# Estimation of Iron Loss in Permanent Magnet Synchronous Motors Based on Particle Swarm Optimization and a Recurrent Neural Network

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## Abstract

**:**

## 1. Introduction

- The proposed method integrates PSO and RNN to establish a comprehensive iron loss calculation model. This model accounts for high-order harmonics, rotating magnetization, and temperature factors, capturing multifaceted influences on iron loss.
- By employing multilayer RNN and PSO for training and optimization, the method overcomes issues associated with conventional polynomial fitting, offering improved accuracy in estimating iron loss even in complex scenarios beyond traditional measurement ranges.
- The developed model offers broad applicability by accurately estimating iron loss in PMSMs under diverse and complex conditions, surpassing the limitations of traditional empirical formulas.

## 2. Impact Factor Analysis of Iron Loss

#### 2.1. Frequencies and Temperatures

#### 2.2. Polynomial Fitting Error

_{copper}: phase current and winding resistance. According to the method described in [46], the mechanical loss P

_{mech}can be calculated from the output power and the stray loss can be calculated using the assumption stated in [47] that it represents 1% of the output power.

## 3. Iron Loss Estimation Based on the Recurrent Neural Network

#### 3.1. Particle Swarm Optimization and the Recurrent Neural Network

- PSO will optimize the RNN architecture, hyperparameters, or training process to enhance the accuracy and efficiency of estimating iron loss.
- RNNs will serve as the predictive model, leveraging their ability to capture sequential dependencies in data for accurate estimation.

**s**, and the input and output layers by

**x**and

**y**, respectively. The weight matrix

**W**is in the middle of the network,

**U**represents the weight matrix between the input and hidden layers,

**V**represents the weight matrix between hidden layers and output layers, and

**L**represents the loss function. The model has the following structure formula:

#### 3.2. Proposed PMSM Iron Loss Method

## 4. Result Analysis

## 5. Conclusions

## 6. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Loss curves of silicon steel sheet with different temperatures at (

**a**) 50 Hz and (

**b**) 200 Hz.

**Figure 3.**Multi-frequency iron loss fitting results: (

**a**) fitting surface and (

**b**) fitting relative error.

**Figure 12.**Comparison between the predicted and the measured values: (

**a**) original RNN and (

**b**) PSO–RNN.

Loss Model Name | Expression | No. of Parameters |
---|---|---|

Steinmetz [39] | ${P}_{stm}={k}_{h}{f}^{n}{B}^{m}$ | 3 |

Steinmetz with eddy current loss | ${P}_{istm}={k}_{h}{f}^{n}{B}^{m}+{k}_{c}{(fB)}^{2}$ | 4 |

Bertotti [5] | ${P}_{Ber}={k}_{h}f{B}^{\alpha}+{k}_{c}{(fB)}^{2}+{k}_{e}{(fB)}^{1.5}$ | 4 |

ANSYS Maxwell [6] | ${P}_{\mathrm{Maxwell}\text{}}={k}_{h}f{B}^{2}+{k}_{c}{(fB)}^{2}+{k}_{e}{(fB)}^{1.5}$ | 3 |

Improved loss model [7] | ${P}_{imp}={\alpha}_{1}{k}_{1}f{B}^{\alpha}+{\alpha}_{2}{(fB)}^{2}+{\alpha}_{2}{\alpha}_{3}{f}^{2}{B}^{{\alpha}_{4}+2}+{\alpha}_{5}{k}_{2}{(fB)}^{1.5}$ | 5 |

Name | Value |
---|---|

Population size | 100 |

Acceleration constant C_{1} and C_{2} | 1.4 |

Inertia weight ${\omega}_{\mathrm{max}}$ | 0.9 |

Inertia weight ${\omega}_{\mathrm{min}}$ | 0.4 |

Particle dimension | 1 |

Maximum number of iterations | 30 |

Name | Value |
---|---|

Dimension of hidden layer | 13 |

Dimension of output layer | 1 |

Dimension of input layer | 1 |

Number of recurrent layers | 3 |

Number of features in the hidden state | 6 |

Number of input sizes | 3 |

Name | Unit | Value |
---|---|---|

Stator outer radius | mm | 196 |

Rotor outer radius | mm | 134 |

Core length | mm | 108 |

Airgap length | mm | 0.5 |

Number of poles | - | 8 |

Number of slots | - | 48 |

Rated power | kW | 20 |

Rated torque | Nm | 53 |

Rated speed | rpm | 3600 |

PM Material | - | NdFeB-35 |

Core material | - | 35WW360 |

Maximum speed | rpm | 5500 |

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**MDPI and ACS Style**

Xu, K.; Guo, Y.; Lei, G.; Zhu, J.
Estimation of Iron Loss in Permanent Magnet Synchronous Motors Based on Particle Swarm Optimization and a Recurrent Neural Network. *Magnetism* **2023**, *3*, 327-342.
https://doi.org/10.3390/magnetism3040025

**AMA Style**

Xu K, Guo Y, Lei G, Zhu J.
Estimation of Iron Loss in Permanent Magnet Synchronous Motors Based on Particle Swarm Optimization and a Recurrent Neural Network. *Magnetism*. 2023; 3(4):327-342.
https://doi.org/10.3390/magnetism3040025

**Chicago/Turabian Style**

Xu, Kai, Youguang Guo, Gang Lei, and Jianguo Zhu.
2023. "Estimation of Iron Loss in Permanent Magnet Synchronous Motors Based on Particle Swarm Optimization and a Recurrent Neural Network" *Magnetism* 3, no. 4: 327-342.
https://doi.org/10.3390/magnetism3040025