Abstract—A photovoltaic array (PVA) simulation model to be
used in Matlab-Simulink GUI environment is developed and
presented in this paper. The model is developed using basic
circuit equations of the photovoltaic (PV) solar cells including the
effects of solar irradiation and temperature changes. The new
model was tested using a directly coupled dc load as well as ac
load via an inverter. Test and validation studies with proper load
matching circuits are simulated and results are presented here.
Index Terms—Photovoltaic models, Photovoltaic power systems,
Power generation, MOSFET Model, Motor drives, Digital
HE use of new efficient photovoltaic solar cells (PVSCs)
has emerged as an alternative measure of renewable green
power , energy conservation
management. Owing to their initial high costs, PVSCs have
not yet been a fully attractive alternative for electricity users
who are able to buy cheaper electrical energy from the utility
grid. However, they have been used extensively for water
pumping and air conditioning in remote and isolated areas
where utility power is not available or is too expensive to
transport. Although PVSC prices have decreased considerably
during the last years due to new developments in the film
technology and manufacturing process , PV arrays are still
widely considered as an expensive choice compared with
existing utility fossil fuel generated electricity. After building
such an expensive renewable energy system, the user naturally
wants to operate the PV array at its highest energy conversion
output by continuously utilizing the maximum available solar
power of the array. The electrical system powered by solar
arrays requires special design considerations due to varying
nature of the solar power generated resulting from
unpredictable and sudden changes in weather conditions
which change the solar irradiation level as well as the cell
operating temperature. Salameh and Dagher  have proposed
a switching system that changes the cell array topology and
connections or the structural connections of the arrays to
establish the required voltage during different periods of a
day. A steady-state analysis of a scheme employing direct
coupling between a series/shunt or separately excited dc
motors and the photovoltaic solar arrays has been given by
Roger . The dynamic performance of a dc shunt motor-
photovoltaic system has been studied by Fam and Balachander
. The starting and steady-state characteristics of dc motors
powered by a solar cell array source have been studied by
Appelbaum  to select the suitable parameters and type of dc
motor for a desired utilization scheme. All these studies
concerning dc motors or permanent magnet (PM) dc motors
powered by PV generators have been done by considering the
direct interface between the motor load and the PV source
generator. For direct coupling of dc motors to PV solar arrays,
the separately excited or PM motors with a ventilator type
load are the most suitable . Owing to changes in the solar
radiation energy and the cell operating temperature, the output
power of a solar array is not constant at all times.
Consequently, during the design process of PVA powered
systems; a simulation must be performed for system analysis
and parameter settings. Therefore an efficient user friendly
simulation model of the PVAs is always needed. The PVA
model proposed in this paper is a circuitry based model to be
used with Simulink. The proposed model was simulated with
various types of loads for performance checking.
II. PVA MODELING
PV arrays are built up with combined series/parallel
combinations of PV solar cells, which are usually represented
by a simplified equivalent circuit model such as the one given
in Fig. 1 and/or by an equation as in (1).
Fig. 1. Simplified-equivalent circuit of photovoltaic cell.
The PV cell output voltage is a function of the photocurrent
that mainly determined by load current depending on the solar
irradiation level during the operation.
Where the symbols are defined as follows:
e: electron charge (1.602 × 10-19 C).
I. H. Altas1,* and A.M. Sharaf2
1: Dept. of Electrical and Electronics Engineering, Karadeniz Technical University, Trabzon, Turkey, firstname.lastname@example.org
2: Dept. of Electrical and Computer Engineering, University of New Brunswick, Fredericton, Canada, email@example.com
*: Currently a visiting scholar at the University of New Brunswick, Canada
A Photovoltaic Array Simulation Model for
Matlab-Simulink GUI Environment
1-4244-0632-3/07/$20.00 ©2007 IEEE. 341
k: Boltzmann constant (1.38 × 10-23 J/oK).
Ic: cell output current, A.
Iph: photocurrent, function of irradiation level and junction
temperature (5 A).
I0: reverse saturation current of diode (0.0002 A).
Rs: series resistance of cell (0.001 Ω).
Tc: reference cell operating temperature (20 °C).
Vc: cell output voltage, V.
Both k and Tc should have the same temperature unit, either
Kelvin or Celsius. The curve fitting factor A is used to adjust
the I-V characteristics of the cell obtained from (1) to the
actual characteristics obtained by testing. Eq. (1) gives the
voltage of a single solar cell which is then multiplied by the
number of the cells connected in series to calculate the full
array voltage. Since the array current is the sum of the currents
flowing through the cells in parallel branches, the cell current
IC is obtained by dividing the array current by the number of
the cells connected in parallel before being used in (1), which
is only valid for a certain cell operating temperature Tc with
its corresponding solar irradiation level Sc. If the temperature
and solar irradiation levels change, the voltage and current
outputs of the PV array will follow this change. Hence, the
effects of the changes in temperature and solar irradiation
levels should also be included in the final PV array model. A
method to include these effects in the PV array modelling is
given by Buresch . According to his method, for a known
temperature and a known solar irradiation level, a model is
obtained and then this model is modified to handle different
cases of temperature and irradiation levels. Let (1) be the
benchmark model for the known operating temperature Tc and
known solar irradiation level Sc as given in the specification.
When the ambient temperature and irradiation levels change,
the cell operating temperature also changes, resulting in a new
output voltage and a new photocurrent value. The solar cell
operating temperature varies as a function of solar irradiation
level and ambient temperature. The variable ambient
temperature Ta affects the cell output voltage and cell
photocurrent. These effects are represented in the model by
the temperature coefficients CTV and CTI for cell output
voltage and cell photocurrent, respectively, as:
β = +
Where, βT = 0.004 and γT = 0.06 for the cell used and Ta=20
oC is the ambient temperature during the cell testing. This is
used to obtain the modified model of the cell for another
ambient temperature Tx. Even if the ambient temperature does
not change significantly during the daytime, the solar
irradiation level changes depending on the amount of sunlight
and clouds. A change in solar irradiation level causes a change
in the cell photocurrent and operating temperature, which in
turn affects the cell output voltage. If the solar irradiation level
increases from Sx1 to Sx2, the cell operating temperature and
the photocurrent will also increase from Tx1 to Tx2 and from
Iphl to Iph2, respectively. Thus the change in the operating
temperature and in the photocurrent due to variation in the
solar irradiation level can be expressed via two constants, CSV
and CSI, which are the correction factors for changes in cell
output voltage VC and photocurrent Iph, respectively:
β α = +
where SC is the benchmark reference solar irradiation level
during the cell testing to obtain the modified cell model. Sx is
the new level of the solar irradiation. The temperature change,
ΔTC, occurs due to the change in the solar irradiation level and
is obtained using
The constant αS represents the slope of the change in the cell
operating temperature due to a change in the solar irradiation
level  and is equal to 0.2 for the solar cells used. Using
correction factors CTV, CTI, CSV and CSI, the new values of the
cell output voltage VCX and photocurrent Iphx are obtained for
the new temperature Tx and solar irradiation Sx as follows:
V C C V
I C C I
VC and Iph are the benchmark reference cell output voltage and
reference cell photocurrent, respectively. The resulting I-V
and P V curves for various temperature and solar irradiation
levels were discussed and shown in [6, 8, 9], therefore they are
not going to be given here again.
III. PVA MODELING FOR SIMULINK
A general block diagram of the PVA model for GUI
environment of Simulink is given in Fig. 2 along with filter
and load models. The block called PVA model for GUI is the
last stage of the model. This block contains the sub models
that are connected to build the final model. A diode (D1) is
connected in series with the load circuit to prevent the reverse
current flow. A filter is connected before the load to maintain
a stable voltage. The filter contains a series R-L and parallel C
elements. The PVA consists of 8 PV cells all connected in
series to have a desired voltage output. Depending on the load
power required, the number of parallel branches can be
increased to 2 or more. The effects of the temperature and
solar irradiation levels are represented by two variables gains.
They can be changed by dragging the slider gain adjustments
of these blocks named as variable temperature and variable
Fig. 2. Operational functional block diagram of the PVA model.
Since the main objective is the development of the PVA
functional model for the Simulink environment, the other parts
of the operational block diagram given in Fig. 2 are not going
to be explained in full detail. However, just to describe the
main diagram, as it can readily be seen, the system is modeled
to supply power to both dc and ac loads. The dc load is
directly coupled while the ac load is fed through a three-phase
inverter and an isolation transformer with a turn ratio 1.
The last stage of the PVA model is shown in Fig. 2. The
other stages are masked as subsystems under the last stage.
The first stage of the PVA modeling is depicted in Fig. 3
where the mathematical model of a single PV cell given by (1)
is represented with the block called Equation 1.
Fig. 3 Modeling stage 1.
The effects of the changing temperature and solar
irradiation level are modeled inside the block called Effect of
Temperature & Solar Irradiation. This block represents the
equations given from (2) to (8) with the modification of (7)
and (8) as follows.
Fig. 3 is a sub-mask of the stage 2, which is given in Fig. 4.
Major inputs and outputs and the conversion of discrete
simulation model into continues circuit model are shown in
Fig. 4 Modeling stage 2.
IV. SIMULATION RESULTS
The proposed PVA model is simulated using the scheme
given in Fig. 2. The system supplies power to a mainly
resistive dc load and an RLC ac load with 500 W, 200 VAr
inductive and 500 VAr capacitive. The system does not have
any controller. The loads are just chosen to match the power
generated by the PVA. Actually the voltage at dc load bus and
the both voltage and frequency at ac load bus must be
controlled and kept constant for the users. The control part is
also done as a part of this work. However, only the PVA
modeling is included in this paper since both parts require
The current-voltage (I-V) characteristic of the PVA during
operation is given in Fig. 5. Since the voltage of the PVA is
equal to the open circuit voltage at stand-still, the I-V
characteristics start at open circuit voltage with current equal
to zero. As the simulation starts an the loads begin draw
current from the PVA, the voltage and the current start moving
toward the operating values, which are shown in Figs. 7 and 8
for voltage and current, respectively. PVA power is given in
Figs. 6 and 9. Although the maximum power is above 750 W
for the current solar irradiation and temperature levels, the
operating power is approximately 750 W. Since there is no
control or maximum power point tracker (MPPT), this is a
reasonable operating power.
The dc bus voltage is given in Fig. 10. Due to the effects of
the inverter switching and there are some oscillations on the
dc bus voltage, which is also the input voltage to the inverter.
The output ac voltage of the inverter is shown in Fig. 11 where
the PWM mode operation of the inverter can be seen on the
output voltage. The output voltage of the inverter is applied to
the load over an isolation transformer with the turn ratio 1.
The effects of the transformer on the voltage can be seen in
Fig. 12 where the there phase line to line voltages have
sinusoidal wave shapes including some harmonics. The
harmonics can be eliminated or reduced by applying proper
filter circuits, which are not considered here for the moment.
120 140160 180200220 240260
PVA Voltage (V)
PVA Current (A)
Fig. 5 Current-Voltage ( I-V) Characteristics of PVA.
120 140160 180200 220240 260
PVA Voltage (V)
PVA Power (W)
Fig. 6 Power-Voltage (P-V) Characteristics of PVA
PVA Voltage (V)
Fig. 7. Time response of the PVA voltage.
PVA Current (A)
Fig. 8. Time response of the PVA current.
PVA Power (W)
Fig. 9. Time response of the PVA power.
Voltage at dc load bus (V)
Fig. 10. Voltage at dc load bus.
Line to line voltage at inverter output (V)
Fig. 11 . Line to line voltage at the output of the inverter.
0.0050.010.0150.02 0.0250.03 0.035
Line to line voltages at ac load bus (V)
Fig. 12. Three phase line to line voltages.
This paper introduces a simulation model for photovoltaic
arrays (PVA) to be used in Matlab-Simulink GUI
environment. The proposed model has a generalized structure
so that it can be used as a PV power generator along with
wind, fuel cells and small hydro system by establishing proper
interfacing and controllers. The model is simulated connecting
a three phase inverter showing that, the generated dc voltage
can be converted to ac and interfaced to ac loads as well as ac
utility grid system. Therefore the model proposed here can be
considered as a part of distributed power generation systems.
I. H. Altas thanks the Scientific and Technological Research
Council of Turkey for the financial support during this work.
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