Electric Field Stress Estimation and Control

Electric Field Stress Estimation and Control

∇² Φ = p/∈_{0 …} (Eqⁿ 1)

Where, Φ = Potential at a given point

   p = Space charge density in the region and

   ∈_{0 =} Electric permittivity of free space (vacuum)

• Equation 1 was given by Poisson and is therefore known as Poisson’s equation for electric field distribution.
• If in Equation ∇² Φ
  = p/∈₀ = 0 as in case of most of the high voltage apparatus, space charges are absent then the potential distribution is given by Laplace’s equation as :

∇² Φ
= 0 … (Eqⁿ 2)

• In Equations 1 and 2, the operator ∇² is called Laplacian and is a vector with properties

∇ . ∇ = ∇² = ∂²/dx² + ∂²/dy²  + ∂²/dz²

There are various methods available for determining the potential distribution, but the few commonly used are :

1. Electrolytic tank method
2. Numerical methods such as finite difference, finite element and charge simulation method.

The direct calculation of potential distribution is difficult except in case of simple geometries. However in many practical cases some simple rules are used to plot the field lines and equipotential ; these rules are

1. The equipotential cut the field lines at right angles.
2. If these (equipotential and field lines) from curvilinear squares then the density of field lies is an indication of the electric stress in a given region and
3. In any region , the maximum electric field is given by dv/dx where dv is the voltage difference between two successive equipment, dx distance apart. Proper choice of symmetry of planes and shape of electrodes could help in saving of labour as well as time. In a given geometry, once the potential distribution is established, it is easy to refashion and redesign the electrodes to minimize the stresses so that the onset of corona is prevented. Such a thing, is normally seen in HV electrodes of bushings, standard capacitors etc.

When two dielectrics of very different permittivities are in series, the electric stress is very much higher in the medium of lower permittivity. Considering a solid insulation in a gas medium, the stress in the gas becomes, times that in solid dielectric where is the relative permittivity of solid dielectric. This high stress occurs at the electrode edges and one method of overcoming this is to increase the electrode diameter. The other methods of stress control are shown in Figures.

Figures methods of stress control.

Figure (a) shows highly stressed area at the edges of electrode.

Figure (b) first method of control of stress by aligning the edge of the electrode and insulation as evenly as possible.

Figure (c) providing a notch in the insulation and securing the electrode properly and effectively in the insulation.

Figure (d) lastly by providing corona rings as shown the stress can be controlled. 

• In HV apparatus, high stresses accelerate the aging of insulation leading to its failure. Over the years many methods for controlling and optimizing electric fields to get the most economical designs have been developed.