# Full Digital Control of an All-Si On-Board Charger Operating in Discontinuous Conduction Mode

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure and Operation

#### 2.1. AC/DC Stage

#### 2.2. DC/DC Stage

## 3. Controller Design

#### 3.1. AC/DC Stage

#### 3.1.1. Grid Synchronization

#### 3.1.2. Current Control Loop

#### 3.1.3. Voltage Control Loop

#### 3.2. DC/DC Stage

#### 3.2.1. Current Control Loop

#### 3.2.2. Voltage Control Loop

## 4. Simulation and Experimental Results

#### 4.1. Simulation Results

#### 4.1.1. AC/DC Stage

#### 4.1.2. DC/DC Stage

#### 4.2. Experimental Results

#### 4.2.1. AC/DC Stage

#### 4.2.2. DC/DC Stage

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Basic waveforms of the interleaved dual-boost PFC operated in DCM, considering ${L}_{\mathrm{i}}=25\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{H}$, ${f}_{\mathrm{sw}}=100\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$, ${v}_{\mathrm{i}}=250\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$, ${v}_{\mathrm{dc}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ and ${i}_{\mathrm{i}}=15\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ (refer to Figure 2 for nomenclature). The difference between average current (${i}_{\mathrm{avg}}$), peak current (${i}_{\mathrm{pk}}$) and sampled current (${i}_{\mathrm{smp}}$) is illustrated.

**Figure 4.**Basic waveforms of the PSFB operated in DCM, considering ${L}_{\mathrm{o}}=21\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{H}$, ${f}_{\mathrm{sw}}=100\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$, ${v}_{\mathrm{dc}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$, ${v}_{\mathrm{o}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ and ${i}_{\mathrm{o}}=5\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ (refer to Figure 2 for nomenclature). The difference between output average current (${i}_{\mathrm{o},\mathrm{avg}}$), peak current (${i}_{\mathrm{o},\mathrm{pk}}$) and sampled current (${i}_{\mathrm{o},\mathrm{smp}}$) is illustrated.

**Figure 5.**Simplified schematic of the OBC multi-loop control structure, including both converter stages.

**Figure 7.**Duty-to-current transfer function dependence on (

**a**) the input voltage ${v}_{\mathrm{i}}=25,\phantom{\rule{0.166667em}{0ex}}75,\dots ,325\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ (with ${i}_{\mathrm{avg}}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$) and (

**b**) the average inductor current ${i}_{\mathrm{avg}}=2,\phantom{\rule{0.166667em}{0ex}}4,\dots ,10\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$ (with ${v}_{\mathrm{i}}=325\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$), considering ${L}_{\mathrm{i}}=25\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}\mathrm{H}$, ${f}_{\mathrm{sw}}=100\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$ and ${v}_{\mathrm{dc}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$.

**Figure 8.**Detailed block diagram of the two identical PFC current (${i}_{\mathrm{i},1}$, ${i}_{\mathrm{i},2}$) control loops.

**Figure 13.**Analytically derived and simulated closed-loop transfer functions of the PFC current controllers (

**a**) and DC-link voltage controller (

**b**).

**Figure 14.**Analytically derived and simulated closed-loop transfer functions of the DC/DC output current controller (

**a**) and output voltage controller (

**b**).

**Figure 15.**Experimental grid-side voltage (${v}_{\mathrm{g}}$) and current (${i}_{\mathrm{g}}$) waveforms for (

**a**) 10% load ($P=330\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$), (

**b**) 50% load ($P=1650\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$) and (

**c**) 100% load ($P=3300\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$). The scale of ${i}_{\mathrm{g}}$ is changed according to P.

**Figure 16.**Experimental waveforms of (

**a**,

**b**) the inductor currents (${i}_{\mathrm{i},1}$ and ${i}_{\mathrm{i},2}$) and (

**c**,

**d**) the input capacitor voltage (${v}_{\mathrm{i}}$) and the input current (${i}_{\mathrm{i}}$) for 50% load ($P=1650\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$).

**Figure 17.**Experimental DC-link voltage (${v}_{\mathrm{dc}}$) response to a load step between $P=800\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$ (≈25%) and $P=2400\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$ (≈75%).

**Figure 18.**Experimental PSFB waveforms at ${V}_{\mathrm{b}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ and ${I}_{\mathrm{b}}=6\phantom{\rule{0.166667em}{0ex}}\mathrm{A}$: (

**a**) primary transformer voltage (${v}_{\mathrm{p}}$) and current (${i}_{\mathrm{p}}$) and (

**b**) secondary rectified voltage (${v}_{\mathrm{r}}$) and output current (${i}_{\mathrm{o}}$).

**Figure 19.**Experimental output current (${i}_{\mathrm{o}}$) response to a reference step from 2 $\mathrm{A}$ ($P=800\phantom{\rule{0.166667em}{0ex}}\mathrm{W}$) to 6 $\mathrm{A}$ ($P=2400\mathrm{W}$) with ${V}_{\mathrm{b}}=400\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$: (

**a**) only integral controller, (

**b**) feed-forward + integral controller.

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

P | rated power | 3300 $\mathrm{W}$ |

f | grid frequency | 50 $\mathrm{Hz}$ |

${f}_{\mathrm{sw}}$ | switching frequency (both stages) | 100 $\mathrm{k}$$\mathrm{Hz}$ |

${V}_{\mathrm{g}}$ | grid RMS voltage | 230 $\mathrm{V}$ |

${V}_{\mathrm{dc}}$ | DC-link voltage | 400 $\mathrm{V}$ |

${V}_{\mathrm{b}}$ | battery voltage | 250–500 V |

${C}_{\mathrm{i}}$ | input capacitance | 1.5 μF |

${L}_{\mathrm{i}}$ | input inductance | 25 μH |

${C}_{\mathrm{dc}}$ | DC-link capacitance | 1.2 mF |

${C}_{\mathrm{o}}$ | output capacitance | 10 μF |

${L}_{\mathrm{o}}$ | output inductance | 21 μH |

n | transformer turns ratio | $2/3$ |

${L}_{\mathrm{r}}$ | transformer leakage inductance | 0.3 μH |

${L}_{\mathrm{m}}$ | transformer magnetizing inductance | 300 μH |

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**MDPI and ACS Style**

Cittanti, D.; Gregorio, M.; Mandrile, F.; Bojoi, R.
Full Digital Control of an All-Si On-Board Charger Operating in Discontinuous Conduction Mode. *Electronics* **2021**, *10*, 203.
https://doi.org/10.3390/electronics10020203

**AMA Style**

Cittanti D, Gregorio M, Mandrile F, Bojoi R.
Full Digital Control of an All-Si On-Board Charger Operating in Discontinuous Conduction Mode. *Electronics*. 2021; 10(2):203.
https://doi.org/10.3390/electronics10020203

**Chicago/Turabian Style**

Cittanti, Davide, Matteo Gregorio, Fabio Mandrile, and Radu Bojoi.
2021. "Full Digital Control of an All-Si On-Board Charger Operating in Discontinuous Conduction Mode" *Electronics* 10, no. 2: 203.
https://doi.org/10.3390/electronics10020203