4.1 Solar Photovoltaic Basic

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

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.

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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

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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

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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

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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].

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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

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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

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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

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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 = ∝

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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

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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

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

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

Only larger series resistances reduce also the short-circuit current whereas very small parallel resistances reduce the open-circuit voltage. However, their influence reduces primarily the

0,00

0,50

1,00

1,50

2,00

2,50

3,00

3,50

4,00

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

Voltage V [V]

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

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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].

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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)

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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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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

]

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

]

Three Cells Two Cells One Cell

-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

4.1 Solar Photovoltaic Basic

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Transcript of 4.1 Solar Photovoltaic Basic