# Phase Shift-Controlled Dual-Frequency Multi-Load Converter with Independent Power Control for Induction Cooking Applications

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of the Circuit and Operating Modes

#### 2.1. Dual-Output High-Frequency Inverter

#### 2.2. Dual-Frequency Pulse Generation and Analysis of the Load

#### 2.3. Selection of Dual Switching Frequency

#### 2.4. Operating Modes

#### 2.5. Phase Shift Control-Based Pulse Generation

## 3. Experimental Results of the Phase Shift Control Technique

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${f}_{r1}$ | Load 1’s resonant frequency |

${f}_{r2}$ | Load 2’s resonant frequency |

${V}_{dc}$ | Input voltage |

${V}_{ab}$ | Load voltage |

${V}_{cr10}$ | Pre-charged capacitor 1 voltage |

${V}_{cr20}$ | Pre-charged capacitor 2 voltage |

${V}_{cr1}$ | Resonant capacitor 1’s voltage |

${V}_{cr2}$ | Resonant capacitor 2’s voltage |

${i}_{01}$ | Load 1’s output current |

${i}_{02}$ | Load 2’s output current |

${R}_{eq1}$ | Load 1’s net resistance |

${R}_{eq2}$ | Load 2’s net resistance |

${L}_{eq1}$ | Load 1’s net inductance |

${L}_{eq2}$ | Load 2’s net inductance |

${C}_{r1}$ | Load 1’s resonant capacitor |

${C}_{r2}$ | Load 2’s resonant capacitor |

${Z}_{eq1}$ | Load 1’s net impedance |

${Z}_{eq2}$ | Load 2’s net impedance |

${P}_{01}$ | Load 1’s output power |

${P}_{02}$ | Load 2’s output power |

${P}_{0}$ | Total power |

${\omega}_{r1}$ | Load 1’s resonant frequency |

${\omega}_{r2}$ | Load 2’s resonant frequency |

${P}_{01,PS}$ | PS-based power for load 1 |

${P}_{02,PS}$ | PS-based power for load 2 |

${\omega}_{sw1}$ | Switching frequency of load 1 |

${\omega}_{sw2}$ | Switching frequency of load 2 |

${\varphi}_{01}$ | Control angle of load 1 |

${\varphi}_{02}$ | Control angle of load 2 |

## References

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**Figure 3.**Operation of the dual-frequency inverter in (

**a**) Mode 1, (

**b**) Mode 2, (

**c**) Mode 3, and (

**d**) Mode 4.

**Figure 6.**Main output voltage and current waveforms for ${\varphi}_{1}$ = 0$\xb0$ and ${\varphi}_{2}$ = 90$\xb0$. (

**a**) Load 1, (

**b**) Load 2.

**Figure 7.**Main output voltage and current waveforms for ${\varphi}_{1}$ = 0$\xb0$ and ${\varphi}_{2}$ = 170$\xb0$. (

**a**) Load 1, (

**b**) Load 2.

**Figure 8.**Main output voltage and current waveforms for ${\varphi}_{1}$ = 90$\xb0$ and ${\varphi}_{2}$ = 0$\xb0$. (

**a**) Load 1, (

**b**) Load 2.

**Figure 9.**Simulated thermal image of (

**a**) load 1 and (

**b**) load 2; Experimental thermal image of (

**c**) load 1 (

**d**) and load 2.

S.No | Parameters | Value |
---|---|---|

1 | ${V}_{in}$ | 80 V |

2 | ${P}_{rated}$ | 500–1000 W |

3 | ${R}_{eq1}={R}_{eq2}$ | 11 $\Omega $ |

4 | ${L}_{eq1}={L}_{eq2}$ | 0.12 mH |

5 | ${C}_{r1}$ | 620 nF |

6 | ${C}_{r2}$ | 38 nF |

7 | ${f}_{r1}$ | 18.5 kHz |

8 | ${f}_{sw1}$ | 20 kHz |

9 | ${f}_{r2}$ | 75 kHz |

10 | ${f}_{sw2}$ | 80 kHz |

11 | ${f}_{PDM}$ | 20 Hz |

12 | Q | 5.5 |

S.No | ${\mathit{\varphi}}_{1}$ (%) | ${\mathit{\varphi}}_{2}$ (%) | ${\mathit{V}}_{\mathbf{in}}$ (V) | ${\mathit{I}}_{\mathbf{in}}$ (A) | ${\mathit{P}}_{\mathbf{in}}$ (W) | ${\mathit{I}}_{01\mathbf{rms}}$ (A) | ${\mathit{P}}_{01}$ (W) | ${\mathit{I}}_{02\mathbf{rms}}$ (A) | ${\mathit{P}}_{02}$ (W) | ${\mathit{P}}_{0}$ (W) | Efficiency (%) |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 80 | 11.26 | 901.10 | 7.07 | 550 | 4.95 | 270 | 820 | 91 |

2 | 36 | 36 | 80 | 9.21 | 737.08 | 6.32 | 440 | 4.43 | 216 | 656 | 89 |

3 | 72 | 72 | 80 | 6.95 | 555.93 | 5.48 | 330 | 3.84 | 162 | 492 | 88.5 |

4 | 99 | 99 | 80 | 5.30 | 424.14 | 4.74 | 247.5 | 3.32 | 121.5 | 369 | 87 |

5 | 135 | 135 | 80 | 2.95 | 236.18 | 3.54 | 137.5 | 2.48 | 67.5 | 205 | 86.8 |

6 | 171 | 171 | 80 | 0.60 | 48.24 | 1.58 | 27.5 | 1.11 | 13.5 | 41 | 85 |

Reference | Converter Topology | Number of Semiconductor Switches | Modulation Technique | Efficiency at Rated Power (%) | Load Handling Capacity | Applications |
---|---|---|---|---|---|---|

[7] | Two output series resonant inverters | 6 | AVC | 90.2 | 2 | Cooking |

[28] | Buck boost converter fed half-bridge inverter | 4 | VFC | 80.1 | 1 | Cooking |

[29] | LLC resonant inverter | 7 | PSC | 92 | 1 | Melting |

[30] | Class-E inverter | 1 | PWM | 88.13 | 1 | Cooking |

Proposed | Dual-frequency converter | 4 | PS | 91 | 2 | Cooking |

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**MDPI and ACS Style**

Vishnuram, P.; Kumar, S.; Singh, V.K.; Babu, T.S.; Kannan, R.; Hasan, K.N.B.M.
Phase Shift-Controlled Dual-Frequency Multi-Load Converter with Independent Power Control for Induction Cooking Applications. *Sustainability* **2022**, *14*, 10278.
https://doi.org/10.3390/su141610278

**AMA Style**

Vishnuram P, Kumar S, Singh VK, Babu TS, Kannan R, Hasan KNBM.
Phase Shift-Controlled Dual-Frequency Multi-Load Converter with Independent Power Control for Induction Cooking Applications. *Sustainability*. 2022; 14(16):10278.
https://doi.org/10.3390/su141610278

**Chicago/Turabian Style**

Vishnuram, Pradeep, Sudhanshu Kumar, Vivek Kumar Singh, Thanikanti Sudhakar Babu, Ramani Kannan, and Khairul Nisak Bt Md Hasan.
2022. "Phase Shift-Controlled Dual-Frequency Multi-Load Converter with Independent Power Control for Induction Cooking Applications" *Sustainability* 14, no. 16: 10278.
https://doi.org/10.3390/su141610278