# Improved Synchronous Machine Rotor Design for the Easy Assembly of Excitation Coils Based on Surrogate Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Original Design Analysis

## 3. Rotor Optimization

#### 3.1. Research on Rotor Shape

#### 3.2. Optimization Plans

## 4. Surrogate Optimization Method

#### 4.1. Problem Definition

- Maximize: Power output
- Minimize: Power Loss
- Constraints:$$\{\begin{array}{l}0\le x\le 20\\ 0\le y\le 20\end{array}$$

#### 4.2. Simplified Analytical Method

- Stator and rotor: ρ = Rs; ρ = Rr
- The arc is descripted as$$\begin{array}{l}{(\rho \mathrm{cos}(\theta )-{x}_{0})}^{2}+{(\rho \mathrm{sin}(\theta )-{y}_{0})}^{2}={r}_{3}{}^{2}\\ \mathrm{when}\text{\hspace{0.17em}}\theta <\rho <{\theta}_{2}\end{array}$$Assume$$\{\begin{array}{l}g(\theta )=2{y}_{0}\mathrm{sin}(\theta )+2{x}_{0}\mathrm{cos}(\theta )\\ {C}_{2}=-{a}^{2}-{b}^{2}+2a{x}_{0}+2b{y}_{0}\end{array}$$The equation can be simplified as$$\rho =\frac{-g(\theta )\pm \sqrt{g{(\theta )}^{2}-4{C}_{2}}}{2}=f(\theta )$$

_{rs}is the start angle of the rotor teeth, θ

_{1}is the angle of the connection point between the outer rotor radius and the additional arc, and θ

_{2}is the angle of the connection point between the additional arc and the pole arm.

_{0}, and y

_{0}are the coordinates of the points shown in Figure 4.

_{0}and y

_{0}, i.e., the coordinates of the center.

#### 4.3 Design of Experiments

#### 4.4. Construction of Surrogate Models

_{1}to θn should be calculated then solved by applying the optimization algorithm in the cost function.

#### 4.5. Heuristic Search Method

## 5. Optimization Results

#### 5.1. Results and Analysis of Preliminary Surrogate Models

#### 5.2. Results and Analysis of Advanced Surrogate Models

- Maximize: Power output
- Minimize: Loss
- Constraints: 0 < x < 20, 0 < y < 30, 2 < R < 10, 27 < θ <36

- Maximize: power output
- Minimize: power loss
- Constraints: 0 < R1 < 6, 0 < R2 < 4, 0 < L1 < 6, 0 < R4 < 4

## 6. Experiment Validation

^{2}for each layer. For the rotor winding, 76 turns of a copper coil (2.3 mm radius) are used.

#### 6.1. Constant Speed-Variable Test

#### 6.2. Analysis of Experiment Results

_{fw}). The iron loss of the machine can be obtained by taking off P

_{fw}in the constant power loss P

_{K}. The power curve is shown in Figure 12 and calculation results are tabulated in Table 4.

#### 6.3. Low-Slip Test

_{d}and X

_{ad}are the per unit direct axis synchronous and magnetizing reactance per each unit of speed, respectively; X

_{q}is the per unit quadrature axis reactance per one unit speed; and Is denotes the phase current.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Changes in rotor geometry and their corresponding performance. (

**a**) Enlarging the arc side; (

**b**) Cutting the teeth side; (

**c**) Fast Fourier transformation (FFT) analysis of induced electromagnetic motive force (EMF).

**Figure 8.**Comparison of two optimized rotor topologies. (

**a**) Induced Electromagnetic motive force (EMF); (

**b**) No-load saturation characteristics.

**Figure 10.**Photographs of the test rigs. (

**a**) Symmetrical and asymmetrical rotor lamination; (

**b**) Test rigs.

Harmonics | P1 (V) | P2 (V) |
---|---|---|

1 | 184.61 | 173.29 |

3 | 0.03 | 0.04 |

5 | 9.26 | 7.08 |

7 | 1.91 | 4.17 |

9 | 0.12 | 0.18 |

11 | 0.70 | 2.85 |

13 | 4.26 | 1.87 |

15 | 0.05 | 0.05 |

17 | 34.78 | 7.92 |

19 | 0.5 | 16.13 |

THD | 0.2 | 0.12 |

Item | Design 1 | Design 2 | Preliminary Prototype |
---|---|---|---|

X1 | 21.65 | 4 | / |

X2 | 24.72 | 1.33 | |

X3 | 2 | 2 | |

X4 | 27 | 2 | |

Torque finite element analysis (FEA) | 154.68 Nm | 163.54 Nm | 162.5 Nm |

Torque (Surrogate) | 154.73 Nm | 163.70 Nm | |

Loss (FEA) | 424.3 W | 462.5 W | 544.4 W |

Loss (Surrogate) | 422.9 W |

Rated Power (kVA) | 27.5 | Rated Speed (rpm) | 1500 |

Rated Line Voltage (V) | 380 | Rated Frequency (Hz) | 50 |

Rated Power Factor | 0.8 | Stack Length (mm) | 200 |

Stator Slot Number | 36 | Pole Numbers | 4 |

Stator OD (mm) | 310 | Stator ID (mm) | 192 |

Rotor OD (mm) | 188 | Winding arrangement | Double-layer Star |

Item | Symmetrical Rotor Design | Preliminary Asymmetrical Rotor Design | Optimized Symmetrical Rotor Design |
---|---|---|---|

FE analysis | 470 W | 544 W | 463 W |

Experiment | 408 W | 493 W | 407 W |

Item | Symmetrical | Asymmetrical |
---|---|---|

X_{d} (FEA) | 19.24 Ω | 16.34 Ω |

X_{d} (Experiment) | 18.75 Ω | 15.4 Ω |

X_{q} (FEA) | 10.99 Ω | 4.71 Ω |

X_{q} (Experiment) | 10.57 Ω | 5.85 Ω |

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## Share and Cite

**MDPI and ACS Style**

Yuan, T.; Yang, N.; Zhang, W.; Cao, W.; Xing, N.; Tan, Z.; Li, G.
Improved Synchronous Machine Rotor Design for the Easy Assembly of Excitation Coils Based on Surrogate Optimization. *Energies* **2018**, *11*, 1311.
https://doi.org/10.3390/en11051311

**AMA Style**

Yuan T, Yang N, Zhang W, Cao W, Xing N, Tan Z, Li G.
Improved Synchronous Machine Rotor Design for the Easy Assembly of Excitation Coils Based on Surrogate Optimization. *Energies*. 2018; 11(5):1311.
https://doi.org/10.3390/en11051311

**Chicago/Turabian Style**

Yuan, Tiejiang, Nan Yang, Wei Zhang, Wenping Cao, Ning Xing, Zheng Tan, and Guofeng Li.
2018. "Improved Synchronous Machine Rotor Design for the Easy Assembly of Excitation Coils Based on Surrogate Optimization" *Energies* 11, no. 5: 1311.
https://doi.org/10.3390/en11051311