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

Executive Summary

This study utilizes Finite Element Analysis (FEA) to model and quantify the impact of low-pressure conditions on Partial Discharges (PDs) in silicone gel encapsulation, specifically targeting Wide Bandgap (WBG) power modules used in electrified aircraft.

Core Problem Addressed: Silicone gel insulation in WBG power modules is subjected to extreme electrical stress (18 kV, 10 kHz square wave, 50 ns rise time) combined with low ambient pressure (down to 4 psi) typical of high-altitude aviation.
Methodology: A coupled FEA (COMSOL Multiphysics) and MATLAB model was used to dynamically calculate electric field distribution and simulate PD events, adjusting key parameters (dielectric constant, inception/extinction fields) based on pressure.
Inception/Extinction Criteria: Low pressure causes the PD inception electric field (E_inc) to increase, while the extinction electric field (E_ext) decreases, fundamentally altering the PD cycle dynamics.
PD Duration Prolongation: The duration of PD events is significantly prolonged at low pressures, primarily because the later extinction time outweighs the slight delay in inception time.
Intensity Escalation: The true charge magnitude of PD events increased by approximately 20% at cruise altitude (low pressure) compared to ground level (NTP), indicating a much higher rate of insulation degradation.
Conclusion for Engineers: Low-pressure environments dramatically intensify and prolong PD activity under high-slew-rate voltage stress, necessitating enhanced insulation design and material selection for reliable WBG operation in aerospace applications.

Technical Specifications

Parameter	Value	Unit	Context
Maximum Applied Voltage (U_max)	18	kV	Unipolar Square Wave
Frequency (f)	10	kHz	Applied Voltage
Rise Time (Slew Rate)	50	ns	High Slew Rate Condition
Minimum Pressure Simulated	4	psi	Aviation Cruise Altitude
Silicone Gel Relative Permittivity (NTP)	2.7	-	Normal Temperature and Pressure
Dielectric Block Height	25	mm	Simulation Geometry
Dielectric Radius	8	mm	Simulation Geometry
Cavity Diameter	1.2	mm	Air-filled Spherical Void
Electrode Material	Copper	-	Spherical Electrodes
PD True Charge Increase (Low P)	~20	%	Compared to ground level (NTP)
PD Duration Increase (Low P)	Nearly Doubled	-	Compared to ground level (NTP)
Air Inception Parameter (E/p)_cr	24.2	V Pa^-1m^-1	Streamer Inception Criterion

Key Methodologies

The study employed a dynamic Finite Element Analysis (FEA) approach coupled with physical models to simulate Partial Discharge activity under varying pressure conditions.

FEA Implementation: The model was built using the Electric Current (ec) interface in COMSOL Multiphysics, operating in a time-dependent mode, linked with MATLAB for algorithmic control, conditional checking, and data analysis.
Geometry and Boundary Conditions: A 2D-axisymmetrical model was used, featuring two spherical copper electrodes embedded in silicone gel, separated by a 1.2 mm air-filled spherical cavity. Boundary conditions included setting the high-voltage electrode to the square wave input and the ground electrode to zero potential.
Pressure Dependence Modeling: The impact of pressure (p) was integrated by adjusting three critical parameters:
- Relative Permittivity (ε_r): Modeled using the Owen and Brinkley expression (related to the Tait equation) for liquid dielectrics, showing a direct relationship with pressure.
- Inception Electric Field (E_inc): Calculated using the streamer inception criterion, which is inversely related to pressure (E_inc increases as p decreases).
- Extinction Electric Field (E_ext): Modeled as a function of the critical electric field and pressure, showing a direct relationship (E_ext decreases as p decreases).
PD Event Simulation: The algorithm checks for PD inception (E_cav(t) > E_inc) at large time steps (Δt_H). Upon inception, the cavity conductivity (σ_cav) is instantaneously increased to its maximum value (σ_cav,max), and the time step is reduced (Δt_L, nanosecond order) to accurately capture the transient discharge event.
PD Extinction and Charge Calculation: The simulation monitors for the extinction criterion (E_cav(t) < E_ext). True charge magnitude is calculated by integrating the current density flowing through the cavity wall and ground electrode over the duration of the discharge event.

Commercial Applications

The research findings are directly applicable to the design, reliability assessment, and material selection for high-power density systems operating under extreme environmental conditions, particularly those leveraging WBG technology.

Electrified Aircraft Propulsion (EAP) Systems: Provides critical data for designing insulation systems for high-voltage motor drives and power converters in aircraft, ensuring reliability when operating at low ambient pressures (high altitude).
High-Voltage Wide Bandgap (WBG) Modules: Essential for packaging SiC and GaN modules (which operate at high frequency and high slew rates) to mitigate accelerated aging caused by intensified PD activity in low-pressure environments.
Aerospace and Defense Power Systems: Applicable to any high-power electronic system deployed in vacuum or near-vacuum conditions, such as space vehicles, high-altitude drones, or specialized military equipment.
Insulation Material Development: The model serves as a tool for evaluating alternative encapsulation materials (beyond silicone gel) and geometric field control techniques (e.g., nonlinear field-dependent conductivity layers) to better withstand the combined stress of high slew rate voltage and low pressure.
Reliability and Lifetime Prediction: The quantified relationship between pressure and PD intensity/duration allows engineers to more accurately predict the operational lifetime of power modules in variable-altitude applications.

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]