# Anti-Interference and Location Performance for Turn-to-Turn Short Circuit Detection in Turbo-Generator Rotor Windings

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## Abstract

**:**

## 1. Introduction

## 2. Principle of Detection Methods

_{i}represents the amplitude of the ith harmonic magnetic potential, i is an odd number, θ

_{r}represents the spatial mechanical angle of the rotor, p represents the pole pair of the turbo-generator, a

_{k}represents the number of windings in the kth slot, γ is the angle at which the large gear of the rotor occupies the circumference of the rotor, I

_{f}represents the excitation current, m is the number of short circuit slots, and Q is the number of short circuit turns.

_{0}represents the average air gap length of the turbo-generator.

_{r}) = g

_{0}and that the air gap permeability is constant. Therefore, this can be expressed as:

_{0}represents the permeability of the vacuum.

_{1}and α

_{3}represent the phase of the fundamental and third harmonics magnetic potential, respectively; and F

_{1}and F

_{3}represent the amplitude of the fundamental and third harmonics magnetic potential, respectively.

_{r}Lv = B

_{r}Lω

_{r}R, where B

_{r}represents the radial component of the air gap flux density at the effective part of U-shaped coil, L is the effective part length of the U-shaped coil, v represents the moving speed of the radial magnetic field relative to the effective part of the U-shaped coil;, ω

_{r}is the mechanical angular speed of rotor rotation, and R is the distance between the effective part of the U-shaped coil and the center of the rotor. As L, ω

_{r}, and R are all constants, the induced voltage waveform of the U-shaped coil is similar to the radial component waveform of gap flux density at the effective part of the coil. Theoretically, during a fully symmetrical state of the turbo-generator air gap magnetic field, the induced voltages of both coils are the same. After decomposition, the harmonics with the faulty characteristics are not included. The result is zero if the induced voltage time domain waveforms of both coils are added together (two-pole generator) or subtracted (four-pole generator). If a turn-to-turn short circuit fault or dynamic eccentricity fault occurs, although the harmonic contents of the induced voltages for both coils are the same, the induced voltages are different due to the different positions of both detection coils. In this case, the voltage time domain waveform is not zero after operation. There is a significant advantage for adopting the use of double coils: the induced voltages of both coils change simultaneously with a change in the turbo-generator’s operating state. Under a normal state, the output voltage waveforms of both coils will always be the same (four-pole generator) or the opposite (two-pole generator); therefore, the double coil method has excellent anti-interference abilities, which helps to reduce the probability of misjudgment.

## 3. Demonstration with Simulation

#### 3.1. Modeling and Simulation of Normal Operation Conditions

#### 3.2. Modeling and Simulation of Turn-to-Turn Short Circuit

#### 3.3. Simulation of a Dynamic Eccentricity Fault

#### 3.4. Extraction Method for Turn-to-Turn Short Circuit Characteristics for Rotor Winding

#### 3.5. Combined Fault Simulation for a Turn-to-Turn Short Circuit in the Rotor Winding and Dynamic Eccentricity

## 4. Conclusions

- (1)
- Two U-shaped detection coils were installed separately at two positions on the stator yoke of the turbo-generator at an interval of 180°. The fault position and short circuit degree of a turn-to-turn short circuit in the rotor winding can be judged exactly using the difference in the induced voltages from the coils.
- (2)
- The interference from dynamic eccentricity faults can be effectively eliminated using the double coil detection method. In the case of combined faults (i.e., a turn-to-turn short circuit and dynamic eccentricity), the turn-to-turn short circuit fault can be still located exactly.
- (3)
- The double-coil detection method can be used to determine whether there is a turn-to-turn short circuit fault in in the turbo-generator rotor winding, and can also be used as a detection sensor for turbo-generator dynamic eccentricity faults. This means that the method can also assist in judging dynamic eccentricity faults and have a good detection effect for slight eccentricity.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Waveform of excitation magneto motive force. F

_{f}is the excitation magneto motive force in a stepped wave after a turn-to-turn short circuit; F

_{f}’ is the excitation magneto motive force of the stepped wave when the winding is normal.

**Figure 3.**Schematic diagram of the detection system: (

**a**) Structure of a single coil; (

**b**) Online detection system.

**Figure 6.**Induced voltage curve for the No. 1 detection coil with different short circuit degrees in slot #3 under no-load conditions: (

**a**) Global map; (

**b**) Local map. Where, SC is the abbreviation of Short Circuit.

**Figure 7.**Induced voltage curve for the No. 1 detection coil with different short circuit degrees in slot #3 under rated load conditions: (

**a**) global map; (

**b**) local map.

**Figure 8.**Induced voltage spectrum for detection coils with different short circuit degrees: (

**a**) no-load; (

**b**) rated load.

**Figure 9.**Induced voltage curves for both detection coils at the dynamic eccentricity of 45° under no-load: (

**a**) global map; (

**b**) local map 1; (

**c**) local map 2; (

**d**) local map 3; (

**e**) local map 4.

**Figure 10.**Induced voltage curves for both detection coils at a dynamic eccentricity of 45° with rated load: (

**a**) global map; (

**b**) local map 1; (

**c**) local map 2; (

**d**) local map 3; (

**e**) local map 4.

**Figure 12.**Difference in the induced voltage change rates for both detection coils with different short circuit degrees in winding slot #3: (

**a**) no-load; (

**b**) rated load.

**Figure 13.**Difference in induced voltage change rates for both detection coils with a one-turn short circuit occurring separately in slots #3#, #6, and #9: (

**a**) no-load; (

**b**) rated load.

**Figure 14.**Difference in the induced voltage change rates for both detection coils with rated load when the dynamic eccentricity was 1% and a 1-turn short circuit occurred.

Parameter | Value |
---|---|

Rated voltage (V) | 24,000 |

Rated current (A) | 30,739 |

Rated power (MW) | 1150 |

Rated excitation current (A) | 5795 |

No-load rated excitation current (A) | 2189 |

Rated rotary speed (rpm) | 1500 |

Frequency (Hz) | 50 |

Phase number | 3 |

Number of stator slots | 48 |

Number of rotor slots | 48 |

Exciting mode | Brushless excitation |

Length of air gap (mm) | 96 |

Connection way of rotor winding | Y-Y |

Number of pole pairs | 2 |

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.; Ma, G.
Anti-Interference and Location Performance for Turn-to-Turn Short Circuit Detection in Turbo-Generator Rotor Windings. *Energies* **2019**, *12*, 1378.
https://doi.org/10.3390/en12071378

**AMA Style**

Wu Y, Ma G.
Anti-Interference and Location Performance for Turn-to-Turn Short Circuit Detection in Turbo-Generator Rotor Windings. *Energies*. 2019; 12(7):1378.
https://doi.org/10.3390/en12071378

**Chicago/Turabian Style**

Wu, Yucai, and Guanhua Ma.
2019. "Anti-Interference and Location Performance for Turn-to-Turn Short Circuit Detection in Turbo-Generator Rotor Windings" *Energies* 12, no. 7: 1378.
https://doi.org/10.3390/en12071378