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Modelling the Non-equilibrium Electric Double Layer at Oil-Pressboard Interface of High Voltage Transformers
H. Zainuddin*, P. L. Lewin and P. M. MitchinsonUniversity of Southampton, Southampton, UK
Model Parameters
Simulation ResultsIntroduction
Dynamic Model Representation
Discussion
Conclusions
In large oil-filled power transformers, cellulose-based pressboard and paper are used throughout to provide electrical insulation. Microscopic views have shown that pressboard insulation is a fibrous and porous structure with a non-homogeneous surface. The porosity of pressboard can result in impurities within the oil being drawn into the oil-impregnated pressboard. The material properties and geometry of pressboard thus lead to a complex oil-pressboard interface.
A 2-D model of oil-pressboard interface has been constructed using Finite Element Analysis software. The model studies the non-equilibrium charge density profile in the EDL at the oil-pressboard interface where the oil is in a near stationary condition.
University of Southampton, Highfield, Southampton, SO17 1BJ, UKContact details :
The porous and non-homogeneous structures lead to an ‘overlap effect’ of the electric double layer which causes a non-uniform charge distribution along the interface as shown in Figures 2 and 3.
The overlap effect leads to the accumulation of negative ions at certain areas in the oil to compensate the high density of positive ions. This in turn leads to unexpected space charge profiles as shown in Figure 5 (curve no. 3)
Figure 4 shows that the space charge profile in the oil when further from the interface fluctuates as charges tend to diffuse towards the ground electrode (right boundary). This effect is clearer at the corner of the pressboard edge.
Table 1 shows the physical parameters that are used in the simulation model.
The parameters are important to determine the initial concentrations of chemical species and reaction rate for the dissociation and recombination processes.
The model of oil-pressboard interface has considered the porous and non-homogeneous structure of pressboard – by using different arrays of cellulose blocks (see Figure 1)
The mathematical model to study the Electric Double Layer (EDL) profile is based on the following physicochemical reactions:
1. Dissociation and recombination of neutral molecules of impurities into positive and negative ions in oil bulk and porous structure of pressboard filled with oil:
2. Adsorption and desorption of ions at the oil-cellulose interface (surface reaction):
SP, SN – free active cellulose sitesSA+, SB- – charged cellulose sites
Field equations:
1. Poisson’s equation:
2. Conservation equation: Source Term, S – depends on physicochemical reaction
3. Nernst-Planck equation:
Table1: Physical parameters for both oil and pressboard
Figure 1: Space charge density of oil-pressboard composite system
SBBSNSAASPdes
ads
des
ads
K
K
K
K
BACr
d
K
K
Oil bulk (i=1) Pressboard (i=2)
Parameter Symbol Value Symbol Value
Permittivity ε1 2.2ε0 ε2 4ε0
Conductivity σ1 5x10-12 σ2 5x10-15
Positive ions mobility µP1 1 x 10-9 m2/Vs µP2 1 x 10-10 m2/Vs
Negative ions mobility µN1 1 x 10-9 m2/Vs µN2 1 x 10-10 m2/Vs
Figure 2: Space charge at interface from pressboard wall (1) to oil bulk (7)
Parameter Symbol Value
Total concentration of active
cellulose radicals
nSP0/SN01 x 1016 sites/m2
Adsorption rate of negative ions Kads,N1.28 x 10-26 m3/s
Desorption rate of negative ions Kdes,N1.28 x 10-7 s-1
For simplicity, the simulation is run by assuming only one ionic species reacts with the cellulose. In this case, only negative ions.
Table 2 defines the parameters used for adsorption and desorption processes at the oil-cellulose interface.
Table 2: Cellulose surface initial concentration and reaction rate
The simulation model assumes that the solid cellulose of the pressboard plays no role in conductivity. The porosity of the pressboard is assumed to play a major role in conductivity, i.e. oil penetrates into the pressboard.
Thus, this also reflects ion mobility, species concentration and reaction rate.
The simulation results have been obtained assuming that the oil is stationary (i.e. convective term in Nernst-Planck equation is neglected) for 8000 steps with a time step of 1s.
Figure 3: Space charge at interface due to porous and non-homogeneous structure from wall (1) to oil bulk (5)
Figure 4: Space charge profile in the oil(1)Corner of pressboard edge(2)Centre of oil-pressboard interface
Figure 5: Effect of porous and non homogeneous structure on space charge profile in the oil
The electric double layer profile does not totally reach an equilibrium. This is due to the use of dynamic mathematical equations that are also known as the non-equilibrium model of the electric double layer.
Based on the simulation results, the assumption that the structure of pressboard is both porous and non-homogeneous has made the modeled space charge distribution at the oil-pressboard interface far more complex.
Further investigation into model performance with different parameters and experiments to validate the model will be undertaken over the next few months.
