# Online Inductance Identification of Permanent Magnet Synchronous Motors Independent of Rotor Position Information

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## Abstract

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## 1. Introduction

## 2. Sensorless Control Systems

#### 2.1. Mathematical Model of PMSMs

#### 2.2. Rotor Position Estimator

## 3. Inductance Identification Accuracy Analysis with Position Error

## 4. Proposed Online Inductance Identification Method

#### 4.1. Parametric Equation Derivation of q-Axis Inductance

#### 4.2. Online Identification of q-Axis Inductance Using PSO

#### 4.3. Parametric Iquation Derivation of d-Axis Inductance

#### 4.4. Online Identification of d-Axis Inductance Using RLS

## 5. Experimental Results

#### 5.1. Execution Time Test

#### 5.2. Experiments under Rated Conditions

#### 5.3. Experiments with Different Initial Values

#### 5.4. Experiments with Different Stator Currents

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Inductance identification results using RLS with different rotor position errors: (

**a**) Identification results of d-axis inductance; (

**b**) identification results of q-axis inductance.

**Figure 4.**Block diagram of the PSO (particle swarm optimization)-based parameter identification method.

**Figure 7.**Simulation results of the proposed PSO-based ${L}_{q}$ identification methods using different numbers of particles after five iterations.

**Figure 9.**The structure of the sensorless control system with online inductance identification (where * denotes the reference values).

**Figure 12.**Experimental results of the proposed inductance identification method under rated conditions of the motor.

**Figure 13.**Identification results with different initial values under rated conditions of the motor: (

**a**) identification results of d-axis inductance; (

**b**) identification results of q-axis inductance.

**Figure 14.**Inductance identification results with different output torque: (

**a**) corresponding relation between the output torque and the stator current; (

**b**) inductance identification results.

Denotation | Value |
---|---|

Rated power (kW) | 30 |

Rated torque (N·m) | 100 |

Rated speed (rpm) | 3000 |

Number of pole pairs | 4 |

Stator resistance (Ω) | 0.02 |

d-axis inductance (mH) | 0.3 |

q-axis inductance (mH) | 0.6 |

Flux linkage (Wb) | 0.081 |

Results | Mean Relative Error with 10 Particles (%) | Mean Relative Error with 5 Particles (%) | Relative Standard Deviation with 10 Particles (%) | Relative Standard Deviation with 5 Particles (%) |
---|---|---|---|---|

Iterations | ||||

5 | −0.80 | −0.47 | 3.23 | 3.15 |

10 | −0.67 | −0.50 | 3.29 | 3.17 |

15 | −0.66 | −0.48 | 3.19 | 3.10 |

20 | −0.62 | −0.46 | 3.16 | 3.05 |

Iterations | 5 | 10 | 15 | 20 |
---|---|---|---|---|

Particles | ||||

10 | 121 µs | 272 µs | 392 µs | 517 µs |

15 | 189 µs | 403 µs | 586 µs | 770 µs |

20 | 290 µs | 536 µs | 778 µs | 1023 µs |

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## Share and Cite

**MDPI and ACS Style**

Xing, J.; Zhang, J.; Zhuang, X.; Xu, Y.
Online Inductance Identification of Permanent Magnet Synchronous Motors Independent of Rotor Position Information. *World Electr. Veh. J.* **2024**, *15*, 35.
https://doi.org/10.3390/wevj15010035

**AMA Style**

Xing J, Zhang J, Zhuang X, Xu Y.
Online Inductance Identification of Permanent Magnet Synchronous Motors Independent of Rotor Position Information. *World Electric Vehicle Journal*. 2024; 15(1):35.
https://doi.org/10.3390/wevj15010035

**Chicago/Turabian Style**

Xing, Jilei, Junzhi Zhang, Xingming Zhuang, and Yao Xu.
2024. "Online Inductance Identification of Permanent Magnet Synchronous Motors Independent of Rotor Position Information" *World Electric Vehicle Journal* 15, no. 1: 35.
https://doi.org/10.3390/wevj15010035