LESSON 5.
SOLAR PHOTOVOLTAIC
ENERGY
⇒
1
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Contents (I)
• Introduction.
• The photovoltaic effect.
–
–
–
–
–
–
Semiconductors.
The p-n junction.
The PV effect in the solar cells.
PV cell response curve.
Voc and Isc.
Point of maximum power, SF and η.
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Contents (II)
• Manufacturing technologies and types of PV
cells.
– Crystalline silicon cells.
– Thin film cells.
– Tandem cells.
• The photovoltaic panel.
–
–
–
–
Series connection.
Parallel connection.
Mathematical models.
Components of PV panels.
3
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Contents (III)
• Other components of PV systems.
– Accumulation subsystem.
– Control subsystem.
– Inverter and converter.
• Array design.
–
–
–
–
–
Sun intensity.
Sun angle.
Shadow effect.
Temperature effect.
Effect of climate.
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Contents (IV)
• Array design.
– Electrical load matching.
– Sun tracking.
• Peak power point operation.
• Isolated PV systems.
– Simplified method.
– Calculation of the storage subsystem.
– Simulation method.
• Bibliography.
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Introduction (I)
• PV effect: generation of e.m.f. (electrical
current) in a semiconductor due to
absorption of light radiation.
• Discovered by Becquerel in 1839.
• First selenium cell made in 1941 with an
efficiency of 1%.
• Since then, space race has improved
technology.
• Current PV cells efficiency: 30% under
laboratory conditions (17% under working
conditions).
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Introduction (II)
• Main problem: high manufacturing and
installation costs.
1980 Cost ($/Wp) 1998 Cost ($/Wp) 1998 Cost ($1980/Wp)
30
6
3
Panel
Other
Panel
Other
Panel
Other
10
20
3.5
2.5
1.75
1.25
• Main application: isolated systems.
• But during the last few years there has been
a large growth in installed power: from 15
MWp in 1980 to 150 MWp in 1998.
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Introduction (III)
Photovoltaic power installed in EU (2000)
87,5
Alemania
19,5
Italia
12,2
12,1
10,6
6,7
2,8
2,5
1,7
1,6
1
0,5
Países Bajos
España
Francia
Austria
Suecia
Finlandia
Dinamarca
Gran Bretaña
Grecia
Portugal
0
20
40
60
MWp
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100
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The photovoltaic effect (I)
• The PhotoVoltaic effect is the conversion of
the energy of the light photons into electric
energy.
• The PV effect can occur in gasses, liquids
and solids.
• Maximum solar radiation: between 0.35 and 3
µm of wavelength ⇒ materials for solar cells
must be sensitive to that radiation ⇒
semiconductor materials, like silicon.
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The PV effect (II)
• Semiconductors:
– Atoms: electrons in orbital shells around
nucleus. There are allowed levels (minimum
energy) and forbidden levels.
– When one atom is in a crystalline structure it
interacts with other atoms and the energy
levels form energy bands.
– Outermost energy band is called the
conduction band and e- are free to move from
one atom to another.
– Outermost level of an atom occupied by e- is
called the valence band.
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The PV effect (III)
• Semiconductors:
– Relation between bands
gives a classification of
materials:
•
•
•
Conductors: valence
band empty of e-.
Insulators (Eg > 3 eV):
valence band full of e-.
Semiconductors (Eg ≈
1 eV): valence band
partly filled with e-.
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The PV effect (IV)
• Semiconductors:
– Pure semiconductors: intrinsic
semiconductors.
– Semiconductors doped with impurities:
extrinsic semiconductors.
•
•
Dopant material with more e- in valence band
than semiconductor: n-type semiconductor.
Dopant material with less e- in valence band
than semiconductor: p-type semiconductor.
– Example: silicon have 4 e- in valence band. In
pure Si each atom shares 2 e- to form stable
structure.
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The PV effect (V)
• Semiconductors:
– Example: Antimony (5 valence e-) as impurity
⇒ n-type silicon with excess of electrons
available for conduction.
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The PV effect (VI)
• Semiconductors:
– Example: Boron (3 valence e-) as impurity ⇒
p-type silicon with a missing electron or
positive hole.
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The PV effect (VII)
• Semiconductors:
– A n-type semiconductor has:
•
•
•
majority charge carriers (free e- in
conduction band);
positive ions belonging to the dopant
element;
minority charge carriers (e- and holes created
by thermal agitation).
– A p-type semiconductor has:
•
•
•
majority charge carriers (holes in valence
band);
negative ions belonging to the dopant
element;
minority charge carriers (e- and holes created
by thermal agitation).
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The PV effect (VIII)
• The p-n junction:
– When p- and n-type semiconductors are
joined together, in the contact zone free e- of
n-type semiconductor jump to fill the holes of
the p-type semiconductor (diffusion
movement).
– It behaves like a diode: an electric field is
generated in the junction zone opposite to
the electric field of the difussion.
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The PV effect (IX)
• The p-n junction under equilibrium
conditions:
– To neutralise charges:
• Free e- in n-type diffuse across junction
to p-type.
• Free holes in p-type diffuse to n-type.
• e- and holes close to junction recombine.
– A depletion (agotamiento) region (free of
mobile charge carriers) develops on either
side of junction with fixed negative ions on pside and fixed positive ions on n-side
preventing further diffusion so that
recombination between holes and electrons
17
is inhibited.
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The PV effect (X)
• The p-n junction under equilibrium
conditions:
– A potential difference develops across the
junction called the equilibrium potential V0.
• The behaviour of the p-n junction may be
altered on application of an external voltage
across its ends:
– Direct polarization: forward potential
difference. Positive pole on p side and
negative pole on n side.
– Inverse polarization: reverse potential
difference. Negative pole on p side and
positive pole on n side.
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The PV effect (XI)
• The p-n junction under direct polarization:
– The p region made positive with respect to n
region.
– The created field (Edp) is opposite to the one
of the junction (Eo), but is in the same
direction that the diffusion field (Edif) .
– The equilibrium condition is disturbed.
– The junction potential is reduced to V0 - V.
– The width of the depletion region is also
reduced.
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The PV effect (XII)
• The p-n junction under direct polarization:
– The electrons in n-type can fall down the
potential barrier to p-type.
– The holes in p-type likewise fall down to the
n-type .
– There is a net flow of current from p to ntype. The diffusion movement can continue.
– We can consider the majority carriers on
each side as being injected across the
junction.
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The PV effect (XIII)
• The p-n junction under inverse polarization:
– The p-type is made negative with respect to
the n-type.
– The external voltage adds to the internal
voltage.
– The potential barrier is increased.
– The width of the depletion region increases.
– Majority carriers are repelled further from
junction.
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The PV effect (XIV)
• The p-n junction under inverse polarization:
– Electrons in n-type and holes in p-type find it
difficult to cross over junction. They move
away from the junction.
– The only current present is that due to a few
thermally-generated minority carriers on each
side of junction ⇒ holes in n-type and e- in ptype ⇒ it produces a reverse leakage current
from n to p.
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The PV effect (XV)
• The p-n junction:
N
P
IL
id
Eo
+
id
Vo
-
Vdirect polarization
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The PV effect (XVI)
• The p-n junction:
 qV

mKT − 1
i
=
I
e

– Total current in the diode: d
D


– ID current: appears with inverse polarization
and relatively high negative tensions ⇒
exponential term nought (zero).
– Taking into account the internal resistance of
the diode:
 q (V − Rs id ) 
id = I D e mKT − 1


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The PV effect (XVII)
• Diode equation
representation:
– Negative tension
increases ⇒
junction becomes
conductor ⇒
avalanche current.
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The PV effect (XVIII)
• The PV effect in the solar cells:
– A photon of light is absorbed by a valence e⇒ its energy increases.
– If photon energy > band gap ⇒ e- jumps into
conduction band.
– If photon energy < band gap ⇒ e- increases
its kinetic energy ⇒ increases its T.
– Free e- generated in n layer can follow three
ways:
•
•
•
An external circuit.
Recombine with positive holes in lateral
direction.
Move toward the p layer.
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The PV effect (XIX)
• The PV effect in the solar cells:
– Negative charges in the p layer of the p-n
junction restrict this last movement.
– Recombination in lateral direction is reduced
making the layer extremely thin.
– If external circuit open ⇒ e- recombines with
holes ⇒ increase of cell temperature.
– If external circuit closed ⇒ The effect is
equivalent to a hole passing from the n zone
to the p zone, generating a current, IL, of
positive charges in the direction of the
electric field.
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The PV effect (XX)
• The PV effect in the solar cells:
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The PV effect (XXI)
• The PV effect in the solar cells:
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The PV effect (XXII)
• The PV effect in the solar cells:
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The PV effect (XXIII)
• The PV effect in the solar cells:
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The PV effect (XXIV)
• The PV effect in the solar
cells:
– The energy content of
the photon is related to
its wavelength: E = h·ν
and c = λ·ν ⇒ there is a
maximum cut-off
wavelength necessary to
excite one valence e-.
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The PV effect (XXV)
• PV cell response curve:
– Equivalent circuit of a PV cell:
IL
I
+
RS
P
Eo
Vout
RSH
N
id
ISH
-
– Equation:
 q (V + Rs I ) 
I = I L − id − I sh = I L − I D e mKT − 1 − I sh


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The PV effect (XXVI)
• PV cell response curve:
– Rs: series resistance depending on p-n
junction depth, impurities and contact
resistance.
– Rsh: shunt-leakage resistance, inversely
related to leakage current to the ground.
– Ideal PV cell: Rs = 0 and Rsh = ∞.
– Silicon cell: Rs = 0.05 - 0.1 Ω and Rsh = 200 –
300 Ω ⇒ Ish ≈ 0.
– PV conversion efficiency is sensitive to small
variations in Rs, but insensitive to variations
in Rsh.
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The PV effect (XXVII)
• PV cell response curve:
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The PV effect (XXVIII)
• PV cell response curve:
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The PV effect (XXIX)
• PV cell response curve:
– Standard Test Conditions, STC (Condiciones
de Ensayo Estándar):
•
•
•
Solar Irradiance: 1 kW/m2.
Air mass: AM 1.5.
Cell temperature: 25 ºC.
– Standard Operating Conditions, SOC
(Condiciones de Operación Estándar):
•
•
•
Solar Irradiance: 0.8 kW/m2.
Wind speed: 1 m/s.
Ambient temperature: 20 ºC.
– Nominal Operating Cell Temperature, NOCT.
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The PV effect (XXX)
• Open circuit voltage and short circuit current:
– Voc: when I = 0 (IL >> ID).
 qVoc

I
 qVoc
I = 0 ⇒ I L = I D e mKT − 1 ⇒ ln L + 1 =
⇒
 ID
 mKT


I 
mKT  I L 
ln  = mVT ln L 
Voc =
q
 ID 
 ID 
– Isc: short-circuiting output terminals with a
resistance almost null (Rload ≈ 0)⇒ Isc ≈ IL. In
the response curve corresponds to V = 0.
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The PV effect (XXXI)
• Open circuit voltage and short circuit current:
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The PV effect (XXXII)
• Point of maximum power, shape factor and
efficiency:
– Development: on blackboard.
– Maximum power = area of the rectangle
defined by Vmp and Imp. The product is smaller
than Voc·Isc.
– The relation is the shape factor:
Vmp · I mp
SF =
Voc · I sc
– Efficiency of the cell:
P
η=
GA
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The PV effect (XXXIII)
• Point of maximum power, shape factor and
efficiency:
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The PV effect (XXXIV)
• Point of maximum power, shape factor and
efficiency:
– The efficiency increases linearly with level of
radiation and cell size and decreases linearly
with cell temperature.
– Increase of working temperature ⇒ increase
of Isc and decrease of Voc.
– There is also an influence of the gap band.
– Maximum theoretical efficiency ≈ 60%.
– Silicon solar cell max. efficiency ≈ 25%.
– Commercial PV panels efficiency ≈ 10-17%.
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The PV effect (XXXV)
• Point of maximum power, shape factor and
efficiency:
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The PV effect (XXXVI)
• Point of maximum power, shape factor and
efficiency:
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The PV effect (XXXVII)
• Point of maximum power, shape factor and
efficiency:
– Variation of efficiency with temperature:
η = η ref [1 + β (Tref − Tcell )]
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Manuf. techn. and types of PV cells (I)
• Silicon used in solar cells: single crystal,
polycrystalline and amorphous.
• Amorphous silicon cells ⇒ thin film cells.
• Manufacturing technology of crystalline
silicon cells:
– Mature, well developed and reliable.
– Highly complex, high tech equipments and
important energy costs.
– It is an outgrowth of manufacturing of
microchips.
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Manuf. techn. and types of PV cells (II)
•
Stages in the manufacturing process of
crystalline silicon cells :
1.
2.
3.
4.
5.
6.
7.
8.
9.
Obtaining of metallurgic grade silicon.
Silicon purification.
Growing of silicon crystals in ingots.
Slicing wafers of p-silicon (base material) from
the ingots.
Polishing and cleaning the surface.
Doping with n material to form the p-n junction.
Deposition of electrical contacts.
Application of antireflection coating.
Encapsulation.
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Manuf. techn. and types of PV cells (III)
1. Obtaining of metallurgic grade silicon.
•
Obtained in arc furnaces (1,800 ºC) from SiO2
with a purity of 98%.
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Manuf. techn. and types of PV cells (IV)
2. Silicon purification.
•
•
•
Reaction with hydrochloric acid obtaining
silicon bars of 2 m length and 30 cm
diameter.
Purity for electronic use: 2 atoms of impurity
by 107 atoms of silicon.
Purity for PV cells: 1 atom of impurity by 106
atoms of silicon.
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Manuf. techn. and types of PV cells (V)
2. Silicon purification.
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Manuf. techn. and types of PV cells (VI)
2. Silicon purification.
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Manuf. techn. and types of PV cells (VII)
3. Growing of silicon crystals in ingots.
•
Czochralsky process: most common method
used for single crystal silicon.
•
•
Cylindrical ingots of D = 10 cm and L = 1 m.
Cell efficiencies: 22% (laboratory) and 17%
(commercial).
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Manuf. techn. and types of PV cells (VIII)
3. Growing of silicon crystals in ingots.
•
•
•
•
Polycrystalline silicon is obtained in molds
where the molten silicon is cooled in a given
direction so as to orient the crystal
structures in that direction.
Ingots size: 400x40x40 cm.
Cell efficiencies: 18% (laboratory) and 13%
(commercial).
Addition of a controlled quantity of
contaminant (boron or phosphorous) to the
molten mass to obtain type p or type n
silicon.
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Manuf. techn. and types of PV cells (IX)
3. Growing of silicon crystals in ingots.
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Manuf. techn. and types of PV cells (X)
4. Slicing wafers from the ingots.
•
To give desired cross-section shape and
thickness (0.2 – 0.5 mm).
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Manuf. techn. and types of PV cells (XI)
5. Polishing and cleaning the surface.
•
•
•
•
•
To eliminate damages and to clean the wafers.
Chemical attack with acids: isotropic, rapid,
expensive, dangerous and contaminant. It
gives very smooth surfaces.
Chemical attack with bases: anisotropic.
Different attacks depending on directions: the
surfaces obtained are rough and reduce
reflection losses but the surface of the
junction is wider and the series resistance too.
Dry chemical attack: with plasma; slow and
expensive.
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Manuf. techn. and types of PV cells (XII)
6. Doping with n material.
•
•
•
n material is diffused into the top layer of the
silicon wafer.
Most commom method: thermal diffusion of
phosphorous in vapor phase at 850-900 ºC.
Backside of wafer covered to prevent
recombination: creation of zones with high
concetration of p-type dopant or with SiO2.
7. Deposition of electrical contacts.
•
•
Top surface: grid pattern covering less than 10%
of the surface. Width about 300 µm. Methods:
vacuum metal vapor deposition or screenprinting.
Bottom surface: solid metallic sheet.
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Manuf. techn. and types of PV cells (XIII)
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Manuf. techn. and types of PV cells (XIV)
8. Application of antireflection coating.
• TiO2 and Ta2O5 are deposited to reduce
•
reflection from 30% of untreated silicon to
3%.
Methods: vacuum metal vapor deposition or
spraying.
9. Encapsulation.
•
•
In transparent material to protect PV cells
from the environment.
Materials: PVB and EVA.
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Manuf. techn. and types of PV cells (XV)
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Manuf. techn. and types of PV cells (XVI)
e-
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Manuf. techn. and types of PV cells (XVII)
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Manuf. techn. and types of PV cells (XVIII)
• Thin film cells:
– Crystalline silicon cells: high thickness
because they have low absorption coefficient
and to reduce transmission losses.
– Thin film cells: thickness of 10 to 50 µm.
– Principal types:
•
•
•
•
•
Amorphous silicon cells.
GaAs cells.
TeCd cells.
CIS cells.
Silicon crystalline thin film cells.
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Manuf. techn. and types of PV cells (XIX)
• Amorphous silicon cells:
– a-Si: atoms not forming structure ⇒
incomplete bonds ⇒ high density of
permissible states into the gap band (1.7 eV).
– Problems with doping because the grid
readapts ⇒ H added to avoid this problem.
– Cells: made from an a-Si:H alloy doped with P
and B to make the n and p layers.
– Cell consist of an n layer, an intermediate
undoped a-Si layer (intrinsic zone) an a p
layer as a substrate. There is a p-i-n junction.
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Manuf. techn. and types of PV cells (XX)
• Amorphous silicon cells:
– Advantages:
•
•
•
The material base is inexhaustible.
The manufacturing process is cheaper and
requires less material and energy than that of
crystalline silicon.
Series connection of cells can be made
during the manufacturing process.
– Disadvantages:
•
•
Instability: degradation by exposure to light
⇒ the efficiency drops to 4%.
Specifications recovered by subjecting the
cell to temperatures over 100 ºC.
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Manuf. techn. and types of PV cells (XXI)
• GaAs cells:
– Band gap = 1.42 eV ⇒ close to maximum
efficiency point.
– High costs but high efficiency ≈ 25%.
– High absorption coefficient.
– Problem of toxic components.
– Used in space applications and concentration
systems.
• TeCd cells:
– Mean efficiencies: 10%.
– Band gap = 1.45 eV.
– Also high absorption coefficient and toxicity.
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Manuf. techn. and types of PV cells (XXII)
• CuInSe2 cells:
– Band gap = 1 eV.
– Highest absorption coefficient.
– Mean efficiencies: 9%.
• Silicon crystalline thin film cells:
– Thinner than conventional cells but thicker
than previously described thin film cells.
– Advantages: No toxicity and abundance of
base material and stable efficiency.
– Efficiencies with multi-layer cells of 10 to 20
µm are about 17%.
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Manuf. techn. and types of PV cells (XXIII)
• Tandem cells:
– In single-junction cells the efficiencies are very
close to the theoretical limits.
– To increase efficiency: multi-junction or tandem
cells.
– Superimposition of cells manufactured with
semiconductors of different band gaps to obtain
better use of the photon’s energy.
– Wider band gap cells at the top and smaller band
gap cells at the bottom.
– Efficiency of 2-junction cells: 35%.
– Efficiency of 3-junction cells: 50%.
– Good combination: GaAs and GaSb.
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The photovoltaic panel (I)
• The solar cell is the base of a PV power
system.
• It is a few square milimeters in size and
produces 1 - 5 W of power.
• Module or panel: several cells connected in
series or parallel circuits.
• Array (serie o conjunto de paneles,
generador fotovoltaico): group of several
modules connected in series-parallel
combinations to generate the required
current or voltage.
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The PV panel (II)
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The PV panel (III)
• Tension supplied by one cell ≈ 0.6 V.
• Direct current circuit tensions > 5 V.
• Usual PV panel: 30 to 36 (or a multiple) cells
in series connection.
• Curves of series or parallel connections: on
blackboard.
• PV module is characterised by its peak
power: power at maximum power operation
point under Standard Test Conditions (STC)
of 1 kW/m2 of irradiance, 25 ºC of cell
temperature and air spectrum of AM 1.5 (air
mass).
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The PV panel (IV)
• The maximun efficiency of a PV panel is 1-2%
smaller than that of individual cells due to the
spaces between cells and to the frame.
• Maximum power of the connection ≠ sum of
maximum powers of the cells due to
dispersion of values of characteristic
parameters.
• PV cells are fragile and sensitive to dust and
humidity ⇒ transparent surface of hardening
glass with low content of iron.
• Frame usually made of aluminium.
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The PV panel (V)
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The PV panel (VI)
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The PV panel (VII)
• Series connection:
– Characteristic curve of 3 cells connected in
series: on blackboard.
– Manufacturing defect or a shadow effect on
c3 ⇒ Isc of a cell is reduced ⇒ Intensity of the
connection higher ⇒ this cell working with
negative tension ⇒ dissipating power instead
of generating.
– I of series connection must be lower than Isc
of every cell to avoid negative V and power
dissipation.
– To avoid this: by-pass diodes installed in
order to short-circuit groups of cells.
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The PV panel (VIII)
• Parallel connection:
– Of several groups of cells connected between
them in series.
– It is most common to make the parallel
connection between panels.
– If working tension of a group of cells connected
in series goes beyond the Voc ⇒ intensity is
reversed and works as a receptor ⇒ To avoid
this: block or blocking diode.
– Usually the tensions for maximum power are not
the same for all the cells ⇒ maximum power of
the connection is smaller than the sum of the
individual maximum powers: diagram on
blackboard
blackboard.
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The PV panel (IX)
• Series and parallel connection:
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The PV panel (X)
• Mathematical models:
– Determination of V and I supplied in the
different working conditions.
– Equivalent circuit of a PV generator formed
by Ns cells in series with a diode as a parallel
current source ⇒ characteristic equation.
IL
I
+
RS
P
Eo
N
Vout
RSH
id
ISH
-
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The PV panel (XI)
• Mathematical models:
 V + Rs I
 V +R I
s
I = I L − I D e a − 1 −
R
sh


mKT
a=
Ns
q
– where
[V], IL is the resultant of the
photon current, ID is the inverse polarization
current of the diode, Rs is the series
resistance and Rsh is the parallel resistance.
This last one can be assumed to be infinite.
– The model is characterised by these 5
parameters: a, IL, ID, Rs and Rsh ≈ ∞.
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The PV panel (XII)
• Mathematical models:
– Parameters supplied by manufacturers: Voc,
Isc and the peak power point in standard
conditions (Vmp and Imp).
– This implies 3 equations.
– It is necessary an additional independent
equation to determine the 4 parameters.
– In short circuit the diode current is null ⇒ IL=
Isc.
– In open circuit the exponential term is greater
V
than 1 and I is null ⇒
− oc
I D = I Le a
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The PV panel (XIII)
• Mathematical models:
– Rs is obtained by applying the characteristic
equation to the peak power point (neglecting
the 1):
I 

a ·ln 1 − mp  − Vmp + Voc
IL 

Rs =
I mp
– This expression limits the values of a and Rs:
both must be positive.
– The fourth equation is obtained considering
the effect of temperature. Equations of
Townsend on blackboard.
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The PV panel (XIV)
• Mathematical models:
– Application example: on blackboard.
– Data from a panel (at Tref): Isc, Voc, Imp, Vmp,
µi,sc, µv,oc ⇒ we can determine IL,ref, ID,ref, aref
and Rs.
– To calculate the curve of the panel at other
temperature the Townsend’s equations are
used.
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The PV panel (XV)
•
Components of PV panels:
– Principal components:
1.
2.
3.
4.
5.
6.
7.
8.
Frame.
Weatherproof junction box.
Rating plate.
Weather protection for 30-year life.
PV cells.
Tempered high transmissivity cover glass.
Outside electrical bus.
Frame clearance.
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The PV panel (XVI)
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The PV panel (XVII)
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The PV panel (XVIII)
• Components of PV panels:
– Cells:
•
Connected with metallic ribbon containing
silver (high conductivity) and welded.
– Cover glass:
•
•
Tempered to resist hail and other impacts.
With low content of iron (more transparency).
– Encapsulating material:
•
•
•
Protect against water and dust.
Reduce reflection losses.
Maintain plasticity to absorb tensions from
hits and dilatations.
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The PV panel (XIX)
• Components of PV panels:
– Encapsulating material:
•
Material: EVA (etileno vinil acetato). Not used
for concentrating systems.
– Bottom cover:
•
•
Usually made of Tedlar (PVF, fluoruro de
polivinilo): flexible and high mechanical,
chemical and thermal resistance.
In panels for buildings another glass cover is
used.
– Frame:
•
Usually made of aluminium.
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Other components of the PV system (I)
• Working point in the I-V characteristic curve:
on blackboard.
• Accumulation system:
– Non grid-connected or stand-alone or
isolated systems ⇒ energy storage ⇒ to
assure the supply during night and cloudy
periods.
– Possible energy storage systems:
compressed air; hydrogen; flywheels;
hydraulic potential energy; electrochemical
batteries.
– The last one the cheapest and the most
widely used.
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Other components of the PV system (II)
• Accumulation system:
– The most common are the lead-acid
batteries.
– Characteristics of PV systems:
•
•
Under partial load for long periods.
Slow discharges during more than 100
hours.
– Required batteries with low autodischarge
and maintenance.
– With transparent container for visual control
of electrolyte level.
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Other components of the PV system (III)
• Accumulation system:
– The capacity, C, of a battery is reduced with
the accumulated cycles ⇒ end of life when C
decreases by 80% of nominal value.
– Discharge depth: % of full charge used.
Recommended value for PV systems: 40%.
– The higher the discharge depth, the longer
the life.
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Other components of the PV system (IV)
• Accumulation system:
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Other components of the PV system (V)
• Control system:
– To regulate and protect elements and to
guarantee good performance of the system.
– Functions:
•
•
•
Open circuit between PV panel and batteries
during night, when panels are working as a
receptor. Blocking diode.
Tension regulator: when panel is generating
more intensity than the necessary to charge
the batteries ⇒ dissipation element.
To avoid the total discharge of the battery
disconnecting the load.
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Other components of the PV system (VI)
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Other components of the PV system (VII)
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Other components of the PV system (VIII)
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Other components of the PV system (IX)
• Control system:
– Peak power tracker: adjusts the operating
point to extract maximum power under the
given climatic conditions.
– Inverter: converts DC current into AC current.
– Battery charger: DC-DC converter.
– Da: blocking diode.
– Db: battery discharge diode: to prevent the
charge of the battery when it is full.
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Other components of the PV system (X)
• Inverter:
– The inverter converts DC current from PV
array into AC current for AC loads or for
feeding the electrical grid.
– Two types:
•
•
Natural commutation type: triggered by
external grid frequency.
Self commutating inverters: used in isolated
systems.
– AC-PV modules: the inverter is integrated
with the module.
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Other components of the PV system (XI)
•
Converter:
– DC-DC converters use capacitors, coils and
commutation devices.
– Transform DC current into DC current with
other values of V and I, maintaining P.
1. Inversor/cargador.
2. Regulador.
3. Convertidor CC/CC
24/12V.
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Other components of the PV system (XII)
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Other components of the PV system (XIII)
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Array design (I)
• Major factors influencing electrical design of
the solar array:
–
–
–
–
–
–
–
Sun intensity.
Sun angle.
Shadow effect.
Temperature effect.
Effect of climate.
Electrical load matching.
Sun tracking.
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Array design (II)
• Sun intensity:
– Current is directly proportional to sun
intensity.
– More reduction in Isc than in Voc.
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Array design (III)
• Sun intensity:
– Photoconversion efficiency of the cell is
insensitive to solar radiation in the working range.
– We get lower
power on a
cloudy day
only because
of the lower
solar energy.
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Array design (IV)
• Sun angle:
– Cell output current: I = I0 cos θ, where I0 is the
normal sun current and θ is the angle of the
sunline measured from the normal.
– Cosine law: valid for angles from 0º to 50º.
– Beyond 50º the electrical output deviates the
former law.
– There is no power generation beyond 85º.
– Kelly cosine value: actual (experimental)
current-angle curve of the cell.
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Array design (V)
• Sun angle:
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Array design (VI)
• Shadow effect:
– An array of series-connected cells gets
shadowed due to a structure interfering with
the sunline ⇒ some cells get shadowed ⇒
they lose photovoltage ⇒ they must carry
current to other cells ⇒ without V, not P
produced ⇒ they act as a load, producing
local heat loss, I2·R.
– The remaining cells must work at higher V to
make up for the losses.
– Higher V means less I ⇒ diagram.
– With several cells shadowed the I-V curve
gets below operating V ⇒ current falls down
to zero ⇒ No power.
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Array design (VII)
• Shadow effect:
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Array design (VIII)
• Shadow effect:
– To eliminate losses due to shadow effect the
circuit is subdivided into several segments
with bypass diodes.
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Array design (IX)
• Temperature effect:
– Tcell increases ⇒ Isc increases and Voc
decreases.
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Array design (X)
• Temperature effect:
– Effect of temperature on the power: on
blackboard.
P = Pref [1 + (α − β )∆T ]
– For single crystal silicon cells: α = 500·10-6
1/ºC and β = 5·10-3 1/ºC.
P = Pref [1 − 0.0045∆T ]
– Net effect is a power decrease at high
operating temperatures.
– PV system designed so that module output V
can increase at low Tcell and can decrease at
high Tcell.
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Array design (XI)
• Temperature effect:
V1
V2
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Array design (XII)
• Effect of climate:
– Reduction in power from partly cloudy day to
extremely overcast day: from 80% to 30%.
– Modules designed to resist golf ball size hail.
• Electrical load matching:
– Operating point: intersection of source and
load line.
P
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Array design (XIII)
• Electrical load matching:
– Operation with constant power:
– Condition for electrical operating stability:
 dP 
 dP 
> 
 dV 
 dV  source
load
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Array design (XIV)
• Electrical load matching:
– Heaters: constant R and P ∝ V2.
– Induction motors: constant power loads.
– Large systems with mix loads: P ∝ V.
• Sun tracking:
– PV array with an actuator to follow the sun
path.
– Two types:
•
•
One-axis tracker: follows sun from E to W.
Two-axis tracker: follows sun from E to W
during the day and from N to S throughout
the year.
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Array design (XV)
• Sun tracking:
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Array design (XVI)
• Sun tracking:
– Increase in energy: up to 40% over the year.
– Suntracker design: on blackboard.
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Peak power point operation (I)
• PV module must operate at a certain voltage
which corresponds to the peak power point
under the given operating conditions.
• Peak power point operation electrical
principle: on blackboard.
Vmp
 dV 
dPmáx = 0 ⇒ 
 =−
I mp
 dI  mp
• Zd = dV / dI: dynamic impedance of the
source.
• Zs = V / I: static impedance.
• Three methods to extract the peak power
from the module.
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Peak power point operation (II)
1. Small signal current injected to the array to
measure Zd and Zs. Operating voltage
increased or decreased until Zd = -Zs, where
the maximum power is extracted (dP = 0).
2. Operating voltage is increased as long as dP
/ dV is positive. If dP / dV is negative, we
must decrease the operating voltage.
Voltage is kept where dP / dV is near zero.
3. For most PV cells the ratio Vmp / Voc is
constant, K. For crystalline silicon cells K =
0.72. The Voc of an unloaded cell is measured
and the operating voltage is set to K·Voc.
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Isolated PV systems (I)
• Two types:
– Installations using solar energy only.
– Installations using an auxiliary electric
generating system, the so-called hybrid
systems.
• Two methods to calculate PV installations:
– Simplified method based on number of
equivalent hours of sun.
– Method based on simulation.
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Isolated PV systems (II)
• In both methods it is necessary to know:
– Current (present) energetic demand.
– Power.
– Working times of the different loads or
receptors.
– Losses in batteries (energy efficiency ≈ 80%).
– Losses in inverters (energy efficiency ≈ 90%).
– Losses in conductors (important due to low
tensions and high currents).
– Efficiency of the electrical installation (≈ 85%).
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Isolated PV systems (III)
•
Simplified method:
– Energy balance established for the most
unfavourable period, determining how far the
PV surface has to tilt (incline) in order to
decrease its size the most.
– System oversized the rest of the year.
– Procedure:
1. The monthly average daily sun radiation
matrix,[H T ], is obtained, where the element H T , jk
[kWh/m2·day] corresponds to the month k and
the inclination j.
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Isolated PV systems (IV)
•
Simplified method:
– Procedure:
2. The demand vector, [D ], is established, where
the element Dk [kWh/day] is the monthly
average daily demand.
3. The matrix of theoretical capture area, [A], is
determined, considering an efficiency equal to
1. The element Ajk = Dk / H T , jk is the necessary
theoretical area for the month k and the
inclination j.
4. The higher value of each row, affected by the
conversion efficiency, will be the critical area
needed for each inclination j.
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Isolated PV systems (V)
•
Simplified method:
– Procedure:
5. The minimum required surface of the
installation would correspond to the optimum
inclination that is obtained after choosing the
minimum value between the maximum of each
row (ie. of each inclination). The ideal
inclination and the critical period are
determined.
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Isolated PV systems (VI)
•
Simplified method:
– Procedure:
6. After that, the size of the PV generator is
determined following these steps:
•
The number of sun equivalent hours is
calculated:
Nh =
•
]
2
The power to be installed is calculated:
Pinstal =
Energy Technology
[
1 standard sun [kW/m ]
H T , jk ·n.º of days of the month kWh/m 2
Dk ·n.º of days of the month [kWh]
N h [h]
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Isolated PV systems (VII)
•
Simplified method:
– Procedure:
6. After that, the size of the PV generator is
determined following these steps:
•
The number of panels in series in one branch
of the PV array is calculated dividing the
nominal V of the installation by the nominal V
Vinstal
of one panel:
npser =
•
Vmodule
The number of branches of panels in parallel is
obtained dividing the required P by the P of
one module and the number of panels in
series:
Pinstal
np paral =
125
Pmodule ·npser
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Isolated PV systems (VIII)
•
Calculation of the storage system:
– Procedure to calculate the days of autonomy:
1. The vector of number of days of autonomy is
established, [Nau], where each element
corresponds to one month. A normal value for
the months of less radiation is between 7 and
15 days.
2. The required accumulation (energy) will be the
maximum value calculated for the different
months: Au = max [Nauk· Dk ] in kWh.
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Isolated PV systems (IX)
•
Calculation of the storage system:
– Procedure to calculate the days of
autonomy:
3. The minimum capacity of the battery may be
the corresponding to a discharge regime of
100 hours:
Au
in kWh.
CB100 =
PD100
PD100 is the depth of maximum discharge,
70% for batteries with deep discharge and
40% for lead-acid batteries.
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Isolated PV systems (X)
•
Calculation of the storage system:
– Procedure to calculate the days of autonomy:
4. To pass from kWh to Ah the nominal tension
of the battery is introduced:
CB100 [Ah ] =
CB100 [Wh ]
Vinstal [V ]
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Isolated PV systems (XI)
•
Calculation of the storage system:
– Procedure to calculate the days of autonomy:
5. It is also necessary to calculate the daily cycle
of the batteries, due to the gap between the
demand hours and the sun hours. The
minimum capacity of the battery for a fast
discharge regime is:
CB10 =
Au· DF
in kWh,
PD10
where DF is the gap consumption in kWh and
PD10 the depth of discharge that must be
higher than 20%.
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Isolated PV systems (XII)
•
Calculation of the storage system:
– The batteries to be installed must have values
of C10 and C100 higher than CB10 and CB100.
– Example: on blackboard.
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Isolated PV systems (XIII)
•
Simulation method:
– For prefixed values of batteries’ capacity and
panels’ area, this method determines the
fraction of the energy to be supplied by an
auxiliary source as consequence of the loss of
charge of the batteries (LC).
– Usable battery capacity: CBu = CB100·PD100.
– Daily energy balance on the battery ⇒ charge
state at the end of the day d:
Balance = Bd = Bd −1 +
H d ·η · A Dd
−
CBu
CBu
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Isolated PV systems (XIV)
•
Simulation method:
– The former value is set to 1 if it is higher than 1.
– If charge state is not enough to meet the
demand of the following day, the battery is
charged with the auxiliary system:
Bd ·CBu ≥ Dd ⇒ Eauxd = 0
Bd ·CBu < Dd ⇒ Eaux d = CBu ·(1 − Bd )
– With fixed values of A and CBu, the values of
Eauxd are calculated for a high enough period
of time.
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Isolated PV systems (XV)
•
Simulation method:
– The fraction of the demand to be covered with
the auxiliary generator is calculated by:
LC =
n
n
d =1
d =1
∑ Eauxd ∑ Dd
– It is possible to get a certain value of LC with
different combinations of values of A and CBu.
– The usual installations are designed for values
of LC between 0.1 and 0.01.
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Bibliography (I)
• José Mª de Juana et al., Energías Renovables
para el Desarrollo, Paraninfo, Madrid, 2002.
• Tomas Markvart, Solar Electricity, John wiley
& Sons Ltd., West Sussex, 1994.
• Mukund R. Patel, Wind and Solar Power
Systems, CRC Press LLC, Boca Raton, 1999.
• Ann-Marie Borbely, Jan F. Kreider,
Distributed Generation, CRC Press LLC, Boca
Raton, 2001.
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Bibliography (II)
• Eduardo Lorenzo, Electricidad Solar.
Ingeniería de los Sistemas Fotovoltaicos,
Progensa, Sevilla, 1994.
• Instituto para la Diversificación y Ahorro de
la Energía (IDAE), Manuales de Energías
Renovables, 6- Energía solar fotovoltaica,
Edición especial Cinco Días, Madrid, 1996.
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