What Is Electrical Stress in High-Voltage Cables?

High-voltage cables are the silent workhorses of modern power grids, carrying immense electrical energy across cities, under seas, and through mountains. But within these cables, an invisible force is constantly at work: electrical stress. This stress, if not properly managed, can destroy the cable from the inside out. Understanding what electrical stress is, where it comes from, and how it is controlled is essential for anyone involved in the design, installation, or maintenance of high-voltage cable systems.

1. The Basic Concept: Stress as a Force

In everyday language, "stress" refers to pressure or tension. In electrical engineering, the term is analogous: electrical stress is the electric field intensity within a dielectric (insulating) material. More precisely, it is the voltage gradient – the change in voltage per unit distance – expressed in volts per millimetre (V/mm) or kilovolts per millimetre (kV/mm).

Imagine water flowing through a pipe. The water pressure pushes against the pipe walls. Similarly, in a cable, the voltage pushes against the insulation. The higher the voltage, or the thinner the insulation, the greater the stress on the material.

Think of it this way: If you have a 10 kV voltage difference across 10 mm of insulation, the average stress is 1 kV/mm. If the insulation thickness is reduced to 5 mm while keeping the same voltage, the stress doubles to 2 kV/mm. This stress can cause the insulation to break down if it exceeds its dielectric strength.

2. Where Does Electrical Stress Come From?

Electrical stress in a cable originates from the fundamental relationship between voltage and distance. In a well-designed cable, the stress is radial – it acts uniformly from the conductor outward to the metallic shield. The stress is highest at the conductor surface and decreases with the square of the distance from the conductor (inverse-square law).

• Conductor surface stress – This is the highest stress point in the cable. It depends on the conductor diameter and the applied voltage.

• Insulation bulk stress – The average stress through the insulation thickness.

• Shield surface stress – Much lower, as the shield is at ground potential.

The stress distribution in a healthy cable is predictable and manageable. Problems arise when this distribution is distorted.

3. Stress Concentration: The Real Problem

The word "concentration" is key to understanding cable failures. Electrical stress is not usually a problem when it is evenly distributed. But when it concentrates at a point, that point becomes a weak spot.

Stress concentration occurs at:

• Sharp edges – The cut end of a metallic shield, a sharp burr on a connector.

• Voids – Air bubbles inside the insulation.

• Contaminants – Metal particles or moisture within the insulation.

• Interfaces – Between different materials (e.g., between the cable insulation and a termination body).

• Geometry changes – Where the cable diameter changes abruptly.

At these points, the stress can be many times higher than the average stress in the cable. This localised stress can exceed the dielectric strength of the material, leading to partial discharge and eventual failure.

4. Types of Electrical Stress

A. Radial Stress
The normal stress in a cable, acting from the conductor outward. This is the stress that the insulation is designed to withstand.

B. Longitudinal Stress
Stress that acts along the length of the cable. This occurs at the end of the cable shield, where the electric field lines bend sharply. This is the stress that terminations and joints must manage.

C. Tangential Stress
Stress that acts parallel to the surface of the insulation. This is particularly important at interfaces between the cable and an accessory. If the tangential stress exceeds the surface dielectric strength, surface tracking (carbonisation) can occur.

D. Switching and Lightning Surges
Transient over-voltages can create stress spikes that are much higher than the normal operating stress. A termination that can withstand the steady-state stress may fail during a lightning strike or switching operation.

5. The Critical Points: Cable Terminations and Joints

The most severe electrical stress occurs at the ends of cables – at terminations and joints. This is because the cable shield ends at these points.

In a continuous cable, the shield confines the electric field inside the insulation. At the shield cut, the field lines are no longer confined; they spill out and concentrate at the cut edge. The peak stress at the shield cut can be 5 to 10 times higher than the average stress in the cable.

This is why terminations require stress control – devices that spread out the electric field and reduce the peak stress to a safe level.

Analogy: Imagine a large crowd of people moving through a wide corridor (the cable). Suddenly, the corridor narrows to a single door (the shield cut). People push and shove, creating intense pressure at the door. Stress control is like installing a series of gradually narrowing passages to ease the transition and reduce the pressure.

6. How Stress Is Controlled

Stress control in cable accessories uses several techniques, often combined:

• Geometric stress control – A stress cone gradually increases the insulation thickness, spreading the voltage drop over a longer distance.

• Refractive (Hi-K) stress control – A material with high dielectric constant (permittivity) placed over the insulation redistributes the voltage, reducing the peak stress.

• Non-linear resistive (NLR) stress control – A material whose conductivity increases with electric field. At high stress, it becomes conductive, effectively extending the shield.

These techniques reduce the stress at the shield cut to a level that the insulation and the surrounding air can withstand.

7. Stress and Material Breakdown

Every insulating material has a dielectric strength – the maximum stress it can withstand before breaking down. For XLPE (cross-linked polyethylene), this is typically around 20–40 kV/mm. For air, it is only about 3 kV/mm (under standard conditions).

If the electrical stress exceeds the dielectric strength:

• In a solid material – A puncture occurs – a permanent hole through the insulation.

• On a surface – Flashover – an arc travels across the surface.

• In a void – Partial discharge – repeated sparks that erode the material.

Partial discharge is particularly dangerous because it does not cause immediate failure, but over time it degrades the insulation until a full breakdown occurs.

8. Factors That Increase Electrical Stress

Several factors can increase the stress on a cable beyond its design limits:

Managing these factors is essential for maintaining cable reliability.

9. Detecting and Measuring Stress

Engineers do not measure electrical stress directly in the field. Instead, they measure its effects:

• Partial discharge – The most sensitive indicator of excessive stress.

• Insulation resistance – A reduction in resistance indicates stress-induced degradation.

• Dielectric loss (tan δ) – An increase in loss indicates insulation heating and stress.

• Thermal imaging – Hot spots may indicate stress-related heating at a connection.

During cable design, stress is calculated using finite element analysis (FEA) software, which models the electric field distribution and identifies areas of high stress.

Electrical stress is not inherently bad. It is the force that allows a cable to transmit power. In a well-designed cable, stress is managed, distributed, and kept within the material's capability. The problem is not stress itself, but uncontrolled stress – stress that concentrates, exceeds the dielectric strength, and causes degradation.

Understanding electrical stress is essential for designing reliable cables, selecting appropriate accessories, and performing careful installations. In the world of high-voltage engineering, stress is a constant companion – but with proper design and installation, it can be kept at a safe level, ensuring that cables continue to deliver power reliably for decades.