COMSOL 6.4 - Positive Streamer Propagation in Transformer Oil

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Positive Streamer Propagation in Transformer Oil

This example simulates the propagation of a positive streamer in transformer oil under a lightning impulse voltage. The space charge density and the electric field are obtained. The simulated streamer radius agrees well with the measured values (Ref. 1).

Model Definition

The Electric Discharge interface is used to simulate the streamer discharge in transformer oil. The numerical model is described as follows:

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e, p, and n denote electrons, positive ions, and negative ions

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ni is the number density of the charge carrier (SI unit: 1/m3)

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E is the electric field (SI unit: V/m)

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zi denotes the carrier charge (SI unit: 1)

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μi denotes the carrier mobility (SI unit: m2/(V·s))

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wi is the drift velocity in the electric field (SI unit: m/s)

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Di is the diffusion coefficient (SI unit: m2/s)

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Ri is the reaction rate (SI unit: 1/(m3·s))

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τa is the attachment time constant (SI unit: s)

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βep is the electron–ion recombination coefficient (SI unit: m3/s)

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βpn is the ion–ion recombination coefficient (SI unit: m3/s)

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SF is the field ionization (SI unit: 1/(m3·s))

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e is the electric charge (SI unit: C)

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nioni is the number density of ionizable species (SI unit: 1/m3)

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a denotes the molecular separation distance (SI unit: m)

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m* denotes the effective electron mass (SI unit: kg)

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φΔ and φγ are ionization potential parameters (SI unit: V)

The above transport equations are fully coupled with Poisson’s equation through the electric field and the space charge:

Results and Discussion

Figure 1 shows the discharge current as a function of time. Figure 2 plots the distribution of different charge carriers density before and during a current pulse. Figure 3 shows the distribution of space charge density and electric field at t = 90 ns.

Figure 1: The axial electric field at t = 0, 10, 20, ..., 90 ns.

Figure 2: The electron number density at t = 0, 10, 20, ..., 90 ns.

Figure 3: The distribution of space charge density and electric field at t = 90 ns.

1. J. Jadidian and others, “Stochastic and deterministic causes of streamer branching in liquid dielectrics,” J. Appl. Phys., vol. 114, no. 6, pp. 63301-1–10, 2013.

Electric_Discharge_Module/Liquid_Dielectrics/streamer_in_transformer_oil

Modeling Instructions

From the menu, choose .

In the window, click

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In the tree, select > .

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In the tree, select > .

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Rectangle 1 (r1)

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In the text field, type 15.

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In the text field, type 30.

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Click to expand the section. Select the checkbox.

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Clear the checkbox.

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In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	0.1

Rectangle 2 (r2)

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Locate the section. Clear the checkbox.

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Select the checkbox.

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In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	0.03

Difference 1 (dif1)

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toggle button for .

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In the text field, type t.

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Locate the section. In the text field, type kV.

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In the table, enter the following settings:


Argument	Unit
t	ns

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Locate the section. In the table, enter the following settings:


Plot	Argument	Lower limit	Upper limit	Fixed value	Unit
√	t	0	90[ns]	0	s

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button in the toolbar.

Electric Discharge (edis)

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Boundary Layer Properties

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Step 1: Time Dependent

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Solution 1 (sol1)

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Setting a maximum timestep variable based on the built-in dielectric relaxation time can help improve both efficiency and accuracy.

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From the list, choose .

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In the text field, type min(0.1[ns],comp1.edis.minDRT*0.8).

The PARDISO direct solver is usually a bit faster and leaner on memory than the default direct solver (MUMPS) on this type of model.

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2D Plot Group 1

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