# Electromagnetic Vibration Simulation of a 250-MW Large Hydropower Generator with Rotor Eccentricity and Rotor Deformation

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## Abstract

**:**

## 1. Introduction

## 2. Transient 2D Modelling

#### 2.1. The Basic Model of the Hydropower Generator

#### 2.2. Rotor Eccentricity and Rotor Ellipse Deformation Models of the Hydropower Generator

## 3. Simulation Principle of Electromagnetic Field

#### 3.1. Transient Electromagnetic Analysis

#### 3.2. Electromagnetic Force Analysis

^{2}). There are three types of methods, such as the Lorentz force, principle of virtual work and maxwell stress tensor (MST) method, which can be used to calculate the electromagnetic force density. The MST method was used to solve the electromagnetic force in this paper. Because only this method could solve the details of the electromagnetic force density distribution on the stator teeth surface, which is necessary to the vibration simulation of the generator based on this method, the electromagnetic force density $F$ on the surface of the stator teeth can be described as [15]:

^{2}), ${\mu}_{0}$ is the permeability of the air, ${B}_{n}$ and ${B}_{t}$ are the normal and tangential components of the flux density on the load at the inner surface of stator teeth, respectively. The parameters $\overrightarrow{n}$ and $\overrightarrow{t}$ are the unit vectors in the normal and tangential direction.

## 4. The Results of Electromagnetic Simulations

#### 4.1. Flux Density on the Stator Teeth End

#### 4.2. Electromagnetic Force Density Simulation

#### 4.3. The Influence of Variable Field Currents and Loads

## 5. Electromagnetic Vibration Analysis

#### 5.1. Principle of Harmonic Response Analysis

#### 5.2. Geometry Modelling

#### 5.3. Electromagnetic Harmonic Response Vibration Coupled Analysis

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**The 2D electromagnetic finite element method (FEM) model and mesh of the hydropower generator.

**Figure 10.**The radial flux densities across the air gap under a no-load field current in space: (

**a**) centric rotor; (

**b**) static eccentricity condition (

**c**) dynamic eccentricity condition (

**d**) rotor ellipse deformation condition.

**Figure 11.**The radial electromagnetic force densities across the air gap under no-load field current in space: (

**a**) centric rotor; (

**b**) static eccentricity condition (

**c**) dynamic eccentricity condition (

**d**) rotor ellipse deformation condition.

**Figure 12.**Radial electromagnetic force densities at the point of stator tooth end under no-load field current in time: (

**a**) centric rotor; (

**b**) static eccentricity condition; (

**c**) dynamic eccentricity condition (

**d**) rotor ellipse deformation condition.

**Figure 13.**Fast Fourier transformation (FFT) of radial electromagnetic force densities with different conditions.

**Figure 15.**The radial electromagnetic force density at the point of the stator tooth end under rated load in time.

**Figure 18.**The installation position of experiment apparatus for vibration measurement: (

**a**) The distribution of vibration sensors; (

**b**) The installation position of vibration sensors.

**Figure 23.**Amplitude frequency of stator deformation under the rotor elliptical deformation condition with various loads: (

**a**) The vibrations with various field current; (

**b**) The vibrations with various load.

Parameters (Units) | Values |
---|---|

Number of poles | 64 |

Number of slots | 528 |

Rated Speed (rpm) | 93.75 |

Number of phases | 3 |

Rated frequency (Hz) | 50 |

Air gap thickness (mm) | 19 |

Rated Power (MW) | 250 |

Rated Line Voltage (kV) | 15.75 |

Rated line current (A) | 10,182.6 |

Rated Power Factor | 0.9 |

Winding Connection | Wye |

Coil Pitch | 7 |

Parameters (Units) | Values | |
---|---|---|

Stator iron core | Internal diameter (mm) | 12,900 |

Outside diameter (mm) | 13,700 | |

Material | coiled silicon steel sheet | |

Density (Kg/m^{3}) | 7650 | |

Young’s Modulus (Pa) | 2.05 × 10^{11} | |

Poisson’s Ratio | 0.25 | |

Stator frame | Internal diameter (mm) | 13,700 |

Outside diameter (mm) | 14,900 | |

Material | structural steel | |

Density (Kg/m^{3}) | 7850 | |

Young’s Modulus (Pa) | 2.0 × 10^{11} | |

Poisson’s Ratio | 0.30 | |

Winding | Material | Copper Alloy |

Density (Kg/m^{3}) | 8300 | |

Young’s Modulus (Pa) | 1.1 × 10^{11} | |

Poisson’s Ratio | 0.34 |

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**MDPI and ACS Style**

Li, R.; Li, C.; Peng, X.; Wei, W.
Electromagnetic Vibration Simulation of a 250-MW Large Hydropower Generator with Rotor Eccentricity and Rotor Deformation. *Energies* **2017**, *10*, 2155.
https://doi.org/10.3390/en10122155

**AMA Style**

Li R, Li C, Peng X, Wei W.
Electromagnetic Vibration Simulation of a 250-MW Large Hydropower Generator with Rotor Eccentricity and Rotor Deformation. *Energies*. 2017; 10(12):2155.
https://doi.org/10.3390/en10122155

**Chicago/Turabian Style**

Li, Ruhai, Chaoshun Li, Xuanlin Peng, and Wei Wei.
2017. "Electromagnetic Vibration Simulation of a 250-MW Large Hydropower Generator with Rotor Eccentricity and Rotor Deformation" *Energies* 10, no. 12: 2155.
https://doi.org/10.3390/en10122155