Simulation Analysis of Metallic Particles Movement in Typical Structure of Oil-immersed Power Transformer

The insulation performance of oil-immersed power transformers is closely involved with the movement of metal particle impurities, and the movement characteristics of metal particles are not only influenced by the electric field, but also by the oil flow. In this paper, a solid-liquid two-phase flow simulation model was constructed, and the effect of electric field on the motion of metal particles was considered. Firstly, the validity of the simulation model was verified by using the experimentally observed motion of metal particles in the horizontal oil channel between parallel flat plate electrodes, based on which the motion of metal particles in the typical oil channels of a 500kV power transformer was studied. It was found that when the metal particles passed through the oil flow inlet, the number of metal particles settling increased with the increase of particle size. All the metal particles with 1mm particle size sank in the oil flow inlet during the oil migration process, it was almost impossible to enter the low, medium and high voltage winding parts. Through the middle or upper end of the high voltage winding, the smaller particles (50μm, 150μm) would easily migrate with the oil flow and move faster; the larger particles (500μm) would move slower or be more easily deposited. This research holds significant practical implications in the engineering study of metal particle motion distribution within transformers.


Introduction
Large oil-immersed power transformers are the core equipment of high-voltage power transmission engineering, and their safe and stable operation is related to the safety and stability of the whole power system.As the main insulating medium of power transformers, the performance of insulating oil is directly related to the safety and reliability of the transformer [1].CIGRE pointed out that one of the main causes of insulation failures in transformers of 400kV and above is the contamination of particulate impurities in transformer oil [2].Many studies have shown that due to material processing, mechanical vibration, oil pump wear and electro-thermal aging, transformer oil will inevitably be contaminated by particulate impurities such as metal, fiber and carbon, among which metal particles pose the greatest threat to the insulation performance of the transformer [3].This is because the free metal particles migrate under the compound effect of oil flow and electric field, and when they are close to the electrodes, they may initiate partial discharge and insulation failure [4].
Scholars at home and abroad have carried out in-depth studies on the motion characteristics of free metal particles.Birlasekaran S proposed a theoretical model to analyze the motion of a small conductive sphere (diameter of 50 μm) under alternating voltages and carried out experimental verification [5], found that micron-sized particles only reciprocate on the surface of the electrodes, and explained this phenomenon by force analysis.The motion of 90-200 μm free metal particles in viscous insulating oil between micro-sized parallel plate electrodes at low DC voltage was investigated by Knutson C R [6], and it was found that the collision frequency of the particles with the electrodes increases with the increase of the externally applied voltage; the higher the viscosity of the oil, the lower the collision frequency.Wang Y et al carried out the motion distribution characteristics of copper particles in insulating oil under AC and DC composite voltage [7], and found that with the increase of the DC component of the applied voltage, the motion speed of copper particles in the insulating oil and the collision frequency with the electrodes will be significantly increased.It is difficult for copper particles to converge and form small bridges in the oil under AC voltage, but when the DC component is included, the copper particles will converge and form dynamic small bridges in the high field strength region.
The above studies were carried out in static transformer oil.However, in actual power transformers， due to the presence of the cooling system and temperature gradient, the insulating oil always keeps flowing.Tang J et al carried out the law of motion of metal particles in flowing transformer oil under AC and DC compound voltage [8].The results show that under AC voltage, the particles only reciprocate up and down near the lower electrode, and frequently collide with the electrode; when the applied voltage contains DC component, the particles reciprocate between the upper and lower electrodes and the spacing between the landing points becomes narrower with the increase of DC component.However, previous studies on the characteristics of metal particles in the transformer oil movement are in the horizontal oil or vertical oil and other simple models, the actual transformer oil channel structure is very complex, not only the horizontal oil channel among the three windings of the turns and vertical oil between each other, there are also winding end of the angular ring and the static ring composed of curved pipe oil channel, the typical oil field and the distribution of the electric and flow fields and the simple model must be also a difference.At present, there is no study for the actual transformer oil channel structure in the metal particle movement characteristics.
For this reason, this paper aims to establish a solid-liquid two-phase flow simulation model and experimentally verify its validity, using a 500kV power transformer as the study object.The simulation investigates the trajectories of metal particles of different sizes in the typical oil path of the transformer, allowing for the summary of the movement patterns of metal particles in various parts of the transformer.

Analysis of Forces on Metal Particles
The metal particles were used to calculate the force on the particles using the kinetic equations in the Lagrangian coordinate system as shown in equation ( 1) [8].The force analysis is shown in figure 1.
where R is the radius of the metal particle; ρp is the density of the particle; and vp is the velocity of motion of the metal particle.The particles are mainly subjected to gravity force FG, electric field force FE, oil flow trailing force FD, buoyancy force FBu, Magnus force FMn, additional mass inertia force FAM, and pressure gradient force Fp.

Simulation Method
In this paper, a solid-liquid two-phase flow model was constructed using COMSOL and the effect of electric field on metal particles was considered.The continuous phase is the flowing transformer oil and the discrete phase is the metal particles in the oil.The transformer oil can be assumed to be an incompressible Newtonian fluid at a constant temperature, so its flow state can be solved by the Navier-Stokes partial differential equation, which is shown in equation ( 2): where u is the oil flow velocity, p is the fluid pressure, η is the kinetic viscosity, which takes the value of η=0.0059Pa• s, 2  and is the Laplace operator.When dealing with discrete-phase metallic particles, the kinetic equations in the Lagrangian coordinate system are used to calculate the particle forces.Finite element calculations of the electric and flow fields of the model are performed first, and then the fluid particle tracking module is used to release the metal particles to calculate their trajectories.The effect of the particles on the electric field is neglected because the particle size of the metal particles in the transformer oil is small and the effect on the macroscopic electric field in the oil channel is weak.At the same time, the overall volume fraction of metal particles in the flowing oil is very small, and the effect of the particles on the flow field can also be neglected.

Experimental Observation of the Motion of Metal Particles in a Horizontal Oil Channel
The transformer oil circulating flow device is shown in figure 2. The device mainly consists of oil pump, plexiglass oil channel, copper flat electrode, flow control system, temperature control system, pressure gauge and other components.The width and height of the parallel plate electrode are 70mm and 10mm, respectively, and the electrode spacing is 10mm.The high voltage end applied AC industrial frequency voltage with a peak value of 29kV, the lower electrode was grounded, the oil flow speed was set to 0.06m/s, and the iron particles with a diameter of 150μm were placed in the oil gap.The high-speed camera was only able to capture the motion of the particles in a section of the oil channel with a length of 21.6 mm due to the limited imaging range, and the typical motion trajectory of the particles is shown in figure 3(a).The particle started from the lower electrode at point A, raised to the highest point B, then fell back to point C and collided with the lower electrode.The whole trajectory was approximated as wave-like.There were about 22.5 wave crests, i.e., the spacing between the two falling points was about 1 mm, and the time interval was 0.19s.

Simulation Study of the Motion of Metal Particles in a Horizontal Oil Channel
The simulation model and parameter settings were kept consistent with the experimental conditions.The metal particles with a diameter of 150 μm were released at the position of 2 mm from the lower electrode plate on the left side of the parallel plate electrode, and the trajectory of the metal particles was obtained in the simulation as shown in figure 3(b).Intercepting the movement in the oil channel with a length of 21.6 mm, there were 21 wave peaks, i.e., the spacing between the two drop points was about 1 mm, and the time interval between the drop points was 0.2 s.The simulation results exhibit strong consistency with the experimental findings, thereby confirming the accuracy of the current model for solid-liquid two-phase flow.

Simulation Model
A simplified two-dimensional axisymmetric model of an oil-immersed transformer model ODFS-334000/500 (capacity of 334 MVA; rated voltage of 500 kV) was developed as a study object, as shown in figure 4. The model consists of low, medium and high windings (wire cake, wire cake insulation), cardboard, transformer oil, core, yoke, and oil flow inlet/outlet piping, and the effects of connecting and supporting parts around the windings are neglected.
The ODFS-334000/500 autotransformer was rated at (525 / 3) / (242 / 3 4 2.5%) / 34.5  kV [9][10][11].The voltage of each line cake was generally set as the first type of boundary condition, and this paragraph described the AC frequency voltage as RMS voltage.The measured flow rate of the oil flow inlet at the submersible oil pump of the transformer is 120 m 3 /h and the diameter of the pipe is 0.14 m.Therefore, the average flow rate of the oil flow inlet was set to 2.16 m/s, and the outlet pressure was maintained at 1 atmosphere.

Trajectory
CIGRE working report "Effect of Particles on Transformer Dielectric Strength" points out that there is a certain distribution of metal particles in transformer oil, with a particle size of 50~200μm [2], but due to wear and corrosion of mechanical parts such as oil pumps and on-load tap-changer contacts, there are also inevitably mixed with large particle size metal particles.Therefore, in the transformer oil flow inlet, a simulation of four particle sizes (50μm, 150μm, 500μm, 1mm) trajectory was researched.For the strong local electric field parts (high-voltage winding on the upper end and the middle), three kinds of metal particles (50μm, 150μm, 500μm) were considered for simulation analysis.and 4, respectively, and the settled particles rolled slowly on the lower surface.That is, when the particle size increased, the increase in gravity FG was much larger than FD, at this time the movement of metal particles by gravity was more affected.Due to the particle size of 1mm metal particles in the oil flow inlet with the oil migration process all settled, almost impossible to enter the high-voltage winding parts, so the subsequent simulation analysis of the particle size of 1mm trajectory was not carried out more.

Middle of High Voltage
Winding.Four metal particles were released from the vertical oil channel in the middle of the high-voltage winding, and the release point is shown in Figure 6, where the trajectories of the metal particles were recorded.All three particle sizes could pass through the vertical oil channel to reach the exit of this area.

Conclusion
In this paper, a two-dimensional cross-section model of a large oil-immersed power transformer containing oil flow inlet and outlet as well as oil-paper composite insulation structure between high and medium-low windings was constructed, and the trajectories of metal particles with different particle sizes in the typical oil channel of the transformer were obtained through the fluid particle tracking module.The conclusions are as follows: When metal particles passed through the oil flow inlet, the number of metal particles settling increased with the increase of particle size.Metal particles with particle size of 1mm in the oil flow inlet with the oil migration process all settled, almost impossible to enter the low, medium, and high voltage winding parts.Through the middle or upper end of the high-voltage winding, smaller particle sizes (50μm, 150μm) particles were easy to migrate with the movement of the oil flow, and the movement speed was faster; larger particle size (500μm) moved slower or were more prone to deposition.

Figure 1 .
Figure 1.Force analysis of metal particles.Figure 2. Transformer oil circulating flow device.

Figure 2 .
Figure 1.Force analysis of metal particles.Figure 2. Transformer oil circulating flow device.
(a) experimental observation (b) simulation results

Figure 3 .
Figure 3. Metal particle motion in horizontal oil channels.

Figure 4 .
Figure 4. Two-dimensional cross-sectional model of the transformer.

4. 2 . 1 .
Inlet of Oil Flow.Four uncharged free metal particles were uniformly released from the inlet of the oil stream, and the trajectories of 50 μm, 150 μm, 500 μm, and 1 mm metal particles were recorded, as shown in figure5.The colour background legend in the figure indicates the flow field distribution, the red arrow indicates the oil flow direction, and the black curve is the particle trajectory.With the increase in particle size, the number of metal particles settling increased.50μm and 150μm size particles were migrating with the oil, with no settlement.500μm and 1mm size particles settled 2,

Figure 5 .
Figure 5. Metal particle movement trajectory of oil flow inlet.

Figure 6 .
Figure 6.Metal particle trajectory of the middle of the high-voltage windings.4.2.3.Upper Part of the High Voltage Winding.Simulating the release of four metal particles from the upper end of the high-voltage winding, the trajectory of the metal particles was recorded, as shown in figure7.50μm and 150μm particles were easy to migrate with the movement of the oil flow and could be moved to the exit of this area after passing through the vertical oil channel and then through the

Figure 7 .
Figure 7. Metal particle trajectory of upper end of high voltage windings.