Photo Voltaic Systems Technology - Kininberg - 2003 (Universi

Photovoltaic Systems Technology

SS 2003

Universität Kassel Rationelle Energiewandlung / Franz Kininger Wilhelmshöher Alle 73 34121 Kassel Germany

[email protected]

www.uni-kassel.de/re

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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

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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

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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

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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].

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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].

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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).

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

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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)

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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 in the 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].

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2.8%

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0.3%

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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%

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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 recoverable reserves of fossil fuels could be sufficient with oil and natural gas for 40-60 years, with coal

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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 new techniques, 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].

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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 E0 = today energy consumption a = number of years measured starting from E0

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)

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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)

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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.

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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

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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

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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 from experiences with their increasing application [11].

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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.

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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

12 −

⋅ Tcec

λλ (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)

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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

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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

surfaceSun surfaceSun 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

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Thus, 0S = orbit Earth

surfaceSun surfaceSun A

A q ⋅

•

=

( )( )2

orbit Earth

2Sun4

surfaceSun R4R4

Tπ

πσ ⋅⋅

= ( )

10149106955762105.67

2

9

648-

××⋅⋅×

= 1360 W/m2

Since REarth orbit is not fully constant, S0 changes slightly throughout a year (1300 W/m2 < S0 < 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.

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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

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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 short distance 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 (blue components).

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 = φcos

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.

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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 Sun without 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

-21-


Figure 2-5: Total solar radiation on a surface

Location Albedo [%]

Ocean 2 - 10

Forest 6 - 18

Grass 7 - 25

Soil 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

Diffuse

Albedo

-22-


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

Ave

rage

dai

ly g

loba

l rad

iatio

n [

kWh/

m2 ]

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. In Central 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].

-23-


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/m2a (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

Ave

rage

dai

ly g

loba

l rad

iatio

n [k

Wh/

m2 ]

Fortaleza - Brazil Kassel - Germany Pitsanulok - Thailand

-24-t 0049- 561 804 6201i www.uni-kassel.de/re

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?REarth2). However, the Earth reradiates energy with its whole surface area (= 4π?REarth2). 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 other 7 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 Earth radiates less energy than the Sun and the energy has longer wavelengths (Fig. 2-10).

10113

152

180

Sensible heat

12

longwave surface radiation

Counter-radiation

Latentheat

33

Absorbed by clouds

Absorbed by gases

26

7

40

M l l

Cl d

7 35 10 175 PW

90

Total radiation to space 70 %T t l ti 30 % Incoming sola r

di ti 100 %

Surfaceabsorption

L d & O

Thermal absorption and emissionin the atmosphere

-25-


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 the atmospheric 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]

Sun-

Spec

tral

Irra

dian

ce

[W/m

2 µm

]

0

25

50

75

100

125

150

175

200

225

Eart

h-Sp

ectr

al Ir

radi

ance

[W

/m2 µm

]

5762 K 288 K

-26-


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 our climate 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

-27-


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 the global 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)

-28-


Figure 2-12: Pyrheliometer and Solar tracker

Figure 2-13: Shadow band

Solar Tracker

Pyrheliometer

-29-


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 measures the reflected radiation of the ground.

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

-30-


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 by Solar 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.

-31-


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 can penetrate into the cell. The surface is normally provided with an antireflection coating to keep the losses from reflection as small as possible.

-32-


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 this blank 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 gridfor current collection

Metallized back surface

p-type material

n-type material

≈ 300 µm

≈ 0.2 µm

Sunlight

Metal gridfor current collection

Metallized back surface

p-type material

n-type material

≈ 300 µm

-33-


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 electron

hole

P

Si

Si

SiSi

Si Si

SiSi

B

Si

Si

SiSi

Si Si

SiSi

(b)(a)

free electron

hole

PP

SiSi

SiSi

SiSiSiSi

SiSi SiSi

SiSiSiSi

BB

SiSi

SiSi

SiSiSiSi

SiSi SiSi

SiSiSiSi

-34-


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 VD, which is called diffusion voltage. It is situated in the order of magnitude of 0.8 eV. This electrical 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

kTqV expI0 (3-1)

where: ID = diode current [A] q = magnitude of the electron charge [1.6 ⋅ 10-19 As] V = applied voltage [V]:

holeselectrons

Cha

rge-

carr

ier c

once

ntra

tion

stationaryelectrical charges

electrons

holesDiffusion currentField current

Diffusion current

Field current

n-region p-regionp-n junction x

space-charge zone

holeselectrons

Cha

rge-

carr

ier c

once

ntra

tion

stationaryelectrical charges

electrons

holesDiffusion currentField current

Diffusion current

Field current

n-region p-regionp-n junction x

space-charge zone

-35-


plus = forward bias, minus = reverse bias k = Boltzmann’s constant [8.65 ⋅ 10-5 eV/K] T = absolute temperature [K]

The quantity 0I 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 charge carriers 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].

-36-


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

Ahole electron

solar radiation

emitter, n-type

base, p-type

space-charge zone

electric field

Ahole electron

solar radiation

emitter, n-type

base, p-type

space-charge zone

electric field

-37-


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 Cell

As 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 (Iph), 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 =

−⋅− 1eII kT

qV

0ph (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):

Iload

V load R load

IcellIph

ID

VD

IloadIload

V loadV load R loadR load

IcellIcellIphIph

IDID

VDVD

-38-


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 (Rload = 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 ID flows (point 1 in Figure 3-6) therefore the entire photocurrent Iph generated from the radiation flows to the output. Thus the cell current has its maximum at this point with the value Icell and refers to the so-called short-circuit current Isc.

Isc = Icell = Iph (3-3)

Iph IscIcell

R load = 0

ID = 0

IphIph IscIscIcellIcell

R load = 0R load = 0

ID = 0ID = 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]

Cur

rent

I [A

] Photo Current Diode Current Cell Current

I sc

V oc

1

1

2

2

3

3

4

4

I D

-39-


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, a rapidly 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 (Icell = 0) and thus the entire photocurrent flows through the internal diode (point 4 in Figure 3-6). The open-circuit voltage Voc can be therefore derived again from (3-2).

Voc =

+⋅ 1

II

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).

Icell = 0

V oc

Iph

ID

VD R load = ∝

Icell = 0Icell = 0

V ocV oc

IphIph

IDID

VDVD R load = ∝R load = ∝

-40-


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 is situated near the bend of the I-V characteristic curve. The corresponding values of VMMP and IMMP can be estimated from Voc and Isc as follows [2]:

In addition, the quantity

FF = ( )

( )scoc

MPP MPP

I VI 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]

Cur

rent

and

Pow

er...

Cell Current [A] Cell Power [W]

V MPP

I MPP

MPP

-41-


Thus the efficiency of the solar cell, which refers to the ratio of the output electrical energy to the input solar radiation (Pin), is defined by the following relation.

η = in

scoc

PFFIV ⋅⋅

(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- (Rs) and parallel resistance (Rp), 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]

Icell = ( )

p

scellloadRIVTk

q

0ph RRIV

1eII scellload ⋅+−

−⋅−

⋅+⋅⋅ (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.

Iph Iload

R p

R s

Icell

ID

VD Vload R load

IphIph IloadIload

R pR p

R sR s

IcellIcell

IDID

VDVD VloadVload R loadR load

-42-


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

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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]

Cur

rent

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]

Cur

rent

I [A

]

500 Ohm 5.00 Ohm 0.50 Ohm 0.20 Ohm 0.10 Ohm

-43-


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 reflection losses 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 I0 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].

-44-


3.7 Effect of Irradiation

According to the relation of the photocurrent to the irradiation the short-circuit current Isc 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 the characteristic curve, open-circuit voltage Voc 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), Voc 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]

Cur

rent

I [A

]

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)

-45-


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 increase slightly. However, this is a small effect (Fig. 3-14):

As Voc 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], I0 is given by

I0 =

+

−

pp

p

nn

ngcv p

LnL

kTE

exp N N qττ

(3-9)

Nv, Nc are the effective densities of states in the valence and conduction band, the band gap energy Eg and Ln, Lp, nn, pp, τn, τp are the diffusion lengths, the densities and the lifetimes of electrons and holes respectively. With (3-9) we can obtain from (3-4), assuming Iph >> I0:

Voc =

+

⋅⋅−

pp

p

nn

ncv

ph

g

pL

nL

N N q I1 ln

qkT

qE

ττ (3-10)

Therefore Voc 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 than the 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

-46-


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 Kennlinie

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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]

Cur

rent

I [A

]

0 °C 25 °C 50 °C 75 °C 100 °C

-47-


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-voltage characteristic 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.

Iph1

Iload

ID1

VD1 Vload R load

IPV

Iph2 ID2

VD2

Iph3 ID3

VD3

Iph1Iph1

IloadIload

ID1ID1

VD1VD1 VloadVload R loadR load

IPVIPV

Iph2Iph2 ID2ID2

VD2VD2

Iph3Iph3 ID3ID3

VD3VD3

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]

Cur

rent

I [A

]

Three Cells Two Cells One Cell

-48-


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 voltage causes 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 three of 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.

Iph1 ID1

VD1

Iph2 ID2

VD2 Voc

ID3≈ 0Iph1Iph1 ID1ID1

VD1VD1

Iph2Iph2 ID2ID2

VD2VD2 VocVoc

ID3≈ 0ID3≈ 0

-49-


Figure 3-19: Series connection of solar cells

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

Iph3

VD3

R load

IPV

VD2

VD1

Iph1

Iph2

ID1

ID3

ID2

Iload

V load

Iph3Iph3

VD3VD3

R loadR load

IPVIPV

VD2VD2

VD1VD1

Iph1Iph1

Iph2Iph2

ID1ID1

ID3ID3

ID2ID2

IloadIload

V loadV 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]

Cur

rent

I [A

]


-50-


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.

VD2

VD1

Iph1

Iph2

ID1

ID2

VD1 + VD2

IPV = 0

VD2VD2

VD1VD1

Iph1Iph1

Iph2Iph2

ID1ID1

ID2ID2

VD1 + VD2VD1 + VD2

IPV = 0IPV = 0

-51-


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

VD2

VD1

Iph1

Iph2

ID1

ID2

BypassDiode

BypassDiode

BypassDiode

Icell 1 = Icell 2

VD2VD2

VD1VD1

Iph1Iph1

Iph2Iph2

ID1ID1

ID2ID2

BypassDiodeBypassDiode



Icell 1 = Icell 2Icell 1 = Icell 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]

Cur

rent

I .[A

]

Three Cells Two Cells One Cell Shading with bypass

-52-


In case that the third cell is partly shaded (Fig. 3-24), e.g. 20 % irradiation incident on the cell (Fig. 3-24), it can produce approx. 20 % of the photocurrent produced by the other two cells (see section 3-7). Regarding series connection, although the other two cells can produce their 100 % photocurrents, the amount of current flowing in the circuit can only equal the amount of the current produced by the third cell (Fig. 3-26). The rest of the current produced by the first cell will flow into its own diode (this is also applied to the second cell). In addition, the diode of the third cell is reverse biased by the voltage generated by the other two cells. Therefore, power dissipation to the third cell arises.

Figure 3-24: Series connection – one cell is partly shaded.

Such power dissipation refers to the so-called hot spot: an intolerable effect, which leads to breakdown in the cell p-n junction and in turn to destructions, i.e. cell or glass cracking or melting of solder. However, this can also happen in case of mismatched cells within the module due to manufacturing differences, degradation (cracked) or even unequal illuminated cells, which then result in different outputs.

By means of the bypass diodes the problems of mismatched cells and hot spots can be avoided. As shown in Figure 3-25, after the bypass of the third cell conducts, the current flowing through it is equal to the different amount between the circuit current and the current produced by the third cell.

The I-V characteristic curve of this case is indicated in Figure 3-26.

VD2

VD1

Iph1

Iph2

ID1

ID2

Icell 1 = Icell 2 = Iph 3

Iph3

20 %

VD1 + VD2

VD2VD2

VD1VD1

Iph1Iph1

Iph2Iph2

ID1ID1

ID2ID2

Icell 1 = Icell 2 = Iph 3Icell 1 = Icell 2 = Iph 3

Iph3Iph3

20 %20 %

VD1 + VD2VD1 + VD2

-53-


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

VD2

VD1

Iph1

Iph2

Iph3

20 %

ID1

ID2

BypassDiode

BypassDiode

BypassDiode

Icell 1 = Icell 2

VD2VD2

VD1VD1

Iph1Iph1

Iph2Iph2

Iph3Iph3

20 %20 %

ID1ID1

ID2ID2




Icell 1 = Icell 2Icell 1 = Icell 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]

Cur

rent

I .[A

]


Shading with bypass Shading without bypass

-54-


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/m2

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].

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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]

Cur

rent

I [A

]

0

10

20

30

40

50

60

70

80

Pow

er P

[W]

Current Power

-55-


Figure 3-28: Power curves with partial shading (Source: Kassel University)

As an example of shading, a cigarette vending machine powered by solar energy is presented in Figure 3-29.

Figure 3-29: Cigarette vending machine shaded by sunshade of a shop; Friedrich-Ebert Str. corner Goethe Str., Kassel (Photo: Kassel University)

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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]

Cur

rent

I [A

]

0

10

20

30

40

50

60

70

80

Pow

er P

[W]

Current without bypass Current with bypass Power with bypass

-56-


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 the module.

Figure 3-31: Dirt on the PV module due to birds’ droppings supply for a glass showcase at Karlsplatz, Kassel (Photo: Kassel University)

-57-


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.


[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.

-58-


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.

ID

IPV

VPV

IPV

VPVVD

Iph

IDID

IPVIPV

VPVVPV

IPVIPV

VPVVPVVDVD

IphIph

-59-


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 for different irradiations are represented for different load curves in Figure 4-3. The load curve II

V load

IPV

VPV

PVGenerator

Iload

R loadV loadV load

IPVIPV

VPVVPV

PVGenerator

IloadIload

R loadR load

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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]

Cur

rent

I [A

]

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

-60-


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 internal losses PL 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.

Vload

IPV

VPV

DC/DC Converter

Iload

Rload

PloadPPV

PVGenerator

PL

VloadVload

IPVIPV

VPVVPV

DC/DC Converter

IloadIload

RloadRload

PloadPloadPPVPPV

PVGenerator

PLPL

-61-


a) Step-down converter (Buck converter)

With the help of these converters the input DC voltage, which is e.g. generated by the PV generator (VPV) as presented in Figure 4-5a, can be stepped down:

Figure 4-5a: Equivalent circuit diagram of a step-down converter

If the switch S1 is turned on at t0, the diode D is reverse biased and a circuit current arises (Fig. 4-5b). The current (= iL) does not increases immediately but rather rises with a rate imposed by the inductor L:

dtdiL =

LV V loadPV −

(4-1)

Meanwhile the inductor stores energy in magnetic form. If S1 is turned off after t = t1, the load is separated from the supplied system. The current is however maintained by the stored energy in the inductor L and flows through the free-wheeling diode instead (Fig. 4-6c). According to (4-1), regardless of dropped voltage across the diode, the current falls down however due to the following equation:

dtdiL =

LV load− (4-2)

IPV

VPV D

S1

Rload

C2

L iL

C1 Vload

IPVIPV

VPVVPV D

S1S1

RloadRload

C2C2

L iLiL

C1C1 VloadVload

-62-


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 (VPV). In principle, S1 is turned on and off with a switching frequency (that is to say: with “ton” and “toff”). With regard to Ohm’s law the behaviour of the load voltage can be obtained from the load current (= iL). 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 (Vload) is lower than VPV. 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 iL

VPV

S1

C2C1 VloadD

L iLiL

VPVVPV

S1S1

C2C2C1C1 VloadVload

D

L iLIPV

VPV

S1

C2C1 VloadD

L iLiLIPVIPV

VPVVPV

S1S1

C2C2C1C1 VloadVload

-63-


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 = ton + toff :

Vload = Tt 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 VPV is stepped up. At a steady state as S1 is still “off”, Vload is equal to the VPV, regardless of a voltage across diode.

VPV

tton toff

t1t0

Vload

VPV

tton toff

t1t0

Vload

IPV

VPV

Rload

C1

L iL

S 1

D

Vload

IPVIPV

VPVVPV

RloadRload

C1C1

L iLiL

S 1S 1

D

VloadVload

-64-


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 (= iL) flows through the inductor L and S1 and rises according to the following equatsion:

dtdiL =

LV 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 VPV, which lie then across the load. iL flows through the inductor and further to the load. Thereby it falls down gradually because Vload > VPV:

dtdiL =

LV V loadPV −

(4-5)

L iL

S 1

D

C1 Vload

IPV

VPV

L iLiL

S 1S 1

D

C1C1 VloadVload

IPVIPV

VPVVPV

Rload

L

iL

S 1

D

C1 Vload

IPV

VPV

RloadRload

L

iLiL

S 1S 1

D

C1C1 VloadVload

IPVIPV

VPVVPV

-65-


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 = PVoff

V tT

(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 Rload 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, Vload has obviously an opposite polarity to VPV. 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 VPV and C2 smoothes Vload. In conclusion the amplitude of Vload can be either lower or higher than VPV depending on the adjusted ton and consequently toff [8]:

Vload = − tt

off

on VPV (4-7)

VPV

tton toff

t0

Vload

VPV

tton toff

t0

Vload

-66-


Figure 4-7a: Equivalent circuit diagram of a step-down/step-up converter

Figure 4-7b: Step-down/step-up converter during “on” state

IPV

VPV L

Rload

D iL

C2C1

S1

Vload

IPVIPV

VPVVPV L

RloadRload

D iLiL

C2C2C1C1

S1S1

VloadVload

IPV

VPV L

Rload

D

iL

C2C1

S1

Vload

IPVIPV

VPVVPV L

RloadRload

D

iLiL

C2C2C1C1

S1S1

VloadVload

-67-


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 this irradiation the PV module could deliver the power P1 represented by the white rectangle if it

VPV L Vload

D

iL

C2C1

S1

VPVVPV L VloadVload

D

iLiL

C2C2C1C1

S1S1

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]

Cur

rent

I [A

]

1000 W/m² 600 W/m² 200 W/m² Load

P 1

P 2

P' 1

-68-


were operated with the voltage of MPP. The matching converter causes that these input MPP voltage and current are transferred to the output values on the load curve, whereby in the loss-free ideal case both powers (areas) P1 and P2 are equal large.

If the described transformation as explained in Figure 4-8 is executed for different irradiations, thus it can be seen that in this example the gain with the help of the matching converter is very large for small irradiations. However, according to the interpretation the influence become smaller for higher irradiations and the total balance including the losses in the converter could also become worse than that of a direct coupling. However, efficiency of > 95 % can be possibly achieved with suitable structure so that the gain predominates altogether clearly.

4.2.2 Maximum Power Point Tracker (MPPT)

The position of the points of maximum power on the PV generator characteristic depends strongly on the irradiation and the cells temperature. In principle this makes a continuous tracking of the working point voltage (MPP tracking) necessary for achieving of a maximum energy yield. The additional energy gains, which can be obtained by this way in comparison to a (correctly selected) certain voltage, are however rather overestimated: detailed examinations, with which both during shorter periods (e.g. one winter month) and longer period (many years) the energy yields were compared with and without MPPT, resulted for an ideal, loss-free MPPT in a gain of 3…5 %. This statement applies also to the initially represented direct coupling of a correctly dimensioned PV generator/battery combination. A tracking of the MPP is therefore only meaningful if components for energy processing e.g. network inverters or DC/DC converter with the possibility of a working point adjustment are available and the tracking of the working point does not bring additional energy losses and only small addition costs.

The development of MPPT’s represents a technically charming theme, so that in the course of the time a great deal of procedures was developed, from which some are to be described here.

a) Indirect MPPT

This type of MPPT’s uses the connection between measured variables, which can be easily determined, and the approximate position of the MPP.

These procedures count for example:

1) Season-dependent tracking (switching) of the PV generator voltage. This measure provides only a small increase in energy in comparison to a certain adjusted voltage for whole year.

2) Temperature-controlled working point voltage. Here the module temperature is determined by a temperature sensor and adjusted according to the working point voltage.

-69-


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 actually measured 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 search direction 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].

-70-


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

-71-


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

+ - + - +

convertto

PbSO4PbSO4

Platesurface

converted

--

PbPb

Pb + 2H2SO4 + PbO2 → 2PbSO4 + 2H2O

PbO2PbO2

H2SO4H2SO4

++ -- ++ -- ++

convertto

convertto

PbSO4PbSO4PbSO4PbSO4

Platesurface

converted

Platesurface

converted

-72-


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

+ - + -

+

convertto

PbO2Pb

Platesurface

PbSO4 PbSO4

Source-

+

+Source-+

Source-

Pb + 2H2SO4 + PbO2 ← 2PbSO4 + 2H2O

--

PbPb PbO2PbO2

H2SO4H2SO4

++ -- ++ --

++

convertto

convertto

PbO2PbO2PbPb

PlatesurfacePlate

surfacePbSO4PbSO4 PbSO4PbSO4

SourceSource--

++

++SourceSource--++

SourceSource--

Pb + 2H2SO4 + PbO2 ← 2PbSO4 + 2H2O

DiffusionPb

2H2O

H2SO4

2e-

2H+

PbSO4

2H+

2e-

PbO2

Anode

H2SO4

Cathode

PbSO4

H2SO4 H2SO4

DiffusionPbPb

2H2O2H2O

H2SO4H2SO4

2e-

2H+

PbSO4PbSO4

2H+

2e-

PbO2PbO2

Anode

H2SO4H2SO4

Cathode

PbSO4PbSO4

H2SO4H2SO4 H2SO4H2SO4

-73-


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 (VE) in series with an internal resistor (Rin) (Fig. 4-13). It must be noted here that this configuration can describe only a current state because the magnitude of VE and Rin 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 VB will be different from the voltage that would be measured at those terminals while the battery were at rest or under open-circuit condition (VB = VE). When current is drawn from the battery, the voltage will be lower than VE. When current is flowing into the battery, the terminal voltage will be higher than VE. 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, to specify the state of the battery by the battery voltage, discharge current should be also measured.

VB

Vin

IBRin

VE RloadVBVB

Vin

IBIBRinRin

VEVE RloadRload

-74-


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 Vin.

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 (Vp) whereas a voltage drop in the grid and in the electrolyte is represented by a resistance RΩ.

For the quasi-static processes, a capacitor Cp, which is connected in parallel to a resistor Rp, 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]

Cur

rent

I [A

]

High SOC Medium SOC Low SOC Load I Load II

V in

-75-


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 RS (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 RS 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: VE = equilibrium voltage [V] Vk = 0.84…0.88 (dependent on battery types [4])

For example, regarding a battery with H2SO4 concentration 1.28 g/cm3 and Vk = 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 as discharge voltage threshold. Falling below this threshold is called deep discharge, with which

RS

IS

I

VB

IB

RloadVE

Vp

Rp

RΩCp

RS

ISIS

II

VBVB

IBIB

RloadRloadVEVE

Vp

RpRp

RΩRΩCpCp

-76-


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 compulsory disconnected 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 increases according 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 and therefore the storage efficiency of the battery is made worse unnecessarily.

-77-


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 RG (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 RG 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.

RS

IS

VB

RG

VG

IPV

VE

Vin

Rin

RS

ISIS

VBVB

RG

VG

IPVIPV

VEVE

Vin

RinRin

-78-


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 [%]

Tem

pera

ture

[°C

]

slushy until hard

- 80°

- 60°

- 40°

- 20°

0°

0 20 40 60 80 100

State of charge [%]

Tem

pera

ture

[°C

]

slushy until hard

Electrode(Pb/PbO2)

Electrolyte(H2SO4)

Electrode(Pb/PbO2)

Electrolyte(H2SO4)

Electrode(Pb/PbO2)

Electrolyte(H2SO4)

Electrode(Pb/PbO2)

Electrolyte(H2SO4)

-79-


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 this average 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]

Dep

th o

f dis

char

ge [%

]

100

100

Industrial batteries

Consumer (starter) batteries

0

20

40

60

80

0 1000 2000 3000 4000 5000

Cycle life [cycles]

Dep

th o

f dis

char

ge [%

]

100

100

Industrial batteries

Consumer (starter) batteries

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The so-called rated battery capacity refers to the capacity of the battery under given standard conditions: it is common practical to define the rated capacity at 20 °C by discharging the battery with a rated battery current (I10), which refers usually to a constant current, with which the battery will be completely discharged in 10 hours. Some battery manufacturers indicate the 100-hour discharge capacity for batteries intended for PV applications. When comparing such capacity, it should be remembered that, for a given battery, the 100-hour capacity is always at least 30 % higher than the 10-hour capacity [1, 7].

Besides, battery capacity is also affected by the temperature: it falls by about 1 % per degree below about 20 °C. Moreover, extreme high temperatures accelerate aging, self-discharge and electrolyte usage [5].

4.3.5 Requirements for the solar batteries

Since battery maintenance can be a major limitation for PV stand-alone systems. Typical requirements for the battery to be used for long-term storages are:

h) low specific kWh-cost, i.e. the stored kWh during the whole life of the battery

i) long lifetime

j) high overall efficiency

k) very low self-discharge

l) low maintenance cost

m) easy installation and operation

n) (high power)

Specific kWh-cost (DM/kWhΣ)

Usually it refers to a sum of investment- and operation costs of the battery divided by the stored kWh (kWhΣ) during its whole life. This cost is thus influenced by the battery’s lifetime.

Lifetime

The lifetime of the battery should be long, especially in order to keep the specific kWh-cost and the installation cost low, particularly in remote areas.

Overall efficiency

The overall efficiency (ηΣ) is derived from charge- or coulombic efficiency (ηI) and voltage efficiency (ηV):

ηΣ = ηI ⋅ ηV (4-18)

The coulombic efficiency is usually measured at a constant discharge rate referring to the amount of charge able to be recalled from the battery (QD) relative to the amount put in during

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charging (QC). Self-discharge will affect coulombic efficiency. Furthermore, it is reduced particularly by the secondary reaction during charging, i.e. gassing.

ηI = QD / QC (4-19)

The battery will usually need more charge than was taken out to fill it back up to its starting point. 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 are therefore 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]

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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]

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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

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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 capacity rating 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 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V400 Ah

(4.8 kWh)

12 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V100 Ah

(1.2 kWh)

12 V400 Ah

(4.8 kWh)

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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 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

24 V 200 Ah(4.8 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

24 V 200 Ah(4.8 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

12 V 400 Ah(4.8 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

6 V200 Ah

(1.2 kWh)

12 V 400 Ah(4.8 kWh)

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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).

IB

Battery

V B

IPV

VPV

PVGenerator

IBIB

BatteryBattery

V BV B

IPVIPV

VPVVPV

PVGenerator

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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

VD

IBIph = 0

IB

V BVDVD

IBIBIph = 0Iph = 0

IBIB

V BV 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]...

Cur

rent

I [A

] ...

1000 W/m² 600 W/m² 200 W/m² Min Nom Max

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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 solar cell, 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 the batteries are close to full state of charge, the same problem will not result as the self regulation

IPV

VPV

PVGenerator

Blocking Diode

D IB

Battery

V B

IPVIPV

VPVVPV

PVGenerator

Blocking DiodeBlocking Diode

D IBIB

BatteryBattery

V BV B

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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 system components 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 battery voltage is limited at 2.5 V/cell, subsequently at 2.35 V/cell [3].

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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 used as 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.

S 1

C

ChargeRegulator

IPV

VPV

PVGenerator

IB

Battery

V B

S 1S 1

C

ChargeRegulator

IPVIPV

VPVVPV

PVGenerator

IBIB

BatteryBattery

V BV B

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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 the energy 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.

S 1

ChargeRegulator

C

I Shunt

D IB

Battery

V B

IPV

VPV

PVGenerator

S 1S 1

ChargeRegulator

C

I ShuntI Shunt

D IBIB

BatteryBattery

V BV B

IPVIPV

VPVVPV

PVGenerator

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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, is interrupted (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].

S 1

ChargeRegulator

C

I Shunt

D S 2

RloadBattery

IPV

VPV

PVGenerator

S 1S 1

ChargeRegulator

C

I ShuntI Shunt

D S 2S 2

RloadRloadBattery

IPVIPV

VPVVPV

PVGenerator

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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 selected voltage 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].

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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 most commercial 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 PV system. In consequence, extremely high efficiency not only in the nominal power range but also

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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)

t0

p(t)

v(t)i(t)

t

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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 MPP deviations. 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]

power [W]

MPP

voltage ripple through imperfect storage

voltage [V]

current [A]

power [W]

MPP

voltage ripple through imperfect storage

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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

ACoutput

DCsource

S1S1

S2S2

ACoutput

DCsource

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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 be obtained 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.

ACoutput

DCsource

S1 S3

S2S4

ACoutput

DCsource

S1S1 S3S3

S2S2S4S4

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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 V2 at the output of the step-down converter can be given as:

V2 = V1 ⋅ Tton (4-24)

Where ton 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

C1C1

L1

Battery

S0S0

D

S1S1

S2S2

C1C1C1C1

L1L1

Battery

-100-


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 %.

-101-


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 ⋅ VAC = 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 the AC 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 the fundamental frequency (10 ms for 50 Hz) the switches S1 and S2 are changing their on- and off-state in such a way that the relation

Tt 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

S1 S3

S2AC

output

D1

D4 S4

D3

D2

S1S1 S3S3

S2S2AC

output

D1D1

D4D4 S4S4

D3D3

D2D2

-102-


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 voltage must 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 levelV V

AC voltage AC voltage

t t

DC voltage level DC voltage levelV V

AC voltage AC voltage

t t

-103-


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 V1 and the output voltage V2 becomes:

V2 =

( )

−−⋅+

⋅−

onoff

ononoff

on1

t tt

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

C1R1L1 R2L2

C2 V2V1 S1S1 S2S2

C1C1R1R1L1L1 R2R2L2L2

C2C2 V2V2V1V1

S1

S2

L3

S5

S6

L1

S3

S4

L2

S1S1

S2S2

L3L3

S5S5

S6S6

L1L1

S3S3

S4S4

L2L2

-104-


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

-105-


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 side of 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

-106-


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 inside the 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 have been 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.

-107-


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. The combination 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

-108-


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 power quality. 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 THD in 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

-109-


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 in the 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∼

-110-


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.

-111-


4.7 References

[1] 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. 74.

[2] Sorokin, Alecsei.: Batteries and charge controllers for PV systems. In: Fraunhofer Institute for Solar Energy Systems: Course book for the seminar: 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 Marktentwicklung; Heiderberg: Müller, 1999. pg. 117-131.

[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.


[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.

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[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.

-113-


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 the different 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 requires lower investment cost whereas the demand equals to the potential. An example of this configuration is PV ventilator.

-114-


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

-115-


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), AC consumers 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 PV generator provides power e.g. for the electrical appliances in a house. Surplus energy is fed into

AC consumerPV generator∼

Inverter AC consumerPV generator∼

Inverter

-116-


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 Wp-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

-117-


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

-118-


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 the coupling 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

-119-


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

-120-


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∼

-121-


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

-122-


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

-123-


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)

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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 Marktentwicklung; Heiderberg: Müller, 1999. pg. 108-116.

[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.

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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 withalternatives, 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 withalternatives, 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

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Figure 6-2: Annual global solar radiation on horizontal surfaces in kWh/m2a (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 are listed 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.

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Appliance Power rating

[W]

Daily consumption

[kWh/d]

Annual consumption

[kWh/a]

1 Incandescent bulb 60 0.25 90

1 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 25

1 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 (Eel), which is normally equivalent to the system load (Edemand) and the theoretical output energy (Eth), which is defined as the output energy from the same system under ideal conditions, i.e. Standard Test Conditions (STC):

Edemand ≤ Esupply

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Q = th

el

EE

(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 (Eth) is defined as the energy output, which is produced by a PV array with an area of Aarray, the global radiation Eglob 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: ISTC = 1000 W/m2; TSTC = 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

globpeak I

EP ⋅ (6-4)

According to the equations (6-1) and (6-4) the quality factor can be found out:

Q = STCpeakglob

el IPE

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:

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Ppeak = QE

IE

glob

STCel

⋅⋅

(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 could however 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 Systems

0.1 kWh/a 1 kWh/a 10 kWh/a 100 kWh/a

1 MWh/a 10 MWh/a

PV-Batterie

PV-Diesel-Batterie

Diesel-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 operation costs in PV- and PV hybrid systems. However, experience has indicated that operation cost of

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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 peak power [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]

Bat

tery

cap

acity

CB

[kW

h]

PVsystems

C B

P peak= 10

SHS

PV hybrid

systems

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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 kPV 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 = fSC ⋅ KPV (6-9)

where: Ksystem = absolute cost of PV system [€] fSC = factor of additional system components

The factor of additional system components (fSC) 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 more components 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 fSC are higher (Tab. 6-4).

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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 kWp) (Source: Kassel University)

After the overall investment costs of the chosen system is approximated, the user can be informed 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 (Ppeak).

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Figure 6-5: An example of a realistic relationship between solar potential and energy consumption over the whole year in Petchabun, Thailand (Source: Kassel University)

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 to characterize 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

Irrad

iatio

n [k

Wh/

m²]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

Load

[kW

h/d]

Global radiation-Petchabun Load

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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]

Ener

gy D

eman

d [k

Wh]

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Sola

r Irr

adia

tion

[kW

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

Dai

ly ra

diat

ion

[kW

h/m

²d]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

Load

[kW

h/d]

Global radiation-Petchabun Load

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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 = BWCT

A

DDODTL

ηηη ⋅⋅⋅⋅⋅

(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

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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’s capacity 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 DT 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 the latitude (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].

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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 (Source: Kassel University)

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:

Ppeak = QE

IE

glob

STCel

⋅⋅

(6-12)

where: Ppeak = peak power of the PV array under STC [kWp] Eel = real electric output energy of the system [kWh] ISTC = incident solar radiation under STC [1 kW/m2] Eglob = 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 integrate varied 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

Tilt

Ang

le

0

30

60

90

100 % 95% 90% 85% 80%

WestEast

Horizontal

Vertical

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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 a comfortable 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.

nB, p ≈ ′B

B

C

C (6-12)

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nB, s ≈ B

sys

VV

(6-13)

nB = nB, p ⋅ nB, s (6-14)

where: nB = number of batteries required nB, p = number of batteries in parallel nB, s = number of batteries in series CB = capacity of battery required [Wh] CB’ = capacity of a selected battery [Wh] Vsys = depending on the system component (charge regulator, converter or inverter) nominal-, peak- or open circuit voltage [V] VB = 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

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location and available place complied are also to be considered. To calculate the number of PV modules the following relations could be used:

nPV, m ≈ mPV

aPV

PP

,

, (6-15)

where: nPV, m = estimated number of PV modules PPV, a = nominal power of the PV array [kW] PPV, m = nominal power of the selected PV mudule [kW] To calculate the number of serial connected modules the following formula could be used:

nPV, m, s ≈ mPV

sys

VV

,

(6-16)

where: nPV, m, s = estimated number of PV modules in series Vsys = depending on the system component (charge regulator, converter or inverter) nominal-, peak- or open circuit voltage [V] VPV, 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:

nPV, s, p ≈ smPV

mPV

nn

,,

, (6-17)

where: nPV, s, p = estimated number of PV strings in parallel nPV, m = estimated number of PV modules nPV, 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 cheap type with shorter lifetime and cycling stability. If this question cannot be clearly answered with

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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 be provided 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]. Cable cross-section can be calculated as follows:

A = sysVv

Il⋅

⋅⋅⋅ 2ρ (6-18)

or A = 2

2

sysVvPl

⋅⋅⋅⋅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) Vsys = depending on the system component (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):

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A = 21201.01201020179.0

⋅⋅⋅⋅

= 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 = 22401.01201020179.0

⋅⋅⋅⋅

= 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.

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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

i1iNPV 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 are discounted 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

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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 = ( ) tn

0tt i1 NCF −

=

+∑ (7-2)

where: NPV = net present value [currency] NCFt = 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.

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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

… … …

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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 14,355.00

Addition 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.

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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).

cel = demand

total

EA (7-3)

where: cel = specific energy cost [currency/kWh] Atotal = total annuity [currency] Edemand = energy demand [kWh]

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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.

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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

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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 the economic calculation could be executed in the same manner.

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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.

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