photovoltaic systems technology ss 2003

8/14/2019 Photovoltaic Systems Technology SS 2003

http://slidepdf.com/reader/full/photovoltaic-systems-technology-ss-2003 1/155

Photovoltaic Systems Technology

SS 2003

Universität Kassel

Rationelle Energiewandlung / Franz Kininger

Wilhelmshöher Alle 73

34121 Kassel

Germany

[email protected]

www.uni-kassel.de/re



-I-

t 0049- 561 804 6201i www.uni-kassel.de/re

Content

1 WORLD ENERGY SITUATION 1

1.1 Introduction 1 1.1 World Energy Consumption 1

1.2 Greenhouse Effect 4

1.3 Reserves and Resources 5

1.4 Regional Energy Consumption 10

1.5 Outlook for Energy Situation 13

1.6 References 14

2 SOLAR RADIATION 15

2.1 Introduction 15

2.2 Solar Radiation outside the Earth’s Atmosphere 17

2.3 Solar Radiation on the Earth’s Surface 18

2.4 Greenhouse Effect 24

2.5 Solar Radiation Measurement 27

2.6 References 30

3 FUNDAMENTALS OF PHOTOVOLTAICS 31

3.1 Introduction 31

3.2 Charge Transport in the Doped Silicon 32

3.3 Effects of a P-N Junction 33

3.4 Physical Processes in Solar Cells 35

3.4.1 Optical absorption 35

3.4.2 Recombination of charge carriers 35

3.4.3 Solar cells under incident light 36

3.5 Theoretical Description of the Solar Cell 37

3.6 Conditions with Real Solar Cells 41

3.6.1 Influence of series- and parallel resistance 41

3.6.2 Sources of losses in solar cells 43

3.7 Effect of Irradiation 44

3.8 Effect of Temperature 45

3.9 From Single Cells to PV Arrays 46

3.9.1 Parallel connection 46

3.9.2 Series connection 48

3.10 References 57

4 CONVERSION PRINCIPLES IN PV SYSTEMS 58



-II-


4.1 Introduction 58

4.2 Coupling of PV Generator and Ohmic Load 58

4.2.1 DC/DC converters 60

4.2.2 Maximum Power Point Tracker (MPPT) 68

4.3 Energy Storage Units 70

4.3.1 Electrochemical processes in the lead-acid batteries 71

4.3.2 Theoretical description of the lead-acid batteries 73

4.3.3 Gassing 76

4.3.4 The battery capacity 79

4.3.5 Requirements for the solar batteries 80

4.3.6 From single batteries to battery banks 83

4.4 Coupling of PV Generator and Battery 86 4.4.1 Self-regulating PV systems 88

4.5 Charge Regulators 89

4.5.1 Basic principles of charge regulators 89

4.5.2 Switching regulators 90

4.5.3 Control instruments 94

4.6 Inverters 94

4.6.1 General characteristics of PV inverters 94

4.6.2 Inverter principles 97

4.6.3 Power quality of inverters 105

4.6.4 Active quality control in the grid 108

4.6.5 Safety aspects with grid-connected inverters 109

4.7 References 111

5 PRINCIPLES OF PV SYSTEM CONFIGURATION 113

5.1 Introduction 113

5.2 Fundamental Structures of PV Systems 113

5.2.1 PV systems without battery storage 113

5.2.2 PV systems with battery storage 116

5.3 Future Trends of PV Systems 124

5.4 References 124

6 INTRODUCTION 125

6.1 Pre-sizing 125

6.2 Approximation of the System Cost 131

6.3 System Optimisation 132

6.3.1 Optimization process by hand 135

6.3.2 Optimization process by simulation programs 137



-III-


6.4 Sizing of System Components 138

6.5 References 142

7 ECONOMIC CALCULATION 143

7.1 Introduction 143

7.2 Annuity Method for Investment Decisions 143

7.3 Scenario Technique 144

7.4 Economic Calculation for the PV/Diesel Hybrid System 144

7.5 References 151



-1-t 0049- 561 804 6201i www.uni-kassel.de/re

1 World Energy Situation

1.1 Introduction

As 1973 the oil-exporting countries organized in the OPEC (Organization of the Petroleum

Exporting Countries) left the oil prices in the western world explode by supply boycotts, car-

free Sunday became reality in Germany. In addition, the national economies were pressed for

the energy shortage and high costs (Fig. 1-1). Then many people understood, how important

the supply security and how serious the consequence of a careless dependence on energy

resources and supplier countries can be. As a result the efficient use of energy ranks since

then quite above in the political priority.

Figure 1-1: Oil Crisis of 1973

Accordingly some experts feared 1973 and also later a lasting energy crisis because coal, oil

and gas are once only limited available. So far it has not come to the large scarceness - from

the reasons mentioned: first of all new fossil energy occurrences are discovered again and

again. Secondly there are in the meantime more efficient extraction techniques, so that the

exploitation of unprofitable sources is economically worthwhile. And thirdly industry and

citizens deal meanwhile substantially more economically with energy [7].

1.1 World Energy Consumption

However world energy consumption has still increased due to expected rapid increase of world

population (Fig. 1-2), especially in the third world and in new industrialized countries (NICs)

because ever more humans also need ever more energy. Continually rapid growth is foreseen in

the near future, with the world population rising from the present 6 billion to about 8 billion

over the next 25 years, and is expected to grow perhaps to 10 billion people by the middle of

21st century. Such a population increase will have a dramatic impact on energy demand, at least

doubling it by 2050, even if the developed countries adopt more effective energy conservation

policies so that their energy consumption does not increase at all over that period [1, 2, 3].




Figure 1-2: World energy situation

(Source: Energy Information Administration 2001, International Energy Agency 2001, Scripps Institution of Oceanography 1999, Shell)

The world primary energy consumption 2000 approximately corresponds to a prediction of the

World Energy Conference 1986 in Cannes illustrated in Figure 1-3. Its further prognoses could

therefore point a global trend in the future. However most prognoses of the future energy

consumption were made before the Asian economic crisis. It was stated at the World Energy

Congress in Houston in September 1998 that the annual demand for primary energy would rise

to approx. 154 × 1012 kWh in the next 20 years. The World Energy Council expects that demand

will rise to 228 × 1012 kWh in 2050. Despite of increase in proportion of renewable energies it is

still expected that the role of fossil energy resources will not basically change in the near future

[5].

1930 1940 1950 1960 1970 1980 1990 2000

20

40

60

80

120

100

T o t a l & p e r c a p i t a e n e r g y c o n s u m p t i o n

0

4

8

12

16

20

W o r l d p o p u l a t i o n ,

C O 2 e m

i s s i o n

0

220

240

280

260

300

320

340

400

380

360

C O2 c on

c en t r a t i oni n t h e a t m o s ph er e

200

Year

World CO2 emission (Billion metric tons carbon equivalent)

World population growth (Billion)

Atmospheric CO2 concentration (ppm)

World energy consumption per capita (MWh)

World energy consumption (PWh)

Nuclear Hydro Other renewable energies

Coal Oil Gas

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

20

40

60

80

120

100

T o t a l & p e r c a p i t a e n e r g y c o n s u m p t i o n

0

4

8

12

16

20

W o r l d p o p u l a t i o n ,

C O 2 e m

i s s i o n

0

220

240

280

260

300

320

340

400

380

360

C O2 c on

c en t r a t i oni n t h e a t m o s ph er e

200

Year

World CO2 emission (Billion metric tons carbon equivalent)

World population growth (Billion)

Atmospheric CO2 concentration (ppm)

World energy consumption per capita (MWh)

World energy consumption (PWh)

Nuclear Hydro Other renewable energies

Coal Oil Gas

1900 1910 1920




Figure 1-3: Prognosis for future consumption (Source: World Energy Conference, 1986)

According to the political and geographical conditions the energy production in the individual

states weights itself very differently. For example, in France 70 % of the current are generated

with nuclear energy, in Norway and Sweden the emphasis is situated with hydropower.

Although Germany can generate higher than 6000 MW (one third of wind power worldwide) with

more than 8500 wind turbines [6], fossil fuels still take primarily here the principal part of the

energy production (Fig. 4).

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Year

C o n

s u m p t i o n [ T W h ]

Hard Coal Brown Coal Oil Natural Gas Nuclear Hydro & Wind Others

Figure 1-4: Energy consumption in Germany (Source: Deutsches Institut für Wirtschaftsforschung 2000)




1.2 Greenhouse Effect

When fossil fuels are combusted, carbon dioxide (CO2) is also produced, which is one of trace

gasses distributing to greenhouse effect (Fig. 1-5). Even more energy demand results more

combustion of fossil fuels and consequently increase in the atmospheric CO2 concentration (Fig.

1-2). Accordingly more of the outgoing terrestrial radiation from the surface is absorbed by the

atmosphere and re-emitted partially back, which warms the lower atmosphere and surface.

Since less heat escapes to space, this is the enhanced greenhouse effect. Although its influence

to the global climate has not finally clarified yet, some effects are obviously seen. The global

average temperature has increased by 0.6 °C since the late 19th century (Fig. 1-6). (more details

in Chapter 2) [8].

Figure 1-5: Greenhouse effect

Figure 1-6: Global average surface temperature (Source: School of environment sciences 1999)




1.3 Reserves and Resources

Since primary energy consumption is dominated worldwide by fossil energy resources such as

crude oil, coal and natural gas, the increase in energy consumption has certainly direct effect to

reserves of them; they are going to be exhausted someday. Therefore the insight to the

restriction of reserves has also to be taken into account.

In order to avoid misunderstandings, the terms “reserves” and “resources” are defined here.

Reserves: that part of the total resources, which are documented in detail and can be recovered

economically by using current technology.

Resources: that part of the total resources, which are proved but at present not economically

recoverable, geologically indicated, or which for some other reasons cannot be assigned to the

reserves.

Total resources: reserves plus resources. It is to be noted that the reserves are not included inthe resources.

Regarding the definition, reserves are the quantity that can be recovered economically with the

available technology. This means that the quantity of reserves is a function of price. The

dependence of the amount of reserves on the price becomes especially clear in the case of

uranium, the only fuel whose reserves and resources have been rated for a long time according

to production costs ($130/kg U in 1993 and up to $80/kg U in 1997).

The increase in reserves and resources of conventional or non-conventional hydrocarbons are

not attributed to new discoveries but to re-evaluation of known fields (changes in the

evaluation criteria) and improved production methods.

According to Figure 1-7 and 1-8 coal is still dominant with the largest quantities of reserves

and resources worldwide. Coal reserves account for about 45 % of all energy resources.

Conventional and non-conventional crude oil, the second most important energy resources,

account for about 33 % (18.5 % and 16.3 %, respectively) of the reserves of all energy resources.

Natural gas follows in third place with approx. 15 %. Nuclear fuels account for approx. 5 %.

Although Thorium is not used for power generation as there are no operating thorium reactors,

the reserves of more that 2 million t Th can be considered as a basis for the future.

Energy resources are not evenly distributed in the world. The order of the countries rich in

energy resources is largely determined by coal reserves. For this reason, the USA is the country

with the largest energy reserves. China has the third larges energy reserves owing to its large

estimated coal reserves, and Russia has the second largest due to its large natural gas reserves.

Coal is also the reason why Australia is fourth in the list and India sixth. The most important oil

country, namely Saudi Arabia, occupies fifth place. Germany’s coal reserves are responsible for

its ninth place [4, 5].




2.8%

39.4%

5.7%

14.6%

0.3%

2.5%

16.3%18.4%

conv. crude oil : 1,848 non-conv. crude oil : 1,636

conv. natural gas : 1,465

non-conv. natural gas : 33

Hard coal : 3,964

Soft brown coal: 578

Uranium : 277

Thorium : 252

Figure 1-7: Reserves at the end of 1997 in PWh (Source: Bundesanstalt für Geowissenschaften und Rohstoffe 1999)

43.8%

2.2%

7.5%

1.0%

2.3%

33.3%

0.3%

9.5%

conv. crude oil: 920

non-conv. crude oil: 7,000

conv. natural gas: 2,173

non-conv. natural gas: 31,095

Hard coal: 40,871

Soft brown coal: 8,864

Uranium: 2,084

Thorium: 269

Figure 1-8: Resources at the end of 1997 in PWh (Source: Bundesanstalt für Geowissenschaften und Rohstoffe 1999)

If the todays’ consumption level would not be changed in the next decades, the recoverablereserves of fossil fuels could be sufficient with oil and natural gas for 40-60 years, with coal




less than 200 years (Fig. 1-9). However, more realistic, in view of rising energy hunger

accordingly to fast increase in world population and rapid running economic development of

many new industrialized countries, the depletion time of reserves would be considerably

shortened.

Even the range could be extended by inclusion of unknown resources and using newtechniques, which lead to a better energy yield, it has to be noticed that they would be

consumed in a short period and be no more available for next generations.

Figure 1-9: Depletion time of primary energy resources

(Source: Bundesanstalt für Geowissenschaften und Rohstoffe 2000)

In addition, structure breakdown and economic rejection is defined when the production cannot

cover the demand anymore is decisive. Since each consumption development proceeds

dynamically, that time is decisive when the maximal production is reached. According to

technical-physical reasons, in case of oil, this time is close to the so-called mid-point-

depletion . The latter defines the year, in which the half of oil is extracted.

Some of the traditional oil-producer countries (e.g. the USA, Germany, Romania) have already

passed the mid-point-depletion and thus have passed their production maximum. Contrary to

most of the OPEC countries; they have not reached the mid-point-depletion yet; they can afford

to increase production if necessary and can exert considerable influence on the market [4, 5].

131

2019

160

63

37

169

65

42

0 500 1000 1500 2000 2500

Oil

Natural Gas

Coal

Uranium

Depletion time [year]

Total resources Reserves




The restriction of reserves can be clearer illustrated with the following experiments:

E(a) = E0 ⋅ (1.03)a (1-1)

where: E(a) = annual energy consumption after “a” years

E 0 = today energy consumptiona = number of years measured starting from E 0

With constant today world energy consumption and production all energy reserves could be

sufficient until 2400. Since actually the consumption however yearly exponentially rises with the

factor 3 % according to (1-1), the reserves would be depleted before 2100 (Fig. 1-10).

Figure 1-10: Energy consumption und reserves (Source: Kassel University)

Figure 1-11: Gain in depletion time with 10-times reserves (Source: Kassel University)




Even in the case of increasing tenfold today proved reserves (Fig. 1-11); if the consumption still

increases with the same rate, a further time gained arises only of 90 years. If today

consumption can be reduced by 50 % by efficient use and production of energy (Fig. 1-12),

then the depletion time will be extended by only 20 years.

Figure 1-12: Gain in depletion time through improved efficiency (Source: Kassel University)

Also with consideration of a minimum growth rate of the renewable energy production it is

recognized that the rapid rise of the energy consumption determines the end of resources by

this exponential growth. In order to be able to cover the requirement in the future with non-

fossil energies, a rate of growth as shown in Figure 1-13 is necessary.

Figure 1-13: Minimum increase in non-fossil energy production (Source: Kassel University)




These so-far scenarios show clearly that moving away from our extreme dependence on fossil

fuels is inevitable and must be carried out as soon as possible. One prognosis points a

conceivable development of the world energy consumption in the future illustrated in Figure 1-

14: Despite of increase in energy requirement, the fossil energy production would decrease

whereas the renewable energies would be produced in upward extent and could reach half of

the requirement in 2050.

Figure 1-14: Conceivable development of the world energy consumption (Source: Shell)

1.4 Regional Energy Consumption

Furthermore it has been found that primary energy resources have not been evenly consumed

worldwide (Fig. 1-15). At present the world energy reserves are most imbalance used: approx.

1 billion altogether, 20 % of world population, who live in the industrialized nations consume

almost 80 % of the available energy whereas 80 % of world population must be satisfied with 20

% of the available energy [7].

With regard to per-capita consumption (Fig. 1-16), there are very big differences in each

region. Whereas an African consumes much less energy than average value, the consumption

level in industrialized nations contrarily lies far above it. In addition, between them however

different amount of energy is required; an American desires 2-times more energy than a

Japanese or a German.




Figure 1-15: World energy consumption 1999 (Source: Enery Information Administration 2001)

Figure 1-16: Per-capita primary energy consumption worldwide 1999

(Source: Enery Information Administration 2001)

Figure 1-17 gives a further overview about electricity consumption. Norway and Sweden

surprise with first and second rank respectively. This can be explained by their geographical

112

32

85

104

50

12

43

50

26

39

15

15

4

54

2

3

2

6

12

2

4

21

1

6

9

28

34

7

9

19

0 20 40 60 80 100 120

World

North America

USA

Asia

China

Japan

Thailand

Western Europe

Germany

Eastern Europe

Former U.S.S.R

Central & South America

Brazil

Africa

Oceania

Total Consumption [PWh] Per-capita Consumption [MWh]

1 %

11 %

3 %

5 %

30 %29 %

17 %

4 %

Europe

(without Germany)

Germany

North America

Oceania

Former U.S.S.R

Africa

Central & South America

Asia




conditions, which enable a use of hydropower in upward extent. Turbines convert then

hydropower into electricity. For this reason current is primarily here used for heating. However

the surplus of oil and the requirement of electrically operated air conditioning systems shift

Kuwait to the fourth rank.

Figure 1-17: Per-capita electricity consumption 1993

Figure 1-18: End energy use in Germany 1997 (Source: Umweltbundesamt, 2000)

In order to achieve a reduction of the per-capita consumption, it is necessary to know, in which

sectors most energy is consumed. Figure 1-18 declares end energy use in Germany for

0 200 400 600 800 1000 1200

Mechanical Energy

Space Heating

Process Heating, incl.

Hot Water

Lighting

Information/Communication

Consumption [TWh]n




example: the requirement for thermal energy, i.e. process- and space heating, takes the largest

proportion and holds therefore here an enormous energy-saving potential [9].

1.5 Outlook for Energy Situation

It is to be considered that about half of the world population lives today in countries, which do

not have even sufficient energy reserves, but they must import and this dependence will rise

even to 80 % for the year 2020 according to World Energy Council. The experience with the oil

price crisis of 1973 shows that political explosive possibly establishes here. Since the largest

oil- and natural gas reserves are concentrated in states with unstable political and economic

conditions, so the danger of supplies and economic crises exists latently.

Due to several reasons the weights on the energy markets would shift in the near future. It is

especially to be counted on the fact that the new industrialized countries with their more than 3

billion population will find means and ways to secure the energy quantities necessary for their

economic processes. That appears already today in the enormous demand of the Asia-Pacific

Countries for oil and natural gas. They step on the world energy markets with increasing

competition to the industrialized countries [7]. Against this background and in view of rising

energy requirement of steady increase in world population, there is a call for action of energy

saving. However if industrialized nations can reduce their today energy demand (ca. 80 % of

total consumption), the energy saving will consequently let additional energy demands, which

will exceed the saving potential, arise by the gradual fulfillment the wish of the new

industrialized countries as well as of the third world. The conclusion is: technically,

economically feasible and sustained effective as well as ecological compatible and safe option

for future energy supply has to be taken into account.

Sometime in the mid-21st century the world will need a new, safe, clean and economical source

of energy to satisfy the needs of both developing and developed nations [10]. The World Energy

Council wrote in a published report 2000:

Renewable energies are nearly unlimited energy sources, if one compares the energy, which we

receive from the Sun, with the energy demand of humankind. Moreover they are available

prevailing inland or local and therefore secure. The problem is that without financial support

renewable energies cannot normally compete with fossil energies. However this does not mean

that it is not important to promote renewable energies according to market economic criterions

in order to get even more profit from reduction in costs with mass production and fromexperiences with their increasing application [11].




1.6 References

[1] Energy Information Administration: Annual Energy Outlook 2001; Washington,

December 2000.

[2] Energy Information Administration: International Energy Outlook 2001; Washington,

March 2001.

[3] International Energy Agency: World Energy Outlook 2000 ; Paris, 2001.

[4] Federal Ministry of Economics and Technology: Energie Daten 2000: Nationale und

internationale Entwicklung , July 2000.

[5] Federal Institute for Geosciences and Natural Resources on behalf of the Federal

Ministry of Economics and Technology: Reserves, Resources and Availability of Energy Resources 1998 ; Hannover, 1999.

[6] Institut für Solare Energieversorgungstechnik: Windenergie Report Deutschland

1999/2000 ; Kassel, 2000.

[7] Institut der deutschen Wirtschaft Köln: Wirtschaft und Untericht: Informationen für

Pädagogen in Schule und Betrieb ; Köln, 2000.

[8] Federal Environmental Agency: Jahresbericht 2000 ; Berlin, 2001, pg. 55-62.

[9] Federal Environmental Agency: Data zur Umwelt ; Berlin, 2000.

[10] Fischedick, Manfred; Langniß, Ole; Nitsch, Joachim: Nach dem Ausstieg; Zukunftskurs

Erneuerbare Energien ; Stuttgart Leipzig: Hirzel Verlag, 2000.

[11] World Energy Council: Energy for Tomorrow’s World – Acting Now! , 2000.




2 SOLAR RADIATION

2.1 Introduction

The Sun is a large sphere of intensely hot gases consisting, by mass, about 75 % of hydrogen,

23 % of helium and others (2 %). This proportion changes slowly over time referring to the

nuclear fusion in its core with temperatures of approximately 15 - 20 million K. Hydrogen

atoms fuse there to form helium and this energy is then delivered as radiation (light and heat)

into space. The Sun’s outer surface, namely photosphere, has an effective blackbody

temperature of approx. 6000 K. This mean, as viewed from the Earth, the radiation emitted

from the Sun appears to be essentially equivalent to that emitted from a blackbody at 6000 K

(Fig. 2-1) [2]. To understand the behaviour of the radiation from the Sun the characteristics of

the blackbody should be discussed here.

The “blackbody” is an absorber and emitter of electromagnetic radiation with 100 % efficiency at

all wavelengths. The theoretical distribution of wavelengths in blackbody radiation is

mathematically described by Planck’s equation. That is to say, Planck’s equation describes the

wavelength (or frequency) and temperature dependence on the spectral brightness of

blackbodies:

S(λ ) =1

1/5

1

2 −⋅

T ce

cλ λ

(2-1)

where: S(λ ) = spectral radiant emittance [W/m3]

λ = radiation wavelength [m]h = Planck’s constant [6.66 × 10-34 W⋅s2]

T = absolute temperature [K]

c = velocity of light [3 × 108 m/s]

k = Boltzmann constant [1.38 × 10-23 W⋅s/K]

c1 = 2π⋅h⋅c2 = 3.74 × 10-16 Wm2

c2 = c⋅h/k = 1.44 × 10-2 mK

Plotting intensity vs. wavelength (Fig. 2-1), the resulting curve peaks at a wavelength that

depends on temperature – the higher the temperature, the shorter its peak wavelength will be.

Also, intensities increase across all wavelengths as temperature increases.

A consequence of Planck’s equation is also known as Wien’s Law. Wien found that the radiative

energy per wavelength interval (brightness) has a maximum at a certain wavelength and that

the maximum shifts to shorter wavelengths as the temperature increases:

λ max [mm] =T

3000(2-2)




Figure 2-1: Radiation distributions from perfect blackbodies (Source: http://zebu.uoregon.edu)

When the temperature is known, the radiation intensity of a blackbody can be calculated using

the Stefan-Boltzmann’s Law:

•

q = σ ⋅ T 4 (2-3)

where:•

q = the radiation intensity [W/m2]

σ = Stefan-Boltzmann constant [5.67 × 10-8 W/m2/K4]

T = absolute temperature of the body [K]

The solar radiation intensity is measured in watts or kilowatts per square metre [W/m2, kW/m2].

The radiation energy, i.e. the power integrated over a certain period of time, is given in watt-hours (also kilowatt-hours, joules) per square metre (Tab. 2-1). It should be noted here that the

term “radiation” is commonly applied to both the radiation intensity and the radiation energy.

Quantity Units

Radiation intensity W/m2, kW/m2

Radiation energy Wh/m2, kWh/m2

Table 2-1: Quantities and units




2.2 Solar Radiation outside the Earth’s Atmosphere

The radiation intensity of the Sun varies from the center to its surface. The outgoing radiant

flux spreads out over sphere’s surface. It is therefore weaker with the square of distance from

the Sun. Due to an extremely large mean distance between the Sun and the Earth the beam

radiation received on the Earth is almost parallel. Measurements indicate that the radiant flux,

received from the Sun outside the Earth’s atmosphere is remarkably constant. The so-called

solar constant , 1367 W/m2, defines the average amount of energy received in a unit of time on

a unit area perpendicular to the path of the radiation outside the atmosphere at the average

distance of the Earth’s orbit around the Sun. This value fluctuates with a few percent resulted

especially from the change of Sun-Earth distance in the orbit during a year [2].

Additionally an approximate value of solar constant can be also derived according to the

following principle: Assume the Sun to be a blackbody. In consequence of energy conservation,

its outgoing radiant flux passes through any imaginary external spherical surface concentric to

the Sun (Fig. 2-2). In particular, this flux passes through a surface of radius equal to the

average distance between Earth and Sun. The flux density observed at this distance is defined

as the solar constant.

Figure 2-2: Schematic geometry of the Sun-Earth relationships

The radiant flux at the Sun’s surface = The radiant flux at the Earth’s orbit

surfaceSunsurfaceSun A q ⋅

•

= orbit Earth0 A S ⋅

where: surfaceSunq

•

= solar radiation at the Sun’s surface [W/m2]

0S = solar constant [W/m2]

ASun surface = area of the Sun’s surface [m2]

AEarth orbit = area of a sphere at the Earth orbit [m2]

R Earth = 6378 km

R Sun = 695000 kmR Earth orbit = 149 million km




Thus, 0S = orbit Earth

surfaceSun

surfaceSun A

A q ⋅

•

=

( )

( )2orbit Earth

2

Sun4

surfaceSun R4

R4 T π

π σ ⋅⋅

=

( ) 10149

106955762105.67

2

9

6 48-

×

×⋅⋅×

= 1360 W/m2

Since R Earth orbit is not fully constant, S 0 changes slightly throughout a year (1300 W/m2 < S 0 <

1390 W/m2).

2.3 Solar Radiation on the Earth’s Surface

The radiation intensity outside the Earth’s atmosphere according to the solar constant is called

the extraterrestrial radiation . The maximum of the spectral distribution is situated in the area

of visible light with a wavelength of 0.38 µm until 0.78 µm and drop steeply out one side to

ultraviolet- (UV: 0.2 - 0.38 µm) and the other side to infrared radiation (IR: 0.78 - 2.6 µm) as

illustrated in Figure 2-3.

0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

Wavelength [nm]

S p e c t r a l d i s t r i b u i t i o n

[ W / m 2 /µ m

]

Cloudy sky Clear sky Extraterestrial radiation

UV visible IR

O2 , H2O

H2O

O3

H2O, CO2

Figure 2-3: Spectral distribution of solar radiation (Source: Kassel University)

Regarding light falling on a surface of glass it can be reflected ( ρ ), absorbed (α ) or transmitted

(τ ) [1], whereby




ρ + α + τ = 1 (2-4)

Similarly, while passing through the atmosphere, the extraterrestrial radiation experiences

attenuation such as reflection, scattering (reflection in many directions) and absorption. The

solar radiation is reflected and scattered primarily by clouds (moisture and ice particles),

particulate matter (dust, smoke, haze and smog) and various gases. Reflection of incident solar

radiation back into space by clouds varies with their thickness and albedo (ratio of reflected to

incident light). Thin clouds may reflect less than 20 % of the incident solar radiation whereas a

thick and dense cloud may reflect over 80 % [5]. Consequently, regions with cloudy climates

receive less solar radiation than cloud-free desert climates. For any given location, the solar

radiation reaching the Earth’s surface decreases with increasing cloud cover.

In addition, local geographical features such as mountains, oceans and large lakes influence the

formation of clouds. Therefore the amount of solar radiation received for these areas may be

different from that received by land areas located a short distance away. For example,

mountains may receive less solar radiation than nearby foothills and plains located a shortdistance away. Winds blowing against mountains force some of the air to rise and clouds form

from the moisture in the air as it cools. Coastlines may also receive a different amount of solar

radiation than areas further inland. Where the changes in geography are less pronounced, e.g.

in the Great Plains, the amount of solar radiation varies less [6].

The two major processes involved in tropospheric scattering are determined by the size of the

molecules and particles. They are known as selective scattering and nonselective scattering .

Selective scattering is caused by smoke, fumes, haze and gas molecules that are the same size

or smaller than the incident radiation wavelength. Scattering in these cases is inversely

proportional to wavelength and is therefore most effective for the shortest wavelengths (bluecomponents).

Selective scattering of Sunlight under clear-sky conditions accounts for the blue sky when the

degree of scattering is sufficiently high. This is determined by the length of the atmospheric

path traversed by Sunlight [5], which refers to the so-called Air Mass (AM). Air Mass represents

the strength or the mass of the atmosphere and can be approximated by the following equation

when the Sun is at an angle φ to overhead as shown in Figure 2-4 [4].

Air Mass =

φ cos

1(2-5)

With the Sun overhead at noon (AM 1), the sky appears white because little scattering occurs at

the minimum atmospheric path length. At Sunrise and Sunset, however, the solar disc appears

red because of the increased atmospheric path associated with relatively high scattering of the

short wavelength blues and greens. As a result, only the longer wavelengths (red components)

are left in the direct beam reaching our eyes.




Figure 2-4: Effect of the Earth’s atmosphere on the solar radiation

Nonselective scattering is caused by dust, fog and clouds with particle sizes more than 10

times the wavelength of the incident radiation. Since scattering in this case is not wavelength-dependent, it is equal for all wavelengths. As a consequence, clouds appear white [5].

Absorption of solar radiation is caused mostly by atmospheric gases and partly by clouds. As

obviously indicated in Figure 2-3 ozone (O3) is primarily responsible for the UV radiation.

Depletion of ozone layer has therefore a harmful effect on the Earth’s biological systems. Water

vapour (H2O) results in the absorption bands around 1 µm and absorbs longer wavelengths

together with carbon dioxide (CO2) [4].

As a result, the maximal radiation falling on the Earth’s surface at midday amounts of 1000

W/m2 when the sky is cloudless. This so-called global radiation is composed of direct radiation ,

diffuse radiation and albedo radiation . Direct (or beam) radiation comes directly from the Sunwithout change of direction whereas diffuse radiation is the result of scattering of the sunbeam

or reducing the magnitude of the sunbeam due to atmospheric constituents as mentioned. It is

incident from all directions in the sky. Therefore the sky appears to be equally bright in all

directions. When the sky is completely overcast or the Sun is below the horizon, only diffusion

radiation reaches the Earth’s surface (Tab. 2-2).

Weather Clear, blue sky Hazy or cloudy, Sun visible

as whitish yellow disc

Overcast sky, dull day

Global radiation 600…1000 W/m2

200…400 W/m2

50…150 W/m2

Diffuse fraction 10…20 % 20…80 % 80…100 %

Table 2-2: Radiation intensity of various weather conditions [3]

Even when the sky is clear, the radiation intensity on the Earth’s surface changes continually

during a day. Less radiation is available early in the morning or late in the afternoon, as then

the radiation has a longer path through the atmosphere and is more strongly attenuated than at

midday.

Albedo radiation refers to reflected light from the ground and surroundings (Fig. 2-6) and

corresponds to the ratio of reflected- to the incident light at a surface considered, namely

albedo, as listed in Table 2-3 for instance.

φ




Figure 2-5: Total solar radiation on a surface

Location Albedo [%]

Ocean 2 - 10

Forest 6 - 18

Grass 7 - 25Soil 10 - 20

Desert (land) 35 - 45

Ice 20 - 70

Snow (fresh) 70 - 80

Table 2-3: Albedo for different terrestrial surfaces [Wells, 1997]

The annual distribution and the total amount of solar energy are determined by climatic and

meteorological factors, which depend on the locations and the seasons. These differences in

the weather over the Earth are due to the changes of the Sun’s position and the length of

daylight within the year, which in turn are caused by the tilt of the Earth’s axis relative to its

orbit around the Sun. As shown in Figure 2-6 for instance the global radiation even at a certain

location changes throughout the year.

Direct




0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

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

Month

A v e r a g e d a i l y g l o b a l r a d i a t i o n

[ k W h

/ m 2 ]

Maximum Mean Minimum

Figure 2-6: Annual distribution of global radiation on a horizontal surface in Kassel

(Source: European Solar Radiation Atlas, 1997)

Whereas an average annual available solar energy for Germany amounts to 1000 kWh/m2

approximately, some regions such as the deserts in Africa, the energy is twice as much

available as in Central Europe (Tab. 2-4).

Locations Energy per year [kWh/m2]

Kassel 1000

Thailand 1700 – 1800 1)

Brazil 2000

Sahara 2200 – 2500

Table 2-4: Solar radiation energy on horizontal surfaces at different locations

(Source: European Solar Radiation Atlas, 1996) 1 ) Source: KMUTT, 2000

Figure 2-7 explains the amount of solar radiation thoughout the year at different locations. InCentral Europe, the amount of incident solar energy during November and January is about five

times less than in summer months whereas the radiation supply is much more uniform at low

latitudes [2, 3].




Figure 2-7: Annual distribution of solar radiation at different locations

(Source: European Solar Radiation Atlas 1996, Solar Energy Research and Training Center)

In addition, annual mean solar radiation for all lands over the world is presented in Figure 2-8.

Here it is obviously seen that the amount of incident solar radiation is different in each part of

the world.

Figure 2-8: Annual mean solar radiation 1961-1990 in kWh/m 2 a

(Source: Intergovernmental Panel on Climate Change)

Fortaleza

Kassel

Pitsanulok

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

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

Month

A

v e r a g e d a i l y g l o b a l r a d i a t i o n [ k W h / m

2 ]

Fortaleza - Brazil Kassel - Germany Pitsanulok - Thailand




2.4 Greenhouse Effect

Satellite measurement confirmed that the radiation balance took place at the boundary of the

atmosphere, i.e. the solar energy received by the Earth balances the energy lost by the Earth

back into space. According to the geometric Sun-Earth relationship (Fig. 2-2) energy absorbed

by the Earth is considered only in area projected against the Sun’s rays (= π⋅ R Earth 2 ). However,

the Earth reradiates energy with its whole surface area (= 4 π⋅ R Earth 2 ). To avoid confusion with

W/m2, it must be here noted that all amounts of solar radiation in the following figure will refer

to solar radiation power and thus be calculated in PW (Peta Watt = 1015 W).

Figure 2-9: Radiation and energy balance in PW [7]

As indicated in Figure 2-9, 30 % of incoming solar radiation at the boundary of the atmosphere

is reflected to space (the Earth’s average albedo from both the atmosphere and the surface): the

biggest part is reflected by clouds, other part by air molecules and aerosols (tiny smoke

particles) and the rest by the Earth’s surface. Approx. 20 % (33 PW) is absorbed in the

atmosphere whereas about 26 PW is absorbed by atmospheric gas, i.e. H2O, CO2 and the other7 PW by clouds. As a result, the rest 50 % (90 PW) is incident on the Earth’s surface

corresponding to the global radiation, which consists of direct-, diffuse-, and albedo

components as mentioned before and warms it up. In comparison to the world primary energy

consumption [2000] of 114 PWh the annual incident solar radiation is nearly 7000 times

greater.

The amount of 70 % of the incoming radiation, which stay in the “Earth-atmosphere” system,

has to be radiated again back to space. The higher the temperature of a body, the higher the

frequency or the longer the wavelength of the energy radiated. Since the Earth’s surface and

atmosphere (with 288 K) are much colder than the Sun’s surface (with 5762 K), the Earthradiates less energy than the Sun and the energy has longer wavelengths (Fig. 2-10).

Sensibl longwaveCounter-Latent

Absorbedby clouds

Absorbed

by gases

Incoming solar

Surface

Thermal absorption and emissionin the atmos here




Figure 2-10: Spectral distribution of the Sun and the Earth (Source: Kassel University)

According to the Figure 2-9 the amount of longwave radiation emitted from the Earth’s surface

is surprisingly more than the incoming solar radiation. This is due to the energy exchange in

the Earth-atmosphere system. Whereas 10 PW passes directly through the atmosphere into

space, a big part of longwave surface radiation (180 PW) is however absorbed by theatmospheric molecules: if the frequency of the radiation is compatible with the molecule’s

rotational frequency or with the frequency, at which the molecule vibrates, then the molecule

can absorb the radiation resulting in increase of the molecule’s rotational frequency or more

vigorously vibration respectively. This absorption is largely due to two gases: water vapor

(moisture) and carbon dioxide (CO2). For example, CO2 molecule has vibration that allows the

molecule to absorb IR at wavelength of 15 µm, which is near the wavelength of the majority of

Earth’s outgoing IR.

Having absorbed this IR, the atmosphere becomes a radiator and therefore emits longwave

energy. This heat is emitted in all directions: 113 PW is released to outer space, however its

substantial part is headed downward to the surface (152 PW). The portion of atmospheric

radiation that is returned to Earth is called counterradiation . As a result, the net radiation loss

of the Earth’s surface amounts to 38 PW. This screening effect of the atmosphere is generally

well known as greenhouse effect whereas vapour, CO2 and other gases such as O3, methane

(CH4), nitrous oxide (N2O) and others, which contribute to this process, are therefore referred to

greenhouse gases .

Regarding energy balance at the Earth’s surface, the difference between the absorbed

shortwave- and emitted longwave radiation is therefore 52 PW. This gap is closed after taking

latent- and sensible heat (40 PW and 12 PW respectively) into account. Sensible heat can be

measured by thermometer. It is transferred through conduction, convection and advection:

when surface is heated by the incident solar radiation, the nearby layer of air is warmed up

0

250

500

750

1.000

1.250

1.500

1.750

2.000

2.250

0 2.000 4.000 6.000 8.000 10.000 12.000 14.000 16.000 18.000 20.000

Wavelength [nm]

S u n - S p e c t r a l I r r a d i a n c e

[ W / m 2 µ m ]

0

25

50

75

100

125

150

175

200

225

E a r t h - S p e c t r a l I r r a d i a n c e

[ W / m 2 µ m ]

5762 K 288 K




through conduction and this warmth is then transferred upward through convection whereas

advection is horizontal convection.

Latent heat is taken up or released on a phase change of water between three forms, i.e. ice,

water and vapour. When water is evaporated from oceans, rivers or moist soils, latent heat of

vaporization is taken up by the resulting vapour. When water vapor condenses to form clouds,the same amount of latent heat is released to the atmosphere.

As a result, the radiation balance at boundary of the atmosphere is completed. Furthermore,

according to Figure 2-9 and by assuming the Earth as a blackbody, the effective radiating

temperature of the Earth (T ) as view from outer space can be derived from total heat radiated

out of the boundary of the atmosphere:

σ ⋅ T4 = (113+10)/4π⋅REarth2

T = 255 K = -18 °C or 0 °F

However, Earth’s average surface temperature is 288 K or 15 °C. The cause of difference

between the effective radiating temperature and the global average surface temperature lies in

the existence of the atmosphere, namely the greenhouse effect. This so-called natural

greenhouse effect warms the surface by 33 °C resulting in a livable climate on Earth [7, 8, 9].

However, since 1860, the beginning of systematic meteorological recording, the global average

temperature has increased approx. 0.6 °C. Nevertheless it is concerned with to the strongest

rise in temperature in the northern Earth’s hemisphere during the past 1,000 years.

Moreover, by means of abundance of scientific studies today it can be already proved that ourclimate has changed in the past two centuries substantially: sea level increased approx. 10 to

20 cm in the past century. Snow cover sank ca. 10 % since 1960. In the 20th century

precipitation in the central and higher latitude increased about 0.5 to 1 % per year.

This leaded especially in the past century to the fact that more often and intensive drought took

place in some parts of Africa and Asia. In the Pacific Ocean, since 1970, more often, longer

continual and intensive temperature anomalies with frequent unfavourable effects to the

mankind’s health, to settlement, to the agriculture and forestry and others are observed.

The rising temperature above that occurring related to the natural greenhouse effect refers to

the enhanced greenhouse effect caused by increase in concentration of the greenhouse gases in

the atmosphere.

Since the industrialization CO2 increased in concentration about 30 %. The meanwhile reached

level (367 ppm in comparison to 280 ppm before the industrialization) as well as the topical

increasing rate (at present, ca. 1.5 ppm per year) is unique for the last 20,000 years. If one

considers far back to the past, no comparable concentration during the last 420,000 years and

no comparable increase speed during the last 20,000 years are not found.

The concentration of CH4 rose more than double. Such a concentration level had not also been

reached in the last 420,000 years. Similarly, the concentration of N2O increased ca. 17 % and




goes on rising. Such a concentration had never appeared according to our knowledge

circumstance in the past 1,000 years.

These increases in concentration of the greenhouse gases are caused almost exclusively by

mankind’s activities, namely the combustion of fossil fuels (coal, gas, oil), deforestation and

particular agricultural methods (since ca. 1750).

As a result, more heat is trapped by the atmosphere and has a consequence that more heat is

reradiated downward to the surface (counterradiation) and therefore contributes to global

warming. However the word "enhanced" is usually omitted, but it should not be forgotten in

discussions of the greenhouse effect [10].

2.5 Solar Radiation Measurement

The solar radiation is usually measured with the help of a pyranometer or a pyrheliometer.

Pyranometer as shown in Figure 2-11 for example is a basic instrument for measuring theglobal radiation. The measuring principle lies on the temperature difference between white and

black painted sectors. A precisely cut glass dome shields the sensing elements from

environmental factors. By that means the measuring result is not affected by ambient

temperature. When the instrument is exposed to solar radiation, a temperature difference is

created between the black and white sectors. This temperature difference is detected by a

thermopile (a set of thermocouples) within the instrument, which then reacts by generating a

small electrical signal. Finally a calibration factor converts the millivolt signal to an equivalent

radiant energy flux in watts per square meter.

Figure 2-11: Model 240-8101 Star Pyranometer (Source: NovaLynx Corporation)




Figure 2-12: Pyrheliometer and Solar tracker

Figure 2-13: Shadow band

Solar Tracker

Pyrheliometer




Direct radiation can be measured by pyrheliometer. In contrast to a pyranometer, the black

sensor disc is located at the base of a tube whose axis is aligned with the direction of the

sunbeam. Thus, diffuse radiation is essentially blocked from the sensor surface. Furthermore,

pyrheliometer is normally mounted on a solar tracker so that it is continually pointed directly at

the Sun throughout the day (Fig. 2-12). However, this makes the measurements complicate and

expensive.

In case of the diffuse radiation, it can be determined by subtracting the measured direct

radiation from the global radiation mathematically. However, it can also be measured by

applying a shadow band to the pyranometer as presented in Figure 2-13. By this means, the

sunbeam is blocked and whereby a value measured refers only to the diffuse component.

By the way, the albedo radiation can be measured as well. As shown in Figure 2-14, for

instance, the instrument consists of two identical pyrradiometers. The upper measures the

global radiation whereas the inner dome protects the detector from infrared radiation from the

outer dome, which may change rapidly with meteorological conditions and the lower measuresthe reflected radiation of the ground.

Figure 2-14: Albedometer CM 7B (Source: ADOLF THIES GmbH & Co. KG)




2.6 References

[1] Schmid, J.: Script for the lecture: Energiemanagement in Gebäudebereich; Kassel

University. pg. 45-51.

[2] Schmid, J.: Photovoltaik: ein Leitfaden für die Praxis; ein Informationspaket; Köln: Verl.

TÜV Rheinland, 1995. pg. 10-12.

[3] Kaiser, R.: Fundamentals of solar energy use. In: Fraunhofer Institute for Solar Energy

Systems: Course book for the seminar: Photovoltaic Systems; Freiburg, 1995. pg. 56-

63.

[4] Wenham, S.R.; Green, M.A.; Watt, M.E.: Applied Photovoltaics; Australia. pg. 1-19.

[5] Acra, A.; Jurdi, M.; Mu'allem, H.; Karahagopian, Y.; Raffoul, Z.: Water Disinfection bySolar Radiation: Assessment and Application; Ottawa, Canada: IDRC, 1990.

[6] Andrew, Marsh: Script for the lecture: Solar Radiation; University of Western Australia.

[7] Grünhage, Ludger: Script for the lecture: Pflanzeökologie I: Strahlungsbilanz

verschiedener Oberflächen; Giessen University. pg. 15-19.

[8] Marshall, John: Script for the lecture: Physics of Atmospheres and Oceans: The global

energy balance; Massachusetts Institute of Institute, USA.

[9] Naumov, Aleksev: Script for the lecture: Physical Environmental Geography: Insolation

and temperature – Earth’s global energy balance; State University of New York at

Buffalo, USA.

[10] Umweltbundesamt: Klimaschutz 2001: Tatsachen - Risiken - Handlungs-

möglichkeiten; Berlin, 2001. pg. 2-3.




3 FUNDAMENTALS OF PHOTOVOLTAICS

3.1 Introduction

The direct transformation from the solar radiation energy into electrical energy is possible with

the photovoltaic effect by using solar cells . The term photovoltaic is often abbreviated to PV.

The radiation energy is transferred by means of the photoeffect directly to the electrons in their

crystals. With the photovoltaic effect an electrical voltage develops in consequence of the

absorption of the ionizing radiation. Solar cells must be differentiated from photocells whose

conductivity changes with irradiation of sunlight. Photocells serve e.g. as exposure cells in

cameras since their electrical conductivity can drastically vary with small intensity changes.

They produce however no own electrical voltage and need therefore a battery for operation.

The photovoltaic effect was discovered in 1839 by Alexandre Edmond Becquerel while

experimenting with an electrolytic cell made up of two metal electrodes. Becquerel found that

certain materials would produce small amounts of electric current when exposed to light. About

50 years later Charles Fritts constructed the first true solar cells using junctions formed by

coating the semiconductor selenium with an ultrathin, nearly transparent layer of gold. Fritts’s

devices were very inefficient: efficiency less than 1 %.

The first silicon solar cell with an efficiency of approx. 6% was developed in 1954 by three

American researchers, namely Daryl Chapin, Calvin Fuller and G.L. Pearson in the Bell

Laboratories. Solar cells proved particularly suitably for the energy production for satellites in

space and still represent today the exclusive energy source of all space probes. The interest in

terrestrial applications has increased since the oil crisis in 1973. Main objective of research and

development is thereby a drastic lowering of the manufacturing costs and lately also a

substantial increase of the efficiency.

The base material of almost all solar cells for applications in space and on earth is silicon. The

most common structure of a silicon solar cell is schematically represented in Figure 3-1:

An approx. 300 µm silicon wafer consists of two layers with different electrical properties

prepared by doping foreign atoms such as boron and phosphorous. The back surface side is

total metallized for charge carrier collection whereas on the front, which exposes to the beam

of incident light, only one metal grid is applied in order that as much light as possible canpenetrate into the cell. The surface is normally provided with an antireflection coating to keep

the losses from reflection as small as possible.




Figure 3-1: Schematic drawing of a silicon solar cell [1, 2]

3.2 Charge Transport in the Doped Silicon

Now we consider the doping of silicon, a tetravalent element, which is the most frequent

applied semiconductor material, also for solar cells.

Replacement of a silicon atom by a pentavalent atom (Fig. 3-2a), e.g. phosphorus (P) or arsenic

(As), leads to a surplus electron only loosely bound by the Coulomb force, which can be ionized

by an energy (ca. 0.002 eV). The quantity eV is an energy unit corresponding to the energy

gained by an electron when its potential is increased by one volt. Since pentavalent elements

donate easily an electron, one calls them donors. The donor atom is positively charged with the

electron donation (ionized). The current transport in such a material practically occurs only by

means of electrons, it is called n-type material.

Replacement by a trivalent element (Fig. 3-2b), e.g. boron (B), aluminium (Al) or gallium (Ga),

leads to a lack of an electron. Now an electron in the neighborhood of a hole can fill up thisblank and leaves a new hole at its original position consequently. This results in the current

conduction by means of positive holes. Therefore this material is called p-type material.

Trivalent atoms, which easily accept an electron, are defined as acceptors. The acceptor atoms

are negatively ionized by the electron reception. At ambient temperature donors and acceptors

are already almost completely ionized in the silicon.

≈ 0.2 µm

Sunlight

Metal grid

for current collection

Metallized back surface

p-type material

n-type material

≈ 300 µm

≈ 0.2 µm

Sunlight

Metal grid

for current collection

Metallized back surface

p-type material

n-type material

≈ 300 µm




Figure 3-2: Doping of silicon (a) with pentavalent atom (b) with trivalent atom

3.3 Effects of a P-N Junction

Usually a p-n junction is generated by the fact that a strong n-type layer is produced in the p-

type material by indiffusion of a donor (P, As) at higher temperatures (ca. 850 °C). Completely

analog in the n-type material, although less common, a p-n junction can be produced by

indiffusion of an acceptor.

In the boundary surface’s neighborhood of the n- or p-type material the following effects

occur: In the n-region so many electrons are available, in the p-region so many holes. These

concentration differences lead to the fact that electrons from the n-region diffuse into the p-

region and holes from the p-region diffuse into the n-region. As a result, diffusion currents of

electrons into the p-region and diffusion currents of holes into the n-region arise (Fig. 3-3).

By the flow of negative and positive charges a deficit of charges develops within the before

electrically neutral regions, i.e. it results a positive charge within the donor region and a

negative charge within the acceptor region. Thus an electrical field develops over the boundary

surface and causes now field currents from both charge carrier types, which are against the

diffusion currents. In the equilibrium the total value of current through the boundary surface is

zero. The field currents compensate completely the diffusion currents: the hole currents

compensate completely among themselves and the electron currents likewise.

(b)(a)

free

electronhole

P

Si

Si

SiSi

Si Si

SiSi

B

Si

Si

SiSi

Si Si

SiSi

(b)(a)

free

electronhole

PP

SiSi

SiSi

SiSiSiSi

SiSi SiSi

SiSiSiSi

BB

SiSi

SiSi

SiSiSiSi

SiSi SiSi

SiSiSiSi




Figure 3-3: Charge carrier distribution at p-n junction and currents through the junction [1]

This electrostatic field extending over the boundary surface refers to the potential difference

V D , which is called diffusion voltage . It is situated in the order of magnitude of 0.8 eV. Thiselectrical field causes the separation of the charge carriers produced by light in the solar cell.

Within the region of the stationary electrical positive and negative charge, in the so-called

space-charge zone , a lack of mobile charge carriers appears, which has very high impedance.

Applying the n-region with a negative voltage (forward bias) reduces the diffusion voltage,

decreases the electrical field strength and thus the field currents. These do not compensate

now the diffusion currents of the electrons and holes, as without external voltage, anymore. As

a result a net diffusion current from electrons and holes flows through the p-n junction. If the

applied voltage is equal to the diffusion voltage, then the field currents disappear and the

current is limited only by the bulk resistors. Contrarily, an applied positive voltage at the

outside n-region (reverse bias) adds itself to the diffusion voltage, increases the space-charge

zone, thus it comes to outweighing the field current. The resulting current whose direction of

the reverse bias is contrary is very small.

The mathematical process at the p-n junction leads to the famous diode equation:

ID =

−

⋅ 1

kT

qV exp I 0 (3-1)

where: I D = diode current [A]

q = magnitude of the electron charge [1.6 ⋅ 10-19 As]V = applied voltage [V]:

holeselectrons

C h

a r g e - c a r r i e r c o n c e n t r a t i o n

stationary

electrical charges

electrons

holesDiffusion current

Field current

Diffusion current

Field current

n-region p-regionp-n junction x

space-charge zone

holeselectrons

C h

a r g e - c a r r i e r c o n c e n t r a t i o n

stationary

electrical charges

electrons

holesDiffusion current

Field current

Diffusion current

Field current

n-region p-regionp-n junction x

space-charge zone




plus = forward bias, minus = reverse bias

k = Boltzmann’s constant [8.65 ⋅ 10-5 eV/K]

T = absolute temperature [K]

The quantity 0 I defines the so-called dark- or saturation current of a diode. It plays a very

large role of the performance of a solar cell.

3.4 Physical Processes in Solar Cells

3.4.1 Optical absorption

Light, which falls on a solar cell, can be reflected, absorbed or transmitted. Since silicon has a

high refractive index (> 3.5), over 30 % of the incident light are reflected. Therefore solar cells

are always provided with an antireflection coating. A thin layer titanium dioxide is usual. Thus

the reflection losses for the solar spectrum can be reduced to about 10 %. More reduction of the reflection losses can be achieved by multi-layer AR layers. A two-part layer from titanium

dioxide and magnesium fluoride reduces the reflection losses of a remainder up to ca. 3 %.

Photons (light quanta) interact with materials mainly by excitation of electrons. The main

process in the field of energy, in which solar cells are applied, is the photoelectric absorption .

Thereby the photon is completely absorbed by a bound electron. The electron takes the entire

energy of the photon and becomes free-electron. However, in semiconductors a photon can be

only absorbed if its energy is larger than the bandgap. Photons with energies smaller than the

bandgap pass through the semiconductor and cannot contribute to an energy conversion.

However, photons with much larger energies than the bandgap are also lost for the energy

conversion since the surplus energy is fast given away as heat to the crystal lattice.

During the interaction of the normal solar spectrum with a silicon solar cell, about 60 % of the

energy for a transformation are lost because many of the photons possess energies, which are

smaller or larger than the bandgap.

3.4.2 Recombination of charge carriers

The absorption of light produces pairs of electrons. The concentration of charge carriers is

therefore higher during the lighting than in the dark. If the light is switched off, the chargecarriers return to their equilibrium concentration in the dark. The return process is called

recombination and is the reverse process for generation by light absorption. Recombination

occurs even naturally also already during the generation. The charge-carrier concentration

appearing with lighting is the result from two opposite running processes.

During their lifetimes the charge carriers can travel a certain distance in the crystal until they

recombine. The average distance, which a charge carrier can travel between the place of its

origin and the place of its recombination, is called diffusion length . This quantity plays an

important role for the behavior of a solar cell [1]. It depends on diffusion coefficient of a

material and a lifetime of a charge carrier (time that it takes for a charge carrier to be captured

according to recombination) [4].




3.4.3 Solar cells under incident light

Figure 3-4 shows the three main parts of a solar cell schematically: the diffused strong n-

doped emitter, the space-charge zone and the p-doped base.

Figure 3-4: Operating principle of a solar cell (schematic) [1]

A photon with sufficient large energy falls on the surface of the solar cell, penetrates emitters

and space-charge zone and is absorbed in the p-base. An electron-hole pair is developed due

to the absorption.

Since electrons are in the minority in the p-base, one calls them minority charge carrier

contrary to the holes, which are majority charge carrier here. This electron diffuses in the p-

base until it arrives at the boundary of the space-charge zone. The existing strong electrical

field in the space-charge zone accelerates the electron and brings it to the emitter side.

Thus a separation of the charge carriers took place. Thereby the electrical field works as

separation medium. A prerequisite is that the diffusion length of the electron has to be large

enough so that the electron can arrive up to the space-charge zone. In case of too small

diffusion length a recombination would occur before reaching the space-charge zone, the

energy would be lost.

Absorption of a light quantum in the emitter leads again to the formation of an electron-hole

pair. According to the strongly doped n-emitter the holes are here the minority charge carrier.

With sufficient large diffusion length the hole reaches the edge of the space-charge zone, is

accelerated by the electric field and is brought to the p-base side. If the absorption occurs in

the space-charge zone, electrons and holes are immediately separated according to the

existing electrical field there.

In consequence of the incident light it yields: If concentration of electrons at the n-emitter side

is increased, concentration of holes at the p-base side increases. An electrical voltage is built

up. If n-emitter and p-base are galvanically connected, e.g. by an ohmic resistor, electrons from the emitter flows through the galvanic connection to the base and recombines with the

A

hole electron

solar radiation

emitter, n-type

base, p-type

space-charge

zone

electric field

A

hole electron

solar radiation

emitter, n-type

base, p-type

space-charge

zone

electric field




holes there. Current flow means however power output. This current flow continues so long as

the incident light radiation is available. As a result, light radiation is immediately converted into

electricity [1].

3.5 Theoretical Description of the Solar CellAs already mentioned, illuminated solar cell creates free charge carriers, which allow current to

flow through a connected load. The number of free charge carriers is proportional to the

incident radiation intensity. So does also the photocurrent (I ph ), which is internally generated in

the solar cell. Therefore an ideal solar cell can be represented by the following simplified

equivalent circuit (Fig. 3-5). It consists of the diode created by the p-n junction and a

photocurrent source with the magnitude of the current depending on the radiation intensity. An

adjustable resistor is connected to the solar cell as a load.

The mathematical process of an ideal exposed solar cell leads to the following equation:

Icell = Iph – ID =

−⋅− 1e I I kT

qV

0 ph(3-2)

Figure 3-5: Equivalent circuit diagram of an ideal solar cell connected to load

In an imaginary experiment, the I-V characteristic curve for a certain incident radiation will now

be constructed, point for point (Fig. 3-6):

I load

V load

Rload

I cell

I ph

I D

V D

I load

I load

V load

V load

Rload

Rload

I cell

I cell

I ph

I ph

I D

I D

V D

V D




Figure 3-6: Construction of the solar cell curve from the diode curve

Figure 3-7: Equivalent circuit diagram of the solar cell – short-circuit current

When the terminals are short-circuited (R load = 0 ) (Fig. 3-7), the output voltage and thus also

the voltage across the diode is zero. According to (3-2): since V = 0 , no current I D flows (point

1 in Figure 3-6) therefore the entire photocurrent I ph generated from the radiation flows to the

output. Thus the cell current has its maximum at this point with the value I cell and refers to the

so-called short-circuit current I sc .

Isc = Icell = Iph (3-3)

I ph

I sc

I cell

R load = 0

I D = 0

I ph

I ph

I sc

I sc

I cell

I cell

R load = 0 R load = 0

I D = 0 I D = 0

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70

Voltage V [V]

C u r r e n t I [ A ]

Photo Current Diode Current Cell Current

I sc

V oc

1

1

2

2

3

3

4

4

I D




If the load resistance is now continually increased, the solar cell voltage also increases whereas

the current remains constant. Up to a certain voltage value the current flowing through the

internal diode remains negligible, thus the output current continues corresponding to the

photocurrent (point 2 in Figure 3-6).

Until the diode voltage threshold is exceeded after the load resistance is further increased, arapidly increasing proportion of the photocurrent flows through the diode. This current leads to

power loss in the internal diode corresponding to an area between the photocurrent curve and

the cell current curve. Since the sum of the load current and the diode current must be equal to

the constant photocurrent, the output current decreases by exactly this amount (point 3 in

Figure 3-6).

For an infinitely large load resistance (open circuit) as shown in Figure 3-8, the output current

is then zero (I cell = 0 ) and thus the entire photocurrent flows through the internal diode (point 4

in Figure 3-6). The open-circuit voltage V oc can be therefore derived again from (3-2).

Voc =

+⋅ 1

I

I ln

q

kT

o

ph(3-4)

Figure 3-8: Equivalent circuit diagram of the solar cell – open-circuit voltage

In addition, typical value of the open-circuit voltage is located ca. 0.5 – 0.6 V for crystalline

cells and 0.6 – 0.9 V for amorphous cells.

From this experiment it becomes obvious that the characteristic curve for a solar generator is

equivalent to an “inverted” diode characteristic curve, which is shifted upward by an offset equal

to the photocurrent (= short-circuit current).

Since electric power is the product of current and voltage, therefore a curve of the power

delivered by a solar cell can be obtained for a given radiation level (Fig. 3-9).

I cell = 0

V oc

I ph

I D

V D

Rload = ∝

I cell = 0 I cell = 0

V oc

V oc

I ph

I ph

I D

I D

V D

V D

Rload = ∝ Rload = ∝




Figure 3-9: Power curve and maximum power point (MPP) (Source: Kassel University)

Although the current has its maximum at the short-circuit point, the voltage is zero and thus

the power is also zero. The situation for current and voltage is reversed at the open-circuit

point, so again the power here is zero. In between, there is one particular combination of

current and voltage, for which the power reaches a maximum (graphically indicated with an

rectangle area in Figure 3-9). The so-called maximum power point (MPP) represent the working

point, at which the solar cell can deliver maximum power for a given radiation intensity. It issituated near the bend of the I-V characteristic curve. The corresponding values of V MMP and

I MMP can be estimated from V oc and I sc as follows [2]:

In addition, the quantity

FF =( )

( ) scoc

MPP MPP

I V

I V

⋅

⋅(3-5)

is called Fill Factor represents the measure for the quality of the solar cell [4]. It indicates how

far the I-V characteristic curve approximates to a rectangle. Normally the value for crystalline

solar cells is about 0.7-0.8.

The maximum output power of the cell is then

PMPP = VMPP ⋅ IMPP = Voc ⋅ Isc ⋅ FF (3-6)

VMMP ≈ (0.75 – 0.9) Voc

IMMP ≈ (0.85 – 0.95) Isc

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70

Voltage V [V]

C u r r e n t a n d P o w e r . . .

Cell Current [A] Cell Power [W]

V MPP

I MPP

MPP




Thus the efficiency of the solar cell, which refers to the ratio of the output electrical energy to

the input solar radiation (P in ) , is defined by the following relation.

η =

in

scoc

P

FF I V ⋅⋅(3-7)

Until now the highest obtained efficiencies of the silicon solar cells with irradiation of a solar

spectrum AM 1.5 are approx. 24 %. The efficiencies of the silicon solar cells from the line

production for terrestrial applications are situated between 10 and 14 %. The theoretical

efficiencies of the silicon solar cell is however ca. 26-27 %.

3.6 Conditions with Real Solar Cells

3.6.1 Influence of series- and parallel resistance

With regard to the behaviour of a real solar cell, two parasitic resistances inside the cell, namely

a series- (R s ) and parallel resistance (R p ), are taken into consideration for more exact

description as indicated in the equivalent circuit diagram in Figure 3-10.

Figure 3-10: Equivalent circuit diagram of a real solar cell [1]

I cell =( )

p

scell load R I V

T k

q

0 ph R

R I V 1e I I

scell load ⋅+−

−⋅−

⋅+⋅⋅ (3-8)

The series resistance arises from the bulk resistance of the silicon wafer, the resistance of the

metallic contacts of the front- and back surface and further circuit resistances from

connections and terminals. The parallel resistance is mainly caused by leakage currents due to

p-n junction non-idealities and impurities near the junction, which cause partial shorting of the

junction, particularly near the cell edges.

I ph

I load

R p

R s

I cell

I D

V D

V load

Rload

I ph

I ph

I load

I load

R p R p

R s

R s

I cell

I cell

I D

I D

V D

V D

V load

V load

Rload

Rload




Figure 3-11: I-V curve for different series resistances (Source: Kassel University)

Figure 3-12: I-V curve for different parallel resistances (Source: Kassel University)

Only larger series resistances reduce also the short-circuit current whereas very small parallel

resistances reduce the open-circuit voltage. However, their influence reduces primarily the

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70

Voltage V [V]

C u r r e n t I [ A ] . . .

0.001 Ohm 0.015 Ohm 0.050 Ohm 0.100 Ohm 0.500 Ohm

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70

Voltage V [V]


500 Ohm 5.00 Ohm 0.50 Ohm 0.20 Ohm 0.10 Ohm




value of the Fill factor (Fig. 3-11, Fig. 3-12). As a result, the maximum power output is

decreased.

3.6.2 Sources of losses in solar cells

a) A part of the incident light is reflected by metal grid at the front. Additional reflectionlosses arise during radiation transition from the air into the semiconductor material due

to different indexes of refraction. These losses are reduced by coating the surface with

antireflection layer. Another possibility is a structuring the cell surface.

b) The solar radiation is characterized by a wide spectral distribution, i.e. it contains

photons with extreme different energies.

Photons with small energy than the bandgap are not absorbed and thus are unused.

Since the energies are not sufficient to ionize electrons, electron-hole pairs will not be

produced.

In case of photons with larger energy than the bandgap, only amount of energy equal to

the bandgap is useful, regardless of how large the photon energy is. The excess energy

is simply dissipated as heat into the crystal lattice.

c) Since the photocurrent is directly proportional to the number of photons absorbed per

unit of time, the photocurrent increases with decreasing bandgap. However, the

bandgap determines also the upper limit of the diffusion voltage in the p-n junction.

A small bandgap leads therefore to a small open-circuit voltage. Since the electrical power is

defined by the product of current and voltage, a very small bandgaps result in small output power,and thus low efficiencies.

In case of large bandgaps, the open-circuit voltage will be high. However, only small part of the

solar spectrum will be absorbed. As a result, the photocurrent achieves here only small values.

Again, the product of current and voltage stays small.

d) The dark current I 0 is larger than the theoretical value. This reduces the open-circuit

voltage according to (3-4).

e) Not all charge carriers produced are collected, some recombine.

Charge carriers recombine preferably at imperfections, i.e. lattice defects of crystal or

impurities. Therefore, source material must have a high crystallographic quality and

provide most purity.

Likewise, the surface of the semiconductor material is a place, in which the crystal structure is

very strongly disturbed, and forms a zone of increasing recombination.

f) The Fill factor is always smaller than one (theoretical max. value ca. 0.85).

g) Series- and parallel resistance result in reduction of the Fill factor [1, 2, 4].




3.7 Effect of Irradiation

According to the relation of the photocurrent to the irradiation the short-circuit current I sc is

linearly proportional to the solar radiation over a wide range.

Anyway, with regard to the explanation of the solar cell equivalent circuit and the shape of thecharacteristic curve, open-circuit voltage V oc refers to the voltage across the internal diode

when the total generated photocurrent flows through it. Similarly to the solar cell characteristic

curve, the dependence of the open-circuit voltage on the radiation corresponds to an inverted

diode characteristic. When the radiation intensity is low (and thus also the photocurrent), V oc is

also low; however regarding (3-4) it increases logarithmically with increasing radiation (Fig. 3-

13).

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

Voltage V [V]


1000 W/m² 800 W/m² 600 W/m² 400 W/m² 200 W/m²

Figure 3-13: I-V characteristic curve at different irradiation (Source: Kassel University)




3.8 Effect of Temperature

Since the band gap energy decreases with rising temperature, more photons have enough

energy to create electron-hole pairs. As a consequence of increasing minority carrier diffusion

lengths the photocurrent, that is to say: the short-circuit current, is observed to increaseslightly. However, this is a small effect (Fig. 3-14):

As V oc can be assumed to be almost independent of the radiation value for the typically high

intensities outdoors, these voltages drop markedly in poorly lit indoor rooms with intensities of

only a few W/m2. However, according to the diffusion theory of Shockley [5], I 0 is given by

I 0 =

+

−

p p

p

nn

n g

cv p

L

n

L

kT

E exp N N q

τ τ (3-9)

N v , N c are the effective densities of states in the valence and conduction band, the band gap

energy E g and L n , L p , n n , p p , τ n , τ p are the diffusion lengths, the densities and the lifetimes of

electrons and holes respectively. With (3-9) we can obtain from (3-4), assuming I ph >> I 0 :

V oc =

+

⋅⋅−

p p

p

nn

ncv

ph

g

p

L

n

L N N q

I

1 ln

q

kT

q

E

τ τ (3-10)

Therefore V oc is strongly temperature-dependent (Fig. 3-14):

This should also be considered during the design phase as solar cells installed outdoors can

reach temperatures depending on the installation (ventilation), which are up to 40 K higher thanthe ambient temperature.

Since the cell voltage and current depend on the temperature, the supplied electric power (P )

also varies with the temperature:

Isc increases by about 0.07 % / K

P sinks by about 0.4 – 0.5 % / K

Voc sinks by about 0.4 % / K




Figure 3-14: I-V characteristic curve at different temperature (Source: Kassel University)

The rated power of a solar cell or a module is basically reported in “peak watts” [Wp] and

measured under internationally specified test conditions, namely Standard Test Conditions

(STC) , which refers to global radiation 1000 W/m2 incident perpendicularly on the cell or the

module, cell temperature 25 °C and AM 1.5. The term “peak power” is misleading as, e.g. at

lower cell temperatures or higher radiation intensities, this value can be exceeded.

3.9 From Single Cells to PV Arrays

Solar cells are rarely used individually. Rather, cells with similar characteristics are connected

and encapsulated to form modules in order to obtain higher power values. These modules are

then in turn combined to construct arrays. PV arrays for a diversity of applications can be

constructed according to this principle in the power range from µW to MW.

3.9.1 Parallel connection

If higher current is required in a system, solar cells are connected in parallel as illustrated in

Figure 3-15.

Solarzellen IU Kennlini

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

Voltage V [V]


0 °C 25 °C 50 °C 75 °C 100 °C




Figure 3-15: Parallel connection of solar cells

Regarding a parallel-connected configuration the voltage across each cell is equal whereas the

total current is the sum of all the individual cell currents. Accordingly, the current-voltagecharacteristic curve of the complete configuration is obtained, as shown in Figure 3-16, by

adding the single cell current values corresponding to each voltage value point for point.

Figure 3-16: I-V characteristic curve for parallel connection (Source: Kassel University)

The question of the system performance arises when part of a module is shaded. As indicated

in Figure 3-17 three identical cells are connected in parallel and one cell is completely shaded,

which then stops generating its photocurrent. The worst case takes place with open-circuit

condition, i.e. if there is no external load. Since the shaded cell is cooler than the other two

cells, the breakdown voltage of its diode is higher according to their I-V characteristic curves

(see section 3-8). Whereas the voltage across all three cells is identical, the diode current of the

shaded cell is therefore extremely small.

I ph1

I load

I D1

V D1

V load

Rload

I PV

I ph2

I D2

V D2

I ph3 I

D3

V D3

I ph1

I ph1

I load

I load

I D1

I D1

V D1

V D1

V load

V load

Rload

Rload

I PV

I PV

I ph2

I ph2

I D2

I D2

V D2

V D2

I ph3

I ph3 I

D3 I

D3

V D3

V D3

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

Voltage V [V]


Three Cells Two Cells One Cell




Figure 3-17: Partial shading in case of parallel connection

Pure parallel connection in order to construct a module is usually not suitable for common

application because high current requires big cross section of conductor. Besides, low voltagecauses high relative losses. For these reasons a series connection is more attractive.

3.9.2 Series connection

In a series connection, as illustrated in Figure 3-19, the same current flows through each cell

whereas the total voltage is the sum of the voltage across each cell.

The I-V characteristic curve of the complete configuration, as shown in Figure 3-20, is obtained

by adding the single cell voltage values corresponding to each current value point for point.

The following characteristic curves result for a given radiation intensity, which is equal for threeof solar cells.

Series connection of the solar cells causes an undesired effect when a PV module is partly

shaded. In contrast with parallel connection, the worst case occurs in case of short-circuit

condition.

I ph1

I D1

V D1

I ph2

I D2

V D2

V oc

I D3≈ 0 I

ph1 I

ph1 I

D1 I

D1

V D1

V D1

I ph2

I ph2

I D2

I D2

V D2

V D2

V oc

V oc

I D3≈ 0 I D3≈ 0




Figure 3-19: Series connection of solar cells

Figure 3-20: I-V characteristic curve for series connection (Source: Kassel University)

I ph3

V D3

Rload

I PV

V D2

V D1

I ph1

I ph2

I D1

I D3

I D2

I load

V load

I ph3

I ph3

V D3

V D3

Rload

Rload

I PV

I PV

V D2

V D2

V D1

V D1

I ph1

I ph1

I ph2

I ph2

I D1

I D1

I D3

I D3

I D2

I D2

I load

I load

V load

V load

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Voltage V [V]

C u r r e n

t I [ A ]





In case of complete shading as shown in Figure 3-21 the shaded cell generates no current and

acts as an open-circuit and therefore no current flows in the circuit. Its diode tends to be

reverse biased by the voltage generated from other two cells. However, there is no power

dissipation to the shaded cell unless the breakdown voltage of its diode is exceeded.

Figure 3-21: Series connection – one cell is completely shaded.

Due to the fact that there is no current flowing in the circuit, the output power in this case is

also zero. One solution to this problem is to connect bypass diode anti-parallel to the cells (Fig.

3-22) so that larger voltage differences cannot arise in the reverse-current direction of the

solar cells. Under normal conditions such as with no shading each bypass diode is reverse

biased and each cell generates power. As shown in Figure 3-22, when the third cell is shaded,

its bypass diode is forward biased and conducts the circuit current.

Regarding the I-V characteristic curve of the PV array in case of shading by assuming that the

load is adjusted from infinity (open-circuit) to zero (short-circuit), the result is shown in Figure

3-23. Under open-circuit condition no current flows through the circuit and there is no voltage

across the third cell. When the load is smaller than infinity, the load voltage is smaller than

open-circuit voltage and the voltage across the third cell increases from zero, its bypass diode

is therefore forwards bised and will conduct the circuit current as soon as its threshold voltage

is reached. Afterwards, the characteristic corresponds to the curve of two cells connected in

series.

V D2

V D1

I ph1

I ph2

I D1

I D2

V D1 + V D2

I PV = 0

V D2

V D2

V D1

V D1

I ph1

I ph1

I ph2

I ph2

I D1

I D1

I D2

I D2

V D1 + V D2V D1 + V D2

I PV = 0 I PV = 0




Figure 3-22: Series connection with bypass diodes – one cell is completely shaded.

Figure 3-23: I-V characteristic curve for series connection – one cell is completely shaded

V D2

V D1

I ph1

I ph2

I D1

I D2

Bypass

Diode

Bypass

Diode

Bypass

Diode

I cell 1 = I cell 2

V D2

V D2

V D1

V D1

I ph1

I ph1

I ph2

I ph2

I D1

I D1

I D2

I D2

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

I cell 1 = I cell 2 I cell 1 = I cell 2

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

Voltage V .[V]

C u r r e n t I . [ A ]

Three Cells Two Cells One Cell Shading with bypass




Figure 3-25: Series connection with bypass diodes – one cell is partly shaded.

Figure 3-26: I-V characteristic curve for series connection – one cell is partly shaded

V D2

V D1

I ph1

I ph2

I ph3

20 %

I D1

I D2

Bypass

Diode

Bypass

Diode

Bypass

Diode

I cell 1 = I cell 2

V D2V D2

V D1

V D1

I ph1

I ph1

I ph2

I ph2

I ph3

I ph3

20 %20 %

I D1

I D1

I D2

I D2

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

Bypass

Diode

I cell 1 = I cell 2 I cell 1 = I cell 2

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0

Voltage V .[V]

C u r r

e n t I . [ A

]


Shading with bypass Shading without bypass




However one bypass diode per cell is generally too expensive. In practice, according to reasons

of permissible power loss, it is sufficient to provide one diode for every 10 to 15 cells, i.e. for a

normal 36-cell module three diodes are needed. In addition, these connections are included in

the connection box by the manufacturer.

It should be noted that the bypass diodes do not cause any losses while current does not flow

through them in normal operation. In addition to protecting the shaded module, the bypass

diode also allows current to flow through the PV array when it is partly shaded even if at a

reduced voltage and power.

The effect of partial shading and the role of bypass diode can be more indicated here in Figure

3-27 and 3-28.

Figure 3-27: Power curve of a module under irradiation 1000 W/m 2

Under normal condition a module has a power curve indicated in Figure 3-27. However,

shading affects the curve by drastically reducing the power output of the module considerably

as obviously seen in Figure 3-28.

As already states, for series connection, the worst module determines the quality of the whole

configuration. For these reasons, modules with different types of solar cells or from different

manufacturers should never be connected to each other. In a larger system it could be well

worthwhile to ensure that all the modules originate from a singe production run. Besides, not

all commercial modules include bypass diodes. Therefore, case must be taken to avoid even

light shadows, e.g. from cables, mounting wire, tree tops, surrounding structure or adjacent

arrays [2].

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0

Voltage V [V]


0

10

20

30

40

50

60

70

80

P o w e r P [ W ]

Current Power




According to Figure 3-29, with an unsuitable mounting the PV module installed on the top of

the machine stays under shadow of the shop’s sunshade during the day. Furthermore, the PV

module faces dirt as well (Fig. 3-30). However, this module is little over-dimensioned according

to a small different of prices and the machine needs only small power for its required function.

Figure 3-30: PV module of the cigarette vending machine (Photo: Kassel University)

Another example of shading, which takes place often with PV modules, is due to birds’

droppings when they settle on the upper edge of the module (Fig. 3-31). A solution in order to

prevent settling of birds, a strip of needles can be mounted along the upper edge of themodule.

Figure 3-31: Dirt on the PV module due to birds’ droppings supply for a glass showcase

at Karlsplatz, Kassel (Photo: Kassel University)




3.10 References

[1] Knobloch, J.; Goetzberger, A.: Physikalische Grundlagen von Solarzellen .

In: Schmid, J. : Photovoltaik: Strom aus der Sonne; Technologie, Wirtschaftlichkeit und

Marktentwicklung; Heiderberg: Müller, 1999. pg. 1-14.

[2] Schmidt, H.: From the solar to the PV generator .

In: Fraunhofer Institute for Solar Energy Systems: Course book for the seminar:

Photovoltaic Systems; Freiburg, 1995. pg. 67-103.

[3] Wenham, S.R.; Green, M.A.; Watt, M.E.: Applied Photovoltaics ; Australia. pg. 69-78.

[4] Wiese, A.; Kaltschmitt, M.: Erneuerbare Energien: Systemtechnik, Wirtschaft-lichkeit,

Umweltaspekte ; Berlin, Heiderberg: Springer, 1997. pg. 177-238.

[5] Shockley, W.: Electrons and Holes in Semiconductors ; New York: van Nostrand, 1950.




4 CONVERSION PRINCIPLES IN PV SYSTEMS

4.1 Introduction

PV generator is a heart of a PV system. For a practical application, however, additional

components are needed, e.g. for the energy storage, for the energy flow regulation or for the

supply of network-conformal alternating voltages and currents. These additional components

represent a considerable share of cost, efficiency reduction and influence the behavior of the

whole system substantially.

Assuming the representation of a solar cell by a current source parallel with a diode its

standard symbol is illustrated in Figure 4-1.

Figure 4-1: Symbol of a PV generator

4.2 Coupling of PV Generator and Ohmic Load

In case that loads are directly connected to linear sources, electric power (voltages and

currents) are supplied to the load. The values of voltage and current for each operating point

can be easily calculated with the help of Ohm’s Law if e.g. a voltage source is connected to a

resistor. However, if the source has a non linear nature, e.g. in case of PV generators (Fig. 4-2),

a graphical method is necessary.

I D

I PV

V PV

I PV

V PV V D

I ph

I D

I D

I PV

I PV

V PV V PV

I PV

I PV

V PV V PV V DV D

I ph

I ph




Figure 4-2: Direct coupling of PV generator and ohmic load

The characteristic curves of both, the PV generator and the resistive load, are overlaid on the

same graphic. The PV genaretor is a source whereas the resistence is a load. The two

components are connected to each other, the voltage is equal across both and the same current

flows through the whole circuit, therefore the intersection of the two characteristic curves is the

resulting working point, as shown in Figure 4-3 [1].

Figure 4-3: Working points for different irradiations (Source: Kassel University)

Assuming that operating temperature of solar cells is constant; I-V curves of a PV generator fordifferent irradiations are represented for different load curves in Figure 4-3. The load curve II

V load

I PV

V PV

PV

Generator

I load

Rload

V load

V load

I PV I PV

V PV

V PV

PV

Generator

I load I load

Rload

Rload

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0

Voltage V [V]


1000 W/m² 600 W/m² 200 W/m² Load I Load II




proceeds nearly through the MPP of the curve for the irradiation 1000 W/m2 and is thus optimal

for this irradiation. However, it results power loss with lower irradiation. In contrast with the

load I, which refers to a higher resistance: it is well adapted for low irradiations but not suitable

for higher irradiations. In both cases noticeable power losses arise. Anyway, with application of

standard system components the characteristic curves of PV generator and load are generally

given, therefore a matching converter is required to avoid such mismatch.

4.2.1 DC/DC converters

Figure4-4 shows the representation of a DC/DC converter that can be used as interface

between the source and the load.

Figure 4-4: Description of input- and output variables of the matching converter

Function of the matching converter is to hold the working point of the PV generator at or as

close as possible to the MPP under all operating conditions (irradiation, temperature, load

characteristic etc.). The necessary transformation of a given ohmic load into an adjusted

optimal resistance (to the MPP) succeeds by means of a DC/DC converter, with which contrary

to commonly applied DC/DC converters: it does not regulate the output voltage but rather the

input voltage to a constant voltage value or to a voltage value given by an MPP regulator. The

output voltage results automatically from the equality of input- and output power if internallosses P L of the converter are negligible [3].

Firstly, the fundamentals of DC/DC converters without intermediate circuit are to be described

here.

The DC/DC converters provide possibility of converting direct current with a certain voltage into

direct current with other (mostly adjustable) voltage with even a change of the voltage polarity.

For the realization of DC/DC converters different circuit concepts are available and will be

mentioned specifically.

V load

I PV

V PV

DC/DC Converter

I load

Rload

P load

P PV

PV

Generator

P L

V load

V load

I PV

I PV

V PV

V PV

DC/DC Converter

I load

I load

Rload

Rload

P load

P load

P PV

P PV

PV

Generator

P L

P L




Figure 4-5b: Step-down converter during “on” state

Figure 4-5c: Step-down converter during “off” state

The capacitor C1 is used to support the supply voltage (V PV ). In principle, S1 is turned on and off

with a switching frequency (that is to say: with “t on ” and “t off ”). With regard to Ohm’s law the

behaviour of the load voltage can be obtained from the load current (= i L ). As shown in Fig. 4-

5d, the resulted load voltage has obviously a ripple, which can be smoothed by additional

capacitor C2. Anyway, its average value (V load ) is lower than V PV . In case that the switching

frequency is increased, e.g. up to the kHz-range, then the necessary inductance can be reduced

considerably.

D

L i L

V PV

S1

C2C1 V load D

L i Li L

V PV V PV

S1

S1

C2C2C1C1 V load V load

D

L i L

I PV

V PV

S1

C2

C1 V

load D

L i Li L

I PV

I PV

V PV

V PV

S1

S1

C2

C2

C1

C1 V

load V

load




Figure 4-5d: Behaviour of the load voltage of step-down converter

Assume that the load voltage is ideal smooth and the inductor cannot absorb DC voltage thus,

with the period T = t on + t off :

Vload =T

t on VPV (4-3)

b) Step-up converter (Boost converter)

Figure 4-6a: Equivalent circuit diagram of a step-up converter

By rearrangement of components of the step-down converter a step-up converter can be

obtained (Fig. 4-6a). Contrarily, here V PV is stepped up. At a steady state as S1 is still “off”, V load

is equal to the V PV , regardless of a voltage across diode.

V PV

t t on t off

t 1t 0

V load

V PV

t t on t off

t 1t 0

V load

I PV

V PV

Rload

C1

L i L

S1

D

V load

I PV

I PV

V PV

V PV

Rload Rload

C1

C1

L i Li L

S1

S1

D

V load

V load




Figure 4-6b: Step-up converter during “on” state

As shown in Figure 4-6b, during “on” state, without C1 the load voltage drops immediately to

zero. The circuit current (= i L ) flows through the inductor L and S1 and rises according to the

following equatsion:

dt

di L = L

V PV (4-4)

Figure 4-6c: Step-up converter during “off” state

After S1 is switched off (Fig. 4-6c), the induced voltage in the inductor adds itself to V PV , which

lie then across the load. i L flows through the inductor and further to the load. Thereby it falls

down gradually because V load > V PV :

dt

di L = L

V V load PV − (4-5)

L i L

S1

D

C1 V

load

I PV

V PV

L i Li L

S1

S1

D

C1

C1 V

load V

load

I PV

I PV

V PV

V PV

Rload

L

i L

S1

D

C1 V

load

I PV

V PV

Rload

Rload

L

i Li L

S1

S1

D

C1

C1 V

load V

load

I PV I PV

V PV

V PV




Figure 4-6d: Behaviour of the load voltage of step-up converter

The proceeding of the load voltage is illustrated in Figure 4-6d. The diode D protects against a

short circuit (that is to say: discharge) of the charged capacitor C1, which is assumed to be so

big that it can smooth the load voltage completely:

Vload = PV

off

V t

T (4-6)

c) Step-down/Step-up converter (Buck/Boost or inverting converter)

This circuit (Fig. 4-7a) enables both step-down and step-up of a DC voltage. During the “on”

state the energy given by the source (PV generator, in this case) is stored in the inductor L (Fig.

4-7b). The stored energy in the inductor L is delivered then to R load during the “off” state (Fig.

4-7c). With the help of the diode D the current flows through the inductor L only in one

direction during both “on”- and “off” state. As a result, V load has obviously an opposite polarity

to V PV . Therefore, the circuit is also called inverting converter . Equations describing the

proceeding of the circuit currents can be derived in the same way to both converters mentioned

before and will not be done here. As stated, the capacitor C1 supports the supply voltage V PV

and C2 smoothes V load . In conclusion the amplitude of V load can be either lower or higher thanV PV depending on the adjusted t on and consequently t off [8]:

V load = − t

t

off

on V PV (4-7)

V PV

t t on t off

t 0

V load

V PV

t t on t off

t 0

V load




Figure 4-7a: Equivalent circuit diagram of a step-down/step-up converter

Figure 4-7b: Step-down/step-up converter during “on” state

I PV

V PV L

Rload

D i L

C2

C1

S1

V load

I PV I PV

V PV V PV L

Rload

Rload

D i Li L

C2

C2

C1

C1

S1S1

V load V load

I PV

V PV L

Rload

D

i L

C2C1

S1

V load

I PV

I PV

V PV V PV L

Rload

Rload

D

i Li L

C2C2C1C1

S1

S1

V load V load




Figure 4-7c: Step-down/step-up converter during “off” state

In Figure 4-8 the transformation of the working point by the example of a ohmic load is

represented, whereby the descriptions of the input- and output variables shown in Figure 4-4

were applied.

Figure 4-8: Transformation of the working point (Source: Kassel University)

With regard to the curve of 200-W/m2 irradiation the resulted working point locates quite left

with the power P ′ 1, which is represented by the small pink rectangle area. However, with thisirradiation the PV module could deliver the power P 1 represented by the white rectangle if it

V PV

L V load

D

i L

C2

C1

S1

V PV

V PV

L V load

V load

D

i Li L

C2

C2

C1

C1

S1

S1

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0

Voltage V [V]


1000 W/m² 600 W/m² 200 W/m² Load

P 1

P 2

P' 1




3) Measurement of the PV generator’s open circuit voltage.

This method is based on the fact that for a certain module the relationship between

open circuit voltage and MPP voltage can be approximated by a constant factor of e.g.

0.8 or also a simple function. With this procedure the open circuit voltage is measured

within regular intervals by short separation of the load and then the desired working

point voltage is determined.

The advantage of the procedures mentioned can be a very simple feasibility - it is however

disadvantageous that in general only an approximation to the actual MPP is achieved and

modifications of the PV generator characteristic, e.g. by contamination, cannot be taken into

account.

b) Direct MPPT

This MPPT’s get the information about the desired optimal working point from actuallymeasured currents, voltages or powers in the system and thus can react also to unforeseeable

modifications in the behavior of the PV generator.

Usually assigned procedures are based on a search algorithm, with which the maximum of the

power curve is determined without interruption of the normal operation. For this, in regular

intervals, the working point voltage is changed around a certain increment - consequently

output power becomes larger, then the search direction is maintained for the next step,

otherwise it is reverse. The actual working point oscillates therefore with a certain range around

the actual point of maximum power. This simple basic principle can be secured by additional

algorithms against misinterpretations, which can occur for example with a wrong searchdirection and nevertheless a rising power due to fast increasing irradiation.

The necessary determination for searching the MPP of the PV generator power requires in

principle a measurement of generator voltage and current as well as a multiplication of these

variables. A substantial simplification results, if one considers that the actual target is not a

maximization of generator output power, but rather achieving a maximum power at the load. It

is therefore meaningful and simpler to detect and maximize either the voltage at the load or

usually the current through the load [3].




4.3 Energy Storage Units

The momentary photovoltaic power is unpredictable. It varies between zero and its maximum

value independent on demand. In most cases storage of the generated PV energy is thus

required. For grid-connected PV systems the public utility grid acts as a convenient and cost-effective means of energy storage: the grid takes the produced energy in and then releases it

again to consumers corresponding to demand. In case of water pumping or ventilators, energy

consumption could be adapted to the supplied energy. However, for many stand-alone PV

systems, which are not connected to the public utility grid, batteries for energy storage are

applied in order to achieve a continual electrical energy supply [6].

The first battery was developed by Alessandro Volta (1745-1827) who discovered a means of

converting chemical energy into electrical energy. Beginning his work in 1793, he found that in

order to produce electric current two different metals must be available and this system must

build a closed circuit. He had developed a basic model, which consisted of two plates of different metals immerged in a chemical solution (Fig. 4-9 left). This basic model was then

modified to the so-called Voltaic cell , which generated a consistent flow of electricity. However,

it was not a rechargable type. The world has honored Volta by naming the unit of electric

potential “Volt” after him.

The next step in the evolution of electrical energy storage was the invention of the lead-acid

storage battery in 1859 by the French physicist Gaston Plante. In 1899 Waldmar Jungner from

Sweden invented the nickel-cadmium battery, which used nickel for the positive electrode and

cadmium for the negative. Due to high material costs compared to dry cells or lead-acid

storage batteries, the practical applications of the nickel-cadmium batteries were limited.

Figure 4-9: Left: forerunner of Voltaic cell Right: lead-acid battery (today)

-

Zn Cu

Acid

(H3O+)

+ - +

Acid

(H2SO4)

Pb PbO2

--

ZnZn CuCu

Acid

(H3O+)

Acid

(H3O+)

++ -- ++

Acid

(H2SO4)

Acid

(H2SO4)

PbPb PbO2PbO2




4.3.1 Electrochemical processes in the lead-acid batteries

In batteries, the electrical energy is converted into chemical energy, which is recalled from the

storage if necessary and converted again into direct current. The lead-acid battery consists of a

container (mostly a polypropylene casing) with diluted sulfuric acid as electrolyte, in which

positive and negative lead electrodes with a lattice- or pocket-form constructed surface hang.

The plates, i.e. supporting structure, are composed of solar lead. Different structures are

possible for positive plate (cathode): lattice, pocket, tube etc., which are filled with lead oxide

(PbO2) in porous structure (to achieve as big surface as possible) during charged phase. The

negative plate (anode) is executed as latticed plate as a rule for enlargement the surface, and

the lattice is filled with pure lead during charged phase. Between the plates, acid-transparent

separators are arranged, which not only prevent short circuit but also supports the active

material at the plates [7]. Figure 4-10 describes the processes of discharge in the lead-acid

battery cell.

Figure 4-10: Discharge process in the lead-acid battery [7]

During discharge the active materials at both plates react with the sulfuric acid according to the

following reaction equations [4]:

Positive plate:Primary reaction: PbO2 + 4H+ + SO4

-2 + 2e- → PbSO4 + 2H2O (4-8)

Secondary reaction: ½O2 + 2H+ + 2e- → H2O (4-9)

Negative plate:

Primary reaction: Pb + SO4-2 → PbSO4 + 2e- (4-10)

Secondary reaction: H2 → 2H+ + 2e- (4-11)

Cell:

Primary reaction: Pb + PbO2 + 2H2SO4 discharge charge 2PbSO4 + 2H2O (4-12)

Secondary reaction: ½O2 + H2 → H2O (4-13)

-

Pb

Pb + 2H2SO4 + PbO2 → 2PbSO4 + 2H2O

PbO2

H2SO4

+ - + - +

convert

to

PbSO4PbSO4

Plate

surface

converted

--

PbPb

Pb + 2H2SO4 + PbO2 → 2PbSO4 + 2H2O

PbO2PbO2

H2SO4H2SO4

++ -- ++ -- ++

convert

to

convert

to

PbSO4PbSO4PbSO4PbSO4

Plate

surface

converted

Plate

surface

converted




At the positive plate a part of lead oxide (PbO2) reacts with a part of the sulfuric acid (SO4-ion)

to produce a part of lead sulphate (PbSO4) whereas at the negative plate a part of lead reacts

with a part of acid to produce a part of lead sulphate and 2 parts of water (Fig. 4-11). Since

with the discharge reaction acid is reduced and water is produced, the acid concentration in the

cell drops with increasing discharge.

Figure 4-11: Discharge process in the lead-acid battery

Figure 4-12: Charging process in the lead-acid battery [7]

By the way, regarding the equation (4-12), charging process with electric current supply

provides a reversal of the reaction (Fig. 4-12), i.e. the lead sulphate at the plates is converted to

sulfuric acid and lead or lead oxide, whereby the acid concentration increases [7].

-

Pb PbO2

H2SO4

+ - + -

+

convert

to

PbO2Pb

Plate

surface

PbSO4 PbSO4

Source

-

+

+

Source

-+

Source

-

Pb + 2H2SO4 + PbO2 ← 2PbSO4 + 2H2O

--

PbPb PbO2PbO2

H2SO4H2SO4

++ -- ++ --

++

convert

to

convert

to

PbO2PbO2PbPb

Plate

surface

Plate

surface

PbSO4PbSO4 PbSO4PbSO4

SourceSource

--

++

++

SourceSource

--++

SourceSource

--

Pb + 2H2SO4 + PbO2 ← 2PbSO4 + 2H2O

DiffusionPb

2H2O

H2SO

4

2e-

2H+

PbSO4

2H+

2e-

PbO2

Anode

H2SO

4

Cathode

PbSO4

H2SO

4H

2SO

4

DiffusionPbPb

2H2O2H

2O

H2SO

4H

2SO

4

2e-

2H+

PbSO4

PbSO4

2H+

2e-

PbO2

PbO2

Anode

H2SO

4H

2SO

4

Cathode

PbSO4

PbSO4

H2SO

4H

2SO

4H

2SO

4H

2SO

4




4.3.2 Theoretical description of the lead-acid batteries

To describe the battery performance, many different physical models are available. However,

only a few models will be described here. A basic equivalent circuit of the lead-acid battery is

modeled by a voltage source with an equilibium voltage (V E ) in series with an internal resistor

(R in ) (Fig. 4-13). It must be noted here that this configuration can describe only a current state

because the magnitude of V E and R in are not actually constant, but is function of many

parameters such as state of charge (SOC), temperature, current density and aging of the

battery. Furthermore, it is to consider that these parameters depend also on the current

direction (charging or discharge) [10].

Figure 4-13: Basic equivalent circuit of the lead-acid battery for a current state [9]

When current is drawn from or injected into a battery, the voltage measured at the battery

terminals, namely the terminal voltage V B will be different from the voltage that would be

measured at those terminals while the battery were at rest or under open-circuit condition (V B

= V E ). When current is drawn from the battery, the voltage will be lower than V E . When current is

flowing into the battery, the terminal voltage will be higher than V E . For example, at each

moment during discharge phase the terminal voltage can be derived as follow:

VB = VE – Vin (4-14)

= VE – Rin⋅ IB (4-15)

where: VB = terminal voltage [V]

VE = equilibium voltage [V]

Vin = internal loss voltage [V]

Rin = internal resistance [Ω]

IB = discharge current [A]

Obviously, higher discharge current results in reduction of the terminal voltage. Therefore, tospecify the state of the battery by the battery voltage, discharge current should be also

measured.

V B

V in

I B Rin

V E Rload V B

V B

V in

I B

I B Rin Rin

V E V E Rload Rload




Figure 4-14 illustrates current-voltage characteristics and working points of a battery, which is

directly connected to 2 different ohmic loads by assuming that SOC and temperator of the

battery are constant. A distance between the green line and dash line corresponds to V in .

Figure 4-14: Working points of the battery for different ohmic loads (Source: Kassel University)

In PV systems it is necessary to know the performance of the batteries for longer period.Additional elements are therefore considered to explain a dynamic- and a quasi-static

processes (Fig. 4-15).

Regarding the dynamic processes overvoltages partly due to the chemical reaction and any

processes such as diffusion processes of ions in the electrolyte are simplified summarized and

are described as a polarization voltage (V p ) whereas a voltage drop in the grid and in the

electrolyte is represented by a resistance R Ω .

For the quasi-static processes, a capacitor C p , which is connected in parallel to a resistor R p ,

disappears. This derived model corresponds to the Shepherd model [10, 11], which is perhaps

the most spread model worldwide [12].

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0

Voltage V [V]

C

u r r e n t I [ A ]

High SOC Medium SOC Low SOC Load I Load II

V in




Figure 4-15: Equivalent circuit of the battery regarding the dynamic- and

quasi-static processes [11]

An additional loss in the battery is due to self-discharge, which is represented by a resistor R S

(Fig. 4-15). This resistance is responsible for the emptiness of charged batteries after they are

left for so long although they are never in use. Good solar batteries should therefore have very

high R S in order to keep this loss as small as possible.

IB = I - IS (4-16)

where: I = battery current, which should be provided [A]IS = self-discharge current [A]

Anyway, the rated voltage of the lead-acid battery cell amounts of 2 V. A common 12-V battery

consists therefore of 6 series connected cells. In practical, the terminal voltage varies according

to operating condition. However, due to the fact that acid concentration changes during

charging and discharge as stated before, the equilibrium voltage can be estimated with

following empirical equations:

VE ≈ Vk + acid concentration [g/cm3] (4-17)

where: V E = equilibrium voltage [V]

V k = 0.84…0.88 (dependent on battery types [4])

For example, regarding a battery with H2SO4 concentration 1.28 g/cm3 and V k = 0.84 for Tudor

batteries [9]: thus the equilibium ≈ 0.84 + 1.28 = 2.12 V.

However, long settling time caused by long diffusion time of sulfuric acid is problematic.

Therefore, the battery should be in neutral situation while the acid concentration is measured

[9].

In case of discharge, the minimum voltage level acceptable for a lead-acid battery is defined asdischarge voltage threshold . Falling below this threshold is called deep discharge , with which

R S

I S

I

V B

I B

Rload V E

V p

R p

RΩC p

R S

I S I S

I I

V BV B

I B

I B

Rload Rload V E V E

V p

R p R p

RΩ RΩC pC p




the battery may suffer damage. In case that the battery is left longer after deep discharge, lead

of the support structure is converted to lead sulphate in rough-crystalline form, which during

charging can be only bad or cannot be converted again anymore. As a result, the battery loses a

part of its storage capacity; besides loss of support structure arises as well.

In practice, harmful deep discharge is to be prevented: the consumers will be compulsorydisconnected from battery as soon as the discharge voltage threshold is reached i.e. with the

help of a so-called deep discharge protection (DDP) (Fig. 4-31). This threshold is basically

given in the data sheets by the manufacturer for different discharge currents. Preferably, the

value of this threshold should depend on the discharge current. The relation between the

discharge current and the voltage during discharge for the lead-acid battery is presented in

Figure 4-16 [6].

Figure 4-16: Discharge characteristic curves (Source: HAGEN)

However in PV systems, which are typically characterized by very slow discharges, this threshold

may be conveniently set at approx. 1.95 V per cell or 11.7 V for 12-V battery [1]. Anyway, if the

battery is deep-discharged, it must be recharged immediately.

In order to charge the battery, i.e. to move the sulphate ions from the plates back into the

electrolyte, a voltage higher than the rated voltage must be applied. Consequently, the charge

voltage is situated between 2.0 – 2.4 V per cell or 12 – 14.4 V for 12-V battery. It increasesaccording to rising charges in the battery.

4.3.3 Gassing

With 2.3 – 2.4 V, namely the so-called gassing voltage , gas is developed at the electrodes in the

battery, by which the water is decomposed into hydrogen and oxygen. Both gases mix together

in the battery providing detonating gas (explosive!) and escape through ventilation opening in

the vent plug. With the gassing the battery loses also water, which must be refilled according to

maintenance within regular intervals. The gas is the unwelcome secondary reaction of the

chemical conversion during charging because current is consumed for the electrolysis andtherefore the storage efficiency of the battery is made worse unnecessarily.




After the gassing voltage is exceeded, voltage stays approximately constant. The whole

charging current during this period results in H2 and O2, which is defined as loss. For this

reason, gassing can be represented by a zenor diode in series with a resistor R G (Fig. 4-17).

Figure 4-17: Quasi-static equivalent circuit with representation of gassing [12]

The zenor diode is reverse biased and therefore does not conduct until the charging voltage

exceeds its breakdown voltage, namely the gassing voltage. Then it functions as a voltage

regulator by keeping the voltage across it constant and allows the whole charging current to

pass through, which is dissipated in R G as heat. It must be noted that this concept can be

applied only for lead-acid batteries because gassing destroys gel batteries (sealed type of lead-acid batteries).

Continually, heavy gassing damages the battery, so that in the data sheet the manufacturers

give the so-called maximum charge voltage , which is not allowed to be exceeded during

charging. This voltage is situated about 2.3 – 2.4 V per cell (with 20 °C) corresponding to 13.8 –

14.4 V for 6 cells. In many battery types, small gassing for a short time is however required to

mix the electrolyte and to provide an equal acid concentration for whole cell volume [7].

Nowadays, a great deal of batteries is available on the market. Most of them are starter

batteries. The difference between solar- and starter batteries will be described as follow:

In the electrolyte, ions next to the surface of electrodes can provide immediately chemical

reaction resulting in a potential difference and contribute to current flow. Figure 4-18 shows a

comparison of porous structures of electrodes’ surfaces in solar batteries and in starter

batteries.

R S

I S

V B

RG

V G

I PV

V E

V in

Rin

R S

I S I S

V BV B

RG

V G

I PV I PV

V E V E

V in

Rin Rin




Figure 4-18: Comparison between the electrode surface in solar batteries (left)

and in starter batteries (right)

Higher porous surface provides more area for the reaction and therefore higher current. For this

reason, starter batteries can provide high currents for a short time as required for their

function. Although starter batteries are discharged with high current, this event occurs only in a

short period and they are then fully recharged immediately also with a high charge current so

that battery voltages are nearly always constant.

Freezing of electrolyte

For applications with low ambient temperature the lead-acid battery must also be protected

against freezing of electrolyte. The risk of freezing depends on the state of charge. Figure 4-19

illustrates the freezing limit as a function of the state of charge.

Figure 4-19: Freezing limit of a lead-acid battery dependent on the state of charge [6]

- 80°

- 60°

- 40°

- 20°

0°

0 20 40 60 80 100

State of charge [%]

T e m p e r a t u r e [ C ]

slushy until hard

- 80°

- 60°

- 40°

- 20°

0°

0 20 40 60 80 100

State of charge [%]

T e m p e r a t u r e [ C ]

slushy until hard

Electrode

(Pb/PbO2)

Electrolyte

(H2SO

4)

Electrode

(Pb/PbO2)

Electrolyte

(H2SO

4)

Electrode

(Pb/PbO2)

Electrolyte

(H2SO

4)

Electrode

(Pb/PbO2)

Electrolyte

(H2SO

4)




Cycle life of lead-acid batteries

The cycle life refers to a capability of the battery to withstand a certain number of

charge/discharge cycles of given depth of discharge (DOD). Since the lifetime of the battery

also depends on the average depth of discharge during cycling (expressed in % of rated

capacity), the cycling capability may be more conveniently expressed by multiplying thisaverage depth of discharge by the battery lifetime expressed in number of cycles. The result is

called the nominal cycling capability , which is expressed as the number of equivalent 100 %

nominal capacity cycles.

The starter battery typically has a low cycling capability of less than 100 nominal cycles, which

means that it is able to withstand for example 500 cycles of maximally 20 % depth of discharge.

The battery appropriate for PV application requires a good cycling capability of at least 500

nominal cycles, which means that it should be able to withstand for example 1000 cycles of 50

% depth of discharge (Fig. 4-20) [1].

Figure 4-20: Cycle life as a function of deep of discharge (Source: VARTA special report 3/1987)

4.3.4 The battery capacity

Previously, the storage capacity of a battery is expressed in Ah (Ampere-hours) showing how

many hours a certain current can be taken from the charged battery until the battery is

discharged, i.e. until the battery voltage drops to the discharge voltage threshold.

Nowadays, it might be more favourable to express a battery capacity in dischargeable energy,

namely Wh (Watt-hours) or kWh (kilowatt-hours). However, these two ways of expressing the

battery capacity are equivalent because they are related via the battery voltage, i.e. Ah ⋅ V = Wh.

Unfortunately, the capacity of a battery is not a constant quantity, but depends on the amount

of discharge current. The manufacturers give therefore the rated capacity of their batteries

always with regard to a certain discharge current.

0

20

40

60

80

0 1000 2000 3000 4000 5000

Cycle life [cycles]

D e p t h o f d i s c h a r g e [ % ]

100

100

Industrial batteries

Consumer

(starter)batteries

0

20

40

60

80

0 1000 2000 3000 4000 5000

Cycle life [cycles]

D e p t h o f d i s c h a r g e [ % ]

100

100

Industrial batteries

Consumer

(starter)batteries




charging (Q C). Self-discharge will affect coulombic efficiency. Furthermore, it is reduced

particularly by the secondary reaction during charging, i.e. gassing.

ηI = Q D / Q C (4-19)

The battery will usually need more charge than was taken out to fill it back up to its startingpoint. Typical average coulombic efficiencies are 80 – 85 % for stand-alone PV systems, with

winter efficiencies increasing to 90 – 95 %, due to higher coulombic efficiencies when the

battery is at a lower state of charge and most of the charge going straight to the load, rather

than into the batteries.

The voltage efficiency, which is determined by the average discharge voltage (VD) and average

charging voltage (VC), is lowered particularly by internal resistance of the battery. It is also

measured at a constant discharge rate and reflecting the fact that charge is recalled from the

battery at a lower voltage than was necessary to put the charge into the battery.

ηV = VD / VC (4-20)

ηΣ should be as high as possible, to be able to pass the biggest proportion of the energy in the

battery, which is generated by the PV generator, further to consumers [4, 5].

Self-discharge

The battery discharges itself even without load connected. This effect is caused by secondary

reactions at it electrodes and proceeds faster with higher temperature or older battery [7].

Thermodynamic instability of the active materials and electrolytes as well as internal- and

external short-circuits lead to capacity losses, which are defined as self-discharge. This loss

should be small, particularly according to annual storage.

Maintenance cost

The maintenance, e.g. water refilling in case of lead-acid batteries, should be kept as low as

possible.

Easy installation and operation

Since batteries are driven often also from non-experts. Easy installation and operation aretherefore favourable.

Power

In special cases battery must be highly loadable for a short time, e.g. at the start of diesel

generators or in case of momentary power extension of PV systems [4, 5].

There are many types of batteries potentially available for use in stand-alone PV systems.

Useful data of available batteries given in Table 4-1 are approximated values and are provided

as a guideline. More information can be found in [1, 2, 4, 5, 7].

Type Cycle life until

80 % DOD

Investment

cost [€/kWh]

Specific kWh

cost [€/kWhΣ]

ηI [%] Self-discharge

[%/month]

Temp. range

[°C]




Pb 500...1500 85...350 0.17…0.30 > 80 3…4 -15°...+50°

NiCd 1500...3500 650…1500 0.30…1.00 71 6…20 -40°...+45°

NiFe 3000 1000 0.33 55 40 0°…+40°

Table 4-1: Comparison between selection criteria of available batteries [4]

Since many values are dependent on charge- and discharge conditions, they have not been

standardized for PV applications and for test purposes until now. Therefore, the comparison

between batteries and selection of the most suitable one for each application are not easy. Due

to particular operating conditions with PV applications in practical operation, the cycle life given

by manufacturer (and in Table 4-1) for cycling load can be reduced more than half.

According to Table 4-1 it follows that in most cases the lead-acid batteries would be the best

choices for PV applications. The selection of suitable choices is to orient in application purpose

[4].

Lead-acid batteries come in a variety of types: deep or shallow cycling, gelled batteries,batteries with captive or liquid electrolyte, sealed or open batteries.

Sealed batteries are regulated to allow for evolution of excess hydrogen gas. However, catalytic

converters are used to convert as much evolved hydrogen and oxygen back to water as

possible. They are called “sealed” because electrolyte cannot be added. They require stringent

charging controls but less maintenance than open batteries.

Open- or flooded electrolyte batteries contain an excess of electrolyte and gassing is used to

reduce electrolyte stratification. The charging regime need not be stringent. However,

electrolyte must be replenished frequently and the battery housing must be well ventilated to

prevent the build-up of hydrogen gas.

Lead-acid batteries are produced with variety of plate types:

o) Pure lead plates have to be handled extremely carefully since the lead is soft and easily

damaged. However, they provide low self-discharge rates and long expectancy.

p) Calcium can be added to the plates (giving lead-calcium plates) to provide strength.

Their initial cost is less than that of pure lead-acid batteries, but they are not suitable

for repeated deep discharge and have slightly shorter lifetimes.

q) Antimony is also often added to lead plates for strength. Lead-antimony batteries are

common in automotive applications. They are substantially cheaper than pure lead or

lead-calcium batteries but have shorter lives and much higher self-discharge rates. In

addition, they degrade rapidly when deep cycled and need to be kept almost fully

charged at all times. They are consequently not ideal for use in stand-alone PV

applications. Lead-antimony batteries are usually only available as “open” batteries, due

to the high rate of electrolyte usage and consequent need for topping-up regularly [5]




Figure 4-21 shows desirable structures of a battery for PV applications.

Figure 4-21: Structures of a lead-acid batter [VARTA]

4.3.6 From single batteries to battery banks

Higher battery storage capacities can be achieved in case of battery banks by connecting

several batteries together by means of parallel, series or series-parallel in order to provide

operating voltage and current levels as required.

Anode

Cathode

Negative plate

Positive plate

Vent plug

Seperator




Parallel connection

Batteries are connected in parallel when all the positive terminals of a group of batteries are

connected and then, separately, all the negative terminals are connected. In a parallel

configuration, the battery bank has the same voltage as a single battery whereas a capacityrating equal to the sum of the individual batteries (Fig. 4-22).

Figure 4-22: Parallel connection of batteries

Only batteries with same voltage rating should be connected in parallel since otherwise the

batteries with higher voltage rating will feed strong currents to the others (with lower voltage

rating) resulting in damaging overload.

Series connection

When batteries are connected with the positive terminal of one to the negative terminal of the

next, they are connected in series. In a series configuration, the battery bank has the same Ah

rating as a single battery, and an overall voltage equal to the sum of the individual batteries

(Fig. 4-23). Only batteries with the same capacity and design can be connected in series since

otherwise, during cycling, the lower capacity batteries will reach deep discharge conditions

earlier than the other higher capacity batteries [1].

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

400 Ah(4.8 kWh)

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

100 Ah(1.2 kWh)

12 V

400 Ah(4.8 kWh)




Figure 4-23: Series connection of batteries

Series-parallel connection

As the name implies, both of the above techniques are used in combination. The result is an

increase in both the voltage and the Ah-capacity of the total battery bank. This is done very

often to make a large, higher voltage battery bank out of several smaller, lower voltage

batteries (Fig. 4-24).

Figure 4-24: Series-parallel connection of batteries

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

24 V 200 Ah

(4.8 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

24 V 200 Ah

(4.8 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

12 V 400 Ah

(4.8 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

6 V

200 Ah

(1.2 kWh)

12 V 400 Ah

(4.8 kWh)




4.4 Coupling of PV Generator and Battery

Due to the fact that PV generators produce direct current and batteries need direct current for

charging, it could be therefore meaningful and practical to charge a battery with a PV generator

by directly connecting them together (Fig. 4-25).

Figure 4-25: Direct coupling of the PV generator and the battery

Regarding the idealized characteristic of the battery its curve can be represented with straight

line (voltage source), which varies, dependent on the each state of charge within a certain

voltage range, e.g. from ca. 11 V to 14.4 V in case of a lead battery with a rated voltage of 12 V.

For three different irradiations the characteristics of the PV generator are represented here at a

same scale with the characteristic curve of the battery resulting in three different working

points as indicated in Figure 4-26.

Although it is found that some losses arise in this case, it should be realized that with a careful

sizing of the PV generator/battery combination the working points could be located within the

area of the maximum power of the PV generator and the resulted energy losses by mismatching

are negligible. Results from practice as well as detailed theoretical examinations have

confirmed this and show that in case of a PV generator/battery coupling a matching converter

(with or without MPP) is not necessary. Experiments on the matching of PV generators and

electrolyte acids led to the same results [3].

However, whenever the voltage of the PV generator is lower than the battery’s voltage, e.g. at

night, discharge current from the battery flows through the solar cells (Fig. 4-27). To prevent a

current reversal, in small systems e.g. house-number lighting or supply of measuring

instruments, which can be possibly operated without a charge regulator, a blocking diode in

series with PV generator and battery is needed (Fig. 4-28).

I B

Battery

V B

I PV

V PV

PV

Generator

I B

I B

BatteryBattery

V BV B

I PV

I PV

V PV V PV

PV

Generator




Figure 4-26: I-V curves of the PV generator and the battery (Source: Kassel University)

Figure 4-27: Self-discharge of the battery through the PV generator

V D

I B

I ph = 0

I B

V B

V D

V D

I B

I B

I ph = 0 I ph = 0

I B

I B

V B

V B

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0

Voltage V [V]...

C u r r e n t I [ A ] . . .

1000 W/m² 600 W/m² 200 W/m² Min Nom Max




4.4.1 Self-regulating PV systems

Figure 4-28 : A self-regulating PV system without charge regulator [3]

Self-regulating systems rely on the natural self-regulating characteristics of the PV panels. The

slope of the I-V characteristic curve for a solar cell or module progressively increases when

shifting from the maximum power point towards the open circuit condition. This automatic

reduction in generating current with increasing voltage above the maximum power point

appears to be well suited for providing charge regulation to a battery, provided the temperature

remains constant. However, due to the large temperature sensitivity of the voltage of a solarcell, the day-to-day temperature variations and wind velocity inconsistencies can make it quite

difficult to design a reliable self-regulating system, particularly one suitable for a range of

locations.

The other complicating factor regarding the design of self-regulating systems is that different

cell technologies are characterized by different effective values of series resistance. The result

of this is that the slope of the I-V curve between the maximum power point and the open

circuit point can vary quite significantly between technologies. This clearly introduces additional

complications when trying to design such a system accurately.

In general, the self-regulating system provides too many compromises in design and runs the

risk of overcharging batteries in cooler locations or on cooler days, while undercharging

batteries in hot weather. Slight errors in design or product variability can, of course, result in

one of these extremes occurring virtually all the time, therefore making such a system quite

ineffective and unreliable.

Another problem with a self-regulating system is that the photovoltaic generating capacity has

to be well matched to the load requirements. For instance, during the night the load must

partially discharge the batteries so that, on the following morning when the weather is cooler

and hence the photovoltaic voltage is higher, the batteries can accept the charge generated.

Later in the day, once the PV panels operate closer to the anticipated design temperature, if thebatteries are close to full state of charge, the same problem will not result as the self regulation

I PV

V PV

PV

Generator

Blocking Diode

D I B

Battery

V B

I PV

I PV

V PV V PV

PV

Generator

Blocking DiodeBlocking Diode

D I B

I B

BatteryBattery

V BV B




will automatically cause the generating current to fall. This charging scenario has important

implications for system maintenance and down-time. Failure to disconnect the batteries from

the PV arrays during periods of no load will result in severe overcharging of the batteries, as

they begin each day already at full state of charge. Examples of this in the field have led to

rapid destruction of the batteries resulting from severe overheating, overcharging and rapid

loss of electrolyte.

However, self-regulating systems are substantially cheaper, not only because of the elimination

of the battery controller, but also because of the reduced wiring and simpler installation.

Self-regulating systems are best suited to batteries such as nickel-cadmium, which can tolerate

substantial amounts of overcharging [5]. Besides, the self-regulating systems with special

modules (33 crystalline cells for a 12-V-lead battery) are also used partly in the higher power

range (e.g. supply of light buoys) and require however an exact knowledge of load profiles and

also irradiation conditions for sizing [3].

4.5 Charge Regulators

Since batteries represent a substantial cost factor for example in case of a typical island house

of about 15 – 20 % of initial investments, which can rise over 50 %, if one considers the

necessity for a repeated replacement of the battery over the lifetime of the total system.

Therefore it is aimed to achieve, by suitable charging and supervision strategies, as long life of

the battery as possible under given operating conditions. Experiences from a great deal of

systems show however that with the presently used technique the obtained life lasting with 2 –

4 years is clearly shorter than the expected values of 5 – 8 years. The determination of the

responsible causes and the derived, from them, development of new concepts and systemcomponents are thus important assignments in the future.

In the following, basic principles of common charge regulators are described. The theme is

limited thereby to charge regulators for the lead acid batteries used in larger systems [3].

4.5.1 Basic principles of charge regulators

Basic function of a charge regulator is operating the battery within the operation limits given by

the manufacturer regarding overcharging or deep discharge. Moreover, a charge regulator can

execute automatically maintenance like regular equalizing charge or gassing charge as well as

inform the user about the status of the system with appropriate displays.

Simple charge regulators have only one voltage threshold for the maximum charge voltage: this

value should be adjusted to 2.3 V/cell with the temperature 20 °C. The maximum charge

voltage must be calibrated regarding the temperature with a correction value of -4…-6 mV/°C,

if this deviates by more than 5 °C from the reference value.

More expensive charge regulators have several voltage thresholds and permit thus for example

a controlled gassing charge. The strategies were rather empirically established and consist i.e.

of a gassing charge within a certain 4-week interval as well as after each deep discharge. The

total gassing time is limited here on 10 hours per month. During gassing phase the batteryvoltage is limited at 2.5 V/cell, subsequently at 2.35 V/cell [3].




4.5.2 Switching regulators

Against overcharging of batteries a protection is always planned with the solar charge

regulators: the regulating unit is either totally closed or completely opened. Ideally the

developing dissipated heat is zero in both cases since either current or voltage at the regulating

unit is zero.

Figure 4-29: Principle of series regulator [2]

In case of the series regulator (Fig. 4-29), the current flow is influenced by a regulating unit,

namely switch S1, which is positioned in series to the PV generator. While relays were quite usedas switches in the past, they are today almost exclusively replaced by semiconductor switches

such as MOSFET’s or IGBT’s. It is to the series charge regulator’s advantage that besides PV

generators also other, not short-circuit proof, energy converters such as wind generators can

be connected. As disadvantage higher power losses were claimed to the series charge regulator

– however, this historical statement is not valid any longer after the power semiconductors

specified above are available.

S1

C

Charge

Regulator

I PV

V PV

PV

Generator

I B

Battery

V B

S1

S1

C

Charge

Regulator

I PV

I PV

V PV

V PV

PV

Generator

I B

I B

BatteryBattery

V B

V B




Figure 4-30: Principle of shunt regulator [2]

Regarding the parallel- or shunt regulator (Fig. 4-30) the characteristic of PV generators is

applied, namely being able to be short-circuited arbitrarily for a long time. During charging the

PV generator current flows through the diode D into the battery. As achieving the maximum

charge voltage the PV generator is short-circuited by the regulating unit according to one of the

further strategies described below, so that no more charging current can flow. The diode

prevents here, on one hand, the current reversal from the battery into this short-circuited path;

on the other hand it prevents discharging of the battery to the unlighted PV generator at night.

It is favourable with the shunt regulator since it makes a charging current also in the case of a

completely discharged battery flow through the diode and thus the system starts reliably. This

is however not guaranteed in the case of the series regulator with a bad connection design

since there is no energy available to turn on the switch.

Moreover, as mentioned before, if the battery is connected to the load, the deep discharge

protection (DDP) is required, which is represented by the switch S2 in Figure 4-31.

The hybrid regulator represents a modification of the shunt regulator, with which in the

charging phase the blocking diode is bridged by a switch situated in parallel and the dissipated

heat is again minimized. However, it must be emphasized here that this is not relevant to theenergy gains for the energy balance of the total system but, in the foreground of discussion,

rather the reduction of the developing dissipated heat in the regulator that leads to savings at

heat sinks and housings, in addition, contributes to a increased reliability.

S1

Charge

Regulator

C

I Shunt

D I B

Battery

V B

I PV

V PV

PV

Generator

S1

S1

Charge

Regulator

C

I Shunt I Shunt

D I B

I B

BatteryBattery

V B

V B

I PV

I PV

V PV

V PV

PV

Generator




Figure 4-31: Shunt regulator with deep discharge protection (DDP) [2]

In case of higher power of PV generator, the so-called sub array switching is applied, with

which the generator is divided into several subfields that operate at a time over assigned

sections on a combined battery. Here either all sections can be controlled together by an

individual control section or can be however advantageously switched off after a given load

strategy, what provides a better control of the total charging current.

An applied method, only sorted in systems of higher voltage, is the so-called partial shunting ,

with which only one part of the modules interconnected in series is short-circuited by an

additional connection and thus the generator voltage for a further charging becomes too low

[3].

At the first achieving of the maximum charge voltage a battery is not yet completely charged. It

is just fully charged if the whole lead sulphate is converted into lead and lead oxide [7]. To

reach the full charging the battery must be further charged for a longer period with constant

voltage, whereby the charging current decreases slowly (I-V charging). This behavior can be

achieved by suitable control of the regulating unit with the series- and also shunt regulator,

whereby two realistic possibilities are available:

By means of two-step regulator the current, as reaching the maximum charge voltage, isinterrupted (by opening the regulating unit of the series regulator or closing in the case of

shunt regulator), thus the battery voltage drops (Fig. 4-32) [3]. At this moment a characteristic

of the battery has an effect: the battery behaves like a big capacitor. Therefore, the battery

voltage does not drop immediately, but rather follows the discharge curve of a capacitor [6].

S1

Charge

Regulator

C

I Shunt

D S2

Rload Battery

I PV

V PV

PV

Generator

S1

S1

Charge

Regulator

C

I Shunt I Shunt

D S2

S2

Rload

Rload Battery

I PV

I PV

V PV

V PV

PV

Generator




Figure 4-32: Voltage and current characteristics during charging [2]

As reaching a lower voltage threshold, about some millivolts [3], the charging current is again

connected and the voltage rises then corresponding to the charging curve of a capacitor. With

increase in state of charge of the battery the resulting charging phases become ever shorter

and intervening pauses become longer, so that the average value of charging current decreases

as required [6]. The cycle duration of the described phenomenon is not constant, but depends

on the state of charge, battery capacity, the charging- or discharge current as well as selectedvoltage hysteresis: it can therefore vary within the range of milliseconds up to minutes.

The pulse-width-modulated (PWM-) charge regulator operates in principle similarly, however,

the switching frequency of the switch is fixed given here by a timer with e.g. 100 Hz. Firstly the

full charging current flows here also, whereby during approximation to the maximum charge

voltage the relation of charging time to the total cycle time is modified continuously by an

appropriate PWM-modulator of 1 until 0. As indicated in the figure above, this has thereby the

required reduction of the average charging current as a result [3].




4.5.3 Control instruments

In many cases the function of a PV system depends strongly on a cooperation of the user. This

requires however meaningful and responsible information about the present status of the

system, especially of the battery. As minimum design a charge regulator should however

provide an optimum display, which informs the status of “full, charge and empty”. A trained

operator can gain furthermore so much information from the observation of battery current or

-voltage as they are displayed, for example, from the charge regulator indicated in Figure 4-33.

Figure 4-33: Solar charge regulator with integrated current-/voltage measuring device

(Source: Uhlmann Solarelectronic)

4.6 Inverters

Since PV generators as well as batteries deliver basically direct current or direct-current voltage

(DC). As many small consumers are suitable for operating directly with DC voltage, the mostcommercial devices need however an alternating voltage (AC). Therefore, power-conditioning

elements, which are commonly called “inverters” because they invert the polarity of the source

in the rhythm of the AC frequency, are often applied to PV systems. Also in grid-connected

systems inverters are basically necessary for the conversion of DC power into grid-compatible

AC power.

4.6.1 General characteristics of PV inverters

Since production cost of PV electricity is several times more expensive than conventional

electric energy, conversion efficiency becomes predominant for the economics of the total PVsystem. In consequence, extremely high efficiency not only in the nominal power range but also




under partial load condition is a requirement for PV inverters in grid-connected as well as in

stand-alone systems.

Figure 4-34 presents a general structure of a grid-connected PV system consisting mainly of

the following components: the PV generator, the inverter, the safety devices and in many cases

the electric meter.

Figure 4-34: General structure of a grid-connected PV system

The actual power fed into the grid can be estimated by multiplying the actual power of the PV

generator with the actual efficiency of the inverter, regardless of losses in the safety device and

in the meter. More important is the energy produced by the system after a certain period of

time e.g. after one year of operation. In this case the mean efficiency of the inverter taken into

account for all load conditions throughout the year becomes important. As a first step, the

inverter must allow the PV generator to operate continuously at the maximum power point

(MPP) according to the maximum power point tracking (MPPT) as described in section 4.2.2.

However, simulation has shown that for grid-connected PV systems constant voltage operation

leads only to losses between 1 and 2 % when properly adjusted.

For optimum use of the PV energy MPPT and constant voltage operation can be seen as

equivalent. As a matter of their operation principle, single phase inverters, which are most

common for small scale PV systems (P ≤ 5 kWP), lead to deviations from the MPP due to DC

ripple as will be explained as follows: When injecting AC power into the grid, the feed in current

should be in phase with the grids voltage which means the power factor equals one as shown in

Figure 4-35.

Figure 4-35: Pulsewise injection of power into single-phase grids needs energy storage

Safety device Meter GridInverterPV generator

DC

AC

773500

Safety device Meter GridInverterPV generator

DC

AC

773500

0

p(t)

v(t)

i(t)

t 0

p(t)

v(t)

i(t)

t




In consequence, the actual power injected into the grid becomes:

p(t) = v(t) ⋅ i(t) (4-21)

= v0 ⋅ sin(wt) ⋅ i0 ⋅ sin(wt) (4-22)

= v0 ⋅ i0 ⋅ sin2(wt) (4-23)

These power pulses with a frequency of 100 Hz are also shown in Figure 4-35. Since the PV

generator provides continuous and quasi-constant power and since power injection into the

grid is pulsewise, each single-phase inverter needs a storage element which can be realized

either using a capacitor or an induction coil. For economic reasons these storage elements must

be limited, a voltage ripple can be found with all single-phase inverters at the DC side. This

ripple forces the PV generator to deviate from the MPP as shown in Figure 4-36.

Well-designed single-phase inverters show DC voltage ripple with negligible influence on MPPdeviations. It should be noted at this point that three-phase inverters inject continuous power

into the grid, which eliminates the need for this kind of storage.

Figure 4-36: Deviations from the MPP through DC voltage ripple caused by the working

principle of single-phase inverters

voltage [V]

current [A]

p o w e r [

W ]

MPP

voltage ripple through

imperfect storage

voltage [V]

current [A]

p o w e r [

W ]

MPP

voltage ripple through

imperfect storage




4.6.2 Inverter principles

The symbol used to describe an inverter is shown in Figure 4-37.

Figure 4-37: Symbol used to describe an inverter

Square-wave inverters

A simple version of such an inverter is shown in Figure 4-38. AC at the primary windings of the

transformer is being produced by alternatively closing the S1 and S2. If S1 is closed, S2 is open

and vice versa. The resulting AC output voltage is of square-wave type, which may be used for

resistive-type loads such as incandescent light bulbs etc.

Figure 4-38: Layout of a simple inverter with square-wave AC output

Anyway, the two primary windings of the transformer can be reduced to one if two more

switches are used (Fig. 4-39).

AC outputDC input

∼AC outputDC input

∼

S1

S2

AC

output

DC

source

S1

S1

S2

S2

AC

output

DC

source




Figure 4-39: H-type bridge inverter

In this configuration the switches are opened and closed pairwise in such a way that S1, S2 and

S3, S4 respectively open and close synchronously. At the output of the H-type bridge formed by

the switches S1 through S4 there is already AC available. The transformer is only necessary in

case of a voltage transformation.

Sine-wave inverters

Since many consumers and the public grid operate on the basis of sine-wave type voltage, high

quality inverters should also be able to provide this type of AC output. This voltage form can beobtained in different ways. Some of the most common layouts will be here presented.

a) Inverters with step-down converters

The basic idea of this concept is to produce a sine-shaped unipolar voltage at the DC side

normally by means of a step-down converter as shown in Figure 4-40.

AC

output

DC

source

S1

S3

S2S

4

AC

output

DC

source

S1

S1

S3

S3

S2S2S

4S

4




Figure 4-40: The combination of a step-down converter with inverter according to

Fig. 4-38 or Fig. 4-39 allow producing sine-shaped AC output voltage

Since in this configuration the actual voltage and the corresponding current at the output of the

step-down converter is no longer constant, the resulting current at the input of the converter

will also fluctuate. In case of using PV generator used as a DC source, a storage capacitor C1

becomes necessary.

The quality of the voltage shape is normally described as total harmonic distortion (THD). The

THD is defined as sum of the amplitudes of all harmonic frequencies compared to the

amplitude of the fundamental signal (the 50 and 60 Hz frequency respectively). In this case

THD is determined by the switching frequency of S0 and by the inductance of L1. With modern

semiconductor switches this frequency can be realized in the range of 100 kHz, which keeps L1

small enough.

The voltage transformation between the DC source V 2 at the output of the step-down converter

can be given as:

V2 = V1 ⋅ T

t on (4-24)

Where t on is the on-time for switch so while T corresponds with the time of one switching

period. This principle, in which the desired output voltage is being produced by means of

variable on-time of the switch is called pulse-width modulation (PWM). The switches S1 and S2

in Figure 4-40 are needed to invert the polarity of every second half-wave in order to form the

AC output.

S0

D

S1

S2

C1

C1

L1

Battery

S0

S0

D

S1

S1

S2

S2

C1

C1

C1

C1

L1

L1

Battery




b) Inverters with digital voltage synthesis

Figure 4-41: Digital waveform synthesis inverter [11]

As indicated in the Figure 4-41, discrete constant voltage sources are connected via electronic

power switches so that the desired voltage is obtained by binary adding of individual power

sources. When using five sources, 32 voltage steps according to 25 adjustable levels can be

created. Depending on the sum of these sources the sine-shape can be approximated. The

resulting THD can be kept well below 5 %.




In this concept, the switches (transistors) S1 through S4 are needed to invert every second sine-

half wave to arrive at AC. If using voltage sources with such voltages that sum of them is at

least as high as the peak voltage of the desired AC output, i.e.

∑=

n

1iiV = 2 ⋅ V AC = 358 Volts for 230 V AC, (4-25)

no transformer is needed. The efficiency is therefore improved, especially under partial load

conditions. This concept provides extremely high efficiency because no induction coils or other

magnetic elements are required. However, one disadvantage can be seen in the use of multiple

power sources resulting in increased cabling needs between the PV generator and the inverter.

c) Inverters with pulse-width modulation

Anyway, the four switches of the H-type bridge itself can also be used to form the desired sine-

shape of the AC output. In this case an inductor has to be inserted between the bridge and theAC output as shown in Figure 4-42.

Figure 4-42: Pulse-width modulated H-type bridge inverter

As has been described in the previous concepts, the switches S1, S2 and S3, S4 respectively act

synchronously but their switching frequency becomes very much higher than the desired AC

output frequency, which is called the fundamental frequency . During the first half period of thefundamental frequency (10 ms for 50 Hz) the switches S1 and S2 are changing their on- andoff-state in such a way that the relation

T

t on becomes proportional to the actual desired voltage

similar to the step-down converter principle shown in Figure 4-40. In fact, the step-down

converter principle has been extended to work under both positive and negative polarities.

The configuration shown in the Figure 4-42 has become popular because only a very few

components are needed resulting in high efficiency and low cost (see also Fig. 4-43 and 4-44).

One possible disadvantage of this concept is the high DC input voltage necessary for proper

working e.g. 358 volts DC for 230 volts at the AC side. Adding a transformer between the load

and the inverters’ output allows reduction the DC input voltage according to its transformation

ratio. This combination can be found in many products on the market today. In comparison

S1S

3

S2

AC

output

D1

D4

S4

D3

D2

S1S1S

3S

3

S2

S2

AC

output

D1

D1

D4

D4

S4S4

D3

D3

D2

D2




with the transformerless version, separation of the potential between source and load becomes

feasible. Reduced efficiency and increased investment costs are the consequences however.

The concept explained in the Figure 4-42 allows further operating in a reversed power flow.

This situation may occur for inverters in stand-alone mode if the load is of reactive type or it

surplus power from the AC side is used to charge the battery. In both cases variable AC voltagemust be transformed to the DC voltage level, which is always higher than any value of the AC

voltage as shown in Figure 4-43. By combining S2 and D3 in Figure 4-42, a complete step-down

converter can be realized this way for the positive AC voltage. For the negative part the

combination of S1 and D4 are forming the step-up converter for reversed power flow.

Figure 4-43: Left: Step-down conversion in the forward power flow mode

Right: Step-up conversion in the reversed power flow mode

The concept described above allows reversed power flow only in cases, in which the DC voltage

level is always higher than the peak voltage of the AC side, i.e. VDC ≥ 358 Volts for 230 Volts

AC. There are two possibilities to lower the DC voltage level however, namely to install a

transformer at the AC side or to install a bi-directional DC/DC converter at the DC side. Since a

conventional step-down converter as described before is not able to act as a step-up converter

in the reversed power flow mode either two converters in anti-parallel-mode or a different

conversion concept would be necessary. One topology developed by S. Cuk in 1977, which is

able to fulfill these requirements, is given in Figure 4-44.

DC voltage level DC voltage level

V V

AC voltage AC voltage

t t

DC voltage level DC voltage level

V V

AC voltage AC voltage

t t




Figure 4-44: Bi-directional Cuk-converter

This conversion principle is actually able to perform step-up as well as step-down conversion

in both directions. Switches S1 and S2 operate complementary. The relation between the input

voltage V 1 and the output voltage V 2 becomes:

V 2 =

( )

−−⋅+

⋅−

onoff

ononoff

on1

t t

t 1 t t

t V (4-26)

The configuration shown in Figure 4-42 is also very well suited to be expanded into a three-

phase version as shown in Figure 4-45.

Figure 4-45: Three-phase PWM inverter

This type of inverter is normally suitable for a power range above 5 kW. Connection efforts at

the AC side are somewhat higher because three terminals have to be dealt with. The most

S1

S2

C1R 1

L1

R 2

L2

C2

V 2

V 1

S1

S1

S2

S2

C1C1R 1

R 1

L1

L1

R 2

R 2

L2

L2

C2

C2

V 2

V 2

V 1

V 1

S1

S2

L3

S5

S6

L1

S3

S4

L2

S1S1

S2

S2

L3L3

S5

S5

S6

S6

L1

L1

S3S3

S4

S4

L2

L2




striking advantage of a three-phase concept can be seen in the fact that power output and thus

power input are absolutely constant. As a result, no storage capacitor at the DC input side is

needed. This concept can also be combined with a three-phase transformer in a way as has

been described before.

If potential separation between DC input and AC output is requested and if the bulky 50 Hz-transformer should be avoided, high-frequency (HF) transformer concepts may be used. Three

topologies using HF concepts will be here described.

In a first concept, the configuration as explained in Figure 4-40 is applied to high frequency

(some 100 kHz) using a high-frequency transformer. The high-frequency square-wave AC

output is then rectified as shown in Figure 4-46. Providing the desired DC voltage necessary for

PWM inversion according to the H-type bridge explained in Figure 4-42.

Figure 4-46: HF transformer combined with PWM H-type bridge inverter

In comparison with the low frequency concepts, it becomes obvious that the savings using the

HF transformer are widely being compensated by extra components. This might be one of the

reasons why HF concepts have not widely been used in inverters offered to the market.

When operating the high frequency generator as described in Figure 4-47 in the PWM mode, in

which the desired low frequency is being used for modulation, a PWM series of unipolar half-

waves are resulting after the rectifier at the secondary windings of the HF-transformer.

By means of the combination of L1 and C2 a unipolar series of sinusoidal half-waves are

resulting, which are finally inverted by the H-type bridge as described in Figure 4-37. The 100-Hz pulsewise power injection requests an adequate storage element, which is realized by means

of the capacitor C2. It should be noted that this storage function is realized with C2 in the

topology presented previously in Figure 4-46.

S1

S2

C1 C2

L1

L2

S1

S2

C1 C2

L1

L2




Figure 4-47: HF transformer combined with PWM high-frequency generator at the input side

and a low frequency H-type bridge at the output side

Finally a HF concept is presented, in which AC is directly being produced at the secondary sideof the HF-transformer. In this case the non-controlled rectifier shown in Figure 4-47 has been

replaced by active switches combining the functions of rectification and inversion. This

configuration is presented in Figure 4-48. It should be noted that in this case the switches in

the H-type bridge have to be operated in the rhythm of the high frequency in contrast to the

topology described in Figure 4-47. Since transistors switched with higher frequencies have

higher losses as well as higher investment costs, the benefit of saving the passive rectifier used

in the concept given in Figure 4-47 might be compensated by these facts to a certain extend.

Figure 4-48: Direct AC synthesis at the secondary winding of the HF transformer.

The PWM high-frequency signal is inverted in the low-frequency rhythm and smoothed by

means of L and C2. C1 is needed to store the input energy in the rhythm, which equals twice the

low frequency.

4.6.3 Power quality of inverters

When dealing with power quality, a distinction has to be made between stand-alone and grid-

connected application.

S1

S2

C1 C2

L1

AC output

S1

S2

C1 C2

L1

AC output

S1

S2

C1

C2

L

AC output

S1

S2

C1

C2

L

AC output




a) for stand-alone systems

For stand-alone application, the output waveform becomes important for many applications.

According to the working principle shown in Figure 4-38 or 4-39 square-wave inverters may be

used to power resistive-type loads such as light-bulbs or similar. When feeding power to

reactive-type loads such as motors, proper operation might become difficult and losses insidethe load created by the square-wave character of the supply might occur. For these types of

load ideal sinusoidal voltage supply would be the best. In reality a compromise between this

ideal voltage, which results in high expenses, and a lower quality for cheaper investments must

be found.

The deviation from the ideal sinusoidal voltage is normally described as total harmonic

distortion (THD) as mentioned before. As an example some harmonics and their influence on

the shape of the fundamental waveform are given in Figure 4-49. For high-quality power

supply, the THD of the output voltage should be less than 5 %, which corresponds with the

quality of the public grid.

Figure 4-49: Influence of harmonics of the waveform

As a second and very important power quality element for stand-alone applications, the ability

to provide and to absorb reactive power should be mentioned. Typical loads requesting reactive

power are electric motors. Under these load conditions the load current is no longer in phase

with the voltage as shown in Figure 4-50.

Proper handling of reactive power is only possible with appropriate topologies such as havebeen described and presented in Figure 4-40 and 4-41. In some inverter designs handling of

reactive power is limited depending on the load type. In this case the acceptable power factor,

which corresponds with the cosine of the phase-angle difference between voltage and current,

is defined and the maximum power of the inverter is given in Kilo-Volt-Amperes (kVA) instead

of Kilo-Watts (kW). The energy of the reactive power, which is to be absorbed and afterwards

re-injected to the load, is normally stored in capacitors of appropriate sizes.




Figure 4-50: Power factors ≠ 1 produced by reactive (inductive or capacitive) loads

If all elements in the inverter allow for reverse power flow, a bi-directional inverter is obtained

which can be used to charge the battery when surplus power at the AC side is available. Thecombination of a Cuk-converter shown in Figure 4-42 with a H-type bridge given in Figure 4-

37 allows for such a concept.

Furthermore, stand-alone inverters should also be able to blow fuses. This requirement is

perfectly fulfilled with only a few inverters. The reason can be seen in the high current needed

to blow fuses (Fig. 4-51).

Figure 4-51: Current-time diagram for different fuse-types: Left: characteristic A and

Right: characteristic B

Some inverters produce this high current by reducing the AC-output voltage significantly. The

resulting flicker observed for loads not to be separated by the fuse in question may be accepted

in most cases.

voltage

current

power factor (cos ϕ)

ϕ

voltage

current

power factor (cos ϕ)

ϕ




b) for grid-connected inverters

Since the output voltage of grid-connected inverters has to correspond with the grids’ voltage,

the quality of the current, which is to be injected into the grid, becomes important. Under ideal

circumstances this current should be in phase with the grids’ voltage (power factor = 1). The

deviation from this power factor becomes therefore important for the description of the powerquality. All modern transistor-based inverters have a power factor near unity at nominal load,

with a tendency towards smaller values under partial load condition (Fig. 4-52).

Figure 4-52: Power factor as a function of the output power of an inverter

A second measure for the power quality is the THD of the injected current, which is defined in

the same way as was done for the voltage. A high quality grid-connected inverter shows a THDin the current, which is below 5 %.

4.6.4 Active quality control in the grid

Since the power factor in modern grid-connected inverters can be adjusted by internal control,

this kind of inverters can be used to compensate reactive power flow in the grid which

otherwise must be performed by extra compensation units such as inductors or capacitors. This

ability can either be fixed to a constant value or, in case of an appropriate communication

system, be controlled by the grid operator according to the actual needs.

As a further means of power quality improvement, high quality inverters are able to compensate

deviations in the sinusoidal voltage of the grid. As shown in Figure 4-52, the inverter injects

surplus power into the grid to compensate for the actual deficit in the voltage.

In a later stage of PV applications, inverters have to prevent grid-overloading. Grid-connected

inverters can easily handle this kind of power control by changing DC input voltage from the

MPP in such a way that the PV generator reduces power production to the desired level. This

request may come in a situation, in which several hundreds of Mega-Watts of PV power are

feeding into a local system. To allow for such ability the grid operator must be able to

communicate with these inverters.

power

1

power

factor

cos ϕ

power

1

power

factor

cos ϕ




In consequence, it can be stated that high quality inverters will be able to improve the power

quality in the grid by adjusting the power factor, by reducing the THD and by stabilizing power

flow through power control. To realize these functions appropriate control and the availability

of a communication element become necessary. A few inverters on the market show these

features already today.

4.6.5 Safety aspects with grid-connected inverters

A big issue for grid-connected systems is associated with islanding protection. Islanding may

occur if a part of the local grid is switched off e.g. for maintenance reasons or if the injected

power is equal to the actual load in the separated part of the grid. This situation is indicated in

the Figure 4-53.

Figure 4-53: After switch-off, the separated part of the grid may continue operation

if the injected power by the PV system equals the actual load.

The situation described above becomes very unlikely because not only the effective power but

also the reactive power must be equal between production and consumption. As a first

measure, frequency and voltage monitoring will identify by far the most situations in grids

turned off because the smallest deviations in production or in consumption will lead to changes

in frequency or voltage or in both of them. The experience with big wind farms has shown that

limitation of voltage or frequency may lead to undesired results however.

In case of heavy loads on the grid, both the voltage and the frequency may fall below the set

point. In this situation cut-off of power sources take place when they would be needed urgently

to support the grid. As a further method to identify islanding conditions, monitoring of the

grids’ impedance is being performed by injecting power peaks, which do not correspond with

the fundamental frequency (50 and 60 Hz respectively) by the inverter into the grid and by

monitoring this influence on the grids voltage-shape. This method is currently accepted by

German safety code.

This code, which applies to grid-connected single-phase PV systems smaller than 5 kW,

requests a separation from the grid if the impedance of the grid exceeds 1.75 Ω or if a jump inthe impedance ≥ 0.5 Ω occurs. Reconnection to the grid is allowed for grid impedance smaller

separated part of the grid

Grid∼

separated part of the grid

Grid∼




than 1.25 Ω. There are two independent monitoring and switching systems requested. One of

the two systems must act on a mechanical switch e.g. a relay whereas, for the second system,

the semiconductors of the inverter output bridge are accepted. Figure 4-54 explains this

configuration.

Figure 4-54: Two independent grid supervision units for safety against islanding

In addition to the monitoring of the grid impedance, frequency deviations above ± 0,2 Hz or

voltage difference bigger than -15 % or +10 % must lead to a separation of the grid as well. The

safety protection device can either be integrated into the inverter or installed separately

between the inverter and the grid. The latter may be used preferably in combination with small-scale inverters e.g. module integrated ones. In these cases the investment cost for integrating

the unit in each of the small inverters with a power of not more than few hundred Watts may be

not economic. In case of a separate installation, one supervision could be used to protect

several small module integrated inverters. As an alternative, also accented as a safety device,

voltage monitoring of all three phases of the grid that leads to a separation if one of the three

phases becomes zero can be used in Germany. In case of a single-phase grid, as it is the case

in many rural areas of the world, this method cannot be applied however.

There is a limitation to be expected if a great deal of inverters are testing the grid this way. In

this case interference between the different inverters may lead to unspecific interpretation of the grids’ response. It might therefore become necessary to equip all inverters with

communication capabilities. This feature would allow switching off all relevant inverters by the

grid operator if needed. As a further benefit, power quality improvements controlled by the grid

operator will become feasible as well.




4.7 References

[1] Schmidt, H.: From the solar to the PV generator .


Photovoltaic Systems; Freiburg, 1995. pg. 74.

[2] Sorokin, Alecsei.: Batteries and charge controllers for PV systems .


Photovoltaic Systems; Freiburg, 1995. pg. 109-142.

[3] Schmidt, H.: Anpaßwandler, Maximum Power Point Tracker und Laderegler .

In: Schmid, J. : Photovoltaik: Strom aus der Sonne; Technologie, Wirtschaft-lichkeit und


[4] Garche, J.; Harnisch, P.: Batterien in PV-Anlagen .In: Schmid, J. : Photovol-taik: Strom aus der Sonne; Technologie, Wirtschaftlichkeit und

Marktentwick-lung; Heiderberg: Müller, 1999. pg. 143-174.

[5] Wenham, S.R.; Green, M.A.; Watt, M.E.: Applied Photovoltaics ; Australia. pg. 95-105.

[6] Schmid, J.: Systemkomponenten .

In: Räuber, A.; Jäger, F.: Photovoltaik: Strom aus der Sonne; Technologie,

Wirtschaftlichkeit und Marktentwicklung; Karls-ruhe: Müller, 1990. pg. 62-72.

[7] Ladener, H.: Solare Stromversorgung : Grundlagen, Planung, Anwenddung ; Freiburg:ökobuch Verlag, 1996. pg. 79-103.

[8] Hagmann, G.: Leistungselektronik: Grundlagen und Anwendungen; mit Auf-gaben mit

Lösungen und Lösungswegen; Wiesbaden: Aula-Verlag, 1993. pg. 199-206.

[9] Stadler, I.: Entwicklung eines Batteriemanagementsystems (BMS) für das Hybridsystem

AREP . Diplomarbeit; Universität Fridericiana (TH) Karlsruhe, 1996.

[10] Shepherd, C. M.: Design of Primary and Secondary Cells II – An Equation Describing

Battery Discharge, Journal of Electrochemical Society, Vol. 112, No. 7, Juli 1965. pg.

657-664

[11] Jossen, A., Späth, V.: Simulation von Batterien und Batteriesystemen – Design und

Elektronik Entwicklerforum ; München, 1998.

www.basytec.de/simulation/Batmodell.html

[12] Saupe, G.: Photovoltaische Stromversorgungsanlagen mit Bleibatteriespei-chern;

Analyse der Grundprobleme, Verbesserung der Anlagentechnik, Entwicklung eines

Simulationsmodells für die Batterie . Doktorarbeit; Universität Stuttgart, 1993. pg. 97-

158.




[13] Wilk, H.: Inverters for Photovoltaic systems . In: Fraunhofer Institute for Solar Energy

Systems: Course book for the seminar: Photovoltaic Systems; Freiburg, 1995. pg. 143-

184.




5 PRINCIPLES OF PV SYSTEM CONFIGURATION

5.1 Introduction

The modular structure of PV generators provides possibility that energy supply systems can be

constructed in an extremely wide power range. The power spectrum extends from a few mW up

to powers in the MW range.

A PV system consists basically of a PV generator and system components, which are responsible

for energy treatment, as well as a consumer. In the following, the fundamental structures of PV

systems will be described at first, with which also deal briefly with the function of system

components.

By means of block diagrams the systems will be introduced for different applications of PV

energy supplies. Examples of realized systems should therefore ease the classification for thedifferent power ranges [1, 2].

5.2 Fundamental Structures of PV Systems

The PV systems could be classified by different aspects. Regarding battery storage the PV

systems can be widely divided into 2 categories, namely PV systems with- and without battery

storage:

5.2.1 PV systems without battery storage

In case that the energy supply and energy demand occur simultaneously, it is unnecessary to

store the energy produced by the PV generators. In addition, grid-connected PV system is

classified in this type because the surplus energy produced by the PV generators can be fed

into the grid whereas energy will be draw from the grid to supply the consumers when the PV

energy is not sufficient so that the battery storage unit is also unnecessary in this case.

1. Direct-coupled PV system

For this configuration PV generators are directly connected with consumers (Fig. 5-1). Main

application is ventilator. The system is simple and reliable, reduces maintenance and requireslower investment cost whereas the demand equals to the potential. An example of this

configuration is PV ventilator.




Figure 5-1: Configuration of direct-coupled PV system

2. PV system with a matching converter

In order to match the voltage of the PV system with the voltage of the consumer, a DC/DC

converter is necessary, which transforms one DC voltage to another (see section 4.2.1) (Fig. 5-

2).

Figure 5-2: Configuration of PV system with DC/DC converter

This configuration has been applied to calculators, water pumps and others. Anyway, one of applications to this configuration is also a thermometer presented in Figure 5-3.

Figure 5-3: Thermometer type 801 [3]

This instrument is designed for local temperature indication. It provides a dual display with LCD

elements (liquid crystal display). Analogue indication is in the form of bar graph with 61

divisions whereas digital indication with 4 digits display. The instrument relies on a periodic

DC consumerPV generator DC/DC converter DC consumerPV generator DC/DC converter

DC consumerPV generator DC consumerPV generator




measurement process with 3 seconds cycle time so that the viewer can take a current reading

even in passing. [3].

3. PV powered AC system

With the help of an inverter, which converts DC power into AC power (see section 4.6), ACconsumers can be supplied with solar energy (Fig. 5-4). This kind of system is often used for

water pumping above a certain power range (approx. 2 kW) [1].

Figure 5-4: Configuration of PV powered AC system

Figure 5-5 shows a PV pumping system for a village in Cardeiros, Brazil as an application of

this configuration. Although water demand tends to be roughly constant throughout the year, it

is very desirable to incorporate a covered storage tank in the system for using during periods of

low irradiation or pump breakdown.

Figure 5-5: PV pumping system for a village in Cardeiros, Brazil (Photo: Kassel University)

4. Grid-connected PV system

PV systems can also be connected to the public grid by means of suitable inverters (Fig. 5-6).

As mentioned before, energy storage is not necessary in this case. On sunny days the PVgenerator provides power e.g. for the electrical appliances in a house. Surplus energy is fed into

AC consumerPV generator

∼Inverter AC consumerPV generator

∼Inverter




the grid. During the night and overcast days, power is drawn from the grid. Figure 5-7 shows a

grid-connected system at Kassel University.

Figure 5-6: Configuration of grid-connected PV system

Figure 5-7: Grid-connected PV system with 900 W p -PV array and 700 W-inverter

(Photo: Kassel University)

5.2.2 PV systems with battery storage

If the energy supply and energy demand do not always take place at the same time, energy

storage unit is necessary. By means of the battery the system can even be operated during

night or bad weather condition periods.

AC consumer

Grid

∼InverterPV generator AC consumer

Grid

∼InverterPV generator




1. DC-coupled PV system

Always when a battery is involved in a system, a charge regulator should be included, which

provide overcharge protection and deep discharge protection (DDP), to ensure an accurate

operation of the battery (see section 4.3) (Fig. 5-8).

Figure 5-8: Configuration of DC-coupled PV system

Figure 5-9: PV lighting system at a bus stop – Talderbaum Str., Industriepark, Kassel Waldau

(Photo: Kassel University)

As shown in Figure 5-9, this configuration is applied to a PV lighting system at a bus stop. The

PV generator charges the battery during the day. By night, strings of LED (light emitting diode),

which are powered by the battery, provide steady distributed light. According to the detection

by infrared sensor, if no one is there, the lighting will be slowly dimmed of 20 %.

PV array

DDP DC consumerPV generator Charge regulator

Battery

DC Bus

DDP DC consumerPV generator Charge regulator

Battery

DC Bus




2. DC-coupled PV hybrid system

In case of high-energy demand, the PV generator alone could not provide sufficient energy. In

other words, the PV generator required would become too large and too expensive. The same

problem occurs if a high reliability is demanded. For those reasons different generators are

coupled, resulting in a so-called hybrid system . One possibility of such a hybrid system is thecoupling of a PV- and a motor generator (Fig. 5-10). In regions with good wind conditions,

even a wind generator could be considered.

Figure 5-10: Configuration of DC-coupled PV hybrid system

By means of backup generator the PV generator and the battery do not have to be oversized,

resulting in significantly reduced investment costs. Basically, backup generator is sized to

supply expected peak loads, which maximizes the supply reliability. When the electric energy

from PV generator and battery is not sufficient to supply the consumers or when the battery is

discharged, the backup generator is switched on. According to conventional generators AC

types are most commonly used. Therefore, rectifier is needed in this configuration.

For the autonomous supply of remote houses or grid-dependent consumers the combination of

the PV generator with other energy generators can be not only reasonable, but also necessary in

order to overcome the solar shortage in winter.

PV generator Charge regulator

Battery

Back-up generator Rectifier

G

DC Bus

∼

PV generator Charge regulator DDP DC consumerPV generator Charge regulator

Battery

Back-up generator Rectifier

G

DC Bus

∼

PV generator Charge regulator DDP DC consumer




3. PV system with both DC- and AC consumers

The following configuration is similar to that in Figure 5-8 only with the difference that an

inverter is now included into the system as a central inverter so that AC appliances can also be

operated (Fig. 5-11).

Figure 5-11: Configuration of PV system with both DC- and AC consumers

Figure 5-12: A school in Limoeiro – Acré, Brazil (Photo: Kassel University)

∼Inverter

AC consumer

DC Bus


Battery

DC Bus

DDP DC consumer

DC Bus

AC Bus

∼Inverter

AC consumer

DC Bus


Battery

DC Bus

DDP DC consumer

DC Bus

AC Bus




As shown in Figure 5-12, a school in Limoeiro, Brazil, which is composed of 2 classrooms and 1

kitchen with applainces as follows: 360 W DC lighting, one satellite – for each classroom, one

television and one video player, is supplied by a PV system consisting of 660 Wp-PV array, 5

kWh-battery and 1 kW-inverter.

4. PV hybrid system with both DC- and AC consumers

The following configuration is similar to that in Figure 5-10 only with the difference that an

inverter is now included into the system as a central inverter so that AC appliances can also be

operated (Fig. 5-13).

Figure 5-13: Configuration of PV hybrid system with both DC- and AC consumers

With favourable solar radiation the consumer’s total energy demand is covered by the PV

generator. Surplus energy is stored in batteries. During the night or unfavourable weather the

energy demand is covered by the batteries at first. If deep discharge tends to occur, a diesel- or

gas-fuelled generator produces the electricity and charges the battery at the same time. At

windy sites the system can also be extended with a wind energy converter. Since PV generator

and wind energy converter can complement each other with correct design, the operating time

of the fossil-fuelled generator and thus the fuel consumption are reduced [1, 2].

This configuration can be found, for example, in the Autonomous Renewable Energy Plant

(AREP) (Fig. 5-14), a project supported by EU, which was begun at the Karlsruhe University and

carried out at the Kassel University under the direction of Prof. Dr.-Ing. Jürgen Schmid. An

objective of this project was a development of an innovative Photovoltaic/Wind hybrid system

for rural electrification, which consists of PV generator (1.6 kWp), Wind generator (0.75 kW),

battery (20 kWh) und motor generator (3 kVA) [4].

∼Inverter

AC consumer

DC Bus


Battery

DC Bus

DDP DC consumer

DC Bus

AC BusBack-up generator Rectifier

G∼ ∼

Inverter

AC consumer

DC Bus


Battery

DC Bus

DDP DC consumer

DC Bus

AC BusBack-up generator Rectifier

G∼




Figure 5-14: Autonomous Renewable Energy Plant (AREP) (Photo: Kassel University)

5. DC-coupled PV system with AC consumer

If higher power is needed or if conventional household appliances and industrial devices are to

be used, a system voltage of 230 V AC is desirable. To this purpose, an inverter is included into

the system (Fig. 5-15).

Figure 5-15: Configuration of DC-coupled PV system with AC consumer

DC Bus

AC consumer

DC Bus AC Bus

∼Inverter


Battery

DC Bus

AC consumer

DC Bus AC Bus

∼Inverter


Battery




A solar lamp presented in Figure 5-16 is an example of applications to this configuration. In

this case, ballast acts as an inverter by converting DC into 30-kHz square-wave AC to supply

CFL (compact fluorescent lamp).

Figure 5-16: Solar lamp (Photo: Kassel University)

6. AC-coupled PV hybrid system

Figure 5-17: Configuration of AC-coupled PV hybrid system

AC consumer

G

AC Bus

∼Inverter

∼

Back-up generator

PV generator

Battery

AC consumer

G

AC Bus

∼Inverter

∼

Back-up generator

PV generator

Battery




Nowadays, some inverters are optionally equipped with an additional circuit for battery

charging referring to the so-called bi-directional inverters (Fig. 5-17). They can turn off the

inverter-function and become efficient battery chargers if required.

In addition, the backup generator can be directly connected to the same inverter as the battery.

The switching circuit inside the inverter allows the backup generator to supply loads, however,also to charge the battery if necessary.

As seen in Figure 5-18, the Starkenburger lodge is one of 305 lodges of the German Alpine

Association and is located 2229 m over see level in the Stubaier Alps. Since 1997 six PV

generators have supplied electricity to the Starkenburger Hütte with power of 4.95 kWp in

combination with six string inverters, three battery-inverter-units (BacTERIE) each with 12

kWh-capacity and with continuous power of 2.5 kVA as well as a gas-operated 14 kW-motor

cogeneration plant [3].

Figure 5-18: Pilot plant Starkenbuger lodge (Photo: Kassel University)




5.3 Future Trends of PV Systems

Photovoltaics provide an extreme wide range of power. The presented examples show that it is

possible in many cases to replace conventional energy supply systems with a PV power supply.

Advantages, e.g. easy handling, low maintenance costs and less use of batteries, provide

further arguments for photovoltaics in photovoltaically powered appliance section.

In addition, in case of grid-dependent PV systems, PV generators can be coupled with other

power supplies, especially in areas where solar radiation fluctuates strongly. In spite of higher

costs, photovoltaics is often more economical than laying grid connection.

The applications of photovoltaics will increase both for small-decentralized power supplies and

for larger power stations. This makes a significant energy contribution. The rate of this

progress will depend on the amount of expert knowledge contributed by those involved in the

planning, construction and operation of PV systems [1, 2].

5.4 References

[1] Roth, W.: Principles of System Configuration and Application Potential .

In: Fraunhofer Institute for Solar Energy Systems: Course book for the seminar: PV

Systems; Freiburg, 1995. pg. 1-42.

[2] Roth, W.: Prinzipieller Aufbau photovoltaischer Energieversorgungssysteme .

In: Schmid, J. : Photovoltaik: Strom aus der Sonne; Technologie, Wirtschaftlichkeit und


[3] Institut für Solare Energieversorgungstechnik: Jahresbericht 1998 , Kassel

[4] Dach, M.: Konzipierung eines Meßsystems zur energetischen Analyse von AC- und DC-

Kopplung des PV-Generators bei Hybridsystemen . Diplomarbeit; Kassel, 2001. pg. 29-

30.




6 Introduction

In order to construct a reliable and long-lasting PV systems an accurate planning is necessary

because it implements the economic evaluation during the planning state. Therefore, a

photovoltaic system should be sized according to following planning process (Fig. 6-1):

Figure 6-1: Procedure for planning and sizing of PV systems

In this chapter, pre-sizing and optimisation of PV systems will be described respectively.However, an economic calculation will be discussed later on in detail in Chapter 8.

6.1 Pre-sizing

The pre-sizing will be executed by means of practical thumb rules. Thumb rules contain

concepts and according formulas, which are easy to remember. With little information they can

quickly give approximate results. For these reasons, they are very practical and can be an

orientation especially for pre-decision.

One of parameters required for presizing the PV systems is a value of annual global solar

radiation. By means of Figure 6-2, the annual global solar radiation at a site can be quickly

approximated at first.

Presizing (Thumb rule)

-Data collection

-Choosing type

-System sizing

-Cost estimation

Decision

(Economic comparison with

alternatives, e.g. utility grid)

Start

yes

no

System optimization-Accurate data collection

-Accurate system sizing

-Choosing system components

-Final cost calculation

Quit

Determination-Energy consumption range

-System type

Presizing (Thumb rule)

-Data collection

-Choosing type

-System sizing

-Cost estimation

Decision

(Economic comparison with

alternatives, e.g. utility grid)

Start

yes

no

System optimization-Accurate data collection

-Accurate system sizing

-Choosing system components

-Final cost calculation

Quit

Determination-Energy consumption range

-System type




Figure 6-2: Annual global solar radiation on horizontal surfaces in kWh/m 2 a

(Source: Intergovernmental Panel on Climate Change)

After the potential of solar energy was approximated, the next parameter is how much energy

is required by consumers, i.e. it is necessary to know which consumers and how many of them

would be included into the system. For example, in case of village electrification it must be

informed if there are schools, health stations, small enterprises or private households. Anyway,

some of common household appliances and their approximate annual energy consumption arelisted in Table 6-1 for instance.

It should be noted that air conditioners and some other electrical heating applications such as

space and water heating should not be included into PV systems due to their relative high-

energy consumption so that they are not economically supplied by PV electricity, but rather by

thermal solar energy. In addition, the user should look for the most efficient appliances or

should also consider all appliances if they are really necessary.




Appliance Power rating

[W]

Daily

consumption

[kWh/d]

Annual

consumption

[kWh/a]

1 Incandescent bulb 60 0.25 901 Typical fluorescent lamp 40 0.15 60

1 Compact fluorescent lamp (CFL) 15 0.07 25

1 Fan, circulating 85 0.15 60

1 Fan, attic 375 0.75 270

1 Radio 55 0.10 35

1 Television, colour 19″ 80 0.14 50

1 Sewing machine 75 - 4

1 Drill, 318″ variable 240 - 10

1 Blender/Mixer 350 0.07 251 Refrigerator (12cu. ft./340 litre) 330 2.75 1000

1 Vacuum cleaner 900 - 45

1 Iron 1000 - 50

1 Clothes dryer, gas 500 - 100

1 Clothes washer 1150 - 120

1 Toaster 1200 0.12 45

1 Coffee maker 1200 0.30 110

1 Hair dryer 1500 0.33 120

1 Microwave oven 2100 0.35 130

Table 6-1: Annual energy consumption of household appliances

(Source: Center for Renewable Energy and Sustainable Technology)

According to the knowledge of the solar potential and the energy demand it is now possible to

size a suitable PV generator, which supplies the system with sufficient energy. The energy

balance from the system could be generally determined as follows:

Due to the uncertainty of demand prediction and the assumed radiation the energy supply

should be basically higher than the energy demand. However, it could sometimes happen that

the supply could not meet the demand and the system fails consequently. For this reason, a

quality factor (Q ) is commonly used to present how well the supply meets the demand.

The quality factor is defined as the quotient of the real electric output energy measured at the

system output (E el ), which is normally equivalent to the system load (E demand ) and the theoretical

output energy (E th ), which is defined as the output energy from the same system under ideal

conditions, i.e. Standard Test Conditions (STC):

Edemand ≤ Esupply




Q =th

el

E

E (6-1)

where: Q = quality factor of the system

Eel = real electric output energy of the system [kWh]

Eth = theoretical output energy of the system [kWh]

The quality factor can be determined over any given time period. In most cases, a time period

of one year is chosen to presize PV systems.

The theoretical output energy (E th ) is defined as the energy output, which is produced by a PV

array with an area of Aarray , the global radiation E glob incident on a horizontal surface and

efficiency η determined under STC:

Eth = η⋅ Eglob⋅ Aarray (6-2)

where: Eth = theoretical output energy of the PV array [kWh]

η = efficiency of the PV array [decimal]

Eglob = global radiation on a horizontal surface [kWh/m2]

Aarray = area of the PV array [m2]

It is often difficult to obtain values like the efficiencies from manufacturers. Besides, the area of

the array is frequently unknown. However, the peak power measured under STC is normally

given (STC: I STC = 1000 W/m2; T STC = 25 °C, AM = 1.5):

Ppeak = η⋅ ISTC ⋅ Aarray (6-3)

where: Ppeak = peak power of the PV array [kWp]

η = efficiency of the PV array [decimal]

ISTC = incident global radiation under STC [1 kW/m2]

Aarray = area of the PV array [m2]

According to the equations (6-2) and (6-3) after substitution of η⋅ Aarray :

Eth =STC

glob

peak I

E P ⋅ (6-4)

According to the equations (6-1) and (6-4) the quality factor can be found out:

Q = STC

peak glob

el I P E

E ⋅

⋅(6-5)

With the quality factor formula above and the empirical quality factors of existing systems it is

easy to presize the PV array:




Ppeak =Q E

I E

glob

STC el

⋅

⋅(6-6)

where: Ppeak = peak power of the PV array under STC [kWp]

Eel = real electric output energy of the system [kWh/a]

ISTC = incident solar radiation under STC [1 kW/m2]

Eglob = annual global solar radiation [kWh/m2a]

Q = quality factor of the system

In the theoretical limiting case, supply and demand values are equivalent and the quality factor

is therefore equal to one (Q = 1). A measured value of, for example, Q = 0.75 means that 75 %

of the electric energy, which is converted from the incident solar energy, is used whereas 25 %

of the electric energy is lost between the solar cell and the system output or it is not used.

The quality factor depends strongly on the system type. In case of grid-connected systems all

produced energy could be used, so there will never be surplus energy. In a PV system it couldhowever happen that the battery storage is full and then PV energy will be dissipated. For this

reason, the quality factor relates to the system type. In order to make a decision reasonably on

the system type the amount of energy consumption could be useful (Tab. 6-2). The quality

factors are then given in Table 6-3.

Annual energy consumption

Systems0.1 kWh/a 1 kWh/a 10 kWh/a

100

kWh/a1 MWh/a 10 MWh/a

PV-Batterie

PV-Diesel-BatterieDiesel-Batterie

Diesel

PV grid-connected

Table 6-2: Suitable type of PV systems and their alternatives depending on regular

energy consumption i.e. at least weekly duty cycle for a longer period

Component/System Q

PV module (Crystalline) 0.85…0.95

PV array 0.80…0.90

PV system (Grid-connected) 0.60…0.75

PV system (Stand-alone) 0.10…0.40

Hybrid system (PV/Diesel) 0.40…0.60

Table 6-3: Quality factors of components and different PV systems [2]

So the PV array is presized and for grid-connected or pumping systems the investment

precalculation could be done as will be described in the section 7.3. For systems with battery

storage the battery capacity and investment costs should be considered.

Due to the fact that the batteries are the second biggest part of the investment and operationcosts in PV- and PV hybrid systems. However, experience has indicated that operation cost of




the battery is sometimes higher than its investment cost. Anyway, the investment cost of the

battery could also be estimated by means of other thumb rule in order to complement the

investment cost of system.

The battery capacity depends on characteristics of radiation, load, and system reliability as well

as intention of the user. From experience, the relation between storage capacity [kWh] and peakpower [kWp] of the PV array is more or less 10:1. In case that the global radiation at the site is

nearly constant throughout the year, this value will be lower than 10:1. When having a system

where the power consumption is mainly during the night this thumb rule must be corrected to

the value higher (up to 20 % more) and vice versa when e.g. a wind generator or a diesel

generator is integrated into the system. This relation for some existing stand-alone systems is

presented in Figure 6-3.

Figure 6-3: Thumb rule for relation of battery capacity and PV nominal power [1]

CB = 10 ⋅ Ppeak (6-7)

where: CB = battery capacity [kWh]

Ppeak = peak power of the PV array [kWp]

The method of thumb rule described above is very easy, requires only little information and

provides a quick system design. However, there are some disadvantages because results are

not optimized solutions due to only rough estimation and therefore contain high degree of

uncertainty. There is also no consideration of different system variants (for example, adapting

the size of the PV array to available values and compensating this decision through smaller or

larger storage installations).

Anyway, when planning a PV system, consumer load is much more uncertain factor and

experience has shown that the empirical method provides as good results as when the system

is sized by simulation programs [1].

0,1

1

10

100

1000

0,01 0,1 1 10 100

Peak power P peak [kWp]

B a t t e r y c a p a c i t y C B

[ k W h ]

PV

systems

C B

P peak

= 10

SHS

PV

hybrid

systems




6.2 Approximation of the System Cost

A factor, which strongly influences the user’s decision to invest in the system, is the system

cost. According to the fact that most users have no idea about this cost. In order to give the

user an imagination about this, overall investment cost should be precalculated by means of the

factor relating to the specific cost of PV module from experience:

KPV = kPV ⋅ Ppeak (6-8)

where: KPV = absolute cost of the PV array [€]

kPV = specific cost of the PV module [€/kWp]

Ppeak = peak power of the PV array [kWp]

The factor k PV depends on the individual country, for example, the value for Germany (2002) is

about 4.0…4.5 €/kWp.

In consequence, with the help of a factor of system components, an absolute cost of the system

can be now calculated:

KSystem = f SC ⋅ KPV (6-9)

where: Ksystem = absolute cost of PV system [€]

f SC = factor of additional system components

The factor of additional system components (f SC ) depends however on the type of system as

indicated in Table 6-4.

Component/System fSC

PV system (Grid-connected) 1.20…1.40

PV system (Stand-alone) 1.80…2.40

Hybrid system (PV/Diesel) 1.60…2.20

Table 6-4: Factors of system components for different PV systems (Source: Kassel Unversity)

To show this effect a comparison of the proportion of the PV generator’s investment cost in a

PV/Diesel hybrid system and in a grid-connected system is presented in Figure 6-4.

According to Figure 6-4 it points out that PV/Diesel hybrid systems consist of morecomponents to be invested than grid-connected systems. Therefore, their proportions of PV

generator’s investment costs are smaller than that in grid-connected systems. As a result, their

values of f SC are higher (Tab. 6-4).




Figure 6-4: Comparison of the proportion of the PV generator’s investment cost in

a PV/Diesel hybrid system and in a grid-connected PV system (10 kW p )

(Source: Kassel University)

After the overall investment costs of the chosen system is approximated, the user can beinformed at this point and can make a decision whether he can afford the system or not. If the

user is interested and willing to invest in the PV system, the design can go on with the system

optimisation.

However, the investment cost is not really relevant. The capital and operation cost are more

important. Anyway, this calculation will be described in detail in Chapter 8.

6.3 System Optimisation

What are obtained from the pre-sizing process and will be used in the phase of system

optimization are the range of energy consumption and the type of the system. The optimization

process can be executed either by computer or by hand.

Regarding Figure 6-5 the potential of energy production is strong in summer and during the

day whereas the highest energy demand takes place in winter and by night. Accordingly, it

becomes clear that rather than a yearly basis, a monthly, daily or hourly basis is required for

calculating the peak power of the PV array (P peak ).




Figure 6-5: An example of a realistic relationship between solar potential

and energy consumption over the whole year in Petchabun, Thailand


For a detailed calculation the load characteristic is important. In most isolated PV systems the

peak load occurs by night as seen in Figure 6-6. Depending on the consumer type there are

local peak loads during the day, especially where small enterprises are supplied. In order tocharacterize such load profiles the share of load during the day can be quantified.

In Figure 6-6 there are two characteristic load profiles. The dark violet load profile has only a

share of 20 % of the whole load during the day in contrast to the light violet load profile with a

share of 50 %. Therefore, the load profiles here could be classified in night- and mixed load

profiles respectively. It is clear that the battery storage in case of the night load profile will be

more deeply discharged than that of the other. In consequence, energy losses are higher and

the PV array must be bigger and so on.

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

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

Month

I r r a d i a t i o n [ k W h / m ² ]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

L o a d [ k W h / d ]

Global radiation-Petchabun Load




Figure 6-6: An example of a realistic relationship between solar potential and energy

onsumption over one day with two different load profiles in

Petchabun, Thailand (Source: Kassel University)

Figure 6-7: An example of a realistic relationship between solar potential

and energy consumption in June regarding a weekend house in

Petchabun, Thailand (Source: Kassel University)

In addition, there is sometimes a weekly load variation (Fig. 6-7). Therefore, it could happen

that there is still more consumption at a weekend than that during a week. If the variation is

small, it can be neglected. However, if it is big, it must be considered during the detailed sizing.

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time [hour]

E n e r g y D e m a n d [ k W h ]

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

S o l a r I r r a d i a t i o n [ k W h / m ² ]

High Solar Irradiation Medium Solar Irradiation

Night Load Profile Mixed Profile

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su

Weekdays

D a i l y r a d i a t i o n [ k W h / m ² d ]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

L o a d [ k W h / d ]

Global radiation-Petchabun Load




6.3.1 Optimization process by hand

1. Energy demand

First of all, the amount of energy required by all loads in the system will be determined again,

but more accurately. At this step, hourly energy consumption is required. This is done by listing

each load and estimating how much energy it will consume in each hour and in each day.

However, the nominal power is not always the right figure to determine the hourly energy

consumption, e.g. a TV set of 50-W nameplate rating will usually consume roughly 70 % of this

value. A refrigerator of 500-W nameplate value will also consume roughly 70 %, however the

compressor-motor will usually not operate 24 hours per day according to a certain duty cycle

(e.g. 30 % of time ON, 70 % of time OFF). For those kinds of appliances the energy consumption

is often given directly in Wh/day [1].

If the load varies widely during a week or from month-to-month (or season-to-season), it must

be considered for each weekday or each month. Usually, the system size will be dictated by the

worst-case month, i.e. the month with the largest load but the lowest solar radiation will be

considered at first. However, even some components such as fuses or inverters are influenced

by the daily or weekly peak load. At the end, some diagrams or tables are available as shown in

Figure 6-5 to Figure 6-7. From these tables the worst-case month will be considered in order

to size the PV array.

2. Battery bank

In case that a storage battery is employed, their total capacity is defined as to ensure an

availability of energy supply within a certain number of autonomy days which is mainly

depending on the radiation profile and the system type. Too big a battery, besides being

prohibitively expensive, will seldom get fully recharged or charged at a sufficient rate to keep

sulfation in check. Too small a battery will be cycled excessively, again leading to an early

death. In hybrid systems the battery storage is generally much more smaller than that in other

stand-alone PV systems. The battery capacity required can be calculated as follows:

CB = BW C T

A

D DOD

T L

η η η ⋅⋅⋅⋅

⋅(6-10)

where: CB = battery capacity [kWh]

L = daily mean energy consumption [kWh/d]

TA = number of autonomy days [d]

DOD = maximum depth of discharge [decimal]

DT = derate for temperature [decimal]

ηC = efficiency of power conversion [decimal]

ηW = efficiency of wiring [decimal]

ηB = efficiency of battery [decimal]

Number of autonomy days refers to how long the consumer can be supplied only by the

battery, e.g. during the period of bad weather. The value to be sensibly chosen depends very

strongly on the application. More autonomy days requires higher capacity of the battery, which




provides higher supply reliability. The maximum depth of discharge refers to how many percent

of battery capacity are usable in practice (see section 4.3.4).

If the battery will be operated with below 20 °C operating temperature, its capacity will be

reduced. Therefore, a factor that derates the battery capacity for cold operating temperatures is

taken into consideration. If no better information is available, derate a lead-acid battery’scapacity one percent for each degree Celsius below 20 °C operating temperature [4].

However, the operating temperature of the battery in Thailand, for example, is often higher

than 20 °C. The battery capacity will be higher but its lifetime will be shortened. In this case the

factor D T should be assumed to be constant.

The efficiency of power conversion accounts for power loss in systems using power

conditioning components (converters or inverters). The efficiency of wiring accounts for loss

due to wiring and switchgear. This factor can vary from 0.95 to 0.99. The battery efficiency can

be obtained from manufacturer’s data for specific battery [4].

3. PV array

In order to size the PV array in an adequate manner the orientation and the tilt angle of the PV

array must be considered at first. The optimal tilt angel is depending on the latitude of the

system location. For the first assumption the tilt angel should be equivalent to the latitude.

However for the location further from the equator, the tilt angle will be smaller than the latitude

in order to obtain an optimal annual solar potential.

An example gives Figure 6-8. The annual solar potential is here given as a function of

orientation and tilt angle for Kassel. The optimum tilt angle of about 30° is smaller than thelatitude (Kassel: 51° 18 ′ N ) due to the major share of solar radiation between April and August

in the northern hemisphere.

Near of the equator a minimum of tilt angle of 15° is recommended in order to realize a self-

cleaning effect during rainfalls.

The best tilt angle for the worst-case month relates to the sun zenith of this month and could

be estimated as follow:

α ≈ 90 – z (6-11)

where: α = tilt angle [°]

z = sun zenith [°]

In addition, the equations explained above are valid in a similar manner for determination of

cable cross-section at the consumer side [2].




Figure 6-8: Available solar energy as a function of tilt angle (vertical) and azimuth angle

(horizontal) in % of maximum available solar energy corresponding

to fixed position of PV array for Kassel (51° 18 ′ N) with ideal orientation


However, it is principally important to size the system not only for the worst-case month, the

tilt angle should be therefore situated in direction to the annual optimum of tilt angle.

Now it is necessary to have the radiation data for this tilt angle in order to size the PV array with

the performance ratio for each month. Theses data can be obtained from METEONORM 4.0 [5]

and European Solar Radiation Atlas [6].

Correspondingly, the peak power of the PV array could be calculated as follows:

P peak = Q E

I E

glob

STC el

⋅

⋅(6-12)

where: P peak = peak power of the PV array under STC [kWp]

E el = real electric output energy of the system [kWh]

I STC = incident solar radiation under STC [1 kW/m2]

E glob = global solar radiation on the module plane with

selected tilt angle [kWh/m2]

Q = quality factor of the system

6.3.2 Optimization process by simulation programs

Detailed dimensioning and yield calculation are offered today by computer programs so that

the real system performance is simulated approximately. It would be more reliable to integratevaried calculations for dimensioning of PV systems into computer program and let a computer

0

30

60

90

-90,0 -45,0 0,0 45,0 90,0

Orientation

T i l t A n g l e

0

30

60

90

100 % 95% 90% 85% 80%

WestEast

Horizontal

Vertical




execute. There are nowadays many programs available for this task; however, one of them will

be here briefly introduced.

PVS is a program for simulation and design of PV systems, namely of autonomy systems (with

or without inverter) as well as of grid-connected systems. PVS was developed by Fraunhofer

Institute for Solar Energy Systems (ISE) in Freiburg. This program is equipped with acomfortable user interface and an extensive help function (Fig. 6-9). In addition, the program

provides a clear presentation of results in form of data and graphics.

Figure 6-9: User interface of PVS 2.000

6.4 Sizing of System Components

1. Battery bank

After the values of rated power of PV array and the storage capacity of battery are determined

according to the calculation described in the previous sections, each component in the PV

system can now be specified.

n B, p ≈ ′

B

B

C

C (6-12)




n B, s ≈ B

sys

V

V (6-13)

n B = n B, p ⋅ n B, s (6-14)

where: n B = number of batteries required

n B, p = number of batteries in parallel

n B , s = number of batteries in series

C B = capacity of battery required [Wh]

C B ’ = capacity of a selected battery [Wh]

V sys = depending on the system component

(charge regulator, converter or inverter)

nominal-, peak- or open circuit voltage [V]

V B = nominal battery voltage [V]

Choice of system voltages

The choice of the system voltage should not depend only on the operating voltage of some

possible already available consumers, but must be particularly considered under the point of

view of “energy consumption” and “coverage of peak load” [2]. Normally, the nominal system

voltage is the voltage required by the largest loads [4]

The system voltage must be chosen so high that the cable cross-sections stay within the scope

and the batteries can supply the occurring peak load. Standard values for the system voltage

are given in Table 6-5.

Mean daily

energy consumption

[kWh/d]

Peak power

for minutes [kW]

Peak power

for seconds [kW]

System voltage not below

[V]

0…4 0.0…1.0 0.0…2.0 12

2…6 1.0…2.0 2.0…4.0 24

4…12 2.0…4.0 4.0…8.0 48

8 and more 4.0…8.0 8.0…16.0 96

Table 6-5: Standard values for the choice of system DC voltage (Source: Kassel University)

Higher system voltage tends to result in smaller electric losses in the system. For consumers

with more than 500 until 1000 W power consumption it is generally suggested – especially in

case of longer cables – to select the supply via a 230-V inverter [2].

2. PV array

Selection and connection of PV modules depends not only on the coverage of the power

required, but also on choosing the correct peak- and open-circuit voltage (e.g. sufficient

voltage reserve when operating in very hot surroundings and corresponding open-circuit

voltage not to damage the inverter when operating in very cold surroundings as well as the look

at the short-circuit current to prevent a charge regulator or inverter damage). At the same time,

the mechanical processing and module measurement regarding mounting conditions on the




location and available place complied are also to be considered. To calculate the number of PV

modules the following relations could be used:

n PV, m ≈ m PV

a PV

P

P

,

, (6-15)

where: n PV, m = estimated number of PV modules

P PV, a = nominal power of the PV array [kW]

P PV, m = nominal power of the selected PV mudule [kW]

To calculate the number of serial connected modules the following formula could be used:

n PV, m, s ≈ m PV

sys

V

V

,

(6-16)

where: n PV, m, s = estimated number of PV modules in series


(charge regulator, converter or inverter)nominal-, peak- or open circuit voltage [V]

V PV, m = nominal-, peak- or open-circuit voltage of the PV

module [V]

To calculate the number of parallel connected strings the following formula could be used:

n PV, s, p ≈ sm PV

m PV

n

n

,,

,(6-17)

where: n PV, s, p = estimated number of PV strings in paralleln PV, m = estimated number of PV modules

n PV, m, s = estimated number of PV modules serial

In case that the number calculated is not an integer it must be rounded and afterwards the PV

array power must be adapted probably.

3. Charge Regulator

The charge regulator must be able to carry the maximum current occurring at the PV generator

side and its voltage must match with the system voltage. Besides, the load disconnection at the

consumer side must be designed for the maximum current consumed by the consumers. The

battery type (Lead acid or lead gel) should be selectable. Some charge regulators known the

system voltage and adjust them self some others are selectable.

4. Inverter

The grid-connected inverter must be able to carry the maximum current occurring at the PV

array side and it must match with the maximum PV array voltage.

An uncertainty, which occasionally occurs when selecting the battery, is whether long-life, but

very expensive stationary type as lead-acid or lead-gel is preferable in comparison to cheaptype with shorter lifetime and cycling stability. If this question cannot be clearly answered with




type and duration, the decision will be finally met by the customer. Since the customer is not

always ready to pay the high investment cost for the technically better and long-life solution

even if the sum of investment- and operation cost counted over lifetime of the system speaks

rather in the expensive system.

The selection of the stand-alone inverter will be determined especially by the AC power to beprovided and the selected DC voltage. A stand-alone inverter must be able to power all of the

loads that might run at the same time, including any starting surges for pumps and other large

motors. When looking at inverter specifications, play close attention to the part load efficiency

of the inverter. Related to the over sizing related to the peak current security the stand alone

inverter is mostly running in part load about 10 to 30 % of nominal load.

5. Cabling

Due to the fact that PV energy is very expensive all system components should be energy

efficient. The efficiency of the cabling don’t should exide 1 % and 3 % respectively [2]. Cablecross-section can be calculated as follows:

A = sysV v

I l

⋅

⋅⋅⋅ 2 ρ (6-18)

or A = 2

2

sysV v

P l

⋅

⋅⋅⋅ ρ (6-19)

where: A = cable cross-section [mm2]

ρ = specific resistance [Ω⋅mm2/m]

= 0.0179 Ω⋅mm2/m for copper

l = single cable length [m]

I = rated current through the cable [A]

v = permissible loss in the cable (e.g. 3 % → v = 0.03)


(charge regulator, converter or inverter)

nominal-, peak- or open circuit voltage [V]

P = power of the PV generator or the device [W]

To calculate size of the cable cross-sections, therefore, the cable’s length of the main cable

(feed line) in the concerned application must be known approximately. The cable length (l ) is

doubled in both of equations above due to single- and return cable.

In practice, according to the value resulted from the calculation the next larger standard size is

to be chosen.

For example, cross-section of a 10-m DC main cable, which connects a 120-W PV generator

with 12-V battery and should show maximum 1 % loss, can be determined by applying (6-4):




A = 21201.0

1201020179.0

⋅

⋅⋅⋅= 29.8 mm2

As a result, a cable with 35 mm2 will be installed. If higher loss is acceptable, a cable with 25

mm2 can be applied instead.

If the system voltage is double chosen with 24 V, the cable cross-section can be reduced to a

quarter.

A = 22401.0

1201020179.0

⋅

⋅⋅⋅= 7.46 mm2

Therefore, a next larger standard cable with 10 mm2 will be used.

In addition, the equations explained above are valid in a similar manner for determination of

cable cross-section at the consumer side [2].

6.5 References

[1] Stadler, I.: PV for the world’s villages Network to Catalyse Sustainable Large Scale

Integration of PV in Developing Countries; Final Report - Task 2; Kassel, 1996.

[2] Ladener, H.: Solare Stromversorgung: Grundlagen, Planung, Anwenddung; Freiburg:

ökobuch Verlag, 1996. pg. 153-182.

[3] Kaiser, R.: Sizing photovoltaic systems. In: Fraunhofer Institute for Solar Energy

Systems: Course book for the seminar: Photovoltaic Systems; Freiburg, 1995. pg. 403-440.

[4] Sandia National Laboratories: Stand-Alone Photovoltaic Systems: A Handbook of

Recommended Design Practices; www.sandia.gov/pv/sysd/Wkshts1-5.html, 1988.

[5] METEOTEST; Swiss Federal Office of Energy: METEONORM 4.0: Global Meteorological

Database for Solar Energy and Applied Meteorology; Bern, Switzerland.

[6] Palz, W.; Greif, J., Commission of the European Communities: Europen Solar Radiation

Atlas: Solar Radiation on Horizontal and Inclined Surfaces: Springer, 1996.




7 ECONOMIC CALCULATION

7.1 Introduction

In general, financial methods are based on estimates of future cash flows of a project. There are

two types of financial methods: static and dynamic methods. In contrast to static methods,

dynamic methods consider the time when a cash flow occurs through a discount factor. That is,

cash flows are more valuable the sooner they occur. The literature [1] provides a description of

the most common static and dynamic procedures for financial evaluation of investment projects

in energy supply.

Among different financial methods, the dynamic annuity method has been chosen as most

appropriate to evaluate different alternatives for remote area power supply in practice. It

provides a good overview of the parameters, which are taken into consideration and the results,

and is precise enough for feasibility studies.

7.2 Annuity Method for Investment Decisions

The idea behind the annuity method is to generate equivalent uniform series of payment, i.e.

the annuities, which correspond to the average annual cash flows. The annuity is calculated as

described in the equation (7-1).

a = ( )

( ) 1i1

i1i NPV

n

n

−+

+⋅⋅ (7-1)

where: a = annuity [currency]

NPV = net present value [currency]

i = fictitious interest [1]

n = planning horizon [a]

The annuity factor, representing the factor, which is multiplied by the net present value in order

to obtain the annuity, is listed in Table 7-1 for typical values for fictitious interest and planning

horizon. To calculate the net present value, one considers the series of payment throughout the

planning horizon. Cash inflows and cash outflows may vary in value and time. All cash flows arediscounted to the point of time before the investment in order to obtain the present value.

Discount factor is the fictitious interest, which is in practice mostly considered to lie in the

range of 5 % to 10 % for investments in rural electrification.

n = 5 n = 10 n = 15 n = 20 n = 25

i = 5 23.10 12.95 9.63 8.02 7.10

i = 8 25.05 14.90 11.68 10.19 9.37

i = 10 26.38 16.27 13.15 11.75 11.02

i = 20 33.44 23.85 21.39 20.54 20.21

Table 7-1: Annuity factor for typical values for fictitious interest i and planning horizon n




The net present value is calculated as the sum of all present values of the net cash flows as

shown in the equation (7-2).

In case that the annual cash flows remain equal, the annual net cash flow equals the annuity

and can be directly used in the annuity calculation.

For the example of photovoltaic power supply, there is often only one investment at the

beginning of the planning horizon whereas all other cash flows consist of uniform payments

such as annual fuel cost or maintenance cost. In this case, one adds the annuity of the

investment, i.e. the investment transformed into average annual cost, directly to all other

annual cost in order to obtain the overall annual cost of the project. The net present value of

the investment equals its value at the time of investment, because the investment takes place at

the beginning of the planning horizon (t = 0).

NPV = ( ) t n

0t

t i1 NCF −

=

+∑ (7-2)

where: NPV = net present value [currency]

NCF t = net cash flow at time t [currency]

t = time of cash flow

i = fictitious interest [1]

n = planning horizon [a]

7.3 Scenario Technique

Scenario technique addresses the problem that future cash flows cannot be predicted precisely

over a period of 20 years. By establishing different scenarios, it is possible to project different

future developments of relevant parameters, e.g. the fictitious interest and lifetimes of system

components.

In this work, a PV/Diesel hybrid system is designed for a village according to certain daily

energy demand. Specific energy cost of the system is then calculated by means of annuity

method. Five scenarios will be established with regard to variation of daily energy demands in

order to find out how specific energy cost depends on daily energy demand. In addition,

variation of load profiles (characteristics of load) will also be considered.

7.4 Economic Calculation for the PV/Diesel Hybrid System

The annuity method described in the previous topic will be applied to calculate the economic

efficiency of a PV-Diesel-Battery System. Values are based on a case study for a village in

Petchabun, Thailand. Result is a specific energy cost [€/kWh] generated by the system at a

given application, i.e. a given energy demand by the users and a given irradiation at the

location.

The calculation will consider investment costs for different system components with their

specific lifetimes as well as a rate for planning and installation.




As an example, Figure 7-1 shows a configuration of a system, which is sized for 50-kWh/d

energy demand with the mixed load profile presented in Figure 7-6.

Figure 7-1: Configuration of the system (Source: Kassel University)

The system consists of 4 subsystems as follows:

1. 3 × PV generator (10 kWp)

2. 1 × Diesel generator (6.6 kW)

3. 2 × Battery Inverter (6.6 kW)

4. 1 × Battery Storage (100 kWh)

Accordingly, investment costs of the system include:

1. PV generator

2. Diesel generator

3. Battery Inverter

4. Battery Storage

5. Additional components, i.e. Balance of System Components (BOS)

6. Planning and Installation

Descriptions of the investment costs are presented in Figure 7-2 and Table 7-2.

CustomerConsumer

Diesel-Generator

BatteryStorage

PV-Generator

Counter

CounterM

AC – Bus

EMS

G

EIB – Bus

SMA – Bus

… … … CustomerConsumer

Diesel-Generator

BatteryStorage

PV-Generator

Counter

CounterCounterMM

AC – Bus

EMSEMS

G

EIB – Bus

SMA – Bus

… … …




Figure 7-2: Proportion of the system investment costs (Source: Kassel University)

Component / Size Price [€]

PV generators / 10 kWp 49,704.25

Diesel generator/ 6.6 kW 8,667.50

Battery Inverters / 6.6 kW 7,149.00

Batteries / 100 kWh 14,355.00Addition components 3,256.00

Planning and Installation 14,598.75

Total 97,730.50

Table 7-2: Investment costs of system components (Source: Kassel University)

Values for this investment are based on a company quotation in January 1999 and on expert

experiences. For each individual part of the investment cost, the annuity is calculated as

described in the equation (7-1), taking into consideration their individual life times n and the

fictitious interest i as discount rate.

In this work, the fictitious interest rate is set to 5 % based on experiences in such investments

in former projects. The planning horizon for the whole project is set to 20 years.

Annuity factors and annuities for above investments are given in Table 7-3 and

Figure 7-3. The annuities refer to sum of capital- and operation costs, which

correspond to levelized investment costs, i.e. the investment is transformed

into average annual payment series.




Component / Size Lifetime [a] Annuity factor [%] Annuity [€]

PV generators / 10 kWp 20 8.02 4,288.71

Diesel generator/ 6.6 kW 11 12.07 4,104.68

Island Inverters / 6.6 kW 10 12.95 1,071.33

Batteries / 100 kWh 8 15.16 2,251.76

Addition components 10 12.95 1,006.36

Planning and Installation dep. on sub-sys. dep. on sub-sys. 1,457.96

Total annuity - - 14,180.80

Table 7-3: Annuity factors and annuities (50-kWh/d mixed load profile) (Source: Kassel University)

Figure 7-3: Proportion of the system capital- and operation costs (Source: Kassel University)

To summarise, total annual cost includes total annuity. The energy cost per kWh

results of the division of total annual cost by annual energy demand (cf. equation 7-3).

c el =

demand

total

E

A(7-3)

where: c el = specific energy cost [currency/kWh]

Atotal = total annuity [currency]

E demand = energy demand [kWh]




Table 7-4 presents results of above calculations. Specific energy cost of above system at the

selected location results as 0.78 €/kWh.

Parameter Value Unit

Total annuity of investment costs 14,181.80 €

Annual energy demand 18,250.00 kWh

Specific energy cost 0.78 €/kWh

Table 7-4: Specific energy cost [€/kWh]

In order to evaluate the sized system a sensitivity study is made to look how the specific energy

cost depends on energy demand as well as characteristics of loads.

Variation of energy demand is taken into consideration. Whereas the energy demand of the

example above is occurred during the day as well as at night, namely mixed load profile (Fig. 7-

6), the case that energy demand mainly occurs at night, that is to say night load profile (Fig. 7-6), will be now considered. Results are different specific energy costs as presented in Table 7-

5, Figure 7-4 and Figure 7-5.

Daily energy demand [kWh/d]Load profile

30 40 45 50 60

Mixed load profile 1.00 0.81 0.78 0.78 0.82

Night load profile 1.02 0.89 0.88 0.89 0.90

Table 7-5: Specific energy costs [€/kWh] according to variation of daily

energy demands and load profiles (Source: Kassel University)

As shown in Figure 7-4 and Figure 7-5 the specific energy cost of the system can be described

with the sum of the specific energy costs regarding individual system components.

According that planning horizon of the PV generator is constant of 20 years independent on

energy demand. Therefore, its capital cost is always constant. However, regarding the equation

(7-3), higher energy demand results in reduction of its specific energy cost. Besides, due to the

fact that the PV generator requires very low maintenance, its operation cost is therefore very

low. With the same reason to its capital cost, the specific energy cost corresponding to its

operation cost decreases with increasing energy demand.




Figure 7-4: Specific energy costs for mixed load profile (Source: Kassel University)

Figure 7-5: Specific energy costs for night load profile (Source: Kassel University)

Contrarily, higher energy demand results basically in more frequently running as well as longer

run time of the diesel generator. Consequently, its lifetime is shorter resulting in higher annuity

factor and therefore higher capital cost.

However, in case of 30-kWh/d energy demand the capital cost of the diesel generator is higher

than that of higher daily energy demand. It is because its lifetime in this case is 20 years but

the energy demand is 30 kWh/d comparing to the case of 40-kWh/d energy demand, with




which the lifetime is also 20 years but with higher demand. This results in the same annuity

factor and therefore the same capital cost but higher the specific energy cost.

Regarding more energy demand the diesel generator runs more frequently and longer in order

to supply load as well as to charge the battery by night (especially in case of night load profile).

Accordingly, the diesel generator is also more frequently operated under partial load condition.As a result, more fuel and maintenance are required, which has higher operation cost as a

consequence.

As obviously seen in the Figure 7-4 and Figure 7-5, with increasing energy demand the specific

energy cost of the operation cost of the diesel generator takes ever bigger part in the specific

energy cost of the system for both load profiles and takes finally the biggest part in case of 60-

kWh/d energy consumption.

This study is executed under a condition that a fuel price including all relevant costs is constant

at 1 €/kWh for all study cases. When more fuels are required, then the fuel price will play a very

big role in the specific energy cost.

If the fuel price in the future is uncertain or seems to be more expensive, it should be realized

that as the energy demand increases, it will come to the point where the system is not

economical anymore to supply the load. For this reason, it would be a good solution to add

more components such as PV generators into the system in order to compensate more fuel

demand.

Battery inverter, which is coupled with the battery, has the constant planning horizon of 10

years independent on energy demand. It is because how often the battery is charged or

discharged has no effect on the inverter’s lifetime. Therefore, its capital cost is always constant.However, higher energy demand results in reduction of its specific energy cost.

Due to the fact that lifetime of the battery depends strongly on its operation condition.

Particularly in case of the Night load profile, the energy demand during the day is low so that

the surplus energy generated from PV genertor is delivered to the batteries (charging) and is

recalled at night to supply load (discharge). Higher energy demand results that the battery is

charged and discharged more frequently. In consequence, the battery lifetime is shortened and

therefore capital cost higher.

For the same energy demand, whereas the operation costs of PV generator, Battery Inverters

and additional components are equivalent for both load profiles, specific energy cost in case of night load profile is expensive than that of mixed load profile. This is due to higher operation

cost of diesel generator because the diesel generator must be switched on more frequently at

night while there is no sunlight. Accordingly the battery is more frequently charged and

discharged and therefore this results also in higher operation cost of the battery.

The variation of energy demand and different load profile results in different specific energy

costs as shown and described before. The results in Figure 7-4 and Figure 7-5 show the trend

of the specific energy cost as a function of the energy demand. This study can show the users

which energy demand results in lowest specific energy cost for each load profile. Anyway, if the

results do not please the users, a new system configuration should be selected. Afterwards theeconomic calculation could be executed in the same manner.



7.5 References

[1] Finck, H.; Oelert, G.: A guide to the financial evaluation of investment projects in

energy supply . Deutsche Gesellschaft für Technische Zusammenarbeit (GTZ) GmbH,

Eschborn, ISBN 3-88085-250-2.

photovoltaic systems technology ss 2003

Documents