AUGUST 2009

DURHAM UNIVERSITY

SCHOOL OF ENGINEERING AND COMPUTING

SCIENCES

MSC IN NEW AND RENEWABLE ENERGY

RESEARCH AND DESIGN PROJECT

FEASIBILITY STUDY FOR SCHOOL RENEWABLE

ENERGY SUPPLY

BY

MARY MWOGEZA

SUPERVISOR: DR KATERINA FRAGAKI

ii

ACKNOWLEDGMENTS

I would like to thank my supervisor, Dr. Katerina Fragaki, for all the guidance she gave me

and for being understanding and patient with me during the course of the project.

PROJECT SUMMARY

This project was aimed at carrying out a feasibility study on supplying Lembo-Menelik

International Academy’s (LMIA) resource centre, located in the Democratic Republic of

Congo (DRC), with electricity generated using renewable energy. The resource centre is

located in Kinshasa, the DRC’s capital, and is currently connected to the country’s electricity

grid. However, grid electricity is very unreliable with frequent power cuts and this is

deterring the resource centre from achieving its development goals which are to increase the

number and quality of services it offers and hence attract more customers. It is because of the

need of reliable electricity and the fact that the DRC is rich in renewable energies such as

Solar, biomass and Hydropower that LMIA is seeking to supplement the grid electricity at its

resource centre with that generated using renewable energy.

The use of a solar photovoltaic’s system to supply the resource centre’s electricity needs was

studied in this project because data about solar energy was more readily available compared

to data about the biomass and Hydropower potential in the vicinity of the resource centre. A

grid back-up solar PV system was considered to be the most appropriate for the centre. This

grid back-up solar PV system was designed as a stand-alone system supplying the centre’s

electricity needs of approximately 28109 Wh/day, the demand during periods when there is

no grid electricity. The design of the stand-alone PV system was carried out using PVSYST

software which determined the required nominal capacity of the PV array as 10.6 kWp and

that of the storage batteries as 600 Ah.

The major challenge faced in the project was obtaining accurate information about: energy

consumption at the resource centre, load shedding periods, geometry and orientation of the

buildings and surrounding objects at the resource centre.

iii

PROJECT PLAN

Task Duration Dec

(last 2

weeks)

Jan Feb Mar Apr May Jun Jul Aug

(1st 2

weeks

Literature Review 26 weeks

Data Collection 20 weeks

Preliminary Design 4 weeks

Project Design 8 weeks

Report Writing 26 weeks

iv

Table of Contents ACKNOWLEDGMENTS ......................................................................................................... ii

PROJECT SUMMARY ............................................................................................................. ii

PROJECT PLAN ..................................................................................................................... iii

List of Figures ........................................................................................................................... vi

List of Tables ........................................................................................................................... vii

Nomenclature ........................................................................................................................... vii

1 INTRODUCTION ............................................................................................................. 1

1.1 Background ................................................................................................................. 1

1.2 Scope of study ............................................................................................................. 2

1.3 Objectives .................................................................................................................... 2

1.4 Tools used and main results ........................................................................................ 2

1.5 Structure of the Report ................................................................................................ 2

2 LITERATURE REVIEW .................................................................................................. 3

2.1 Solar Radiation ............................................................................................................ 3

2.1.1 The nature of solar radiation ................................................................................ 3

2.1.2 Sun – Earth Relationships .................................................................................... 4

2.1.3 Radiation on an inclined surface .......................................................................... 5

2.2 Solar Cell ..................................................................................................................... 7

2.2.1 Energy Bands ....................................................................................................... 8

2.2.2 Semiconductor Junction ....................................................................................... 8

2.2.3 The structure of a solar cell .................................................................................. 9

2.2.4 Equivalent circuit of a solar cell .......................................................................... 9

2.2.5 Characteristic I-V curve of a solar cell under illumination................................ 10

2.2.6 Solar cell performance losses............................................................................. 12

2.2.7 Temperature and Irradiance effects ................................................................... 13

2.3 The Photovoltaic Generator ...................................................................................... 14

2.3.1 Interconnection of PV modules ......................................................................... 16

2.3.2 Hot-spot effect ................................................................................................... 16

2.3.3 Orientation of Flat-plate Arrays ......................................................................... 17

2.4 Power Conditioning and Regulation ......................................................................... 18

2.4.1 Charge regulator................................................................................................. 19

2.4.2 DC–DC Converter ............................................................................................. 20

2.4.3 DC – AC Converter/Inverter .............................................................................. 21

2.5 Types of PV systems ................................................................................................. 21

2.6 Sizing stand-alone photovoltaic systems with battery storage .................................. 23

2.6.1 Intuitive methods ............................................................................................... 23

v

2.6.2 Numerical methods ............................................................................................ 24

2.6.3 Analytical methods ............................................................................................ 24

2.6.4 Sizing procedure using the intuitive method for a constant load ....................... 24

2.7 Conclusions ............................................................................................................... 28

3 RENEWABLE ENERGY POTENTIAL IN KINSHASA .............................................. 29

3.1 Democratic Republic of Congo ................................................................................. 29

3.2 Renewable energy in Kinshasa ................................................................................. 30

3.2.1 Wind energy ....................................................................................................... 30

3.2.2 Biomass energy .................................................................................................. 30

3.2.3 Hydropower ....................................................................................................... 30

3.2.4 Solar energy ....................................................................................................... 31

4 SOLAR PV SYSTEM FOR LMIA’S RESOURCE CENTRE ....................................... 33

4.1 Daily energy consumption at the Resource centre .................................................... 33

4.2 Type of System.......................................................................................................... 35

4.3 Preliminary Design of a Stand-alone PV System, at Kinshasa, using PVSYST ...... 36

4.3.1 PVSYST Preliminary design input data Procedure ........................................... 36

5 PROJECT DESIGN OF THE STAND-ALONE PV SYSTEM USING PVSYST ......... 39

5.1 PVSYST input data Procedure .................................................................................. 39

5.2 PVSYST’s Simulation Process ................................................................................. 43

5.2.1 Effective incident solar energy calculation ........................................................ 43

5.2.2 Array Maximum Power Point (MPP) “Virtual” energy .................................... 45

5.2.3 System energy .................................................................................................... 45

6 RESULTS AND DISCUSSION ...................................................................................... 48

6.1 Results of the North-facing array orientation ............................................................ 50

7 ECONOMIC EVALUATION ......................................................................................... 55

7.1 Capital costs of the major system components ......................................................... 55

7.2 Operation and Maintenance cost ............................................................................... 55

7.3 Economic evaluation in PVSYST ............................................................................. 56

8 CONCLUSIONS AND RECOMMENDATIONS .......................................................... 58

8.1 Conclusions ............................................................................................................... 58

8.2 Recommendations ..................................................................................................... 59

9 REFERENCES ................................................................................................................ 60

APPENDICES ......................................................................................................................... 61

vi

List of Figures

Figure 2.1: The Ecliptic plane, Equatorial plane, polar axis and solar declination angle [7] .... 4

Figure 2.2: (a) Zenith angle, slope, surface azimuth angle, and solar azimuth angle for a tilted

surface. (b) Plan view showing solar azimuth angle [5]. (c) Incidence angle on a tilted surface

.................................................................................................................................................... 5

Figure 2.3: The apparent daily motion of the sun showing the hour angle [6] .......................... 5

Figure 2.4: The silicon solar cell [6] .......................................................................................... 9

Figure 2.5: Equivalent circuits of a solar cell [7, 8] ................................................................. 10

Figure 2.6: (a) I – V characteristic of an illuminated solar cell (b) Maximum Power point and

other operating parameter [7]................................................................................................... 11

Figure 2.7: Effect of series and parallel resistances on the I-V characteristics of solar cells [7].

.................................................................................................................................................. 13

Figure 2.8: (a) Temperature (b) Irradiance dependence of the I- V characteristic of a solar cell

[6] ............................................................................................................................................. 13

Figure 2.9: Interconnection of PV modules [6] ....................................................................... 16

Figure 2.10: The hot-spot formation [6] .................................................................................. 16

Figure 2.11: Circuit diagrams of shunt and series regulators [7] ............................................. 19

Figure 2.12: Circuit diagram of a boost converter [9] ............................................................. 20

Figure 2.13: Single-phase full bridge inverter ......................................................................... 21

Figure 2.14: Stand-alone (a) DC; (b) AC system without battery [9] ..................................... 22

Figure 2.15: Stand-alone (a) DC; (b) AC/DC system with battery [9] ................................... 22

Figure 2.16: Stand-alone AC/DC system with battery and back-up generator [9] .................. 22

Figure 2.17: Grid back-up system ............................................................................................ 23

Figure 2.18: Grid-interactive system ....................................................................................... 23

Figure 3.1: (a) Location of DR Congo on the World Map (b) Map of DR Congo .................. 29

Figure 3.2: Pictures of different views of the Resource centre in Kinshasa ............................ 31

Figure 3.3: Availed Sketch of the plan view of the Resource centre ....................................... 32

Figure 3.4: Monthly average daily rising and setting times of the sun in Kinshasa ................ 32

Figure 4.1: Proposed grid back-up PV system at the resource centre ..................................... 35

Figure 4.2: Circuit diagram of the grid back-up PV system at the resource centre ................. 36

Figure 5.1: Hourly load profile at the resource centre during load shedding periods ............. 40

Figure 5.2: North-facing PV field and its environment at LMIA’s resource centre ................ 42

Figure 5.3: An outline of a project's organisation and simulation process in PVSYST .......... 47

vii

Figure 6.1: Annual loss diagram for the North-facing PV array ............................................. 48

Figure 6.2: Annual loss diagram for West-facing PV array .................................................... 49

Figure 6.3: Annual loss diagram for East-facing PV Array ..................................................... 49

Figure 6.4: Monthly average daily global irradiation on a horizontal and inclined surface .... 50

Figure 6.5: Optimisation of the Plane tilt and orientation ....................................................... 51

Figure 6.6: A graph showing the ambient and module temperatures during the month of

March. ...................................................................................................................................... 52

Figure 6.7: Monthly effective array output energy, energy supplied to user and unused energy

loss ........................................................................................................................................... 53

Figure 7.1: Economic evaluation of proposed PV system at the resource centre .................... 57

List of Tables

Table 4.1: Daily energy consumption at the Resource centre ................................................. 34

Table 6.1: Monthly average daily missing energy and duration of loss-of-load ..................... 54

Nomenclature

AC Alternating Current

AM Relative air mass

B Beam radiation (kW/m2 or kWh/m

2.day)

D Diffuse radiation ((kW/m2 or kWh/m

2.day)

DC Direct current

DRC Democratic Republic of Congo

e Charge of an electron (1.602 X 10-19

C)

Ec Energy level of conduction band (eV)

Ev Energy level of valence band (eV)

Eg Band or energy gap (eV)

E Energy of a photon

EWB Engineers Without Borders

g Acceleration due to gravity (m/s2)

G Global Solar radiation (kW/m2 or kWh/m

2.day)

h Planck’s constant (6.626068 × 10-34

m2 kg / s)

H Available water head (m)

viii

I Current output of a solar cell / PV module / PV generator (Amps)

ID Current through a diode or dark current (Amps)

IL Photogenerated current (Amps)

IM Maximum power point current of a solar cell / PV module / PV generator (Amps)

IO Saturation current of a solar cell (Amps)

Isc Short-circuit current of a solar cell / PV module / PV generator (Amps)

IAM Incident angle modifier

IGBT Insulated Gate Bipolar Transistor

k Boltzmann’s constant (1.381 X 10-23

JK-1

)

LED Light Emitting Diode

LMIA Lembo-Menelik International Academy

m Ideality factor (1 ≤ m ≤ 2)

MOSFET Metal oxide semiconductor field effect transistor

MPP Maximum power point of a solar cell / PV module / PV generator

NOCT Normal operating cell temperature (oC)

Ns Number of series connected modules in a PV generator

Np Number of parallel connected modules in a PV generator

P Power output of a solar cell / PV module / PV generator (Watts)

PMAX Maximum power output of a solar cell/module under standard test conditions (W)

PL Radiant power incident on a solar cell / PV module / PV generator (Watts)

P LOL Loss-of-load probability

Q Water flow (m3/s)

R Resistive load (Ohms)

Rs Series resistance of a solar cell (Ohms)

Rp Parallel resistance of a solar cell (Ohms)

SOC State of charge

T Absolute temperature (K)

Ta Ambient temperature (oC)

Tc Temperature of a solar cell (oC)

V Voltage across a solar cell / PV module / PV generator (Volts)

Voc Open-circuit voltage of a solar cell / PV module / PV generator (Volts)

VM Maximum power point voltage of a solar cell / PV module / PV generator (volts)

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Greek letters

η Energy conversion efficiency

θ Angle of incidence

ω Hour angle

δ Solar declination angle

φ Geographical latitude

γ Surface azimuth angle

ν Radiation frequency

θz Zenith angle

γs Solar azimuth angle

β Slope or inclination angle to the horizontal

αs Solar altitude angle

ρ Water density (Kg/m3) and ground reflectivity

1

1 INTRODUCTION

1.1 Background

Lembo-Menelik International Academy (LMIA), located in the Democratic Republic of

Congo (abbreviated as DR Congo or DRC), is an organisation established in September 2008

through partnership between MenelikEducation Ltd and Groupe Scolaire Lembo. The

organisation’s main objective is to increase the number of children going to school and equip

adults with useful skills; in the deprived areas of the Congolese capital, Kinshasa. It currently

works with the communities in five of these deprived areas to: provide learning programmes

to those who have been denied primary education, support vulnerable children, rehabilitate

schools, and train adults in various skills. The academy’s schools are free of charge for those

who cannot afford to pay for the education and these account for about 35% of all students

but this number is expected to double in the near future. The schools also provide lunch to

students, which for many is the only guaranteed meal for the day. In order for the academy to

continue providing services to these students, it is looking to develop partnerships with local

and international businesses, organisations, and communities. It is also hoping to

collaborate/merge with other schools and colleges in the capital and beyond in order to raise

education standards, locally and nationally. The Academy’s immediate target is to refurbish

its schools, to increase the chances of collaboration with other schools, and a resource centre.

The resource centre is intended to generate funds to run the academy by providing access to:

various training courses, an internet café, lodging, bar and restaurant facilities. The centre

will also have a library, the first of its kind in Kinshasa, where books ranging from science

and geography to drama and novels will be available to the general public.

In order for the Academy’s schools to run smoothly, provide good standard education

facilities such as laboratories, teaching material and so on, and compete favourably with other

schools; they require reliable electricity supply. The resource centre also requires reliable

electricity in order to effectively deliver its services and hence attract customers. However the

country’s electricity grid is very weak and cannot meet all the demand and hence there are

frequent power cuts otherwise known as load shedding experienced throughout Congo. The

schools, located in the outskirts of Kinshasa, can go for weeks without electricity while the

resource centre, because of its more strategic location, has no electricity for approximately

six hours per day. It is because of this electricity shortage and the fact that the Democratic

Republic of Congo is rich in renewable energy resources that Lembo-Menelik International

2

Academy asked Engineers Without Borders UK (EWB – UK) to help them carry out a

feasibility study to determine the most appropriate renewable energy systems to supply their

electricity needs at the schools and resource centre. EWB – UK is a student-led charity that

focuses on removing barriers to development using engineering. Its programmes provide

opportunities for young engineers in the UK to learn about technology’s role in development.

I was introduced to this renewable energy project, for Lembo-Menelik International

Academy, through the research programme of EWB – UK; which offers final year projects to

students in UK universities.

1.2 Scope of study

The study was focussed on the resource centre of Lembo-Menelik International Academy.

1.3 Objectives

The main objective was to carry out a feasibility study on supplying Lembo-Menelik

International Academy’s resource centre with renewable electricity

The specific objectives were;

Identify the available renewable energy resources in Kinshasa, DRC

Design the most appropriate renewable energy system for the resource centre

Estimate the cost of the designed renewable energy system

1.4 Tools used and main results

The solar potential in Kinshasa was studied in this project and modelling using PVSYST

software carried out to design the solar PV system at LMIA’s resource centre and also

simulate the performance of this system. The nominal capacity of the PV array was

determined to be 10.6 kWp and that of the battery was 600 Ah.

1.5 Structure of the Report

Chapter two is literature review on solar photovoltaic systems and their applications, chapter

three is about the renewable energy potential in Kinshasa, chapter four is about the PV

system suitable for LMIA’s resource centre and its preliminary design using PVSYST

software, chapter five involves a more detailed project design of the PV system at the

resource centre using PVSYST, chapter six discusses the results obtained from PVSYST’s

project design, chapter seven evaluates the economics of the designed PV system at the

resource centre and finally chapter eight talks about the conclusions and recommendations of

the project.

3

2 LITERATURE REVIEW

The study in this report was focussed on using solar energy, in particular solar Photovoltaics,

to supply the energy needs of LMIA’s resource centre because of the reasons mentioned in

the next chapter. The literature review therefore covers aspects related to solar PV systems

such as solar radiation incident on the collector plane, solar cells as the fundamental units that

convert sunlight to electricity, PV modules and arrays which produce the required amount of

power by the load, power conditioning and regulation, various types of PV systems, and

sizing of stand-alone PV systems.

2.1 Solar Radiation

The solar radiation at a particular location is of crucial importance to the design of a

photovoltaic system. Therefore this section reviews the various components of solar radiation

on the Earth and also explains how the amount of solar energy, falling on the surface of

photovoltaic modules, can be determined.

2.1.1 The nature of solar radiation

The sun’s structure and characteristics determine the nature of the energy it radiates into

space [5]. The sun is a sphere of intensely hot gaseous matter with a surface temperature of

5777 K.

In general, the rate of change, per unit time, of incident radiant energy on a unit surface area

is known as irradiance and is measured in kW/m2 while irradiation, measured in kWh/m

2, is

the incident energy per unit area of a surface and is determined by integration of irradiance

over a specified period of time, usually an hour or day.

The average amount of solar radiation that is incident on the outside of the Earth’s

atmosphere is 1367 W/m2. When the solar radiation enters the Earth’s atmosphere, some of

this radiation is reflected by the clouds, scattered by water droplets and suspended dust and

also absorbed by ozone, oxygen, carbon dioxide and water vapour. The solar radiation which

is not modified by any of the above mentioned atmospheric process and travels in a straight

line directly from the sun to the Earth’s surface is called direct or beam radiation. The solar

radiation which reaches the Earth’s surface after being scattered by the atmosphere is called

diffuse radiation. Some of the solar radiation that reaches the Earth’s surface is reflected from

the ground and is called albedo radiation. Therefore the total radiation falling on a surface is

the sum of the direct, diffuse and albedo radiations and is called global radiation.

4

2.1.2 Sun – Earth Relationships

The Earth moves around the sun in an elliptical orbit with the sun at one of the foci of the

ellipse. The plane of this orbit is called is called the ecliptic plane and the time taken by the

earth to make a complete revolution round this orbit defines a year.

At the same time, the sun rotates around its own axis, the polar axis, once every day. The

angle between the polar axis and the axis of rotation of the Earth in the elliptical orbit is equal

to 23.45o which is a constant. This constant tilt of the polar axis with respect to the ecliptic

plane results in a constantly changing solar declination angle, δ, which is the angle between

the equatorial plane and a straight line drawn between the centre of the Earth and the centre

of the sun. Solar declination δ varies from – 23.45o to 23.45

o, with north positive. The ecliptic

plane, equatorial plane, polar axis, and solar declination angle are shown in Figure 2.1 below.

Figure 2.1: The Ecliptic plane, Equatorial plane, polar axis and solar declination angle [7]

The angle between the vertical line through a point on the Earth’s surface and a straight line

from this point to the sun is called the zenith angle, θz, which is equal to the angle of

incidence of beam / direct radiation on a horizontal surface. The angle of incidence, θ is the

angle between the beam radiation on a surface and the normal to that surface [5]. The

complement of the zenith angle that is the angle between the line to the sun and the horizontal

is called the solar altitude angle, αs. The Slope β is the angle between the plane of the surface

in question and the horizontal and lies in the range; 0o ≤ β ≤ 180

o. γ is the surface azimuth

angle which is the deviation of the projection on a horizontal plane of the normal to the

surface from the local meridian, with zero due south, east negative and west positive; - 180o ≤

γ ≤ 180o. γs is the solar azimuth angle which is the angular displacement from south of the

projection of beam radiation on a horizontal plane, with zero due south, east negative and

west positive. ω is the hour angle (Figure 2.3) and is the angular displacement of the sun east

or west of the local meridian due to rotation of the earth on its axis at 15o per hour; morning

5

negative and afternoon positive [5]. The zenith angle, angle of incidence, solar altitude angle,

slope, surface azimuth angle and solar azimuth angle are shown in Figure 2.2.

(a) (b) (c)

Figure 2.2: (a) Zenith angle, slope, surface azimuth angle, and solar azimuth angle for a tilted

surface. (b) Plan view showing solar azimuth angle [5]. (c) Incidence angle on a tilted surface

Figure 2.3: The apparent daily motion of the sun showing the hour angle [6]

2.1.3 Radiation on an inclined surface

Solar radiation data is usually given in the form of global radiation on a horizontal surface,

however most PV panels are inclined at an angle, β, to the horizontal and hence there is need

to convert this radiation data to that on the plane of the PV panels. This global radiation, as

mentioned earlier, is made up of three components; beam or direct, diffuse and albedo

radiations and each of these must be converted from the horizontal to the plane of the PV

panels. Many models have been developed for the conversion of solar radiation from a

horizontal to an inclined plane. All the different models differ in their treatment of the diffuse

radiation. The beam and albedo radiations are treated in the same way in all the models.

Sun

Normal to

Surface

6

Beam (Direct) radiation

The conversion of the beam component from the horizontal to an inclined surface involves a

purely geometrical transformation (cosine effect), which does not involve any physical

assumption, by means of the equation:

B (β) = B cos 𝜑−𝛽 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 + 𝑠𝑖𝑛 𝜑−𝛽 𝑠𝑖𝑛 𝛿

𝑐𝑜𝑠 𝜑 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 +𝑠𝑖𝑛 𝜑 𝑠𝑖𝑛 𝛿 for south-facing panels (2.1a)

or

B (β) = B cos 𝜑+𝛽 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 + 𝑠𝑖𝑛 𝜑+𝛽 𝑠𝑖𝑛 𝛿

𝑐𝑜𝑠 𝜑 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 + 𝑠𝑖𝑛 𝜑 𝑠𝑖𝑛 𝛿 for north-facing panels (2.1b)

Where;

B (β) is the beam radiation on a collector inclined at an angle β to the horizontal

B is the beam radiation on a horizontal surface

φ is the geographical latitude of the location that is the angular location north or south of the

equator with the north being positive. This angle varies from -90o to 90

o.

δ is the declination angle at solar noon that is when the sun is on the local meridian.

ω is the hour angle

Diffuse radiation

The diffuse irradiance received by any surface is physically related to the distribution of

radiance over the celestial sphere (sky dome) which is a function of conditions of cloudiness

and atmospheric clarity [5, 7]. Clear-day data suggests the diffuse radiation as being

composed of three parts. The first is an isotropic part received uniformly from the entire sky

dome. The second is circumsolar diffuse resulting from forward scattering of solar radiation

and is concentrated in the part of the sky around the sun. The third, horizon glow, is

concentrated near the horizon and results for the earth’s albedo. It is difficult to obtain

theoretical models of general applicability that can predict the distribution of radiance over

the sky dome, partly because of its highly variable nature and partly the lack of routine

observations.

The simplest model, isotropic model, assumes that the diffuse radiation is distributed

isotropically over the sky that is every point of the sky emits light with equal radiation. The

diffuse radiation on an inclined surface is then calculated using the equation;

D (β) = 1

2 (1 + cos β) D; D is the diffuse radiation on a horizontal surface (2.2)

The assumption of diffuse radiation being isotropic has been shown to be inaccurate

especially for estimation of winter radiation which is of particular interest in photovoltaic

7

engineering. Better results are obtained using anisotropic models which take into account the

different components of diffuse radiation from the sky.

Klucher’s anisotropic model (1979) multiplies the result of diffuse radiation as given by the

isotropic model by two factors that represent the effects of the horizon glow and circumsolar

radiation respectively [7]. Hay and Davies anisotropic model (1980) considers two regions of

the sky as distinct sources of diffuse radiation: first, the entire celestial hemisphere that emits

isotropically; second, a circumsolar region that emits from the same direction as the beam

radiation [5, 7]. This model does not consider the horizon glow. Reindl et al (1990b) add a

horizon glow term to Hay and Davies model, as proposed by Klucher, giving a model

referred to as the HDKR model [5]. Perez et al (1987, 1988, 1990) divide the sky into three

zones; each acting as a source of diffuse radiation: a circumsolar region which occupies a

certain angle, a horizon band occupying another angle and the isotropic region which

occupies the rest of the celestial hemisphere. In this model, the radiation coming for each

zone is constant.

Albedo radiation

The reflectivity of most types of ground is rather low and as a result the contribution of

albedo irradiance to the global irradiance falling on a receiver is rather small. Therefore it is

usual to assume that the ground is horizontal and of infinite extent and that it reflects

isotropically [7]. On the basis of this, the albedo radiation on an inclined surface is

determined using the equation given in [6];

R (β) = 1

2 (1 – cos β) ρ G (2.3)

Where ρ is the reflectivity of the ground and depends on the composition of the ground and G

is the global radiation on a horizontal surface.

The total solar radiation on the inclined surface G (β) is then given by;

G (β) = B (β) + D (β) + R (β) (2.4)

2.2 Solar Cell

The conversion of the energy carried by optical electromagnetic radiation into electrical

energy is a physical phenomenon known as photovoltaic effect [7]. Solar cells are the

fundamental devices that carry out the above conversion in a solar photovoltaic’s system.

They are made from semiconductors and have much in common with other solid-state

electronic devices, such as diodes, transistors and integrated circuits [6]. Semiconductors are

8

either crystalline or amorphous giving rise to many different solar cells on the market but

crystalline silicon cells dominate the market because of their long lifetime (over 20 years) and

their best production efficiency which is approaching 18% [6].

2.2.1 Energy Bands

According to quantum theory, the electrons of isolated atoms have well defined discrete

energy levels. In a solid material, in which the atoms are close to each other and interact, the

individual levels spread out and form bands. For electronic and photovoltaic applications the

major bands are the conduction band, with an energy level of Ec, and the valence band, with

an energy level Ev. These two bands are separated by a band or energy gap Eg whose width is

equal to the difference between the energy levels of the two bands that is Ec – Ev. The energy

gap is an important characteristic of semiconductors and is given in electron volts (eV). An

electron volt is the energy acquired by one electron moving through a potential difference of

one volt.

Incident solar radiation can be considered as discrete “energy units” called photons. The

energy of a photon is a function of the frequency ν of the radiation (and thus also the

wavelength λ) and is given in terms of the Planck’s constant h by;

E = hν (2.5)

Thus the most energetic photons are those of high frequency and short wavelength. Therefore

when sunlight is shone on a semiconductor material, the photons making up the sunlight can

be absorbed by the atoms if, and only if, their energy is equal to or greater than the difference

between the energy levels of the two bands that is the energy gap. The absorption of a photon

then excites the atom sending the electron from the valence to the conduction band. Therefore

only photons with certain discrete frequencies are absorbed. The number of electrons that

appear in the conduction band varies rapidly with the energy gap and temperature of the

semiconductor.

2.2.2 Semiconductor Junction

Consider two pieces of a given semiconductor, say silicon, with one piece, the n-type, doped

with tiny amounts of phosphorus so that almost every thousandth silicon atom is replaced by

a phosphorus atom. This creates free moving negative charges called electrons. The other

piece of the silicon semiconductor, p-type, is doped with miniscule amounts of boron so that

almost every millionth silicon atom is replaced by a boron atom. This creates free moving

positive charges called holes. When the n and p-type layers are placed close together, as they

9

are in a solar cell, the positively charged holes and the negatively charged electrons are

attracted to each other. As they move into their respective neighbouring layers they cross a

boundary layer called the p-n junction. This movement of negatively and positively charged

particles generates a strong electrical field across the p-n junction. When sunlight strikes this

field it causes the electrons and the holes to separate, which in turn creates a voltage of

around 0.5V across the p-n junction. This voltage pushes the flow of electrons or DC current

to contacts at the front and back of the cell where it is conducted away along the wiring

circuitry that connects several cells together.

2.2.3 The structure of a solar cell

The electrical current generated in the semiconductor is extracted by contacts on the top and

bottom of the cell. The bottom contact is made in the form of a metal base while the top

contact, which must allow light to pass through, is made in the form of widely-spaced thin

metal strips (usually called fingers) that supply current to a larger bus bar [6]. The cell is

covered with a thin layer of dielectric material called an antireflection coating (ARC) to

minimise reflection of light from the top surface. Figure 2.4 shows the structure of a silicon

solar cell.

Figure 2.4: The silicon solar cell [6]

2.2.4 Equivalent circuit of a solar cell

Figure 2.5 (a) shows an equivalent circuit of an ideal solar cell. When a load is connected to

an illuminated ideal solar cell, the current I that flows through it is the net result of two

counteracting components of the internal current and is given by the equation as found in [6];

I = IL – ID

I = IL – IO 𝑒𝑒 𝑉

𝑘 𝑇 − 1 (2.6)

Where;

IL is the photogenerated current or simply the photocurrent due to the generation of carriers

by the light [7].

10

ID is the diode current due to the recombination of carriers across the junction and is driven

by the external voltage V. This voltage is needed to deliver power to the load [7].

IO is the dark saturation current due to the diode being reverse biased. The p-n junction acts

as a diode.

e is the magnitude of the electron charge, k is the Boltzmann’s constant, and T is the absolute

temperature.

(a) (b)

Figure 2.5: Equivalent circuits of a solar cell [7, 8]

However, real solar cells have series and parallel resistances as shown in Figure 2.5 (b). The

solar cell equation, as given in [7], is then;

I = IL – IO 𝑒𝑥𝑝𝑒 𝑉+𝐼𝑅𝑠

𝑚 𝑘 𝑇− 1 −

𝑉+𝐼 𝑅𝑠

𝑅𝑝 (2.7)

Where;

Rs is the series resistance; Rp the parallel resistance; and m an empirical non-ideality factor

whose value is usually close to unity [6].

2.2.5 Characteristic I-V curve of a solar cell under illumination

Equation 2.6 is used to draw the characteristic I-V curve of a solar cell (Figure 2.6). The sign

convention used is that generated current is positive (the opposite of the convention used with

diodes as normal circuit elements) [7]. By this convention, the solar cell functions as a

generator of energy in the first quadrant where the cell delivers current to a load to which a

positive voltage is applied.

As can be seen from Figure 2.6 (a), the maximum value of current from an illuminated solar

cell is obtained under short circuit conditions that is when V = 0. According to Equation 2.6,

the short circuit current ISC is equal to the photogenerated current IL. Also the maximum

voltage that can be developed across the terminals of an illuminated solar cell is under open

circuit conditions that is when the terminals are isolated (infinite load resistance) and the

current I from Equation 2.6 is equal to zero. In this case all the photogenerated current IL

IL

ID I

Load V Junction

V Junction

IL

ID

I

Rp

Rs

11

passes through the diode that is IL = ID. This maximum voltage is called the open circuit

voltage VOC and according to Equation 2.6 is equal to;

VOC = 𝑘 𝑇

𝑒 𝑙𝑛

𝐼𝐿

𝐼𝑂+ 1 (2.8)

Figure 2.6: (a) I – V characteristic of an illuminated solar cell (b) Maximum Power point and

other operating parameter [7]

No power is delivered to a load under short or open circuit. If energy from the solar cell is to

be supplied to a resistive load, then the power dissipated in this resistance is given by the

product P = IV. The maximum power PMax produced by the solar cell is reached at a point on

the I-V characteristic where the product IV is maximum [6]. This operating point (IM, VM) at

which maximum power is dissipated in the load is called the Maximum Power Point (MPP)

and it defines the largest area of the rectangle below the I-V characteristic (Figure 2.6 (b)).

The area of the rectangle corresponding to the product IMVM is obviously smaller than the

area corresponding to the product ISCVOC and the ratio of the two areas is defined by the fill

factor FF as;

FF = 𝐼𝑀𝑉𝑀

𝐼𝑆𝐶 𝑉𝑂𝐶 (2.9)

From the above definition of fill factor, the maximum power produced by the cell is;

PMax = IM VM = FF VOC ISC (2.10)

The fill factor gives a quantitative measure of the form of the characteristic curve and is in

the range 0.7 to 0.8 for many crystalline semiconductor cells [7].

The energy conversion efficiency η of a solar cell is defined as the ratio of the power PMax

produced by the cell at the maximum power point under standard test and the power PL of the

radiation incident on it.

η = 𝐼𝑀 𝑉𝑀

𝑃𝐿 =

𝐹𝐹 𝐼𝑆𝐶 𝑉𝑂𝐶

𝑃𝐿 (2.11)

Most frequent standard conditions are: irradiance of 100 mW / cm2 (or 1 kW / m

2), standard

reference AM1.5 spectrum, and temperature 25oC. The use of this standard irradiance value is

12

particularly convenient since the cell energy conversion efficiency in percent is then

numerically equal to the power output from the cell in mW / cm2 [6].

2.2.6 Solar cell performance losses

There are a number of physical and technological loss mechanisms that result in a low solar

cell energy conversion efficiency which are discussed below.

There is a minimum energy level (and thus a maximum wavelength) of photons that can cause

the creation of an electron – hole pair. For silicon, the maximum wavelength is 1.15 μm.

Radiation at higher wavelength does not produce electron – hole pairs but just heats up the

cell leading to a power loss. Also, each photon causes the creation of a single electron – hole

pair and the energy of photons in excess of that required to create electron – hole pairs is

converted to heat [5].

A certain fraction of photons of all energies are reflected on hitting the surface of the

semiconductor due to the difference in refractive index [7]. These reflection losses can be

reduced by putting an antireflective coating composed of a thin optically transparent

dielectric layer on the top surface of the cell.

Recombination of the photogenerated carriers results into losses because these carriers do not

reach the electrical contacts and are hence not collected. Recombination is most common at

impurities or defects of the crystal structure where excited charges are trapped and

subsequently recombine before being collected. It may also occur at the surface of the

semiconductor where energy levels may be introduced inside the energy gap [6]. These

energy levels act as stepping stones for the electrons to fall back into the valence band and

recombine with holes. Another site for possible recombination is at the ohmic metal contacts

to the semiconductor. The effect of recombination is that it reduces both the current, through

the probability of carrier collection, and the voltage output by increasing the dark current.

Part of the top layer of a cell is shaded by the contact grid which reduces the active cell area

that is the area exposed to the incident solar radiation, hence leading to a power loss.

Series and parallel resistances of the cell: The series resistance within the cell itself and in

its contacts causes a power loss during transmission of the electric current produced by the

solar cell. The series resistance is a particular problem at high current densities that is under

concentrated light. The parallel resistance also called shunt resistance arises from the

leakage of current around the edges of the cell and between contacts of different polarity.

13

Both the series and parallel resistances affect cell operation mainly by reducing the fill factor

as shown in Figure 2.7.

Figure 2.7: Effect of series and parallel resistances on the I-V characteristics of solar cells [7].

All the above mentioned losses explain the efficiency of about 23% for the best silicon cell

today [6].

2.2.7 Temperature and Irradiance effects

In practical applications, solar cells do not operate under standard conditions. The two most

important effects that must be allowed for are due to the variable temperature and irradiance

as shown in Figure 2.8.

(a) (b)

Figure 2.8: (a) Temperature (b) Irradiance dependence of the I- V characteristic of a solar cell

[6]

Effect of Temperature

Temperature variations have a pronounced effect on the voltage output from the cell whereas

the effects of temperature on the current and fill factor are less pronounced and are often

neglected in the design of PV systems. The cell voltage decreases with increasing

14

temperature (has a negative temperature coefficient). The voltage decrease of a silicon cell is

typically 2.3 mV per Celsius degree rise in temperature [6]. From Figure 2.8 (a) it can be

observed that an increase in temperature results in a decrease in the maximum power that the

cell can deliver and hence a decrease in the cell efficiency.

Effect of irradiance

The photogenerated current is proportional to the flux of photons whose energy is equal to or

greater than the energy gap of the semiconductor. Increasing the irradiance increases the flux

of photons with high enough energy to create electron-hole pairs and consequently the

photogenerated current. Therefore the short-circuit current Isc of a solar cell depends

exclusively on the irradiance G (kW/m2) according to the linear relation:

Isc (G) = Isc (at 1kW/m2) X G (2.12)

The voltage variation, as can be seen from equation (2.8) and Figure 2.8 (b), is much smaller

and is usually neglected in practical applications [6].

Although it is desirable to operate the solar cell at the maximum power point, this may not be

easy to realise in practice. A simpler but less efficient solution is to operate the cell at a

constant voltage below the voltage of the maximum power point [6]. If the operating voltage

remains in the linear part of the I – V characteristic, temperature will have little effect on the

power output of the solar cell therefore the power delivered to the load will be proportional to

the short circuit current and thus also to the irradiance.

2.3 The Photovoltaic Generator

One solar cell’s voltage and current output is too small for most applications. The output

voltage can be increased by connecting individual solar cells in series whereas the output

current is increased by connecting the solar cells in parallel. Therefore in order to produce

the required power and voltage, solar cells are interconnected in series to form modules. In

addition to supplying the required voltage and power, photovoltaic modules provide

protection and mechanical strength to the solar cells [7]. Several configurations of modules

are on the market but the most common have 30 to 36 crystalline silicon cells and can work

with 12 V batteries. The number of cells in a module is governed by the nominal operating

voltage of the system which should be matched to the nominal voltage of the storage

subsystem [6]. In the case of 12 V battery storage, the module output voltage should be

higher than 12V in order to be able to charge the battery and also compensate for lower

output under less-than-perfect conditions. The power of silicon modules usually falls between

15

40 and 60 W [6]. The module parameters are specified by the manufacturer under the same

standard conditions as those used to characterise solar cells that is: irradiance of 100 mW /

cm2, standard reference AM1.5 spectrum, and temperature 25

oC.

The nominal output is usually called the peak power of a module, and expressed in peak

watts, Wp [6].

The I – V characteristic of a module is similar to that of a solar cell the only difference being

that a module has a higher open-circuit voltage than that of a solar cell. Also the voltage at

the maximum power point of a module is higher than that of a solar cell; however the current

output of a module is equal to that of one solar cell. A module’s performance is affected by

irradiance and temperature in a manner that is similar that of a solar cell. As mentioned

before, for an individual solar cell, its voltage decreases with increasing temperature at a

coefficient of - 2.3 mV / oC for the open-circuit voltage Voc. Therefore for a module which

has nc cells connected in series, the negative temperature coefficient of the open-circuit

voltage will be big and will equal to;

dVoc / dT = - 2.3 nc mV / oC (2.13)

This is the reason why in practical applications modules should not be installed flush against

a surface. Air should be allowed to circulate behind the back of each module so that its

temperature does not rise to a level that there is a significant reduction in its output. An air

space of 4 – 6 inches is usually required to provide proper ventilation [10]. It is important to

note that the module voltage is determined by the operating temperature of the cells which is

different from the ambient temperature [6].

For much of its operational life, a module works in irradiances lower than 1 kW / m2 and at

temperatures higher than 25oC. Therefore the use of peak power to compare the performance

of different modules is not adequate. The characterisation of a PV module is completed by

measuring the Normal Operating Cell temperature (NOCT) defined as the cell temperature

when the module operates under the following conditions at open-circuit [6]:

Irradiance 80 mW / cm2 (or 0.8 kW / m

2)

Spectrum AM 1.5

Module tilt angle At normal incidence to the direct solar beam at local solar noon

Ambient temperature 20oC

Wind speed 1 m/s

The NOCT, which is usually between 42oC and 46

oC, is then used to determine the

temperature of the solar cells during module operation. In practice it is assumed that the

16

working temperature of the cells Tc depends exclusively on the irradiance G (kW/m2) and the

ambient temperature Ta, according to the linear relation:

Tc – Ta = 𝑁𝑂𝐶𝑇−20

0.8 × 𝐺 (2.14)

2.3.1 Interconnection of PV modules

Figure 2.9: Interconnection of PV modules [6]

In many applications the power available from one module is inadequate for the load. A PV

generator, also called an array, is made up of several modules connected in series and parallel

combinations in order to obtain the desired voltage and current (Figure 2.9). The voltages in

series connected modules are additive while in parallel connected modules, the currents are

additive.

2.3.2 Hot-spot effect

The hot-spot effect can be provoked by partial shadowing or soiling of cells, cracked or

mismatched cells or interconnection failures. Consider a series connected string of matched

cells in which one of the cells is partly shaded, soiled or damaged so as to reduce the current

it can generate to a value below that of the others (Figure 2.10).

Figure 2.10: The hot-spot formation [6]

The shaded, soiled or damaged cell will be forced into reverse bias because all the cells must

carry the same current and for the affected cell to do this, the voltage must be negative [9]. In

this condition, power is dissipated in the shaded or damaged cell of a magnitude equal to the

product of the string current and the reverse voltage developed across this cell. This leads to a

considerable temperature rise in the affected cell. If the temperature exceeds 85oC there exists

17

a risk of damaging the entire module irreversibly [7]. The hot-spot effect can be alleviated by

connecting bypass diodes (as shown in Figure 2.9) across a block of several cells in a string,

such as across a module, in order to limit the power which can be dissipated in this block and

providing a low resistance path for the current generated by the other modules (or cells) in the

generator. It is also possible for hot spots to arise when cells /modules of differing voltage are

connected in parallel. The module with a lower open-circuit voltage (Voc) behaves as a load

dissipating the power generated by the others leading to heating of this module. To avoid this

problem blocking diodes are connected in series with each of the parallel components as

shown in Figure 2.9.

2.3.3 Orientation of Flat-plate Arrays

The transmittance of optical materials usually depends on the angle of incidence. Glass

covers of solar collectors present no exception and therefore the efficiency of collectors is

affected by their orientation with respect to the sun [6]. The transmittance of a glass cover is

highest when the sunlight strikes it perpendicularly, normal incidence, and decreases as the

angle of incidence increases from zero (normal incidence) to 90o (rays of sunlight parallel to

the plane of the solar panel). The decrease in the transmittance is because of an increase in

the reflectance and absorptance of the glass cover with increasing angle of incidence.

Therefore the efficiency of a solar panel is highest when the sunlight strikes it

perpendicularly and decreases with increasing angle of incidence. This is the reason why flat-

plate solar collectors are placed at an inclination to the horizontal in order to increase the

amount of sunlight striking them perpendicularly.

In most arrays, the modules are supported at a fixed inclination facing the Equator because of

its simplicity, low cost and the fact that there are no moving parts. However as the solar beam

is seldom at normal incidence to the modules, the daily energy output from a fixed tilt array is

not as high as it could be when the array is mounted on a 2-axis sun tracker.

By mounting the array on a 2-axis sun tracker, up to 40% more solar energy can be collected

over the year than in a fixed tilt installation, moreover the gain is mostly in the early morning

and late evening when it is particularly valuable in meeting peak demand [9]. However the

additional complexity of full 2-axis tracking and the introduction of moving parts is not

generally worthwhile except in large generators in the megawatt range.

The optimum angle in a fixed tilt installation depends mainly on the latitude, and the

proportion of diffuse radiation at the site, as well as other factors such as the load profile,

18

seasonal weather variations and storage battery capacity [9]. For systems, for example those

connected to the grid, whose most important consideration is the collection of maximum

energy over the year, panel inclination to the horizontal should be close to the latitude angle

of the site. However in many stand-alone systems which rely on energy storage by batteries,

the principal consideration may not be to collect maximum energy over the year but to

maximise the daily irradiation during the worst month (the month having the least favourable

ratio between irradiation and consumed energy [7]). An inclination steeper than the latitude

angle (as a rule of thumb 15 degrees higher) is better for applications where the peak

consumption occurs during the winter whereas an inclination smaller than the latitude angle

is better for places where there is a high proportion of diffuse radiation and also for

applications whose peak consumption occurs during the summer (for example, crop

irrigation). In many places, the weather in the afternoons is often sunnier than in the

mornings therefore it is advantageous in such situations to make the modules face slightly

west of the direct line to the Equator [9].

A better and less complex way to increase output from PV modules, instead of using either a

fixed tilt installation or mounting of an array on a two axis sun tracker, may be the manual

adjustment of the orientation at regular time intervals. This can only be used in places where

labour is available. It has been estimated that, in sunny climates, a flat plat array moved to

face the sun twice a day (at mid-morning and mid-afternoon) and given a quarterly tilt

adjustment can intercept nearly 95% of the energy collected with a full 2-axis tracking [9].

2.4 Power Conditioning and Regulation

A photovoltaic system is an integrated assembly of modules and other components designed

to convert solar energy into electricity to provide a particular service either alone or in

conjunction with a back-up supply. PV systems involve a functional circuit composed of

different stages [11];

Conversion

Storage

Load consumption

Regulation

These systems experience fluctuating power output from the PV generator in conjunction

with a varying load consumption pattern; implying that energy flow within the system

requires management in order to avoid system malfunction. The energy flow management is

performed through the regulation process.

19

2.4.1 Charge regulator

To conserve battery life, overcharging and discharging too deeply must be avoided. For lead-

acid batteries, there is a direct relation between the voltage and the state of charge that makes

it easy to detect whether the battery is in a satisfactory condition [7]. Excessive discharge is

associated with a very low voltage and can be avoided by disconnecting the load from the

battery, using a switch, when the voltage falls below a certain threshold USD.

Overcharge is associated with a very high voltage. It can be avoided by either incorporating

an electronic device to dissipate the excess potential generated by the modules, shunt or

parallel regulator (Figure 2.11 (a)), or disconnecting the batteries from the generator using a

series regulator (Figure 2.11 (b)). In the first case the modules are shunted with an electronic

device (such as a transistor) acting as a load through which no current flows in normal

operation. When the battery voltage exceeds a threshold value USC, the power generated by

the modules is dissipated in this load. The blocking diode between the electronic device and

battery (Figure 2.11 (a)) prevents the battery from discharging in case of device failure. A

disadvantage of the shunt regulator is that it may dissipate a large amount of power and is

thus only used in small photovoltaic generators (less than 10A output current) [7].

For larger generators it is better to disconnect the battery from the generator using a switch or

series regulator (Figure 2.11 (b)). The on/off condition of the switch is controlled by the

battery voltage. A disadvantage of this regulator is the additional voltage drop over the switch

in normal operation (switch is on). The switch may be electromechanical (relays, contactors,

etc.) but more usually a field effect transistor (MOSFET) or an insulated gate bipolar

transistor (IGBT) is used.

(a) Shunt regulator (b) Series regulator

Figure 2.11: Circuit diagrams of shunt and series regulators [7]

IPV

PV

Array Load

IB IT

IPV Load disconnection

switch

IB

20

Energy flow in a PV system with a charge regulator

Case 1: PV array provides excess energy than is needed by the load and battery is partially

discharged

Case 2: PV array provides less energy than is needed by the load

Case 3: Battery fully charged or PV voltage lower than that of the battery because of very

low solar radiation and there is adequate charge in the battery; charge regulator disconnects

the PV (series regulator)

Case 4: Battery fully discharged; charge regulator disconnects the load (loss-of-load)

2.4.2 DC–DC Converter

This device is used to convert the DC output from the array to a voltage or voltages suited to

the requirement of the battery or load(s) [9]. There are two basic types of this converter; buck

converter which reduces the voltage and boost converter which increases it. In this project we

are interested only in the boost converter (Figure 2.12).

Figure 2.12: Circuit diagram of a boost converter [9]

Current flowing in the inductor, Figure 2.12, rises while the switch is on, storing energy in

the magnetic field of the inductor. The rate of rise of the current is proportional to the voltage

across the inductor. When the switch is turned off the current in the inductor must continue to

PV array

Load

Battery

PV array

Battery

Load

Battery Load

PV array Battery

Inductor

Vi Vo Switch

Diode

Capacitor

21

flow. The voltage across the inductor changes sign rapidly and the current is diverted to flow

through the diode. The inductor current then falls until the switch is turned on again. The

ratio of the converter’s output voltage Vo to its input voltage Vi is determined by the duty

ratio D, ratio of the time the switch is on (TON) to the period, and is given by:

𝑉𝑜

𝑉𝑖=

1

1−𝐷 (2.15)

D = 𝑇𝑂𝑁

𝑇; T = TON + TOFF

Typical values of the duty ratio D lie between 1 and 2. In real converters, losses are incurred

in the diode, inductor and switch hence equation (2.15) is not obeyed exactly. Typical

efficiencies of DC – DC converters lie between 90 and 95% [7].

2.4.3 DC – AC Converter/Inverter

An inverter converts power from DC to AC. It does this using electronic switches to reverse

the polarity of the electricity supplied to the load periodically [6]. Low power (up to tens of

kW) single-phase inverters generally use four controlled Insulated Gate Bipolar Transistors

(IGBTs), which are able to switch rapidly, in a bridge arrangement as shown in Figure 2.13.

When operated simply the inverter generates a square wave by closing S1 and S4 while S2

and S3 are open, for one half cycle, then closing S2 and S3 while S1 and S4 are open, for the

second half cycle. The diodes are necessary to provide a path for the load current when both

S1 and S2, or S3 and S4, are open simultaneously especially during the changeover [6]. The

filter is used to smooth the inverter’s output voltage waveform by removing odd order

harmonics.

Figure 2.13: Single-phase full bridge inverter

2.5 Types of PV systems

The simplest system is a stand-alone system consisting of an array which supplies the load

directly (Figure 2.14 (a)). Such a system can be used for battery charging (with a simple

charge regulator) or for water pumping where the storage medium is a water tank [9].

S1 S2

Filter

DC source S3 S4

22

(a) (b)

Figure 2.14: Stand-alone (a) DC; (b) AC system without battery [9]

The addition of a self-commuted inverter (Figure 2.14 (b)) makes it suitable for an ac pump

or other ac loads. For DC systems such as telecommunication equipment where the load has

to be supplied overnight and during periods of low irradiance, a storage battery with a charge

regulator must be added to the basic DC system (Figure 2.15 (a)).

(a) (b)

Figure 2.15: Stand-alone (a) DC; (b) AC/DC system with battery [9]

Combining systems of the types shown in Figures 2.14 (b) and 2.15 (a) gives a mixed AC/DC

system with battery (Figure 2.15 (b)) and is appropriate for domestic supplies in remote areas

[9]. A back-up generator is commonly used to improve the security of supply, reduce the

required storage and lower the capital cost (Figure 2.16)

Figure 2.16: Stand-alone AC/DC system with battery and back-up generator [9]

Turning to the grid-connected category, Figure 2.17 illustrates a simple ac system with a self

commutated inverter and grid back-up. Figure 2.18 shows a grid-interactive system, where

surplus power is fed to the grid through a second inverter. This inverter can also serve as a

rectifier for charging the battery from the grid [9].

DC loads PV array AC loads PV array Inverter

PV

Array

Charge

Regulator

Battery

DC

loads

PV

Array

Charge

Regulator

Battery

DC

loads

AC

loads Inverter

PV

Array

Charge

Regulator

Battery

Inverter

Back-up

generator

DC loads

AC

loads

o

o o

23

Figure 2.17: Grid back-up system

Figure 2.18: Grid-interactive system

2.6 Sizing stand-alone photovoltaic systems with battery storage

Sizing a stand-alone PV system is an important part of its design since the equipment capital

cost is a major component of the price of solar electricity. Over-sizing a stand-alone system

has detrimental effects on the price of the generated power while under-sizing it reduces the

supply reliability [6]. In order to size a stand-alone PV system the following must be known:

solar radiation data for the particular location, load profile, expected supply reliability that is

the percentage of time the system is capable of meeting the load requirements, and the related

economics. The sizing procedure then recommends the array tilt angle, array size, and the

battery capacity which are optimum for the application in terms of economy and reliability.

There are many methods of sizing PV systems with no universally applied rules. The various

methods can be divided into three groups.

2.6.1 Intuitive methods

These methods are based on experience and no quantitative relationships between the

generator size, battery size and supply reliability is established. The size of the generator is

chosen to ensure that the energy produced during the worst month exceeds the demand of the

load by a margin that the designer chooses based on experience [7]. The same is done to size

the battery.

PV

Array

Charge

Regulator

Battery

Inverter

From grid

AC

loads

o

o o

PV

Array

o

Inverter/

rectifier

Charge

Regulator

Battery

Inverter

From grid

AC

loads

o

o o

o

24

2.6.2 Numerical methods

A relationship between the generator size, battery size, and the Loss-of-Load Probability (P

LOL) is established by means of a detailed simulation of the system. P LOL is defined as the

fraction of time during which electricity is unavailable divided by the total time it is required

[7]. The advantages of these methods are that they are more precise and allow refinements to

be made in order to incorporate more accurate models of each element of the system. They

also allow other issues apart from sizing to be studied such as the benefits of using a

maximum-power point tracker, the effect of using a charge regulator etc. However these

methods are complex, their calculation time is very long and a large series of irradiation data

is needed.

2.6.3 Analytical methods

These methods develop analytical expressions, in terms of the battery and generator sizes, to

describe isoreliability lines. Isoreliability lines are lines having the same value of P LOL on a

graph of generator size against battery size. From the analytical expressions, it is possible to

find different combinations of generator and battery sizes that lead to the same value of P

LOL. Analytical methods allow sizing to be carried out very simply and manual calculations

are often enough. However they are inaccurate in important respects [7].

2.6.4 Sizing procedure using the intuitive method for a constant load

Determination of the load demand

The load data of the equipment or appliances to be powered by the PV system that is their

number, nominal power, nominal operating voltage, and their operating period and duration

in a typical day is obtained. From the load data a daily load profile, which is a plot of the load

in W or kW against the time in a day, is determined by estimating the periods when various

electrical appliances (loads) will be operated. From the load profile, the average daily energy

consumption in kWhday-1

can be determined. A load profile gives an indication of the

periods when there is peak demand which must be considered during system design because a

PV system powering a load whose peak matches periods of high solar radiation will have

smaller storage requirements [6].

Determination of the energy input

The radiation data for a particular site, together with the panel orientation, are used to

determine the incident solar radiation on the panel for a typical day in every month of the

year [6]. Radiation data for a particular site is usually given in form of global irradiation on a

25

horizontal surface and this should be converted into radiation received by a panel at an

inclined orientation. The radiation incident on a PV panel is usually expressed in peak solar

hours (PSH) where PSH is the number of hours of standard irradiance (1kW/m2) which

would produce the same radiation.

Numerically; Incident radiation = PSH X 1kW/m2

Therefore PSH = Incident radiation in kWh/m2 per day

The concept of PSH is introduced because it simplifies the calculation of the electrical energy

output of a PV array operating at constant voltage during a day by just multiplying the array’s

peak power produced under standard test conditions by the typical average value of PSH, as

shown in the next section.

Determination of the PV generator size for a constant load

The peak power Pc (kW) of a PV array is the power produced under standard irradiance

(1kW/m2) and when the array is operated at its Maximum Power Point (MPP). The electrical

energy Uout (kWh/day) produced by a PV array operating at its peak power for a period equal

to the PSH is; Uout = Pc X PSH (2.16)

Assuming the PV generator will be supplying a constant load of Um (kWh/day), then the

energy balance which equates the daily energy demand (Load) to the supply (electrical

energy produced by the PV array), is;

Pc X PSH = Um (2.17)

Therefore the minimum number of peak watts necessary to meet the daily energy

consumption of Um is;

Pc = Um

PSH (2.18)

In practice the PV panel is not always operated at its maximum power point and there are

also additional losses which occur in the array, battery and inverter. To take the above factors

into account an efficiency factor η is introduced. Therefore the minimum generator size in

peak watts becomes;

Pc = Um

η PSH (2.19)

Determination of the number of series-connected modules

The number of modules Ns to be connected in a series string is determined by the DC

operating bus bar voltage VDC of the system. It is usual to take VDC as a multiple of the

nominal battery voltage of 12 V [6]. Therefore;

Ns = VDC

Vm (2.20)

26

Where Vm is the operating voltage of one module and is equal to 12 V for a module

consisting of 36 cells.

Determination of the number of parallel strings

The number of parallel strings Np is determined by the current required by the load from the

generator. The equivalent load current IL in Amps is calculated from the equation

IL = Um X 103

24 X VDC (2.21)

The nominal current IPV produced by a photovoltaic generator with peak power Pc can be

calculated from the equation;

Pc = Um

η PSH = IPV VDC (2.22)

Therefore;

IPV = Um X 103

η PSH X VDC (2.23)

Substituting IL in the above equation gives;

IPV = 24 X IL

η PSH (2.24)

The number of parallel strings is then calculated from the equation;

Np = (SF) IPV

ISC (2.25)

Where ISC is the short circuit current supplied by an individual photovoltaic module when

illuminated under standard conditions and SF is a sizing factor which is introduced to

oversize the amount of current available from the array [6].

Determination of the battery size

The output of photovoltaic systems fluctuates and is unpredictable because solar radiation is

by nature a variable with respect to time. As a result of this, stand-alone photovoltaic systems

need some form of energy storage to store energy in periods when the amount of electrical

energy available from the PV generator exceeds the load demand, for use during periods

when the reverse is true that is when there is little or no solar radiation. There are a variety of

energy storage methods available but the majority of stand-alone PV systems use lead-acid

battery storage because of being available and cost effective. In addition to the general

functions of a storage medium, batteries also serve as a regulator for the system voltage.

However their use introduces some complications in that a charge controller is required in

many cases, to prevent excessive discharge or overcharge of batteries, there is also an

27

increased maintenance requirement for example battery replacement and finally the system

cost increases [8]. Most batteries would need to be replaced every after three or four years

and when compared to the life of a PV generator which is about 20 to 25 years, the frequency

of battery replacement is high and this results in an increase in the overall system cost.

Some important parameters of batteries [7, 8]

The nominal capacity CB is defined as the number of ampere hours (Ah) / charge or the

amount of energy (Wh) that can be extracted from the battery. The value of this capacity

depends on the temperature, the current used in charging and discharging and the minimum

allowable voltage level at which discharge must be stopped. The state of charge SOC is the

available capacity of a partially charged battery divided by the nominal capacity. If SOC is

equal to one, then the battery is fully charged and if it is equal to zero then the battery is fully

discharged. The depth of discharge is equal to 1 – SOC. The charge (or discharge) regime is

used to express the relationship between the nominal capacity of a battery and the current at

which it is charged (or discharged). This parameter is normally expressed in hours and is

represented by a subscript against the current symbol [7]. The Faraday (or Ah) efficiency in a

certain state of charge is defined as the ratio of the amount of charge (Ah) that can be

extracted from the battery to the amount of charge needed to restore the battery to its initial

state of charge. The energy (or Wh) efficiency in a certain state of charge equals the amount

of energy (Wh) extracted from the battery during discharge divided by the amount of energy

required to restore the battery to its initial state of charge. Both the Faraday and energy

efficiencies depend on the state of charge of the battery and on the charging and discharging

current [8]. Typical values of these efficiencies during ideal conditions depend on the kind of

battery but can be as high as 90 to 95% for the Faraday efficiency and considerably lower, 60

to 85%, for the energy efficiency [8].

Batteries have specific features that must be considered when designing PV systems as they

affect both battery life and the efficiency of the battery operation. The most prominent feature

is cycling which includes both the daily cycle, where the battery is charged during the day

and discharged by the night time load and the climatic / seasonal cycle, which is due to the

variable climatic conditions. The climatic cycle occurs anytime when the daily load exceeds

the average energy supply from the PV generator [6]. The depth of discharge associated with

the daily cycling depends only on the ratio between the night-time energy consumption

(KWh) and the battery capacity CB (KWh). This depth of discharge is shallow and varies

between 0.05 and 0.2. The depth of discharge and duration associated with the climatic

28

cycling depends on; the daily energy consumption (including the night), the size of the PV

generator and the local climate. This depth of discharge is deep and in order to avoid damage

to the battery, is limited to a certain maximum value DODMAX lying between 0.5 and 0.8. A

charge regulator is used to control this depth of discharge such that when the set maximum

value is reached, the supply to the load is cut off. This implies that the available or useful

battery capacity CU is less than its nominal capacity CB and is equal to;

CU = CBDODMAX (2.26)

The useful battery capacity can also be calculated from the empirical formula below:

F1Um ≤ CU ≤ F2Um (2.27)

Where Um is the monthly average daily energy consumption of the load and the constants F1

and F2 are the lower and upper limits of the storage sizing factor FS2. The storage sizing

factor FS2 is the number of consecutive days without sunshine (or storage days) for which the

system is designed and depends on the location and the reliability required. For example in

Spain, the values of F1 and F2 for rural electrification as recommended by Lorenzo are 3 and

5 respectively.

The nominal battery capacity CB can then be calculated from equation (2.26).

2.7 Conclusions

Based on the literature reviewed and fact that LMIA’s resource centre is connected to the

grid, there are two options of the type of PV system that can be installed at the centre: a grid

back-up system or a grid-interactive system. The grid back-up system has been considered for

this project because of being much simpler to design. This grid back-up system may be

designed as a stand-alone system supplying the load only during periods of power cuts.

Sizing of a stand-alone PV system is an important part of its design and it will be carried out

with the aid of PVSYST software. The PV modules should be inclined at an appropriate

angle to increase the amount of sunlight striking them perpendicularly and hence increase

their efficiency. A charge regulator should be used to prevent excessive discharge or

overcharge of the batteries. A DC-DC boost converter may be used to increase the output

voltage of the PV array to that required by the load and hence reduce the number of series

connected modules. An inverter will be used to convert the DC output power of the PV array

to AC, required by the load.

29

3 RENEWABLE ENERGY POTENTIAL IN KINSHASA

This chapter looks at the resources of renewable energy available in Kinshasa that can be

used to provide electricity to LMIA’s resource centre.

3.1 Democratic Republic of Congo

The Democratic Republic of Congo (DRC) is situated in Central Africa and has a tropical

climate. Figure 3.1 shows the location of DRC on a world map as well as its map. The DRC

lies on the Equator, with one-third of the country to the north and two-thirds to the south. The

capital, Kinshasa, is located 4.19o south of the Equator. As a result of its equatorial location,

the DRC experiences large amounts of precipitation and has the highest frequency of

thunderstorms in the world. The country’s tropical climate has produced the Congo River

system, with the second largest flow in the world, which dominates the region along with a

rainforest, the second largest in the world, through which the river flows [1]. The river and its

tributaries form the backbone of Congolese economics and transportation and have a vast

hydroelectric potential, approximately 150 GW, which remains largely untapped.

(a) (b)

Figure 3.1: (a) Location of DR Congo on the World Map (b) Map of DR Congo

Although the DRC has 60 percent of Africa’s hydroelectric potential, only 7 percent of the

country’s population have access to grid electricity. The grid electricity is very unreliable

with frequent load shedding so even those who are connected to the grid spend a lot of time

without electricity. This shortage of electricity is deterring the development of LMIA’s

resource centre in terms of the number and quality of services it can offer such as computing

classes. This is the reason why the resource centre is looking at using a renewable energy

system to supply its electricity needs during periods when there is no grid electricity.

30

3.2 Renewable energy in Kinshasa

3.2.1 Wind energy

The annual mean wind speed in Kinshasa is 2.1 m/s. Good sites appropriate for the use of

wind energy technology should have annual mean wind speeds of around 7 m/s [2] which

implies that the wind speed at Kinshasa is too low for the use of this technology.

3.2.2 Biomass energy

There is a vast amount of biomass in DR Congo especially in the form of wood from the

tropical rainforest. Unfortunately the Congo Rainforest is one of the world's most threatened

ecosystems due to commercial logging, clearing for subsistence and plantation agriculture,

mining, hydroelectric projects and fuel wood collection for household cooking [3, 4].

Development of an energy system, at the resource centre, based on wood from the rainforest

would be aggravating the deforestation problem and would thus not be sustainable.

Information about alternative biomass resources in Kinshasa, which could fuel the energy

system at the resource centre, was not available hence eliminating the option of using

biomass for renewable energy supply at the centre.

3.2.3 Hydropower

DR Congo has 13 percent of the world's hydroelectric potential [4]. The hydroelectric

potential at a particular site can roughly be calculated using the formula;

P = H ρ g Q η (3.1)

Where;

P = available power (W)

H = water head available (m)

ρ = water density (Kg/m3)

g = acceleration due to gravity (m/s2)

Q = water flow available (m3/s)

η = efficiency of the power plant

From equation (1) the two parameters specific to a particular site are the water head and flow.

In Kinshasa, there is a river approximately 300 metres from the resource centre. However

information about the flow of this river and the available head was not available, hence could

not further investigate the use of hydropower for renewable energy supply at the resource

centre.

31

3.2.4 Solar energy

Because of being located very close to the Equator, 4.19o south, Kinshasa receives high solar

radiation with an annual average of the global daily irradiation on a horizontal surface of 4.57

kWh/m2day. The development of a solar energy system requires data about the amount of

solar radiation received at a site which in the case of Kinshasa is readily available.

Of all the above mentioned renewable energy resources available in Kinshasa, solar energy

was the only resource for which data could easily be obtained hence my study was focussed

on using a solar photovoltaic system at the resource centre.

In order to design the solar photovoltaic system, the following information was required from

the resource centre: daily energy consumption; technical drawings of the buildings showing

dimensions, roof structure and orientation of these buildings; objects in the surrounding that

could cause shading of PV modules, their dimensions and relative positions to the buildings.

The actual daily energy consumption at the centre was not known however a rough idea of

the appliances used was provided which were used to estimate the daily energy consumption

(section 4.1). Technical drawings of the centre and its surrounding were not available but

pictures (Figure 3.2) and a rough sketch of the plan view were availed (Figure 3.3) and these

were used to produce a plan drawing of the centre and its surroundings (Appendix 1). All the

information about the resource centre was received from Mr Theodore Menelik, Director of

MenelikEducation Ltd, via email and speaking over the telephone.

Figure 3.2: Pictures of different views of the Resource centre in Kinshasa

Another picture showing the shape of the roof on the buildings at the resource centre is

shown in appendix 1

32

Figure 3.3: Availed Sketch of the plan view of the Resource centre

Data on the rising and setting times of the sun in Kinshasa was obtained from [16] and this

data was analysed using Microsoft Excel to produce the graph shown in Figure 3.4 below.

Figure 3.4: Monthly average daily rising and setting times of the sun in Kinshasa

00:00

02:24

04:48

07:12

09:36

12:00

14:24

16:48

19:12

21:36

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

Tim

e o

f d

ay

Month

sunrise (annual average: 05:55)

sunset (annual average: 18:01)

solar noon (annual average: 11:58)

33

4 SOLAR PV SYSTEM FOR LMIA’S RESOURCE CENTRE

PVSYST was used in the design of the solar PV system for Lembo-Menelik International

Academy’s resource centre. PVSYST is a computer software used for the study, sizing and

data analysis of complete PV systems. It deals with grid-connected, stand-alone, pumping

and DC-grid (public transport) PV systems, and includes extensive meteo and PV systems

components databases, as well as general solar energy tools. The software offers two levels of

PV system study; one level is the preliminary design and the other is the project design.

Before the design could be carried out, information about the daily energy consumption at the

resource centre was required and the determination of this information is detailed in the next

section. It is important to state here that many assumptions were made in coming up with the

daily energy consumption because data was not available. The choice of the PV system type

was also required before the design using PVSYST could be carried out.

4.1 Daily energy consumption at the Resource centre

The information received from Kinshasa was that the resource centre has 6 fridges, 4

freezers, 2 Video Cassette Recorders (VCR), 4 DVD players, and 4 televisions (TVs). In the

near future the centre is expected to acquire 50 computers, which will be used for up to 12

hours per day, and 10 printers. The centre has got 16 rooms, 13 of which have their own toilet

and bath area. It also has a restaurant, bar, internet café, library and 5 kitchens. The total

number of the different rooms was used to estimate the number of lights in addition to

assuming that the restaurant, internet café and library would each have two lights. A further

assumption made was that the centre had 4 security lights outside the building to come up

with the total number of lights as being 45. Assuming that the security lights are on from 7pm

till 6am (11 hours); those in the 16 rooms, restaurant, and kitchens are on from 7pm till 11pm

and then for one hour in the morning (5 hours); toilet/bathroom lights for a total of say 2

hours; bar light from say 7pm to 2am (8 hours); internet café and library lights from 6pm to

8pm (2 hours). This gave a mean daily use of each light as 4.5 hours. As for the TVs, an

assumption was made that two of them, one in the reception area and another in the

restaurant, were on from 9am till 11pm (14 hours) while the other two, used to show films

and documentaries to students trained at the resource centre, had an average daily use of 2

hours. The mean daily use of each television then amounted to 8 hours. The TVs were all

taken to be 20 inches colour. Each printer was taken to have a mean daily use of 2 hours and

34

on stand-by for 10 hours. The stand-by consumption was taken to be 5 W per printer as

obtained from PVSYST’s appliances information. An assumption was made that 2 of the

DVD players, used to show videos in the reception area and in the restaurant, had an average

daily use of 5 hours while the other 2, used in the training sessions to show

films/documentaries, had an average daily use of 2 hours. This gave a mean daily use of each

DVD player as 3.5 hours. Finally, each VCR was assumed to have a mean daily use of 2

hours. The power ratings of all the appliances were obtained from PVSYST and [11]. The

daily energy consumption at the resource centre is shown in Table 4.1.

Table 4.1: Daily energy consumption at the Resource centre

Appliance No. Power (W/

appliance)

Mean

daily use

(h/day)

Daily

energy

(Wh)

Mean daily

use during

power cuts

(h/day)

Daily energy

during power

cuts (Wh)

lights 45 18 4.5 3645 0.8 648

TV 4 80 8 2560 3 960

Computers 50 100 12 60000 4.5 22500

Printers 10 100 2 2000 0.5 500

Fridge/freezer 10 900

Wh/day

9000 300 Wh/day 3000

Stand-by

consumers

10 5 10 500 4.5 225

VCR 2 40 2 160 1 80

DVD Player 4 35 3.5 490 1.4 196

Total

(Um)

78355 28109

The resource centre is connected to the national electricity grid but this grid is very weak and

as a result the centre experiences frequent power cuts and is on average without power for 6

hours per day with most of power cuts occurring during the day. There is a strong need to

have continuous electricity supply, especially during the day, to power the appliances used

for the various kinds of activities offered by the centre. This is the reason why a solar PV

system was considered to provide back-up power supply to the centre.

35

The last column of table 4.1 gives the daily energy required by the different appliances during

periods of no electricity from the grid and it is this energy that is to be supplied by the solar

PV system. The mean daily use of each appliance during power cuts was assumed relative to

their overall mean daily use taking into consideration the time of day of their operation. It

was also assumed that the power cuts last a total of 5 hours during the day and 1 hour in the

night.

4.2 Type of System

Since the resource centre is currently connected to the grid, there were two options for the

type of system; a grid back-up system, where at any one time the load is either supplied from

the grid or the PV system but not both, or a grid-interactive system where the load is supplied

by either the grid or the PV system or both and in cases of surplus power from the PV system,

this is fed to the grid. The grid back-up system was chosen for this project because of being

much simpler to design and the lack of information about the operation of DR Congo’s

electricity distribution networks (whether they accept the connection of distribution

generators). This grid back-up system can be designed as a stand-alone system supplying the

load only during the power cuts. The layout of the proposed grid back-up PV system at

resource centre is shown in Figure 4.1.

Figure 4.1: Proposed grid back-up PV system at the resource centre

Since the PV system will be supplying a single phase AC load with a nominal voltage of

230V rms, the DC output voltage of the array should be well over the peak value of the AC

voltage waveform that is 325 V (230× √2). Consider using an array output voltage of 360V,

bearing in mind the volt drops within the inverter and cables, to provide a nominal AC

voltage of 230V rms. The number of series-connected modules required to produce the 360 V

would be many for example when using 12 V modules this number would be 30. This

number seems to be rather high and may be impractical due to the cost implications and area

PV

Array

Charge

Regulator

Battery

Inverter DC-DC

Booster

From grid

AC

loads

o

o o

36

required for all the modules. By incorporating a DC – DC boost converter in the circuit

(Figure 4.1), to step-up the array output voltage, it is possible to reduce the number of series-

connected modules. From literature the duty ratio of a DC – DC boost converter should lie

between 1 and 2. Taking a duty ratio of 2 and an output voltage of the boost converter as

360V, the required array output voltage is reduced to 180V. A detailed circuit diagram of the

proposed grid back-up PV system at the resource centre is shown in Figure 4.2.

Figure 4.2: Circuit diagram of the grid back-up PV system at the resource centre

4.3 Preliminary Design of a Stand-alone PV System, at Kinshasa, using PVSYST

This is the initial pre-sizing step carried out during a project design and its aim is to give a

rough estimate of the general features of a planned PV system. In this mode, PVSYST carries

out evaluations of the expected PV system yield very quickly in monthly values, using very

few general system characteristics or parameters, without specifying actual system

components. The software also gives a rough estimate of the system cost.

4.3.1 PVSYST Preliminary design input data Procedure

The first step in the preliminary design was to specify the system type that is either a grid-

connected, stand-alone or pumping system. In this project a stand-alone system was

considered in which mode the software sizes the required PV power and battery capacity, for

a given load profile and probability that the user will not be satisfied ("Loss of Load"

probability).

The next step involved choosing a location where Kinshasa, found in the Democratic

Republic of Congo (or Zaire), was selected as the site. On selecting the site, PVSYST

automatically uploaded, from its geographical site database, various site parameters such as

Filter 360 V

180 V

IB

IPV

Battery

Sensing

230 V

Load

37

its geographical coordinates, and the monthly climate data that is global and diffuse

irradiation, temperature and wind velocity. The source of the climate data used by PVSYST

is meteonorm ’97, a tool which uses a combination of measured data along with models of

solar geometry and climate types to produce a range of climate data for almost anywhere in

the world. The software then carried out quick meteo evaluations, known as meteo monthly

calculations, using the geographical site data to determine the horizon line and sun paths

diagram at the site. The horizon, a line created where the sky and earth appear to meet, is

used by PVSYST to describe far shading effects on the PV field and it acts in a global way

that is at any given moment the sun is either visible or not visible on the PV field. Sun path

diagrams are a convenient way of representing the motion of the Sun through the sky within a

single 2D diagram. They provide a unique summary of solar position that the designer can

refer to when considering shading requirements and design options [12].

After choosing the location, the next step was to define the system parameters such as the

collector plane orientation, and the daily energy consumption. Within the collector plane

orientation, the inclination angle of the panel to the horizontal (tilt) and its surface azimuth

angle were required. The optimum angle of inclination for fixed tilt collectors in a stand-

alone system is one that maximises the available daily irradiation during the worst month. In

the Kinshasa project, the worst month corresponds to the month with least irradiation since

the load is constant throughout the year. An angle steeper than the latitude angle is

recommended when trying to maximise the available daily irradiation during the month with

the least irradiation. Therefore a tilt angle of 10o, steeper than the latitude angle, was used in

this project. Another reason for the choice of this angle was the assumption that the panels

would be installed on and parallel to the existing roof of the building. The azimuth angle was

taken as 0o, PV plane facing due north, as this is the optimum for flat plate collectors in the

southern hemisphere in which Kinshasa is located. PVSYST has built within it an orientation

optimising tool which makes use of the monthly meteo calculations to perform quick

transpositions, convert horizontal irradiation to that incident in the collector plane, for a given

optimising period. The optimising period could be a year, winter or summer periods

depending on the planned use of the PV energy (system type). For a stand-alone system,

PVSYST carries out an orientation optimisation for the winter meteo yield. For the winter

meteo yield in Kinshasa, the global irradiation incident on the collector plane was computed

by the software as 780 kWh/m2 with a transposition factor of 1.03 and a loss by respect to the

optimum of 0.9%.

38

The next step after defining the collector orientation was to define the daily energy

consumption to be supplied by the PV system. Within the software, this consumption could

be defined as constant either throughout the year or for the different seasons or months. In

this project the consumption was considered to be constant throughout the year as the daily

demand is expected to remain approximately constant. The number of the different

appliances to be used, their power consumption and mean daily use; were specified here. As

PVSYST does not have a built in option for including an inverter in stand-alone systems, it

was advised that the power consumption of appliances with an AC distribution be increased

by 10% to account for the inverter efficiency. In the Kinshasa Project, the resource centre is

currently connected to the grid which implies that all appliances use an AC distribution. The

power consumption of all the appliances was therefore increased by 10%. The software then

computed the total daily and monthly energy consumption as 30923 Wh/day and 927.7

kWh/month respectively.

The next and final step was to open the results in which the following parameters were

specified.

The required autonomy, number of consecutive days without sunshine for which the

system is designed, which determines the battery pack capacity. For this project, 3 days

were considered.

The required Loss-of-Load probability (P LOL), fraction of time during which electricity

is unavailable over the total time it is required. A 5% P LOL was considered.

The Battery / system voltage: 180V was considered.

These parameters led to the determination of the array nominal power and battery pack

capacity as 9.5 kWp and 571 Ah respectively.

Manual sizing calculations, of the stand-alone PV system at LMIA’s resource centre, were

also carried out using the procedure stipulated in section 2.6.4 and the results are in Appendix

2. The isotropic model (section 2.1.3) was used to convert solar radiation from the horizontal

to an inclined surface. The results from these manual sizing calculations were similar to those

from PVSYST’s preliminary design for example the array nominal power and battery pack

capacity from the manual calculations were 9.13 kWp and 586 Ah respectively.

A rough investment cost of the system was computed by PVSYST as GBP 89873 and the

energy price as 1.15 £/kWh. Other results of the preliminary design using PVSYST are given

in Appendix 2

39

5 PROJECT DESIGN OF THE STAND-ALONE PV SYSTEM USING PVSYST

The project design option in PVSYST is aimed at performing a thorough PV-system design

and performance analysis using detailed hourly simulations. Optimisations and parameter

analysis can be performed through different simulation runs, called variants, within the

framework of a project, which essentially holds the geographical location and meteorological

hourly data of the site.

5.1 PVSYST input data Procedure

After choosing Project Design and the system type, stand-alone in this case, in the main

window, the procedure is as follows:

First, define the Project. The stand-alone project at Kinshasa, used in the preliminary

design, was retrieved here.

Within the same project, the software has an option that allows the construction of

different system variants. 3 system variants were constructed; each with its own PV

plane orientation (North-facing, East-facing and West-facing) but all with the same

system properties. The simulation results of the different variants were later compared to

determine the orientation that gave the best results.

For each variant, plane orientation was then defined. PVSYST supports simulations with

eight plane orientation modes for example fixed tilted plane, seasonal tilt adjustment, two

axes tracking etc. The fixed tilted plane orientation was chosen where the definition of

the plane tilt and azimuth was required. A plane tilt of 10o was used for all three variants

but each with a different azimuth.

The system properties were then defined. System definitions are primarily aimed at

defining all the PV system components necessary to fulfil the user's wishes. Parameter

definitions are different depending on the system type. In stand-alone systems, the

system definition was carried out in the following steps:

o Definition of the user’s needs. For the Kinshasa project, these were defined in the

same way as in the preliminary design that is a constant daily load over the year. In

addition to the daily energy consumption, the hourly distribution of the load, over the

day, was also defined (Figure 5.1). This hourly distribution was taken to be the same

over the year.

40

Figure 5.1: Hourly load profile at the resource centre during load shedding periods

o The next step required the definition of the required Loss-of-Load probability (P

LOL), autonomy and battery (system) voltage. The same values as in the preliminary

design were used. PVSYST then performed a system sizing, in a manner similar to

that done in the pre-sizing section, to determine the array nominal power and battery

pack capacity. The array nominal power in all three variants was computed to be 10.6

kWp and the battery pack capacity as 600 Ah.

o A battery model was then chosen from the software’s database. The 12V, 100Ah

Volta 6SB100 battery was chosen. The software then determined the number of

batteries in series and parallel which was 15 and 6 respectively in all three variants of

the Kinshasa project.

o A PV model choice, from the database, was then required. An 80Wp BP 380 module

was chosen. The number of modules in series and parallel was determined, by the

software, according to the battery voltage which was computed to be 12 and 11

respectively for the Kinshasa project.

o PVSYST then asked for the regulator definition. This could be chosen from the

database, with constraints specific to each commercial model (operating voltage

thresholds, input and output currents, etc ), but for the first simulations of a project the

software recommends to use the Generic Default regulator, which ensures standard

behaviour of the system regardless of regulator constraints. In this case the regulator

parameters are adjusted by default values corresponding to the actual system at the

simulation time (for example charging/discharging thresholds according to the battery

pack configuration). This way, the software does not produce compatibility warnings

which often occur when commercial models are used.

The next step was verification of the consistency of all parameters by PVSYST; which

then produced Warnings as Orange (acceptable for simulation) or Red (preventing

simulation) LED's. When all parameters had been properly defined and hence acceptable

41

(green or orange LED's), the software gave access to the hourly simulation. Simulation

dates are based on the Meteo file dates, and can be restricted to a limited period which

for the Kinshasa project was from January to December of the year 1990.

The simulation process involves several variables which are available as monthly tables

and graphs in the results file. This is because the software cannot store all the data in

hourly values. Data of interest to the user should be defined before the simulation, in

order to be accumulated as hourly or daily values during the simulation process.

PVSYST offers three ways for the output of detailed hourly or daily data:

o Accumulating Hourly values: the user may choose a set of variables of interest, to be

accumulated in hourly values. By default, the program chooses about ten fundamental

variables.

o Special graphs: the user can pre-define four kinds of special graphs (time evolution,

scatter plot, histogram and sorted values) for any variable in daily or hourly values.

About ten specific and usual graphs are already defined with each new simulation.

o ASCII export files: the user can choose any among the variables, to be written in daily

or hourly values on an ASCII file for exporting to another software (spreadsheet, e.g.

Microsoft Excel). The ASCII file is generated during the simulation process.

When the simulation was completed, the Results dialogue became accessible where the

following could be obtained: A printable report which holds an exhaustive table of all

parameters used during the simulation as well as a short description of the main results;

Pre-defined tables, several tables grouped by parameter themes, of monthly results;

Custom monthly graphs, where up to four variables can be simultaneously displayed

according to one’s choice; Hourly and daily plots for some pre-chosen variables; and a

detailed economic evaluation of the project can be performed while taking into account

the defined system components/parameters and simulation results.

Simulation results for a particular variant, with all involved parameters, could then be

stored for further comparisons in a file called the project's file, with the extension .VCi (i

= 0..9, A..Z).

For a given project, the software advises to first construct a rough variant keeping all

parameters to their proposed default values. In the next variant, necessary refinements can be

made such as:

42

In the System definition panel, the Detailed losses (temperature parameters, wiring

resistance, module quality, mismatch, soiling, IAM) can be modified. These losses affect

the available array output power with respect to its nominal power as specified by the

manufacturer at standard test conditions. The default losses were used in this project.

A Horizon profile can be defined. The horizon is used by PVSYST to describe far

shadings effects on the PV field. Its use is limited to distant obstacles of say twenty times

the PV array size. The horizon acts on the PV field in a global way that is at any given

instant; the sun is either visible or invisible on the field. The default profile was used.

Near shadings, that is partial shadings of near objects which affect only a part of the PV

field, can also be defined. The shaded part changes during the day and over the seasons.

Near shading calculations necessitate the construction of the exact geometry of the PV

field and its environment, in 3D-space. The near shading scene at the resource centre was

constructed using approximate dimensions because the actual ones were not provided.

The software then calculated the shading factor (ratio of the illuminated part to the total

area of the PV field) of the beam component during the day and for the different seasons.

PVSYST also calculated the shading factor for the diffuse component (as well as for the

albedo), which is independent of the sun’s position and therefore constant over the year.

Simulation results included shading loss calculations for Beam, Diffuse and Global

irradiation components.

Figure 5.2: North-facing PV field and its environment at LMIA’s resource centre

43

Figure 5.2 shows a 3D drawing, generated using PVSYST, of the surroundings at LMIA’s

resource centre and the positioning of a North-facing PV array on the roof of one of the

buildings at the centre. 3D drawings showing the resource centre and the positioning of the

other two PV array orientations (East-facing and West facing) are in Appendix 3 as well as

the procedure used in generating these drawings.

5.2 PVSYST’s Simulation Process

The simulation involves about fifty variables which are all accumulated in monthly values.

Hourly simulations are carried out in the following steps:

5.2.1 Effective incident solar energy calculation

If only monthly meteorological data is available the software generates hourly synthetic

meteo data since numerous simulation processes have to be computed as instantaneous

values (or pseudo-instantaneous as hourly averages) such as the transposition model

which closely depends on the solar geometry. This is done by disposing of well-

established random algorithms which produce hourly distributions with statistical

properties very close to real data. The algorithm first constructs a random sequence of

daily values using a Library of Markov Transition Matrices (probability matrices);

constructed from real meteo hourly data of several dozen stations all over the world, then

it applies a time-dependent, autoregressive, Gaussian model for generating the hourly

sequences for each day.

If the measured horizontal diffuse irradiance (Dh) data is not available then the software

estimates it from the horizontal global irradiance using Liu and Jordan’s correlation

model. This model results from an experimental correlation between the diffuse to global

irradiance ratio (D/G) and the clearness index Kt.

The horizontal beam irradiance (Bh) data is then computed using; Gh = Dh + Bh. The

effect of the horizon on the beam component is taken into account during the

computation. This effect is of the “ON/OFF” kind since at any given instant the sun is

either visible or not visible on the PV field. PVSYST assumes that the effect of the

horizon on the diffuse and albedo components is negligible and is hence not considered

in the software.

44

Computation of the incident irradiance on the PV tilted plane is then done using a

transposition model. Transposition is the calculation of the incident irradiance on a tilted

plane from the horizontal irradiance data. PVSYST offers two transposition models; Hay’s

model, a classic and robust model which gives good results even when the knowledge of the

diffuse irradiance is not perfect, and the Perez – Ineichen model which is a more

sophisticated model that requires well measured horizontal data (section 2.1.3). Hay’s model

was used in the Kinshasa Project.

At this stage the plane irradiance is composed of global, diffuse, beam and albedo

components, with the relation: Gp = Dp + Bp + Ap.

If near shadings have been defined, PVSYST then applies shading factors on the beam,

diffuse and albedo components. For the beam component, a shading factor has to be

established for each sun’s position that is every hour. The calculation of a shading factor

for each hour would spend too much computing time therefore the software uses a table

of shading factors, established as a function of the sun’s height and azimuth, from which

the hourly shading factor can be obtained by interpolation. PVSYST makes the following

assumptions for the calculation of the diffuse component’s shading factor: the diffuse

irradiance is isotropic, at any given time the shading effect on the diffuse irradiance can

be thought to be an integral of the shading factor over the visible part of the vault of

heaven (sphere between collector and horizontal planes), and finally that it is

independent of the sun’s position hence constant throughout the year. For the albedo

component, the software assumes that the albedo is only visible from the collectors if no

close obstacle is present till the level of the ground and hence integrates the shading

factor at zero height, over the portion of the sphere under the horizon, included between

the horizontal plane and the plane of the collector.

Diffuse and Albedo shading factors are computed from the above mentioned table of

shading factors.

An incident angle modifier (IAM) Kθ is then applied to beam component to account for

the incidence effect corresponding to the weakening of the irradiation actually reaching

the PV cells’ surface with respect to the irradiation under normal incidence. The

weakening effect is caused by the transparent protective covering (glazing), on top of the

PV collector surface, which reduces the irradiation actually reaching the PV cells due to

reflection and absorption losses occurring within it. These losses increase as the angle of

incidence increases. They are minimum when the angle of incidence at the surface of the

45

glazing is zero (that is when sunlight strikes the glazing perpendicularly) and maximum

at an incidence angle of 90o. For a fixed flat-plate solar collector, the incidence angle of

solar radiation changes continually as the sun moves across the sky. In practice the

irradiation reaching the PV cells’ surface is measured only for normal incidence, hence

the irradiation values have to be corrected for different incidence angles using an

incident angle modifier Kθ. Kθ is evaluated using the formula;

1

cos

11 0

bK ; bo is the incident angle modifier constant and θ is the incidence

angle on the plane. In PVSYST a default value of bo = 0.05 is used but the user is free to

choose his own value.

This finally results in the effective incident irradiance (in W / m2) useable for PV

conversion. The effective irradiation (in kWh / m2) is evaluated over a given time period.

5.2.2 Array Maximum Power Point (MPP) “Virtual” energy

The simulation then calculates

The array temperature through an energy balance between the absorbed solar energy and

the energy lost in the form of heat.

The virtual energy available at the array’s terminals when operated at its maximum

power point (MPP). The computation of this array virtual energy takes into

consideration array losses; that is thermal, wiring, module quality, mismatch and IAM

losses, but excludes other system losses such as regulator or inverter losses.

5.2.3 System energy

The next simulation stages are system dependent. For a stand-alone system, the simulation

simultaneously manages array production, Battery, and user consumption. At the meeting

point (battery terminals), all voltages are the same and simulation has to perform a current

balance. For each component, the current is a complex function of the voltage:

PV - array: PVSYST determines a suitable operating point on the array’s I-V

characteristic, irradiation and temperature already known, while ensuring that ohmic,

module quality and mismatch losses have an effect on the actual current for a given

voltage

46

Battery: voltage characteristics of the battery model depend on the state of charge (SOC),

temperature and current.

Load: for any given energy demand, PVSYST determines the load current as a function

of the voltage.

Once the currents are determined, SOC and battery voltage are calculated for the end of the

time interval. In addition, the system behaviour depends on the regulation state / SOC hence

the PV-array and load could be disconnected from the battery in the following situations:

PV-array disconnected when full battery,

Load disconnected in case of deep battery discharge,

Due to battery voltage evolution, these operating conditions may change during the time step.

In this case the software determines the exact time when a regulator threshold condition is

met, evaluates the energies for this hour fraction, and starts again a balance loop according to

the new operating conditions.

Several variables are computed during this process: array running characteristics, battery

storage and ageing, energy use, etc. For example, the energy supplied to the user is computed

using the array output energy and/or battery energy taking into consideration losses in the

system components such as within the array, battery, regulator, and converter (if included).

PVSYST computes the missing energy by subtracting the energy supplied to the user from

the energy demand of the user, determined from the input data.

The Probability of Loss-of-Load (P LOL) is calculated using a simplified and fast yearly

simulation. The software first splits monthly meteo values into a realistic random sequence of

365 days (according to Collares- Pereira model), each day being divided into 3 periods

(morning, day and evening), then performs a day-by-day balance and finally reports the daily

system state in order to accumulate a realistic P LOL yearly value. This process is repeated

with different PV-array sizes in order to find the exact PV size matching the required LOL

probability.

Figure 5.3 shows an outline of a project's organisation and simulation process in PVSYST.

47

Figure 5.3: An outline of a project's organisation and simulation process in PVSYST

Shading factor for beam component: "linear" or according to modules

Shading factor for diffuse: spherical integral of the "linear" shading factor

Simulation variant

(Many simulation variants may be defined for a given project)

Far shadings (Horizon definition)The far shadings affect the whole field at a time

Near shadings (partial shadings on the field)

Shading of near objects require a detailed 3D description of the system

Hourly meteo measurements

Generation of

synthetic hourly values

Project

Specification of the site (geographic coordinates)

Hourly meteorological data(Reference Year, TMY, Satellight)

Monthly meteorological data

(Sites database)

Simulation of the system (by hourly steps)

Results for a simulation version:

Customised Tables, monthly, daily and hourly graphs. - Detailed Loss diagram

ASCII export file.

Complete engineer report - Economical evaluation

User's load

Constant, monthly or daily profiles, or custom file data

Necessary for Stand-alone and Pumping systems sizing(Optional for Grid-connected)

System

Grid-connected, Stand-alone, Pumping, DC-Grid

Choice of the components and configuration

PV array

Choice of PV modules (library)

Number and interconnections of modules

Specification of Losses (In a second step) :

Module quality, Mismatch, Thermal, Wiring resistance, Incidence angle (IAM)

Incident irradiance in the collector plane:

Transposition from horizontal values to the collector plane

(fixed plane, tracking 1 or 2 axes, seasonal adjusment, heterogeneous fields)

If "infinite" sheds or sun-shields: mutual shadings calculation

(Custom, horiz. or in coll. plane)

Hourly meteorological data

Eventually Meteorological corrections (Albedo, Altitude, etc)

48

6 RESULTS AND DISCUSSION

This section involves discussion of the results from PVSYST’s Project Design. Three

different orientations of the PV array, on the roof of the resource centre, were investigated in

order to determine the optimum orientation for the specified load. Figures 6.1, 6.2 and 6.3

show annual loss diagrams for the three orientations.

Figure 6.1: Annual loss diagram for the North-facing PV array

From figures 6.1 to 6.3, it can be observed that the loss from converting the horizontal global

irradiation to the global irradiation incident in the collector plane is the same for the North

and West-facing arrays (0.8%) whereas for the East-facing array this loss is higher (1%).

From literature, fixed flat plate collectors should face the direction of the Equator and since in

many places the afternoons are often sunnier than the mornings, it is advised to make

modules face slightly west of the direct line to the Equator. It may be the case that Kinshasa

is sunnier in the afternoons than the mornings hence resulting in the above loss being the

same for the North and West- facing arrays. However, mainly due to shading from the nearby

trees, the effective irradiation incident on the North-facing PV array (1587 kWh/m2) is less

than that on the West (1600 kWh/m2) and East (1593 kWh/m

2) facing PV arrays. This results

into a lower PV energy conversion by the North-facing array of 16890 kWh as compared to

17021 kWh and 16949 kWh from the West and East-facing arrays respectively.

49

Figure 6.2: Annual loss diagram for West-facing PV array

Figure 6.3: Annual loss diagram for East-facing PV Array

50

In spite of the fact that the North-facing array has a lower PV energy conversion, it delivers

the most energy (10991 kWh) to the user compared to the other two orientations and

therefore has the least missing energy (295.8 kWh) that is when the user is not supplied by

the PV system. This is mainly because the losses associated with battery efficiency (4.6%),

unused energy (full battery) (6.2%) and those with respect to MPP running (1.1%) are lower

in the North-facing PV array system than in the other two orientations. Because of delivering

more energy to the user and hence having the least missing energy, the North-facing array

orientation was chosen as the optimum for LMIA’s resource centre. Therefore all the results

that follow are based on the North-facing PV array.

6.1 Results of the North-facing array orientation

The global irradiation on a horizontal surface was converted into irradiation received by a PV

array at an inclined orientation, 10o, and this was then corrected for the shading loss and the

results are shown in Figure 6.4.

Figure 6.4: Monthly average daily global irradiation on a horizontal and inclined surface

From literature, the reason why flat-plate solar collectors are placed at an inclination is to

increase the amount of sunlight striking them perpendicularly and hence increase their

conversion efficiency. The optimum angle of inclination for fixed tilt collectors depends

mainly on the latitude and the type of system and for a stand-alone system this angle should

be one that maximises the available daily irradiation during the worst month which in our

case corresponds to the month with least irradiation since the load is constant throughout the

0

1

2

3

4

5

6

Jan

uar

y

Feb

ruar

y

Mar

ch

Ap

ril

May

Jun

e

July

Au

gust

Sep

tem

ber

Oct

ob

er

No

vem

ber

Dec

emb

er

Irra

dia

tio

n (

kWh

/m2

.day

)

Month

Horizontal global irradiation (annual average 4.585 kWh/m2.day)

Global incident in Collector plane (annual average 4.549 kWh/m2.day)

Global corrected for shading loss (annual average 4.507 kWh/m2.day)

51

year. For the stand-alone system at Kinshasa, an inclination greater than the latitude angle

was used which results in more irradiation incident on the collector plane than that on the

horizontal for the months of April to September (Figure 6.4) that is the period with least

global irradiation. It can be observed from Figure 6.4 that there is a small difference between

the annual average daily horizontal global irradiation (4.585 kWh/m2.day) and the global

irradiation incident in the collector plane (4.549 kWh/m2.day). This is because Kinshasa is

located very close to the Equator (4.19oS) and hence the chosen inclination (10

o) which is

relatively small hence resulting in almost the same irradiation on the horizontal and the

inclined plane. Figure 6.5 shows an optimisation of the plane tilt and orientation/azimuth

produced by PVSYST. The round spot shows the chosen angle in this project. It can be

observed that the chosen plane azimuth of 0o is the optimum while the plane tilt (10

o) is just

below the optimum (approx 20o). However the loss with respect to the optimum tilt is small

(0.9%) and is therefore acceptable.

Figure 6.5: Optimisation of the Plane tilt and orientation

The resource centre has several trees in its surroundings and these could cause shading on

parts of the PV array. The effect of partial shading on a PV generator is that it can cause the

hot-spot effect, described in literature review, which can degrade the performance of the

generator. Although in practice bypass diodes are used to alleviate this effect, there is still

energy lost due to less irradiation present for PV conversion due to partial shading.

PVSYST’s simulation results for the global irradiation corrected for shading loss are shown

in Figure 6.4 above. It can be observed that the energy lost due to shading of the PV array by

its surroundings is very small; only about 0.9% of the global incident irradiation in the

collector plane, calculated on an annual basis.

The hottest month in Kinshasa is March with an average temperature of 27.1oC. The

operating temperatures of the PV modules during this month are shown in the graph below.

52

Figure 6.6: A graph showing the ambient and module temperatures during the month of

March.

From the above graph it can be observed that the maximum module temperature during the

hottest month, March, is just over 50oC. From literature we know that the module

temperature significantly affects its open-circuit voltage and hence the maximum power that

it can deliver. However if the operating voltage of a module remains in the linear part of the I

– V characteristic, temperature will have little effect on its power output and the power

delivered to the load will be proportional to the short-circuit current and thus also to the

irradiance. The operating voltage of the BP 380J modules is 15V. At a temperature of 50oC,

the voltage at the maximum power point of the BP 380J module is 15.6V [17]. This implies

that an operating voltage of 15V is in the linear part of the module’s I – V characteristic and

thus temperature will have a relatively small effect on its power output as can also be

observed from Figure 6.1 where the loss due to temperature is 8.4% of the converted energy.

Figure 6.7 is a graph showing the monthly effective array output energy, energy delivered to

the user/load and unused energy (full battery) loss. It can be observed that the energy

supplied to the load is less than the effective array output energy by approximately 6.9% on

an annual basis. This is mainly because of the losses within the battery as shown in the loss

diagram in Figure 6.1. The energy lost by the PV system due to the batteries being full, PV

array disconnected, is 6.2% of the converted solar energy on an annual basis.

0

10

20

30

40

50

60

1 6 11 16 21 26 31

Tem

pe

ratu

re (

de

gre

es

cels

ius)

Day of the Month

Ambient temperature (Average: 27.1 oC)Module Temperature (Average: 41.62 oC)

53

Figure 6.7: Monthly effective array output energy, energy supplied to user and unused energy

loss

The efficiency of the PV generator system (energy supplied to user / horizontal global

irradiation incident on the collector) is only 7.6% because of the various losses shown in

Figure 6.1. The energy supplied to the load is 97.4% of the energy required by the load

leaving the remaining 2.6% to be met from somewhere else. Since the resource centre

currently has a diesel generator, this can be used to supply this energy balance. The capacity

of the generator is not known but the information I was given is that it is currently used to

providing lighting, when load shedding occurs at night, and it can run at full capacity for 7

hours. From the table of daily energy consumption at the resource centre, I assumed that there

were 45 lights of 18 W each. Therefore if the generator can power all these lights at the same

time then its rating could be approximately 850 W and the energy it can produce when run

continuously for 7 hours is 5950 Wh. The monthly average daily distribution of missing

energy and duration of loss-of-load are given in the Table 6.1 below.

0

200

400

600

800

1000

1200

Jan

uar

y

Feb

ruar

y

Mar

ch

Ap

ril

May

Jun

e

July

Au

gust

Sep

tem

ber

Oct

ob

er

No

vem

ber

Dec

emb

er

Ene

rgy

(kW

h)

Month

Effective energy at output of array (Total annual energy: 11811 kWh)

Energy supplied to the load (Total annual energy: 10991 kWh)

Unused energy (full battery) loss (Total annual energy: 1040 kWh)

54

Table 6.1: Monthly average daily missing energy and duration of loss-of-load

Missing energy

(Wh/day)

Duration of loss-of-load

(h : min) per day

Power required from

generator (W)

January 0.3 0:21 0.8

February 4.1 0:30 8.2

March 4.3 0:56 4.6

April 3 1:12 2.5

May 0.2 0:48 0.2

June 4308 3:14 1335.8

July 3178 2:56 1080.6

August 2202 1:40 1325.7

September 0 0:00 0.0

October 4.4 0:39 6.8

November 7.3 0:18 24.3

December 0.4 0:06 4.1

The last column was computed by dividing the first by the second to come up with the power

that would be needed from the generator to supply the missing energy. It can be observed that

in all the months apart from June, July and August, the power required can readily be

supplied by the available diesel generator. The values in the above table are just averages

over each month. The actual daily missing energy and duration of loss-of load are higher on

some days than others. However I observed that the missing energy in all the days of the

year, apart from a few days in the months of June, July and August, was never more than 0.4

kWh/day and likewise the duration of loss-of load was always less than 4 h/day. These values

show that the missing energy can be supplied by the diesel generator in most of the months.

However in the months of June, July and August, there are some days when the load is not

supplied at all by the PV generator system and in these days, the diesel generator is not able

to meet all the demand. But since the resource centre is connected to the grid; grid electricity

could be used, on these days, to charge the batteries when available for use during load

shedding periods. This option has not been considered in this project and therefore requires

further study to determine whether it is viable.

The total annual duration of loss-of-load was simulated by PVSYST to be 386.4 hours that is

4.4% of the time in a year (8760 hours).

55

7 ECONOMIC EVALUATION

The major obstacle to widespread use of PV is currently the high capital and installation costs

of the system. Owing to the absence of moving parts and to the simplicity and reliability of

PV systems, operating and maintenance costs can be very low if the lifetime is long enough.

There are also no fuel costs when using PV.

7.1 Capital costs of the major system components

PV module prices have fallen sharply during the past two decades, as the global market grew,

from US$ 30 / Wp in 1975 to US$ 3 / Wp today [13]. In Africa, PV module prices range from

US$ 6 to 10 per Wp [14]. The information received from Kinshasa is that there are currently

no companies selling solar panels hence all panels have to be imported from other countries.

Taking the above information into account, the module price for the Kinshasa project was

taken as US$ 10 / Wp. Therefore for an 80 Wp module the cost would be US$ 800. The cost

of a 100 Ah deep cycle lead-acid battery, suitable for PV applications, is US$ 200 [14]. At

the resource centre 90 batteries, each with 100 Ah storage capacity, will be required giving

the total cost of the batteries as US$ 18000. Currently inverter costs range from 0.5 Euro/Wp

(large system) to 0.8 Euro/Wp (small system) [15]. Taking the 10.6 kWp system at Kinshasa

as relatively small, the inverter cost used was 0.8 Euro/Wp giving a total cost for the inverter

required by the PV system at the resource centre as 8480 Euros. An assumption was made

that the costs of the Charge regulator and the DC-DC boost converter were approximately the

same as the inverter cost.

7.2 Operation and Maintenance cost

The operation and maintenance cost in a PV system is mainly associated with the storage

batteries which require frequent checking of the electrolytes and topping up with distilled

water. This cost lies between 5 – 10% of the PV system’s annual cost. An additional cost is

involved due to the periodic replacement of batteries. This is because the lifetime of storage

batteries lies between 3 and 5 years [14].

The economic evaluation for the PV system at the resource centre was carried out in

PVSYST. The currency used for the evaluation was Euros and the conversion rate from US

dollars to Euros used was 1 US$ = 0.7114 Euros

56

7.3 Economic evaluation in PVSYST

After simulation, an economic evaluation of the system was performed on the basis of the

defined parameters and the simulation results. The special economic tool was accessible in

the Results dialog. Costs could be defined globally, by pieces, by installed peak watts or by

m². The cost per piece was used in this evaluation. Any currency could be used and the

conversion from one currency to another was also possible. The Euro was used in this case.

The procedure for the economic evaluation was as follows:

The first step was calculation of the investment. The number and type of system

components (PV modules, converters, batteries, etc.) were automatically updated from

the simulation parameters. Prices were then defined for each component using the values

described before. After defining the component prices, PVSYST calculated the gross

investment excluding taxes. The net investment, for the owner, was derived from the

gross investment by adding a tax percentage (VAT) taken as 18%. The DRC does not

have Value Added Tax (VAT) at present but is in the process of introducing it [18]. The

18% VAT rate was chosen because of being the rate in DRC’s neighbouring countries

such as Uganda and the Republic of Congo.

By choosing a loan duration, which PVSYST took to correspond to the expected lifetime

of the system, and an interest rate the software computed the annual financial cost,

assuming the loan pay back as constant annuities. The expected lifetime of the system

was taken as 20 years [7] and the interest rate as 5%.

The next step was determination of the running costs which depended on the system

type. For a stand-alone system, a provision for the maintenance and periodical

replacement of the batteries was added. The running costs were taken as 5% the annual

financial cost plus a battery replacement cost of 2320 Euro/year (set by PVSYST). This

last contribution was calculated through simulation as a function of the expected lifetime

of the battery pack taken as 5.5 years by the software.

The total annual cost was then determined as the sum of the annuities and running costs. This

total annual cost divided by the effectively produced and used energy gave an evaluation of

the energy cost (price per used kWh).

57

The results of this economic evaluation are shown in Figure 7.1.

Figure 7.1: Economic evaluation of proposed PV system at the resource centre

58

8 CONCLUSIONS AND RECOMMENDATIONS

8.1 Conclusions

Lembo-Menelik International Academy has a desire to improve the quality of services it

offers at its resource centre and hence attract more customers but the frequent load

shedding experienced, due to a weak electricity grid in the Democratic Republic of

Congo, is making it difficult for LMIA to achieve this goal. The Democratic Republic of

Congo is rich in renewable energy resources such as Biomass, Hydro and Solar;

therefore LMIA is interested in using a renewable energy system to supplement grid

electricity hence ensuring a reliable electricity supply at the centre.

The biomass mainly comes from the tropical rainforest that covers a large part of the

country. However this forest is currently under threat due to too much deforestation.

Therefore the use of biomass from the forest, for renewable energy supply of Lembo-

Menelik International Academy’s resource centre, was ruled out in order not to aggravate

the deforestation problem. Data about other biomass resources in the country was not

available hence eliminating the biomass option.

The Congo River, with the second largest flow in the world, has a vast hydroelectric

potential. Part of this river flows 300 metres from the resource centre however

information about the flow and available head in this part, essential for hydropower

design, was not available hence eliminating this option.

Being located close to the equator (4.19 oS), Kinshasa receives a lot of solar radiation

with an annual average daily global irradiation on a horizontal surface of 4.57

kWh/m2day. Solar data for Kinshasa was readily available hence a solar PV system was

deemed the most appropriate to supply the energy needs of the resource centre. The

approximate total energy demand at the centre is 78355 Wh/day and that required when

there is no grid electricity is 28109 Wh/day. The PV system was designed to meet the

latter energy demand.

The resource centre is currently connected to the country’s electricity grid therefore a

grid back-up solar PV system was proposed, with a nominal capacity of the PV array of

10.6 kWp and a nominal battery capacity of 600 Ah, to supply the load at the centre

during periods when there is no grid electricity.

59

The above solar PV system will have a 4.4% loss-of load probability in a year that is the

time when the load is not supplied by the system. During the periods of loss-of load the

diesel generator, present at the resource centre, can be used to supply the missing energy

during most days of the year apart from a few days in the months of June, July and

August.

The net investment cost of the proposed solar PV system will be approximately 118647

Euros. This money can be obtained through a loan payable over a period 20 years, the

lifetime of the system, with annual payments of 9521 Euros.

8.2 Recommendations

To accurately size the solar PV system, more information about the appliances, their

ratings, the period and duration of operation is required in order to determine the actual

daily energy consumption and its hourly distribution.

More detailed information about the periods of load shedding and their duration is

required to more accurately simulate when the solar PV system is required and the

energy it is required to supply.

The actual dimensions of the buildings and surrounding objects at the resource centre

and their relative distances is required to more accurately define the shading scene and

hence the shading loss.

Further research could be carried out to determine the applicability of a grid-interactive

solar PV system where electricity can be sold to the grid and grid electricity used to

charge the batteries in periods of low or no solar radiation.

Further research could also be carried out to determine the possibility of using the back-

up generator, present at the resource centre or a different one, to charge the batteries

during periods of low or no solar radiation.

If more data can be obtained about the biomass and hydropower options, another study

should be carried out to determine the most feasible option, of the three renewable

energy sources that is solar, biomass and hydro or even a combination of sources; to

supply the resource centre.

60

9 REFERENCES

1. http://en.wikipedia.org/wiki/Democratic_Republic_of_the_Congo accessed on 28/07/09

2. K. Fragaki, Lecture notes on Wind Energy Basics, Durham University, 2009

3. http://rainforests.mongabay.com/congo/deforestation.html accessed on 28/07/09

4. http://siteresources.worldbank.org/INTAFRICA/Resources/Congo_DRC_Country_Note.

pdf accessed on 28/07/09

5. J A Duffie and W A Beckman, Solar Engineering of Thermal Processes, 3rd

Edition,

John Wiley and Sons, New Jersey, USA, 2006.

6. T. Markvart (ed), Solar Electricity, Second Edition, John Wiley and Sons, Chichester,

England, 2000.

7. E. Lorenzo et al., Solar Electricity. Engineering of Photovoltaic Systems, Progensa,

Spain, 1994.

8. R. J. Van Overstraeten and R. P. Mertens, Physics, Technology and Use of Photovoltaics,

Adam Hilger, Bristol, 1986.

9. Fred C Treble, Generating Electricity from the Sun, Pergamon Press, Oxford, England,

1991.

10. K. Mahkamov, Lecture notes on Solar PV systems, Durham University, 2008.

11. http://www.green-trust.org/2003/pvsizing/default.htm accessed on 24/06/09

12. http://squ1.org/wiki/Sun_Path_Diagram accessed on 22/06/09

13. http://practicalaction.org/practicalanswers/product_info.php?products_id=194 accessed

on 30/06/09

14. http://imfundo.digitalbrain.com/imfundo/web/plan/documents/kb12/kb12.doc?verb=view

accessed on 30/06/09

15. http://www.leonardo-energy.org/cost-development-pv-energy accessed on 30/06/09

16. http://www.timeanddate.com/worldclock/astronomy.html?n=121&month=1&year=2009

&obj=sun&afl=-11&day=1 accessed on 07/08/09

17. http://www.becosolar.com/documents/BP380J.pdf accessed on 25/06/09

18. http://www.gfip.org/storage/gfip/documents/capital%20flight%20from%20drc.pdf

accessed on 11/08/09

61

APPENDICES

Appendix 1: Picture and plan view of the resource centre

The yellow

building in this

picture was said to

have the same roof

as that on resource

centre’s building

and was therefore

used to come up

with the roof

shape and tilt on

the buildings of

the resource

centre.

This is a sketch of

the plan view of the

resource centre and

its surroundings

which I drew from

the pictures,

drawing and other

information

received.

62

Appendix 2: Preliminary Design of the stand-alone system at LMIA’s resource centre

PVSYST Preliminary design main results

63

Horizon Line for Kinshasa

Sun path diagram at Kinshasa

Manual Sizing calculations of the stand-alone PV system at the resource centre using

the intuitive method

Determination of the daily energy use

The daily energy consumption shown in Table 4.1 was used where Um = 78355 Wh /day for

a stand-alone PV system that supplies all the energy needs at the resource centre and Um=

28109 Wh /day for a stand-alone PV system acting as a grid back-up that is supplying the

load only during periods of power cuts.

Determination of the solar energy input

The graph below shows the monthly average daily global and diffuse irradiation on a

horizontal surface in Kinshasa. It can be observed, from the graph, that the irradiation does

64

not vary too much throughout the year therefore I considered the yearly average daily

irradiation in my computation of the solar energy input. The irradiation on a horizontal

surface must be converted into that received by a PV panel at an inclined orientation which in

this case was taken to be 10o. An inclination of 10

o was chosen because I assumed the PV

modules would be installed on the roofs of the buildings at the resource centre, whose pitch

angle is 10o. An inclination close to the latitude angle at Kinshasa (4.19

o) would have been

adequate but due to purposes of self-cleaning of the modules and the need maximise the daily

irradiation during the month with least sunshine, a slightly steeper inclination of 10o was

chosen.

The isotropic model was used for the conversion to the inclined surface. Therefore;

Yearly average global daily irradiation on a horizontal surface, G = 4.57 kWh/m2day

Yearly average diffuse daily irradiation on a horizontal surface, D = 2.46 kWh/m2day

Inclination angle of the PV plane to the horizontal, β = 10o

Yearly average beam daily irradiation on a horizontal surface, B = G – D = 2.11 kWh/m2day

φ = geographical latitude of the location = – 4.19o

The beam irradiation on an inclined surface is calculated using the following equation:

B (β) = B cos 𝜑+𝛽 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 + 𝑠𝑖𝑛 𝜑+𝛽 𝑠𝑖𝑛 𝛿

𝑐𝑜𝑠 𝜑 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝜔 + 𝑠𝑖𝑛 𝜑 𝑠𝑖𝑛 𝛿 for the southern hemisphere

Where δ is the declination angle at solar noon and calculated using the equation below;

δ = – 23.45 sin 360284+𝑑𝑛

365 ; dn is the number of the day in the year

0

1

2

3

4

5

6

Jan. Feb. Mar. Apr. MayJune July Aug.Sep. Oct. Nov.Dec.

Irra

dia

tio

n (

kW

h/m

2.d

ay)

Month

Monthly Average Daily Irradiation on a Horizontal surface in Kinshasa

Horizontal Global Irradiation

Horizontal Diffuse Irradiation

65

dn = 172 for the 21st of June

δ = – 23.45o

ω = hour angle and is equal to zero at solar noon

Therefore the beam irradiation at solar noon on a surface inclined at 10o to the horizontal is;

B (10o) = 1.9499 kWh/m

2day

The diffuse irradiation on an inclined surface is calculated using the isotropic model as;

D (β) = 1

2 (1 + cos β) D

Therefore D (10o) = 2.4413 kWh/m

2day

The albedo irradiation on the inclined surface is calculated using the equation below.

R (β) = 1

2 (1 – cos β) ρ G; where ρ is the ground reflectance of the total solar radiation and as

a rule of thumb is usually taken as 0.2. Therefore;

R (10o) = 0.006943 kWh/m

2day

The total solar irradiation on the inclined surface is then equal to;

G (β) = B (β) + D (β) + R (β)

G (10o) = 4.3981 kWh/m

2day

Therefore Peak Solar Hours (PSH) = 4.3981 h/day

PVSYST uses Hay’s model to convert the irradiation falling on a horizontal surface to that

received on an inclined PV plane and for PV panels inclined at 10o to the horizontal, in

Kinshasa, the yearly average total daily irradiation on the inclined plane is 4.5 kWh/m2day

which is also equal to 4.5 h/day in terms of peak solar hours.

Determination of the PV generator size

The minimum generator size in peak watts (Pc) necessary to mean the daily energy

consumption (Um) was calculated using the equation below.

Pc = Um

η PSH ; where η is the efficiency factor which takes into account losses in the array,

battery and inverter. In the above equation it is assumed that the PV generator operates at its

maximum power point for simplification purposes. The energy loss in the inverter was

assumed to be 15% and a further 5% allowed for losses in the array, including the effects of

dust and shading. Assuming that 60% of the load is met using the solar irradiation available

during the day, leaving 40% to be supplied from the battery. Therefore the overall battery

loss, for a battery with an energy efficiency of 75%, is 25% X 40% = 10%. A battery’s

energy efficiency in a certain state of charge equals the amount of energy extracted from the

66

battery during discharge divided by the amount of energy required to restore the battery to its

initial state of charge. The total losses are therefore 30% giving an efficiency η of 70%.

Therefore the minimum generator size (Pc) for a stand-alone solar PV system at the resource

centre in Kinshasa is approximately 25451 peak watts while that for a grid back-up solar PV

system is approximately 9130 peak watts.

From PVSYST’s preliminary design, the minimum generator size for the stand-alone system

was 27088 peak watts while that for the grid back-up system was 10656 peak watts.

Determination of the number of series-connected modules

The number of modules Ns to be connected in a series string is determined by the DC

operating bus bar voltage VDC of the system according to the equation: Ns = VDC

Vm ; where Vm

is the operating voltage of one module. As the PV generator system will be supplying a single

phase AC load with a nominal voltage of 230V rms, the DC output voltage of the array would

have to be well over the peak value of the AC voltage waveform that is 325 V (230× √2).

Therefore a VDC of 360V was considered, bearing in mind the volt drops within the inverter

and cables, in order to provide a nominal AC voltage of 230V rms. Vm was determined

considering an 80 peak watt module with the following characteristics.

Typical Electrical Characteristics of BP 380J module at

standard conditions

[http://www.becosolar.com/documents/BP380J.pdf

accessed on 25/06/09]

Nominal Peak Power (Pmax) 80 W

Voltage at maximum power

(Vmp)

17.6 V

Current at maximum power

(Imp)

4.55A

Warranted minimum Pmax 76 W

Short-circuit current (Isc) 4.8A

Open-circuit Voltage (Voc) 22.1V

Temperature coefficient of lsc (0.065±0.015)%/°C

Temperature coefficient of Voc –(80±10)mV/°C

67

Temperature coefficient of

Power

–(0.5±0.05)%/°C

NOCT 47±2°C

Maximum series fuse rating 20A

Maximum System Voltage 600V

The mean ambient temperature in Kinshasa is shown in the table below

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Ambient

Temp.

(oC)

26.0 26.6 27.1 26.6 26.0 23.8 22.7 23.8 25.5 26.0 26.0 26.0

From the above table it can be seen that the maximum ambient temperature Ta is 27.1 oC. The

operating cell temperature Tc of the above module at Ta = 27.1 oC and G = 1 kW/m

2 is given

by:

Tc – Ta = 𝑁𝑂𝐶𝑇−20

0.8 × 𝐺

Therefore, Tc = 60.85 oC, for NOCT = 47

oC, and this the maximum temperature at which the

cells will operate. From the I – V performance curves of the BP 380J module, at 1000 W/m2

and 60.85oC, the module gives its maximum power at about 14.7V. Therefore a suitable

operating voltage Vm, bearing in mind the ± 10% tolerance on module output, is 13V.

At this voltage, the number of series-connected modules for a DC bus voltage of 360 is 28.

This number seems to be rather high and may be impractical due to the cost implications and

area required for all the modules. By incorporating a DC – DC boost converter in the circuit,

to step-up the array’s output voltage, it is possible to reduce the number of series-connected

modules. The duty ratio of a DC – DC boost converter should lie between 1 and 2. Taking the

duty ratio as 2 and the output voltage of the boost converter as 360V, the required array

output voltage is reduced to 180V. At a VDC of 180V the number of series-connected

modules would be 14.

Determination of the number of parallel strings

The number of parallel strings Np is determined by the current required by the load from the

generator. The nominal current IPV produced by a photovoltaic generator operating at peak

power Pc can be calculated from the equation;

68

Pc = Um

ηPSH = IPV VDC;

Therefore for a stand-alone solar PV system at Kinshasa with Pc = 25451 W and VDC = 180V,

IPV = 141.3944 A; whereas for a grid back-up system with Pc = 9130 W and VDC = 180V, IPV

= 50.7222 A.

The number of parallel strings is then calculated from the equation;

Np = (SF) IPV

Im

Where Im is the current supplied by an individual photovoltaic module at the operating

voltage Vm when illuminated under standard conditions and SF is a sizing factor which is

introduced to oversize the amount of current available from the array. The current Im supplied

by the BP 380J module at Vm = 13V and 1000 W/m2 is 4.8 A.

Therefore, for a stand-alone solar PV system at Kinshasa with VDC = 180V and IPV =

141.3944 A, the number of parallel strings is 30 with an effective SF of 1.018; whereas for a

grid back-up system with VDC = 180V and IPV = 50.7222 A, the number of parallel strings is

11 with an effective SF of 1.041.

Determination of the battery size

The nominal battery capacity, CB, is calculated using CU = CBDODMAX; where CU is the

useful battery capacity and DODMAX is the maximum permissible depth of discharge of the

battery. The useful battery capacity is calculated from the empirical formula: F1Um ≤ CU ≤

F2Um; where F1 and F2 are the lower and upper limits of the storage sizing factor FS2. The

storage sizing factor FS2 is the number of consecutive days without sunshine (or storage days)

for which the system is designed and depends on the location and the reliability required.

Considering FS2 to be 3 days and DODMAX to be 80%, then the nominal battery capacity for a

stand-alone solar PV system will be 294 kWh while that for a grid back-up system will be

105 kWh. For a VDC of 180V this is equivalent to 1633 Ah, for the stand-alone system, and

586 Ah for the grid back-up system.

From PVSYST’s preliminary design, the nominal battery capacity for the stand-alone system

with a VDC of 180V was 1447 Ah whereas that for a grid back-up system was 571 Ah.

69

Appendix 3: Construction of the Near shading scene in PVSYST

The global scene of the PV system is built by assembling parameterised elements available in

PVSYST’s objects library (Menu "Create"; shown in the figure below) that is:

Five kinds of PV planes: rectangular, polygonal, in "sheds", sunshields and tracking,

Elementary objects (a variety of 2D an 3D predefined shapes),

Building / Composed object: an assembly of elementary shapes. “Buildings” can be saved

as models for reuse in other shading scenes. They can’t include PV fields, which should be

added independently in the global scene.

PVSYST proposes a library of elementary shapes, basic or usual in architecture:

2D shapes: Triangles (whatever, isosceles or rectangle), rectangles, trapezium, regular

polygon, pseudo-circle sectors.

3D shapes: Parallelepiped, square pyramid, triangular, hexagonal or octagonal prism,

portion of cylinder.

Building elements: House + 2-sided roof, Tree, Roof-like Deidre, 2-sided roof + gables, 4-

sided roof, prism chimney.

70

The Elementary object dialog allows building one elementary object at a time in its own

referential. The user chooses the shape, size and colour of each elementary object. The

elementary object is then positioned in the global scene or in a building element.

Although elementary

objects can be readily

integrated in a global

scene, PVSYST allows

the assembly of several

elementary objects to

build a more complex

object (for example a

complete building), in the

Building/Composed

objects dialog, which can

be manipulated as a

whole in the global scene. The construction takes place in a secondary perspective view

similar to the global scene construction as shown in the figure below.

71

The upper tool bar (blue icons), shown in the previous figure, provides means for defining the

observer's point of view (perspective or orthogonal - top, front and side - views) and the

Zoom. There is another icon, to the right of the zoom icons, which allows switching between

the realistic view and the technical view of the construction. Colours defined for each

elementary object are shown in the realistic view. The left tool bar, in the previous figure,

gives access to the following actions on the system and its components:

Undo allows retrieving of up to ten last operations

Copy creates a copy of the selected object (Each object can be selected by clicking on it. A

selected object becomes purple); this copy is kept "permanently" and may be passed to

another scene.

Paste allows pasting the copied object

Delete removes the selected object

Modify opens a dialog for modifying the selected object in its own referential. Double-

clicking an object also opens its modification dialog.

Position allows the editing of the position and orientation of the selected object.

Rotate the whole scene: very useful tool which allows building the scene in its natural

referential (parallel to the building according to architect's plans), and then rotate the

whole scene according to the cardinal points.

Measurement tools allow to easily get real distances and angle measurements between

points of the scene.

Shadows drawing: with completed shading scene, allows visualising the shadows on PV

planes for any sun position or time-of-year.

Shadows animation: sweeps the sun position every 15 minutes over a given day. Shows

the shadings and draws the shading loss evolution, gives the overall loss on beam

component over the whole day.

For this project, I used the Building / composed object dialog to construct the environment at

the resource centre which was then integrated into the global scene where rectangular PV

planes where added.

72

The figures below show the realistic views of the near shading scene for the west-facing and

east-facing PV fields at LMIA’s resource centre.

West-facing PV array and its surrounding shading scene

East-facing PV array and its surrounding shading scene