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ANALYSIS AND DESIGN OF DYE SENSITIZED SOLAR CELLS
Karthik Nithyanandam and Ranga Pitchumani*
Advanced Materials and Technologies Laboratory
Department of Mechanical Engineering
Virginia Tech
Blacksburg, Virginia 24061-0238
and reduces to Tri-iodide ion by transferring an electron to the
excited dye, thus returning the dye to its ground state, ready
for its next cycle. This process occurs billions of times per
second within the cell thus producing electricity from sunlight.
Contrary to photovoltaic cells, the process of light absorption
and charge transport are separated. The dye molecules absorb
the light and generate charge carriers, while charge transport
occurs in the TiO2 layer and electrolyte.
Over the last decade, numerous papers concerned with the
mathematical simulation of the transport and physical phenomena in DSC have been published which provide valuable
insight into the functioning of the cell. There has been a continuous increase in the number of researches in this new class of
cell with significant commercialization interest as well. Papageorgiou et al. [2] presented a comprehensive analysis of the
migration and diffusion process in the steady state operation of
the cell without considering the electron transport in the TiO 2
network and the back reaction between the electrons and the
electrolyte at the cathode. The effects of design parameters on
the concentration potential of the cell were discussed.
Papageorgiou et al. [3] discussed the stability of acetonitrile
electrolyte and presented a detailed account of the diffusion of
ABSTRACT
Dye sensitized solar cells (DSC) are an attractive alternative to
the conventional photovoltaic cell because of their low cost
electricity production from solar radiation. The advantages of
a DSC include the ability to generate power without emitting
pollutants and requiring no fuel. While modeling of the physical and transport phenomena in DSC has been widely reported
in the literature, a thorough analysis to quantitatively determine the optimal design and operating configuration in installation is lacking. The present study incorporates a model of the
DSC coupled with a model to predict global irradiance on a
terrestrial surface to analyze the hourly, daily, monthly and
annual performance of a DSC installation over a wide range of
design and operating parameters. Optimum design and operating parameters are derived from the analysis.
INTRODUCTION
The pursuit of environmentally benign and efficient means
of producing energy has accelerated researches in the field of
renewable energy sources. Solar cells utilize the clean, abundant energy of the sun, thus aiding in the direct conversion of
sunlight into electricity. Solar technologies pave way to reducing the world’s dependence on fossil fuels, and offset green
house gas emissions. The focus of the present study is on dye
sensitized solar cell (DSC), also called the Grätzel cell, which
is one of the cost-effective solar technologies with reported
efficiency of 11.2% [1].
A typical DSC is composed of a dye adsorbed over a nanoporous semiconductor film (usually titanium oxide, TiO2) on a
conducting glass, an electrolyte solution and Platinum sputtered conducting glass electrode as shown in Fig. 1. Light absorbed by the dye excites an electron which is transferred to
the nanoporous TiO2 film. The electrons diffuse through the
nanoparticles until they reach the electrically conductive surface for current collection. After doing work, the electrons
enter the conducting substrate on the anode and, with the aid
of the Platinum catalyst, interact with the Tri-iodide (I3-) ion in
the catalyst and combined another electron oxidizes it to an
Iodide (I-) ion. The Iodide ion moves toward the photoanode
* Corresponding author. +1 540 231 1776; pitchu@vt.edu
TCO
TiO2/Dye/Electrolyte Pt
Glass
tTCO
x
tTiO2
FIGURE 1: Schematic of a DSC
1
1
Copyright © ASME 2010
Copyright © 2010 by ASME
the ions in the electrolyte. Papageorgiou et al. [4] developed a
mass transfer simulation model of a DSC that describes the
interfacial oxidation-reduction reaction at the cathode using
the Butler-Volmer equation. Ferber et al. [5] developed a
complete model of the DSC considering the interfacial loss
mechanism associated with the recombination of injected electrons in the TiO2 network with the oxidized species (I3– ions)
in the electrolyte. Tanaka et al. [6] extended the model of Ferber et al. [5] to solid state cells and discussed the dependence
of energy efficiency on the thickness of cell. Korifatis et al. [7]
numerically modeled a DSC as that of Ferber et al. [5] and
examined the effects of cell thickness and porosity on the performance of cell. Penny et al. [8,9] presented a detailed mathematical model of the semiconductor-dye-electrolyte interface which accounts for each interfacial charge injection and
recombination reaction within the DSC. The model accounts
for the transport of charged species due to concentration gradient and electric field as presented by Penny et al. [9], which
compared favorably with their experimental results. They concluded that the main recombination loss mechanism that affects the photovoltage and photocurrent is the reduction of
iodide by the injected electrons in the TiO2 electrode at the
interface. Ni et al. [10] studied the effect of electrode thickness on the maximum power point of a DSC and determined
that the power density becomes limiting for a TiO 2 thickness
in the vicinity of 10μm when N3 dye is used. Ni et al. [11]
developed a relation for the effect of porosity on the diffusion
coefficient of electron in the TiO2 layer. A complete model of
a DSC was not considered for the simulations and only the
diffusion of electrons in the TiO2 electrode was accounted for.
Though the studies in the literature report on the modeling
of the physical and transport phenomena in DSC, an outdoor
simulation to quantitatively determine the optimal design and
operating configuration for a DSC installation is lacking.
Accordingly two major groups of parameters are identified:
thickness of TiO2 electrode and porosity constituting the design parameters and tilt angle as representative of operating
parameters for the study. Unlike a photovoltaic cell, whose
performance is governed primarily by the incident irradiation
intensity, the performance of a DSC is governed by the combined effects of the spectral distribution of incident irradiation
and the spectral absorption coefficient of the dye. The primary goal and contribution of the paper is to present a methodology for analysis-based design of DSC, and to this end, the
model employed in the present study is a combination of the
models for a DSC available in the literature combined with a
global terrestrial irradiation model. Using the models, a systematic analysis of the effects of the various parameters on the
performance of a DSC installation is presented and optimal
combination of design and operating parameters that delivers
the maximum energy density over a year is determined. To 
this end, the model adopted in this study follows the description of the transport and electrochemical phenomena presented
by Ferber et al. [5] and Penny et al. [9], which is briefly reviewed in the following section.
MATHEMATICAL MODEL
To illustrate the methodology for analysis and optimization
of the selected cell design and operational parameters for maximum energy density, a one-dimensional model along the cell
thickness presented by Ferber et al. [5] and Penny et al. [9] is
employed. While many configurations of DSC can be used,
the following analysis considers TiO2 semiconductor electrode
chemisorbed with Ruthenium based N3 dye. The mediator is
acetonitrile electrolyte comprising I–/I3– ions. Considering the
cell operation at steady state, the governing equations for a
DSC are developed in the following discussion.
Light incident on the DSC is considered to be absorbed by
the charge transfer dye only. Within the photoanode, electron
injection from the dye into the TiO2 layer takes place. Subsequently, the excited dye is returned to its ground state by the
oxidation of iodide ion into tri-Iodide ion as given by the following equation:

Dyeadsorbed

3 
1
I  I 3  Dyeadsorbed
2
2
(1)
The ions are assumed to move either by diffusion or migration due to the presence of an effective macroscopic electric
field built up in the cell as a result of unbalanced local particle
concentrations [9]. Therefore, the continuity and transport
equations in the porous TiO2/dye/electrolyte layer, taking into
account the stoichiometry of the reaction given by Eq. (1) becomes

dn 
d 
Species e–:
(2)
De e  e ne E Re Ge
dx 
dx


dnI 
d 
3
3
  I  n I  E  Re  Ge
Species I–: DI 
(3)
dx 
dx
2
2

 1
dnI 3

d 
1
  I 3 n I 3 E Re  Ge (4)
Species I3–: DI 3
dx 
dx
2
 2



dn c 
d
  c  n c  E 0
Species c+:
(5)
Dc 
dx 
dx

 E is the electric field, Di  i and n i are the diffusion
where
coefficient, mobility and concentrations of the species,
i  e–
, I  , I 3 , c of which the cations, i  c , are considered
to be present only to
promote the
electroneutrality of the elec
trolyte. The diffusivity and mobility of the species are interrelated through the Einstein’s equation: Di  kT eo  i . The

diffusion coefficient of the electrons is calculated by means of
the relations deduced by Ni et al. [11] as a function of porosity, p:


4
3
1.6910
17.48p
 7.39p 2  2.89p  2.15


De  
0  p  0.41
(6)

0.82
4
0.41 p  0.76
4 10 p  0.76

The loss mechanism considered in this study is the relaxation rate of the conduction band electrons in the stationary
state with illumination and is expressed by [5]:



n 3
 n 3
Re ( x)  ke ne I  n e n I  I
nI 

n 3

I





(7)
where ni represents the equilibrium concentration of the species. The generation rate of electrons assuming 100% quantum
efficiency due to the fast rate of electron injection process can

be expressed by the Beer-Lambert’s law as follows:

Ge (x)    (  ) (  ) exp[ (  )x]dx
2
(8)
Copyright © 2010 by ASME

where  ( ) represents the absorption coefficient of the dye
given as ()  ()cdye log10e; ()  Rf a where  ( )
denotes the spectral molar extinction co-efficient of the dye,
the values for which are extracted as a function of wavelength
from Tanaka et al. [6],  ( ) denotes the incident photon flux
 and x represents the distance along the thickness as
density,
shown in Fig. 1. Furthermore, the electric field built in the cell
is characterized by the equation
dE
e
(9)

(nc  ne  nI  nI3)
dx 0
Equations (2)–(5) and (9) representing the governing equations for the four unknown species concentrations and the unknown electric field require nine boundary conditions to complete
the problem formulation, as discussed below:
 The metal semiconductor contact is assumed to be ohmic,
for which
(10)
E0
 Due to the conservation of particle numbers the integral
of the concentration of the charge carriers is always equal
to the equilibrium concentration of the species.
Iint
Iext
DSC



From the stoichiometry of reaction given by Eq. (1), it
follows that

tT IO2
1
1





 nI 3 ( x)  nI  ( x).dx  nI 3  nI  . p.tTiO2 (12)
3
3



0 
1
1
1

1

  ne ( x)  nI  ( x).dx   ne  nI  . p.tTiO2 (13)
2
3
2
3



0 
At the TiO2-Pt interface ( x  tTiO 2 ), the contribution from
electron current density is zero and the charge carriers are
only the ionic species.
je  0
(14)


Further, at x  0 , the net current carried by the electrons
through the interface should be similar in magnitude to
the current generated by the redox reaction occuring at the

TiO2-Pt interface, I 3
 2e  3I(cathode
)
(cathode)
which is governed by Nernst potential coupled with the
Butler-Volmer equation, expressed as:
oc
 n (t


e
 3 TiO 2 ).n I  (tTiO 2 )
j e  (0)  j o  Io c
exp(1   )
U Pt 
k BT
n I 3 (tTiO 2 )n I  (tTiO 2 )




(16)

n I  (tTiO 2 )


e
 oc
exp  
U Pt  
k
T
n I  (tTiO 2 )
B



where UPt is the overpotential developed at the counter


OC
electrode, given by U Pt  1 E Fn (0)  E redox
 U int
e
32
, where m *e



RP
I ext  
I int , where RP is the shunt resisRext  RTCO  RP 
tance of the cell which characterizes internal leakage in the
cell, RTCO represents series resistance of the TCO, and Rext is
the external load. From the above relation, the internal voltage
of the cell is calculated as U int  (RTCO  Rext )I ext and the
external photovoltage as Uext  I ext Rext .
The equilibrium concentrations of the species appearing in
Eqs. (11)–(13) are 
given by n I 3  C Io3 nI   CIo . By the
,
charge neutrality
condition, the equilibrium concentration of
cations is given by n c   n I 3  n I   n e . The equilibrium


concentration of electrons, n e , can be found by solving the
set of governing equations with the condition je 0  0 .

The nonlinear coupled set of governing equations, Eqs. (2)–
(5) and (9) along 
with the boundary conditions Eqs. (10)–(16)
was discretized using a finite difference formulation and
solved using the Newton's Relaxation method. The integral
boundary conditions, Eqs. (11)–(13), were solved by transforming them into differential equations, thus generating two
local boundary conditions with one of them replacing the former integral boundary condition. Also, the final boundary
condition, Eq.(16), which involves properties at two different
locations in the domain, is converted into a standard two-point
in
which the quasi-Fermi level of the electrons at x  0 is
expressed as a function of energy of the TiO2 conduction


and h represent the electron effective mass and Planck constant, respectively. The redox energy at the open-circuit,
oc

,
can
be
expressed
as
Eredox

 n oc (t

3
k T 
TiO 2 ) nst 
o
oc
o
where Eredox
Eredox
 Eredox
 B ln I
3 
oc
2
 n  (tTiO 2 ) nst 
 I

 3
stands for the standard potential of the I I
redox couple
and nst is the standard reference concentration.
In an open circuit, UPt = 0 and the internal voltage of the cell, U in t, gives the
open circuit photovoltage. The
internal voltage of the cell in
other cases is usually found by considering the equivalent circuit of the cell as shown in Fig. 2, for which, from Kirchoff's

I in t  Aje (0) and
law it can be shown that
(11)
At the TiO2-TCO interface ( x  0 ), there are no contributions from the iodide, tri-iodide or cation current densities, which yields the following three conditions:
j I
(15)
  j 3  j   0
I
c
Uext
term N CB is, in turn, given by 2 m*ekBT 2h 2
0

RP
band edge, E CB , concentration of thermally excited conduction electrons electron density at x = 0, n e (0), and density of
n (0)
conduction band states, N CB : E Fn (0)  ECB  k BT ln e . The
N CB
tTIO2

Uint
Rext
FIGURE 2: Electrical resistance network equivalent of a
DSC
tTiO 2
 nc (x).dx  nc .p.tTiO 2
RTCO
3
Copyright © 2010 by ASME
TABLE 1: Base case parameters
16
Electron relaxation rate constant, k e (s-1)
Electron mobility,  e (cm2/Vs)
Iodide diffusion constant, D I  (cm2/s)

Tri-iodide diffusion constant,
D 3 (cm2/s)
12
I
Ferber et al. [5]
8

Initial concentration
of iodide, C I0 (M)

Initial concentration of tri-iodide, C I03 (M)

Effective mass of electron, m *e
 of the platinum elecExchange current density
trode, j 0 (A/cm2)

 
Symmetry parameter,

Effective relative dielectric constant, 
Difference in conduction band and standard

0
electrolyte redox
 energy level, ECB  Eredox

(eV)
Sheet resistance of TCO glass substrate, RTCO
(ohm/sq.)

Shunt resistance, RP (ohm)
Present Model
4
0
0.0
0.2
0.3
0.5
0.6
Photovoltage, V [volt]
0.8
FIGURE 3: Validation of the present numerical model with
the results of Ferber et al [5].
boundary value problem by the inclusion of an additional trivial differential equation with two local boundary conditions
[5]. Apart from the design and operating parameters studied,
the other major inputs to the model include the absorption coefficient of the dye per unit wavelength, solar irradiation
which depends on the geographical location of the terrain and
the climactic conditions - temperature, surface pressure, relative humidity, CO2 concentration, ozone amount, visibility.
The outputs from the model comprise of the concentration
profiles of the species involved, electron density profile, current density profile with 'x' and the current density variation
with the photovoltage, referred to as the j-V curve.
 ( )
Incident spectral photon flux density,

Thickness of TiO2 layer, tTiO 2 (μm)

Porosity, p
Temperature, T (K)
Concentration of dye adsorbed on an ideal flat

surface,  (mol/cm2)
104
0.3
8.510–6
8.510–6
0.45
0.05
5.6 m e
0.1
0.78
50
0.93
6
10,000
AM1.5
global
10
0.5
298
1.310–10
Colorado Springs, USA (Latitude: 38.8o N, Longitude: 104.8o
W, Northern Hemisphere). The design parameters considered

in the present study are the thickness of TiO2 layer, tTiO 2 , and
RESULTS AND DISCUSSION
In order to validate the present numerical model, the simulation results are compared with the numerical results found in
the literature. Figure 3 compares the j-V curve obtained from
the present simulation with the results of Ferber et al. [5]. It
can be seen from the plot that as the current density increases,
the diffusion of the tri-iodide towards the cathode becomes
limiting primarily due to its low initial concentration [2] and
the limiting current density obtained for this case is 15.44
mA/cm2. The plot shows very good agreement with the numerical results obtained from Ferber et al. [5] whose model
forms the basis of the present model. Parametric studies based
on the validated model are discussed throughout the rest of the
section.
Solar radiation, which is nearly constant outside the earth’s
atmosphere, varies with changing atmospheric conditions and
the position of the earth relative to the sun. In an effort to determine the optimal design and operating conditions of a dye
sensitized solar cell installation, the simulation code SMARTS
v2.9.5 developed by Guyemard et al. [19,20] which has the
capability to simulate solar spectrum for various regions is
used. The major input parameters that govern the solar irradiation at a particular time of day and at a particular region are
the latitude, longitude, elevation, surface pressure, temperature, relative humidity, ozone amount and visibility, which are
obtained from the literature sources [12,13]. The other input
parameters required to generate the solar spectrum are documented in [14,15], which the readers are referred to for more
information. The region selected for the present simulation is
the porosity, p, while the tilt angle, α, is the operating parameter considered. The default case pertains to tTiO 2 of 10 μm, p
of 0.5 and α of 37.5o.

To begin with, the performance of dye sensitized solar cell
is analyzed for a particular time of a day namely, June 5, 2008

at 11:54 hrs. Figures 4(a)–(c), respectively, show the j-V
curves as the thickness of TiO2 layer, the porosity and the tilt
angle are varied. It can be seen in Fig. 4(a) that beyond a TiO2
layer thickness of about 10μm, the increase in current density
due to further increase in tTiO 2 is minimal. It was found that
there is significant generation of electrons even beyond TiO 2
thickness of 10μm which signifies that the incident irradiation
has not reached its critical penetration depth and offers poten
tial for increased current density. However, the minimal increase in the current density noted for thickness beyond 10 μm
can be attributed to the fact that the electrons injected at the
far end of photoanode become more prone to recombination
reaction and do not contribute to the production of electricity.
Correspondingly, the open circuit voltage decreases from
0.823V for tTiO 2 of 3μm to 0.793V for tTiO 2 of 24μm due to
the reduction in electron density. From Fig. 4(b) it can be seen
that increasing the porosity of the dye-sensitized solar cell has
a negative impact on the performance of DSC mainly due to


the decrease in diffusion coefficient of electrons in TiO 2 nanopores, as can be inferred from Eq. (6). This is because a decrease in De decreases the diffusion length leading to fewer
4
Copyright © 2010 by ASME
2
(a)
t
= 3 m
t
= 10 m
t
= 24 m
TiO2
TiO2
TiO2
0
(b)
2
9
6
3
0
0
20
2
[mW/cm ]
2
5
p = 0.2
p = 0.4
p = 0.5
p = 0.7
0
(c)
20
2
 = 15.5o
12
9
6
3
0
0.2
0.3
 = 70o
0.2
0.4
0.5
0.6
Porosity, p
0.7
0.8
15
(c)
12
max
 = 37.5o
0.4
0.6
Max. Power Density, P
0
0.0
[mW/cm ]
 = 0o
5
25
(b)
15
10
TiO2
20
[m]
max
15
10
5
10
15
TiO Layer Thickness, t
15
Max. Power Density, P
Current Density, j [mA/cm ]
12
Max. Power Density, P
15
5
(a)
max
20
10
15
[mW/cm ]
25
0.8
Photovoltage, V [volt]
FIGURE 4: Parametric effects of (a) TiO2 layer thickness,
(b) Porosity, and (c) Tilt angle on the j-V curve.
electrons being extracted. Hence as porosity decreases, the
current density, j, increases. The tilt angle governs the amount
of photon flux incident on the DSC which in turn influences
the j-V curve of the DSC Fig. 4(c). As the sun’s position relative to the earth changes through the day, the incident
irradiation on the cell varies for different tilt angle. Correspondingly, the tilt angle for which the maximum current density is obtained varies throughout the day. Based on the incident photon flux distribution for various tilt angles provided
by SMARTS v 2.9.5, for the simulated time of the day, α of
15.5o is found to have the highest incident photon flux distribution, which in turn gives the maximum current density in
Fig. 4(c).
9
6
3
0
0
15
30
45
60
Tilt Angle,  [deg]
75
FIGURE 5: Variation of maximum power density as a function of (a) TiO2 layer thickness, (b) porosity, (c) tilt angle.
Since the maximum power density, Pmax, that could be generated from a DSC is one of the factors that govern its design,
the parametric effects on Pmax are analyzed in Figures 5(a)–(c).
The Pmax value is derived from the j-V curve, Fig. 4, as the
maximum of the product of j and the corresponding V values.
From Fig. 5(a), it can be observed that Pmax reaches a maximum value beyond a TiO2 layer thickness of 10 μm
5
Copyright © 2010 by ASME
18
t
= 3 m
t
= 10 m
TiO2
60
14
TiO2
50
t
TiO2
= 24 m
(a)
11
40
 = 0o
30
7
o
 = 15.5
20
o
 = 37.5
4
o
 = 70
2
10
[mW/cm ]
G
2
Global Irradiation, I [mW/cm ]
70
0
5:54
7:37
9:20 11:03 12:45 14:28 16:11 17:54
Time of Day [hh:mm]
14
Max. Power Density, P
d,max
FIGURE 6: Global Irradiance as a function of time for different values of tilt angle.
0
corresponding of the invariance of the j-V curve with the TiO2
layer thickness beyond this value observed in Fig. 4(a). Following the discussions for Fig. 4(b), it is also seen in Fig. 5(b)
that Pmax decreases with porosity due to the corresponding
decrease in De. For the present simulation the maximum power density peaks at α = 15.5o which follows from the peak of
the j-V variation observed in Fig. 4(c). Though the effect of
design parameters— tTiO 2 and p— on the maximum power
density will be the same for different times of a day, the tilt
angle, , will have a nonmonotonic effect on Pmax as it so does
with the incident
photon flux distribution on the cell. Amongst

the three plots in Fig. 5, the highest maximum power density
is obtained as 12.52 mW/cm2 for the configuration of tTiO 2 =
11
(b)
p = 0.2
p = 0.4
p = 0.5
p = 0.7
7
4
0
=0
o
 = 37.5
o
 = 15.5
o
14
 = 70
(c)
o
11
10 μm, p = 0.2 and α = 37.5o [Fig. 4(b)]. Figure 6 presents the
global incident irradiation for various configurations of the
cell on the day considered for simulation namely, June 15,

2008. The curve is obtained by integrating the intensity of
sunlight over a wavelength of 300–800 nm, (which is the active region of the dye used in the DSC) for various times of
the day considered in the simulation. The tilt angle, α, of 0o
corresponds to the horizontal position of the cell parallel to the
ground where the intensity is found to be the highest except at
certain times of the day. Though it can be argued that the horizontal position of the cell receives the maximum amount of
insolation, the concentration of irradiation also depends on the
relative position of the sun with respect to the earth that
changes continuously during the day. This nonmonotonic effect caused the global irradiance to peak during the afternoon
for α of 15.5o. Also, the curves will differ for various days of a
year although the profile for a certain tilt angle will remain the
same in that the incident irradiation at sunrise and sunset of a
day is minimum and peaks sometime during the day.
Using the irradiance information such as that presented in
Fig. 6, the maximum power density obtained from the cell at
various times of the day is analyzed and presented in Figs.
7(a)–(c). The power delivered by the cell at sunrise and sunset
is negligible and assumed to be zero at these conditions. In
Figs. 7(a) and 7(b), it can be seen that Pd,max peaks in the afternoon, where the DSC receives the maximum amount of solar
irradiance as seen in Fig. 6 for the default case of α = 37.5 o.
All the curves follow the same trend as explained with
7
4
0
5:54
7:37
9:20 11:03 12:45 14:28 16:11 17:54
Time of Day [hh:mm]
FIGURE 7: Parametric effects of (a) bulk electrolyte layer
thickness, (b) porosity, (c) tilt angle on the maximum power density simulated for a day, June 15, 2008.
reference to the irradiation variation through the day in Fig. 6.
Figure 7(c), which portrays the maximum power density as a
function of time for various tilt angles, follows almost the
same trend as in Fig. 6. The discrepancies can be explained
with reference to Eq. (8) which relates the dependence of electron generation rate to the distribution of number of incident
photons and that of the spectral absorption coefficient of the
dye. Though Fig. 6, the global irradiance as a function of time
governs the principal variation of the maximum power density
with time of day, it is the incident photon flux as a function of
wavelength that governs the electron generation in a DSC,
which is reflected in the variation seen in Fig. 7(c).
6
Copyright © 2010 by ASME
300
TABLE 2: Optimum tilt angles that maximize energy density for various months in 2008
(a)
240
180
120
70
Jul
15.5
Feb
1
Feb
2
70
0
1
15.5
2
Aug
0
Aug
Sep
0
t
= 10 m
0
Oct1
0
t
= 24 m
Apr
2
[mJ/cm ]
d,max
Max. Energy Density, E
Jan
37.5
TiO2
(b)
240
p = 0.2
p = 0.4
p = 0.5
p = 0.7
60
(c)

o
 = 15.5
o
 = 37.5
o
= 70
70
15.5
Nov
70
month.
Figures 8(a)–(c)
present the parametric effects on the maximum energy density as a function of each half-month in the
 In general, it is seen that the maximum eneryear considered.
gy density increases from January (winter) to the middle of the
year (summer) and decreases later in the year. It is observed
that the effects of tTiO 2 and p follow the same trend as those
180
= 0
Oct
(1)
ty for Day 1 of a month ( Pd,max
) applies to the first 15 days
(15)
and that for Day 15 ( Pd,max ) applies to the remainder of that
0
240
May
15.5
2
where d represents the duration of a month, which can take
one of the following values—28, 29, 30, or 31 depending on
the month, and the limits of integration SR and SS represent
the time of sunrise and sunset, respectively, for the day under
consideration. The integration is carried out numerically using
the trapezoidal rule based on the respective daily variation
profiles for Day 1 and Day 15 of each month, to obtain the
daily-total maximum power density. In the calculation of
Ed,max is assumed that the daily-total maximum power densi-
180
120
2
Jun
15.5
Dec
70
Superscripts 1 and 2 represent the first half and
second half of a month respectively.
0
0
α (deg.)
Mar
TiO2
60
Month
Apr1
TiO2
120
α (deg.)
= 3 m
t
60
Month
observed in Fig. 6, in that the maximum energy density levels
off with increasing thickness of the TiO2 layer and monotonically decreases as the porosity increases. Figure 8(c) shows

that the variation of the maximum energy density is nonmonotonic with the tilt angle. Figure 8(c) can be used to determine
the optimum tilt angle that maximizes the maximum energy
density for the first and fifteenth day of each month. The optimum tilt angles which give the maximum energy density for
various months in the year 2008 are listed in Table 2, where
only one value is given for those months in which there was
no variation observed from the first to the fifteenth day. The
data in Table 2 provide information for an active tracking control of the tilt angle of a cell during its operation so as to maximize the energy collection.
o
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
FIGURE 8: Parametric effects of (a) TiO2 layer thickness,
(b) porosity, (c) tilt angle on the maximum energy density
simulated for the year 2008.
Using the daily variation of the maximum power density,
such as in Fig. 7, the maximum energy density, Ed,max for each
half month of a year is calculated from the following equation:
 SS

 Pd ,max dt 
 15
first15 day s


 Day 1
SR




(1)
Pd , max

(17)
E d ,max  

 SS

 (d  15) rem ainingday s
 Pd ,max dt 
 SR
 Day 15


 
)

Pd(15
, max

CONCLUSIONS
The results presented in this paper illustrate a methodology
to determine the daily and monthly variation of the performance of a DSC in installation as a function of selected example design and operational parameters. For the parametric studies adopted, it is found that a low porous material enhances
the performance of DSC while increase in TiO2 layer thickness increases the current density until a limiting value. The
tilt angles govern the incident irradiation and showed a non-

7
Copyright © 2010 by ASME









monotonic effect on the energy density obtained. The methodology may be extended to include other parameters as well as
other locations in a future study.
REFERENCES
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[2] Papageorgiou, N., Grätzel, M., Infelta, P.P., 1996, ―On
the Relevance of Mass Transport in Thin Layer Nanocrystalline Photoelectrochemical Solar Cells,‖ Sol. Energy
Mater. Sol. Cells, 44, pp. 405–438.
[3] Papageorgiou, N., Athanassov, M., Armand, P., Bonhote,
H., Pettersson, A., Grätzel, M., 1996, ―The Performance
and Stability of Ambient Temperature Molten Salts for
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3099–3108.
[4] Papageorgiou, N., Liska, P., Kay, A., Grätzel, M., 1999,
―Mediator Transport in Multilayer Nanocrystalline Photoelectrochemical Cell Configurations,‖ J. Electrochem.
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[5] Ferber, J., Luther, J., Stangl, R., 1998, ―An Electrical
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[6] Tanaka, S., 2001, ―Performance Simulation for DyeSensitized Solar Cells: Toward High Efficiency and Solid
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[7] Korifatis, D.P., Potamianou, S.F., Thoma, K.A.Th., Proceedings of the 11th Euro Conference on the Science and
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[8] Penny, M., Farrell, T., Please, C., 2008, ―A Mathematical
Model for Interfacial Charge Transfer at the Semiconductor-Dye-Electrolyte Interface of a Dye-Sensitized Solar
Cell,‖ Sol. Energy Mater. Sol. Cells, 92, pp. 11–23.
[9] Penny, M., Farrell, T., Will, G., 2008, ―A mathematical
model for the anodic half cell of a dye-sensitized solar
cell,‖ Sol. Energy Mater. Sol. Cells, 92, pp. 24–37.
[10] Ni, M., Leung, M.K.H., Leung, D.Y.C., 2008, ―Theoretical Modeling of the Electrode Thickness Effect on Maximum Power Point of Dye-Sensitized Solar Cell,‖ Canadian J. Chem. Eng., 86(1), pp. 35–42.
[11] Ni, M., Leung, M.K.H., Leung, D.Y.C, Sumathy, K.,
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[12] Weather Underground, Inc., www.wunderground.com,
viewed: September–October, 2009.
[13] McPeters, R., 2009, Principal Investigator, Earth Probe
TOMS,
http://jwocky.gsfc.nasa.gov/teacher/ozone_overhead_arch
ive_v8.html viewed: September, 2009
[14] Gueymard, C., 2001, ―Parameterized Transmittance Model for Direct Beam and Circumsolar Spectral Irradiance,‖
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[15] Gueymard, C., 1995, ―SMARTS, A Simple Model of the
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[16] van de Lagemaat, J., Benkstein, K.D., Frank, A.J., 2001,
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12433–12436.
ACKNOWLEDGMENTS
This work was supported by a grant from the U.S. Department of Energy under Award Number DE-FG36-08GO18146.
Their support is gratefully acknowledged.
NOMENCLATURE
A
cell area (m2)
cdye concentration of monolayer dye
C
concentration in bulk electrolyte (m-3)
D
diffusion constant (m2/s)
E
macroscopic electric field (V/m)
e0
elementary charge (As)
ECB conduction band energy (J)
EFn quasi-Fermi energy (J)
Eredox redox energy (J)
G e generation rate of electrons (m-3s-1)
h
I
j
j0
ke
k
K
me
m *e
n
NCB
Planck’s constant (Js)
electric current (A)
current density (A/m2)
exchange current density at Pt electrode (A/m2)
electron relaxation rate constant (s-1)
Boltzmann’s constant (J/K)
chemical equilibrium constant (m-3)
electron mass (kg)
effective electron mass (kg)
particle density (m-3)
effective density of the states in the TiO2 conduction
band (m-3)
porosity
resistance (ohms)
relaxation rate (m-3s-1)
p
R
Re
Rf
roughness factor
tTiO 2 thickness of the TiO2 layer (μm)
T
UPt
V
x
temperature (K)
overpotential at the cathode (V)
photovoltage (volt)
position co-ordinate along the cell thickness (m)
Greek symbols:
α(λ) absorption coefficient (m-1)
β
symmetry parameter (dimensionless)
є
dielectric constant (dimensionless)
єo
permittivity of free space (As/Vm)
є(λ) molar extinction co-efficient of the dye (M/cm)
(λ) spectral incident photon flux density (m-3s-1)
η
electrochemical potential (J)
λ
wavelength (m)
μ
mobility (m2/Vs)
Subscripts:
iodide ions
I
I 3 tri-iodide ions
cations
c
e
electrons
8
Copyright © 2010 by ASME