2014 First International Conference on Green Energy ICGE 2014

Modeling, Simulation and Parameters Estimation for

Photovoltaic Module
Badr Aldwane
Electrical Engineering Department - Polytechnic Institute -Sukna
Aljufra-Libya
Badr_engineer2012@Yahoo.com

Abstract - Integration and application of Solar Panels as clean operation cost since no fuel to consume, PV systems are easy
energy resources in electricity production and distribution is to transport and easy to install, Furthermore ,PV systems are
gaining wide spread implementation in market, to implement flexible, Photovoltaic systems can be built in virtually any
these resources successfully and to operate them in efficient way.
size, these systems are flexible as more panels can be easily
It is so important to model solar cell and analyze its behavior and
added to increase output to meet continuously growing loads.
dynamics in proper method. In this paper, Photovoltaic module
is analyzed, modeled and simulated in Simulink /Matlab
Currently there are many electrical Applications powered by
environment using basic circuit equations, one - diode model is PV systems include communications, remote monitoring,
implemented. Pure Analytical approach is introduced to lighting, water pumping, and battery charging.
estimate unknown Parameters of PV module; performance of
circuit is evaluated with different environmental conditions and Modeling of Photovoltaic system is very crucial to achieve
compared with real results as presented by datasheets supplied integration and optimization of PV based power system as
by manufacturer renewable energy resources. Building accurate model of PV
Array helps in understanding its dynamics and the influence
Keywords: Photo-Effect, Solar cell, simulation, Explicit Method,
of external factors and parameters changes on the overall
Parameter Estimation, Photovoltaic, irradiance
performance. Many models for PV cells, modules and arrays
I. INTRODUCTION were developed and presented; [2] presented generalized
photovoltaic model that was developed in Matlab/Simulink
The Photovoltaic systems (PV) have been under platform; the results of simulation were validated with
continuous development and study works for many years by commercial PV modules. This model is based on one-diode
many research projects worldwide, the main objectives of model; [3] proposed two-diode model implemented on Matlab
these researches were to develop, improve, and design Simulink environment for PV systems. This model provides
reliable, efficient and cost effective energy resources better accuracy especially in the case of low irradiance levels.
alternatives for fossil fuel based resources as Petroleum, coal Based on work of [4] PV model is developed in Mat-
and natural gas. As the demand for clean and sustainable lab/Simulink by using basic circuit equations, the effect of
energy resources are sharply increasing worldwide and solar insolation and temperature variations were included, the
become public concern in many countries; solar energy model response is tested for both DC loads and AC loads.
represents very promising clean energy for mankind. Every Matlab/Simulink model for PV array is presented [5]; this
day, the earth receives extremely huge amount of solar energy model is based on power system block offered in Simulink,
that can be utilized for electricity production. Up to now, the model is integrated with DC-DC boost convertor and
although still PV systems are operating with low efficiency, results of simulations are verified by lab setup. [6] Introduced
less than 18% [1] under uncontrolled environment conditions, general model which can be implemented on simulation
and they still require high initial investment cost, but on other platforms such as PSPICE or SABER. Many research efforts
hand, utilization of PV systems brings many benefits: they are have been made to calculate unknown parameters of PV cell,
clean energy provider, where no emissions produced during including numerical based methods, analytical approaches and
operation, PV systems Require minimal maintenance, curve fitting techniques, [6] proposed curve fitting technique
because there is no need to lubrication, or heat transfer for estimating parameters for PV model, this technique
equipments, no parts to be replaced due of wearing or damage requires I-V measurements which in not quit convenient, as
since they do not use any heat engine or rotating equipment in outlined by [7] iterative algorithm introduced to compute the
process of electricity production, they are almost silent during five unknown parameters of one -diode model presuming a
working , no noise is caused, PV systems have very low value of diode ideality factor. [8] Presented technique to

978-1-4799-3602-1/14/$31.00 ©2014 IEEE 101

extract parameters of one-diode model by solving a system of
simultaneous non-linear equations. [9] And [10] proposed
neglecting the shunt resistance, resulting in one-diode four
based model for PV array. This enables analytical calculation
of parameters, this assumption considers that slope of I-V
curve is flat at the short circuit conditions. This model
predicts reliably the performance of both mono-crystalline and
polycrystalline PV systems. Pure analytical methods were
used to calculate parameters for Solar cell for both single and
double-diode PV models [11]. Fig. 2 Equivalent Circuit of Solar Cell

II. PV CELL The current source generates photocurrent Iph, which is

directly proportional to solar irradiance and the working
Photovoltaic (PV) modules are solid-state devices that temperature of cell. By referring to fig. 2 applying Kirchhoff
convert sunlight directly into electricity, this is due to current Law to circuit:
photo-effect phenomena [12]; A PV cell is basic unit of PV
module, it basically consists of two or more thin layers of (1)
semiconducting material, most commonly silicon. When the
solar cell is exposed to sun light, pairs of hole and electrons
are generated; these charges are swept apart by internal
electric field in P-n junction, if the cell is connected to
external circuit, these charges can be conducted as form of
direct current. The electrical output from a single PV cell is
extremely small, so multiple cells are connected in series and
parallel, packed into modules that produce a specific voltage
and current. A typical PV generator consists of PV panel,
Battery, charge controller, dc-dc converter and ac inverter,
this inverter is used to transfer dc power into ac power, Fig. 1 Fig. 3 Equivalent Circuit of PV array

shows typical PV generator.

Where I: Cell's output current measured in Ampere (A);
IPH is photocurrent generated in cell measured in (A); ID is a
diode current and Ish is current flows in parallel resistance.
As this paper concerns the modeling of PV array, not a single
solar cell, Fig. 3 represents equivalent circuit of PV array
composed of series and parallel connected solar cells, by using
Shockley equation for diode current, (1) becomes:

( )
1 (2)

Fig. 1 Typical PV generator system

IS: Dark saturation current dependant on temperature; q is
a charge of electron, 1.6x10-19 coulomb (C); V is Cells output
III. PV CELL MODELING voltage, measured in volts; Rs represents interstice losses of
PV cell; Rsh represents earth leakage current to ground. K is
A PV cell is modeled basically as current source in Boltzmann's gas constant, 1.381 x 10-23 Joule/Kelvin (J/K); Ns
parallel with a diode; To account for losses occurs inside solar is number of cells in series and Np are number of cells in
cell, Rs ( series resistance) and Rsh (parallel resistance) are parallel, A is Ideality factor of cell, depends on type of
included in this model as shown in fig. 2; Rs is very low in material and manufacturing technology, its value ranges [1-5];
value usually < 1 Ω. Rsh is usually high as compared to Rs, i.e. T is absolute Temperature of the cell, measured in Kelvin
Rsh >> Rs; Rsh represents leakage current to ground in cell (K); I is function of cells' voltage V. In modeling; V is
[2]. considered as input, I as output, Iph is related mathematically
to insolation (G) and temperature T as follows:

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 (3) other hand ; it behaves as combination of both sources near
MPP.
Diode dark saturation current depends strongly on temperature
of solar cell [3] [4], this is expressed as:

(4)

Where Ego is band-energy gap of semiconductor =1.12eV.

It is clear that (2) is implicit nonlinear equation, so there is no
analytical solution. In order to solve it, numerical iterative
method must be used. But firstly we need to calculate the
values of parameters (Iph, Is, Rs, Rsh and A ); these parameters
determine overall performance of solar cell, unfortunately
these parameters are not listed in photovoltaic panels data- Fig. 5 three Key operating points of PV module as specified in Data Sheet
sheet as supplied by manufacturer, so it is necessary to esti-
mate parameters of the circuit to achieve the simulation, Data Fig. 6 display the Voltage - Power characteristic curve of
sheets for PV panels provide some important operating spe- PV panel under STC, Note that there is only one maximum
cifications of solar panel, including short circuit current Isc, power point corresponding to maximum power that can PV
open circuit voltage and maximum power point, these infor- panel produce; to optimize the working of PV cell in practice,
mation can be used to estimate the unknown parameters for it must be operated as near as possible to MPP, to achieve this,
solar cell and solar array as explained in section IV. maximum power point tracking algorithm techniques are used
to control dc-dc converter controlling the outputs of PV panel
Fig. 4 illustrates voltage current characteristics (I-V) for
solar panel of Polycrystalline type, under standard test
conditions (STC); i.e. solar irradiance of 1000 W / m2,
T =25C0, and Air mass =1.5.

Fig. 6 Power vs. voltage curve for typical PV module

IV. ESTIMATION OF PARAMETERS OF SOLAR CELL

Fig. 4 current vs. voltage curve for typical PV module Analytical solution for parameters calculation can be
adopted by introducing some simplification and
The curve shows nonlinear behavior of solar module for approximation in (2); it is confirmed in [9] and [10], that Rsh is
fixed Sun irradiance, fixed temperature. With reference to very large, assuming it as open circuit Rsh=∞; assuming Np=1,
fig. 5 three remarkable points can be identified on V- I curve (2) becomes:
shown as red circuits; these point are: short circuit point
( )
(0, Isc) where current is maximum and cell voltage = 0; Open 1 (5)
voltage point (Voc, 0) where voltage of cell is maximum and
cell current = 0; maximum power Point MPP (Vmpp, Impp); PV The exponential term in (5) very big compared to 1
cell works as current source near the short circuit point area,
while it works as almost voltage source near the point Voc, on exp [q (V + RsI) / KAT] >> 1, so omitting term 1 from (5);

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 ( )
(6) (
0 1 (14)

Is is very low as compared to Iph value, usually Is in range of

At MPP:
μA ( 10-10 to 10-5) [1]:
(
Iph >> Is exp [q ( v + RsI )/ NsKAT] 1 (15)

Photocurrent approximately becomes:

Using equation (10) & (13) for Is and Rs respectively.
Isc ≈ Iph (7) ( )

Employing (7) and the knowledge of point (Voc, 0), 1 (16)

substituting it in (6), we get:
Where:
( )
0 (8)
1
Rearranging (7) to: (17)

( )
(9)
(
Now solving (8) for saturation current Is (18)

( ) (10)

Solving (17) for A, pure analytical formula to calculate A:

(1) Becomes:
2
( ) (19)
1 (11) 1

Now we need third equation to find third parameter Rs, using

the point (Vmpp, Impp) in (12):
V. MAKING OF SIMULINK/MATLAB MODEL
1 (12)
The equations (3), (4), (5) and (10) are modeled in Simulink
simulation environment as subsystems blocks, connected
Solving this equation to find Rs
together to form overall system as shown in fig. 7. The inputs
for subsystem are: Voltage, solar irradiation and temperature,
(13) while the output is current. Function block parameters box are
used to access the PV panel specifications. The Unknown
To find A, forth equation must be introduced. It is ma- parameters are calculated during model's initialization by
thematically clear that the derivative of Power curve at maxi- associated M File - code Script. Since the environmental
mum power point is zero. Since the power is P =VI: so conditions are not controlled, testing the proposed Model for
different levels of solar intensity G and Temperature
variations is very crucial for PV module efficiency,
0 Simulation results are verified by comparing them against
experimental results provided in PV data sheets, mono-
crystalline based PV system and Polycrystalline based PV
system were used for comparison .

Now differentiating (5) in term of V

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 Fig. 10 Simulink model representing formula for PV's output current
Fig. 7 Simulink-Based Subsystem Model of PV module

Fig. 11 Function block Parameters dialog box to access PV's Parameters

Fig. 8 Under-Mask view of block diagrams of subsystems making PV

module

Fig. 12 Simulink Block model representing equation of temperature

dependency of Saturation Current

VI. RESULTS AND CONCLUSIONS

Fig. 9 Simulink Block model representing Photocurrent dependency on the
Fig. 13 shows the influence of solar irradiance G on the I-V
solar insolation and temperature
Characteristics of PV Module, the Current of PV module is

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 Fig. 13 Effect of Solar radiation variation on output current of PV module Fig. 16 Effect of module working temperature variation on generated power
of PV module
directly proportional to the solar irradiance G; while voltage V
is slightly increasing with irradiance; points out that Irradiance The influence of temperature fluctuation on PV's output
has little effect on the voltage of PV module. voltage is remarkable as indicated in fig. 15; voltage drops
considerably with increasing of temperature, while current is
not sensitive to temperature changes, as result power P
generated by solar panel experiences sever drop as T rises as
shown in Fig. 16

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