# A Novel Combined Control Strategy for a Two-Stage Parallel Full-Wave ZCS Quasi Resonant Boost Converter for PV-Based Battery Charging Systems with Maximum Power Point Tracking

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## Abstract

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## 1. Introduction

## 2. Operating Principle and Circuit Analysis

**Mode I**$({t}_{0}\le t\le {t}_{1})$: In this mode of operation, both switches ${Q}_{1}$ and ${Q}_{2}$ are turned on at $t={t}_{0}$ as shown in Figure 2a. The current through the resonant inductors starts to increase from zero until the sum of both currents reach the input current ${I}_{in}$. Using Kirchhoff’s circuit laws, we have

**Mode II**$({t}_{1}\le t\le {t}_{2})$: The two auxiliary diodes ${D}_{1}$ and ${D}_{2}$ remain reverse biased (off) from the previous mode. Further, switches ${Q}_{1}$ and ${Q}_{2}$ continue to be on in this mode as shown in Figure 2b. This mode is mainly called the resonance mode, as the resonant components ${{L}_{r}}_{1}$, ${{L}_{r}}_{2}$, ${{C}_{r}}_{1}$ and ${{C}_{r}}_{2}$ are resonating at a resonant frequency of ${\omega}_{r}$. Using Kirchhoff’s circuit laws, we have

**Mode III**(${t}_{2}$≤ t ≤${t}_{3}$): In this mode of operation, the resonant capacitors, ${{C}_{r}}_{1}$ and ${{C}_{r}}_{2}$, each continue to charge until reaching the value of the output voltage ${V}_{o}$. The two auxiliary diodes ${D}_{1}$ and ${D}_{2}$, as well as ${Q}_{1}$ and ${Q}_{2}$, remain turned off in this mode as shown in Figure 2c. Similar to the previous modes, by manipulating the algebraic expressions and using Kirchhoff’s circuit laws, we have

**Mode IV**(${t}_{3}\le t$): In mode 4, the switches ${Q}_{1}$ and ${Q}_{2}$ remain off, however, in this mode, diodes ${D}_{1}$ and ${D}_{2}$ are on as shown in Figure 2d. By applying Kirchhoff’s circuit, we have

## 3. Modeling of PV Module and Maximum Power Point Tracking Algorithm

#### 3.1. Photo Voltaic Characteristics

#### 3.2. Maximum Power Point Tracking Algorithm

## 4. Conversion Ratio and Controller Design

## 5. Design Procedure of the Converter

#### 5.1. Switch-Mode Battery Charger Design

#### 5.2. Converter Design

## 6. Evaluation Results and Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MOSFET | Metal Oxide Semiconductor Field Effect Transistor |

MPPT | Maximum Power Point Tracking |

P&O | Perturb and Observe |

PV | Photovoltaic |

PWM | Pulse Width Modulation |

$SOC$ | State Of the Charge |

ZCS | Zero Current Switching |

ZVS | Zero Voltage Switching |

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**Figure 2.**Two-stage parallel full-wave ZCS quasi-resonant boost converter operation modes: (

**a**) Mode I; (

**b**) Mode II; (

**c**) Mode III; (

**d**) Mode IV. The parts of circuit that are not contributing in each mode of operation have been faded out with dashed line.

**Figure 6.**Characteristics of the utilized two-stage parallel full-wave ZCS quasi-resonant boost converter.

**Figure 7.**The proposed control strategy and switching regime with MPPT implementation for the two-stage parallel full-wave ZCS quasi-resonant boost converter.

**Figure 9.**Waveforms for the converter along with the proposed control strategy and switching regime when irradiance = 1000 W/m${}^{2}$: (

**a**) resonant inductor current ${i}_{{{l}_{r}}_{1}}$ and ${i}_{{{l}_{r}}_{2}}$; (

**b**) switch voltage ${{V}_{Q}}_{1}$ and ${{V}_{Q}}_{2}$; (

**c**) resonant capacitor voltage ${V}_{{{C}_{r}}_{1}}$ and ${V}_{{{C}_{r}}_{2}}$.

**Figure 10.**Waveforms for the battery load with the nominal voltage of 24 V and irradiance of 1000 W/m${}^{2}$: (

**a**) battery $SOC$; (

**b**) battery voltage ${V}_{b}$; (

**c**) battery current ${I}_{b}$.

**Figure 11.**Waveforms for the converter along with the proposed control strategy and switching regime when irradiance = 950 W/m${}^{2}$: (

**a**) resonant inductor current ${i}_{{{l}_{r}}_{1}}$ and ${i}_{{{l}_{r}}_{2}}$; (

**b**) switch voltage ${{V}_{Q}}_{1}$ and ${{V}_{Q}}_{2}$; (

**c**) resonant capacitor voltage ${V}_{{{C}_{r}}_{1}}$ and ${V}_{{{C}_{r}}_{2}}$.

**Figure 12.**Waveforms for the battery load with the nominal voltage of 24 V and irradiance of 950 W/m${}^{2}$: (

**a**) battery $SOC$; (

**b**) battery voltage ${V}_{b}$; (

**c**) battery current ${I}_{b}$.

**Figure 13.**Waveforms for the converter along with the proposed control strategy and switching regime when irradiance = 900 W/m${}^{2}$: (

**a**) resonant inductor current ${i}_{{{l}_{r}}_{1}}$ and ${i}_{{{l}_{r}}_{2}}$; (

**b**) switch voltage ${{V}_{Q}}_{1}$ and ${{V}_{Q}}_{2}$; (

**c**) resonant capacitor voltage ${V}_{{{C}_{r}}_{1}}$ and ${V}_{{{C}_{r}}_{2}}$.

**Figure 14.**Waveforms for the battery load with the nominal voltage of 24 V and irradiance of 900 W/m${}^{2}$: (

**a**) battery $SOC$; (

**b**) battery voltage ${V}_{b}$; (

**c**) battery current ${I}_{b}$.

**Figure 15.**Waveforms for the converter along with the proposed control strategy and switching regime when irradiance is changed from 900 to 1000 W/m${}^{2}$: (

**a**) resonant inductor current ${i}_{{{L}_{r}}_{1}}$ and ${i}_{{{l}_{r}}_{2}}$; (

**b**) switch voltage ${{V}_{Q}}_{1}$ and ${{V}_{Q}}_{2}$; (

**c**) resonant capacitor voltage ${V}_{{{C}_{r}}_{1}}$ and ${V}_{{{C}_{r}}_{2}}$.

**Figure 16.**Waveforms for the battery load with the nominal voltage of 24 V with sudden change of irradiance from 900 to 1000 W/m${}^{2}$: (

**a**) irradiance W/m${}^{2}$; (

**b**) battery voltage ${V}_{b}$; (

**c**) battery $SOC$.

Parameter | Symbol | Value | Unit |
---|---|---|---|

Minimum Input Current | ${I}_{in,min}$ | 5 | A |

Maximum Input Current | ${I}_{in,max}$ | $6.4$ | A |

Output Capacitor | ${C}_{o}$ | 120 | $\mathsf{\mu}$F |

Input Inductor 1 | ${{L}_{i}}_{1}$ | 25 | mH |

Input Inductor 2 | ${{L}_{i}}_{2}$ | 25 | mH |

Resonant Inductor 1 | ${{L}_{r}}_{1}$ | 14 | $\mathsf{\mu}$H |

Resonant Inductor 2 | ${{L}_{r}}_{2}$ | 14 | $\mathsf{\mu}$H |

Resonant Capacitor 1 | ${{C}_{r}}_{1}$ | 10 | $\mathsf{\mu}$F |

Resonant Capacitor 2 | ${{C}_{r}}_{2}$ | 10 | $\mathsf{\mu}$F |

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**MDPI and ACS Style**

Sabzehgar, R.; Ghali, R.; Fajri, P.
A Novel Combined Control Strategy for a Two-Stage Parallel Full-Wave ZCS Quasi Resonant Boost Converter for PV-Based Battery Charging Systems with Maximum Power Point Tracking. *Electricity* **2022**, *3*, 145-161.
https://doi.org/10.3390/electricity3010009

**AMA Style**

Sabzehgar R, Ghali R, Fajri P.
A Novel Combined Control Strategy for a Two-Stage Parallel Full-Wave ZCS Quasi Resonant Boost Converter for PV-Based Battery Charging Systems with Maximum Power Point Tracking. *Electricity*. 2022; 3(1):145-161.
https://doi.org/10.3390/electricity3010009

**Chicago/Turabian Style**

Sabzehgar, Reza, Rami Ghali, and Poria Fajri.
2022. "A Novel Combined Control Strategy for a Two-Stage Parallel Full-Wave ZCS Quasi Resonant Boost Converter for PV-Based Battery Charging Systems with Maximum Power Point Tracking" *Electricity* 3, no. 1: 145-161.
https://doi.org/10.3390/electricity3010009