# Accumulation Behaviors of Different Particles and Effects on the Breakdown Properties of Mineral Oil under DC Voltage

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## Abstract

**:**

## 1. Introduction

## 2. Simulation and Experiment

#### 2.1. Motion Model of Metal Particles

_{DEP}

_{1}) [25], the viscous drag force (F

_{drag}

_{1}) [25], and the Coulomb force (F

_{C}

_{1}) [25]. Based on the microstructure of metal particles in Figure 1a, the dielectrophoretic force of spherical metal particles with the radius r can be calculated:

_{m}represents the permittivity of insulation oil, and σ

_{m}and σ

_{p}stand for the conductivity of insulation liquid and the metal particle respectively.

_{drag}

_{1}) acts on the metal particle, as shown in Formula (2). Because of the nonlinearity of the viscous drag force, the correction factor (C

_{d}) related to the Reynolds coefficient (Re) should be used to correct the viscous drag force.

_{m}are the viscosity and density of the insulation liquid, and v

_{p}

_{1}represents the velocity of the metal particle.

_{1}) is obtained, as calculated by Formula (5). Then, plugging Formula (5) into (6) yields the following expression:

#### 2.2. Motion Model of Cellulose Particles

_{m}and ε

_{p}represent the permittivity of insulation oil and cellulose impurities, and d and l stand for the diameter and length of the cellulose particle. Using Formulas (8)–(15), the velocity of the cellulose particle v

_{p}

_{2}can be attained using

#### 2.3. Accumulation Model of Particles

_{p}) is closely related to the concentration (c). There is a certain particle concentration (c

_{crit}) that prevents particle movement, because a large number of particles are bound to form bridges [26]. Thus, the relationship between the velocity and concentration of particles is as follows [26]:

_{i}is equal to 0. The flux vector (or molar flux) N is associated with the Fick equation and is used under boundary conditions and for flux computation. u

_{m}(10

^{−7}s*mol/kg) is the charge mobility, where c is the concentration of impurities, and D (10

^{−11}m

^{2}/s) is seen as the diffusion parameter:

**J**is an externally generated current density, and

_{e}**J**= 0. σ is the collective conductivity of insulation oil and impurities, which is derived according to the Looyenga Formula (31). The static form of the equation of current continuity then reads

_{e}#### 2.4. Particle Accumulation and Oil Breakdown Measurement

## 3. Experimental Results and Discussion

#### 3.1. Particle Accumulation Simulation Results

#### 3.2. Experimental Results of Particle Accumulation.

#### 3.3. Effect of Particles Accumulation on Oil DC Breakdown Voltage

_{n}(t

_{i}) could be calculated by Formula (23), where i represents the order of test samples, and n is the number of samples. Figure 6 is the Weibull probability distribution plot of different samples under the DC breakdown voltage. With an increase in the concentration of particles, the Weibull curve moved to the left. Namely, the average breakdown values of samples reduced as the particle concentration increased. The relationship between the average breakdown voltages of mineral oil containing cellulose particles, metal particles, and mixed particles and the particles concentration are shown in Figure 7. The DC breakdown voltages of oil samples contaminated with metal particles and mixed particles were found to be lower than those of mineral oil containing cellulose particles. In summary, metal impurities and mixed particles have more significant impacts on the DC breakdown characteristics of mineral oil:

#### 3.4. Difference Analysis of the Effects of Different Particles on the Oil DC Breakdown Voltage

_{max}) of contaminated mineral oil at 600 s. It can be seen that metal particles almost play a more prominent part in electrical field distortion than cellulose particles. Additionally, the saturated current of metal particles is larger than that for cellulose impurities, so the breakdown voltage of mineral oil polluted by metal particles is smaller than that contaminated by cellulose particles. Figure 10 and Figure 11 also imply that cellulose particles as well as metal particles cannot have a superposition effect on the electric field distortion of insulation oil. For mineral oil contaminated by cellulose or metal particles, E

_{max}increases as the particle concentration increases, which indicates that electrical field distortion combined with the conductivity variation leads to degradation of the insulation strength of mineral oil. As for mineral oil containing mixed particles, though electrical field distortion weakens with an increasing concentration, conductivity obviously increases because of the increasing accumulation degree. Hence, changes in the electrical field distribution together with an increase in conductivity collectively affects the DC breakdown characteristics of mineral oil.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Simulation results of different kinds of particle accumulation in mineral oil at different times.

**Figure 5.**Motion trajectory of cellulose particles (

**a**) and metal particles (

**b**) under DC voltage in mineral oil.

**Figure 6.**Weibull probability distribution plot of DC breakdown voltage for different samples DMCP (

**a**), DMMP (

**b**) and DMCM (

**c**).

**Figure 7.**Average DC breakdown voltage of mineral oil with cellulose or metal particles (

**a**), and mixed particles (

**b**).

**Figure 8.**Changes in the current in mineral oil containing different particles under the same DC voltage.

**Figure 10.**Particle accumulation patterns under three different initial concentrations for cellulose particles (

**a**), copper particles (

**b**) and mixed particles (

**c**) at 600 s.

**Figure 11.**DC electric field distribution of mineral oil contained cellulose particles (

**a**), copper particles (

**b**) and mixed particles (

**c**) under three different initial concentrations at 600 s.

**Figure 12.**E

_{max}of mineral oil and natural ester containing different particles under three different initial concentrations at 600 s.

Contamination Level | |||||
---|---|---|---|---|---|

Cellulose particles | 0.001% | 0.003% | 0.006% | 0.009% | 0.012% |

Metal particles | 0.1 g/L | 0.3 g/L | 0.6 g/L | 1 g/L | 1.5 g/L |

Mixed particles | 0.003% + 0.1 g/L | 0.003% + 0.3 g/L | 0.003% + 0.6 g/L | 0.003% + 1 g/L | --- |

0.012% + 0.1 g/L | 0.012% + 0.3 g/L | 0.012% + 0.6 g/L | 0.012% + 1g/L | --- |

Parameters | Mineral Oil |
---|---|

Density in g/cm^{3} | 0.89 |

Dynamic viscosity in mm^{2}/s (20 °C) | 25.70 |

Permittivity (20 °C, 50 Hz) | 2.20 |

Volume resistivity in Ω·m (20°) | 4.68 × 10^{13} |

Samples | Sample Composition |
---|---|

DMCP | Dry mineral oil + cellulose particles |

DMMP | Dry mineral oil + metal particles |

DMCM | Dry mineral oil + mixed particles of cellulose and metal particles |

MO | Pure mineral oil |

Parameters | Cellulose Particles | Metal Particles |
---|---|---|

Density, g/cm^{3} (20 °C) | 1.2 | 8.6 |

Permittivity (20 °C, 50 Hz) | 4.4 | 10^{5} |

Size, μm | 63–150 | 15 |

Volume resistivity, Ω·m (20 °C) | 2 × 10^{6} | 2 × 10^{−8} |

Initial concentration (c_{0}), mol/m^{3} | 0.0005 | 0.0005 |

DC voltage, kV | 11.25 | 11.25 |

Distance, mm | 7.5 | 7.5 |

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**MDPI and ACS Style**

Dan, M.; Hao, J.; Liao, R.; Cheng, L.; Zhang, J.; Li, F.
Accumulation Behaviors of Different Particles and Effects on the Breakdown Properties of Mineral Oil under DC Voltage. *Energies* **2019**, *12*, 2301.
https://doi.org/10.3390/en12122301

**AMA Style**

Dan M, Hao J, Liao R, Cheng L, Zhang J, Li F.
Accumulation Behaviors of Different Particles and Effects on the Breakdown Properties of Mineral Oil under DC Voltage. *Energies*. 2019; 12(12):2301.
https://doi.org/10.3390/en12122301

**Chicago/Turabian Style**

Dan, Min, Jian Hao, Ruijin Liao, Lin Cheng, Jie Zhang, and Fei Li.
2019. "Accumulation Behaviors of Different Particles and Effects on the Breakdown Properties of Mineral Oil under DC Voltage" *Energies* 12, no. 12: 2301.
https://doi.org/10.3390/en12122301