# Fuzzy Logic Based MPPT Controller for a PV System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Modeling of PV System

#### 2.1. Modeling of the PV Module

_{x}and I

_{x}are the open circuit voltage and short circuit current with dynamic values for solar irradiance and temperature, which are defined by Equations (2) and (3); b is the characteristic constant, it does not have units and is the unique parameter that has to be calculated.

_{i}: effective irradiation of the PV module; E

_{iN}: irradiation constant of 1000 W/m

^{2}; T: temperature of the PV module; T

_{N}: temperature constant of 25 °C; T

_{cv}: temperature coefficient of voltage; T

_{ci}: temperature coefficient of current; V

_{oc}: open circuit voltage; I

_{sc}: short-circuit current; V

_{max}: voltage for irradiations under 200 W and operating temperature of 25 °C (this value is 103% of V

_{oc}); V

_{min}: voltage for irradiations over 1200 W and operating temperature of 25 °C (this value is 85% of V

_{oc}).

_{x}= 21.7 V; I

_{x}= 4 A; I = 3.71 A and V = 17.5 V; the value of b is 0.07375.

_{i}= 1000 W/m

^{2}, T = 25 °C) correspond to the electrical parameters of the PV module presented in Table 1. Additionally, it is worth noting that the decreases in the solar irradiance considerably affect the short-circuit current, while the open circuit voltage is affected in smaller proportion.

^{2}and variable temperature. In this case, it can be noted that increases in temperature considerably affect the open circuit voltage, while the short-circuit current is affected in a smaller proportion. Table 2 and Table 3 will be used as references in the results and discussion section, in which a comparison with the fuzzy and P&O controllers will be made; with variations of the solar irradiance and the operating temperature of the PV module.

#### 2.2. DC-DC Converter Model

_{on}). Using Equation (5), the ripple of the inductor is obtained as shown in Equation (6).

_{d}, R

_{L}y V

_{DS}are very small values, Equations (8) and (9) are obtained.

_{s}= T

_{off}+ T

_{on}, Equation (10) for the duty cycle D is obtained.

#### 2.2.1. Inductor Design

_{on}= DT

_{s}, the Equation (12) for the design of the inductor is obtained.

_{s}= 17.71 V, P

_{max}= 64.984 W, i

_{o}= 5.41 A, f

_{s}= 20 KHz. Using a ripple value of 10% for a maximum output current, Equation (13) is obtained.

#### 2.2.2. Capacitor Design

#### 2.2.3. Modelling of Buck Converter

^{2}and temperature of 25 °C; in which it is observed that the converter works in the CCM according to that established in the design conditions.

#### 2.3. Fuzzy Controller Design

#### 2.3.1. Membership Functions

#### 2.3.2. Fuzzy Rules

#### 2.3.3. Fuzzy Controller Modelling

#### 2.4. P&O Controller Design

- Case A: ΔP < 0 y ΔV < 0.
- Case B: ΔP < 0 y ΔV > 0.
- Case C: ΔP > 0 y ΔV > 0.
- Case D: ΔP > 0 y ΔV < 0.

#### 2.5. PV System Modelling

#### 2.6. Limitations

## 3. Results and Discussion

^{2}and temperature of 25 °C. Figure 14a shows the results obtained for the power delivered to the battery with a simulation time of 0.03 s. It can be seen that the two controllers extract the maximum power of 65 W with a good stabilization time of 0.005 s, which is consistent with the results obtained in [15,16]. In Figure 14b, it is observed that the duty cycle of the P&O control presents small oscillations between 0.6926 and 0.7, in contrast to the fuzzy control that is stabilized at a value of D = 0.694.

^{2}, starting at 200 W/m

^{2}and ending at 1000 W/m

^{2}. Changes in irradiance were made every 0.2 s with a total simulation time of 1 s (see Figure 15a). Subsequently, a test signal with decreases in solar irradiance between 1000 W/m

^{2}and 200 W/m

^{2}was used (see Figure 15b).

_{i}= 200 W/m

^{2}, which is evidenced in the duty cycle of Figure 16b, in times between 0 and 0.2 s.

^{2}

^{2}. Initially, the signal shown in Figure 18a was used, with temperature increases every 0.2 s between 0 °C and 100 °C, for a test time of 1 s. Subsequently, the signal shown in Figure 18b was used, with decreases in temperature between 100 °C and 0 °C.

^{2,}in which the power oscillates between 11.5 and 37.5 W. The highest average power losses with the P&O control occurred between the times 0.2 s to 0.3 s and 0.3 s to 0.4 s with values of 8.52 W and 30.48 W, respectively.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

V_{x} | Open circuit voltage for variable values of solar irradiance and operating temperature. |

I_{x} | Short-circuit current for variable values of solar irradiance and operating temperature. |

MPP | Maximum power point of the PV module. |

P_{max} | Maximum power of the PV module. |

V_{mpp} | Voltage at P_{max}. |

I_{mpp} | Current at P_{max}. |

s | Number of PV modules connected in series. |

p | Number of PV modules connected in parallel. |

E_{i} | Effective irradiation of the PV module. |

E_{iN} | Irradiation constant of 1000 W/m^{2}. |

T | Temperature of the PV module. |

T_{N} | Temperature constant of 25 °C. |

T_{cv} | Temperature coefficient of voltage. |

T_{ci} | Temperature coefficient of current. |

V_{oc} | Open circuit voltage. |

I_{sc} | Short-circuit current. |

V_{max} | Voltage for irradiations under 200 W and operating temperature of 25 °C. |

V_{min} | Voltage for irradiations over 1200 W and operating temperature of 25 °C. |

V_{L} | Voltage in the inductor. |

R_{L} | Internal resistance of the inductor. |

R_{c} | Internal resistance of the capacitor. |

T_{on} | The on time in the dc-dc converter. |

T_{off} | The off time in the dc-dc converter. |

T_{s} | Sampling time. |

D | Duty cycle. |

V_{s} | Input voltage in dc-dc converter. |

V_{dc} | Transistor voltage in the on mode. |

V_{d} | Diode forward voltage. |

V_{o} | Output voltage of the dc-dc converter. |

ΔI_{L} | Ripple current in the inductor. |

ΔI_{L}(+) | Ripple current in T_{on}. |

ΔI_{L}(−) | Ripple current in T_{off}. |

I_{o} | Critical output current. |

ΔQ | Charge variation in the capacitor. |

ΔV | Voltage variation in the capacitor. |

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**Figure 2.**PV module in Matlab. (

**a**) Model implemented with Simulink function blocks; (

**b**) Subsystem implemented for the simulation.

**Figure 14.**PV system with E

_{i}= 1000 W/m

^{2}and T = 25 °C. (

**a**) Output power of the PV module; (

**b**) Duty cycle.

**Figure 21.**Irradiance and temperature signals to evaluate the performance of fuzzy and P&O controllers. (

**a**) Increases in solar irradiance; (

**b**) Variable temperature.

Parameter | Value |
---|---|

Short-circuit current (I_{sc}) | 4 A |

Open circuit voltage (V_{oc}) | 21.7 V |

Voltage at P_{max} (V_{mpp}) | 17.5 V |

Current at P_{max} (I_{mpp}) | 3.71 A |

Temperature coefficient of voltage (T_{cv}) | −0.0802 V/°C |

Temperature coefficient of current (T_{ci}) | 0.0024 A/°C |

Maximum voltage (V_{max}) | 22.35 V |

Minimum voltage (V_{min}) | 18.44 V |

Parameter | 1000 W/m^{2} | 800 W/m^{2} | 600 W/m^{2} | 400 W/m^{2} | 200 W/m^{2} |
---|---|---|---|---|---|

Short-circuit current I_{sc} (A) | 4.0 | 3.2 | 2.4 | 1.6 | 0.8 |

Open circuit voltage V_{oc} (V) | 21.70 | 21.42 | 21.02 | 20.44 | 19.62 |

Voltage at P_{max} V_{mpp} (V) | 17.66 | 17.55 | 17.37 | 16.78 | 16.08 |

Current at P_{max} I_{mpp} (A) | 3.679 | 2.924 | 2.171 | 1.459 | 0.730 |

Maximum Power Point (W) | 64.98 | 51.31 | 37.72 | 24.48 | 11.75 |

Parameter | 0 °C | 25 °C | 50 °C | 75 °C |
---|---|---|---|---|

Short-circuit current I_{sc} (A) | 3.94 | 4.00 | 4.06 | 4.12 |

Open circuit voltage V_{oc} (V) | 23.71 | 21.7 | 19.69 | 17.69 |

Voltage at P_{max} V_{mpp} (V) | 19.39 | 17.66 | 16.47 | 14.47 |

Current at P_{max} I_{mpp} (A) | 3.606 | 3.679 | 3.617 | 3.771 |

Maximum Power Point (W) | 69.92 | 64.98 | 59.59 | 54.55 |

E/ΔE | Very Low | Low | Neutral | High | Very High |
---|---|---|---|---|---|

Very Low | VH | VH | H | VL | VL |

Low | H | H | H | VL | L |

Neutral | H | H | N | L | L |

High | H | H | L | L | VL |

Very High | H | H | L | L | VL |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Robles Algarín, C.; Taborda Giraldo, J.; Rodríguez Álvarez, O.
Fuzzy Logic Based MPPT Controller for a PV System. *Energies* **2017**, *10*, 2036.
https://doi.org/10.3390/en10122036

**AMA Style**

Robles Algarín C, Taborda Giraldo J, Rodríguez Álvarez O.
Fuzzy Logic Based MPPT Controller for a PV System. *Energies*. 2017; 10(12):2036.
https://doi.org/10.3390/en10122036

**Chicago/Turabian Style**

Robles Algarín, Carlos, John Taborda Giraldo, and Omar Rodríguez Álvarez.
2017. "Fuzzy Logic Based MPPT Controller for a PV System" *Energies* 10, no. 12: 2036.
https://doi.org/10.3390/en10122036