# Power Efficiency Improvement of a Boost Converter Using a Coupled Inductor with a Fuzzy Logic Controller: Application to a Photovoltaic System

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Inductor Sizing in a Conventional Boost Converter for PV Applications

_{1}, R

_{2}, R

_{3}, and R

_{4}in Figure 2) [2,3,11]. For a given radiation value, there is a particular operating point, called “Maximum Power Point” (MPP), noted MPP1 and MPP2 in Figure 2, which leads to getting the maximum power from the PVG. We can observe that there is a difference between the MPP that the PVG can produce and the power transferred to the load in direct connection mode.

_{pv}and output current I

_{pv}. It detects the MPP and gives the output voltage where the power is maximum [1,6].

_{i}, and the input current I

_{i}. The components to be sized and selected accordingly are the inductance of the inductor L, the diode D, the values of capacitors C

_{1}and C

_{2}, and the switching transistor K. When these components are properly chosen, the energy loss can be neglected [18,19]. The element mainly influencing the boost converter losses is the inductor because its sizing depends directly on the input voltage as well as on the input current. In the case of PV applications, the voltage and current changes depend on climate parameters G and T.

#### 2.2. Proposed DC/DC Converter

_{i}= 42 V (the value of V

_{i}corresponds to the nominal MPP value of a SANYO HIP-215NKHE5 PV panel, which will be used in experimental measurements) with three values of duty cycle (d = 0.1, 0.5 and 0.9) for different current levels at a switching frequency 20 kHz and a ripple of 10%.

_{1}–L

_{2}, is adopted instead of a simple inductor.

_{1}adaptive to the input current, I

_{i}. The current I

_{2}that flows through L

_{2}is controlled to generate a variable electromagnetic field, therefore changing the value of L

_{1}. The reference current I

_{2ref}that I

_{2}must follow is calculated based only on the measured current I

_{i}.

#### 2.2.1. Coupled Inductor Analysis and Implementation

_{loss_wdg}= Ri

^{2}. In this study ohmic winding losses are not considered and the focus is mainly on the core losses. Based on theory and empirical tests [16,17,18,19,20] core losses depend directly on the hysteresis loop and to the maximum flux, B

_{max}. Consequently, we must avoid flux saturation on the core to avoid losses.

_{1}traversed by the current i

_{1}produces the flux ${\phi}_{11}$ self-induction through each turn of L

_{1}and the mutual flux ${\phi}_{21}$ through each turn of L

_{2}. Similarly, the coil L

_{2}traversed by the current i

_{2}produces the self-induction flux ${\phi}_{22}$ through each turn of L

_{2}and the mutual flux ${\phi}_{12}$ through each turn of L

_{1}. Fluxes ${\phi}_{11}$, ${\phi}_{21}$ and fluxes ${\phi}_{21}$, ${\phi}_{22}$ are added to each part (Figure 7b), or subtracted (Figure 7c), according to the positive direction of currents chosen arbitrarily, and the winding of the coils direction [17,18,19,20].

_{1}, L

_{1}and i

_{1}(N

_{2}, L

_{2}and i

_{2}) are the number of turns, self-inductance and current of the first (second) coil, parameter a is equal to 1 or −1 for additive or subtractive case, respectively, and M is the mutual inductance between L

_{1}and L

_{2}. Note that the sign of M is equal to that of a.

#### 2.2.2. Design of the Fuzzy Controller

_{2}and its reference, I

_{2ref}, coming from the measured I

_{pv}, we can decide whether to increment, decrement or keep the same duty cycle. One of the advantages of this strategy is that only one measurement is required, namely the inductor current i

_{2}.

_{2ref}) in red color and measurement current (I

_{pv}) in blue. We note that the FC achieved good tracking performances.

## 3. Results

#### 3.1. Simulation Results

_{e}= 211 mm

^{2}, Area product = 57,600 mm

^{4}, magnetic conductance A

_{L}= 4200 nH, with L = A

_{L}·N

^{2}). Our inductor was calculated by taking d = 0.5 and I = 3 A. We have to wire a coil of N = 28 turns for L

_{1}and N = 12 turns for L

_{2}using a wire of 2 mm and density of (2.5 A/mm

^{2}), and the PSpice Model Editor was used [21]. A co-simulation between Orcad and Simulink was used to simulate the system by using the SLPS block, as shown in Figure 12. SIMULINK was used to implement control part (P&O algorithm) and the PV panel of the system, while PSpice was used to model the conventional and proposed boost converter in Figure 3 and Figure 4, respectively.

_{1}= 200 µF, C

_{2}= 400 µF, and L

_{1}= 3500 µH), which are chosen corresponding to the used PV panel characteristics (SANYOHP). It can be observed that the power conversion efficiency of the proposed converter is about 9% higher than that of the conventional one when the radiation is equal to 1000 W/m

^{2}(i.e., when the input current value is maximum), whereas the two converters show similar performance for values of radiation lower than 300 W/m

^{2}.

#### 3.2. Experimental Results

_{2}; this current must track the reference current evaluated on PV current measurement, I

_{1}. The buck topology has been chosen because the output current of a buck is always greater than its input current. In this case we ensure that the second windings draws lower current even when I

_{2}has greater value.

## 4. Discussion

^{2}.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Operation of the Converter in Continuous Conduction Mode

_{L}> 0). To ensure operation in CCM mode, we follow the following steps to calculate the inductor value. For the boost converter circuit presented in Figure 3, two cases are possible. When the switch K is closed, we have

_{L}, is defined as,

_{o}, is necessarily greater than the input voltage, V

_{i}.

_{i}is input voltage, d is the duty cycle, I

_{L}is the inductor current and f is the frequency of the PWM signal.

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**Figure 1.**Adaptation block as a power interface between a photovoltaic generator(PVG) and load, to transfer the maximum power.

**Figure 2.**(

**a**) Direct electrical connection between a PV generator and a load; (

**b**) different operating points for two levels of radiation with different loads.

**Figure 10.**(

**a**) Membership functions of the input variable; (

**b**) membership functions of the output variable.

**Figure 13.**Transient simulation results: (

**a**) solar panel radiation; (

**b**) output power of the conventional and proposed converter; (

**c**) power conversion efficiency.

**Figure 16.**(

**a**) Schematic of the experimental setup for the proposed boost DC/DC converter. (

**b**) Schematic of the small Buck converter.

I_{L} (A) | L (µH) | ||
---|---|---|---|

d = 0.1 | d = 0.5 | d = 0.9 | |

0.5 | 4200 | 21,000 | 37,800 |

1 | 2100 | 10,500 | 18,900 |

1.5 | 1400 | 7000 | 12,600 |

2 | 1100 | 5300 | 9500 |

2.5 | 800 | 4200 | 7600 |

3 | 700 | 3500 | 6300 |

3.5 | 600 | 3000 | 5400 |

4 | 525 | 2600 | 4700 |

4.5 | 466 | 2300 | 4200 |

5 | 400 | 2100 | 3800 |

DE\E | NB | NS | Z | PS | PB |

NB | PB | PS | PS | NS | NB |

NS | PB | PS | Z | NS | NB |

Z | PB | PS | Z | NS | NB |

PS | PB | PS | Z | NS | NB |

PB | PB | PS | PS | NS | NB |

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**MDPI and ACS Style**

Abouchabana, N.; Haddadi, M.; Rabhi, A.; Grasso, A.D.; Tina, G.M.
Power Efficiency Improvement of a Boost Converter Using a Coupled Inductor with a Fuzzy Logic Controller: Application to a Photovoltaic System. *Appl. Sci.* **2021**, *11*, 980.
https://doi.org/10.3390/app11030980

**AMA Style**

Abouchabana N, Haddadi M, Rabhi A, Grasso AD, Tina GM.
Power Efficiency Improvement of a Boost Converter Using a Coupled Inductor with a Fuzzy Logic Controller: Application to a Photovoltaic System. *Applied Sciences*. 2021; 11(3):980.
https://doi.org/10.3390/app11030980

**Chicago/Turabian Style**

Abouchabana, Nabil, Mourad Haddadi, Abdelhamid Rabhi, Alfio Dario Grasso, and Giuseppe Marco Tina.
2021. "Power Efficiency Improvement of a Boost Converter Using a Coupled Inductor with a Fuzzy Logic Controller: Application to a Photovoltaic System" *Applied Sciences* 11, no. 3: 980.
https://doi.org/10.3390/app11030980