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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
Particle Swarm Optimization based Maximum Power Point Tracking for Partially
Shaded Photovoltaic Arrays
a
Kenneth Tze Kin Teo, a Pei Yi Lim, aBih Lii Chua, b Hui Hwang Goh, a Min Keng Tan
a
b
Modelling, Simulation & Computing Laboratory
Faculty of Engineering, Universiti Malaysia Sabah
Kota Kinabalu, Sabah
e-mail: [email protected], [email protected]
Faculty of Electrical and Electronic Engineering
Universiti Tun Hussein Onn Malaysia
Batu Pahat, Malaysia
Abstract — This paper presents particle swarm optimization based perturb and observe (PSO-P&O) algorithm for maximizing
output power of photovoltaic (PV) array under partially shaded conditions (PSC). During PSC, the P-V characteristic of PV will
become more complex with multiple maximum power points (MPP). Most of the conventional maximum power point tracking
(MPPT) algorithms, such as P&O, will be trapped at the local MPP and hence limiting the maximum power generation. As such,
investigation on PSO-P&O algorithm is carried out to maximize the PV generated power principally under PSC operation. The
performances of conventional P&O and the proposed PSO-P&O algorithms are investigated particularly on the transient and
steady state responses under various shaded conditions. The simulation results show the developed PSO- P&O algorithm is able to
facilitate the PV array to reach the global MPP and assist the PV array to produce more stable output power compared to the
conventional P&O algorithm.
Keywords - photovoltaic array; partially shaded conditions; particle swarm optimization; perturb and observe; MPPT
I.
INTRODUCTION
The photovoltaic (PV) power generation has shown a
significant potential in supplying renewable and
environmental friendly energy. The recent report of REN21
showed the global operation of solar power generation had
increased from 139 GW in year 2013 to 177 GW in year
2014 or equivalent to 27.3 % increment [1]. Although
research and development on solar cell design and
fabrication are carried out continuously to improve the
efficiency of energy conversion, the improvement on
optimizing the operating condition of PV system using
maximum power point tracking (MPPT) approach is
important to empower the solar energy generation [2, 3].
The MPPT approach is implemented to track the
maximum available output power of the PV system, or
known as maximum power point (MPP), hence it ensures the
maximum power can be extracted regardless of the dynamic
environmental changes, such as irradiance and temperature.
Various studies have been carried out on MPPT approaches.
For instance, perturb and observe (P&O) algorithm and hill
climbing (H&C) algorithm are widely used as MPPT due to
their simplicity [4, 5]. Although these approaches perform
well in high solar irradiance, the tracking efficiency will drop
significantly when they are operated under low solar
irradiance condition.
Recently, the MPPT research trend has been focusing on
partially shaded condition (PSC) [6, 7]. In practice, multiple
PV modules will be connected together to create a solar farm
with desired voltage and capacity of loading current. The
PSC is inevitable because each PV module in the array will
DOI 10.5013/IJSSST.a.17.34.20
receive different levels of sunlight intensity due to shadow
effects from clouds, buildings, etc.
Under the non-uniform irradiance conditions, multiple
peaks will appear in the P-V characteristic graph of the PV
array. The complication of the characteristics is depending
on the orientation of the PV array and the shading patterns.
The occurrence of multiple MPPs will cause the
conventional MPPT algorithms to trap at the local MPP.
Therefore, several artificial intelligence (AI) techniques have
been introduced for adapting conventional MPPT algorithms
to allocate the global MPP (GMPP) and consequently
optimizing the power generation of PV array [8, 9, 10].
Punitha et al. [11] proposed artificial neural network
(ANN) based incremental conductance algorithm for GMPP
tracking in PSC. Their simulation studies have shown a
significant improvement in tracking via ANN compared to
fuzzy based H&C and P&O algorithms. Genetic algorithm
based MPPT algorithm has been proposed by Ramaprabha
and Mathur [12]. The results show that the proposed GA is
able to track the GMPP for various shading patterns. Chin et
al. [13] proposed fuzzy logic controller (FLC) to adapt P&O
algorithm for manipulating the step size of the perturbed
voltage, ∆V, so that the GMPP can be tracked and reached
faster. They also tested their algorithm under variable
changes of solar irradiance and cell temperature. The results
showed the fuzzy based MPPT is able to optimize the PV
power with less oscillation in the output power compared to
P&O algorithm [14].
Although the AI techniques are able to track the GMPP
faster with less oscillation in the steady state, investigations
on the various MPPT algorithms are still ongoing with the
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
ultimate goal to find a simple, low cost and highly efficient
algorithm. Kamarzaman and Tan [15] have compared the
characteristics and performances of AI based MPPT. They
summarized that the algorithm structures of FLC and ANN
are complex, whereas the sensitivity of GA to the
environmental changes is moderate.
Therefore, this paper aims to formulate PSO based P&O
algorithm to acquire the optimum operating point for the PV
system in order to extract maximum power from the PV
array. In this study, the PV array is formed by four PV panels
connected in series. The P&O algorithm is developed to
track the GMPP while the PSO algorithm will tune the
perturbation size of P&O algorithm for having faster tracking
speed (transient response) and more stable output power
(steady state response).
II.
  V  IRs   V  IRs 
  1  
I  I PV  I o exp
  
  nVT    R p 
where I is the solar cell terminal current, IPV is the solar cell
light-generated current, Io is the reverse biased saturation
current of Dm, V is the solar cell terminal voltage, n is the
ideality factor of the diode, and VT is the thermal voltage.
The function of thermal voltage is described as (2):

V
I
DC-DC
Converter
Load
PWM
Digital
Controller
Figure 1. Block diagram of photovoltaic system.
PV 1
PV 2
PV 3
PV 4
MODELLING OF PHOTOVOLTAIC SYSTEM
This section describes the mathematical model of a solar
cell, which can be further implemented for PV array
modeling. A PV system basically consists of a PV array, a
controller unit, and load, as illustrated in Fig. 1.
The PV array presented in this paper consists of four PV
modules connected in series, as shown in Fig. 2. A buckboost converter can be used to interface the voltage from the
PV array to the load. While the PV array generates power for
the load, the output voltage and current of PV are fed to the
digital controller to perform iterative tracking for the MPP.
The controller will determine the new operating voltage for
the PV array by adjusting the duty cycle of the buck-boost
converter.
A PV module or PV panel is formed by m connected PV
cells in series or parallel. The equivalent circuit of PV cell is
demonstrated in Fig. 3. A PV cell consists of a photo current
source, Ipv, a diode, Dm, the equivalent parallel resistor, Rp,
and the equivalent series resistor, Rs. Rp in the solar cell is
caused by the usual p-n junction leakage current in the cell
whereas Rs is due to the contact resistance of the metal base
within the semiconductor layer.
The I-V characteristic of a solar cell comprised of Dm is
described by the Schockley equation, as derived in (1):

Photovoltaic
Array
VT 
kTN s

q

where Ns is the numbers of solar cells connected in series, k
is the Boltzman constant (1.381 x 10-23 J K-1), T is the
DOI 10.5013/IJSSST.a.17.34.20
Figure 2. PV array consists of four identical PV modules.
Figure 3. Equivalent circuit for solar cell.
operating temperature of the solar cell in unit Kelvin, q is the
electron charge (1.602 x 10-19 C).
The external influences, such as solar irradiance and cell
temperature will affect the generation of charge carrier in PV
module and eventually affect the IPV, as described in (3):
I PV  I PVn  K I T 


where IPVn is the PV module light-generated current in the
nominal condition, KI is the ratio of short-circuit current to
temperature coefficient, ∆T is the difference of actual
temperature to the nominal temperature.
III.
PARTICLE SWARM OPTIMIZATION BASED MPPT
Inspired by the behaviors of nature bird flocking under
environment with little knowledge to search for food, PSO is
a computational intelligence method that optimizes a
problem by emulating a flock searching over candidate
solutions (information carried by the particles) through
search space [16, 17]. Fig. 4 illustrates the flowchart of PSO.
In this paper, the particles of PSO are referred to the
potential perturbation sizes of P&O. This algorithm allows
all the random particles to search for the optimum solution in
the search space through iterative process. Each particle will
learn their best experience while interacting with each other
to share their knowledge.
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
best position of particle i, GB is the global best position, xi is
the current position of particle i respectively.
The PSO searching process will be terminated when the
maximum number of iteration is fulfilled. Parameters of the
PSO algorithm are shown in Table I.
Start
Initiate vi and xi
TABLE I.
Parameters
Evaluate the fitness of xi
Update LBi and GB
Update vi and xi
Typical Value
Number of particles in a swarm
-
20
Stopping criteria
-
100 iterations
Cognition learning factor
c1
0.7
Social learning factor
c2
0.3
Range of perturbance voltage
IV.
No of particle =
max number?
-
0.01
∆V
0 V ≤ ∆V ≤ 2 V
PERTURB AND OBSERVE
The P&O algorithm has been selected to track MPP of
the PV array due to its simplicity and ease of
implementation. P&O is initiated by applying a perturbed
voltage, ∆V to alter the operating voltage of the PV array.
The change of output power at the present and the previous
sampling interval are subsequently compared. Based on the
instantaneous output power of the two sampling intervals,
the algorithm will decide to regulate the PV array to be
operated either at larger or lower operating voltage. The PV
array will pursue numerous iteration processes but eventually
the PV system will operate at a particular optimum power
point. At this stage, PV array will be generating maximum
output power. The tracking principal of P&O algorithm is
illustrated in Fig. 5.
Yes
Stopping criteria
fulfilled?
Symbol
Random search probability
Evaluate the fitness of xi
No
PARAMETERS OF PSO ALGORITHM
No
Yes
Obtain the optimized
perturbation size
End
Figure 4. Flowchart of PSO algorithm.
The learning process of particles is based on two rules:
attracted towards the global best position discovered by
others (social influence) and drawn towards its local best
promising position (cognition influence) [18]. The position
of each particle will be evaluated by a fitness function. In
this work, the fitness function utilizes the output voltage, V
and output current, I to calculate the fitness value (output
power) of each particle. The global and local best positions
are defined by how much power generated by a specific
operating voltage. The highest power generated is the best.
During the searching process (iterative process), the
velocity and position of each particle is updated based on the
inertia, social component and cognitive component, as
shown in (4) and (5):


vi 1  vi  c1r1 LBi  xi   c2 r2 GB  xi   
xi 1  xi  tvi 1 

where vi is velocity of particle i, c1 is the cognition learning
factor, c2 is the social learning factor, r1 and r2 are random
numbers distributed in the range of 0 to 1, LBi is the local
DOI 10.5013/IJSSST.a.17.34.20
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
Start
Measure Vi, Ii, Vi–1, Ii–1
Calculate the output power:
Pi = Vi × Ii
Pi–1 = Vi–1 × Ii–1
Yes
Vi > Vi–1?
No
Pi > Pi–1?
No
No
Vi > Vi–1?
Yes
Yes
Vi+1 = Vi + ∆V
PSC is different from the current generated under standard
test condition (STC). At STC, constant current of
approximate 5.2 A is produced along the functional
operating voltage from 0 V to 60 V. However, when the PV
array is under PSC, the generating current is unable to
maintain at a constant value (dropping like a staircase). For
example, Case III, the PV array generated 5.2 A from 0 V to
15 V, then decrease to 4.1 A from 15 V to 30 V. The
generated current further decrease to 3.6 A and 3.1 A from
32 V to 50 V and 55 V to 70 V respectively.
Fig. 7 shows that the P-V characteristic of PV array
exhibits multiple peaks under PSC. The Case I exhibits two
peaks because it receives only two different levels of
irradiance, whereas the Case II and III exhibit four peaks as
both cases receive four different levels of irradiance. The
Case III has the highest GMPP because it receives more
average insolation on its PV panels.
Vi+1 = Vi – ∆V
TABLE II.
MPP continue
track?
Parameters
Open circuit voltage
Short circuit current
Maximum power voltage
Maximum power current
Maximum power
Temperature coefficient for current
Temperature coefficient for voltage
Numbers of solar cell
Yes
No
End
Figure 5. Flowchart of P&O algorithm.
Even though the optimal operating voltage is successfully
identified, P&O algorithm will continuously iterate the
operating voltage with the aim to track the next MPP. As a
result, the perturbation process will lead to the voltage and
power fluctuation issues. The fluctuation is obvious when a
large perturbation size is applied. By optimizing the
perturbation size of ∆V, the oscillation of the PV operating
voltage is anticipated to be minimum hence reducing power
loss in the PV system.
V.
TABLE III.
In this paper, the simulation study is carried out with
Matlab m-file. The Sharp NE-80E2EA multi-crystalline
silicon PV module with 80 W maximum power is selected as
the reference model for this work. Parameters of the selected
PV module are tabulated in Table II.
The partially shaded effect of PV array is simulated by
arbitrarily setting the insolation on the series-connected PV
modules. The unshaded PV module is considered to be fully
illuminated at 1,000 W m-2, whereas the insolation on the
shaded PV module is varied from 0 to 1,000 W m-2. The
proposed PSO based P&O algorithm and the conventional
P&O algorithm are tested for three different shading
patterns, as described in Table III.
The I-V and P-V characteristics for the three Cases are
shown in Fig. 6 and Fig. 7 respectively. Fig. 7 shows the
GMPP occurs at the first peak (most left side) in Case I; in
Case II, the GMPP occurs at the third peak (middle);
whereas the GMPP occurs at the last peak (most right side)
in the Case III. The current generated by PV array under
Symbol
Voc
Isc
Vmp
Imp
Pm
KI
KV
-
Typical Value
21.3 V
5.16 A
17.1 V
4.68 A
80.0 W
0.053 % °C-1
– 0.360 % °C-1
36 (in series)
SHADING PATTERNS
Ambient Conditions
Case
MODELLING AND SIMULATION
DOI 10.5013/IJSSST.a.17.34.20
PARAMETERS OF SHARP NE-80E2EA PV MODULE
PV Panel 1
PV Panel 2
PV Panel 3
PV Panel 4
Case
I
800 W m-2
31 °C
800 W m-2
31 °C
250 W m-2
25 °C
250 W m-2
25 °C
Case
II
800 W m-2
31 °C
1,000 W m-2
33 °C
700 W m-2
30 °C
400 W m-2
27 °C
Case
III
600 W m-2
25 °C
1000 W m-2
25 °C
800 W m-2
25 °C
700 W m-2
25 °C
I-V Characteristic
6
Case I
Case II
Case III
STC
5
Current (A)
4
3
2
1
0
0
10
20
30
40
50
60
Voltage (V)
70
80
90
100
Figure 6. I-V characteristics of PV array at PSC.
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
P-V Characteristic
PV Array Operating Voltage
35
350
Case I
Case II
Case III
STC
300
30
25
Operating Voltage (V)
Power (W)
250
200
150
15
10
50
5
0
10
20
30
40
50
60
Voltage (V)
70
80
90
0
100
VI.
100
200
300
400
500
600
Iteration
700
800
900
1000
Figure 8. Performances of PSO-P&O and P&O in Case I.
RESULTS AND DISCUSSION
The performances of the proposed PSO-P&O algorithm
in all cases are compared to the conventional P&O
algorithm. The perturbation size for P&O algorithm is preset
as 2.0 V during the transient state and 0.4 V during the
steady state based on STC for reducing oscillation in output
power. The simulation results of proposed PSO-P&O and
P&O algorithms in Case I, II and III are shown in Fig. 8,
Fig. 9 and Fig. 10 respectively.
PV Array Output Power
140
120
P&O
PSO-P&O
100
0
(b) Operating voltage of PV array
Figure 7. P-V characteristics of PV array at PSC.
Output Power (W)
20
100
0
P&O
PSO-P&O
80
60
40
20
In Case I, the GMPP occurs at the first peak. Hence both
P&O and PSO-P&O algorithms are able to track the GMPP
without trapped at local MPP, as shown in Fig. 8. Although
both algorithms have obtain same output power, PSO-P&O
algorithm has shown a better steady-state response compared
to P&O algorithm. In 260th iteration, PSO-P&O algorithm
showed an outlier point. This is due to the inherent learning
ability (social influence) of PSO that try to search for other
global best solution.
The results in Fig. 9 indicate the PSO-P&O algorithm has
better performance than P&O algorithm in Case II (nonuniform irradiance and operating at various temperatures).
The conventional P&O algorithm is trapped at the local MPP
and the output power is fluctuated during the steady state.
The PSO-P&O algorithm is able to decide various size of ∆V
according to the instantaneous environmental circumstances.
Large perturbation size is chosen to reduce the iteration
process and improve the transient response at the beginning
stage. When the output power is reaching GMPP, the
proposed algorithm will determine the suitable ∆V for the
MPPT so that the output power consist less fluctuation, or
better steady state response.
PV Array Output Power
180
0
0
100
200
300
400
500
600
Iteration
700
800
900
1000
160
P&O
PSO-P&O
140
(a) Output power of PV array
Output Power (W)
120
0.6 W
100
80
60
40
20
0
0
100
200
300
400
500
600
Iteration
700
800
900
1000
(a) Output power of PV array
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
PV Array Operating Voltage
PV Array Operating Voltage
60
70
P&O
PSO-P&O
P&O
PSO-P&O
60
50
Operating Voltage (V)
Operating Voltage (V)
50
40
0.4 V
30
20
40
0.4 V
30
20
10
0
10
0
100
200
300
400
500
600
Iteration
700
800
900
0
1000
0
100
200
300
400
500
600
Iteration
700
800
900
1000
(b) Operating voltage of PV arrays
(b) Operating voltage of PV array
Figure 9. Performances of PSO-P&O and P&O in Case II.
Figure 10. Performances of PSO-P&O and P&O in Case III.
In Case III, the PV array receives non-uniform irradiance
from the sunlight but operates at constant temperature. The
conventional P&O algorithm slowly increases the operating
point at the beginning of the process. When it reaches the
first peak (around 60 W), the algorithm is trapped at the local
MPP, as shown in Fig. 10. During 90th to 100th iteration, the
output power of P&O has bigger fluctuation compared to the
output power after 100th iteration due to the perturbation size
of P&O algorithm at that respective period (2.0 V) is higher.
On the other hand, the proposed PSO-P&O algorithm is
able to tack the GMPP (around 210 W) in Case III. The
results in Fig. 10 also shows the fluctuation of operating
voltage for PSO-P&O algorithm is smaller and hence its
output power is very stable compared to P&O algorithm.
This is because the PSO-P&O algorithm will adapt its
control actions in changing the operating voltage based on
the situation. During the transient response, the PSO will
boost to the maximum perturbation size for the PV system.
Once the GMPP is tracked, the PSO will stop to manipulate
the perturbation size. The performances of P&O and PSOP&O algorithms in the three cases are tabulated in Table IV.
TABLE IV.
PERFORMANCES OF P&O AND PSO-P&O ALGORITHMS
Output Power (W)
P&O
PSO-P&O
Improvement
(%)
Case I
121.3
121.6
0.25
Case II
76.9
174.5
126.9
Case III
80.0
209.8
162.3
Case
VII. CONCLUSION
The performances of the proposed particle swarm
optimization based perturb and observe (PSO-P&O) are
investigated when PV array performs under partially shaded
conditions. In this work, PV array is modeled based on four
series connected PV modules. The developed PSO-P&O
algorithm is tested under three different cases and its
performances in optimizing the output power are compared
PV Array Output Power
250
P&O
PSO-P&O
Output Power (W)
200
150
0.3 W
100
50
0
0
100
200
300
400
500
600
Iteration
700
800
900
1000
(a) Output power of PV array
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KENNETH TZE KIN TEO et al: PARTICLE SWARM OPTIMIZATION BASED MAXIMUM POWER POINT . . .
to the conventional P&O algorithm. From the simulation
results, PSO-P&O algorithm is able to optimize the
generation of PV system by tracking the GMPP faster when
the ambient conditions (solar irradiance and temperature) are
changed. When the output power is approaching GMPP,
PSO-P&O algorithm will select smaller voltage perturbation
size to minimize the fluctuation of the output power in the
steady state. In addition, the proposed algorithm can control
the PV system to perform at a more precise operating
voltage. Based on the simulation findings, the PSO-P&O
algorithm has managed to track GMPP and provides better
steady state response over the conventional P&O algorithm
particularly during the PSC. In future, the performance and
robustness of the proposed algorithm will be tested in
practical.
ACKNOWLEDGMENT
The authors would like to acknowledge the Ministry of
Higher Education (KPT) for supporting this research under
the Research Acculturation Grant Scheme (RAGS), grant no.
RAG0010-TK-1/2012 and under Fundamental Research
Grant Scheme (FRGS), grant no. FRG0404-TK-2/2014.
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ISSN: 1473-804x online, 1473-8031 print