# Development of a Fuzzy Logic based Photovoltaic Maximum Power Point Tracking Control System using Boost Converter

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2 II. MODELLING THE PHOTOVOLTAIC ARRAY An ideal solar cell is a current source present in parallel with diode. But, practically number of series and parallel resistances are connected to obtain the desired voltages and current values. Fig. 1. Representation of a practical PV cell. Hence, equation [2] of the elementary photovoltaic cell does not represent the I-V characteristic of a practical photovoltaic array. Practical arrays are composed of several connected photovoltaic cells and the observation of the characteristics at the terminals of the photovoltaic array requires the inclusion of additional parameters to the basic equation [2]. Fig. 2. I-V characteristics of a practical Photovoltaic device. Current versus voltage (I-V) curve is obtained by exposing a cell to a constant magnitude of light, maintaining a constant cell temperature, varying the resistance of the load and measuring the produced current. I-V curve typically passes through two points: Short circuit current point and open circuit voltage point. Short-circuit current is the current produced when the positive and negative terminals of the cell are short-circuited, and the voltage between the terminals is zero, which corresponds to zero load resistance. Open-circuit voltage is the voltage across the positive and negative terminals under open-circuit conditions, when the current is zero, which corresponds to infinite load resistance. (1) where, and are the photovoltaic and saturation currents of the array and is the thermal voltage of the array with cells connected in series. Cells connected in parallel increases the current and cells connected in series provide greater output voltages. If the array is composed of expressed as parallel connections of cells the photovoltaic and saturation currents All Rights Reserved 59

3 = (2) = (3) In equation 1, is the equivalent series resistance of the array and is the equivalent parallel resistance. This equation originates from the I-V curve shown in figure 2, where three remarkable points are highlighted i.e., short circuit current, maximum power point and open-circuit voltage. All photovoltaic array data sheets give basic information about nominal open-circuit voltage, nominal short-circuit current, voltage at the maximum power point, current at the maximum power point, open-circuit voltage temperature coefficient, short-circuit current temperature coefficient and the maximum experimental peak output power. This information is always provided with reference to the nominal or standard test conditions (STC) of temperature and solar irradiation. The practical photovoltaic device has a series resistance whose influence is stronger when the device operates in the voltage source region and a parallel resistance with stronger influence in the current source region. The series resistance is the sum of several structural resistances of the device and parallel resistance exists mainly due to the leakage current of the p-n junction and depends on the fabrication method of the photovoltaic cell. The value of parallel resistance is generally high, whereas the value of series resistance is very low and sometimes this parameter is neglected too. The I-V characteristic of the photovoltaic device shown in figure 2 depends on the internal characteristics of the device and on external influences such as irradiation level and temperature. The modeling of the PV system is done using the equations 4, 5 and 6. (4) (5) (6) SIMULINK model of PV system employed in the present work is shown in figure 3. Fig. 3. Simulink model of PV system. Series and parallel resistances are connected to the PV system. The diode is modeled using Shockley diode equation. The inputs to the PV system are irradiance and temperature. The PV output voltage and PV output current are measured at port 1 as shown in figure All Rights Reserved 60

4 III. MAXIMUM POWER POINT TRACKING AND DC-DC BOOST CONVERTER The role of MPPT is to ensure the operation of the PV system at its MPP, extracting the maximum available power. The general block diagram for a charge battery system is shown in figure 4, along with MPPT Controller and DC/DC converter. This converter is connected to the PV generator, a battery and a load profile (such as a resistance, DC/DC motor). A resistance load is used in the present work. The main objective of the MPPT technique is to obtain the maximum power from the PV generator [3 & 4]. Fig. 4. Block diagram of solar panel with MPPT and Fuzzy control. In a boost converter, the output voltage is greater than the input voltage and hence the name boost. The operation of boost converter can be divided into two modes. The pulse from the MPPT controller is fed to the gate terminal of MOSFET. Mode 1 begins, when the MOSFET is switched on at t = 0 and hence the input current rises, and flows through inductor and MOSFET. Mode 2 begins when the MOSFET is switched OFF and hence the current flowing through the MOSFET would now flow through inductor, capacitor, load and Diode. The inductor current falls until MOSFET is turned ON again in the next cycle. The energy stored in the inductor L is transferred to the load. IV. FUZZY LOGIC BASED CONTROLLER The main components used in fuzzy logic based MPPT [4 & 5] Controller are Fuzzification, Rule- Base, Inference and Defuzzification as shown in the figure 5. Fig. 5. Structure of fuzzy logic controller. Fuzzification is the process of converting the crisp data into fuzzy data. First phase of fuzzy logic proceeding is to deliver input parameters for given fuzzy system based on which the output result will be calculated. These parameters are fuzzified with the use of pre-defined input membership functions. The inputs to MPPT fuzzy logic controller are usually an error E and a change of error. The two FLC input variables error E and change of error CE at sampled times k are defined by (8) The input E(k) shows whether the load operation point at the instant k is located on the left or on the right of the maximum power point on the PV characteristic, while the input E(k) expresses the All Rights Reserved 61

5 moving direction of this point. Inference mechanism allows mapping of given input to an output using fuzzy logic. It uses membership functions, logical operations and if-then rules. The most common types of inference systems are Mamdani and Sugeno. They vary in ways of determining outputs. The fuzzy logic controller output is typically a change in duty ratio of the power converter. The linguistic variables are assigned to for the different combinations of E and. The advantages of fuzzy controller, besides dealing with imprecise inputs, without an accurate mathematical model and handling nonlinearity, are fast convergence and minimal oscillations around the MPP. Furthermore, they have been shown to perform well under step changes in the irradiation. The final step in the fuzzy logic controller is to combine the fuzzy output into a crisp system output. The result of the defuzzification has to be a numeric value which determines the change of duty cycle of the MOSFET. There are various methods to calculate the crisp output of the system. The SIMULINK model of fuzzy logic controller is shown in figure 6. The Maximum power is obtained when the slope of power versus voltage curve is zero, as in [5]. (9) (10) (11) Fig. 6. SIMULINK model of Fuzzy Logic controller. The equation 11 must be satisfied to obtain maximum power. When this condition fails, the error is generated which is given as first input to the fuzzy logic controller. The change in error is given as second input to the controller. The output obtained from the fuzzy logic controller is duty cycle. Fuzzy inference process comprises of Fuzzification of the input variables. Application of fuzzy operator in the All Rights Reserved 62

6 Implication from the antecedent to the consequent. Aggregation of the consequents across the rules. Defuzzification. International Journal of Recent Trends in Engineering & Research (IJRTER) Step 1: Fuzzify Inputs The first step is to take the inputs and determine the degree to which they belong to, through each of the appropriate fuzzy sets via membership functions which has been discussed in fuzzification process. Step 2: Apply Fuzzy operator After the inputs are fuzzified, degree to which each part of the antecedent is satisfied for each rule is known. If the antecedent of a given rule has more than one part, the fuzzy operator is applied to obtain one number that represents the result of the antecedent for that rule. This number is then applied to the output function. The input to the fuzzy operator is two or more membership values from fuzzified input variables. The output is a single truth value. Among the two built-in AND methods i.e., min (minimum) and prod (product), prod method is used. Also two built-in OR methods are also supported i.e., max (maximum) and probor (probabilistic OR) methods are supported. The probabilistic OR method (also known as the algebraic sum method) is used in the present work and is calculated as per the equation 12. probor(a, b) = a + b ab (12) Step 3: Apply implication method Before applying the implication method, the rule's weight is determined. Every rule has a weight (a number between 0 and 1), which is applied to the number given by an antecedent. Generally, this weight is 1 and thus has no effect on the implication process. After proper weighing has been assigned to each rule, the implication method is implemented. A consequent is a fuzzy set represented by a membership function, which weighs appropriately the linguistic characteristics that are attributed to it. The consequent is reshaped using a function associated with the antecedent (a single number). The input for the implication process is a single number given by an antecedent, and the output is a fuzzy set. Implication is implemented for each rule. The two built-in methods are supported, and they are the same functions that are used by the AND method: min (minimum), which truncates the output fuzzy set and prod (product) which scales the output fuzzy set. Step 4: Aggregate all outputs Aggregation is the process by which the fuzzy sets that represent the outputs of each rule are combined into a single fuzzy set. Aggregation only occurs once for each output variable, just prior to the fifth and final step defuzzification. The input of the aggregation process is the list of truncated output functions returned by the implication process for each rule. The output of the aggregation process is one fuzzy set for each output variable. Three built-in methods are supported they are max, probor (probabilistic OR), sum (simply the sum of each rule's output set). Step 5: Defuzzification The input for the defuzzification process is a fuzzy set (the aggregate output fuzzy set) and the output is a single number. However, the aggregate of a fuzzy set encompasses a range of output values, and so must be defuzzified in order to resolve a single output value from the set. Figure 7 shows the SIMULINK model of integrated PV panel with fuzzy logic controller used in the present work. The output current and voltage from the PV system is given to boost converter to boost the voltage to the required value. The error is calculated according to equation 11 and is given as input to the fuzzy logic controller and the second input (change in error) evaluated. The suitable fuzzy rules are inserted into the MPPT controller, using Fuzzy Inference System (FIS) editor All Rights Reserved 63

7 box. The fuzzy inference process is carried out and the output from the fuzzy controller is the duty cycle which is given as pulse to the gate terminal of MOSFET of boost converter. Fig. 7. SIMULINK model of Integrated PV Panel with MPPT Controller developed in MATLAB. Fuzzy logic controller provides better performance and improves accuracy than any other conventional MPPT techniques. V. SIMULATION RESULTS AND ANALYSIS The output from the fuzzy logic controller is converted into pulses using Pulse Width Modulated generator. These pulses are given to the gate terminal of MOSFET of Boost Converter to step up the output voltage from the PV array. Due to both charging and discharging operations of boost converter, the voltage is boosted. The output voltage obtained from the simulated model is shown in figure 8. Output voltage (v) Output Current (A) Time (s) Fig. 8. Output voltage obtained from PV array with MPPT controller of the present work. Figure 9 shows the output current waveform with MPPT controller. The value of current obtained with MPPT controller will be less than that without employing a All Rights Reserved 64

8 Time (s) Fig. 9. Output current obtained from PV array with MPPT controller of the present work. Figure 10 shows the output power obtained from the boost converter circuit. Output Power (W) Output Power (W) Time (s) Fig. 10. Output power obtained from PV array with MPPT controller of the present work. During the boost converter operation, the current value reduces in order to boost the voltage which in turn maintains the output power to be same as that of the input power fed to the boost converter. From the simulation results, the output power obtained from the boost converter is approximately same as that of input power applied to the boost converter. Hence the total power is conserved during this operation. VI. CONCLUSIONS The Photovoltaic MPPT system models using Fuzzy Logic controller and boost converter are successfully developed. The simulation of controller system models in MATLAB/SIMULINK software is made. In general, the accuracy of the system is expected to be improved using Fuzzy Logic approach, compared to other conventional methods of MPPT techniques. The module developed in the present work increases the effectiveness of the overall PV system. REFERENCES 1. Ahmed K. Abdelsalam, Ahmed M. Massoud, Shehab Ahmed and Prasad N. Enjeti, High-Performance Adaptive Perturb and Observe MPPT Technique for Photovoltaic Based Micro grid, IEEE Transactions on Power Electronics, volume 26, number 4, pp , April Villalva, Modelling and circuit based Simulation of Photovoltaic Arrays, IEEE Transactions on Power Electronics, volume 25, number 5, pp , May Mummadi Veerachary Tomonobu Senjyu and Kastumi Uezato, Neural Network Based Maximum Power Point Tracking of Coupled Inductor Interleaved Boost Converter Supplied PV System Using Fuzzy Controller, IEEE Transactions on Industrial Electronics, volume 50, number 4, pp , August Z. Salameh and Daniel Taylor, "Step-up Maximum Power Point Tracker for Photovoltaic Array", Solar Energy, volume 44, number 1, pp , Azadeh Safari and Saad Mekhilef, Simulation and Hardware Implementation of Incremental conductance MPPT with Direct Control Method Using Cuk Converter, IEEE Transactions on Industrial Electronics, volume 58, number 4, pp , April All Rights Reserved 65