Evaluation of Fuzzy Logic Subsets Effects on Maximum Power Point Tracking for Photovoltaic System

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Introduction
Fossil fuel is a very common choice in many countries worldwide due to its large sources, but nowadays by increasing concerns about some issues such as fossil fuel storage, global warming, and skyrocketing oil costs, it is desirable to consider substitute possible energy source that has high productivity and low outpouring [1,2].
All of the PV systems have some main problems affected by weather conditions such as dirt, changing irradiation, temperature, and other factors.The PV systems have two main characteristics, P-V and I-V, where P, V, and I are PV output power, voltage, and current, respectively.Changing the irradiation has the most effect on these characteristics.
The PV system has an operating point that can be specified by the crossing point between I-V curve of the PV panel and load line in I-V characteristic.The variation of some factors such as irradiation, temperature, and dust can change the operating point.There is single point in I-V and P-V curves of PV panel that power poses the maximum value and it is called maximum power point (MPP) [3].In changing weather condition such as irradiation, the MPP controller should be capable of tracking MPP at minimum time in order to minimize the power loss.
In order to find the MPP, various methods have been proposed which can be classified in two general methods: conventional and soft computing methods.Conventional methods include perturb and observe (P&O), constant voltage (CV), and conductance increment (IC), and soft computing methods cover fuzzy logic controller, neural network predictor, genetic algorithm, and so on [4][5][6][7][8][9][10][11][12].Every tracking control method has its advantages and disadvantages.One of the main factors for finding the best MPPT algorithm is that the MPP should be found by controller in the minimum time especially under changing condition.Another significant factor is that the controller can operate at this point with minimum oscillation.The conventional methods have drawbacks such as low tracking speed and also oscillation around MPP [13,14].In order to solve this problem, the artificial intelligent method such as fuzzy logic (FL) can be used which keeps strength in changing weather condition such as temperature and radiation.In fuzzy logic method the main points are defining a rule table and the related range of membership function.The rules are defined according to specific range of membership functions and vice versa.By changing the range of membership functions, the rules can be changed for obtaining the expected result and, also, by changing the rules, the range of membership functions should be changed.
In this paper, in Section 2 the PV system is explained and modeled by MATLAB in base of the KC200GT panel type.In Section 3 the DC-DC boost converter is explained.In Sections 4 and 5, fuzzy logic controller (FLC) and different subsets for this method are explained.Then, in Section 6, the results of simulations are analyzed.Finally, the last section concludes and discusses the results of simulations for studied fuzzy rules subsets.

Photovoltaic System
2.1.Equivalent Model of Photovoltaic System.In Figure 1, the tantamount circuit for PV cell is shown that is relative to the incident radiation which is connected in parallel with shunt resistance ( SH ) and diode.The internal series resistance (  ) can be considered for modeling the internal losses that are created by the flowing current and also connection between cells [15].
The PV efficiency is so sensitive to variation of the series resistance such that a small changing in value of   has a big effect on PV characteristics such as power and voltage.On the other hand, the effect of shunt resistance on PV efficiency can be ignored because the PV efficiency is not responsive to changing of  SH , so the shunt resistance can be assumed to be almost infinite and it becomes open circuit.By these assumptions, the net current of a cell can be defined by (1) and I-V characteristic can be described according to In (1),  and  are the output solar cell current and voltage, respectively.  and   are the cell saturation and photocurrent, respectively.In this equation, there are some constant coefficients:  (=1.38 × 10 −23 J/K) is a Boltzmann's  C) is an electron charge,  is the ideality factor that its value ranges are between 1 and 2,  is the cell's working temperature, and   is the series resistance that is explained before.
In order to draw the I-V curve, (1) needs to be solved.This equation is nonlinear and, with the purpose of solving it, Newton Raphson's method as a numerical method is used.
In (1), there are some subequations such as saturation current, photocurrent, and open circuit current equations that are dependent on temperature.These subequations can be expressed as follows: In these equations,  is the irradiation and the band gap energy is shown by   that its value is 1.12 eV for silicon.The "ref " subscript recognizes the standard test conditions (STC) expressed in the IEC 61215 international standard [16].According to this standard,  ref and  ref are equal to 25 ∘ C ( 1 in equations) and 1000 W/m 2 , respectively. OC and  SC in reference temperature are specified in PV panel data sheet.
As mentioned before, series resistance has a big effect on the PV characteristics.Gow and Manning first time defined (3) in order to calculate the value of series resistance (  ) [17].This equation is obtained by differentiating (1) and evaluating it in open circuit conditions:

Electric Characteristic of Photovoltaic System.
In this paper, simulation results are based on the KC200GT panel.
In Table 1, the key specifications of this panel are shown according to datasheet [18].In the previous section, it was mentioned that I-V and P-V characteristics of the PV system depended on irradiance () and temperature.In Figures 2 and 3, the I-V and P-V curves of the KC200GT PV module in different irradiations and fixed temperature (25 ∘ C) are shown.As shown in Figure 3, the maximum power point is decreased by decreasing the irradiation.The maximum power in 1000 W/m 2 irradiation is 200 watts.

DC-DC Boost Converter
The boost converter is a famous switched-mode converter where its produced output voltage is bigger than dc input voltage in extent.The ideal and simple form of this converter is shown in Figure 4 that is including switch and diode for switching the system.
When the switch is ON (first subinterval) diode, capacitor, and load are connected to ground and the inductor is  charged through the input voltage source (  ).In this subinterval, load is supplied by capacitor and the inductor current is increased.When the switch is off (second subinterval), the load is supplied by inductor current and additionally recharges the capacitor.
In Figures 5 and 6, voltage and current of the boost converter inductor are shown.According to these two figures and also using the principles of voltage and ampere second balance [19], the voltage conversion ratio () and the converter elements values are obtained.The voltage conversion ratio is defined as a proportion of the output voltage to input voltage of boost converter: where   and  are the input and output voltages of the boost converter and  is duty cycle that is defined as a ratio of the ON duration to the switching time period and it is adjusted by controller that in this case is fuzzy logic controller.
It can be noticed that when the boost converter is connected to PV panel, by increasing the duty cycle, the input voltage and current are decreased and increased, respectively, and it leads to shifting the operating point to the left side of the P-V curve of the PV panel.In a similar manner, by decreasing the duty cycle, the input voltage and current are increased and decreased, respectively, and it leads to shifting the operating point to the right side of the P-V curve of the PV panel.

Fuzzy Logic Controller (FLC)
Fuzzy logic (FL) is a strategy of processing degrees of truth instead of Boolean logic.The fuzzy logic rules were first proposed by Professor L. Zadeh in 1965 and can be implemented for the complex and unknown systems.The conventional methods are not satisfied for the system especially for nonlinear and complex systems and cannot obtain the desirable results.The FL systems are more flexible rather than classical and conventional methods and they are capable of modelling and approximating the nonlinear systems.The structure of the fuzzy logic systems is based on the changing the control linguistic to form of the if-then in an automatic control system and a good knowledge and experience can be more useful instead of understanding a technical behavior and model of system [20][21][22].
As mentioned in previous sections, the conventional methods such as P&O have some drawbacks such as oscillation around the MPP and also take a long time to obtain the steady state, so in this paper the fuzzy logic control method is considered for maximum power point in order to evaluate the best structure of the interface and rules for obtaining the best fuzzy subset rules.The fuzzy logic diagram is shown in Figure 7 that is including two inputs and one output.The inputs of the FLC system are the error () and change of error (CE) that are defined by (6).The output of FL is duty cycle () that should operate to the boost converter [23,24].Consider PV () and  PV () are the PV voltage and power, respectively, at instant .If  will be positive it means that the operating point is in left side of the MPP and when it will be negative, the operating point is in right side of the MPP.The MPP will be obtained when  is equal to zero.The moving direction in I-V and P-V curves is specified by CE [25][26][27][28].
The fuzzy logic fundamentally consists of three steps: fuzzification, rule base and inference engine, and defuzzification.

Fuzzification.
In process of fuzzification, all variables used to describe the control rules should be converted to linguistic fuzzy labels.These variables are demonstrated in different fuzzy levels: PB (positive big), PM (positive medium), PS (positive small), ZE (zero), NB (negative big), NM (negative medium), and NS (negative small).In this study, different fuzzification subsets with different levels and membership function ranges are considered.

Rule Base and Inference Engine.
Rules base is if-then functions that are used for the fuzzified inputs in order to apply for the controlled parameters.Defining these rules is dependent on operation of the system and experience.In this study, different subsets include forty-nine, thirty-five, and twenty-five fuzzy control rules with different specific range of membership functions being considered.Fuzzy inference engine is the process of devising the logical decision based on the rules.The fuzzy rules should be transferred into fuzzy linguistic output.In this work, Mamadani's fuzzy inference method has been used.

Defuzzification.
In this stage, the output fuzzy data that is defined by the rules and inference engine should be converted to the numerical value by creating the union of the output from each rule.In this study, the center of gravity defuzzifier is used which is the common one.

Fuzzy Logic Subsets
As mentioned in previous section, implementing the fuzzy logic controller needs to have enough experience more than knowing the technical model of the system because in process of designing the fuzzy logic controller, rules and inference and also the range of membership functions are the important and crucial sections.Each fuzzy system has a subset rule that will be defined according to the specific range of membership function and vice versa [29][30][31][32].In systems with the boost converter, different fuzzy logic subsets with different rules and range of membership functions have been used in order to obtain MPP.In each subset, range of membership function is defined according to the specific rule table and vice versa.In this paper, the main goal is to achieve the best fuzzy subset for obtaining MPP by comparative study of different common fuzzy subsets with considering main factors such as MPP's reaching time, oscillation, steady state time, ripple, efficiency, and some other factors.In this work, different subsets (S1, S2, S3, S4, and S5) which include different rules and range of membership functions will be introduced and the best one will be selected.For S1, S2, and S3, five subsets based on twenty-five rules have been used where their rules and membership functions are different.For S4, seven subsets based on forty-nine rules and, for S5, seven and five subsets based on thirty-five rules have been used.The triangular and trapezoid shaped membership functions have been used for all models.For the range of membership function, the oscillation of each signal has been checked and the best one is considered [33][34][35].Figure 8 shows the fuzzy logic controller at which  and CE are the inputs and  is output of the controller.

First Subset (S1).
It is as shown in Table 2 and Figure 9.

Second Subset (S2).
It is as shown in Table 3 and Figure 10. 4 and Figure 11.

Simulation Result
In this work, the simulations are carried out by MAT-LAB/Simulink to validate the performance of the system.The source of the system is PV that is modeled by script in MATLAB.The five studied subsets are implemented in control unit for the same system and performance of the system is considered for evaluation of the different fuzzy logic subsets.In Figure 14, the configuration of the system includes PV, boost converter, and MPPT controller and input filter is shown.The input capacitance of the converter,  in , is 2000 F, the inductance, , is 25 H, the resistance of inductor,   , is Goto 0.02 Ω, the output capacitance,  out , is 450 F, and the load resistance, , is 20 Ω.The switching frequency of the system is 25 kHz.For investigation and analyzing behavior of the system, there are some important factors which will be considered such as maximum power point reaching time, efficiency, and ripple in input and output voltage and power.The simulation values for these factors at irradiation of 1000 W/m 2 and 25 ∘ C are summarized in Tables 7 and 8.These factors are defined as follows:  ripp is the ripple in current at steady state time (A);   is the efficiency (%).
In Figure 15, the PV available maximum power at irradiation of 1000 W/m 2 and 25 ∘ C for different fuzzy subsets is shown.In all subsets, the maximum power point is obtained after a small stilling time for S1, S2, and S4 with the average value of 200 watts that is exact value according to data sheet, but, for S3 and S5, the values are 199.3 and 199 watts, respectively.As shown in Figure 15 and Table 7, the MPP is obtained at 0.0085 ( 1 PV ) second for S1, S2, S3, and S5, but, for S4, it is 0.022 second.Other than that, S2 has the lower steady state time for obtaining MPP.The important point is that, in  1 , there are oscillations ( ripp PV ) in power for S1, S2, S3, and S5 with values of 0.3, 1.2, 4.2, and 5.4 watts, respectively, that can lead to some losses, but, for S4, the power oscillation is zero from the first time that MPP is obtained.The power ripple at steady state time of MPP is zero for S1, S2, and S4, but, for S3 and S5, the values are 1.4 and 1.9 watts, respectively.
The PV available maximum voltage at 1000 W/m 2 and 25 ∘ C for different subsets is shown in Figure 16.According to  this figure and Table 7, the time for reaching the maximum point of voltage for S4 is more than other subsets but this subset has the minimum ripple voltage value in  1V and approximately in  SV .
In Figures 17 and 18, the output power and voltage of the system are shown.According to these figures and Table 8, S1, S2, and S4 have much more average power in comparison with S3 and S5 as the main reason is bigger oscillations in power and voltage.S2 has the minimum ripple in power and voltage that are 0.7 watt and 0.1 volt, respectively.
The output currents for all subsets are shown in Figure 19.According to this figure and Table 8, S2 has the maximum average value and also the minimum ripple in current.S4 is the next subset that has maximum average current value and the minimum ripple in current.
Another important factor for selecting the best fuzzy subset is the efficiency of the system that is defined by ratio of the output power to input power of the system.Among the discussed subsets, S2 has the maximum efficiency with 95.7% and S5 has the minimum one with 88.52%.
In Figures 20 and 21, the bar graphs of this comparative study are plotted that is beneficial for better general survey.According to these graphs and Tables 7 and 8, S2 and S4 have the better performance among all subsets.In comparison between S2 and S4, the maximum power point reaching time for S2 is less than S4 that is so important for controller to track the MPP.The ripple values of power and voltage are important when the MPP is obtained so that the minimum ripple value makes a significant reduction in switching and power losses.According to

Conclusion
This paper presents a detailed comparative survey of five general fuzzy logic subsets that are used for fuzzy logic (FL) based on maximum power point tracking technique.In this work, simulation has been done in MATLAB.The main objective of this work was to obtain the most efficient fuzzy subset among the general FL subsets used for FLC in boost converter applications.The obtained results show that the rules and range of membership functions are so significant for implementing the fuzzy logic controller in the main system.By considering the main factors for different subsets in same conditions, it is observed that second and fourth subsets have better performance in comparison with other subsets.The second subset (S2) has minimum MPP's reaching time and zero ripple value for power at steady state time with maximum efficiency.The fourth subset (S4) has the minimum ripple in voltage and current at reaching time of MPP but it needs much more time for reaching the MPP.Therefore, considering all above analyzed factors, it can be concluded that S2 is the best fuzzy subset which can track MPP in minimum time and low oscillation with high efficiency.

Figure 5 :
Figure 5: Voltage waveform of the boost converter's inductor.

Figure 9 :
Figure 9: The membership functions of , CE, and  for S1.

Figure 10 :
Figure 10: The membership functions of , CE, and  for S2.

Figure 11 :
Figure 11: The membership functions of , CE, and  for S3.

Figure 12 :
Figure 12: The membership functions of , CE, and  for S4.

Figure 13 :
Figure 13: The membership functions of , CE, and  for S5.

Figure 19 :
Figure 19: Boost output current at irradiation of 1000 W/m 2 and 25 ∘ C.

Figure 20 :
Figure 20: The bar graph for PV variables.

Figure 21 :
Figure 21: The bar graph for boost converter variables.

Table 2 :
The twenty-five fuzzy rules of the first fuzzy subset (S1).

Table 3 :
The twenty-five fuzzy rules of the second fuzzy subset (S2).

Table 4 :
The twenty-five fuzzy rules of the third fuzzy subset (S3).

Table 5 and
Figure 12.It is as shown in Table6and Figure13.

Table 5 :
The forty-nine fuzzy rules of the fourth fuzzy subset (S4).

Table 6 :
The thirty-five fuzzy rules of the fifth fuzzy subset (S5).

Table 7 :
The simulation values for PV variables.

Table 8 :
The simulation values for boost converter variables.

Table 7 ,
S4 and S2 have the minimum ripple values in MPP's reaching time, respectively.So, considering all above analyzed factors, it can be concluded that S2 is the best fuzzy subset which can track MPP in minimum time and low oscillation with high efficiency.