A Finite Element Analysis Model for Partial Discharges in Silicone Gel under a High Slew Rate, High-Frequency Square Wave Voltage in Low-Pressure Conditions

At a Glance

Metadata	Details
Publication Date	2020-05-01
Journal	Energies
Authors	Moein Borghei, Mona Ghassemi
Institutions	Virginia Tech
Citations	34
Analysis	Full AI Review Included

Technical Analysis and Documentation: Partial Discharge in WBG Power Modules

Executive Summary

This analysis focuses on the critical reliability challenges identified in the research regarding Partial Discharges (PDs) in silicone gel encapsulation, particularly under the extreme conditions relevant to Wide Bandgap (WBG) power modules used in electrified aircraft propulsion.

Core Challenge: High-frequency, high slew rate square wave voltages, combined with low-pressure conditions (down to 4 psi, simulating cruise altitude), severely accelerate insulation degradation in standard silicone gel encapsulants.
WBG Relevance: The study directly supports the need for advanced materials like diamond, which can tolerate the higher voltages and currents inherent to next-generation WBG devices (SiC, GaN, Diamond).
FEA Methodology: A Finite Element Analysis (FEA) model was successfully employed to dynamically simulate PD inception and extinction criteria based on pressure-dependent material properties.
Quantified Degradation: Low-pressure operation resulted in a significant increase in PD intensity (True Charge magnitude increased by approximately 20%) and a near doubling of the PD event duration.
Material Imperative: The findings underscore that current commercial encapsulants (silicone gel) are inadequate for extreme low-pressure environments, necessitating the adoption of more robust, high-dielectric-strength materials, such as those offered by 6CCVD.
6CCVD Value Proposition: 6CCVD provides the SCD and PCD diamond substrates necessary to build power modules that inherently manage high electric fields and thermal loads, mitigating the PD risks identified in this research.

Technical Specifications

The following hard data points were extracted from the analysis of the high-frequency, high slew rate unipolar square wave voltage applied to the silicone gel/air cavity system.

Parameter	Value	Unit	Context
Applied Voltage (U_max)	18	kV	Unipolar Square Wave
Frequency (f)	10	kHz	High-Frequency Operation
Rise Time	50	ns	High Slew Rate
Minimum Pressure Tested	4	psi	Simulated Cruise Altitude
Dielectric Constant (ε_r) at NTP	2.7	-	Silicone Gel (Normal Temperature/Pressure)
Cavity Diameter	1.2	mm	Air-filled void geometry
PD True Charge Increase (4 psi vs. NTP)	~20	%	Result of low-pressure operation
PD Duration Increase (4 psi vs. NTP)	~2x	-	Result of low-pressure operation
E_inc at 4 psi (Approx.)	7.5	kV/mm	PD Inception Electric Field (Decreases with pressure)
E_ext at 4 psi (Approx.)	0.3	kV/mm	PD Extinction Electric Field (Increases with pressure)

Key Methodologies

The study utilized a sophisticated numerical approach to model the complex Partial Discharge dynamics under transient, high-stress conditions.

Modeling Platform: The core simulation was performed using a Finite Element Analysis (FEA) model implemented in COMSOL Multiphysics (electric current interface, time-dependent mode). This was linked with MATLAB (LiveLink^TM) for algorithm control, conditional checking, and charge calculation.
Geometry and Setup: A 2D-axisymmetrical geometry was used to model two spherical copper electrodes embedded in a cylindrical block of silicone gel (ε_r = 2.7), containing a 1.2 mm spherical air-filled cavity.
Voltage Application: Boundary conditions included setting the high-voltage electrode to the 18 kV, 10 kHz square wave and the ground electrode to zero potential.
Pressure Dependence Integration: The model dynamically adjusted critical parameters—specifically the relative permittivity (ε_r), the PD Inception Electric Field (E_inc), and the PD Extinction Electric Field (E_ext)—based on the applied pressure (p).
PD Criteria:
- Inception: Determined by the streamer inception criterion, which is highly dependent on the pressure-adjusted critical electric field (E/p)_cr.
- Extinction: Determined by the Extinction Electric Field (E_ext), which is a function of the critical electric field and pressure (p).
Charge Quantification: True and apparent charge magnitudes were calculated by integrating the current density flowing through the cavity wall and the ground electrode over the duration of the PD event.

6CCVD Solutions & Capabilities

The research highlights the severe limitations of conventional insulation systems (silicone gel) when paired with high-performance WBG devices in extreme environments like aviation. 6CCVD’s MPCVD diamond materials offer the necessary thermal and electrical robustness to overcome these challenges.

Applicable Materials for High-Reliability WBG Modules

To replicate or extend this research toward developing reliable power modules for electrified aircraft propulsion, 6CCVD recommends the following materials:

Optical Grade Single Crystal Diamond (SCD): Ideal for high-voltage, high-frequency WBG devices (e.g., diamond MOSFETs or SiC/GaN devices mounted on diamond heat spreaders). SCD offers the highest dielectric strength (>10 MV/cm) and thermal conductivity (up to 2200 W/mK), drastically reducing the thermal and electrical stress that leads to PD initiation.
High-Purity Polycrystalline Diamond (PCD) Plates: Recommended for large-format power modules requiring robust insulation and thermal management. PCD offers excellent mechanical stability and dielectric properties, serving as a superior substrate compared to traditional ceramics.

Customization Potential for Advanced Module Design

The paper emphasizes that PD phenomena are strongly dependent on geometry and metallization edges. 6CCVD provides the customization required to engineer solutions that actively mitigate these field stresses.

Research Requirement/Challenge	6CCVD Customization Capability	Benefit to Customer
Large-Scale Power Modules	Custom Dimensions: PCD plates/wafers available up to 125 mm diameter.	Enables scaling of high-density WBG modules for aviation applications.
Precise Insulation Thickness	Thickness Control: SCD and PCD layers available from 0.1 µm up to 500 µm. Substrates available up to 10 mm thick.	Allows precise engineering of insulation barriers and thermal paths for optimal electric field distribution.
Mitigating Sharp Field Edges	Custom Metalization: Internal capability to deposit Au, Pt, Pd, Ti, W, and Cu metal stacks.	Enables the integration of optimized field grading layers or complex electrode patterns directly onto the diamond substrate, reducing localized electric field intensity.
FEA Input Quality	Ultra-Smooth Polishing: SCD surfaces polished to Ra < 1 nm; Inch-size PCD polished to Ra < 5 nm.	Ensures minimal surface defects that could act as PD initiation sites, providing reliable, predictable performance matching FEA models.

Engineering Support

6CCVD’s in-house PhD team can assist with material selection, thermal modeling, and geometric optimization for similar Electrified Aircraft Propulsion and high-density power module projects. We specialize in translating theoretical FEA results into practical, high-reliability diamond solutions.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Wide bandgap (WBG) devices made from materials such as SiC, GaN, Ga2O3 and diamond, which can tolerate higher voltages and currents compared to silicon-based devices, are the most promising approach for reducing the size and weight of power management and conversion systems. Silicone gel, which is the existing commercial option for encapsulation of power modules, is susceptible to partial discharges (PDs). PDs often occur in air-filled cavities located in high electric field regions around the sharp edges of metallization in the gel. This study focuses on the modeling of PD phenomenon in an air filled-cavity in silicone gel for the combination of (1) a fast, high-frequency square wave voltage and (2) low-pressure conditions. The low-pressure condition is common in the aviation industry where pressure can go as low as 4 psi. To integrate the pressure impact into PD model, in the first place, the model parameters are adjusted with the experimental results reported in the literature and in the second place, the dependencies of various PD characteristics such as dielectric constant and inception electric field on pressure are examined. Finally, the reflections of these changes in PD intensity, duration and inception time are investigated. The results imply that the low pressure at high altitudes can considerably affect the PD inception and extinction criterion, also the transient state conditions during PD events. These changes result in the prolongation of PD events and more intense ones. As the PD model is strongly dependent upon the accurate estimation electric field estimation of the system, a finite-element analysis (FEA) model developed in COMSOL Multiphysics linked with MATLAB is employed that numerically calculates the electric field distribution.

Tech Support

Original Source

DOI: https://doi.org/10.3390/en13092152

References

2019 - Accelerated Insulation Aging due to Fast, Repetitive Voltages: A Review Identifying Challenges and Future Research Needs [Crossref]
2018 - PD Measurements, Failure Analysis and Control in High Power IGBT Modules [Crossref]