A Glowworm Swarm Optimization-Based Maximum Power Point Tracking for Photovoltaic / Thermal Systems under Non-Uniform Solar Irradiation and Temperature Distribution

The output power of a photovoltaic (PV) system depends on the external solar irradiation and its own temperature. In order to obtain more power from the PV system, the maximum power point tracking (MPPT) is necessary. However, when the PV is partially shaded, there will be multiple peaks in the power-current (P-I) curve. The conventional MPPT methods may be invalid due to falling into the local peak. In addition, in a photovoltaic-thermal (PV/T) system, the non-uniform temperature distribution on PV will also occur, which complicates the situation. This paper presents a MPPT method with glowworm swarm optimization (GSO) for PV in a PV/T system under non-uniform solar irradiation and temperature distribution. In order to study the performance of the proposed method, the conventional methods including the perturbation and observe algorithm (P and O), and the fractional open-circuit voltage technique (FOCVT) are compared with it in this paper. Simulation results show that the proposed method can rapidly track the real maximum power point (MPP) under different conditions, such as the gradient temperature distribution, the fast variable solar irradiation and the variable partial shading. The outcome indicates the proposed method has obvious advantages, especially the performance being superior to the conventional methods under the partial shading condition.


Introduction
With the sharp increasing global demand for energy, the shortage of the conventional fossil fuels and environmental pollution are becoming more and more serious.Thus, renewable energy resources are paid more and more attention from scholars due to their easy accessibility to humankind around the world.Renewable energy is meeting, at present, 13.5% of the global energy demand [1].In recent years, there has been a rapid development in solar photovoltaic power generation systems due to various advantages of solar energy, including limitlessness, zero production of pollution, noiselessness, and good reliability.The output power of photovoltaic (PV) depends on the external environment and its own temperature.Thus, maximum power point tracking (MPPT) technology is necessary to control and keep the PV system working at the maximum power point (MPP) under any conditions.Many MPPT techniques have been proposed.The most commonly used are the fractional open-circuit voltage technology (FOCVT) [2], perturbation and observation (P and O) [3][4][5][6], and incremental conductance (IncCond) [7][8][9].The P and O method and IncCond method usually implement the perturbation on the control variable to search the MPP based on the feedback of the output power.The main advantages of these two methods are that they are compatible with any PV module, require no information about the PV module, and are easily implemented.However, the selection of the perturbation step size is difficult to meet the demand of efficiency and precision at the same time.Thus, the variable step-size P and O MPPT technique is proposed.The performance of different variable step-size P and O MPPT techniques is compared by Chen et al. [10].In addition, there will be multiple peaks in the P-I characteristic curve under the partial shading condition in actual applications.These conventional methods reach the local MPP, but cannot analyze and compare all peaks to determine the true MPP [11].Many advanced methods using artificial intelligence are presented, including artificial neural networks (ANN) [12,13] and fuzzy logic (FLC) [14][15][16].Kofinas proposed an intelligent MPPT control scheme based on a direct neural control (DNC), which consists of a single adaptive neuron and a hybrid learning mechanism [17].However, these methods usually need an enormous volume of data for training, professional experience, or a complex leaning process.
Recently, bio-inspired algorithms have drawn considerable attention due to their excellent characteristics in dealing with the non-linear and stochastic optimization problems.Many algorithms, like genetic algorithms (GA) [18], particle swarm optimization (PSO) [19], and artificial bee colony (ABC) [20], have been utilized for MPPT application.Larbes et al. improved the performance of the FLC controller by using genetic algorithms (GA) for optimization [21].Sundareswaran combined the PSO algorithm and the P and O algorithm for MPPT application of PV under the partial shading condition [22].
Glowworm swarm optimization (GSO) is a novel bionic algorithm for the optimization of multimodal functions.It is firstly proposed by Krishnanand and Ghose, who were inspired from the natural phenomenon that glowworms exchange information of searching for food with their peers in 2005 [23].The GSO algorithm shows outstanding performance in finding the optimal solution for the multimodal functions but, at present, it is still rarely used in MPPT for PV.Considering the characteristic of multiple peaks in a P-I curve caused by the non-uniform solar irradiation conditions, GSO may be very suitable for MPPT.In addition, the photovoltaic-thermal energy (PV/T) system has the common phenomenon of the non-uniform temperature distribution on PV.Thus, the conditions are complex for PV/T under the non-uniform solar irradiation and temperature distribution.Currently, there are much fewer studies using GSO under these conditions.Therefore, in this paper, the novel GSO algorithm is presented to track the PV maximum power point for the PV/T application.In addition, in order to study the performance of the proposed method, the P and O method and FOCVT method are compared with it under four different complex conditions.The results indicate that the novel algorithm GSO is suitable for PV/T MPPT applications under non-uniform solar irradiation and temperature distribution.

PV Cell
The characteristic curve (the voltage-current curve and the power-current curve) of the solar cell is nonlinear.From the equivalent circuit in Figure 1 [24], the output characteristic of the PV cell is given by Equations ( 1)-( 9): where I sh is the current of the parallel resistance and I ph is the light-generated current, which is proportional to the given solar irradiation.It can be calculated by: where I sc is the short-circuit current at standard test condition (STC) (T = 25 • C, S = 1000 W/m 2 ) and α is the current temperature coefficient of the cell.T c and T r are the operating temperature and the reference temperature of the cell, respectively.I d represents the diode current, which is given according to the Shockley equation: where q is the electronic charge (q = 1.6 × 10 −19 ), k is Boltzmann's constant (k = 1.38 × 10 −23 ), A is the ideal factor of the diode, I O is the reverse saturation current of the diode, where I o varies with the change in temperature and is given by: where E g is the band gap energy of the semiconductor and I ro is the saturation current of the diode at 25 • C, which is calculated by: where V oc is the open-circuit voltage of the PV module at STC (T = 25 • C, S = 1000 W/m 2 ).U d is the voltage of the equivalent diode which is given by: where R s is the series resistance.
where q is the electronic charge ( where s R is the series resistance.sh I is the current of the parallel resistance, which is given by: ( ) / sh s sh where sh R is the parallel resistance.
From the former analysis, the input-output characteristic of the PV cell is: The output power of the PV cell is given by: The parameters values of the silicon solar cell used in simulation are illustrated in Table 1.I sh is the current of the parallel resistance, which is given by: where R sh is the parallel resistance.
From the former analysis, the input-output characteristic of the PV cell is: The output power of the PV cell is given by: The parameters values of the silicon solar cell used in simulation are illustrated in Table 1.

PV Module
The output power of one PV cell is limit, as shown in Figure 2.So in order to acquire the desired power, the PV cells are usually connected with each other in series and parallel.In this paper, the series mode is adopted.In PV/T application, there is the similar gradient temperature distribution on the PV module due to the heat exchange structure.The temperatures of the water inlet and the water outlet are different in photovoltaic-thermal (PV/T) systems.Thus, we assume that the temperature gradient scope is 0.2 • C. In the simulation, the temperature of the first cell is set to 20 • C, and the temperature gradient scope is 0.2 • C, as shown in Figure 3.

PV Module
The output power of one PV cell is limit, as shown in Figure 2.So in order to acquire the desired power, the PV cells are usually connected with each other in series and parallel.In this paper, the series mode is adopted.In PV/T application, there is the similar gradient temperature distribution on the PV module due to the heat exchange structure.The temperatures of the water inlet and the water outlet are different in photovoltaic-thermal (PV/T) systems.Thus, we assume that the temperature gradient scope is 0.2 °C .In the simulation, the temperature of the first cell is set to 20 °C , and the temperature gradient scope is 0.2 °C , as shown in Figure 3.The P-I curves of the PV module under different solar irradiation is shown in Figure 4.This shows that the output power is a nonlinear function and is affected by the solar irradiation.Additionally, the electrical current corresponding to maximum power ( mp I ) varies with the solar irradiation.Thus, in order to find the real mp I as the reference operating point, the application of MPPT technology is necessary.The P-I curves of the PV module under different partial shading conditions is shown in Figure 5.The shading situation is shown in Figure 6.In this situation, the temperature distribution is assumed to be unaltered with Figure 3 since the shading area is small.The curves are characterized by multiple peaks in this condition.Most of the traditional MPPT methods usually may converge into the LMPP (local maximum power point) instead of the global GMPP (global maximum power point).Thus, this paper applies the GSO algorithm to complete the MPPT.

PV Module
The output power of one PV cell is limit, as shown in Figure 2.So in order to acquire the desired power, the PV cells are usually connected with each other in series and parallel.In this paper, the series mode is adopted.In PV/T application, there is the similar gradient temperature distribution on the PV module due to the heat exchange structure.The temperatures of the water inlet and the water outlet are different in photovoltaic-thermal (PV/T) systems.Thus, we assume that the temperature gradient scope is 0.2 °C .In the simulation, the temperature of the first cell is set to 20 °C , and the temperature gradient scope is 0.2 °C , as shown in Figure 3.The P-I curves of the PV module under different solar irradiation is shown in Figure 4.This shows that the output power is a nonlinear function and is affected by the solar irradiation.Additionally, the electrical current corresponding to maximum power (I mp ) varies with the solar irradiation.Thus, in order to find the real I mp as the reference operating point, the application of MPPT technology is necessary.The P-I curves of the PV module under different partial shading conditions is shown in Figure 5.The shading situation is shown in Figure 6.In this situation, the temperature distribution is assumed to be unaltered with Figure 3 since the shading area is small.The curves are characterized by multiple peaks in this condition.Most of the traditional MPPT methods usually may converge into the LMPP (local maximum power point) instead of the global GMPP (global maximum power point).Thus, this paper applies the GSO algorithm to complete the MPPT.

MPPT Algorithm
MPPT algorithm is used for finding the current, the voltage, or the duty cycle corresponding to the maximum power, keeping the PV work on the MPP.This paper applies the GSO algorithm to the PV for the PV/T application.In order to evaluate the performance of this method, the P and O and FOCVT methods are applied for comparison.

The Proposed GSO-Based MPPT
This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents.In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then

MPPT Algorithm
MPPT algorithm is used for finding the current, the voltage, or the duty cycle corresponding to the maximum power, keeping the PV work on the MPP.This paper applies the GSO algorithm to the PV for the PV/T application.In order to evaluate the performance of this method, the P and O and FOCVT methods are applied for comparison.

The Proposed GSO-Based MPPT
This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents.In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then

MPPT Algorithm
MPPT algorithm is used for finding the current, the voltage, or the duty cycle corresponding to the maximum power, keeping the PV work on the MPP.This paper applies the GSO algorithm to the PV for the PV/T application.In order to evaluate the performance of this method, the P and O and FOCVT methods are applied for comparison.

The Proposed GSO-Based MPPT
This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents.In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then

MPPT Algorithm
MPPT algorithm is used for finding the current, the voltage, or the duty cycle corresponding to the maximum power, keeping the PV work on the MPP.This paper applies the GSO algorithm to the PV for the PV/T application.In order to evaluate the performance of this method, the P and O and FOCVT methods are applied for comparison.

The Proposed GSO-Based MPPT
This algorithm uses glowworms with a luminescent quantity, called luciferin, as their agents.In the beginning, glowworms, as initial solutions, are randomly distributed in the problem space, then they move to a brighter state in their own sensor range.Finally, they gather around the brightest ones, which correspond to the optimized solution of the problem.There are three phases in this process: luciferin update phase, movement phase, and the local-decision range update phase [23].

Luciferin Update Phase
The value of luciferin glowworms carry mainly depends on the objective function value of the current position.The formula for updating luciferin is given by: where ρ is the luciferin decay constant (0 < ρ < 1) set as 0.4, (1 − ρ) * I i (t) to simulate the decay of the luciferin with time.γ is the luciferin enhancement constant set as 0.6, 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 objective function which is the output power of the PV module in this paper, given by: where V PV is the total voltage of the PV cells in series.The voltage of each PV cell can be expressed as a function of the current I by deriving from Equations ( 1) to ( 8) in Section 2. Thus, F is the function of solar irradiation S, the current I, and the temperature T. In this study, the temperature distribution is set as shown in Figure 3, I is the parameter to be optimized through this algorithm, which is regarded as the location of the glowworm, and S is the input variable.

Movement Phase
Each agent decided to move to a superior individual according to a probability mechanism.The probability of the agent i moving to the agent j is calculated by: where N i (t) is the neighborhood group of the agent i: d i,j (t) = x i −x j is the Euclidean distance between glowworms i and j at iteration t. r i d represents the variable neighborhood range associated with glowworm i at time t.
Glowworms are attracted by neighbors that glow brighter; that is, glowworms will move to the neighbors that have larger luciferin values than the other neighbors.The movement is decided by the probability given by Equation (12).If p ij0 (t) = max j (p ij (t)), set the position of glowworm i equal to the position of glowworm j.Then glowworms update their position.
The movement update rule can be stated as follows: where s is the step size and x i (t) and x i (t + 1) are the locations of agent i at iteration t and t + 1, respectively.

Local-Decision Range Update Phase
The decision radius should be updated according to the number of individuals in the current range: where β is the variation coefficient of the decision radius and n t is the number of individuals with high luciferin values in the local-decision range.The flowchart of this algorithm is shown in Figure 7.
Energies 2017, 10, 541 7 of 13 where  is the variation coefficient of the decision radius and t n is the number of individuals with high luciferin values in the local-decision range.The flowchart of this algorithm is shown in Figure 7.The algorithm parameters work well for a wide range of simulation scenarios and that only n and s r are parameters that influence the algorithm's behavior [23].Therefore, if the setting conditions are changed, these algorithm parameters will remain the same and do not need to be specifically tuned for every problem.Only n and s r need to be selected to reduce the computing time and obtain higher peak-capture levels.The values of maximum iteration number and glowworm number used in the simulation of the GSO algorithm are set as 20 and 50 respectively.

Perturbation and Observe Algorithm
The traditional perturb and observe algorithm imposed a fixed-size disturbance on the control variables (voltage), and judged the next direction of the disturbance by observing the change of the power.In this method, the operating voltage is perturbed in a given direction; if the power increased (the operating point is moving towards to the MPP), the direction would be maintained, otherwise the direction would be the opposite.This method is impossible to considerate of the tracking efficiency and the steady state accuracy at the same time.In this paper, the step-size is set 0.5 V.The flow chart of the P and O algorithm is shown in Figure 8.If

old PP 
, it means that the operating point is moving towards the MPP.Further voltage perturbations will be provided in the same direction as earlier in order to move operating point much closer to the MPP.If old PP  , it means that the operating point is moving away from the MPP.Further voltage perturbations will be provided in the reverse direction in order to move operating point much closer to the MPP.The algorithm parameters work well for a wide range of simulation scenarios and that only n and r s are parameters that influence the algorithm's behavior [23].Therefore, if the setting conditions are changed, these algorithm parameters will remain the same and do not need to be specifically tuned for every problem.Only n and r s need to be selected to reduce the computing time and obtain higher peak-capture levels.The values of maximum iteration number and glowworm number used in the simulation of the GSO algorithm are set as 20 and 50 respectively.

Perturbation and Observe Algorithm
The traditional perturb and observe algorithm imposed a fixed-size disturbance on the control variables (voltage), and judged the next direction of the disturbance by observing the change of the power.In this method, the operating voltage is perturbed in a given direction; if the power increased (the operating point is moving towards to the MPP), the direction would be maintained, otherwise the direction would be the opposite.This method is impossible to considerate of the tracking efficiency and the steady state accuracy at the same time.In this paper, the step-size is set 0.5 V.The flow chart of the P and O algorithm is shown in Figure 8.If P > P old , it means that the operating point is moving towards the MPP.Further voltage perturbations will be provided in the same direction as earlier in order to move operating point much closer to the MPP.If P < P old , it means that the operating point is moving away from the MPP.Further voltage perturbations will be provided in the reverse direction in order to move operating point much closer to the MPP.

Fractional Open-Circuit Voltage Technique
In this method, the voltage at the MPP is considered proportional to the open-circuit voltage of the PV.The relation is given by: where Vmp is the voltage corresponding to MPP, Kv is the coefficient of proportionality, usually ranging from 0.65 to 0.8.Voc is the open-circuit voltage which can be calculated by analyzing the PV system.

Simulation Results
In order to compare the tracking performance of different methods mentioned above, the PV system is simulated in MATLAB/Simulink (R2015b, MathWorks, Natick, MA, USA).The system consist of a PV module, a DC-DC boost converter, a battery, the MPPT algorithm, and the pulse width modulation (PWM) module.The boost converter is used for MPPT to adjust the operating voltage by using PWM technique to control the opening and closing of the metal-oxide semiconductor fieldeffect transistor (MOSFET) switch at 10 kHZ.The inductor is set to 10 mH.The PWM technique uses the deviation of the Vmp and VPV to form the closed-loop control.The structure diagram with the GSO algorithm is shown in Figure 9.In order to the study the performance and the suitable occasion of the proposed method, the simulation is implemented in the following cases:

Fractional Open-Circuit Voltage Technique
In this method, the voltage at the MPP is considered proportional to the open-circuit voltage of the PV.The relation is given by: where V mp is the voltage corresponding to MPP, K v is the coefficient of proportionality, usually ranging from 0.65 to 0.8.V oc is the open-circuit voltage which can be calculated by analyzing the PV system.

Simulation Results
In order to compare the tracking performance of different methods mentioned above, the PV system is simulated in MATLAB/Simulink (R2015b, MathWorks, Natick, MA, USA).The system consist of a PV module, a DC-DC boost converter, a battery, the MPPT algorithm, and the pulse width modulation (PWM) module.The boost converter is used for MPPT to adjust the operating voltage by using PWM technique to control the opening and closing of the metal-oxide semiconductor field-effect transistor (MOSFET) switch at 10 kHZ.The inductor is set to 10 mH.The PWM technique uses the deviation of the V mp and V PV to form the closed-loop control.The structure diagram with the GSO algorithm is shown in Figure 9.In order to the study the performance and the suitable occasion of the proposed method, the simulation is implemented in the following cases:

Fractional Open-Circuit Voltage Technique
In this method, the voltage at the MPP is considered proportional to the open-circuit voltage of the PV.The relation is given by: where Vmp is the voltage corresponding to MPP, Kv is the coefficient of proportionality, usually ranging from 0.65 to 0.8.Voc is the open-circuit voltage which can be calculated by analyzing the PV system.

Simulation Results
In order to compare the tracking performance of different methods mentioned above, the PV system is simulated in MATLAB/Simulink (R2015b, MathWorks, Natick, MA, USA).The system consist of a PV module, a DC-DC boost converter, a battery, the MPPT algorithm, and the pulse width modulation (PWM) module.The boost converter is used for MPPT to adjust the operating voltage by using PWM technique to control the opening and closing of the metal-oxide semiconductor fieldeffect transistor (MOSFET) switch at 10 kHZ.The inductor is set to 10 mH.The PWM technique uses the deviation of the Vmp and VPV to form the closed-loop control.The structure diagram with the GSO algorithm is shown in Figure 9.In order to the study the performance and the suitable occasion of the proposed method, the simulation is implemented in the following cases:

Gradient Temperature Distribution Condition
In this condition, the solar irradiance is supposed to be constant (S = 1000 W/m 2 ), while the temperature distribution of the PV module for PV/T system is shown in Figure 3.The simulation results show that the proposed GSO and the FOCVT methods can rapidly track the MPP in comparison with the P and O algorithm shown in Figure 10.The output power of PV module can reach a steady state in 0.0018 s by using the GSO and FOCVT methods in less than half of the settling time by using the P and O algorithm.

Gradient Temperature Distribution Condition
In this condition, the solar irradiance is supposed to be constant ( 2 1000 W/m S  ), while the temperature distribution of the PV module for PV/T system is shown in Figure 3.The simulation results show that the proposed GSO and the FOCVT methods can rapidly track the MPP in comparison with the P and O algorithm shown in Figure 10.The output power of PV module can reach a steady state in 0.0018 s by using the GSO and FOCVT methods in less than half of the settling time by using the P and O algorithm.

Fast Variation in Solar Irradiation
The temperature is assumed to be constant ( 25 T  °C ), while there is a fast variation in the solar irradiation, as shown in Figure 11.This shows that the GSO algorithm and the FOCVT method can rapidly and correctly track the MPP under the condition of fast variation in solar irradiation in comparison with the P and O algorithm, as shown in Figure 12.As Figure 12 shows, it is obvious that the GSO algorithm can improve the maximum tracking power by 8% and 13.3% compared to the conventional P and Obased MPPT controller, respectively, when the solar irradiation changes from 600 W/m 2 to 800 W/m 2 at 0.02s and from 800 W/m 2 to 1000 W/m 2 at 0.03 s, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT method.The steady state errors of using P and O will increase obviously with the solar irradiation increase.When the solar irradiation is 600 W/m 2 , the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and 0.5701, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT and P and O methods.

Fast Variation in Solar Irradiation
The temperature is assumed to be constant (T = 25 • C), while there is a fast variation in the solar irradiation, as shown in Figure 11.

Gradient Temperature Distribution Condition
In this condition, the solar irradiance is supposed to be constant ( 2 1000 W/m S  ), while the temperature distribution of the PV module for PV/T system is shown in Figure 3.The simulation results show that the proposed GSO and the FOCVT methods can rapidly track the MPP in comparison with the P and O algorithm shown in Figure 10.The output power of PV module can reach a steady state in 0.0018 s by using the GSO and FOCVT methods in less than half of the settling time by using the P and O algorithm.

Fast Variation in Solar Irradiation
The temperature is assumed to be constant ( 25 T  °C ), while there is a fast variation in the solar irradiation, as shown in Figure 11.This shows that the GSO algorithm and the FOCVT method can rapidly and correctly track the MPP under the condition of fast variation in solar irradiation in comparison with the P and O algorithm, as shown in Figure 12.As Figure 12 shows, it is obvious that the GSO algorithm can improve the maximum tracking power by 8% and 13.3% compared to the conventional P and Obased MPPT controller, respectively, when the solar irradiation changes from 600 W/m 2 to 800 W/m 2 at 0.02s and from 800 W/m 2 to 1000 W/m 2 at 0.03 s, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT method.The steady state errors of using P and O will increase obviously with the solar irradiation increase.When the solar irradiation is 600 W/m 2 , the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and 0.5701, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT and P and O methods.This shows that the GSO algorithm and the FOCVT method can rapidly and correctly track the MPP under the condition of fast variation in solar irradiation in comparison with the P and O algorithm, as shown in Figure 12.As Figure 12 shows, it is obvious that the GSO algorithm can improve the maximum tracking power by 8% and 13.3% compared to the P and O-based MPPT controller, respectively, when the solar irradiation changes from 600 W/m 2 to 800 W/m 2 at 0.02 s and from 800 W/m 2 to 1000 W/m 2 at 0.03 s, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT method.The steady state errors of using P and O will increase obviously with the solar irradiation increase.When the solar irradiation is 600 W/m 2 , the RMSE of the output power by using P and O, GSO, and FOCVT are 0.9623, 0.4528, and 0.5701, respectively.It can be seen that the GSO algorithm has the better steady-state performance than the FOCVT and P and O methods.

Partial Shading Condition
Under this condition, the temperature distribution and the shaded condition are shown in Figures 3 and 6, respectively.The solar irradiance of the shaded part is

Variation in the Degree of Shading
Under this condition, the situation of the temperature distribution and shading are the same with case 3, however the solar irradiance of the shaded part changes, as shown in Figure 14.The solar irradiance of the other part is normal ( 2 1000 W/m S  ).It is can be seen that the GSO algorithm can rapidly track the GMPP even when the shading degree varies, whereas the FOCVT method converge to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in Figure 15.

Partial Shading Condition
Under this condition, the temperature distribution and the shaded condition are shown in Figures 3 and 6, respectively.The solar irradiance of the shaded part is 600 W/m 2 and that of the other part is normal (S = 1000 W/m 2 ).It is obvious that the GSO algorithm can determine the GMPP in this condition, whereas the P and O and FOCVT algorithms converge to the LMPP from Figure 13.The GSO algorithm can improve the output power value by 12.5% compared to P and O-and FOCVT-based MPPT controllers under partial shading conditions.In addition, the P and O algorithm has a slow speed and greater fluctuation in the steady state.

Partial Shading Condition
Under this condition, the temperature distribution and the shaded condition are shown in Figures 3 and 6, respectively.The solar irradiance of the shaded part is

Variation in the Degree of Shading
Under this condition, the situation of the temperature distribution and shading are the same with case 3, however the solar irradiance of the shaded part changes, as shown in Figure 14.The solar irradiance of the other part is normal ( 2 1000 W/m S  ).It is can be seen that the GSO algorithm can rapidly track the GMPP even when the shading degree varies, whereas the FOCVT method converge to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in Figure 15.

Variation in the Degree of Shading
Under this condition, the situation of the temperature distribution and shading are the same with case 3, however the solar irradiance of the shaded part changes, as shown in Figure 14.The solar irradiance of the other part is normal (S = 1000 W/m 2 ).It is can be seen that the GSO algorithm can rapidly track the GMPP even when the shading degree varies, whereas the FOCVT method converge to the LMPP, the P and O algorithm diverged from the MPP in the limited time, as shown in Figure 15.

Conclusions
In this paper, a novel MPPT method based on the GSO algorithm is proposed and its performance is compared with P and O and FOCVT methods.The simulations used three different methods and are implemented through MATLAB/Simulink under four conditions (gradient temperature distribution condition, fast variation in solar irradiation, partial shading condition, and variation in the degree of shading).The output power of the photovoltaic (PV) system is affected by the external solar irradiation and its own temperature.Additionally, there will be multiple peaks in the P-I curves under the partial shading condition.In addition, the non-uniform temperature distribution appears on PV for PV/T applications.Taking into account the superiority in multi-peak function optimization, the GSO is applied to the MPPT control algorithm.It is confirmed by a simulation study that the GSO algorithm performs better than P and O and FOCVT.It can track the real MPP under different solar irradiation and temperature distributions with high accuracy, as well as partially-shaded conditions.However, the P and O and FOCVT will converge into the LMPP under the partially-shaded condition.Moreover, the GSO algorithm has a better time response in comparison with the P and O algorithm, and its convergence speed is higher than the two other algorithms.
Author Contributions: Yi Jin designed and developed the main parts of the research work, including simulation model and analyses of the obtained results.Wenhui Hou contributed in simulation and writing parts.Guiqiang Li contributed in theoretical analysis.Xiao Chen also involved in verifying the work and actively contributed to finalize the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In this paper, a novel MPPT method based on the GSO algorithm is proposed and its performance is compared with P and O and FOCVT methods.The simulations used three different methods and are implemented through MATLAB/Simulink under four conditions (gradient temperature distribution condition, fast variation in solar irradiation, partial shading condition, and variation in the degree of shading).The output power of the photovoltaic (PV) system is affected by the external solar irradiation and its own temperature.Additionally, there will be multiple peaks in the P-I curves under the partial shading condition.In addition, the non-uniform temperature distribution appears on PV for PV/T applications.Taking into account the superiority in multi-peak function optimization, the GSO is applied to the MPPT control algorithm.It is confirmed by a simulation study that the GSO algorithm performs better than P and O and FOCVT.It can track the real MPP under different solar irradiation and temperature distributions with high accuracy, as well as partially-shaded conditions.However, the P and O and FOCVT will converge into the LMPP under the partially-shaded condition.Moreover, the GSO algorithm has a better time response in comparison with the P and O algorithm, and its convergence speed is higher than the two other algorithms.
Author Contributions: Yi Jin designed and developed the main parts of the research work, including simulation model and analyses of the obtained results.Wenhui Hou contributed in simulation and writing parts.Guiqiang Li contributed in theoretical analysis.Xiao Chen also involved in verifying the work and actively contributed to finalize the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In this paper, a novel MPPT method based on the GSO algorithm is proposed and its performance is compared with P and O and FOCVT methods.The simulations used three different methods and are implemented through MATLAB/Simulink under four conditions (gradient temperature distribution condition, fast variation in solar irradiation, partial shading condition, and variation in the degree of shading).The output power of the photovoltaic (PV) system is affected by the external solar irradiation and its own temperature.Additionally, there will be multiple peaks in the P-I curves under the partial shading condition.In addition, the non-uniform temperature distribution appears on PV for PV/T applications.Taking into account the superiority in multi-peak function optimization, the GSO is applied to the MPPT control algorithm.It is confirmed by a simulation study that the GSO algorithm performs better than P and O and FOCVT.It can track the real MPP under different solar irradiation and temperature distributions with high accuracy, as well as partially-shaded conditions.However, the P and O and FOCVT will converge into the LMPP under the partially-shaded condition.Moreover, the GSO algorithm has a better time response in comparison with the P and O algorithm, and its convergence speed is higher than the two other algorithms.

Figure 1 .
Figure 1.Equivalent circuit of the solar cell.

Figure 1 .
Figure 1.Equivalent circuit of the solar cell.

Figure 2 .
Figure 2. Output power of the photovoltaic (PV) cell.

Figure 3 .
Figure 3.The ideal temperature distribution on PV for a photovoltaic-thermal (PV/T) system.

Figure 2 .
Figure 2. Output power of the photovoltaic (PV) cell.

Figure 2 .
Figure 2. Output power of the photovoltaic (PV) cell.

Figure 3 .Figure 3 .
Figure 3.The ideal temperature distribution on PV for a photovoltaic-thermal (PV/T) system.

Figure 4 .
Figure 4. Output power of the PV module under different levels of solar irradiation.

Figure 5 .
Figure 5. Output power of the PV module under partial shading.

Figure 6 .
Figure 6.The partial shading condition of PV for a PV/T system.

2 Figure 4 . 13 Figure 4 .
Figure 4. Output power of the PV module under different levels of solar irradiation.

Figure 5 .
Figure 5. Output power of the PV module under partial shading.

Figure 6 .
Figure 6.The partial shading condition of PV for a PV/T system.

Figure 5 .
Figure 5. Output power of the PV module under partial shading.

Figure 4 .
Figure 4. Output power of the PV module under different levels of solar irradiation.

Figure 5 .
Figure 5. Output power of the PV module under partial shading.

Figure 6 .
Figure 6.The partial shading condition of PV for a PV/T system.

Figure 6 .
Figure 6.The partial shading condition of PV for a PV/T system.

Figure 8 .
Figure 8.The flowchart of the perturbation and observe (P and O) algorithm.

Case 1 :
Gradient temperature distribution condition Case 2: Fast variation in solar irradiation Case 3: Partial shading condition Case 4: Variation in the degree of shading.

Figure 9 .
Figure 9.The structure diagram of the system.PWM: pulse width modulation; and MPPT: maximum power point tracking.

Figure 8 .
Figure 8.The flowchart of the perturbation and observe (P and O) algorithm.

Case 1 :
Gradient temperature distribution condition Case 2: Fast variation in solar irradiation Case 3: Partial shading condition Case 4: Variation in the degree of shading.

Figure 8 .
Figure 8.The flowchart of the perturbation and observe (P and O) algorithm.

Case 1 :
Gradient temperature distribution condition Case 2: Fast variation in solar irradiation Case 3: Partial shading condition Case 4: Variation in the degree of shading.

Figure 9 .
Figure 9.The structure diagram of the system.PWM: pulse width modulation; and MPPT: maximum power point tracking.

Figure 9 .
Figure 9.The structure diagram of the system.PWM: pulse width modulation; and MPPT: maximum power point tracking.

Figure 10 .
Figure 10.Output power under a gradient temperature distribution.

Figure 11 .
Figure 11.Variation of the solar irradiation.

Figure 10 .
Figure 10.Output power under a gradient temperature distribution.

Figure 11 .
Figure 11.Variation of the solar irradiation.
is obvious that the GSO algorithm can determine the GMPP in this condition, whereas the P and O and FOCVT algorithms converge to the LMPP from Figure13.The GSO algorithm can improve the output power value by 12.5% compared to P and O-and FOCVTbased MPPT controllers under partial shading conditions.In addition, the P and O algorithm has a slow speed and greater fluctuation in the steady state.
is obvious that the GSO algorithm can determine the GMPP in this condition, whereas the P and O and FOCVT algorithms converge to the LMPP from Figure13.The GSO algorithm can improve the output power value by 12.5% compared to P and O-and FOCVTbased MPPT controllers under partial shading conditions.In addition, the P and O algorithm has a slow speed and greater fluctuation in the steady state.

Figure 14 .
Figure 14.The solar irradiation of the shading part.

Figure 15 .
Figure 15.Output power under the variable degree of shading.

Figure 14 . 13 Figure 14 .
Figure 14.The solar irradiation of the shading part.

Figure 15 .
Figure 15.Output power under the variable degree of shading.

Figure 15 .
Figure 15.Output power under the variable degree of shading.

Table 1 .
Parameters of the silicon solar cell.

Table 1 .
Parameters of the silicon solar cell.

Table 1 .
Parameters of the silicon solar cell.