# Space Charge Modulated Electrical Breakdown of Oil Impregnated Paper Insulation Subjected to AC-DC Combined Voltages

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

^{#}(Kunlun KI25X) transformer oil, which has been widely used in various types of transformers in China.

^{#}transformer oil was firstly filtered with a double-stage vacuum oil purifier. Then, the filtered oil was heated at 80 °C and 50 Pa for 4 h. After this treatment, the water content in the transformer oil was ≤5 ppm, the air content was ≤0.1%, and the impurity granularity was ≤3 μm.

^{#}transformer oil was injected. Finally, the vacuum oiling chamber with OIP samples inside was kept at 90 °C for 24 h.

#### 2.2. Test System

^{#}transformer oil. The upper spherical electrode was connected to the high voltage source, and the lower plate electrode was grounded.

#### 2.3. Breakdown Test Procedure

#### 2.4. Simulation Model

^{7}V/m) obeys hopping conduction [19]. In this investigation, based on the theory of hopping conduction, space charge dynamics of OIP in AC-DC combined voltage breakdown process were simulated. The assigned parameters in numerical simulation were obtained based on our previous simulations [23,24] and through isothermal surface potential decay (ISPD) experiments, as shown in Nomenclature [19]. To be noted is that the Maxwell-Wagner polarization between layers of oil impregnated paper is ignored in the current stage of simulation.

_{in}is the Schottky emission current in A/m

^{2}; A is the Richardson constant; T is the absolute temperature in K; ϕ

_{in}is the Schottky injection barrier in eV; EF is the electric field in V/m; k

_{B}is the Boltzmann constant; q

_{e}is the elementary charge in C; ε

_{0}is the vacuum permittivity in F/m; and ε

_{r}is the dielectric constant (ε

_{r}= 3.4 for OIP).

_{c}is the conduction current in A/m

^{2}; x is the position of sample in m; t is time in s; Q is total charge density in the dielectric in C/m

^{3}; μ is the carrier mobility in m

^{2}/V; φ is the potential of the charged material in V; S is the source term, R is the recombination coefficient; Q

_{e}is negative charge density in C/m

^{3}; and Q

_{h}is positive charge density in C/m

^{3}.

## 3. Experimental Results

#### 3.1. The Breakdown Characteristics under Pre-Applied DC Method

_{DC}is the pre-applied DC voltage; V

_{AC}is the AC breakdown voltage in peak value, which is applied after pre-applied DC voltage. It can be observed that V

_{AC}decreases with increasing V

_{DC}. Moreover, a small increase in V

_{AC}can lead to about a two times decrease in V

_{DC}, which indicates that the AC breakdown strength of OIP is about half of its DC breakdown strength.

_{total}is the sum of V

_{AC}and V

_{DC}, labeled as the total breakdown voltage, and k is the AC content ratio in V

_{total}.

_{total}, and k for one to four layers of OIP can be obtained through Figure 5, and is demonstrated as Figure 6. It can be observed that V

_{total}increases with increasing sample layers. This increase becomes smaller as increasing sample layers, which can be explained by geometrical effect observed in dielectric breakdown [25]. Moreover, V

_{total}decreases with increasing AC content ratio k. It implies an easier breakdown process of OIP under AC-DC combined voltage with large AC content ratio. Compared to the breakdown characteristics of OIP under single DC and AC voltage, V

_{total}is smaller than its DC breakdown voltage, but is larger than 50 Hz AC breakdown voltage, whatever the content ratio k is (for one layer OIP, AC breakdown occurs at 9.1 kV, and DC breakdown occurs at 18.7 kV).

#### 3.2. The Breakdown Characterisitics under Pre-Applied AC Method

_{AC}is the pre-applied AC voltage, and V

_{DC}is the DC breakdown voltage. It can be observed that the breakdown voltage, V

_{DC}, decreases with increasing pre-applied voltage, V

_{AC}, which is in accordance with the trend in pre-applied DC method. The relationship between total breakdown voltage, V

_{total}, and k is shown in Figure 8. For different layers of OIP, there is a rise in total breakdown voltage, V

_{total}, from one layer to four layers sample. The total breakdown voltage decreases with increasing content ratio, k. Compared to the pre-applied DC method, the absolute slope of V

_{total}is smaller. Through a joint observation of Figure 6 and Figure 8, it is observed that the total breakdown voltage in the pre-applied AC method is larger than that in the pre-applied DC method, whatever the content ratio, k, is.

## 4. Discussion

^{3}near the left electrode.

^{3}near the left electrode.

^{3}, which is much smaller compared to −34.1 C/m

^{3}in the pre-applied DC method. After the application of AC component, a DC component is applied, forming AC-DC combined voltage waveform. It can be observed that the positive charges previously injected are firstly neutralized near the left electrode. After that, the negative charge density starts to increase. At the end of 22 s, the maximum negative charge density reaches −182.5 C/m

^{3}near the left electrode, which is smaller than that in pre-applied DC method (−251.8 C/m

^{3}). Correspondingly, positive charges accumulate near the right electrode, and the maximum charge density is 217.1 C/m

^{3}at 22 s.

^{3}at the end of pre-applied DC period (11 s). As the AC component begins to ramp after 11 s, the average space charge density increases tremendously and reaches 7.44 C/m

^{3}at 22 s. Comparatively, in the pre-applied AC method, the average space charge density is extremely small (0.01 C/m

^{3}) at the end of the pre-applied AC period. These charges are insufficient to significantly distort the electric field distribution inside the OIP sample. During the later AC-DC combined voltage ramping period (11–22 s), large amount of charges are continuously injected into the sample. With the increase in amplitude of AC-DC combined voltage, the charge injection is gradually strengthened. At the end of 22 s, the average space charge density reaches 4.63 C/m

^{3}. This accumulation is smaller compared to pre-applied DC method (7.44 C/m

^{3}).

^{8}V/m in the pre-applied DC method and 1.60 × 10

^{8}V/m in the pre-applied AC method), as shown in Figure 13c, which indicates that the applied voltage in the pre-DC method only needs to reach a relatively small value, and the induced maximum electric field could reach the intrinsic breakdown strength of insulating material and triggers the breakdown process. More specifically, the differences in maximum electric fields between the two methods imply that the breakdown voltage in the pre-DC method shall be 0.42 kV (0.03 × 10

^{8}V/m × 0.14 mm) lower than in the pre-AC method, which is in accordance with the experimental results in Figure 9 (about 0.5 kV).

^{3}near the left electrode, but it is nearly −250 C/m

^{3}in two layers breakdown). However, the total amount of space charge is increased, as some of the charges moves into the inner space of the sample. This increase can be verified in Figure 16.

^{3}and 2.46 C/m

^{3}in the pre-DC and pre-AC methods, respectively, in four layers breakdown, which indicate 0.012264 C/m

^{2}and 0.006888 C/m

^{2}of total space charges. In two layers breakdown, the data are 0.010416 C/m

^{2}and 0.006482 C/m

^{2}for the pre-DC and pre-AC methods, respectively. Therefore, it is concluded that the amount of injected space charges is larger in four layers breakdown, which could lead to more distorted electric field, as shown in Figure 17.

^{8}V/m (1.342 × 10

^{8}in pre-DC and 1.301 × 10

^{8}in the pre-AC method), indicating a 1.15 kV (0.041 × 10

^{8}V/m × 0.28 mm) difference in breakdown voltages. In two layers breakdown, the difference is 0.42 kV (0.03 × 10

^{8}V/m × 0.14 mm). Therefore, the model anticipates larger difference in breakdown strength for four layers breakdown, which is in accordance with the experimental results, demonstrated in Figure 9.

## 5. Conclusions

- The total AC-DC breakdown voltage, V
_{total}(V_{AC}+ V_{DC}), of oil impregnated paper decreases as the increasing AC content ratio, k (V_{AC}/V_{total}), and is smaller than DC breakdown voltage, but larger than AC breakdown voltage. V_{total}in the pre-applied AC method is larger than that in the pre-applied DC method, whatever the value of k is. This deviation in total breakdown voltages between the two pre-applied methods is enlarged with increasing sample thickness. - Large amount of space charges are formed during the AC-DC breakdown of oil impregnated paper insulation. These accumulated charges form dramatically distorted inner electric field in insulation, which leads to variations of breakdown strengths of oil impregnated paper. Therefore, space charges must be considered in the design of converter transformers. By considering the amplitude and applied duration of ramped voltages in operating conditions, the changes in breakdown voltages can be estimated through numerical simulations.
- During the AC-DC combined voltage breakdown of oil impregnated paper, homo-charges are formed in both the pre-AC and pre-DC methods, and more charges are accumulated in the pre-applied DC method. These injected charges accumulate within 5μm in the vicinity of the sample-electrode interface, inducing a significantly distorted electric field in oil impregnated paper samples. This induced electric field distortion is more dramatic in the pre-applied DC method, which leads to its smaller AC-DC breakdown voltage compared with the pre-applied AC method.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Parameters | Unit | Value |

Absolute temperature, T | K | 300 |

Boltzmann constant, k_{B} | J/K | 1.38 × 10^{−23} |

Charge attempt-to-escape frequency, ν_{ATE} | Hz | 3 × 10^{12} |

Charge hopping distrance, a | m | - |

Electron hopping distance, a_{(e)} | m | 2.5 × 10^{−9} |

Hole hopping distance, a_{(h)} | m | 1.4 × 10^{−9} |

Charge hopping barrier height, u_{0} | eV | - |

Electron hopping barrier height, u_{0(e)} | eV | 0.68 |

Hole hopping barrier height, u_{0(h)} | eV | 0.78 |

Dielectric constant of OIP, ε_{r} | - | 3.4 |

Elementary charge, q_{e} | C | 1.6 × 10^{−19} |

Richardson constant, A | A/m^{2} K^{2} | 1.2 × 10^{−6} |

Schottky injection barrier, ϕ_{in} | eV | 1.1 |

Vacuum permittivity, ε_{0} | F/m | 8.85 × 10^{−12} |

Carrier mobility, μ | m^{2}/V | variable |

Conduction current, j_{c} | A/m^{2} | variable |

Electric field strength, EF | V/m | variable |

Electric potential, φ | V | variable |

Position, x | m | variable |

Sample thickness, L | m | variable |

Schottky emission current, j_{in} | A/m^{2} | variable |

Source term, S | - | variable |

Time, t | s | variable |

Total charge density, Q | C/m^{3} | - |

Electron density, Q_{(e)} | C/m^{3} | variable |

Hole density, Q_{(h)} | C/m^{3} | variable |

AC content ratio in total breakdown voltage, k | - | variable |

AC component in breakdown voltage, V_{AC} | kV | variable |

DC component in breakdown voltage, V_{DC} | kV | variable |

Total breakdown voltage, V_{total} | kV | variable |

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**Figure 3.**Schematic of voltage waveforms in AC-DC combined voltage breakdown (

**a**) pre-applied DC method (

**b**) pre-applied AC method (Schematic, the frequency in this figure does not represent the real situation of 50 Hz).

**Figure 5.**The variations of 50 Hz AC breakdown voltage as pre-applied DC voltage changes for one to four layers of oil impregnated paper.

**Figure 6.**The variations of total breakdown voltage, V

_{total}, as k changes for one to four layers of oil impregnated paper in pre-applied DC method.

**Figure 7.**The variations of DC breakdown voltage as pre-applied 50 Hz AC voltage changes for l–4 layers of oil impregnated paper.

**Figure 8.**The variations of total breakdown voltage, V

_{total}, as k changes for one to four layers of oil impregnated paper in the pre-applied AC method.

**Figure 9.**Comparisons of total breakdown voltages as k changes between the pre-applied DC and pre-applied AC methods for two layers and four layers of oil impregnated paper.

**Figure 10.**Space charge distributions of two layers of oil impregnated paper in the voltage ramping process of 11 kV DC and 11 kV AC combined voltage in the pre-applied DC method.

**Figure 11.**Space charge distributions of two layers of oil impregnated paper in the voltage ramping process of 11 kV AC and 11 kV DC combined voltage in the pre-applied AC method.

**Figure 12.**The variations of average space charge densities as time changes in two layers of oil impregnated paper between the pre-applied AC and pre-applied DC methods.

**Figure 13.**Electric field distributions in two layers of oil impregnated paper under AC-DC combined voltages (

**a**) the evolutions of electric field distortion in the pre-applied DC method under 11 kV DC and 11 kV AC combined voltages (90°); (

**b**) schematic of voltage waveform in the pre-applied DC method (11 kV DC and 11 kV AC); (

**c**) comparison of electric field distributions between the pre-DC and pre-AC methods under 11 kV DC + 11 kV AC combined voltage.

**Figure 14.**Space charge distributions of four layers of oil impregnated paper in voltage ramping process of 18 kV DC and 18 kV AC combined voltage in the pre-applied DC method.

**Figure 15.**Space charge distributions of four layers of oil impregnated paper in voltage ramping process of 18 kV AC and 18 kV DC combined voltage in the pre-applied DC method.

**Figure 16.**The variations of average space charge densities as time changes in four layers of oil impregnated paper between the pre-applied AC and pre-applied DC methods.

**Figure 17.**Comparison of electric field distributions between the pre-DC and pre-AC methods under 18 kV DC + 18 kV AC combined voltage (90°) for four layers of oil impregnated paper.

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## Share and Cite

**MDPI and ACS Style**

Zhu, Y.; Li, S.; Min, D.; Li, S.; Cui, H.; Chen, G. Space Charge Modulated Electrical Breakdown of Oil Impregnated Paper Insulation Subjected to AC-DC Combined Voltages. *Energies* **2018**, *11*, 1547.
https://doi.org/10.3390/en11061547

**AMA Style**

Zhu Y, Li S, Min D, Li S, Cui H, Chen G. Space Charge Modulated Electrical Breakdown of Oil Impregnated Paper Insulation Subjected to AC-DC Combined Voltages. *Energies*. 2018; 11(6):1547.
https://doi.org/10.3390/en11061547

**Chicago/Turabian Style**

Zhu, Yuanwei, Shengtao Li, Daomin Min, Shijun Li, Huize Cui, and George Chen. 2018. "Space Charge Modulated Electrical Breakdown of Oil Impregnated Paper Insulation Subjected to AC-DC Combined Voltages" *Energies* 11, no. 6: 1547.
https://doi.org/10.3390/en11061547