Simulation of Effect on Charge Accumulation Distribution in Laminar Oil Flow with Bubbles in Oil Passage of Converter Transformer
Abstract
1. Introduction
2. Fluid Model of Bubbles in Transformer Oil Passage
2.1. Model of Transformer Oil Passage
2.2. Laminar Flow Model of Transformer Oil
2.3. Dynamic Analysis of Bubbles in Transformer Oil Flow
3. Charge Accumulation Theory
3.1. Charge Drift Diffusion in Fluid
- 1.
- Poisson equation:
- 2.
- Nernst–Planck equation:
- 3.
- Navier–Stokes Equation describing fluid motion:
- 4.
- Continuity equation:
3.2. Bipolar Charge Carrier Transport in Insulating Paper
3.3. Charge Accumulation Process
4. Simulation Modeling
4.1. Simplified Conditions of Fluid Model
- Ions are regarded as point charges without considering their volume effects.
- Fluid is continuous and incompressible Newtonian fluid.
- The dielectric constant ε is constant and does not change with position or field strength.
- Ignoring the magnetic effect, that is, quasi-static approximation, without considering the change of magnetic field.
- In the case of no ionization, the source term of the chemical reaction can be ignored, that is, in Formula (3).
- The calculation area of this model is obviously smaller than the winding size of the converter transformer, so the temperature is constant and the thermal effect is ignored; that is, the temperature T in Formula (4) is constant in the individual model and does not change with time, and there is no coupling with the temperature field in the model.
- The dilute solution hypothesis is that the ion concentration is low enough that the interaction between them can be ignored, and the activity coefficient is approximately 1.
4.2. Model Establishment and Boundary Conditions
4.3. Physical Field Decoupling Simplification
5. Simulation Analysis
5.1. Movement of Bubbles in the Oil Passage
5.2. Effect of Deformation Bubble on Charge Accumulation
5.3. Influence of Bubbles and Oil Flow on Charge Accumulation and Insulation State
- Under the condition of no bubble and no laminar flow, the total charge accumulation is the least, and the range of positive and negative charge accumulation values in oil and paper is very small, which is an order of magnitude smaller than the value of the same charge under other conditions. It can be seen that there is no bubble distortion effect on the field, the electric field strength in each region is closer to the uniform electric field, the charge injection is significantly reduced and the oil flow takes away the accumulated charge, making the whole insulation environment better.
- In the case of the same bubble, the fluid flow has an obvious effect on the accumulation of positive charge in transformer oil. Because the migration and diffusion rate of positive ions in oil is lower, the degree of accumulation can be significantly reduced by the convection effect of oil flow. In the simulation case of this paper, the oil flow velocity near the corner of the upper paperboard increases due to the change of pipeline structure, and the convection effect is significantly faster than that in the same abscissa area of the lower paperboard. However, the accumulation of negative charges in oil is significantly increased, because the diffusion and migration rate of electrons is faster, and the negative charge injection rate at the contact position between the paperboard and the electrode is higher than that of the positive charge (the electron injection barrier is lower than that of the positive charge). When the negative charge is taken away by the slower oil flow, the new negative charge is replenished faster and passes through the oil–paper interface faster, and the slightly thinner positive charge layer attracted by the outside of the negative charge accumulation layer increases the local electric field distortion.
- In the case of the same bubble, the laminar flow plays a significant role in increasing the charge accumulation in the insulating paper. The existence of bubbles distorts the electric field, obviously, and the charge injection rate of the two electrodes increases significantly compared with that without bubbles. The fluid in the oil takes away the charge, which makes the charge density gap between paper and oil larger, the degree of electric field distortion deepened and the injection increased.
- In the case of the same bubble, the laminar flow rate of 0.2 m/s and 0.4 m/s has no obvious difference compared with the charge accumulation, so it is not detailed.
- Under the same condition without laminar flow, the existence of bubbles mainly affects the positive charge accumulation in insulating paper. Compared with the two sides, the positive and negative charges in the oil and the negative charge accumulation in the paper are not significantly different, only the positive charge accumulation in the paper is three times larger due to the existence of bubbles. Because, in the simulation model in this paper, the bubble is closer to the high potential side, the electric field on the paperboard is severely distorted.
- In this paper, the charge accumulation of the model at 1 s under various conditions is calculated. When there is no ionization reaction, the charge accumulation level is positively correlated with the duration. The transformer has been running for many years. When the bubbles are stuck in a certain position due to the internal structure of the transformer, the electric field distortion caused by the charge accumulation will aggravate the deterioration of the insulation state and affect the service life of the internal insulation.
6. Conclusions
- The existence of bubbles will significantly increase the degree of charge accumulation, and under the same laminar flow conditions, the extreme range of charge density will increase by about 104 times. It aggravates the distortion of the electric field, and the insulation strength of bubbles is lower, which becomes the weak link of insulation.
- In the laminar flow environment, the oil flow will take away part of the accumulated charge in the oil, but in the case of trapped bubbles, the charge accumulation in the insulating paper will increase from the order of 10−2 to 10−1. In the case of no bubbles, the transformer oil layer flow will increase the charge accumulation in the insulation paper by 4–5 orders of magnitude. So, the oil flow promotes the deterioration level of insulating paper.
- When the transformer oil is already in the laminar flow state, the effect of laminar flow velocity on charge accumulation is not obvious.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
UHVDC | Ultra-High-Voltage Direct Current |
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Conditions | Charge Density Range in Oil (C/m3) | Charge Density Range in Paper (C/m3) | ||
---|---|---|---|---|
Negative Charge | Positive Charge | Negative Charge | Positive Charge | |
Bubble (√) Laminar flow (√) | −1.62 × 103 | 3.94 × 10−2 | −0.15 | 0.20 |
Bubble (√) Laminar flow (×) | −2.58 × 10−4 | 1.72 × 102 | −3.70 × 10−2 | 8.78 × 10−2 |
Bubble (×) Laminar flow (√) | −2.75 × 10−7 | 4.58 × 10−7 | −1.62 × 10−6 | 5.07 × 10−6 |
Bubble (×) Laminar flow (×) | −2.21 × 10−4 | 1.64 × 102 | −3.72 × 10−2 | 2.73 × 10−2 |
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Si, W.; Li, H.; Liu, H.; Gu, X. Simulation of Effect on Charge Accumulation Distribution in Laminar Oil Flow with Bubbles in Oil Passage of Converter Transformer. Energies 2025, 18, 3992. https://doi.org/10.3390/en18153992
Si W, Li H, Liu H, Gu X. Simulation of Effect on Charge Accumulation Distribution in Laminar Oil Flow with Bubbles in Oil Passage of Converter Transformer. Energies. 2025; 18(15):3992. https://doi.org/10.3390/en18153992
Chicago/Turabian StyleSi, Wen, Haibo Li, Hongshun Liu, and Xiaotian Gu. 2025. "Simulation of Effect on Charge Accumulation Distribution in Laminar Oil Flow with Bubbles in Oil Passage of Converter Transformer" Energies 18, no. 15: 3992. https://doi.org/10.3390/en18153992
APA StyleSi, W., Li, H., Liu, H., & Gu, X. (2025). Simulation of Effect on Charge Accumulation Distribution in Laminar Oil Flow with Bubbles in Oil Passage of Converter Transformer. Energies, 18(15), 3992. https://doi.org/10.3390/en18153992