Insulation Design
Insulation Design: Theoretical Foundations
Approach to Insulation Design
Professor, is insulation design essentially about "keeping the electric field below the dielectric strength"?
Exactly. The design flow is:
1. Determine electrode shape and insulation configuration
2. Calculate electric field distribution using FEM
3. Verify that the maximum electric field $E_{max}$ is below the dielectric strength $E_b$ of each material
4. Evaluate the safety factor $SF = E_b / E_{max}$
Electric Field Mitigation Techniques
| Technique | Principle | Application Example |
|---|---|---|
| Fillet (Rounding) | Increase the curvature radius of edges to mitigate electric field concentration | High-voltage electrodes |
| Corona Ring | Enlarge the equipotential surface to homogenize the electric field | Transmission line insulators |
| Stress Cone | Push out the electric field using high-permittivity material | Cable terminations |
| Shield Electrode | Shield the electric field with a grounded electrode | GIS (Gas Insulated Switchgear) |
| Graded Insulation | Gradually change the $\varepsilon_r$ (relative permittivity) | Bushings |
Summary
- $E_{max} < E_b / SF$ — Fundamental condition for insulation design
- Electric Field Mitigation — Fillet, corona ring, stress cone
- Predict electric field distribution with FEM — Optimization of design
The Dawn of Insulation Engineering—The History of Cable Insulation and Gutta-Percha (1850s)
The engineering use of electrical insulating materials began in the 1850s during the era of submarine cable laying. When the Dover Strait submarine cable connecting England and France was laid in 1851, a natural rubber from Malaysia called "Gutta-percha" was used as the insulating material. However, the first transatlantic cable (1858) failed due to insulation breakdown after just three weeks—insulation engineering at the time relied solely on empirical rules. Subsequently, the electric line of force theory, which evolved from Coulomb's law (1785), was systematized by Maxwell (1873), establishing the foundation for modern electric field analysis. Today's FEM electric field analysis solves Maxwell's equations through discretization, with theories from 170 years ago forming the mathematical basis for cutting-edge insulation design tools.
Computational Methods for Insulation Design
FEM Flow for Insulation Design
1. CAD Model Construction (Electrodes + Insulators + Surrounding Space)
2. Material Settings ($\varepsilon_r$ for each region)
3. Boundary Conditions (Electrode potential, ground, symmetry plane)
4. Mesh (Refine areas of electric field concentration)
5. Solve (Laplace/Poisson equation)
6. Postprocessing ($E_{max}$, safety factor map)
How does mesh coarseness affect the results?
The electric field has high mesh dependency (derivative of potential). Place at least 4–6 layers of elements at electrode edges. Second-order elements are recommended.
Summary
- Mesh quality in electric field concentration areas is key
- Ensure electric field accuracy with second-order elements
- Visualize design margin with safety factor maps
FEM Analysis of Solid Insulation—Mesh Refinement and Convergence Verification of Electric Field Concentration Factor
In FEM electric field analysis of solid insulating materials (epoxy, XLPE, ceramic), electric field concentration occurs at shape corners, edges, and electrode ends. Mesh refinement in these concentrated areas is crucial for accuracy. Practical procedure for verifying electric field convergence: ① Analyze the target area with three mesh levels (coarse, medium, fine) and judge convergence when the change rate of the maximum electric field value is below 1%. ② Set the minimum mesh size to R/20 or less relative to the edge curvature radius R (e.g., mesh ≤5um for R=0.1mm). ③ At interfaces where the relative permittivity ratio (er) differs significantly (e.g., air er=1 vs. epoxy er=4), the electric field changes abruptly due to discontinuity in normal electric flux density, so ensure equally dense meshes on both sides of the interface. Underestimating the electric field concentration factor Kt by more than 3% risks insufficient design safety factor in actual equipment.