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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
ISSN 1843-6188
REAL-TIME EMULATOR OF PHOTOVOLTAIC ARRAY
IN PARTIAL SHADOW CONDITIONS
BASED ON CLOSED-LOOP REFERENCE MODEL
Riad KADRI, Jean-Paul GAUBERT, Gérard CHAMPENOIS, Mohamed MOSTEFAÏ
Laboratoire d’Automatique et d’Informatique Industrielle (LAII-ESIP)
Université de Poitiers, France
E-mail: [email protected]
Abstract: Solar photovoltaic systems technology have known
an extensive research in recent times due to their suitability
for use in low, medium and high power generation. In recent
years, the grid connected photovoltaic systems have become
more popular because they do not need battery back-ups to
ensure maximum power point tracking (MPPT). However,
partial shading is one of the main causes that reduces energy
yield of photovoltaic array. Hence research activities have
mainly focused on the influences of array configuration on
the energy yield while in contrast very little attention has been
drawn to the performance of the MPPT under shaded array
conditions. Consequently, photovoltaic array emulator is
indispensable (essential) for the operational evaluation of
system components. The dynamic response of the photovoltaic
array emulator is of particular importance in order to avoid
any significant impact on the maximum power point tracker
and current control of the inverter. In numerous papers, the
current and voltage vectors of the photovoltaic array are preloaded into a look-up table and the system is iteratively
converging to the solution. The purpose of this paper is to
design and develop a new real-time emulator of photovoltaic
array output characteristics based on closed-loop reference
model. The proposed system consists of a programmable
power supply, which is controlled by a dSPACE DS1104
board under the Matlab/SimulinkTM environment. The
control software uses feedback of the output voltage, current
and reference model to regulate through PI regulator the
actual operating point for the connected load. The
experimental results show that the output characteristics of
the emulator are very close to those of the actual photovoltaic
modules with dynamic characteristics much lower than the
possible climatic variations.
installed anywhere. In addition, manufacturers have
designed various models, which can be placed at a
variety of different types of houses or buildings to
achieve better performance. However, performance
analysis of this scheme in real conditions is generally a
difficult task because several factors should be taken into
account such as the partial shading.
In a Classical grid connected PV system topology, a
series connected of photovoltaic module is used Fig.1,
performance is negatively affected if all its modules are
inhomogeneous illuminated. All the modules in a series
array are forced to carry the same current even though a
few modules under shade produce less photocurrent. The
shaded modules may get reverse biased, acting as loads
and dissipates power from fully illuminated modules in
the form of heat. If the system is not appropriately
protected, hot-spot problem [1]-[2] can arise and in
several cases, the system can be irreversibly damaged.
Keywords: photovoltaic, maximum power point tracking,
real-time PV emulator, shadow conditions.
Fig. 1. Classical grid connected PV system topology
PV
VSI
L
Grid
In the new trend of integrated PV arrays, it is difficult to
avoid partial shading of array due to neighboring
buildings throughout the day in all the seasons. This
makes the performance study of partial shading of
modules an important issue.
Field testing is conducted to ensure the quality of
installation and the performance of the product, in fact,
is costly, time consuming and strongly dependent on
actual climatic conditions. In addition, it is not without
its risks since the direct employment of the PV modules
for prototyping test can damage the source itself. A
solution for developing experimentations without the
need of real PV panels is thus very important, at least for
1. INTRODUCTION
The importance of the renewable energy like
photovoltaic systems in the generation of electricity is
rapidly increasing currently. Beside the plants in a large
resource, one of the main focus areas in the introduction
of photovoltaic (PV) as renewable energy power source
connected to the grid is the use of building surfaces for
photovoltaic installations. The PV systems are modular,
hence the major advantage of these systems is that they
can be simply adopted in existing buildings and can be
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
ISSN 1843-6188
the first stage of testing. This has increased the interest
on the development of laboratory tools useful for
carrying out measurements and analyses, with no need to
perform field tests or to wait for particular atmospheric
conditions [3].
A wide range of photovoltaic array emulators based
in power converters have been proposed and developed
during last years. Some of them without galvanic
isolation [4], based on structures with low frequency
transformer [5] or on HF transformers [6] and using
Pulse Width Modulation (PWM) principle [7] or linear
converters to avoid EMC-measurements [8]. Trying to
emulate the PV current-voltage curve (I-V curve)
converters amplified the curve of a reference solar cell
[9] or obtained the I-V curve from a discrete table stored
in a memory and then interpolated the points [10] [11],
but most of them used mathematical models of panel’s IV curve and calculated it from array‘s parameters [12]
[13], making possible to modify and simulate the PV
curve under different situations easily.
In this paper, the development of real-time emulator
of photovoltaic array based on closed-loop reference
model structure is presented. With this scheme it is
possible to analyze at the laboratory the behavior of both
the maximum power point tracking (MPPT) techniques
and the complete photovoltaic system under special
conditions like partial shading. On the other hand, the
emulation of the electrical behavior of photovoltaic
generators allows performance analysis of photovoltaic
inverters to be carried out at the laboratory without
requiring real photovoltaic energy sources.
In section 2, the characteristic I-V curve of a PV module
is explained, and the final model under partial shading
conditions used in this emulator is introduced while
section 3 discusses ways of implementing a closed-loop
reference model for regulating the output voltage as a
function of the output current. Sections 4 and 5 present a
simulation and experimental results, respectively. Finally
the conclusions are stated in section 6.
is not an active device, it works as a diode, i.e. a p-n
junction. It produces neither a current nor a voltage.
Thus the diode determines the I-V characteristics of the
cell. For this paper, the electrical equivalent circuit of a
solar cell is shown in Fig. 2. The output current I and
output voltage V of solar cell is given by (1) and (2).
2. SOLAR CELL AND PV ARRAY MODEL
If the circuit is shorted, the output voltage V = 0, the
average current through diode is generally neglected, and
the short-circuit current Isc is expressed by using (6).
V
q.V

 V
I  I ph  I do  do  I ph  I 0  exp( do )  1  do
Rsh
n.k .T

 Rsh
V  Vdo  Rs I
Ido
Vdo
Ir
I
q

  V  Rs I 
I  I ph  I 0  exp(
(V  Rs I ))  1   

n.k .T

  Rsh 
(3)
Where the resistances can be generally neglected and
(3) is simplified to (4).
q


I  I ph  I 0  exp(
.V )  1
n.k .T

(4)

If the circuit is opened, the output current I = 0 and
the open-circuit voltage Voc is expressed by (5).
  n.k .T
 n.k .T   I ph
In 
 1  


  q
 q   I0

Voc  
I sc  I 
  I ph
 In  I
  0




I ph
(5)
(6)

R 
 1  s 
R
sh 

Finally, the output power P is expressed by (7).
Rs
Rsh
(2)
Here, Iph is the photocurrent, I0 is the reverse saturation
current, Id is the average current through diode, n is the
diode factor, q is the electron charge, q = 1.6*10 -19, k is
Boltzmann’s constant, k = 1.38*10-23, and T is the solar
arrays panel temperature. Rs is the intrinsic series
resistance of the solar cell, this value is normally very
small. Rsh is the equivalent shunt resistance of the solar
array and its value is very large. In general, the output
current of solar cell is expressed by (3):
A photovoltaic generator is the whole assembly of
solar cells, connections, protective parts, supports etc. In
the present modeling, the focus is only on cells. Solar
cells consist of a p-n junction, various modeling of solar
cells have been proposed in the literature [14]-[17].
Iph
(1)

V
P  VI   I ph  I do  do

Rsh

V

 V

(7)
Two or more modules can be pre-wired together to be
installed as a single unit called a PV or solar panel.
Additional PV panels can be added as electricity
production needs increase. The entire PV system,
consisting of more panels in series connected, is known
as an array Fig. 3.
Fig. 2. Solar cell electrically equivalent circuit
Thus the simplest equivalent circuit of a solar cell is a
current source in parallel with a diode. The output of the
current source is directly proportional to the light falling
on the cell (photocurrent). During darkness, the solar cell
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
ISSN 1843-6188
Iph
Ido
3. DESCRIPTION OF THE PROPOSED SYSTEM
I
Ir
Rs
In order to obtain the I–V characteristics of the seriesconnected modules (series assembly) conducting a
current I, the voltages across these modules, V1, V2 and
Vn , are added to determine the resultant output voltage.
The characteristics for series assembly are, thus,
obtained internally by the software by applying similar
procedure at all the points on the I–V curve of the seriesconnected modules.
Rsh
Vdo
Iph
Ido
I
Ir
Rs
Rsh
Vdo
V
T1
Iph
Ido
Ir
I
G1
Rs
Ipv
Rsh
Vdo
if I  Icc1
V1 = f(I)
else
V1 = VBd
end
V1
V2
Vn-2
Tn
Because the series connection of the PV generator forces
all modules to operate at the same current (string
current), the shaded cell within a module becomes
reverse biased which leads to power dissipation and thus
to heating effects. To avoid thermal overload and the
formation of hot spots, sub-strings of cells inside the
interconnection circuit of modules are bridged by bypass
diodes (Fig.4). This measure limits the bias voltage at
the shaded cell and thus the dissipated power. Another
reason to use bypass diodes is to preserve more of the
power output of the module in case of partial shading.
For economic reasons whole strings of cells are
bypassed, and therefore, even if only one cell is shaded,
the whole string is affected, and produce considerably
less power than it would have done without the bypass
diode. This phenomenon can move the maximum power
point to unexpected places.
Ido
Rsh
Vdo
Iph
Ido
Ido
Vdo
I
Ir
Rsh
Vdo
Iph
I
Ir
Ir
Rsh
I
Gn
Ipv
if I  Iccn
Vn = f(I)
else
Vn = VBd
end
Vn
Fig. 5. Configuration synoptic when the modules are
bypassed.
4. SIMULATION RESULTS
This section describes the procedure used for simulating
the I–V and P–V characteristics of a partially shaded PV
array. Based on the above equations, the PV model has
been implemented using Matlab. The Graphical-UserInterface, allows to plot the I–V and P–V characteristics
of a PV array. The user has access to choose the
irradiation intensity (0 to 1000 W/m2), the cell
temperature, as well as the number of panels in series,
which form the string and the number of strings in
parallel. These options offer a very high flexibility and a
wide range of different PV plant configurations with
different voltage and current levels can be simulated.
Furthermore, the effects of the partial shading can be
visualized by choosing the Irradiation level. Modeling
the partial shading effects has been made based on the
assumption that every module has its own bypass diode.
Firstly, Figures 6, 7 and 8 shows the simulation
results of the emulating operation mode under
homogeneous illuminated.
The I–V and P–V characteristics of the PV (shaded and
unshaded modules) modules at the same temperature but
at different irradiation levels are shown in Figures 9, 10
and 11.
Rs
Bd
Rs
Vpv
Vn-1
Fig. 3. Equivalent circuit model of PV array in series
connection.
Iph

V
Bd
Rs
Bd
Fig. 4. Equivalent circuit model of PV array bridged by
bypass.
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
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ISSN 1843-6188
200
3
Power (W)
Current (A)
3.5
2.5
2
1.5
150
100
50
1
0.5
0
0
0
20
40
60
80
100
120
140
0
20
40
60
80
100
120
140
Voltage (V)
Voltage (V)
Fig. 10. P(V) characteristic of PV array with three
irradiation levels.
Fig. 6. Typical I(V) of PV array.
400
300
250
200
150
Power (W)
Power (W)
350
100
50
0
0
20
40
60
80
100
120
140
Voltage (V)
Fig. 7. Typical P(V) characteristic of PV array.
Voltage (V)
Time
Power (W)
Power (W)
Fig. 11. 3D P(V) characteristic of PV array under
inhomogeneous irradiation variation.
Time
Voltage (V)
Fig. 8. 3D typical P(V) characteristics of PV array under
homogeneous irradiation variation.
Voltage (V)
4
Time
Current (A)
3.5
3
Fig. 12. Comparison of 3D P(V) characteristics.
2.5
2
1.5
5. EXPERIMENTAL RESULTS
1
The real-time emulator of photovoltaic experimental test
bench used was developed in LAII-ESIP laboratory (Fig.
13 and 16). It was achieved with a programmable power
supply: TDK-Lambda GEN300-11. The control strategy
is implemented using a single-board DS1104
manufactured by dSPACE Company and developed
0.5
0
0
20
40
60
80
100
120
140
Voltage (V)
Fig. 9. I(V) characteristic of PV array with three
irradiation levels.
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
ISSN 1843-6188
200
under the integrated development environment of
Matlab/SimulinkTM RTW provided by The MathWorks
Inc. The control is achieved by two PI regulators with
reference model and uses feedback of outputs voltage and
current to regulate the operating point for the connected
load.
Figures 14 and 15 show respectively the I(V) and P(V)
characteristics for three irradiation levels or shadow
conditions: 1000 W/m², 700 W/m² and 400 W/m². Red
line corresponds to the reference model results and blue
crosses are experimental points. In both cases, the realtime emulator output follows perfectly the trajectories of
the statement PV arrays for the three shadow conditions.
Other results are exposed on figures 17 and 18 where red
line corresponds to the reference model also and blue line
to the output of the emulator. On the right side of these
figures, shadow conditions are fixed through irradiation
differences: for the first module irradiation is equal to
1000 W/m², for the second 700 W/m², for the third 400
W/m². On the other hand the temperature is identical for
the three cells since they are laid out at the same place.
180
Power (W)
160
140
120
100
80
60
40
20
0
20
40
60
80
100
120
Voltage (V)
Fig. 15. Experimental P(V) characteristics of PV array
with three irradiation levels.
Programmable
Power
supply
dSPACE
DS1104
Screen of
ControlDesk
Load
Fig. 13. Photovoltaic experimental test bench structure.
4
3.5
Current (A)
3
2.5
2
1.5
1
0.5
0
20
40
60
80
100
120
Voltage (V)
Fig. 16. Control synoptic of the experimental test bench
structure.
Fig. 14. Experimental I(V) characteristics of PV array with
three irradiation levels.
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
ISSN 1843-6188
Fig. 17. Screen of real-time experiment environment ControDesk for I(V) characteristics.
Fig. 18. Screen of real-time experiment environment ControDesk for P(V) characteristics.
control circuit is implemented in real time by using a
single-board dSPACE DS1104 with excellent results and
dynamic characteristic much lower than the climatic
variations since its band-width is equal at 10 Hz. Now,
new algorithms are in progress in order to fit to its
conditions and to detect the true point of maximum
power.
6. CONCLUSION
In this study, a real-time emulator of photovoltaic array
based on closed-loop reference model structure is
investigated. With this development, it is possible to
analyse the behaviour of PV array on the one hand and
on other hand to work out the maximum power point
tracking (MPPT) techniques in case on partial shading at
the laboratory test bench. Our solution allows evaluating
the maximum power point places and their number
according to the atmospheric conditions as well in
simulation that an experimental. Thus, in function of
different irradiation on PV arrays, we can plotted or
emulated characteristics I(V) and P(V) and estimate the
performances of the system under these conditions. The
ACKNOWLEDGMENT
This work was supported in part by the local council of
Poitou Charentes, France under research project N°:
08/RPC-R-003.
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Scientific Bulletin of the Electrical Engineering Faculty – Year 10 No. 3 (14)
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