# Design Methodology and Analysis of Five-Level LLC Resonant Converter for Battery Chargers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Topology

_{r}), a capacitance (C

_{r}), an inductance (L

_{m}) in parallel, and a full-wave rectifier with a filter capacitor and a battery at the converter’s output side, respectively. The switch pairs S1, S2 and S3, S4 operate in a complementary fashion and the same is true for S5, S6, S7, S8. In contrast to conventional single-stage converters, the voltage delivered to the LLC stage contains five discrete levels (see Figure 2). The key steady-state waveforms of the converter are shown in Figure 3. Summing Vin1 = Vin2 = Vdc condition, the five-level inverter can generate five output voltage (VAB) levels: +Vdc, +2Vdc, 0, −Vdc, and −2Vdc, as shown in the equivalent circuits presented in Figure 4. This paper focuses on the issue of charging the battery by CV method by MLI integrated with resonant converter and a transformer-less. The operation modes of the proposed approach are outlined in the next section.

## 3. Modes of Operation

#### 3.1. Mode1 (t0 < t < t1)

_{r}, stops decreasing. The rectifier diodes D1 and D4 are conducted. Figure 4a depicts this mode of operation.

#### 3.2. Mode2 (t1 < t < t2)

_{r}begins to shift from negative to positive polarity (zero crossing). The energy stored in the resonant tank is transferred to the battery through the rectifier diodes D1 and D4. Figure 4b shows this mode of operation.

#### 3.3. Mode3 (t2 < t < t3)

_{r}increases. Rectifier Diodes D2 and D3 are conducted and their current is increasing. Figure 4c represents this mode of operation.

#### 3.4. Mode4 (t3 < t < t4)

_{r}reaches the maximum value and stops increasing, while resonant capacitor voltage Vcr reaches the positive polarity. Rectifier diode D2 and D3 are still conducted and their current is at the maximum value, as the energy stored in the resonant tank is transferred to the battery through them.

#### 3.5. Mode5 (t4 < t < t5)

_{r}begins to reduce. VAB drops to negative 2Vdc and this voltage goes to the LLC resonant tank. At the end of the previous stage, the rectifier diodes D1 and D4 are still switched OFF, thus, the energy stored in the resonant tank is transferred through rectifier diodes D2 and D3.

## 4. Design Consideration

_{gain}) of the LLC stage can be calculated using the analogous circuit depiction in Figure 5.

_{n}is the ratio of the magnetizing inductance L

_{m}to the resonant inductance L

_{r}, defined as follows:

_{r}= resonant inductance, C

_{r}= resonant capacitor, and L

_{m}= magnetizing inductance.

_{ac}is equivalent to the load and rectifier stage. V

_{bat}and P

_{bat}denote the output voltage and power, respectively. Additionally, the output voltage is clamped by the battery and is considered the same while the charging is carried out.

_{n}determines the switching frequency in relation to the higher resonance frequency of the resonant tank f

_{r}

_{1}. The resonant tank’s typical impedance is Z

_{o}. Variables L

_{n}and Q are incorporated to make (1) independent of the actual L

_{m}, L

_{r}, and C

_{r}values. P

_{bat}represents the transferred power to the battery. The frequency fr2, at which the voltage gain M

_{gain}is maximum, is the lower resonance frequency f

_{r}

_{2}. As shown in (1), it is used to plot the normalized dc gain against normalized frequency for various values of the quality factor (Q), as seen in Figure 6a, which depicts the voltage gain under various loading situations (changes in Q value) and varying designs (changes in L

_{n}) as in Figure 6b at different relative switching frequencies.

_{n}and Q are chosen and used to compute the L

_{r}and C

_{r}values. The gain is calculated using the lower and maximum switching frequency values to check the range of the selected switching frequency. Q value must be 0.39 to achieve the necessary output voltage of 48 Vdc at a 100 kHz resonant frequency.

#### Calculation of Components in Resonant Tank Circuit

_{n}and quality factor Q values. Plotting the voltage gain equation of the LLC resonant high-voltage DC–DC converter for multiple L

_{n}and Q values, as illustrated in Figure 6a,b, is the simplest way to choose L

_{n}and Q values. The graph aids in finding the L

_{n}and Q values that will meet the converter’s gain requirement. As a result, the chosen values for L

_{n}and Q are 3 and 0.39, respectively, depending on the desired gain. Having chosen the L

_{n}and Q values, the sizes of LLC resonant tank components are then determined. To begin, the resonant capacitor C

_{r}can be obtained using the formula:

_{r}, can be estimated using:

_{n}, the value of the magnetising inductor, L

_{m}, can be calculated as follows:

## 5. Simulation Results

## 6. Experimental Results

_{Cr}), and the resonant inductor current iL

_{r}at Vin = 100. The resonant current and the voltage across the resonant capacitor are almost inverted in this diagram, as in Figure 11. It was evident that the resonant current began with a negative polarity in each half cycle, which allowed for the achievement of the ZVS for switching frequency at the resonant frequency (100 KHz). The obtained experimental output voltage resonant capacitor and current resonant were approximately 40 V and 5 A, respectively. Furthermore, it is worth noting that these findings are consistent with the simulation results depicted in Figure 7.

## 7. Conclusions

## 8. Future Challenges

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Controlled gate signals and output voltage VAB of five level inverter and simulated waveforms of system VAB, V

_{cr}, iL

_{r}, ID1-4.

**Figure 4.**Operation stages for the proposed five-level converter during: (

**a**) VAB = +2Vdc; (

**b**) VAB= +Vdc; (

**c**) VAB = 0; (

**d**) VAB = −Vdc; (

**e**) VAB= −2Vdc.

**Figure 6.**Voltage gain versus normalized frequency of the proposed converter. (

**a**) Different load factors with constant L

_{n}= 3. (

**b**) Different inductance ratios with constant Q = 0.39.

**Figure 7.**Simulation waveforms of proposed converter of five-level inverter voltage VAB, resonant capacitor voltage V

_{Cr}, and resonant inductor current iL

_{r}.

**Figure 8.**Simulation waveforms of gate voltage VGE and collector voltage VCE of switches (

**a**) switch 3, (

**b**) switch 4, (

**c**) switch 7, and (

**d**) switch 8.

**Figure 11.**Experimental waveforms of voltage across multilevel inverter VAB, resonant capacitor, V

_{Cr}and resonant current, iL

_{r}, for the output load resistance of 23 Ω.

**Figure 12.**Measured waveforms of gate voltage VGE and collector voltage VCE for switches (

**a**) S1 and S2, (

**b**) S5 and S6.

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

Input voltage range | Vin,min~Vin,max | 60–140 V |

Input voltage Nominal | Vin,nom | 100 V |

Output voltage | Vb | 48 V |

Output power | Pbat | 100 W |

Resonant frequency | Fr_{1} | 100 kHz |

Switching frequency | Fsw | 91–110 kHz |

Parameter | Symbol | Calculated Value | Measured Value |
---|---|---|---|

Input voltage Nominal | V_{in},nom | 100 V | 100 V |

Resonant capacitances | c_{r} | 218.5 nF | 215 nF |

Resonant inductances | L_{r} | 11.5 µH | 12 µH |

Magnetizing inductance | L_{m} | 34.7 µH | 35 µH |

Equivalent load resistance | R_{ac} | 18.67 Ω | 18.67 Ω |

Output voltage | V_{o} | 48 V | 48 V |

Component | Part Number |
---|---|

Active Switches (S1–S8) | GP35B60PD |

Microcontroller | LAUNCHXL-F28379D LaunchPad |

Magnetic ferrite core | ETD 34/17/11 |

Resonant capacitor | KEMET R75 Film Capacitor |

Diodes D1–D4 | MUR1560G |

Topology | No of Switches | No of Rectifier | No of Transformer | Input Voltage V | Output Voltage V | Power Rated w | Swathing Frequency Range kHz | Modulation | Efficiency |
---|---|---|---|---|---|---|---|---|---|

Half-bridge LLC [6] | 2 | 8 | 1 | 200 | 100 | 200 | 100 | PWM ^{1} | 97% |

Full bridge LLC [29] | 4 | 4 | 1 | 250–310 VAC | 25.6–33.6 | 1000 | 30–100 | PFM ^{2} | 96.4% |

Dual Half-bridge LLC [30] | 2 | 8 | 2 | 340–380 | 120–160 | 320 | 100 | MC ^{3} | 95.5% |

Full bridge LLC [31] | 4 | 4 | 1 | 400 | 250–450 | 3300 | 154.7–220 | - | 98.2% |

Three level LLC [34] | 4 | 2 | 1 | 600 | 48 | 800 | 50 | PFM | 95.1% |

Proposed | 8 | 4 | 0 | 100 | 48 | 100 | 91–110 | (PWM) (PFM) | 96.9% |

^{1}Pulse width modulation.

^{2}Pulse Frequency modulation.

^{3}Magnetic control.

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**MDPI and ACS Style**

Alatai, S.; Salem, M.; Alhamrouni, I.; Ishak, D.; Bughneda, A.; Kamarol, M.
Design Methodology and Analysis of Five-Level LLC Resonant Converter for Battery Chargers. *Sustainability* **2022**, *14*, 8255.
https://doi.org/10.3390/su14148255

**AMA Style**

Alatai S, Salem M, Alhamrouni I, Ishak D, Bughneda A, Kamarol M.
Design Methodology and Analysis of Five-Level LLC Resonant Converter for Battery Chargers. *Sustainability*. 2022; 14(14):8255.
https://doi.org/10.3390/su14148255

**Chicago/Turabian Style**

Alatai, Salah, Mohamed Salem, Ibrahim Alhamrouni, Dahaman Ishak, Ali Bughneda, and Mohamad Kamarol.
2022. "Design Methodology and Analysis of Five-Level LLC Resonant Converter for Battery Chargers" *Sustainability* 14, no. 14: 8255.
https://doi.org/10.3390/su14148255