# Analysis and Verification of Traction Motor Iron Loss for Hybrid Electric Vehicles Based on Current Source Analysis Considering Inverter Switching Carrier Frequency

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## Abstract

**:**

## 1. Introduction

## 2. Overview of the Ideal Current Source Analysis and the Proposed Method

#### 2.1. Comparison of the Ideal Current Source Analysis and the Proposed Method

_{a}= Asin(2πft)

_{b}= Asin(2πft + 120°)

_{c}= Asin(2πft − 120°)

_{a}, I

_{b}, and I

_{c}are the input currents of each phase. A and f denote the amplitude and frequency of the input current, respectively.

_{ah}= A(1 − p

^{k})sin(2πft) + A

_{sf}psin(2π(f

_{sf}/f)t)

_{bh}= A(1 − p

^{k})sin(2πft + 120°) + A

_{sf}psin(2π(f

_{sf}/f)t + 120°)

_{ch}= A(1 − p

^{k})sin(2πft − 120°) + A

_{sf}psin(2π(f

_{sf}/f)t − 120°)

_{sf}denotes the amplitudes of the switching frequency harmonics; I

_{ah}, I

_{bh}, and I

_{ch}are the harmonic injected currents of each phase; p means a coefficient of harmonic injection within over 0 and under 0.5. For example, the p-value of 0.1 means 10% harmonic injecting. f and f

_{sf}denote the frequencies of the ideal current and the switching frequency harmonics, respectively. k is a constant [11,12,13,14].

#### 2.2. Modeling and Analysis of the Target Model

#### 2.3. Comparison of Loss Analysis Using the Ideal Current Source and the Proposed Method

_{copper}= nI

^{2}R

_{iron}= P

_{h}+ P

_{e}

_{h}= k

_{h}fB

^{m}(1.5 < m < 2.5)

_{e}= k

_{e}f

^{2}B

^{2}

_{h}and P

_{e}denote the hysteresis and eddy-current losses, respectively; k

_{h}is the coefficient of the hysteresis loss; m is an empirically determined constant; k

_{e}is the coefficient of the eddy-current; f is the frequency; and B is the magnetic flux density.

_{iron}is affected by the frequency and magnetic flux density. Therefore, if the analysis of the iron loss is performed in the frequency domain using fast Fourier transform (FFT), different values will be obtained for the total iron loss for the analysis of the ideal current source and the proposed method [19,20].

## 3. Experimental Results of the Proposed Method

_{out}/P

_{in}= Tω

_{m}/(Tω

_{m}+ P

_{copper}+ P

_{iron}+ P

_{mech})

_{out}and P

_{in}denote the output and input power of the motor, respectively; T and ω

_{m}are the torque and mechanical angular velocity, respectively; and P

_{mech}is the mechanical loss of the motor.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Topology of the designed model. (

**a**) Full designed model; (

**b**) Periodic part of the designed model.

**Figure 4.**Waveform of torque, magnetic flux density, and magnetic flux line of the designed model in load condition. (

**a**) Torque waveform of the designed model; (

**b**) Magnetic flux density of the designed model.

**Figure 6.**Comparison of magnetic flux and iron loss densities. (

**a**) Magnetic flux density of in the stator core: θ-direction; (

**b**) Magnetic flux density in the stator core: r-direction; (

**c**) Iron loss density at 8000 Hz (ideal current source); (d) Iron loss density at 8000 Hz (proposed method).

**Figure 8.**Iron loss comparison between the ideal current source analysis and the proposed method for cases 1 and 2. (

**a**) Case 1. (

**b**) Case 2.

**Figure 9.**Iron loss comparison between the ideal current source analysis and the proposed method for cases 3 and 4. (

**a**) Case 3; (

**b**) Case 4.

**Figure 10.**Iron loss comparison between the ideal current source analysis and the proposed method in case 5.

Category | Unit | Value |
---|---|---|

Outer diameter | [mm] | 280 |

Magnetic steel sheet | [-] | 27PNX1350F |

Magnet grade (Br) | [-] | N44 (1.33T) |

Maximum input current | [A_{rms}] | 205 |

DC-link voltage | [V_{dc}] | 360 |

Switching frequency | [Hz] | 8000 |

Maximum Torque | [Nm] | 250 |

Maximum Power | [kW] | 50 |

Maximum Speed | [rpm] | 6000 |

Case Number | Torque [Nm] | Speed [rpm] |
---|---|---|

1 | 125 | 1000 |

2 | 155 | 1000 |

3 | 100 | 2500 |

4 | 125 | 2500 |

5 | 99 | 3000 |

Speed [rpm] | Mechanical Loss [W] |
---|---|

1000 | 20.94 |

2500 | 119.9 |

3000 | 166.5 |

Method | I_{rms} [A] | Copper Loss [W] | IronLoss [W] | Mech Loss [W] | Efficiency [%] |
---|---|---|---|---|---|

Ideal current source analysis | 81.9 | 543.9 | 60.1 | 20.94 | 95.4 |

Proposed method | 82.2 | 547.6 | 305.99 | 20.94 | 93.7 |

Experimental data | 81.9 | 543.9 | 393.5 (expected) | 20.94 | 93.2 |

Method | I_{rms} [A] | Copper Loss [W] | Iron Loss [W] | Mech Loss [W] | Efficiency [%] |
---|---|---|---|---|---|

Ideal current source analysis | 102.9 | 858.0 | 65.5 | 20.94 | 94.5 |

Proposed method | 103.3 | 863.9 | 387.53 | 20.94 | 92.7 |

Experimental data | 102.9 | 858.0 | 477.0 (expected) | 20.94 | 92.3 |

Method | I_{rms} [A] | Copper Loss [W] | Iron Loss [W] | Mech Loss [W] | Efficiency [%] |
---|---|---|---|---|---|

Ideal current source analysis | 81.6 | 539.7 | 130.7 | 119.9 | 97.1 |

Proposed method | 81.9 | 543.4 | 429.1 | 119.9 | 96.0 |

Experimental data | 81.6 | 539.7 | 402.9 (expected) | 119.9 | 96.1 |

Method | I_{rms} [A] | Copper Loss [W] | Iron Loss [W] | Mech Loss [W] | Efficiency [%] |
---|---|---|---|---|---|

Ideal current source | 107.6 | 937.7 | 134.2 | 119.9 | 96.5 |

Proposed method | 107.9 | 944.1 | 600.9 | 119.9 | 95.2 |

Experimental data | 107.6 | 937.7 | 506.8 (expected) | 119.9 | 95.5 |

Method | I_{rms} [A] | Copper Loss [W] | Iron Loss [W] | Mech Loss [W] | Efficiency [%] |
---|---|---|---|---|---|

Ideal current source | 98.3 | 782.9 | 150.4 | 166.5 | 96.6 |

Proposed method | 98.6 | 788.2 | 564.4 | 166.5 | 95.3 |

Experimental data | 98.3 | 782.9 | 785.2 (expected) | 166.5 | 94.7 |

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**MDPI and ACS Style**

Lee, J.-H.; Kim, W.-J.; Jung, S.-Y.
Analysis and Verification of Traction Motor Iron Loss for Hybrid Electric Vehicles Based on Current Source Analysis Considering Inverter Switching Carrier Frequency. *Electronics* **2021**, *10*, 2714.
https://doi.org/10.3390/electronics10212714

**AMA Style**

Lee J-H, Kim W-J, Jung S-Y.
Analysis and Verification of Traction Motor Iron Loss for Hybrid Electric Vehicles Based on Current Source Analysis Considering Inverter Switching Carrier Frequency. *Electronics*. 2021; 10(21):2714.
https://doi.org/10.3390/electronics10212714

**Chicago/Turabian Style**

Lee, Jin-Hwan, Woo-Jung Kim, and Sang-Yong Jung.
2021. "Analysis and Verification of Traction Motor Iron Loss for Hybrid Electric Vehicles Based on Current Source Analysis Considering Inverter Switching Carrier Frequency" *Electronics* 10, no. 21: 2714.
https://doi.org/10.3390/electronics10212714