Understanding Liquid Insulation Breakdown in High Voltage Systems

Liquid Dielectrics: Applications

Used in transformers, circuit breakers, high-voltage cables, and capacitors.
Functions:
- Insulation between live and grounded parts.
- Heat dissipation in transformers.
- Arc quenching in circuit breakers.
Common liquids: Petroleum oils, synthetic hydrocarbons, silicone oils, fluorinated hydrocarbons.

Application of liquid dielectrics in electrical
equipments — Application of liquid dielectrics in electrical equipments

Key Properties of Liquid Dielectrics

Primary Properties:
1. Dielectric strength
2. Dielectric constant (relative permittivity)
3. Electrical conductivity
Other Properties:
- Viscosity, thermal stability, specific gravity, flash point.
Dielectric strength affected by:
- Fine water droplets (0.01% water reduces strength to 20% of dry oil).
- Fibrous impurities (sharply reduce strength).
- Temperature and pressure variations.

Selection of Liquid Dielectrics

Primary Consideration: Chemical stability.
Other Factors:
- Cost
- Space savings
- Environmental susceptibility
- Fire safety (flash point)
- Biodegradability
Impact: Liquid dielectrics enable compact equipment (e.g., 765kV transformers infeasible with air insulation).

Dielectric Properties of Common Liquids

Property	Transformer Oil	Capacitor Oil	Cable Oil	Silicone Oil
Relative permittivity (50Hz)	2.2–2.3	2.1	2.3–2.6	2.7–3.0
Breakdown strength (20\(^{\circ}C\), 2.5mm, 1min)	12kVmm⁻¹	18kVmm⁻¹	25kVmm⁻¹	35kVmm⁻¹
Tan \(\delta\) (50Hz)	1×10⁻³	2.5×10⁻⁴	2×10⁻³	1×10⁻³
Tan \(\delta\) (1kHz)	5×10⁻⁴	1×10⁻⁴	1×10⁻⁴	1×10⁻⁴
Resistivity (\(\Omega \mathrm{cm}\))	1×10¹²–1×10¹³	1×10¹³–1×10¹⁴	1×10¹²–1×10¹³	2.5×10¹⁴
Max. permissible water (ppm)	50	50	50	<40
Acid value (mg/g) KOH	0.2	0.03	0.2	0.05
Saponification (mg/g) KOH	0.01	0.01	0.01	<0.01
Specific gravity (\(20~^{\circ}C\))	0.89	0.89	0.93	1.0–1.1

Pure vs. Commercial Liquids

Pure Liquids:

Chemically pure, structurally simple
Minimal impurities (1 per billion)
Consistent behavior
Higher dielectric strength
Expensive and difficult to maintain

Commercial Liquids

Chemically impure, complex organic mixtures
Erratic behavior; no two samples behave identically
Lower dielectric strength
Cost-effective
Practical for industrial use

Dielectric strength of liquid and its purity
level — Dielectric strength of liquid and its purity level

Breakdown Mechanisms in Liquids

Breakdown theory less understood compared to gases or solids.
Four main breakdown mechanisms:
1. Electronic breakdown (avalanche ionization)
2. Suspended particle breakdown
3. Cavity breakdown (gas bubble formation)
4. Electroconvection breakdown

Breakdown mechanism of liquid dielectrics

Breakdown Mechanism: Electronic Model

Based on avalanche ionization from electron collisions.
Electrons ejected from cathode via:
- Field emission.
- Field-enhanced thermionic effect (Schottky’s effect).
Applies to highly pure liquids, not commercial ones.
Conduction behavior:
- Low field (1kV/cm): Ionic, linear increase.
- Moderate field: Saturation.
- High field (100kV/cm): Rapid increase, leading to breakdown.

Current vs. Electric Field Characteristics

Three Regions:

Linear region (ionic)
Saturation region
Rapid increase region

Current vs electric field characteristics

Electronic Breakdown Mechanism

Process Description

Electrons gain energy from an applied electric field.
Some electrons gain more energy than they lose in collisions, leading to acceleration.
Accelerated electrons gain sufficient energy to ionize molecules, initiating an avalanche.

Threshold Condition

The avalanche begins when the energy gained equals the energy lost during ionization:

\[e \lambda E = C h \nu\]

where:

\(\lambda\): mean free path
\(h \nu\): ionization energy
\(C\): constant

Dielectric Strengths of Pure Liquids

Dielectric Strengths of Highly Purified Liquids
Liquid	Strength (MV/cm)
Benzene	1.1
Transformer Oil	1.0–4.0
Hexane	1.1–1.3
Nitrogen	1.6–1.88
Oxygen	2.4
Silicone Oil	1.0–1.2

Observation

The electronic theory predicts dielectric strength well but overestimates formative time lags compared to observations.

Suspended Solid Particle Mechanism

Introduction

Commercial liquids contain solid impurities (fibers or dispersed particles) with permittivity \(\epsilon_1\) different from the liquid’s \(\epsilon_2\).

Force on Particles

A spherical particle of radius \(r\) in an electric field \(E\) experiences a force:

\[F = r^3 \frac{\epsilon_1 - \epsilon_2}{\epsilon_1 + 2\epsilon_2} E \cdot \frac{dE}{dx}\]

Directed toward higher field stress if \(\epsilon_1 > \epsilon_2\).
Directed toward lower field stress if \(\epsilon_1 < \epsilon_2\).

Particle Force in Limiting Cases

High Permittivity Limit

If \(\epsilon_1 \to \infty\):

\[F = r^3 \frac{1 - \epsilon_2 / \epsilon_1}{1 + 2 \epsilon_2 / \epsilon_1} E \frac{dE}{dx}\]

As \(\epsilon_1 \to \infty\):

\[F = r^3 E \frac{dE}{dx}\]

Behavior in Uniform Field

In a uniform field (e.g., small sphere gap), \(\frac{dE}{dx} \to 0\), so \(F = 0\). Particles remain in equilibrium and are dragged into the uniform field region.

Particle-Induced Breakdown

Mechanism:

Particles with \(\epsilon_1 > \epsilon_2\) cause flux concentration at their surface.
Large particles align to form a bridge across the gap, increasing the field.
If the field exceeds the dielectric strength, breakdown occurs.
Insufficient particles cause local field enhancement, leading to gas bubble formation and eventual breakdown.

Dielectric breakdown due to conducting
particles — Dielectric breakdown due to conducting particles

Particle Motion and Forces

Viscous Force

The viscous force opposing particle motion (Stokes’ relation):

\[F_v = 6 \pi \eta r v\]

where \(\eta\): viscosity, \(r\): radius, \(v\): velocity.

Equating Forces

Balancing electrical and viscous forces:

\[6 \pi \eta r v = r^3 E \frac{dE}{dx} \quad \text{or} \quad v = \frac{r^2 E}{6 \pi \eta} \frac{dE}{dx}\]

Key Insight

Particle velocity depends on:

Particle size (\(r^2\) dependence)
Field gradient (\(dE/dx\))
Liquid viscosity (\(\eta\))

Including Diffusion Effects

Drift Velocity Due to Diffusion

The drift velocity due to diffusion (Stokes-Einstein relation):

\[v_d = -\frac{D}{N} \frac{dN}{dx} = -\frac{k T}{6 \pi \eta r} \frac{dN}{N dx}\]

where \(D = \frac{k T}{6 \pi \eta r}\), \(k\): Boltzmann constant, \(T\): temperature.

Equating Velocities

Equating electrical and diffusion velocities:

\[-\frac{k T}{6 \pi \eta r} \cdot \frac{dN}{N dx} = \frac{r^2 E}{6 \pi \eta} \cdot \frac{dE}{dx}\]

Simplifying:

\[\frac{k T}{r} \frac{dN}{N} = -r^2 E \, dE\]

Cavity Breakdown: Overview

Dielectric strength of liquids depends on hydrostatic pressure.
Higher pressure increases electric strength, suggesting phase change involvement.
Smaller liquid head increases chances of partially ionized gases escaping, leading to breakdown.
Vapour bubble formation is key to the breakdown process.

Processes Leading to Bubble Formation

Gas pockets on electrode surfaces.
Point charge concentration at irregular electrode surfaces causing corona discharge, vaporizing liquid.
Changes in temperature and pressure.
Dissociation of products by electron collisions producing gaseous products.

Electric Field in Gas Bubble

Field in a gas bubble immersed in a liquid of permittivity \(\epsilon_2\):
\[E_b = \frac{3 E_0}{\epsilon_2 + 2}\]
where \(E_0\) is the field in the liquid without the bubble.
Bubble elongates under \(E_0\), maintaining constant volume.
When \(E_b\) equals gaseous ionization field, discharge occurs, potentially causing liquid decomposition and breakdown.

Bubble Elongation and Breakdown

Bubble Dynamics

Bubble elongates in field direction while maintaining constant volume.
Elongation increases field enhancement factor.
Critical field reached when discharge initiates in the bubble.

Breakdown Criterion

Breakdown occurs when:

\[E_b = \frac{3 E_0}{\epsilon_2 + 2} \geq E_{\text{gas breakdown}}\]

Electroconvection Mechanism

Occurs in pure liquids with low electrical conductivity.
Current flow creates space charge, leading to mechanical forces.
Mechanical forces cause fluid motion (electroconvection).
Fluid motion brings impurities to high-field regions, causing breakdown.

Electroconvection Process

Charge injection from electrodes
Space charge formation
Coulomb forces on charge carriers
Fluid motion and turbulence
Impurity concentration in high-field regions
Breakdown initiation

Electroconvection Flow Pattern

Factors Affecting Electroconvection

Promoting Factors:

High electric field
Low viscosity
Charge injection efficiency
Electrode geometry
Temperature increase

Inhibiting Factors:

High viscosity
Uniform field distribution
Low charge mobility
Hydrostatic pressure
Temperature control

Breakdown Prevention Strategies

Liquid Purification:
- Remove water content below 50ppm
- Filter out solid particles
- Degassing to remove dissolved gases
Electrode Design:
- Smooth, rounded electrodes to avoid field concentration
- Proper spacing and geometry
- Surface treatment to minimize roughness
System Design:
- Pressurized systems to prevent bubble formation
- Temperature control
- Circulation and filtration systems

Testing and Monitoring

Routine Tests:

Dielectric strength test
Water content analysis
Dissolved gas analysis (DGA)
Acidity and neutralization tests
Interfacial tension measurement

Monitoring Parameters:

Partial discharge activity
Temperature variations
Pressure changes
Current leakage
Color and appearance

Summary

Liquid dielectrics are essential for high-voltage equipment insulation.
Four main breakdown mechanisms exist:
- Electronic breakdown (pure liquids)
- Suspended particle breakdown (commercial liquids)
- Cavity breakdown (gas bubble formation)
- Electroconvection breakdown (fluid motion)
Practical breakdown is usually a combination of these mechanisms.
Proper maintenance, purification, and monitoring are crucial for reliable operation.
Understanding breakdown mechanisms helps in designing better insulation systems.

Future Developments

Development of biodegradable dielectric liquids
Nano-enhanced dielectric fluids
Advanced diagnostic techniques
Computational modeling of breakdown processes
Smart monitoring systems with AI integration

Introduction to Liquid Dielectrics