# Full Operating Range Optimization Design Method of LLC Resonant Converter in Marine DC Power Supply System

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## Abstract

**:**

## 1. Introduction

## 2. Performance Analysis of LLC Resonant Converter Based on Impedance Model under Different Operating Conditions

_{r}, C

_{r}and L

_{m}, respectively. R

_{L}and C

_{o}mean the load and output capacitor, respectively. And T represents the transformer, which turns ratio is n. The primary side of the transformer adopts a full-bridge structure (Q

_{1}–Q

_{4}), and the secondary side is a rectifier bridge consisting of diodes (D

_{1}–D

_{4}). The design of the parameters in the resonant tank can realize the converter within a wide range of ZVS, and it can also adjust its switching frequency to adjust the voltage gain of the converter so as to achieve voltage regulation. In order to obtain the relationship between the voltage gain and switching frequency, the conventional method mainly uses a fundamental wave analysis to achieve this. However, because it does not take into account the parasitic parameters of the switch and diode, this will lead to a sudden change in the voltage gain when the switching frequency increases to reduce the voltage gain under light load conditions. Meanwhile, when the switching frequency is reduced in order to increase the voltage gain under heavy load conditions, an improper parameter design can lead to the problem that the voltage gain cannot be increased.

_{p}and C

_{s}mean the parasitic capacitor of switching and diode, respectively. This method starts by plotting the topology of the converter circuit into three impedance sections: Z

_{1}, Z

_{2}, and Z

_{3}as shown in Figure 1, in which the secondary diode junction capacitor and the load need to be converted to the primary side. By the calculation method proposed by the authors in [18], the voltage gain G

_{c}can be calculated as follows.

_{1}is the resonant inductance and resonant capacitor and Z

_{2}is the impedance connected in parallel to the primary side of the transformer. Since the primary-side switching network of the LLC resonant converter is a full-bridge structure, this means that there are always two switching devices with junction capacitor connected in parallel. Therefore, these junction capacitors will change the impedance of the resonant tank, thus adding an impedance cell, Z

_{3}, whose expression is shown below.

_{ac}is the equivalent AC resistance of the load R converted to the transformer’s primary side.

## 3. Full-Operating-Range Performance Optimization Design Method for LLC Resonant Converter

_{add}, R

_{add}and Q

_{a}mean the auxiliary inductor, auxiliary resistant and auxiliary switching, respectively. Since the LLC resonant converter does not have the problem of the sudden change in voltage gain under heavy load conditions, there is no need to open the auxiliary circuit, and thus a switching device is added to the auxiliary circuit branch to change the auxiliary circuit’s open state under different operating conditions. Therefore, our main focus is on how to optimize the converter parameters under heavy load conditions.

#### 3.1. Multi-Objective Parameter Optimization Method for Heavy Load Conditions

#### 3.1.1. Objective Function: Loss Breakdown and Voltage Gain

#### 3.1.2. Multi-Objective Particle Swarm Parameter Optimization Method for LLC Resonant Converter

_{j}and p

_{j}are the velocity and position of the jth particle; r() is a stochastic function; and copl

_{j}and gopl

_{j}are the current best result of the jth particle and the global best result of the overall particle, respectively. k and n are the current number of iterations and parameter dimensions.

#### 3.2. Critical Operating Point and Window Condition Switching Method

_{s}j and then convert Equation (1) to the complex frequency domain. Then, the voltage gain G can be calculated by the amplitude-frequency equation as follows.

_{c}. And there is no need to be too fine when considering the load power, as long as the unit power accuracy can meet the performance requirements. Therefore, the critical operating point can be determined in the mathematical simulation software by substituting a certain power range to plot the gain variation.

#### 3.3. Proposed Full-Operating-Range Performance Optimization Design Method

#### 3.3.1. Step 1: Determination of Soft-Switching Conditions

_{d}and C

_{zvs}are the dead time and junction capacitor, respectively.

#### 3.3.2. Step 2: Loss Calculation

#### 3.3.3. Step 3: Determination of Voltage Gain Calculation

_{2}of the LLC resonant converter with the shunt auxiliary circuit can be recalculated as follows.

_{add}and R

_{add}are the auxiliary inductor and auxiliary resistor, respectively.

#### 3.3.4. Step 4: Multi-Objective Optimized Parameter Design for Heavy Load Condition

_{r}, the resonant capacitor C

_{r}, and the magnetic inductance L

_{m}.

#### 3.3.5. Step 5: Parameter Design for Auxiliary Circuits

_{add}can be determined and selected to be consistent with the resonant inductor L

_{r}. Then, the auxiliary resistance calculation is shown below, with the auxiliary circuit loss not exceeding 1.5% of the light load power as the upper boundary.

_{a}in the auxiliary circuit is mainly based on the transformer primary voltage and the current flowing through the auxiliary circuit. Therefore, considering the voltage withstand margin, the V

_{ds}voltage withstand value of Q

_{a}should be selected as 1.5 × nV

_{o}, and the current withstand value can be calculated according to the calculation process of R

_{add}. According to engineering experience, the margin of 1.5 times these values is considered.

#### 3.3.6. Step 6: Auxiliary Circuit Critical Operating Point Calculation

## 4. Results

#### 4.1. Calculation and Analysis of Experimental Parameters

#### 4.2. Analysis of Experimental Results

_{o}, converter output voltage V

_{o}, resonant current i

_{Lr}, and auxiliary switch drive signal Q

_{a}, respectively. From the experimental results, it can be seen that when the converter is operating under the light load condition, the auxiliary switch is opened, and the output voltage is stabilized at 60 V, which indicates that the auxiliary circuit can improve the voltage gain of the converter. When the converter is operating in the heavy load condition, the auxiliary switch is closed, the auxiliary circuit does not participate in the operation, and the output voltage is also stabilized at 60 V. Therefore, the proposed method can keep the steady-state output voltage at the desired output voltage of 60 V under different operating conditions.

#### 4.3. Comparison of Conventional Methods and Performance

#### 4.4. Comparison of Loss Breakdown

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Impedance bode plots for different operating conditions considering parasitic parameters of power devices.

**Figure 3.**Equivalent LLC resonant converter circuit topology based on full-operating-range performance optimization design method.

**Figure 11.**Steady-state waveforms for different load conditions. (

**a**) Heavy load condition; (

**b**) light load condition.

**Figure 12.**Experimental waveforms for step changes in different operating conditions. (

**a**) Step from light load to heavy load. (

**b**) Step from heavy load to light load. (

**c**) Step from light load to heavy load after setting the output voltage bias. (

**d**) Step from heavy load to light load after setting the output voltage bias.

**Figure 14.**The loss breakdown comparison and efficiency comparison. (

**a**) Loss breakdown comparison under rated power. (

**b**) Efficiency comparison over the full load range.

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

V_{in} | Input Voltage | 60 V |

V_{o} | Output Voltage | 60 V |

P_{H} | Heavy Load | 180 W |

P_{L} | Light Load | 10 W |

C_{p} | Switch Junction Capacitor | 600 pF |

C_{s} | Diode Junction Capacitor | 400 pF |

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

L_{r} | Resonant Inductor | 2.3 μH |

C_{r} | Resonant Capacitor | 0.97 μF |

L_{m} | Magnetic Inductor | 50 μH |

L_{add} | Auxiliary Inductor | 3 μH |

R_{add} | Auxiliary Resistor | 1500 Ω |

Component | Symbol | Part Number/Core Type |
---|---|---|

Primary Switching | Q_{1}–Q_{4} | IRFP3710PBF |

Secondary Diode | D_{1}–D_{4} | IRFP9140NPBF |

Resonant Inductor | L_{r} | PQ2020/DMR95 |

Transformer | T | PQ3225/DMR95 |

Adding Inductor | L_{add} | PQ2020/DMR95 |

Adding Resistor | R_{add} | Aluminum Case Resistor |

Ref. | Considering | Objective Number | |||||
---|---|---|---|---|---|---|---|

Voltage Regulation Capability | Parasitic Parameters | Loss | Light Load Voltage Gain Problem | Full Operating Range | Design Method | ||

[17] | Yes | Yes | No | Yes | No | 1 | Impedance |

[18] | Yes | Yes | No | No | No | 1 | Impedance |

[22] | No | No | Yes | No | No | 1 | PSO |

[23] | No | No | No | No | No | 1 | IPSO |

[24] | No | No | Yes | No | No | 3 | MO-PSO |

[25] | No | Yes | Yes | No | No | 3 | RODD-PSO |

[26] | No | No | Yes | No | No | 3 | MO-PSO |

Proposed | Yes | Yes | Yes | Yes | Yes | 2 | MO-PSO |

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## Share and Cite

**MDPI and ACS Style**

Han, X.; Yao, X.; Liao, Y.
Full Operating Range Optimization Design Method of LLC Resonant Converter in Marine DC Power Supply System. *J. Mar. Sci. Eng.* **2023**, *11*, 2142.
https://doi.org/10.3390/jmse11112142

**AMA Style**

Han X, Yao X, Liao Y.
Full Operating Range Optimization Design Method of LLC Resonant Converter in Marine DC Power Supply System. *Journal of Marine Science and Engineering*. 2023; 11(11):2142.
https://doi.org/10.3390/jmse11112142

**Chicago/Turabian Style**

Han, Xiao, Xuliang Yao, and Yuefeng Liao.
2023. "Full Operating Range Optimization Design Method of LLC Resonant Converter in Marine DC Power Supply System" *Journal of Marine Science and Engineering* 11, no. 11: 2142.
https://doi.org/10.3390/jmse11112142