Proceedings of the 8th

World Congress on Intelligent Control and Automation

July 6-9 2010, Jinan, China

An Adaptive Solar Photovoltaic Array Reconfiguration

Method Based on Fuzzy Control*
Ze Cheng, Zhichao Pang, Yanli Liu and Peng Xue
School of Electrical Engineering and Automation
Tianjin University
Tianjin, China
chengze@tju.edu.cn

Abstract - As the complicated structure of the PV generation were caused by the partially shaded solar photovoltaic module,
systems and variety of application environments, the mismatch and will improve the P-V characteristics of solar PV array,
and hot spot phenomena caused by partial shade or non-uniform avoid using the complex MPPT algorithm [7, 8] for multi-
illumination not only heavily affect the output characteristics of summit and multi-target problems.
photovoltaic arrays, but also create safety and reliability
The shade of solar cells is a complex phenomenon. At
problems. This paper proposes a self-adaptive reconfiguration
method based on fuzzy control, introduces how to apply it to the present, most of the photovoltaic cells reconfiguration method
photovoltaic power generation systems, and explains why fuzzy cannot timely accurately measure the shading conditions of
control based on the shading degree of PV arrays can quickly PV cells, and most of control strategies adapted are not
respond to the changes of external environments. The flexible, and etc. Each of these drawbacks might produce
experimental results show when the partial shade phenomenon vibration at the point of target, therefore they will cause the
occurs, changing the connections of the solar PV submodules photovoltaic cells compensate overly or defectively. So this
using switching matrix can quickly reduce the loss of output paper proposes shading degree model-based fuzzy control
power. reconfiguration method.
Index Terms - fuzzy control, photovoltaic array, adaptive,
II. SHADING DEGREE MODEL-BASED FUZZY CONTROL
shading degree, reconfiguration
RECONFIGURATION METHOD
I. INTRODUCTION A. Experiment of the solar PV cells at the different shading
Non-uniform illumination is the general problem when conditions
using solar energy. The reasons that create non-uniform Solar cells are connected in series firstly and then in
illumination might be anything in the nature. Such as clouds, parallel, this configuration is SP (series-parallel) [4] (Fig. 1).
Iout
leaves, electric poles, the shadow of buildings, even guano and
so on. Non-uniform illumination brings low output of power +
and high power consumption to photovoltaic cells as lack of
the sunlight. Series connection style is generally used between PV(1,1) PV(1,2) PV(1,n-1) PV(1,n)
solar cells due to the voltage produced by a solar cell is too
low. The same problem occurs on the current of PV modules
when solar cells are connected in series. If part of photovoltaic PV(2,1) PV(2,2) PV(2,n-1) PV(2,n)
cells was shaded, the current which a shaded cell generates Vout
would be less than the current which a non-shaded cell does.
According to Kirchhoff's voltage law, the shaded PV cells will
carry negative voltage and become loads of the circuit. It also PV(m-1,1) PV(m-1,2) PV(m-1,n-1) PV(m-1,n)
consumes the power produced by other non-shaded PV cells in
the form of heat, (with the continual) over a long period of
time of heat accumulation, the high temperature may damage PV(m,1) PV(m,2) PV(m,n-1) PV(m,n) -
the packaging material of the modules, or even destroy the
internal physical structure of photovoltaic cells, and cause Fig.1. Series-parallel (SP) solar PV array
permanent damage, known as "hot spot" phenomenon [1-3]. A new grid-connected configuration of the PV cells is
For solving "hot spot" problem, we use TCT (total-cross-tied) [4] (Fig. 2). In this configuration, a
"reconfiguration"[4-6] method. The method of the connection single PV cell was shaded, and would not affect the work of
of photovoltaic cells in the module dynamically changes based other cells.
on the environment changes, the cells that are not shaded are
going to “compensate" the cells that are shaded, which would
effectively prevent the decrease of the output power which

*
This work is partially supported by National Basic Research Program of China (973 Program) # 2009CB219700 and Tianjin science and technology supported
program #09ZCGYGX01100.

176
978-1-4244-6712-9/10/$26.00 ©2010 IEEE
 TABLE I
ONE ROW OF THE SOLAR ARRAY IS SHADED FROM LEFT TO RIGHT
Shading area 0 1/4 1/2 3/4 full
Voltage (V) 0.47 0.46 0.44 0.40 0.02
Power (W) 0.028 0.026 0.024 0.020 0
Solar cells of 9 cells in parallel, the output power
decreases with the shading area increases.

TABLE II
TEN ROWS OF THE SOLAR ARRAY ARE SHADED FROM LEFT TO RIGHT
Shading area 0 1/4 1/2 3/4 full
Voltage (V) 3.94 3.72 3.27 2.15 0.05
Power (W) 1.940 1.730 1.337 0.578 0
10 rows of solar cells in series, the output voltage
Fig.2. Total-cross-tied (TCT) solar PV array increases, the output power decreases with the shading area
In practice, the solar cells are affected by the different increases more clearly. 10 rows of the solar cells are shaded
shading area and irradiation, and it causes a great loss of from left to right make the output current decrease, so the
output power. For reconfiguration, we need to study on the output power decreases.
impact of shaded PV cells through experiment.
TABLE III
The following experimental data (Table I–Table IV) is TEN ROWS OF THE SOLAR ARRAY ARE SHADED FROM THE TOP DOWN
tested by the solar PV cells from Tianjin Top Industry Shading area 0 1/4 1/2 3/4 full
Equipment CO.LTD. The PV cells are composed of 10 big
Voltage (V) 3.97 1.01 0.33 0.16 0.05
cells and 10 small cells. Every cell has its own terminal. The
area of big cell is 9 times of the small one. The TCT Power (W) 1.970 0.128 0.014 0.003 0
configuration (Fig. 3) contains 10 rows and 9+1 columns. Test 10 rows of the solar cells in series are shaded from the top
conditions: Solar panel angles 45°, temperature 28 , connect down make the output voltage and current decrease quickly,
the load 8 Ω . Conditions of shade are divided into different so the output power decreases with the shading area increases
areas and different irradiations. The output voltage of every seriously.
cell is only about 0.5V in the TCT configuration.
TABLE IV
TEN ROWS OF THE SOLAR ARRAY ARE UNDER DIFFERENT ILLUMINATIONS
irradiation 100% 70% 50% 30%
Short-circuit 1.13 0.33 0.20 0.09
current (A)
Voltage (V) 3.89 2.85 1.52 0.68
Power (W) 1.892 1.015 0.289 0.058
10 rows of the solar cells in series, the output power
decreases with the irradiation decreases, the output current is
affected by the irradiation.(irradiation is measured by MS6610
(a)
from MASTECH)
The SP configuration solar cells, when the shading area of
more than 1/2, the output power dropped to 1% of the original
[9]. Based on the above experiment, the TCT configuration
solar cells’ output power will decrease as shading area with an
increase. Compared with the SP configuration solar cells, the
loss of power is less, so we can see the advantages of the TCT
configuration. In addition, the irradiation decreases, the output
power is also reduced very seriously in TCT configuration.
Therefore, it is necessary to research on the irradiance at the
problem of the shaded PV cells.
B. The shading degree model of PV cells
(b) For solving the “hot spot” problem with the
Fig.3. 10×(9+1) TCT solar PV array outdoor test reconfiguration method, we need some PV cells for
compensation except for the normal PV cells. When the array
is partial shaded, part of the system's interconnection will be
got reconfiguration, in order to compensate for the shading

177
cells. Due to the complexity and changes of shading use the shading degree model-based method to calculate the
conditions, the shading area and irradiation of each submodule irradiance of partially shaded PV cells, and then study the PV
(one row of the TCT PV array is defined as a submodule) of cells reconfiguration strategy.
PV arrays are different, and the cells in the adaptive bank In TCT configuration, one submodule is n cells in
which are fixed with others might be partially shaded, so it is parallel.
difficult to determine the number of cells in the adaptive bank I out Output current of a solar array
which are required to compensate the shaded submodules.
This paper uses "shading degree" to show the change of V j Voltages of submodules
shading conditions at each submodule, the size of decline in Photo-generated current of submodules in a fixed part
the irradiance of each submodule is defined as "shading
degree". From Fig. 4, by the model of a PV cell, the photo-
I Fj :
generated current of PV cells: qV j
VOCAj qVOCAj I Fj = I out + nI S [exp( ) − 1] (2)
I Aj = + I S [exp( ) − 1] (1) akT
RSH akT a Ideality factor of a solar cell

VOCAj Open-circuit voltage of solar cells in the adaptive bank

k Boltzmann’s constant
T Cell operating temperature
IS Saturation current of a solar cell diode q Electron charge
RSH Shunt resistance of a solar cell or a submodule
As the photo-generated current of the PV cells is
proportional to the irradiance, in order to control the
I out reconfiguration circuit conveniently, use the variation of
output current and voltage to reflect the variation of irradiance.
α is the proportionality coefficient, G is the irradiance of PV
IL RS cells, according to (2) the irradiance of solar cells in the
RSH V j adaptive bank:
VOCAj qVOCA j
Fig.4. Circuit model of a PV cell
GAj = α { + I S [exp( ) − 1]} (3)
RSH akT
The irradiance of submodules:
mA / cm 2

qV j
GFj = α {I out + nI S [exp( ) − 1]} (4)
akT
V

From (3) (4), the irradiance of cells is reflected by the

voltage and current of PV cells.
C. Shading degree model-based fuzzy control
reconfiguration algorithm
For TCT photovoltaic arrays, the irradiance of the
submodule that is not shaded is the standard, calculated the
irradiance of each submodule and compare with the standard,
so the ΔGFi is the "shading degree", use the experience and
W / m2
knowledge of the expert system to divide the shading degree
Fig.5. The relationship of voltage, current and irradiance into different levels, make some fuzzy rules, according to the
different shading levels of solar PV submodules, determine the
Photovoltaic cells receive the radiation energy of the number of PV cells required to compensate. The flowchart of
direct light and scattered light to electrical energy conversion. the algorithm is shown in Fig. 6.
The relationship of voltage, current and irradiance is shown in 1) Check whether partial shade happened. Generally, the
Fig. 5, curve a shows that the open-circuit voltage of the PV fixed solar array and the adaptive bank are connected in the
cells is approximately proportional to the logarithm of
irradiance, which means that when the weather is sunny and original configuration. The voltage Vi of each row of
cloudy, the open-circuit voltage of PV cells doesn’t change a photovoltaic arrays is detected. In the uniform illumination
lot, so the maximum power point voltage of the cells is not conditions, the value of voltage in each row is basically the
greatly affected by the irradiance. Curve b shows that the same. In the non-uniform illumination conditions, when one or
short-circuit current of the cells increases in direct proportion some rows are shaded, the shaded PV cells carry negative
with the irradiance increases. The output current of the PV voltage and become loads of the circuit. It consumes the
cells is almost proportional to the irradiance. From this we can power produced by other PV cells, the more cells shaded, the
see that in the normal working conditions, the output power of lower voltage of this row, and it is less than the threshold
PV cells is determined by the irradiance. Therefore, we can

178
voltage, i.e., Vi < δ , it indicates that this row is shaded 3) Reconfiguration of PV arrays. After the fuzzy
calculation, the controller make some switches of the
seriously, the adaptive reconfiguration starts automatically. switching matrix to be closed, the solar cells in the adaptive
2) Calculation of shading degree and determine the rules bank are connected to the shaded submodules, and the
on compensation. According to 1), we calculate the irradiance
configuration of the PV array has been changed.
by Vi. ΔGFi as the shading degree.
We have ΔGFi = GF0 - GFi
GF0 Irradiance of non-shaded submodule
V 1 , ...,V m

GFi Irradiance of each submodule

According to the fuzzy rules, the number p of PV cells in

the adaptive bank to compensate is given by:
p Vi < δ
ΔGFi ≈ ∑ GAj
j =1
The design of Fuzzy rules: the shading degree of each
•
submodule ΔGFi and the derivative of irradiance G Fi are the GF1 ,..., GFm
inputs of the fuzzy controller, the sum of the irradiance of
p

∑G
•
cells to compensate each submodule is the output of ΔGFi G Fi
Aj
j =1
the fuzzy controller.
• •
ΔGFi G Fi
After the Fuzzification, ΔGFi and G Fi are transformed to
G (k ) − G (k − 1)
E and CE = .
U (k ) − U (k − 1)
After the Fuzzy Inference, we can get the fuzzy control
output U . After the Defuzzification, we use the output
p

∑G
j =1
Aj to execute.
ΔGFi < θ
When the submodule is shaded, the irradiance must be
lower, and it is less than the irradiance of the submodule
which is not shaded, so ΔGFi is positive. Then E only
changes in the positive direction. PS(Positive Small)and PB
（Positive Big）stand for the small and big of fuzzy language Fig.6. Flowchart of the Shading Degree Model-Based Fuzzy Control
Reconfiguration Algorithm
variable in the positive direction.
TABLE V
FUZZY RULES As the irradiation changes in a larger time constant, so the
| CE | algorithm sets the delay, when measure the shading degree of
rules E U
each submodule again, if ΔGFi less than the set threshold θ ,
R1 PS — S
then the loss of power has been compensated by the
R2 PB S B reconfiguration, the switching matrix keeps its state.
Otherwise, it means irradiation changes once again, such as
R3 PB B S
the shape of the shadow is changing or the shaded things is
moving, so that the shading degree of each submodule is
As the fuzzy rules, E is PB, the shading degree is rising. different from the previous time, PV arrays need
It means the irradiance is decreasing seriously. When | CE | is reconfiguration again. The system avoids a large number of
B, the derivative of irradiance is high, it means the irradiation reconfigurations when irradiance changes fast such as cloudy
is changing rapidly. In case to change the connection days, so it preserves the lifetime of the switches and enhance
the stability of the system. The structure of PV cells after
frequently by mistakes, so make U to be S.
reconfiguration is shown in Fig. 7.

179
 (VOCA1 ,VOCA2 ,...,VOCA( m−1) ,VOCAm ) I out (V1 , V2 ,..., Vm −1 , Vm )
I A1 I out
PV1 I F1 Detection
PVA1 circuit

VOCA1 V1

I A2 PV2 I F2
PVA2
VOCA2 V2
m×m
The
Switching MCU
PVA( m−1)
I A( m−1) PVm−1 I F( m−1) Vout
Matrix R
VOCA( m−1) Vm −1

I Am PVm I Fm
PVAm
Control
VOCAm Vm
signal

Fig.7. The interconnection after reconfiguration

At present, the usual reconfiguration algorithm is
connecting the solar cells after checking whether partial shade
happened. It will make the photovoltaic cells compensate The fixed solar array The adaptive bank
overly or defectively. This method is inefficient. While the Fig.8. Reconfiguration system of solar PV array
shading degree model-based fuzzy control algorithm resolves
this problem. Since the cells in the adaptive bank might be III. EXPERIMENT RESULT & CONCLUSION
also partly shaded, the number of cells in the adaptive banks is In order to verify the effectiveness of fuzzy control
limited. According to the fuzzy rules, the cells are algorithm, we experiment at another solar panel. The TCT
compensated for the submodules which are shaded seriously configuration (Fig. 9) contains 3 rows and 10 columns. Every
first. The cells with the most irradiance of the adaptive bank cell has its own terminal.
are connected to the most shaded submodule with the least
irradiance. The power losses of the submodules are different,
so it needs to find the right amount of cells to compensate in
the adaptive bank. It reduces the waste of resources.
D. Reconfiguration system of solar PV array
The PV cells are divided into two parts: a fixed part and
an adaptive bank. Fig. 8 shows the right dotted line part is the
fixed solar array, and the left is the adaptive bank. In the
uniform illumination, the adaptive bank can form one
additional column to the fixed part. If the cells are shaded, the (a)
system works with the shading degree model-based fuzzy
control algorithm, measures the shading degree of the cells in
the adaptive bank, according to the shading degree of each
submodule, compensate the shaded submodules with the cells
required in the adaptive bank, and then change the connection
of the switching matrix, eliminate the effect of partial shading
and "hot spot", compensate for the loss of output power
caused by partial shading. In the system, voltages of
submodules in the fixed part and open-circuit voltages of cells
in the adaptive bank are measured through the external
(b)
detection circuit. The output current of the fixed part is
Fig.9. Solar PV array for Reconfiguration experiment
measured through a Hall-effect current transducer, and these
The experiment shows the effect of the shading degree
inputs are calculated in the MCU. The core device of the
model-based fuzzy control reconfiguration method. One row
controller is DSP56F801 from Freescale, using the PE
of the PV cells is a submodule. The output voltage of the PV
(Processor Expert) software of CodeWarrior, the output signal
of controller amplified to drive the switching matrix composed cells is about 1.5V, connect the load 1.75 Ω . The experiment
of relays. result is shown in Table VI– Table VIII

180
 Table VI shows 4 cells of submodule1 are 24% of As can be seen through the above experimental data,
shading, one none shading cell is connected to compensate. adaptive solar array reconfiguration method based on fuzzy
TABLE VI control is effective. The reconfiguration improves the P-V
EXPERIMENT RESULT
characteristics of solar PV array and avoids using the
Shading and Load Submodule1 Submodule2 Submodule3 complicated MPPT algorithm with multi-summit and multi-
compensation voltage(V) voltage(V) voltage(V) voltage(V) target problems, and minimizes use of DC-DC converters,
none
1.535 0.516 0.509 0.515
voltages or current sensors and switches. Another can be seen
shading from the table, after the reconfiguration the voltage of the
Submodule1 submodule is less than the voltage of the submodule was
4 cells with before it is shaded. It is caused by the shading PV cells are
1.519 0.501 0.510 0.513
24% of not removed from the circuit. They also consume the power
shading produced by the submodule. Therefore, the ideal
1 none reconfiguration method is to change the whole structure,
shading cell 1.530 0.510 0.509 0.513 compensate the submodule while the shading cells are
to compensate removed from the array to avoid the loss of output power, it
will be the following work. One cell in the experiment stands
Table VII shows 2cells of submodule1 are 50% of for one or a few solar arrays in the actual solar photovoltaic
shading, one none shading cell is connected to compensate. power station, and the adaptive reconfigurable circuits can be
TABLE VII built by the FPGA or CPLD, even develop the SoC to reduce
EXPERIMENT RESULT costs.
Shading and Load Submodule1 Submodule2 Submodule3 REFERENCES
compensation voltage(V) voltage(V) voltage(V) voltage(V)
[1] Cuiyan, C.R., “A Research of Hot Spot on PV Array,” [Proceedings of
the 15th International Photovoltaic Science & Engineering Conference,
none 1.535 0.516 0.509 0.515 pp. 446-447, 2005].
shading [2] Adelmann, P., G. Rimpler, and M.Schneider, “Danger of Hot Spot by
Submodule1 Shunt Controller,” [Proceedings of the 8th China Photovoltaic
Conference, pp. 534-537, 2004].
2 cells with 1.525 0.506 0.511 0.514 [3] Meyer EL, van Dyk EE, “Assessing reliability and degradation of
50% of photovoltaic module performance parameters,” IEEE Transactions on
shading Reliability, no. 3, pp. 83-92, 2004.
1 none [4] Dzung Nguyen, Brad Lehman, “An Adaptive Solar Photovoltaic Array
shading cell 1.532 0.512 0.510 0.514 Using Model-Based Reconfiguration Algorithm,” IEEE Trans. On
to compensate Industrial Electronics, vol. 55, no. 7, pp. 2644-2654, 2008.
[5] Guillermo Velasco, Francesc Guinjoan, Robert Piqué, “Grid-Connected
PV Systems Energy Extraction Improvement by means of an Electric
Table VIII shows 3 cells of submodule1 are 70% of Array Reconfiguration (EAR) Strategy: Operating Principle and
shading, 3 cells with 50% of shading are connected to Experimental Results,” [Power Electronics Specialists Conference, pp.
1983-1988, 2008].
compensate defectively, 3 none shading cells are connected to [6] R. Candela, V. Di Dio, E. Riva Sanseverino, P. Romano,
compensate overly. “Reconfiguration Techniques of Partial Shaded PV Systems for the
TABLE VIII Maximization of Electrical Energy Production,” [ICCEP '07.
EXPERIMENT RESULT International Conference on Clean Electrical Power, pp. 716-719, 2007].
[7] Patel, H.; Agarwal, V., “Maximum Power Point Tracking Scheme for PV
Shading and Load Submodule1 Submodule2 Submodule3
Systems Operating Under Partially Shaded Conditions,” IEEE
compensation voltage(V) voltage(V) voltage(V) voltage(V) Transactions on Industrial Electronics, vol. 55, no. 4, pp. 1689-1698,
2008.
[8] Miyatake, M.; Toriumi, F.; Endo, T.; Fujii, N., “A Novel maximum
none power point tracker controlling several converters connected to
1.535 0.516 0.509 0.515 photovoltaic arrays with particle swarm optimization technique,” [Power
shading
Electronics and Applications, 2007 European Conference on, pp. 1-10,
Submodule1 2007].
[9] Zhang Li, “Research on photovoltaic cell character,” [North China
3 cells with 1.517 0.497 0.510 0.514 Electric Power University, pp. 18-27, 2008].
70% of
shading
3 cells with
50% of
1.520 0.501 0.511 0.515
shading to
compensate
3 none
shading cells 1.523 0.510 0.511 0.515
to compensate

181