective sheet beneath the modules was

removed during the measurement period.

Two front- and rear-facing ISET sensors [59] are mounted between the modules in the

same plane and can also be seen in figure 4.1, enabling the measurement of the tilted

front and rear side solar irradiance in W/m2. Other measurements included the module

temperature, the ambient temperature, and most importantly, the output power of the

module in W .

74 4.1. Short-term experiments

30°1.2m

measured module

ISETsensors

Figure 4.1: Photo of the measurement setup on the roof of the ISC Konstanz, where the mea-

sured module, the ISET sensors, and the ground beneath the modules can be seen.

4.1.2 Experiment I: Reflective surface size

Different areas of the ground contribute differently to the reflected irradiance on the rear

side of a module. The further away a certain region of the ground is from the module,

the less it contributes to Irefl,r. The results of the simulation in chapters 3.3.4.4 and

3.3.4.5 suggested, that most of the ground-reflected irradiance reaching the rear side of

the module comes from the area up to 4−5 m behind it, while the contribution of the area

further away is less significant. According to the simulation in chapter 3.3.7.2, a second

module row can consequently be mounted at a distance between the rows of 3 ± 0.5 m,

depending on the requirements of the solar park. Therefore, the first two-part experiment,

is dedicated to determining the size of the relevant reflective surface.

4.1.2.1 Description

Part I

The first part of the experiment consists of using a white reflective plate (WRP) [60] with

a constant size of 1.6 m × 1 m, which is made from plastic materials and has an even

surface. The WRP is placed on the ground beneath the module, in order to increase the

albedo of the ground from 0.35 to an estimated 0.8. The exact reflection of the plate

could not be measured using the spectrometer, due to the wavy structure of the plate.

The plate is placed on the ground beneath the module at various distances dw of the front

edge of the WRP to the front edge of the considered module. The distance dw is varied

between 0 m and 5 m in 0.5 m steps, while measuring the output power of the module

for five minutes with a frequency of 1/min, providing five datapoints for each distance.

The setup of the measurement is depicted in figure 4.4.

The power is then divided by the measured radiation intensity to provide a measure of the

module performance independent on the instantaneous irradiation, which varies with time


Chapter 4. Validation 75

reflective platedw

1.2m

1.66m

0.99m

1m

30°

α≈0.35

α≈0.8

gravel

Figure 4.2: Schematic of the measurement setup of the first part of the first experiment, with all

relevant values, where dw is varied from 0 m to 5 m. Measured module is highlighted

in yellow.

throughout the experiment. Each five datapoints are then averaged, yielding a ratio inW/W/m2 for each dw. A five minute measurement of the power to irradiance ratio without

the WRP is carried out before each actual measurement, and then averaged, providing

each measurement with temporally close reference data. The relative power gain gP in

%, which is defined as the ratio of the difference between the actual and the reference

measurement to the reference measurement, is given by

gP =Pi/Ii − Pref/Iref

Pref/Iref, (4.1)

where Pi and Pref are the module output powers of the actual and reference measurement

respectively, and Ii and Iref are the solar irradiances during the actual and reference

measurement respectively. The experiment is conducted on a clear sunny day with no

clouds, first at noon, where the shadow of the module is directly beneath the module, and

repeated in the afternoon, when the shadow of the module has completely moved from

underneath the module.

Part II

In the second part of the experiment, the size of the reflective plate is not kept constant,

but its length lw is increased 0.5 m every five minutes until it reaches a length of 5 m.

The width of the WRP is equal to the width of the module of 1.6 m and kept constant

during the entire experiment. The length of the plate is measured from the front and

lower module edge. The execution of the measurement is similar to the first part of the

experiment, where a five minute reference measurement completely without the WRP

is undertaken before each actual measurement. The power of the module is measured,

divided by the solar irradiance and consequently averaged for each length. The relative



power gain of each measurement to its reference gP is then calculated using equation 4.1.

The measurement setup is visualized in figure 4.5.

reflective platelw

1.2m

1.66m

0.99m

30°

α≈0.35

α≈0.8

gravel

Figure 4.3: Schematic of the measurement setup of the second part of the first experiment,

with all relevant values, where lw is varied from 0 m to 5 m. Measured module is

highlighted in yellow.

4.1.2.2 Results

Part I

The relative power gain resulting from the first part of the experiment is given in figure

4.4 for varying distances dw between the module front edge and the WRP front edge.

0 1 2 3 4 5 6

0

1

2

3

4

5

6

noon

afternoon

Distance dw [m]

Rel

ativ

epo

wer

gain

g P[%

]

Figure 4.4: Measured relative power gain when using 1.6 m2 white reflective plate. gP decreases

with increasing distance dw between module and WRP, while for dw > 3.5 m gP = 0



At noon gP is lower than in the afternoon, possibly due to the module shadow covering

parts of the WRP, hence decreasing its enhancement of the ground reflection of the inci-

dent solar irradiation. Both however decrease with increasing distance dw to the module

front edge, which corresponds to the expectation. The results show, that the area up to

3 − 4 m behind the module contributes the most to its output power, whereas the gain

is negligible for dw > 4 m, confirming the results of the simulation presented in chapter

3.3.4.5. From figure 4.4 it is also visible, that a WRP with an area of just 1.6 m2 al-

ready increases the output power of a bifacial module by almost 6 %, emphasizing the

importance of a high α for the performance of bifacial modules.

Part II

The results of the second part of the experiment, given by the dependency of gP on the

size of the reflective plate, are given in figure 4.5. As expected, the output power of the

module, given by gP , increases with increasing reflective plate size, given by its length

lw. The maximum power gain of a significant 10 % is reached at lw = 4 m and stays

constant for lw > 4 m. According to the results of the second part of the experiment, the

contribution of the region of the ground further than 4 m from the module to the output

power is negligible. The results of the simulation presented in chapter 3.3.4.5 and the

first part of the experiment are herewith further affirmed. With a power gain of up to

10 %, compared to an already relatively high albedo of 0.35, a WRP may be a profitable

investment for a solar park, depending on its price, maintenance costs and initial albedo

of the ground.

0 2 4 6

0

2

4

6

8

10

1 3 5 7

afternoon

Length lw [m]

Rel

ativ

epo

wer

gain

g P[%

]

Figure 4.5: Relative power gain, due to 1.6 m wide white reflective plate, increases with increas-

ing length lw with respect to module front edge. Saturation reached at lw = 4 m.



4.1.3 Experiment II: Blocking effect

In the design of solar parks using monofacial modules, the determination of the distance

between the individual module rows is mainly based on the tolerable amount of module

front side shading by other module rows. While this is still a factor in designing solar

parks with bifacial modules, the blocking of the ground-reflected irradiance by the rear

module rows also has to be taken into account. A simulation was conducted using bifacial

modules with varying distances between the module rows, the results suggesting, that at

dR ≥ 3 m the bifacial gain is no longer strongly reduced. In chapter 4.1.3.1, the short-

term experiment carried out to verify the results of the simulation is described, while the

results are presented in chapter 4.1.3.2.

4.1.3.1 Description

Compared to the first experiment, the basic setup of the measurement, which is visualized

with all the relevant values in figure 4.6, remains unchanged, with two bifacial modules

mounted adjacently at hM = 1.2m and γM = 30. An additional module row, consisting of

a single module with the same installation parameters, is mounted behind the considered

module, highlighted yellow in figure 4.6, at a variable distance dR. To increase the chance

of observing the influence of dR on the module power, a 1.6 m wide and 4 m long WRP

is placed beneath the module.

reflective plate

1.2m

1.66m

0.99m

4m

30°

α≈0.35

α≈0.8

gravel

dR

Figure 4.6: Schematic of the measurement setup of the second experiment, with all relevant

values, where dR is varied from 0 m to 2.5 m. Measured module is highlighted in

yellow.

The module power is measured for five minutes at each dR and the measured data is

consequently analysed similarly to the first experiment, resulting in a relative power gain

gP for each dR. The reference measurement in the second experiment is conducted with

the WRP, but without an additional module row. Therefore, gP represents, the gain, or



in this case loss, of output power in the case of an additional rear module row at varying

distances dR, compared to the output power of a module with no further module rows

behind it.

4.1.3.2 Results

The results of the second experiment, given as the dependency of the loss in power gain

gP on the distance between the module rows dR, are shown in figure 4.7. The decreasing

losses for greater dR, observed during the measurement, correspond to the expectations.

The further away the second module row is, the less it negatively affects the output

power of the bifacial module in front of it. The result obtained from the simulation and

depicted in figure 3.35, that the loss in BF is negligible for dR ≥ 3 m, is affirmed by this

experiment, which yielded the same result. But whereas the trend of the measured curve

corresponds to the expectations, the absolute values of the power loss gP are relatively

low, at a maximum of 1 % output power loss, when the module rows are directly behind

each other with dR = 0 m. A repetition of the experiment resulted in the same relatively

low values, the reason for which could not be determined.

0 1 2 3

0

0.25

0.5

0.75

1

0.5 1.5 2.5Distance dR [m]

Neg

ativ

epo

wer

gain

g P[%

]

Figure 4.7: Measured negative power gain, due to blocking effect by second module row at

varying distances dR, decreases with increasing dR. Loss in module power is zero for

dR ≥ 3 m.

4.2 Long-term measurement

The bifacial gain has played a major role in the context of this thesis, and has been used

to examine the performance of bifacial modules for different configurations and weather

conditions. To verify the accuracy of the calculation of BF , simulations are carried out


80 4.2. Long-term measurement

using the exact configuration of a test site mounted in the TUB campus in El Gouna, and

consequently compared to the measurement data of the power of monofacial and bifacial

modules, obtained during 2014 from the test site. The measurement setup is described in

chapter 4.2.1, the input data of the simulation is explained in chapter 4.2.2, and the results

obtained from both the simulation and measurement are compared in chapter 4.2.3.

4.2.1 Location and setup

The measurement campaign was carried out in the TUB campus in El Gouna, where

several bifacial and monofacial modules from various manufacturers are installed and

continuously monitored. The test site is shown in figure 4.8. The south-facing modules

are mounted in pairs, each consisting of a monofacial and bifacial module. The modules

are tilted at 20 and are mounted at a height of the lower edge from the ground of 1.2 m.

In addition to the monitoring of the module output powers, several other parameters,

such as the global horizontal irradiance GHI, the ambient temperature, the wind speed

and wind direction, are continuously measured. Two front- and back-facing ISET sensors

are mounted between the modules in the same plane, measuring the front and rear side

irradiance reaching the module plane, and can be seen in figure 4.8. The electrical param-

eters of the modules, how the required weather data was obtained and how the average

albedo of 0.3 was determined, are explained in the following chapter 4.2.2.

1.2 m

20°Monofacial Bifacial

ISETsensors

cement sandα≈0.3 α≈0.3

Figure 4.8: Photo of measurement setup in El Gouna, with all relevant values.

4.2.2 Input data

The developed simulation tool requires several parameters for the calculation of the bifa-

cial gain, including the module elevation and tilt angle, given in figure 4.8. The required

parameters also include the global, diffuse and direct horizontal irradiance, whereby the

third component can be determined using the other two, and most importantly, the av-

erage ground albedo, which has a significant influence on the calculation of BF .



Whereas GHI was continuously monitored during the entire measurement period of

01.01.2014-31.05.2014, regrettably neither DHI or BHI were measured separately. The

monthly average of the diffuse irradiance factor fD is relatively constant over the years, as

visible in figure 4.9, which depicts the monthly fD for the years from 2002 to 2005, using

data obtained from SoDa. The high resolution fD data, available from SoDa only for

2005, can therefore be applied to the high resolution GHI data, measured in El Gouna in

2014, providing DHI data for the measurement period in 2014. BHI is then calculated

by subtracting DHI from GHI.


10

20

30

40

50 2002200320042005

Diff

use

irrad

ianc

efa

ctor

f D[%

]

Figure 4.9: Monthly diffuse irradiance factor fD measured from 2002 to 2005. Notice how the

monthly fD is relatively constant over the years.

To determine the average albedo of the ground surrounding the module, two upward- and

downward-facing pyranometers were used to measure the solar radiation. The measure-

ment was conducted on the cement foundation, with the modules dismounted, for one

hour during September, 2015 at noon, delivering a result of 0.28. However, the albedo

varies during the day, with the minimum at noon, as explained in chapter 2.1.2. A several

day measurement of the albedo of a grass surface, conducted by Chiodetti [10], which

shows the deviation between the average and the measured albedo, is used to estimate

the average albedo in El Gouna from the measured 0.28. A value of 0.3 is presumed to

represent the average albedo of the area beneath the modules, including the foundation

and the sand surrounding it.

The electrical parameters of the considered bifacial and monofacial modules are given in

table 4.1. The glass-glass bifacial module installed in El Gouna is manufactured by GSS

using ISC Konstanz’s n-type bifacial cells, called BiSoN [61]. The considered monofacial

module with a white backsheet is fabricated at Bosch Solar Energy AG within the Ger-

man publicly funded project nSolar [62]. The I-V-parameters were measured at the PI

Photovoltaik-Institute Berlin AG, where the front and rear sides of the bifacial module

were characterized separately , with the other side covered by a black sheet.


82 4.2. Long-term measurement

Table 4.1: I-V-curve measurement results of the bifacial and monofacial modules considered

in the validation of the simulation. Bifacial module front and rear sides measured

separately.

Type Side Voc [V ] Isc [A] FF [%] Pmpp [W ] Vmpp [V ] Impp [A] fB [%]

Monof. front 39.13 9.781 77.18 295.4 32.20 9.174 −

Bif.front 38.97 8.852 74.15 255.8 31.08 8.231

91.4rear 38.81 8.052 74.84 233.9 30.92 7.564

4.2.3 Results

Figure 4.10 shows the measured and simulated monthly bifacial gain of the modules

installed in El Gouna. The results of the simulation correlate very well with the measured

monthly BF , except in February, where the deviation of circa 1.5 % absolute is comparably

large. The stronger deviation between simulated and measured data might be caused

by an actual fD in February 2014 that is deviating stronger from the respective 2005

data, than it is the case for the other considered months. The otherwise good agreement

between the measured and the simulated BF shows the reliability of the developed model,

and the correctness of the assumptions made in the simulation. However, the developed

model is only to be viewed as a first step in the development of a tool for simulating

bifacial modules, which still requires several improvements, to also accurately determine

the annual energy yield Yb, and not just the bifacial gainBF . These improvements include,

among others, a more accurate electrical model, a variable albedo, the consideration of

mutual front side shadowing, a soiling model for desert applications and the reduction of

the required calculation time.

Jan Feb Mar Apr May0

...

18

20

22

24

mea

sure

dsi

mul

ated

19.2

819

.0

21.0

519

.5

18.8

518

.8

21.2

521

.2 22.2

222

.1

Mon

thly

bifa

cial

gain

BF

[%]

Figure 4.10: Small deviation between measured and simulated monthly bifacial gain of modules

installed in El Gouna.


Chapter 5

Conclusions

In the framework of this thesis, a software tool, which enables the simulation of stand-alone

and field installations of bifacial modules, is developed. Assuming the appropriate weather

data exists, it is possible to carry out the simulations for any given location. The developed

tool is then used to estimate the performance of bifacial modules for various installation

parameters, such as the tilt angle, installation height, distance between module rows and

ground albedo coefficient. Finally, short term experiments are carried out to verify the

results yielded by the simulation, the most important of which, are summarized in the

following paragraphs.

The results of the simulation suggest, that a bifacial module mounted in El Gouna would

have to be installed at a tilt angle of 25 and a height of the lower edge of 1.5 m, in

order to maximize its energy production. The module would have a 13 % higher yearly

energy production at α = 0.2 and 34 % at α = 0.5, than a comparable monofacial mod-

ule, confirming the statement that bifacial modules are highly advantageous compared

to standard modules, strongly reducing the cost of the produced electricity, due to the

higher energy production per module. Furthermore, it was observed, that the bifacial gain

is heavily influenced by the installation parameters and weather conditions, for example

reaching up to 15 % and 40 %, for α = 0.2 and α = 0.5 respectively, in the theoretical case

of completely diffuse incident irradiation. Additionally, increasing the ground albedo to

0.85 using white reflective plates, was found to enhance the energy yield of bifacial mod-

ules, causing them to produce up to 55 % more energy than standard modules, depending

on the size of the WRP.

Special setups, aimed at further increasing the energy yield, have also been examined.

While in Constance, at α = 0.5, the energy yield of an east-west-facing vertical bifacial

module, was found to be 15 % higher than the yield of a south-facing monofacial module,

in El Gouna a vertical bifacial module would produce 6 % less energy. Despite the lower

energy yield, a vertical installation in El Gouna might still be considered advantageous,

84

due to the shift of the electricity production to the morning and afternoon, compared to

a south-facing module, where the peak production occurs at noon. In addition, a hori-

zontally mounted PV module with a single-axis tracking system, located at the Equator

in Kasese, Uganda, has been examined. The results showed, that while adding tracking

to a monofacial module would increase its yield by up to 18 %, a fixed bifacial module

would increase the yield by up to 44 %. Hence, the investment in bifaciality would be

more profitable than the investment in a tracking system, again affirming the advantages

of bifaciality. On the other hand, a single-axis tracked bifacial module, has a 62 % higher

energy yield than a fixed monofacial module.

The bifacial gain of stand-alone bifacial modules, is however slightly irrelevant, since PV

modules are rarely installed on their own, but rather in a field with several adjacent mod-

ules and module rows. Hence, the bifacial gain of each module in a field was determined

using the simulation tool developed within this thesis, showing on the one hand, that the

bifacial gain of a module is only influenced by the first two adjacent modules on each side

of it, and on the other hand, that it is only influenced by the first row in front of it and

the first row behind it. A distance of 3 m between the rows only insignificantly reduces

BF , hence bifacial modules do not necessarily require more space than standard modules.

This result was additionally verified by the results of the experiment, which showed no

reduction in BF at dR ≥ 2.5 m. The reduction of BF , due to the installation in a field,

compared to a stand-alone system, was found to be tolerable, dropping from 33.8 % to

31.4 % and 27.7 % for the best and worst performing modules in a field installed in El

Gouna with α = 0.5 and dR = 2.5 m, respectively. A simulation was also carried out,

using the actual parameters of an existing installation in El Gouna. The results were

then compared to the actual measurements, showing very good agreement between the

measured and the simulated BF in the considered months of January to May, except in

February, where the deviation of 1.5 % absolute was comparably large. Even though, the

correlation of the results from the measurement and simulation provides an indication of

the reliability of the developed model, various improvements are still necessary, including,

among others, a more accurate electrical model, a variable albedo, the consideration of

mutual front side shadowing, a soiling model for desert applications and the reduction of

the required calculation time.

In addition to the much higher energy yield of bifacial modules, the glass-glass structure

provides higher durability, and therefore a longer lifetime. The high compatibility of the

bifacial cell process with existing solar cell production lines greatly adds to the appeal

and profitability of bifaciality, which explains the growing trend towards bifacial cells

and modules. However, the shift to bifaciality requires several changes in the PV indus-

try. Institutes and universities continue to differently measure the I-V-curve of bifacial

modules, some measuring the front and rear side separately, and others combining both

measurements with the use of a reflective sheet behind the module to imitate albedo, with

its color varying between white, gray and black. A unified and standardized I-V-curve


Chapter 5. Conclusions 85

measurement is therefore of absolute necessity for the proper measurement and cross com-

parison of the performance of bifacial modules from different manufacturers. To this day,

to compare bifacial modules to monofacial modules, an equivalent peak power is defined

for bifacial modules as the sum of the front power and e.g. 20 % of the rear power, which

is not representative of their performance for all setups and locations. Hence, a shift

from the conventional use of the peak power in Wp for the comparison of different module

technologies, to the more relevant and better suited use of the annual energy production

in kWh or the annual energy yield in kWh/kWp, is imperative for a proper assessment

of the performance of bifacial modules. Furthermore, the determination of the bifacial

gain needs to be standardized, in order to prevent misleading indications of the gain of

bifacial modules compared to monofacial modules, either positively, by choosing a badly

performing standard module as the reference, or negatively, by choosing an especially

strong performing standard module as the reference. Such misleading indication of the

bifacial gain is still possible in the industry, due to the lack of proper standards for the

assessment of the performance of bifacial modules.

To conclude, bifaciality is a highly promising concept for driving down the LCOE of

photovoltaics, with a gain of 10 % to 60 % in the annual energy yield, compared to

standard modules, depending on the various installation parameters. However, proper

standardization of the measurement and assessment of the performance of bifacial modules

is an absolute necessity, without which the growth of the market share of bifacial modules

is bound to be slowed down.


86


Appendix A

Annual energy yield Y

Comparable to the bifacial gain BF of a module, the annual energy yield Y also depends

on the various installation parameters and weather conditions. The estimated energy

yields, with which the bifacial gains were calculated in the framework of this thesis, are

presented in the following sub-chapters of the appendix. It is however important to note,

that the estimated energy yields might slightly deviate from realistic measurements. Rea-

sons include the lack of a model for soiling, the exclusion of the shadowing of the front

side by other module rows, and the use of a simple electrical model. While these simpli-

fications have little effect on the calculated bifacial gain, since they affect the calculation

of both the yields of monofacial and bifacial modules, and are cancelled out in the de-

termination of BF using equation 3.56. However, the accuracy of the estimated absolute

values of Ym and Yb are negatively affected by these simplifications, hence the following

results are not to be viewed as absolute results, but as a qualitative analysis of the effect of

different installation parameters and weather conditions on the energy yield of monofacial

and bifacial modules.

88 A.1. Module elevation hM

A.1 Module elevation hM

0 0.5 1 1.5 2 2.51,000

1,500

2,000

2,500

α = 0.5 α = 0.2

El Gouna

Constance

Module height hm [m]

Ann

uale

nerg

yyi

eld

Yb

[kWh

kWp]

Figure A.1: Elevation dependent Annual energy yield Ybif increases for higher albedos. Module

height optimum is between 1m and 1.5m for all configurations.

A.2 Diffuse irradiance factor fD

0 20 40 60 80 100

1,000

1,500

2,000

2,500

3,000

10 30 50 70 90

El Gouna

Constance

α = 0.5

α = 0.2

monofacial


Ann

uale

nerg

yyi

eld

Y[kW

hkW

p]

Figure A.2: Yield of monofacial module decreases the most with increasing fD. Ybif also de-

creases, regardless of albedo, because the increase of Itot,r, due to reduced module

shadow, is smaller than the decrease of Itot,f , due to DHI from the portion of the

hemisphere behind the module, not reaching module front side.


Appendix A. Annual energy yield Y 89

A.3 Reflective surface size

0 5 10 15 20 25 30 35 40 45 501,000

1,500

2,000

2,500

α = 0.5 α = 0.2

El Gouna

Constance


Ann

uale

nerg

yyi

eld

Yb

[kWh

kWp]

Figure A.3: Annual energy yield Yb increases with increasing reflective surface size. Increase of

Yb insignificant for LS > 15 m and L1 > 15 m.

A.4 Ground albedo α

0 1 2 3 4 5 6 7 8

1,500

2,000

2,500

3,000

α = 0.5α = 0.2

El Gouna

Constance


Ann

uale

nerg

yyi

eld

Yb

[kWh

kWp]

Figure A.4: Annual energy yield Yb increases with increasing WRP size. Increase of Yb stagnates

at wS > 3 m and w1 > 3 m, reaching up to 3000 Wm2 in El Gouna and 1500 W

m2 in

Constance.


90 A.5. Time and date

A.5 Time and date


100

200

300

α=

0.2

α=

0.5

mon

ofac

ial

a) El Gouna

Een

ergy

yiel

dY

[kWh

kWp]


100

200

300

α=

0.2

α=

0.5

mon

ofac

ial

b) Constance

Een

ergy

yiel

dY

[kWh

kWp]

Figure A.5: Monthly energy yield at α = 0.5 in a) El Gouna and b) Constance reaches maximum

of circa 280 W/m2 and 220 W/m2 respectively in the summer. Difference in Y

between the summer and winter is less pronounced in El Gouna.



A.6 Adjacent modules

0 2 4 6 8 10 121,000

1,500

2,000

2,500

3,000

α = 0.5α = 0.2

El Gouna

Constance


Ann

uale

nerg

yyi

eld

Yb

[kWh

kWp]

Figure A.6: Yield Yb decreases for increasing number of adjacent modules in both a) El Gouna

and in b) Constance. Saturation point reached for row with five modules, meaning

two modules on each side, with third module no longer influencing Yb.

A.7 Additional module rows

0 1 2 3 4 5 6 7

1,000

1,500

2,000

2,500

α = 0.5α = 0.2

El Gouna

Constance


Ann

uale

nerg

yyi

eld

Yb

[kWh

kWp]

Figure A.7: Annual energy yield Yb increases with increasing distance between rows dR in both

a) El Gouna and in b) Constance. Saturation point reached for dR ≈ 3 m, further

than which, additional module rows have a negligible influence on Yb.


92 A.8. Module field

A.8 Module field

A.8.1 El Gouna

2147

2145

2145

2137

2124

2135

2132

2118

2130

2147

2145

2145

2137

2124

2135

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

2,110 2,120 2,130 2,140 2,150

Annual energy yield Yb [kWh/kWp]

2515

2510

2511

2492

2460

2486

2480

2444

2475

2515

2510

2511

2492

2460

2486

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

2,440 2,460 2,480 2,500 2,520


Figure A.8: Annual energy yield of all modules in a field in El Gouna with α = 0.2 (top) und

α = 0.5 (bottom). Outer modules have a higher energy production. Notice how in

El Gouna the first row, has a higher Yb than the last row, where the shadow of the

front rows decrease Irefl,r strongly reducing Yb.



A.8.2 Constance

1197

1192

1200

1193

1187

1196

1190

1184

1194

1197

1192

1200

1193

1187

1196

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

1,175 1,180 1,185 1,190 1,195 1,200 1,205


1339

1386

1406

1389

1374

1396

1383

1366

1391

1339

1386

1406

1389

1374

1396

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

1,360 1,370 1,380 1,390 1,400 1,410


Figure A.9: Annual energy yield of all modules in a field in Constance with α = 0.2 (top) und

α = 0.5 (bottom). Outer modules have a higher energy production. Notice how in

Constance the last row, has a higher Yb than the first row, where the blocking of

Irefl,r strongly reduces Yb.


Appendix B

Bifacial gain BF

The bifacial gain BF of modules is strongly influenced by other nearby objects, such

as neighbouring modules and module rows. As a result, not all bifacial modules in a

field have the same rear side performance. The bifacial gain of all modules in a field is

calculated at an albedo of 0.2 and a distance of 2.5 m between the rows, and depicted in

figures B.1 and B.2 for El Gouna and Constance respectively.

B.1 El Gouna

13.70

13.59

13.61

13.19

12.49

13.07

12.92

12.16

12.83

13.70

13.59

13.61

13.19

12.49

13.07

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

12 12.5 13 13.5 14Bifacial gain BF [%]

Figure B.1: Bifacial gain of all modules in a field in El Gouna with α = 0.2. The outer modules

have a higher energy production. Notice how in El Gouna the first row, has a higher

BF than the last row, where the shadow of the front rows decrease Irefl,r strongly

reducing BF .

Appendix B. Bifacial gain BF 95

B.2 Constance

15.15

14.64

15.43

14.78

14.19

15.05

14.53

13.88

14.83

15.15

14.64

15.43

14.78

14.19

15.05

1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

5

Module column [−]

Mod

ule

row

[−]

13.5 14 14.5 15 15.5Bifacial gain BF [%]

Figure B.2: Bifacial gain of all modules in a field in Constance with α = 0.2. The outer modules

have a higher energy production. Notice how in Constance the last row, has a higher

BF than the first row, where the blocking of Irefl,r strongly reduces BF .


96 B.2. Constance


Figures

1.1 Global energy mix up to 2100 as forecast by the Scientific Advisory Board

of the German government [1]. . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Module average selling price trend from 1991 to 2014 in $/W [2]. . . . . . . 2

1.3 Worldwide market shares for monofacial and bifacial monocrystalline solar

cells [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Solar irradiation versus established global energy resources and global an-

nual energy consumption [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . 6

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]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 The two reflection mechanisms, spectral and diffuse reflection. . . . . . . . 9

2.4 Spectral reflectance of sand against wavelength of incident light for different

moisture contents [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Structure of a standard industrial p-type Cz-silicon solar cell with a selec-

tive emitter and full surface back contact. . . . . . . . . . . . . . . . . . . 11

2.6 Two-diode model of a standard solar cell with the illumination dependent

current sourve Jph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 World market shares for different wafer types [3]. . . . . . . . . . . . . . . 13

2.8 Structure of a bifacial n-type Cz-silicon solar cell. . . . . . . . . . . . . . . 14

2.9 Two-diode model of a bifacial solar cell. . . . . . . . . . . . . . . . . . . . . 16

2.10 Schematic of the layers in a standard solar module [27]. . . . . . . . . . . . 16

2.11 Front (left) and rear (right) side of a bifacial module with a redesigned

junction box to reduce shadowing losses. . . . . . . . . . . . . . . . . . . . 17

2.12 Schematic of a field with twelve bifacial modules in three rows with their

respective shadows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.13 Schematic of blocking of ground reflected irradiance by rear module row. . 18

2.14 Results of the two simulated and the measured output powers of several

bifacial modules tested in El Gouna, Egypt [28]. . . . . . . . . . . . . . . . 19

2.15 Optimum tilt angle of bifacial modules for maximized annual energy yield

in Oslo and Cairo depending on the albedo and module elevation [29]. . . . 20

2.16 Results of measurements of both stand alone bifacial modules and bifacial

modules in a field installation in Jerusalem [31]. . . . . . . . . . . . . . . . 21

98 Figures

3.1 Stand-alone module setup and definition of the module installation param-

eters and the position of the sun. . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 In field module setup and definition of the field installation parameters and

other input parameters of the simulation. . . . . . . . . . . . . . . . . . . . 25

3.3 Incoming solar irradiance on a horizontal surface Ahor and a surface per-

pendicular to the incoming sunlight AS. . . . . . . . . . . . . . . . . . . . 27

3.4 Geometry for determining the view factor between two surfaces. . . . . . . 31

3.5 Geometry for determining the view factor between the ground surface Asand the module rear surface AM ,r inclined at the angle γM . . . . . . . . . . 32

3.6 Geometry for determining the view factor between the shadow region Ashand the module rear surface AM ,r inclined at the angle γM . . . . . . . . . . 34

3.7 The different reductions of the reflective surface length L1 by the back

module row for each cell row in the considered module. . . . . . . . . . . . 35

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.9 Monthly diffuse and direct horizontal irradianceDHI andBHI, and diffuse

irradiance factor fD for a) El Gouna and b) Constance. . . . . . . . . . . . 42

3.10 Monthly average of the ambient temperature during daytime depending on

the location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.11 The position of the Sun given by the azimuth and elevation angles for a)

El Gouna and b) Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.12 Annual energy yield of monofacial module Ym depending on the location,

albedo coefficient and the module tilt angle γM . . . . . . . . . . . . . . . . 45

3.13 Optimum module tilt angle against module height for ground albedo coef-

ficients of 0.2 and 0.5 for a) El Gouna and b) Constance. . . . . . . . . . . 47

3.14 Total irradiance on module rear side Itot,r for tilt angles a) 25 and b) 60. 48

3.15 Yearly bifacial gain of bifacial modules at varying module heights for

ground albedo coefficients of 0.2 and 0.5 for a) El Gouna and b) Constance. 49

3.16 Total irradiance on module rear side Itot,r for elevations a) 1 m and b) 10 cm. 50

3.17 Yearly bifacial gain of bifacial modules at varying diffuse irradiance factors

for ground albedo coefficients of 0.2 and 0.5 for a) El Gouna and b) Constance. 51

3.18 Total irradiance on module rear side Itot,r for diffuse irradiance factors a)

25 % and b) 100%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.19 Yearly bifacial gain of bifacial modules at varying ground reflective surface

size for ground albedo coefficients of 0.2 and 0.5 for a) El Gouna and b)

Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.20 Yearly bifacial gain of bifacial modules at varying white reflective surface

sizes, given by wS and w1, for ground albedo coefficients of 0.2 and 0.5 for

a) El Gouna and b) Constance. . . . . . . . . . . . . . . . . . . . . . . . . 53


Figures 99

3.21 Total irradiance on module rear side Itot,r for albedo coefficients a) 0.2 and

b) 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.22 Inaccuracy of the simulation of a stand-alone module, depending on the

number of rows and columns the module is divided into, with reference to

most accurate simulation with 60 parts for a) El Gouna and b) Constance. 55

3.23 Hourly dependence of the total irradiance reaching the module front and

rear sides at α = 0.2 and α = 0.5 for a) El Gouna and b) Constance. . . . . 56

3.24 Hourly dependence of the bifacial gain at α = 0.2 and α = 0.5 for a) El

Gouna and b) Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.25 Total irradiance on module rear side Itot,r a) at noon and b) in the afternoon. 57

3.26 Monthly bifacial gain at α = 0.2 and α = 0.5 for a) El Gouna and b)

Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.27 Schematic depiction of a vertically mounted, east-west-facing bifacial module. 59

3.28 Hourly dependence of the irradiance reaching both sides of a vertical bi-

facial module and the front side of a standard module for a),b) El Gouna

and c),d) Constance, in the summer and winter respectively. . . . . . . . . 60

3.29 Schematic of a module installation with the rotation axes of a) a one-axis

and b) two-axis tracking system. . . . . . . . . . . . . . . . . . . . . . . . . 61

3.30 PV module mounted on a horizontal rotation axis, enabling using an east-

west tracking of the Sun. Module is horizontal and facing upwards at noon. 62

3.31 Hourly dependence of the irradiance reaching the front and rear sides of a

bifacial module with sun-belt tracking, Itrk,f and Itrk,r, their sum Itrk,sumand the front side of a standard module Istd in Kasese, Uganda. . . . . . . 63

3.32 Total irradiance on module rear side Itot,r for a) stand-alone module and

b) two adjacent modules in one row. . . . . . . . . . . . . . . . . . . . . . 65

3.33 Yearly bifacial gain of bifacial modules depending on number of adjacent

modules, for ground albedo coefficients of 0.2 and 0.5 for a) El Gouna and

b) Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66


b) for front module of two rows with one module each. . . . . . . . . . . . 67

3.35 Yearly bifacial gain of bifacial modules depending on distance between

module rows dR, for ground albedo coefficients of 0.2 and 0.5 for a) El



b) the module in the middle of a field. . . . . . . . . . . . . . . . . . . . . 69

3.37 Inaccuracy of the simulation of a module in a field, depending on the num-

ber of rows and columns the module is divided into, with reference to most

accurate simulation with 60 parts for a) El Gouna and b) Constance. . . . 70

3.38 Bifacial gain of all modules in a field in El Gouna with α = 0.5. . . . . . . 71

3.39 Bifacial gain of all modules in a field in Constance with α = 0.5. . . . . . . 71


100 Figures

4.1 Photo of the measurement setup on the roof of the ISC Konstanz. . . . . . 74

4.2 Schematic of the measurement setup of the first part of the first experiment. 75

4.3 Schematic of the measurement setup of the second part of the first experiment. 76

4.4 Measured relative power gain when using 1.6 m2 white reflective plate at

varying distances dw from front edge of the module to front edge of the

reflective plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.5 Measured relative power gain due to 1.6 m wide white reflective plate with

varying length lw with respect to module front edge. . . . . . . . . . . . . . 77

4.6 Schematic of the measurement setup of the second experiment. . . . . . . . 78

4.7 Measured negative relative power gain due to blocking effect by second

module row at varying distances dR. . . . . . . . . . . . . . . . . . . . . . . 79

4.8 Photo of measurement setup in El Gouna, with all relevant values. . . . . . 80

4.9 Monthly diffuse irradiance factor measured from 2002 to 2005. . . . . . . . 81

4.10 Measured and simulated monthly bifacial gain of modules installed in El

Gouna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.1 Annual energy yield Ybif of bifacial modules at varying module heights for

ground albedo coefficients of 0.2 and 0.5 for El Gouna and Constance. . . . 88

A.2 Annual energy yield Y of PV modules at varying diffuse irradiance coef-

ficients fD for ground albedo coefficients of 0.2 and 0.5 for El Gouna and

Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.3 Annual energy yield Yb of bifacial modules at varying diffuse irradiance

coefficients fD for ground albedo coefficients of 0.2 and 0.5 for El Gouna

and Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.4 Annual energy yield Yb of bifacial modules at varying white reflective sur-

face sizes, given by wS and w1, for ground albedo coefficients of 0.2 and 0.5

for El Gouna and Constance. . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.5 Monthly energy yield at α = 0.2 and α = 0.5 for a) El Gouna and b)

Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.6 Annual energy yield of bifacial modules depending on number of adjacent

modules, for ground albedo coefficients of 0.2 and 0.5 for a) El Gouna and

b) Constance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.7 Annual energy yield of bifacial modules depending on distance between

module rows dR, for ground albedo coefficients of 0.2 and 0.5 for a) El


A.8 Annual energy yield of all modules in a field in El Gouna with α = 0.2 and

α = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.9 Annual energy yield of all modules in a field in Constance with α = 0.2

and α = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.1 Bifacial gain of all modules in a field in El Gouna with α = 0.2. . . . . . . 94

B.2 Bifacial gain of all modules in a field in Constance with α = 0.2. . . . . . . 95


Tables

2.1 Approximate ranges of albedo of various surfaces [8]. . . . . . . . . . . . . 10

2.2 Annual bifacial gain and its dependence on site, module elevation and

albedo [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Constants for estimating F1 and F2 as a function of ε [37]. . . . . . . . . . 30

3.2 Indices used for the calculation of the view factor and their meaning. . . . 36

3.3 Indices used for calculation of the output power of monofacial and bifacial

modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 I-V-curve measurement results of a standard and a bifacial module. . . . . 43

3.5 Results of γM ,opt and Ym of simulated monofacial module. . . . . . . . . . . 46

3.6 Results of hM ,opt and BF of simulated bifacial modules. . . . . . . . . . . . 49

3.7 Gain or loss of vertically mounted bifacial module with reference to an

optimally mounted monofacial module. . . . . . . . . . . . . . . . . . . . . 60

3.8 Gains from cross comparison of fixed and tracked monofacial and bifacial

modules in Kasese at α = 0.2 and α = 0.5. . . . . . . . . . . . . . . . . . . 63

4.1 I-V-curve measurement results of the bifacial and monofacial modules con-

sidered in the validation of the simulation. . . . . . . . . . . . . . . . . . . 82

102 Tables


Abbreviations

GDP Gross domestic product

LCOE Levelized cost of electricity

ITRPV International Technology Roadmap for Photovoltaic

PV Photovoltaics

ISC International solar energy research center

TUB Technical University Berlin

DLR German Aerospace Center

Cz Czochralski

Si Silicon

AR Anti reflective

SiNx Silicon-nitride

Al-BSF Aluminium back surface field

LID Light induced degradation

IBC Interdigitated back contact

EVA Ethyl-vinyl-acetate

MPP Maximum power point

VF View Factor

STC Standard Test Conditions

UTC Coordinated universal time

VMBM Vertically mounted bifacial module

WRP White reflective plate

Symbols

AU − Astronomical unit

AM − Air mass coefficient

L km Direct optical path length light takes through the atmosphere

L0 km Shortest possible optical path length light takes through the atmosphere

θz Zenith angle of the sun

GHI W/m2 Global horizontal irradiance

DHI W/m2 Diffuse horizontal irradiance

BHI W/m2 Beam (direct) horizontal irradiance

fD % Diffuse irradiance factor

Itot W/m2 Total irradiance on tilted plane

Idir W/m2 Direct irradiance on tilted plane

Idiff W/m2 Diffused irradiance on tilted plane

Irefl W/m2 Ground-reflected irradiance on tilted plane

J A/cm2 External current density

V V External voltage

RP Ω Parallel resistance

RS Ω Series resistance

JD1 A/cm2 Current through diode 1

JD2 A/cm2 Current through diode 2

Jph A/cm2 Light generated photo current

fB % Bifaciality factor

ηcell,f/r % Efficiency of bifacial cell front/rear side

Jph,f/r A/cm2 Front/rear side photo current

α − Albedo coefficient of surface

Idir,f/r W/m2 Direct irradiance on module front/rear side

Idiff ,f/r W/m2 Diffuse irradiance on module front/rear side

Irefl,f/r W/m2 Reflected irradiance on module front/rear side

Itot,f/r W/m2 Total irradiance on module front/rear side

nS − Vector in the direction of the sun

nM − Normal vector of module

αS Azimuth angle of the sun

γS Elevation angle of the sun

106 Symbols

αM Azimuth angle of the module

γM Tilt angle of the module

θSM ,f/r Angle of incidence respective module front/rear side

hM m Module elevation

LS m Length from module center to side edge of ground surface

L1 m Length from module center to rear edge of ground surface

L2 m Length from module center to front edge of ground surface

wS m Length from module center to side edge of reflective sheet

w1 m Length from module center to rear edge of reflective sheet

w2 m Length from module center to front edge of reflective sheet

dR m Distance between module rows

dM m Distance between adjacent modules

δ Declination angle

J ′ Day angle

ϕ − Latitude

λ − Longitude

ω Hour angle

EOT min Equation of time

MLT min Mean local time

λst − Local time zone

Ahor m2 Horizontal surface

AS m2 Surface perpendicular to the Sun

Φdir W Direct radiant power

Idir,S W/m2 Direct irradiance on the surface normal to the Sun

nM ,f/r − Normal vector of module front/rear surface

ε − Atmospheric clearness index

∆ − Atmospheric brightness factor

κ − Constant equalling 1.041

F1 − Circumsolar brightening coefficient

F2 − Horizon brightening coefficient

αM ,f/r Azimuth angle of module front/rear side

γM ,f/r Tilt angle of module front/rear side

FA1→A2 − View factor from area A1 to area A2

Ax m2 Area of index x

r m Distance between differential areas

θ1/2 Angles between surface normal and line connecting differential areas

Pmpp W Maximum power point power

Voc V Open circuit voltage

Voc,0 V Open circuit voltage measured at STC

Isc A Short circuit current

Isc,0 A Short circuit current measured at STC


Symbols 107

Vmpp V Maximum power point voltage

Vmpp,0 V Maximum power point voltage measured at STC

Impp A Maximum power point current

Impp,0 A Maximum power point current measured at STC

FF % Fill Factor

I0 W/m2 Irradiance at STC

αmpp 1/C Maximum power point temperature coefficient

ϑm Module temperature

ϑamb Ambient temperature

TNOCT ,m/b Nominal operating cell temperature of monofacial/bifacial module

Ym,b kWh/kWp Annual energy yield of monofacial/bifacial module

BF % Bifacial gain

∆BF % Relative inaccuracy of bifacial gain

gP % Relative gain in module output power


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