# A Novel Maximum Power Point Tracking Algorithm Based on Glowworm Swarm Optimization for Photovoltaic Systems

Authors: Wenhui Hou; Yi Jin; Changan Zhu; Guiqiang Li
Journal: International Journal of Photoenergy
 (2016)

---

## Abstract

In order to extract the maximum power from PV system, the maximum power point tracking (MPPT) technology has always been applied in PV system. At present, various MPPT control methods have been presented. The perturb and observe (P&O) and conductance increment methods are the most popular and widely used under the constant irradiance. However, these methods exhibit fluctuations among the maximum power point (MPP). In addition, the changes of the environmental parameters, such as cloud cover, plant shelter, and the building block, will lead to the radiation change and then have a direct effect on the location of MPP. In this paper, a feasible MPPT method is proposed to adapt to the variation of the irradiance. This work applies the glowworm swarm optimization (GSO) algorithm to determine the optimal value of a reference voltage in the PV system. The performance of the proposed GSO algorithm is evaluated by comparing it with the conventional P&O method in terms of tracking speed and accuracy by utilizing MATLAB/SIMULINK. The simulation results demonstrate that the tracking capability of the GSO algorithm is superior to that of the traditional P&O algorithm, particularly under low radiance and sudden mutation irradiance conditions.


---

## Body

## 1. Introduction

In the past few decades, the world’s energy demand has risen steadily with the growth of the population and the change in people’s lifestyles. However, traditional fuels are limited, and environmental conditions worsen on a daily basis. These conditions urge people to seek renewable energy. Solar energy is a promising renewable energy because of its various advantages, such as limitlessness, zero production of pollution and noise, and good reliability. Hence, photovoltaic (PV) power systems have gained increasing attention from governments and researchers in various countries. Global PV power technology has developed rapidly because of government support. However, two major defects hinder its development: the high installation cost of the system and its low photoelectric conversion efficiency at 9%–17% [1]. Improving the maximum power tracking technology to extract the highest amount of power from PV systems is one of the most practical methods to address this problem.The basic concept of maximum power point tracking (MPPT) is to adjust the operating point of a converter up to the maximum in real time such that the system can constantly operate at the maximum power point (MPP). In this way, MPPT improves conversion efficiency and reduces power loss. However, the MPP changes with the variable external environment, thereby further complicating the maximum power tracking problem [2].In recent years, many MPPT control methods have been proposed. A detailed description and classification of numerous MPPT techniques are made by Subudhi and Pradhan [3]. Among these methods, the most commonly used approaches are perturb and observe (P&O) [4–6] and incremental conductance (IncCon) [7–9]. A traditional P&O algorithm does not need to understand the characteristics of a PV system. Thus, this algorithm is simple and easy to develop. It works by imposing a fixed step perturbation on a reference voltage or current, measuring the output power of the PV system, and comparing the values before and after disturbance to determine the direction of the disturbance for the next step. If PV power increases, then the direction of the disturbance is the same as that in the last step (i.e., the system is moving toward the MPP); otherwise, the direction is reversed [4]. Despite the simple structure of the P&O algorithm, the fluctuation among the MPP is inevitable. In the selection of the tracking step, it is difficult to take account of both tracking precision and response speed. In some instances, the P&O algorithm generates an erroneous direction when a sudden change in irradiance occurs. By contrast, the incremental conductance method is used to determine the disturbance of a control parameter by comparing incremental conductance with instantaneous conductance. The tracking performances of four conventional methods including the constant voltage method, the IncCon method, the P&O method, and the variable step size perturb and observe are compared under fixed solar insolation by Mohanty et al. [9]. The results show that the proportion of the respond time between the IncCon method and the P&O method is about 1 : 2. However, the IncCon method has the same limitation as the P&O algorithm. To overcome these disadvantages, many researchers explored a new direction for MPPT control, which combines artificial intelligence and evolutionary computation techniques [2]. The main methods for MPPT control are artificial neural networks (ANN) [2, 10, 11] and fuzzy logic control (FLC) [12, 13]. A MPPT technique based on the ANN method which is compared with the traditional P&O algorithm is proposed by Rezk and Hasaneen [11]. The simulation results show that the tracking speed of the proposed method is faster than the traditional P&O. The proportion of the respond time is about 3 : 7 at high radiation change rate. The comparison between the advanced methods (FLC) and the conventional methods (P&O) is presented by Bendib et al. [13]. The simulation results show the performance of the FLC based method is better than the conventional methods, and the proportion of the respond time between them is about 4 : 15. These methods do not require an accurate mathematical model. However, they entail training a large amount of data; hence, the calculation is complex, and a large storage space is necessary. In addition, most of the MPPT methods require the expensive current sensor, which increases the inherent cost of the PV system. In order to reduce costs, many MPPT technologies without the current sensor have been proposed over the last decade. A review and summary of some main current sensorless MPPT technologies are made by Samrat et al. [14]. With the development of bionic algorithms, more and more scholars focused on these algorithms, such as genetic algorithms, artificial bee colony algorithm (ABC), and particle swarm optimization algorithms [15]. Many scholars have employed these bioinspired algorithms for the MPPT of PV systems [16–19].Glowworm swarm optimization (GSO), which is a new type of bioinspired algorithm, shows superior performance in dealing with nonlinear problems, although this approach has yet to be applied in PV systems. In this work, the GSO algorithm is used to track the MPP of a PV system. To evaluate the performance of the algorithm, the proposed GSO-based MPPT method is implemented on a boost converter, and its performance is compared with that of the traditional P&O algorithm.The information on the PV and boost converter is presented in Section2. The proposed algorithm is discussed in Section 3. The simulation of MPPT using SIMULINK and a discussion of the results are shown in Section 4. Finally, the conclusion is presented in Section 5.


## 2. PV and Boost Converter Model

### 2.1. PV Equivalent Circuit Model

A PV module is used to convert sunlight into direct current and thus facilitates the conversion of light energy to electric energy. A PV-based system can be independently used for streetlights, water pumps, and grid connected systems [20].The typical equivalent circuit model of a PV cell is a single diode (Figure1), which consists of a photo current, a diode, a series resistor, and a parallel shunt resistor.Figure 1
Equivalent circuit of a PV cell.Based on Kirchhoff’s current law, the mathematical equation for the output current of an ideal cell is given by(1)
I
=
I
p
h
-
I
d
-
I
s
h
,where I
s
h is the parallel resistance current and I
p
h is the light-generated current, which is proportional to the intensity of light. It can be calculated by(2)
I
p
h
=
I
s
c
+
K
I
T
c
-
T
r
·
G
,where I
s
c is the short-circuit current at STC (T
=
25°C, S
=
1000
W
/
m
2) and K
I is the short-circuit current temperature coefficient of the cell. T
c and T
r are the operating temperature of the cell and the reference temperature, respectively. G is the relative irradiance coefficient, which is calculated by S
/
1000 (G
=
1 under nominal condition).I
d is the diode current, which, according to the Shockley equation, is given by (3)
I
d
=
I
O
e
x
p
q
U
d
A
k
T
c
-
1
,where q is the electronic charge (q
=
1.6
×
1
0
-
19), k is Boltzmann’s constant (k
=
1.38
×
1
0
-
23), A is the ideal factor of the diode, I
O is the reverse saturation current of the diode, and U
d is the voltage of the equivalent diode. According to Kirchhoff’s voltage law, U
d is given by(4)
U
d
=
U
+
I
R
s
,where R
s is the series resistance.The voltage and current generated by a single PV cell are very low. Thus, PV cells are usually connected in series and parallel to achieve the desired power. A PV module is usually connected in series by batteries, and the series number is generally 26, 36, 54, or 72.The output current equation of the PV module is given by(5)
I
=
I
p
h
-
I
O
e
x
p
q
U
+
I
·
R
s
A
k
T
c
N
s
-
1
-
U
+
I
·
R
s
R
p
,where N
s is the number of series resistance cells and R
p is the parallel resistance, which is very high that its current can be neglected [14]. Equation (5) can be simplified as(6)
I
=
I
p
h
-
I
O
e
x
p
q
U
+
I
·
R
s
A
k
T
c
N
s
-
1
,where I
O varies with the change in temperature and is given by(7)
I
O
=
I
r
o
T
c
T
r
3
e
x
p
q
E
g
1
/
T
r
-
1
/
T
c
A
k
,where E
g is the band gap energy of the semiconductor and I
r
o is the saturation current of the diode at 25°C, which is calculated by(8)
I
r
o
=
I
s
c
e
x
p
q
U
o
c
/
A
k
T
r
N
s
-
1
,where U
o
c is the open-circuit voltage of the PV module at STC (T
=
25°C, S
=
1000
W
/
m
2).


### 2.2. Simulation of the PV Module

According to the mathematical model of the PV module, output power depends on two factors, namely, irradiance and temperature. The present work focuses on the influence of irradiance (assuming that the temperature is 25°C). The parameters of the PV module type CS6X-305P used in the simulation are listed in Table1. The module is composed of 72 solar cells connected in series to achieve a maximum power output of 305 W.Table 1
Parameters of the PV module type CS6X-305P.
Parameter
Value
Maximum power (P
m
a
x)
305 W
Open-circuit voltage (U
o
c)
44.8 V
Short-circuit current (I
s
c)
8.97 A
Number of cells (N
s)
72
Ideal factor (A)
1.3The simulation of the considered PV under variable irradiance via SIMULINK is illustrated in Figure2.Figure 2
PV module with radiance variation.Figures3 and 4 present the current-voltage (I-V) characteristic and power-voltage (P-V) characteristic of the PV module, respectively. The maximum power of the PV is achieved at the extreme point of theP-V curve, which is known as the MPP. The maximum power and short-circuit current increase with irradiance.Figure 3
I-V characteristic of the PV module under different radiances.Figure 4
P-V characteristic of the PV module under different radiances.


### 2.3. Boost Converter and Its Simulation

Generally, MPPT is used to track the MPPs of PV systems. The efficiency of MPPT mainly depends on the MPPT control algorithm and MPPT circuit. The MPPT circuit usually uses a DC-DC converter [21]. In the present work, a boost converter is used for MPPT to adjust the operating voltage by changing the duty cycle of the switch. The voltage gain of the converter is calculated by (9)
G
n
=
U
o
u
t
U
i
n
=
1
1
-
D
,where D is the duty cycle of the switch.Figure5 shows the subsystem of the boost converter in SIMULINK. Figure 6 indicates that the converter is connected to the PV module. The input of the boost converter is the output of the PV module. The simulation results of the system at constant D and variable D are shown in Figures 7 and 8, respectively.Figure 5
Subsystem of boost converter.Figure 6
PV-fed DC-DC boost converter.Figure 7
Output current and voltage of boost converter at constantD.Figure 8
Output power of PV at variableD.Figure7 illustrates the output current and voltage of the boost converter at constant D (D
=
0.34). Figure 8 demonstrates the influence of different input duty cycles on the output power of a PV system. The figure indicates that an optimal duty cycle allows the PV system to function at the MPP.


## 2.1. PV Equivalent Circuit Model

A PV module is used to convert sunlight into direct current and thus facilitates the conversion of light energy to electric energy. A PV-based system can be independently used for streetlights, water pumps, and grid connected systems [20].The typical equivalent circuit model of a PV cell is a single diode (Figure1), which consists of a photo current, a diode, a series resistor, and a parallel shunt resistor.Figure 1
Equivalent circuit of a PV cell.Based on Kirchhoff’s current law, the mathematical equation for the output current of an ideal cell is given by(1)
I
=
I
p
h
-
I
d
-
I
s
h
,where I
s
h is the parallel resistance current and I
p
h is the light-generated current, which is proportional to the intensity of light. It can be calculated by(2)
I
p
h
=
I
s
c
+
K
I
T
c
-
T
r
·
G
,where I
s
c is the short-circuit current at STC (T
=
25°C, S
=
1000
W
/
m
2) and K
I is the short-circuit current temperature coefficient of the cell. T
c and T
r are the operating temperature of the cell and the reference temperature, respectively. G is the relative irradiance coefficient, which is calculated by S
/
1000 (G
=
1 under nominal condition).I
d is the diode current, which, according to the Shockley equation, is given by (3)
I
d
=
I
O
e
x
p
q
U
d
A
k
T
c
-
1
,where q is the electronic charge (q
=
1.6
×
1
0
-
19), k is Boltzmann’s constant (k
=
1.38
×
1
0
-
23), A is the ideal factor of the diode, I
O is the reverse saturation current of the diode, and U
d is the voltage of the equivalent diode. According to Kirchhoff’s voltage law, U
d is given by(4)
U
d
=
U
+
I
R
s
,where R
s is the series resistance.The voltage and current generated by a single PV cell are very low. Thus, PV cells are usually connected in series and parallel to achieve the desired power. A PV module is usually connected in series by batteries, and the series number is generally 26, 36, 54, or 72.The output current equation of the PV module is given by(5)
I
=
I
p
h
-
I
O
e
x
p
q
U
+
I
·
R
s
A
k
T
c
N
s
-
1
-
U
+
I
·
R
s
R
p
,where N
s is the number of series resistance cells and R
p is the parallel resistance, which is very high that its current can be neglected [14]. Equation (5) can be simplified as(6)
I
=
I
p
h
-
I
O
e
x
p
q
U
+
I
·
R
s
A
k
T
c
N
s
-
1
,where I
O varies with the change in temperature and is given by(7)
I
O
=
I
r
o
T
c
T
r
3
e
x
p
q
E
g
1
/
T
r
-
1
/
T
c
A
k
,where E
g is the band gap energy of the semiconductor and I
r
o is the saturation current of the diode at 25°C, which is calculated by(8)
I
r
o
=
I
s
c
e
x
p
q
U
o
c
/
A
k
T
r
N
s
-
1
,where U
o
c is the open-circuit voltage of the PV module at STC (T
=
25°C, S
=
1000
W
/
m
2).


## 2.2. Simulation of the PV Module

According to the mathematical model of the PV module, output power depends on two factors, namely, irradiance and temperature. The present work focuses on the influence of irradiance (assuming that the temperature is 25°C). The parameters of the PV module type CS6X-305P used in the simulation are listed in Table1. The module is composed of 72 solar cells connected in series to achieve a maximum power output of 305 W.Table 1
Parameters of the PV module type CS6X-305P.
Parameter
Value
Maximum power (P
m
a
x)
305 W
Open-circuit voltage (U
o
c)
44.8 V
Short-circuit current (I
s
c)
8.97 A
Number of cells (N
s)
72
Ideal factor (A)
1.3The simulation of the considered PV under variable irradiance via SIMULINK is illustrated in Figure2.Figure 2
PV module with radiance variation.Figures3 and 4 present the current-voltage (I-V) characteristic and power-voltage (P-V) characteristic of the PV module, respectively. The maximum power of the PV is achieved at the extreme point of theP-V curve, which is known as the MPP. The maximum power and short-circuit current increase with irradiance.Figure 3
I-V characteristic of the PV module under different radiances.Figure 4
P-V characteristic of the PV module under different radiances.


## 2.3. Boost Converter and Its Simulation

Generally, MPPT is used to track the MPPs of PV systems. The efficiency of MPPT mainly depends on the MPPT control algorithm and MPPT circuit. The MPPT circuit usually uses a DC-DC converter [21]. In the present work, a boost converter is used for MPPT to adjust the operating voltage by changing the duty cycle of the switch. The voltage gain of the converter is calculated by (9)
G
n
=
U
o
u
t
U
i
n
=
1
1
-
D
,where D is the duty cycle of the switch.Figure5 shows the subsystem of the boost converter in SIMULINK. Figure 6 indicates that the converter is connected to the PV module. The input of the boost converter is the output of the PV module. The simulation results of the system at constant D and variable D are shown in Figures 7 and 8, respectively.Figure 5
Subsystem of boost converter.Figure 6
PV-fed DC-DC boost converter.Figure 7
Output current and voltage of boost converter at constantD.Figure 8
Output power of PV at variableD.Figure7 illustrates the output current and voltage of the boost converter at constant D (D
=
0.34). Figure 8 demonstrates the influence of different input duty cycles on the output power of a PV system. The figure indicates that an optimal duty cycle allows the PV system to function at the MPP.


## 3. Glowworm Swarm Optimization

The GSO algorithm, which is a new type of stochastic and metaheuristic optimization algorithm, was first proposed by Indian scholars [22]. GSO uses a swarm of glowworms as its agents, which are regarded as the potential solutions to a problem. The fitness of optimality is measured by the objective function defined by users. In the present work, GSO is adopted to generate an optimal reference voltage that varies with radiance to extract the maximum power from the PV module. GSO is an optimization method that is easy to implement with a rapid convergence speed and few parameters to adjust.


### 3.1. Description of the Algorithm

The GSO algorithm is based on glowworms, each of which is considered a potential solution to the given objective problem. In the first iteration, a swarm of glowworms is randomly distributed in a search space with an initial luciferin value, which determines the brightness of the glowworms. The luciferin is updated according to the objective function value at the current position of the glowworm. Each glowworm, which has its own decision radius0
<
r
d
i
<
r
s (r
s is the largest sensing radius of glowworms), seeks a bright individual with high luciferin in its local-decision range and moves toward such individual. After such move, the decision radius of this glowworm is updated according to the number of optimal individuals in a decision radius. Finally, most of the glowworms gather at the peak point after several iterations. Each iteration consists of a luciferin-update phase, a movement phase based on a transition rule, and a local-decision range update phase [23].


#### 3.1.1. Luciferin-Update Phase

Updating luciferin mainly depends on the objective function value of the current position. At the same time, the decay in luciferin with time should be eliminated. Thus, the formula for updating luciferin is given by(10)
I
i
t
+
1
=
1
-
ρ
∗
I
i
t
+
γ
∗
F
x
i
t
+
1
,where ρ is the luciferin decay constant (0
<
ρ
<
1), γ is the luciferin enhancement constant, I
i
(
t
) and I
i
(
t
+
1
) are the luciferins at iterations t and t
+
1, respectively, and F
(
x
i
(
t
+
1
)
) represents the value of the objective function at agent i’s location at iteration t
+
1. In this work, objective function F is the output power of the PV module, which is calculated by(11)
F
=
P
P
V
=
U
∗
I
,where the relationship between U and I can be derived from (1)–(8) in Section 2. Thus, F is the function of G and U, G is the system variable, and U is the parameter to be optimized, which is regarded as the location of the glowworm.


#### 3.1.2. Movement Phase

Each agent is attracted by a superior individual, but such attraction is limited by the perception range of the individual. Thus, the neighborhood of the agent should be first defined by(12)
N
i
t
=
j
:
d
i
,
j
t
<
r
d
i
,
I
i
t
<
I
j
t
.
d
i
,
j
(
t
)
=
x
i
-
x
j represents the Euclidean distance between glowworms i and j at iteration t.The probability that glowwormi moves toward neighbor j is given by(13)
p
i
j
=
I
j
t
-
I
i
t
∑
m
∈
N
i
t
I
m
t
-
I
i
t
.The location update formula for this movement can be stated as follows:(14)
x
i
t
+
1
=
x
i
t
+
s
∗
x
j
t
-
x
i
t
x
j
t
-
x
i
t
,where s is the step size and x
i
(
t
) and x
i
(
t
+
1
) are the locations at iterations t and t
+
1, respectively.


#### 3.1.3. Local-Decision Range Update Phase

If many individuals with high luciferin values exist in the local-decision range of glowwormi, the decision radius should be appropriately reduced. The update formula of the decision radius is(15)
r
d
i
t
+
1
=
m
i
n
r
s
,
m
a
x
0
,
r
d
i
t
+
β
∗
n
t
-
N
i
t
,where β is the variation coefficient of the decision radius and n
t is the number of outstanding individuals with high luciferin values in the local-decision range.


### 3.2. Flowchart of the Algorithm

The flowchart of the GSO algorithm is shown in Figure9.Figure 9
Flowchart of the GSO algorithm.


## 3.1. Description of the Algorithm

The GSO algorithm is based on glowworms, each of which is considered a potential solution to the given objective problem. In the first iteration, a swarm of glowworms is randomly distributed in a search space with an initial luciferin value, which determines the brightness of the glowworms. The luciferin is updated according to the objective function value at the current position of the glowworm. Each glowworm, which has its own decision radius0
<
r
d
i
<
r
s (r
s is the largest sensing radius of glowworms), seeks a bright individual with high luciferin in its local-decision range and moves toward such individual. After such move, the decision radius of this glowworm is updated according to the number of optimal individuals in a decision radius. Finally, most of the glowworms gather at the peak point after several iterations. Each iteration consists of a luciferin-update phase, a movement phase based on a transition rule, and a local-decision range update phase [23].


### 3.1.1. Luciferin-Update Phase

Updating luciferin mainly depends on the objective function value of the current position. At the same time, the decay in luciferin with time should be eliminated. Thus, the formula for updating luciferin is given by(10)
I
i
t
+
1
=
1
-
ρ
∗
I
i
t
+
γ
∗
F
x
i
t
+
1
,where ρ is the luciferin decay constant (0
<
ρ
<
1), γ is the luciferin enhancement constant, I
i
(
t
) and I
i
(
t
+
1
) are the luciferins at iterations t and t
+
1, respectively, and F
(
x
i
(
t
+
1
)
) represents the value of the objective function at agent i’s location at iteration t
+
1. In this work, objective function F is the output power of the PV module, which is calculated by(11)
F
=
P
P
V
=
U
∗
I
,where the relationship between U and I can be derived from (1)–(8) in Section 2. Thus, F is the function of G and U, G is the system variable, and U is the parameter to be optimized, which is regarded as the location of the glowworm.


### 3.1.2. Movement Phase

Each agent is attracted by a superior individual, but such attraction is limited by the perception range of the individual. Thus, the neighborhood of the agent should be first defined by(12)
N
i
t
=
j
:
d
i
,
j
t
<
r
d
i
,
I
i
t
<
I
j
t
.
d
i
,
j
(
t
)
=
x
i
-
x
j represents the Euclidean distance between glowworms i and j at iteration t.The probability that glowwormi moves toward neighbor j is given by(13)
p
i
j
=
I
j
t
-
I
i
t
∑
m
∈
N
i
t
I
m
t
-
I
i
t
.The location update formula for this movement can be stated as follows:(14)
x
i
t
+
1
=
x
i
t
+
s
∗
x
j
t
-
x
i
t
x
j
t
-
x
i
t
,where s is the step size and x
i
(
t
) and x
i
(
t
+
1
) are the locations at iterations t and t
+
1, respectively.


### 3.1.3. Local-Decision Range Update Phase

If many individuals with high luciferin values exist in the local-decision range of glowwormi, the decision radius should be appropriately reduced. The update formula of the decision radius is(15)
r
d
i
t
+
1
=
m
i
n
r
s
,
m
a
x
0
,
r
d
i
t
+
β
∗
n
t
-
N
i
t
,where β is the variation coefficient of the decision radius and n
t is the number of outstanding individuals with high luciferin values in the local-decision range.


## 3.1.1. Luciferin-Update Phase

Updating luciferin mainly depends on the objective function value of the current position. At the same time, the decay in luciferin with time should be eliminated. Thus, the formula for updating luciferin is given by(10)
I
i
t
+
1
=
1
-
ρ
∗
I
i
t
+
γ
∗
F
x
i
t
+
1
,where ρ is the luciferin decay constant (0
<
ρ
<
1), γ is the luciferin enhancement constant, I
i
(
t
) and I
i
(
t
+
1
) are the luciferins at iterations t and t
+
1, respectively, and F
(
x
i
(
t
+
1
)
) represents the value of the objective function at agent i’s location at iteration t
+
1. In this work, objective function F is the output power of the PV module, which is calculated by(11)
F
=
P
P
V
=
U
∗
I
,where the relationship between U and I can be derived from (1)–(8) in Section 2. Thus, F is the function of G and U, G is the system variable, and U is the parameter to be optimized, which is regarded as the location of the glowworm.


## 3.1.2. Movement Phase

Each agent is attracted by a superior individual, but such attraction is limited by the perception range of the individual. Thus, the neighborhood of the agent should be first defined by(12)
N
i
t
=
j
:
d
i
,
j
t
<
r
d
i
,
I
i
t
<
I
j
t
.
d
i
,
j
(
t
)
=
x
i
-
x
j represents the Euclidean distance between glowworms i and j at iteration t.The probability that glowwormi moves toward neighbor j is given by(13)
p
i
j
=
I
j
t
-
I
i
t
∑
m
∈
N
i
t
I
m
t
-
I
i
t
.The location update formula for this movement can be stated as follows:(14)
x
i
t
+
1
=
x
i
t
+
s
∗
x
j
t
-
x
i
t
x
j
t
-
x
i
t
,where s is the step size and x
i
(
t
) and x
i
(
t
+
1
) are the locations at iterations t and t
+
1, respectively.


## 3.1.3. Local-Decision Range Update Phase

If many individuals with high luciferin values exist in the local-decision range of glowwormi, the decision radius should be appropriately reduced. The update formula of the decision radius is(15)
r
d
i
t
+
1
=
m
i
n
r
s
,
m
a
x
0
,
r
d
i
t
+
β
∗
n
t
-
N
i
t
,where β is the variation coefficient of the decision radius and n
t is the number of outstanding individuals with high luciferin values in the local-decision range.


## 3.2. Flowchart of the Algorithm

The flowchart of the GSO algorithm is shown in Figure9.Figure 9
Flowchart of the GSO algorithm.


## 4. Simulation of MPPT Using SIMULINK and Result Discussion

### 4.1. Simulation of MPPT

In this work, the GSO algorithm is adopted to optimize the reference voltage of the PV system under invariant and variant radiances. The boost converter adjusts the duty cycle of the switch according to the reference voltage. Finally, the output power of the PV system is controlled. The simulation result of the GSO algorithm is compared with that of the traditional P&O algorithm under the constant irradiance. The structure diagram of the system is presented in Figure10.Figure 10
Typical diagram of MPPT using GSO.The proposed GSO algorithm and conventional P&O method are simulated using MATLAB/SIMULINK. The PV module temperature is considered to be unchanged at 25°C during the simulation. Figure11 presents the simulation of the GSO approach for the considered PV system.Figure 11
Simulation of GSO approach for the considered PV.Pulse width modulation (PWM) is a technique to create control pulses for switches. PWM is carried out in SIMULINK, as shown in Figure12.Figure 12
PWM intersect in SIMULINK.The proposed scheme is simulated under two conditions: constant radiance (including high and low irradiance) and variable irradiance (mutation in irradiance).


### 4.2. Discussion of Results

Figure13 illustrates the output power of the PV module for the GSO method and conventional method at 100
0
W
/
m
2, 25°C. The figure indicates that the tracking efficiency of the proposed GSO algorithm is higher than that of the traditional P&O algorithm. The proportion of the respond time between them is about 1 : 6. Different tracking effects for P&O could be shown when various step sizes are used. This work selects a result with small and steady oscillations but slow tracking speed.Figure 13
Output power of the PV module for the GSO method and P&O method under1000
W
/
m
2, 25°C.Figure14 illustrates the output power of the PV module for the GSO method and conventional method under low solar radiance (300
W
/
m
2, 25°C). The result indicates that the GSO algorithm can track the theoretical maximum power, whereas the conventional P&O method has low efficiency and is not capable of converging to the maximum power.Figure 14
Output power of the PV module for the GSO method and P&O method under300
W
/
m
2, 25°C.Figure16 presents the tracking performance of the proposed GSO algorithm under varying radiance conditions. The figure shows the output power of the PV module and boost converter, which is coupled with the load. The change in irradiance, as shown in Figure 15, exhibits sudden mutation at 0.05, 0.10, 0.15, and 0.20 s.Figure 15
Condition of variable radiance.Figure 16
Output power of the PV and boost converter under variable irradiance.As shown in Figure16, the proposed GSO algorithm can accurately track the MPP of the PV module under variable irradiance. The power losses of the system are 2.43%, 2.3%, 2.32%, 2.5%, and 2.41%. The output current and output voltage of the PV module are shown in Figure 17.Figure 17
Output current and voltage of PV under variable irradiance.


## 4.1. Simulation of MPPT

In this work, the GSO algorithm is adopted to optimize the reference voltage of the PV system under invariant and variant radiances. The boost converter adjusts the duty cycle of the switch according to the reference voltage. Finally, the output power of the PV system is controlled. The simulation result of the GSO algorithm is compared with that of the traditional P&O algorithm under the constant irradiance. The structure diagram of the system is presented in Figure10.Figure 10
Typical diagram of MPPT using GSO.The proposed GSO algorithm and conventional P&O method are simulated using MATLAB/SIMULINK. The PV module temperature is considered to be unchanged at 25°C during the simulation. Figure11 presents the simulation of the GSO approach for the considered PV system.Figure 11
Simulation of GSO approach for the considered PV.Pulse width modulation (PWM) is a technique to create control pulses for switches. PWM is carried out in SIMULINK, as shown in Figure12.Figure 12
PWM intersect in SIMULINK.The proposed scheme is simulated under two conditions: constant radiance (including high and low irradiance) and variable irradiance (mutation in irradiance).


## 4.2. Discussion of Results

Figure13 illustrates the output power of the PV module for the GSO method and conventional method at 100
0
W
/
m
2, 25°C. The figure indicates that the tracking efficiency of the proposed GSO algorithm is higher than that of the traditional P&O algorithm. The proportion of the respond time between them is about 1 : 6. Different tracking effects for P&O could be shown when various step sizes are used. This work selects a result with small and steady oscillations but slow tracking speed.Figure 13
Output power of the PV module for the GSO method and P&O method under1000
W
/
m
2, 25°C.Figure14 illustrates the output power of the PV module for the GSO method and conventional method under low solar radiance (300
W
/
m
2, 25°C). The result indicates that the GSO algorithm can track the theoretical maximum power, whereas the conventional P&O method has low efficiency and is not capable of converging to the maximum power.Figure 14
Output power of the PV module for the GSO method and P&O method under300
W
/
m
2, 25°C.Figure16 presents the tracking performance of the proposed GSO algorithm under varying radiance conditions. The figure shows the output power of the PV module and boost converter, which is coupled with the load. The change in irradiance, as shown in Figure 15, exhibits sudden mutation at 0.05, 0.10, 0.15, and 0.20 s.Figure 15
Condition of variable radiance.Figure 16
Output power of the PV and boost converter under variable irradiance.As shown in Figure16, the proposed GSO algorithm can accurately track the MPP of the PV module under variable irradiance. The power losses of the system are 2.43%, 2.3%, 2.32%, 2.5%, and 2.41%. The output current and output voltage of the PV module are shown in Figure 17.Figure 17
Output current and voltage of PV under variable irradiance.


## 5. Conclusion

The MPPT control strategy based on the GSO algorithm is implemented in this work. The GSO algorithm is a new type of bioinspired algorithm that is employed for the maximum power tracking of PV systems. The control mechanism involves optimizing the reference voltage of the PV module using the proposed GSO, adjusting the operating voltage through the boost converter, and finally allowing the system to work at the MPP. The proposed control scheme is verified using SIMULINK. The simulation results indicate that the scheme can track the MPP under constant irradiance and determine the MPP under changing irradiance. Thus, minimal power loss occurs after connecting with the load. The results of the GSO algorithm at constant irradiance are compared with those of the traditional P&O algorithm. The tracking speed and precision of the proposed method are obviously higher than those of the P&O method, particularly at low irradiance. Hence, the control strategy based on the GSO algorithm can be utilized for the MPPT of PV systems.



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*Source: 4910862-2016-05-05.xml*