10-2131-TIE 1

Abstract— The paper introduces the issue of the typical defects

in PhotoVoltaic (PV) cells and focuses the attention on three

specific defects: linear edge shunt, hole and conductive intrusion.

These defects are modeled by means of Finite Element Method

(FEM) and implemented in Comsol Multiphysics environment in

order to analyze the temperature distribution in the whole

defected PV cell. All the three typologies of Silicon-based PV cells

are considered: mono-crystalline, poly-crystalline and

amorphous. Numerical issues (simulation times, degrees of

freedom, mesh elements and grid dependence analysis) are

reported.

Index Terms— Defects, FEM, PV cell, Silicon, Thermal

NOMENCLATURE

C

Capacity, pF

Cp Specific heat at constant pressure, J kg-1 K-1

d Distance between capacitor plates, m

h Heat transfer coefficient, W m-2 K-1

I Current intensity, A

J0 Irradiative flux

J Current density, A m-2

k Thermal conductivity, W m-1 K-1

L, l Length, m

NOCT Nominal Operative Cell Temperature, °C

q0 Incoming flux, W m-2

R Resistance, Ω

A Heated surface, m2

Τenv Environmental temperature, K

Tinf Initial cell temperature, K

V0 Constant voltage, V

vc Capacitor voltage, V

w0 Wind speed, m s-1

ε Emissivity

ε0 Vacuum dielectric constant, 8.85 × 10-12 F m-1

εr Relative dielectric constant

Manuscript received December 14 ,2010. Accepted for publication July

11, 2011.

Copyright © 2011 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

The authors are with the Department of Electrotechnics and Electronics of

Politecnico di Bari, BARI, Italy (e-mail: vergura@poliba.it,

acciani@poliba.it, ottavio.falcone@gmail.com).

ρ Density, kg m-3

ρel Electrical resistivity, Ω m

σ Stefan-Boltzmann constant, 5.67 *10-8 W m-2 K-4

σel Electrical conductivity, S m-1

τ µ kf

cf

Time constant, s

Dynamic viscosity of the air, 1.81×10−5 Pa s

Thermal conductivity of the air, 0,026 W m-1 K-1

Specific heat of the air, 1005 J kg-1 K-1

I. INTRODUCTION

HE efficiency of common solar cells is in a range from

5% to 18 % (the lower is referred to the amorphous PV

cells, the higher to the mono-crystalline ones). This low value

is strongly affected by the temperature. According to NOCT

(Nominal Operative Cell Temperature), the typical operating

temperature for solar cells is about 46°C ± 2°C, depending on

manufacturer specifications. The abnormal temperature

increase of a PV-cell, over the NOCT, causes a drastic

efficiency loss and then a reduction of the totally produced

energy. In fact, it results that a temperature increase of 10°C of

the cell surface causes about 4% power loss (the hot spot is

said light), while 18°C temperature increase reduces the power

of about 7÷10% (the hot spot is said strong). The low value of

7% is valid when the power losses are linearly-dependent with

the temperature (as usually happens), the value of 10% is valid

when the relationship is not linear; Table 3 of [1] lists several

correlations available in literature for PV electrical power as a

function of cell/module operating temperature. It is important

to observe that while VOC (open circuit voltage) strongly

decreases when temperature increases, the short circuit current,

ISC, shows only slight variation [2]. Also the efficiency η and

the output power of the PV cell are strongly influenced by

temperature variations as well as the fill factor FF [3].

As the system cannot be investigated point-to-point through

a thermometer, the issue is overcome by means of thermo-

graphy. The thermography allows highlighting hot spots, if

present, but does not give information about their origins.

Nevertheless, it allows performing an efficient and systematic

investigation on typical defects in solar cells [4]. Lock in

thermography allows to evaluate the I-V local characteristic of

the defects (usually named shunts) [5] and to perform a good

investigation on hot areas of the module; this technique allows

to discriminate defected areas from the well-working ones. IR

(Infra Red) analysis, allowing a direct view of the temperature

A Finite Element Approach to Analyze the

Thermal Effect of Defects on Silicon-based PV

Cells

Silvano Vergura, Member, IEEE, Giuseppe Acciani, Ottavio Falcone

T

10-2131-TIE 2

distribution on PV cells and on the other PV system

components, may be considered as a valid diagnostic tool,

useful during the development, production and monitoring of

all PV system components [6].

The origin of the hot spots in PV cells is due to the defects,

some of them reported in [7]-[8]-[9]. Some authors have

modeled an electro-thermal PV module, but not for the aim to

study the defects [10]. Other authors have proposed thermal

model for photovoltaic panels under varying atmospheric

conditions [11].

The aim of the paper is to model three typologies of defects

by means of FEM and to simulate the thermal behavior of the

different PV cells. Until some years ago the FEM analysis was

not largely used because the most of the PCs was not able to

manage the high computational burden required by the FEM

analysis. Nowadays, instead, the PCs have highest

performances for both the processing and storage of the data.

For this reason, FEM analysis is now used in very different

fields and whenever detailed and accurate results are needed.

In fact FEM analysis is used for studying the electromagnetic

vibrations in electrical machine [12], the thermal effects in

power devices carrying large currents [13], the axial flux and

fault diagnoses in synchronous motors [14]-[15], and so on.

In this paper FEM will be used for analyzing the thermal

behavior of defected PV cells. Specifically, it will be studied

three defects occurring in the three different typologies of

Silicon-based PV cells: mono-crystalline (mono-Si), poly-

crystalline (poly-Si) and amorphous (a-Si).

Specific defects for mono-Si and poly-Si PV cells are

reported in [16]. This paper adds to the previous one the

theoretical basis of the thermal and electrical constraints, the

modeling and analysis for specific defects of a-Si cells and,

finally, a numerical analysis of the simulation results of all the

three typologies of PV cells. Specifically, linear edge shunt

and hole are typical defects of mono-Si and poly-Si cells; then

both of them will be modeled, implemented and simulated for

these specific typologies of Silicon cells. The defects will be

inserted into the 3-D model of well-operating PV cells [17],

even if the model of this paper is an upgraded version, because

the glass has been added and thermal insulation has been

imposed. On the other hand, conductive intrusion is typical

defect of a-Si cells. Also this defect will be modeled,

implemented and simulated for an a-Si cell. All the simulations

will be run in Comsol Multiphysics environment and

simulation times, grid dependence analysis and solvers will be

compared each other.

The paper is organized as follows: defects of PV cells and

IR analysis are presented in Sec. II, geometrics and physics of

PV cells are introduced in Sec. III, thermal and electrical

constraints are studied in Section IV, models and simulation

results are reported in Sec. V, conclusions end the paper.

II. CHARACTERISTIC DEFECTS AND THERMO-GRAPHY

IR analysis allows performing an efficient and systematic

investigation on the defects in solar cells [4]. A division of

typical defects in two categories is possible according to the I-

V characteristic: the shunt is defined resistive-like if it is

highlighted under forward bias as well as under reverse bias. If

the shunt compares only under forward bias it is defined

diode-like. From a physical point of view another

classification is possible. The shunts can be grouped in two

categories: material induced and process induced. The former

one comes from specific features of the substrate, the latter one

is related to the fabrication steps. In this paper the attention is

focused only on the second one, specifically linear edge shunt

and hole for mono-Si and poly-Si PV cells and conductive

intrusion for a-Si ones.

Let us introduce the three defects. Linear edge shunt comes

from a bad edge insulation of the solar cell; when this

incomplete insulation occurs, a low resistivity walk stats

between top and bottom electrodes of the cell. This low

resistivity walk acts like a short circuit on one side of the cell.

Figs. 1 and 2, transferred from [7], report such a shunt

highlighted through lock-in thermo-graphy under both forward

and reverse bias, respectively.

The second defect, the hole, comes from the manufacture

step, known as laser cutting. During screen printing some

metal paste may penetrate the hole coming from laser cutting;

then, after firing, a strong linear shunt may occur [8].

The last one, conductive intrusion, comes from the contact

Fig. 2. Linear edge shunt visible under reverse bias in lock-in thermography.

Fig. 1. Linear edge shunt visible under forward bias in lock-in

thermography.

10-2131-TIE 3

setup. The conductive material penetrating the structure may

lead to a direct contact of the different areas of the wafer. If

this direct contact stats between cell electrodes, these will be

short-circuited.

Other existing defects classified as process induced, but not

studied in this paper, are the following:

• entrapped air, which comes from mistakes that may occur

in the setting of the different parameters (temperature,

vacuum, operating time) that characterize the fabrication

step, known as rolling-mill process.

• non linear edge shunt, which can be interpreted as

recombination sites.

• Schottky-type which generates when the emitter

metallization is sintered and acts as a Schottky diode with

non-unity ideality factor.

• Scratches, which determine a p-n junction with a surface

with high density of recombination centers, if present at

the surface of solar cell across the emitter layer (this

shunt is non-linear).

• Aluminum particles, which can create a tunnel contact

between base and emitter generating a shunt.

III. GEOMETRICS AND PHYSICS

The photovoltaic cell is a three-dimensional-five-layer

structure obtained from the superposition of different materials

each one with specific thickness. Each layer has been carried

out with the characteristic thickness it has in real PV cell

structure. The model of a defect has to be inserted into the

model of a well-working PV cell. For this aim, the defects for

mono-Si and poly-Si cells have been inserted into the 3D

model described in [17] (upgraded by adding the glass), while

the well-working model of the a-Si cell is reported in the

following. The structure of the modeled a-Si cell has been

developed according to geometric dimensions of a real

amorphous PV cell: 12,5 cm length and an overall thickness of

about 340 µm.

The upper layer, glass, has been modeled with thickness of 4

mm; the top plate of the cell has been modeled with thickness

of 150 µm and as to be composed of silver; the lower layer,

bottom plate of the cell, has thickness of 100 µm; the thickness

of ITO (Indium Thin Oxide) layer is 85 µm. Finally for the

silicon layer a thickness of 5 µm has been set up.

As the model has to be analyzed by means of FEM based

software, the perfect overlap of the single layers is a critical

factor during Comsol’s mesh generation step. In fact an

incomplete overlapping of the layers may cause the presence

of empty spaces and an incomplete mesh error may occur. To

overcome this problem two utilities available in the Comsol

CAD interface, (Geometric Entities Union and Coerce to

solid) have been successfully used. In this way no problem

occurs during mesh generation.

To complete the model definition the physical features of

each layer have to be set up. The setting of these specific

features depends on the analysis to be run. The value of

thermal conductivity or specific heat has to be set for the

thermal analysis, while the value of the electrical conductivity

has to be imposed for the electrical one. Each metallization has

been modeled with Silver.

For studying the behavior of the defects, multiphysical

analysis has been run using two modules of Comsol (Heat

Transfer and AC/DC).

IV. THERMAL AND ELECTRICAL CONSTRAINTS

After defining the geometric and physic structure, it is

needed to set correctly the thermal parameters for analyzing

the thermal behavior of a PV cell. Table I summarizes the

values of thermal conductivity k, specific heat CP and density ρ

of each material constituting the 3 typologies of Silicon-based

PV cells.

Note that the parameters of the support oxide layer as well

as of the a-Si one are expressed by a temperature-dependent

equations, as reported in standard Comsol libraries.

TABLE I

THERMAL PARAMETERS VALUE

The problem is completely defined when correct constraints

on temperature and radiation have been imposed on domain

boundaries. A widening is necessary about boundary

conditions. Comsol environment allows choosing between two

different typologies of boundary conditions:

• Dirichlet’s condition: values of the solution on

boundaries must be fixed;

• Neuman’s condition: values of solution derivatives on

boundaries must be fixed.

When the Heat Transfer Module is used, boundary

conditions can be set up on temperature or on thermal flux. If a

temperature constraint is considered, the condition is:

0T=T (1)

It is clearly a Dirichlet’s condition. Instead, equation (2)

expresses the constraint on thermal flux and is a Neuman’s

condition:

tot-n q=q⋅ (2)

For the proposed model the Neuman’s condition has been

imposed and the mathematical model is the following:

4 4

0 env inf-n q=q +σε(T -T )+h(T -T)⋅ (3)

where the values of the parameters have to be set as follows

(according to NOCT specifications). The term q0, which

corresponds to the incoming flux, is set up equal to 800 W/m2,

Material k [W/(m*K)] ρ [kg/m3] Cp [J/(kg*K)]

Glass

Ag

mono-Si

poly-Si a-Si

ITO TiO2

χ(T) 429

163

34 α(T)

87 δ(T)

φ(T) 10,500

2,330

2,320 β(T)

7,120 ε(T)

ψ(T) 235

703

678 γ(T)

753 ζ(T)

10-2131-TIE 4

the second term is the radiative contribution to the total flux on

the cell while the third term is the convective contribution to

the total flux. The parameters in the second term are the

Stefan-Boltzmann constant σ and the emissivity ε whose

values are shown in the Table II; Tenv represents the

environment temperature.

TABLE II

EMISSIVITY VALUES

The third term depends by the heat transfer coefficient h and

the difference between the initial cell temperature, Tinf, and the

unknown temperature. The value of the initial temperature of

the cell has been set up equal to 293.15 K while the h value

has been computed equal to 11 W/m2K, as follows.

The heat transfer coefficient h is the factor that links the heat

swapped for convection between a solid and the fluid lapping

it and the difference between the temperatures of the solid and

the fluid, according to the well known Newton’s equation:

s 0Q=hA(T -T ) (4)

where Q is the total heat transfer, A is the heated surface area,

Ts the surface temperature and T0 the mean temperature of the

fluid. For the convection heat transfer to have a physical

meaning, there must be a temperature difference between the

heated surface and the moving fluid. According on convective

heat transfer theory, the value of the following dimensionless

numbers has to be computed in order to evaluate the correct

value of h:

0

e

ρ w LR =

µ

⋅ ⋅(Reynolds number) (5)

where ρ is the fluid density (1,204 kg/m3 for air at NOCT

conditions), w0 the fluid speed (1m/s for air in NOCT

conditions), L the length of the cell and the dynamic

viscosity of the air;

fu

h LN =

k

⋅ (Nusselt number) (6)

where kf is the thermal conductivity of the air and, finally,

f

fr

cP

k

µ ⋅= (Prandtle number) (7)

with cf specific heat of the air. With a length value of 12.5 cm

set up on the modeled PV cell, the value of Reynolds number

is 7890 and the flux is still laminar. Using the Nusselt relations

which applies for constant surface temperature and horizontal

flat surfaces (valid for laminar flow [18]) it results:

0.5 0.33Nu 0.664 Re Pr= ⋅ ⋅ (8)

The Nu value has been computed to be equal to 52.9. Using

this value in (6) the value of the heat transfer coefficient to be

set up on both surfaces of the implemented solar device is

equal to 11 W/m2K. This value agrees with the hypothesis of

air in natural convection incoming on the cell [19]. So the

thermal setting for the FEM-based analysis is complete.

Now, the implemented model has to be validated from the

electrical point of view considering a system including a

parallel RC circuit connected to the solar device: it

corresponds to simulate the cell acting as a current source.

This procedure has been used for all the three typologies of PV

cells. Through the CAD Module a resistor and a capacitor

have been modeled. The starting points for their modeling are

the well known equations (9) and (10) which link the value of

capacity and resistance to their geometrical and physical

features:

el

lR = ρ

S⋅ (9)

where ρel is the resistivity of the modeled material, l the length,

S the section.

0 r

SC = ε ε

d (10)

with ε0 vacuum dielectric constant, S the section, d the distance

between the two plates of the capacitor and finally εr the

relative dielectric constant whose value has been set equal to 6

(mica has been chosen as capacitor dielectric layer). The

values of resistance and capacity have been fixed as

R=1Ω, C=200 pF, then the time constant of the circuit is -10 -1

τ = RC = 2×10 [s ] . Other choices for the value of R and

C could be equally valid; in fact, as we are validating the

model from the electrical point of view, then each possible

operating point can be chosen. Obviously, even if the optimal

operating point is the Maximum Power Point (MPP),

nevertheless often the real operating point is different from

MPP (e.g., well functioning PV cells do not work in their

MPP, when connected in series with a defected one); in these

cases the PV cell works, but do not produce the maximum

energy.

This value has to be set up into the model available in

Comsol’s equation setting mask for AC/DC module:

( ) a∂ ∂ ∂ ∂ +∇⋅ − ∇ − + + + ⋅∇ =a

e t V t c V V V V f2 2

aV +d α γ β (11)

A suitable setting of the parameters in (11) has to be set to

obtain the correct Kirchhoff Voltage Low for RC circuits

Material ε

Ag

Si(mono)

Si(poly)

TiO2

0.01

0.85

0.85 0.9

10-2131-TIE 5

according to circuit theory. So the value of c, ea, α, β, γ will

be set up to zero, a to 1, da to the value of the time constant as

expressed in (10).

A boundary condition of incoming current flux has been

imposed on the cell surface directly connected to the RC

bipolar circuit. Equation (12) is the Neuman’s condition while

(13) reports the model used to compute the correct value for

the current density to be set in (12):

- n J=Jn

⋅ (12)

I=Jn

S⋅ (13)

Finally on the upper electrode a zero voltage condition has

been set while on the lower one a Dirichlet’s condition has

been imposed (equal to 0.6 V).

The simulation has been run in transient analysis and the

time parameters have been set up as follows:

• beginning t = 0

• final time t = 6τ

• simulation steps two orders lower than τ.

Fig. 3 allows verifying the capacitor voltage reaches the final value after 4-5 times the time constant value. Then, also the electrical validation is complete.

Fig. 3. Time domain voltage for the capacitor pins.

V. SIMULATIONS AND NUMERICAL RESULTS

This Section reports the results of the simulated defects and

some numerical aspects. Particularly,

• simulation results for linear edge shunts for both mono-

Si and poly-Si cases (Subsection A);

• simulation results for the hole defect for both mono-Si

and poly-Si cases (Subsection B);

• simulation results for conductive intrusion for a-Si case

(Subsection C);

• computational burden and grid dependence analysis

(Subsection D).

A. Linear edge shunt

It comes from a not correct electrical insulation of some

areas on the side of the cell. It can be considered as a short

circuit on one side of the device and it has been implemented

just as short-circuit. The linear edge shunt has been modeled

with a thin layer of conductive material connecting top and

bottom electrode of the cell. Its geometric dimension is 1 cm

length and 250 µm height. According to the theory it has to be

modeled as a low resistivity walk; so the value of conductivity

σel has been set to the 2× 104 S/m value. Across the cell pins a

voltage of 0.6 V(as start condition) has been applied while the

conditions on domains, sub-domains and boundaries are those

explained in [17], coming from NOCT specifications. These

are the initial conditions (valid for t =0-) imposed in the

simulation settings. At the instant t = 0, the simulation run and

the currents flowing in the circuit and the voltages across the

pins vary as LKC and LKT, respectively. Fig. 4 reports the

simulation results for a mono-Si PV cell. As already said, this

model is upgraded with respect to that of [17], because the

superior glass has been added and the thermal insulation has

been imposed . It can be noted that the maximum value of the

temperature reaches about 53.9 °C while the minimum value is

about 51.5 °C. Fig. 5 shows simulation results for a linear edge

shunt on the poly-Si model. The temperature of the hot spot is

54.7 °C, while the remaining part of the cell shows a

temperature of 51.5 °C. As the temperature difference between

the two regions is less than 10°C, the hot spot is light.

Fig. 4. Linear edge shunt for the mono-Si cell.

Negligible hot spots, related to linear edge shunts, have

been modeled setting different values for the electrical

conductivity. Simulations for light and negligible hot spots are

reported in [16].

Comparing the simulation results for the two developed

models it is possible to highlight as the linear edge shunt is

stronger for poly-Si cell than for mono-Si one. Simulation

results agree with the temperature values of hot spots obtained

by through infrared analysis [5].

10-2131-TIE 6

Fig. 5. Linear edge shunt on the poly-Si cell.

B. Hole

It has been considered the same model of the hole defect

for both mono-Si and poly-Si PV cells. A thin cylindrical

connection between top and bottom plats has been put into the

upgraded well-operating PV cell structure [17]. Hole defect

has been modeled as a 2 mm-diameter cylinder (Fig. 6)

constituted of metal paste. In this case the conductivity σel of

the low resistivity walk has been set to 103S/m. Electrical and

thermal conditions on domains, sub-domains and boundaries

have been set according to [17]. Fig. 7 diagrams the

temperature distribution for the defected cell. It is possible to

note that the value of the temperature of the area interested by

the shunt is about 52°C, i.e. 1,5°C higher than the temperature

of the remaining part of the cell. This result represents a light

hot spot.

Finally, Fig. 8 shows the temperature distribution on the

poly-Si cell affected by hole. In this case the hot spot

connected to the hole is negligible. In fact, the hot spot reaches

a temperature of about 53.2°C while the remaining cell shows

a temperature of 52°C.

Fig. 6. Model of hole defect.

C. Conductive intrusion for an a-Si cell

This section proposes the simulation results for the modeled

defect of an a-Si cell: conductive intrusion.

The conductive intrusion has been modeled as a 2 mm

diameter cylinder. Fig. 9 shows the temperature distribution

when a light hot spot occurs, modeled as a low resistivity walk

(σel equal to 103 S/m) across cell pins. The over-heating of the

hot spot is 1,4°C higher than the remaining cell.

Fig. 7. Temperature distribution for mono-Si cell affected by hole defect

Fig. 8. Temperature distribution for poly-Si cell affected by hole defect

D. Numerical issues

From a numerical point of view, PARDISO direct solver

[17] has been used to solve the simulated models for mono-Si

and poly-Si cases, because it has resulted the most efficient

solver. For the linear edge shunt, the resulting mesh is

constituted by 607,571 elements, while the degrees of freedom

are 1,747,192. This numerical values are valid for both mono-

Si and poly-Si cases, because the only difference consists in

the physical features of the active layer; this last one does not

influence the grid features. For the hole defect, the resulting

10-2131-TIE 7

mesh is constituted by 609,015 elements, while the degrees of

freedom are 1,881,148.

Fig. 9. Amorphous silicon cell affected by conductive intrusion.

Tables III and IV report the simulation times required by

each solver for the a-Si case. Also for a-Si case (as just

reported in [17] for mono-Si and poly-Si cases) PARDISO has

resulted the most efficient solver.

From the meshing point of view, the mesh for the a-Si case

has been generated using the predefined Very Coarse Size, this

resulting into 560,638 mesh elements that corresponds to

1,782,028 degrees of freedom to be solved. Also for the a-Si

case, the memory is soon saturated if reduced mesh element

size is imposed.

Comsol Multiphysics offers different settings in the

definition of the mesh element size. As the element size

strongly conditions the number of degrees of freedom (linear

equations) to be solved, all models have been solved using the

Very Coarse size. All the simulations have been run on a dual-

core workstation Dell, two 2-GHz processors INTEL XEON

5130 and 16 GB RAM. They have required about 800

seconds.

TABLE III

SIMULATION TIME FOR THERMAL MODEL (A-SI)

TABLE IV

SIMULATION TIME FOR ELECTRICAL MODEL (A-SI)

Another important numerical aspect is the grid dependence

analysis which allows highlighting the computational

limitations depending on the PC memory.

The model complexity is strongly influenced by the grid

element size: reducing the element dimension, the number of

mesh elements increases. It corresponds to the increasing of

the number of degrees of freedom to be solved, i.e. the number

of linear equations that have to be solved by the solver

algorithm. Table V reports the grid dependence analysis

referred to a-Si cell; it is worth noting that when the mesh size

is set up to Very dense, the calculator memory is saturated.

TABLE V

GRID DEPENDENCE ANALISYS

Mesh elements

(Size)

Mesh elements

(Number)

Degrees of

freedom

Extra coarse

Very coarse

Medium coarse

Coarse

Normal

Dense

Medium dense

Very dense

Extra dense

215,743

560,638

983,1244

1,213,591

1,982,751

2,781,264

3,941,986

-

-

781,147

1,728,028

2,112,541

2,378,135

2,987,587

4,281,751

5,895,482

-

-

VI. CONCLUSIONS

Three common defects, among all the known defects, have

been modeled by means of FEM and implemented in Comsol

environment. Defects with different criticalities have been

modeled. The proposed model of the linear edge shunt has

allowed to highlight a different thermal behavior for poly-Si

PV-cell and mono-Si one. This difference happens in the real

case. Also the simulation results obtained for a specific defecta

of a-Si PV cells are confirmed by real IR acquisitions. The

paper shows that the FEM approach can give correct and

detailed information about the thermal behavior of a PV cell.

All the defects have been implemented into the models of

upgraded well-working Silicon-based PV cells. Thanks to

these encouraging results, other known defects will be

implemented in the same geometrical and physical models. A

drawback of the FEM approach has been the computational

burden. Even if a powerful PC is used, it is very difficult to

complete a simulation with a Very Dense Size of the mesh.

Nevertheless, these applications do not require this hard

fitting.

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UMFPACK

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SOLVER SIMULATION

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10-2131-TIE 8

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Silvano Vergura received the MSc degree and the PhD

degree in Electrical Engineering from Politecnico di

Bari, Italy, in 1999 and 2003, respectively. From 2004

he is Assistant Professor in Politecnico di Bari, where

he is currently teaching Electrotechnics and Circuit

Simulation. His main research interests concern the

monitoring of renewable energy sources. He has devoted

particular attention to the energy performance analysis

of photovoltaic plants by means of statistical approach

and infrared analysis. Another research area concerns the modelling and

simulation of switching circuits. Co-simulation, homotopy methods and

topological techniques are the principal approaches utilized to study the

transient analysis of switching circuits. He is member of the reviewer board of

the International Journal of Computational Science and reviewer of IEEE-

Trans. on Circuits and Systems, IEEE-Trans. on Industrial Electronics and

other international journals and conferences. He is CEO of an academic Spin-

off of the Politecnico di Bari.

Giuseppe Acciani received the M.Sc. degree (summa

cum laude) in Electrical Engineering from the

University of Bari Italy in 1981. After graduation, he

had got a grant at a Computer Research Centre

(CSATA, Italy) attending to microprocessor interfacing.

In 1985 he joined the Electrical Engineering

Department of the Politecnico di Bari (Technical

University), Italy, as an Assistant Professor, where he is

currently an Associate Professor. At present he has in charge the following

courses: “Electric circuits”, “ Innovative Materials for Electrical Engineering”

and “Intelligent systems for industrial diagnostics”. His main research

interests concern the fields of photovoltaic plants monitoring and neural

networks, in particular unsupervised networks for clustering, and soft

computing for non destructive diagnostics by means of Ultrasonic waves and

Infrared techniques.

Ottavio Falcone was born in Policoro (Matera) in March

1979. He received his MSC degree in October 2008 at

the Politecnico di Bari debating a degree thesis

concerning the non destructive diagnostics of

photovoltaic modules. Since November 2008 until

December 2009 he was an assistant researcher inside the

team of electrotechnics at the department of

electrotechnics and electronics. His research activity has

been focused on the study of typical defects of different

typologies of PV cells and their modeling and analysis by means of finite

element method. Another research activity concerning the development of a

Matlab based software that allows pointing out defects on thermal images has

been carried out during the collaboration with the electrotechnics team until

April 2010. His main interest involve all aspects connected to renewable

energy plants, specifically photovoltaic plants. From January 2011 he works

as an inspector of commissioning of large grid connected PV plants.