A Can-Ortiz

Z Valdez-Nava

L Laudebat

S Diaham

Epoxy-Based SiC Composites with Non-Linear Electrical Properties for Field Grading Applications

Different methods of dispersion for fabrication of SiC/epoxy resin composites were studied in order to obtain an homogeneous filler dispersion. Composites with different filler concentration were also fabricated in order to develop the nonlinear electrical conductivity. The filler concentration was between 0-30 vol%. The thickness of composites was 300 μm. The composites were characterized using a current-voltage technique with an applied voltage between 35-12500 V. The effects of the filler concentration in the nonlinear behavior of materials is presented.

I. INTRODUCTION

In high voltage (HV) applications the insulating material is one of the weakest elements of the electrical system, leading to reliability loss [START_REF] Pascoli | Experiences with Online Partial Discharge Diagnoses on Turbogenerators[END_REF]. It is known that the rate of aging depends on the nature of the applied stress. The most important stress types to which insulation is subjected are electrical, thermal, and mechanical stresses [START_REF] Hoof | PD diagnostics on rotating machines. Possibilities and limitations[END_REF][START_REF] Kimura | The Role of Microscopic Defects in Multistress Aging of Micaceous Insulation[END_REF][START_REF] Srinivas | Multifactor Aging of HV Generator Stator Insulation Including Mechanical Vibrations[END_REF]. When high electric stress is applied to most polymers, charges are injected and accumulated within them, distorting the internal electric field distribution. Consequently, insulation degrades because of space charge accumulation, partial discharge, and electrical treeing across the whole material, which may lead to breakdown [START_REF] Farahani | Partial Discharge and Dissipation Factor Behavior of Model Insulating Systems for High Voltage Rotating Machines under Different Stresses[END_REF][START_REF] Farahani | Partial Discharge and Dielectric Response Behaviour of Insulation Systems for High Voltage Rotating Machines under Electrical Stress[END_REF]. One of the key subjects in HV engineering is the control of the electric field strength. The aim is to achieve the lowest possible electrical field strength at a fixed system voltage [START_REF] Eigner | 50 Years of Electrical-Stress Control in Cable Accessories[END_REF]. One effective technique to control the distribution of the electric field is the nonlinear stress control. It uses materials whose resistivity varies with the applied voltage [START_REF] Ghorbani | HVDC Cable Systems-Highlighting Extruded Technology[END_REF]. These materials can be developed using a base material, which is usually an insulating polymer with an additive that provides nonlinear functionalities. Common additives used are SiC, ZnO, carbon black, or blends of different oxides such as BaTiO3, TiO2, SiO2, Fe3O4, and mica [START_REF] Eigner | 50 Years of Electrical-Stress Control in Cable Accessories[END_REF][START_REF] Christen | Nonlinear Resistive Electric Field Grading Part 1: Theory and Simulation[END_REF][START_REF] Song | Electric Field Control in DC Cable Test Termination by Nano Silicone Rubber Composite[END_REF]. Finite element method simulations showed that the application of a nonlinear resistive layer at the metallization edge of power electronic substrates significantly reduces the electric field at the critical point between the copper metallization, ceramic substrate, and silicone gel or polyimide encapsulation [START_REF] Donzel | Nonlinear Resistive Electric Field Control for Power Electronic Modules[END_REF].

In general, nonlinear resistive field-grading materials have a field-dependent conductivity, σ(E), which increases strongly from a low conductivity value, σ(0), to a high value in a narrow field region ΔE near the switching field (𝐸 ! ) [START_REF] Christen | Nonlinear Resistive Electric Field Grading Part 1: Theory and Simulation[END_REF][START_REF] Boucher | Study of the Influence of Nonlinear Parameters on the Efficiency of a Resistive Field Grading Tube for Cable Termination[END_REF][START_REF] Rivenc | An Overview of Electrical Properties for Stress Grading Optimization[END_REF]. The value of 𝐸 ! indicates where field grading becomes active [START_REF] Christen | Nonlinear Resistive Electric Field Grading Part 1: Theory and Simulation[END_REF]. Efficient nonlinear resistive field grading needs a sufficiently large nonlinearity coefficient, α [START_REF] Christen | Nonlinear Resistive Electric Field Grading Part 1: Theory and Simulation[END_REF]:

𝛼 = " #$(&) " #$(() = 1 + " #$()) " #$(() (1)
The final properties of the composite (switching field and nonlinearity coefficient) depend on the characteristics of the filler, such as the filler concentration, size, morphology, and composition. Due this background, we present the fabrication and characterization of composite materials formed by an epoxy matrix and SiC particles, studying the effect of the filler concentration in the nonlinear properties of the composites.

II. MATERIALS AND METHODS

A. Materials

For composite manufacturing, silicon carbide micropowder (SiC) with a diameter < 1 μm, purity 99+%, crystal type 85% β was utilized as filler. The two component epoxy resin (ER) Polytec EP 630 from was used as the matrix material.

B. Fabrication of homogeneous materials with different filler dispersion methods

In order to study the impact of the fabrication method on the particle dispersion, SiC/ER composites with a filler concentration of 10 vol% were prepared using different dispersion methods. For all the process the particles were dried at 300 °C for 1 h and after kept at 100 °C for one day.

Process 1: The dried fillers were mixing with the epoxy resin part A in a concentration of 10 vol% using a planetary vacuum mixer with a vacuum of 1.0 kPa and 800 rpm for 3 min, then 1.0 kPa and 1800 rpm for 1 min. After, 10 wt% (with respect to part A) of epoxy resin part B (hardener) was added and mixed using the same process in the planetary vacuum mixer.

Process 2: The dried fillers were dispersed on epoxy part A with a filler concentration of 10 vol% using the shear mixer at 500 rpm for 15 min. Then, 10 wt% of epoxy resin part B was added and mixed using the planetary vacuum mixer with vacuum of 1.0 kPa and 800 rpm for 3 min, then 1.0 kPa and 1800 rpm for 1 min.

Process 3: The dried fillers were dispersed on epoxy part A with a filler concentration of 10 vol% using the ultrasonic probe with a power of 950 watts, amplitude of 40 %. Then, 10 wt% of epoxy resin part B was added and mixed using the planetary vacuum mixer with vacuum of 1.0 kPa and 800 rpm for 3 min, then 1.0 kPa and 1800 rpm for 1 min. The effective time of ultrasound was 15 min, with a cycle of 5s on/15s off.

For all the process, samples with a thickness of 300 μm and diameter of 44 mm were manufacturing using a pressing process. The composites were fabricated using a temperature of 100 °C, a pressure of 150 N/cm 2 for a time of 55 min. Finally, the samples were post-curing in an oven at 120 °C for 1 h.

C. Fabrication of homogeneous materials with different filler concentration

In order to study the impact of the filler concentration, SiC/ER composites with different filler concentrations were prepared. The particles were dried at 300 °C for 1 h and after kept at 100 °C for one day. Then, the dried fillers were dispersed on epoxy part A with filler concentrations of 0, 5, 10, 15, 20 and 30 vol% using the ultrasonic probe with a power of 950 watts, amplitude of 40 %, 15 min of effective time with 5s on/15s off cycle. After, 10 wt% of epoxy resin part B was added and mixed using the planetary vacuum mixer with vacuum of 1.0 kPa and 800 rpm for 3 min, then 1.0 kPa and 1800 rpm for 1 min. After, samples with a thickness of 300 μm and diameter of 44 mm were manufacturing using a pressing process. The composites were fabricated using a temperature of 100 °C, a pressure of 150 N/cm 2 for a time of 55 min and post-curing in an oven at 120 °C for 1 h.

D. Morphological and electrical characterization

In order to analyze the dispersion and distribution of fillers in the epoxy resin, scanning electron microscopy (SEM) was used.

In order to describe the electrical behavior of composites and to find the nonlinearity, the current-voltage (I-V) dc characterization was carried out. Samples of 300 µm were metalized with gold using a configuration of three electrodes (see Fig. 1). The diameter of top electrode was 33 mm and the guarded electrode was 25 mm.

For I-V characterization, a dc voltage source "FUG HCN 35-3500" was used for electrical characterization between 10-3500 V and a dc voltage source FUG HCN 350-12500 for electrical characterization between 1.0-12.5 kV. The current was measured using a picoammeter Keithley 6485. The connection was made in a Faraday cage. The voltage was applied by steps with logarithmic increment, using 20 points per decade. For each step, the voltage was applied for 300 s (polarization). Then, the corresponding current for the applied voltage was measured. After, the voltage was set to 0 V for 300 s (depolarization). Then, the voltage was set to the next value and the process was repeated. After I-V measurements, the electric field 𝐸 and conductivity 𝜎 for each sample were calculated, and the graph of 𝜎 as a function of 𝐸 was plotted. Finally, the switching field 𝐸 ! and the nonlinear coefficient 𝛼 were calculated.

III. RESULTS AND DISCUSSIONS

A. Effect of the fabrication method on filler distribution on composite materials

In order to compare the filler dispersion difference between the dispersion made with the planetary mixer, the shear mixer and ultrasonic probe, the SEM images for 10 vol% SiC/ER composites for process are presented in Fig. 2. It can be observed in Fig. 2a y b that composites fabricated with planetary and shear mixer presented SiC agglomeration with a considerable size. On the other hand, for composites prepared with the ultrasonic probe (Fig. 2c) no agglomerate was observed; for that reason, composites with different filler concentrations were prepared with this method.

B. Influence of filler on the nonlinear properties of composite materials

In order to describe the influence of SiC concentration on the electrical behavior of composites, the 𝜎 as a function of 𝐸 is presented in Fig. 3 for different filler concentrations. The nonlinear behavior of composites was analyzed, the switching field and the nonlinear coefficient were calculated and presented in Table 1. As we can observed in Fig. 3 and Table 1, for epoxy resin material the conductivity is constant for low electric field. When the electric field arrive around 12.7 kV/mm the conductivity behavior changes and the nonlinearity begins. As it can be observed, after the switching, field the electrical conductivity increases as a function of electric field applied with a nonlinear coefficient of 2.39. When 5 vol % of SiC is added to epoxy resin, it can be observed that the switching field reduce to 9.4 kV/mm and the nonlinear coefficient is bigger than for epoxy material. As it can be observed in Table 1, the switching field reduces when the filler concentration increases. The lowest switching field obtained was 4.21 kV/mm for 30 vol% composite. This behavior is consistent with results reported for materials fabricated with SiC as fillers and silicone rubber (SiR) or ethylene propylene diene monomer as matrix [START_REF] Du | Field-Dependent Conductivity and Space Charge Behavior of Silicone Rubber/SiC Composites[END_REF][START_REF] Du | Surface Charge Behavior of Silicone Rubber/SiC Composites with Field-Dependent Conductivity[END_REF][START_REF] Li | Nonlinear Conductivity and Interface Charge Behaviors between LDPE and EPDM/SiC Composite for HVDC Cable Accessory[END_REF]. The dependence of nonlinear properties with the filler concentration is explained by Gao et al. [START_REF] Gao | ZnO Microvaristors Doped Polymer Composites with Electrical Field Dependent Nonlinear Conductive and Dielectric Characteristics[END_REF], when the filler size increases, the probability to form conducting paths increases, and the contact resistance decreases; thus, the switching field of composites decreases. On the other hand, for nonlinear coefficient it can be observed that the value is between 2.39 and 6.40, where the lowest value correspond to epoxy resin and the highest value correspond to 30 vol % SiC/ER material. As it can be observed, the nonlinear coefficient increases slightly when the concentration of SiC increases. It can be also observed that the nonlinear coefficient for epoxy resin is bigger than the coefficient reported for SiR where the value was ~1.0 [START_REF] Du | Field-Dependent Conductivity and Space Charge Behavior of Silicone Rubber/SiC Composites[END_REF][START_REF] Du | Surface Charge Behavior of Silicone Rubber/SiC Composites with Field-Dependent Conductivity[END_REF].

IV. CONCLUSIONS

Three methods of filler dispersion for fabrication of composite materials were studied: Planetary mixer, shear mixer and ultrasonic probe. Composites prepared with ultrasonic probe showed the composites with the best dispersion between the three methods analyzed. The influence of SiC concentration on the nonlinear electrical behavior of composites were studied for composites fabricated with filler concentration between 0-30 vol%. The switching field for the composites reduces when the SiC concentration increases and it was between 12.74 and 4.2 kV/mm. The nonlinear coefficient increases slightly when the concentration of SiC increases and it was between 2.39 and 6.40. ACKNOWLEDGMENT ??????????

Figure 1 .

 1 Figure 1. Three electrode connections for I-V characterization.

Figure 2 .

 2 Figure 2. SiC distribution for 10 vol% SiC/ER composites fabricated with different methods. a) Planetary mixer b) shear mixer and c) ultrasonic probe.

Figure 3 .

 3 Figure 3. Electrical conductivity as a function of electric field for composite materials with different SiC concentrations.

TABLE I NONLINEAR

 I PARAMETERS FOR COMPOSITES

	SiC vol%	𝛼	𝐸 ! (kV/mm)
	0	2.39	12.74
	5	3.95	9.44
	10	5.56	9.49
	15	5.93	7.91
	20	5.94	5.15
	30	6.40	4.21


Youcef Kemari
email: youcef.kemari@irt-saintexupery.com

Guillaume Belijar
email: guillaume.belijar@irt-saintexupery.com

Lionel Laudebat
email: laudebat@laplace.univ-tlse.fr

Sombel Diaham
email: sombel.diaham@laplace.univ-tlse.fr

Zarel Valdez-Nava

Partial Discharge Inception Voltage: Precise and Robust Numerical Estimation Based on Extensive Dielectric Spectroscopy Measurements

Keywords: partial discharges, PDIV, dielectric spectroscopy, modeling, aeronautical environment 0

This paper provides a robust experimentalsimulation approach in predicting the Partial discharge inception voltage (PDIV) for aeronautical applications. First, two polymers used as insulators in aeronautic components have been selected in this work, a polyimide and a polyetheretherketone. To study the electrical behavior of these materials, extensive dielectric spectroscopy measurements are carried out for different electric fields, temperatures and frequencies (E, T, and f). Then, a needleplane configuration is adopted for PDIV modeling using finiteelement method (FEM). As the model is strongly dependent upon the accurate estimation of the electric field, dielectric characterizations results are integrated in simulations to improve the precision of calculations. Thereafter, the PDIV can be estimated with the aid of Townsend's theory. Finally, a comparison between measured and computed PDIV values is presented and discussed.

I. INTRODUCTION

With the concept of "More Electrical Aircraft", substantial efforts are being paid on increasing the voltage in the onboard systems. For instance, in the Airbus A350, a 230/400 VAC system has been adopted [START_REF] Billard | Non-Intrusive Partial Discharges Investigations on Aeronautic Motors[END_REF]. To enable hybrid propulsion or full-electric aircraft, even higher voltage will be required to maintain high power density. However, high electric fields combined with high operating temperatures and with low ambient pressure will increase the risk of PD occurrence in aeronautical cables and connectors [START_REF] Sili | Polyimide lifetime under partial discharge aging: effects of temperature, pressure and humidity[END_REF].

On the other hand, experimental measurement of PD is not trivial to be performed in every test configuration and does not always provide sufficient information about the location of the discharge. Thus, a lot of work is still needed to make significant progress in PD modeling and prediction [START_REF] Van De Steen | Partial discharge detection, Experimental-Simulation Comparison and actual limits[END_REF]. Moreover, dielectric properties of insulating materials can impact the distribution of the electric field and thus, the occurrence of the PD. These material properties strongly depend on temperature, frequency and also on the electric field magnitude itself.

In the framework of HYBELEC project at IRT Saint Exupéry, the case study considered in this paper for PDIV calculations and measurements consists in an insulating film deposited between a needle and a flat electrode. Two materials used in standard aeronautical components are chosen here; a polyimide (PI/FEP) and a polyetheretherketone (PEEK), to examine the proposed PDIV estimation approach. Also, it can be found in many models existing in the literature that the dielectric constant εr' and the conductivity sAC are generally defined from suppliers datasheets and their variations with temperature, frequency and electric field are not always considered [START_REF] Van De Steen | Partial discharge detection, Experimental-Simulation Comparison and actual limits[END_REF][START_REF] Pin | Ageing study in aircraft electromechanical chain: systems modeling for property evolution monitoring[END_REF][START_REF] Parent | Determination of Partial Discharge Inception Voltage and Location of Partial Discharges by Means of Paschen's Theory and FEM[END_REF]. In some cases, this can affect the accuracy of the electric field calculation and thus, the estimation of PDIV. This could lead to suboptimal insulation system and overweight or unreliability. In light of this, this study puts forth the investigation of material properties impact on electric field distribution and PDIV by proposing an extensive measurements of polymers dielectric properties under different constraints (E, T, and f). According to the literature, high AC voltage dielectric spectroscopy measurements up to 1414 Vrms have never been carried out on the studied materials here few times before. The obtained data are then used through a numerical model based on for precise PDIV estimation at 50 Hz. Also, simulated and experimental results are compared.

II. PROCEDURE

A. Materials

The studied polyimide material, under the trade name Kapton FN ® , is intended for aeronautic cables manufacturing. The polyimide, was provided in the form of tapes with a thickness of 30 µm. It consists of 25 µm of pure polyimide (Kapton HN ® type) covered on each side by 2.5 µm of Fluorinated ethylene propylene (FEP) layer. Besides, PEEK circular shaped samples were provided with a thickness of 400 µm and a diameter of 30 mm. This material is used in different aeronautical connectors.

B. High voltage-frequency domain dielectric spectroscopy

A broadband dielectric analyzer (Novocontrol Alpha-A, Montabaur, Germany) was used for εr' and sAC measurements from 20 °C up to the maximum rated temperature (260 and 200 °C for PI and PEEK respectively). Measurements were performed thanks to a high voltage amplifier (Novocontrol HVB-4000, Montabaur, Germany) that allows to apply voltage up to 1414 Vrms in the frequency range from 1 to 10 3 Hz. Also, all samples are metallized by sputtering on both sides with 30 nm-thick gold layer of diameter 10 mm to ensure perfect electric contact. Prior to measurements, samples were dried in an oven at 150 °C for 48 h.

C. PDIV measurements

In aeronautical components, partial discharges may occur in defects or air-filled voids or gaps between high voltage conductors and the insulation material. To simulate such a structure and the PD process, we adopted a needle-plane configuration in the experiment with the tip of the needle in contact with the sample. The schematic diagram of the experimental setup for PD measurements under AC voltages is shown in Fig. 1. After being dried, the samples were mounted in an in-house made test cell between a needle electrode, with an edge curvature radius of 1 mm, and a grounded flat electrode. Also, a 30 nm-thick gold layer was deposited on the other side of the sample in order to ensure the absence of air layer between the ground and the sample. After, the test cell was placed in an oven that can span from room temperature to 210 °C which corresponds to the maximum operating temperature of the test cell.

The 50 Hz high voltage was applied to the needle by a PD free test transformer (delivering up to 5 kVpeak and a maximum of 100 mArms) associated to an AC power source (CFS330 Adaptive Power Systems, Taiwan). For PD detection, two nonintrusive sensors were placed on the cable connected between the test cell and the ground: a Jack-SMA connector with a capacitive effect and a wideband fast current transformer (Bergoz FCT-016-1.25, France). The acquisition tool used is an oscilloscope (Keysight DSOS204A, France) with a sampling rate of 20 GSa/s and numerical bandwidth of 2 GHz. All PDIV measurements were performed in peak detect mode with frequency sampling fixed at 5 GS/s. PDIV values were measured 5 times at each temperature for both materials.

D. Electric field simulation

The same needle-plane configuration considered in this paper for PD experiments was analyzed by FEM with the aid of COMSOL Multiphysics ® (5.5). We used the AC/DC module (Electric current) to compute the potential and the electric field lines. First, the electrode geometry was extracted from the real object and then drawn with the insulation material and the flat grounded electrode as shown in Fig. 2. Due to the symmetry of this configuration, it can be also modeled in a 2D-axisymetrical format. Thereafter, the entire domain has been discretized during the mesh process into triangle type finite elements of size between 0.5 and 20 µm. To increase the number of elements and thus to improve the precision of the solution, a refinement of the mesh, as shown in Fig. 3, has been implemented in the region of great interest where PDs firstly ignite. Dielectric properties of the studied PI/FEP and PEEK were successfully defined by interpolating values obtained from dielectric measurements.

Whereas εr' and sAC of air are considered unchanged with the modification of temperature (1 and 10 -16 S.m -1 respectively).

E. AIRLIFT

PDIV has been computed thanks to a specific numerical software named "pArtial dIscharge Risk evaLuatIon soFTware" (AIRLIFT). AIRLIFT is based on Paschen's law established from Townsend's theory in air between electrodes. Paschen's law gives the voltage Vb corresponding to the initiation of the PD in gases between parallel conducting plates as [START_REF] Parent | Determination of Partial Discharge Inception Voltage and Location of Partial Discharges by Means of Paschen's Theory and FEM[END_REF]:

(1)

PI/FEP ) 1 1 ( ; . . . ) ln( A ln C with d) ln(p C d p B b V g + = + =
where p is the gas pressure in Torr, d is the distance in cm, A and B are the coefficients that depend on the considered gas and temperature and g is the Townsend's secondary emission coefficient. The previous parameters were set from literature as: A = 15 (Torr.cm) -1 , B = 365 V. (Torr.cm) -1 [START_REF] Sili | Polyimide lifetime under partial discharge aging: effects of temperature, pressure and humidity[END_REF] and g = 4.8x10 -4 [START_REF] Collin | About the relevance of using Paschen's criterion for partial discharges inception voltage (PDIV) estimation when designing the electrical insulation system of inverter fed motors[END_REF]. For a given set of environmental parameters, the computed electric potential is used to estimate PDIV. In the current work, PD measurements and simulations are performed at the atmospheric pressure (1,013 bar).

III. RESULTS AND DISCUSSIONS

A. Dielectric Spectroscopy Results

We present in Fig. 4 In addition, the curves of the conductivity as a function of the frequency deviate at 210 °C towards a form of a horizontal plateau at low frequencies. This can be referred to the displacement of charge carriers at the interfaces within the bulk of the polyimide (interfacial or Maxwell-Wagner-Sillars (MWS) polarization phenomenon). In fact, MWS polarization is generally characterized by a slight increase in permittivity (De'r <0.3) [START_REF] Khazaka | Broadband dielectric spectroscopy of BPDA/ODA polyimide films[END_REF].

As the MWS phenomenon is thermally activated, we can observe the progressive shift of εr' and sAC towards higher frequencies as the temperature increases to 260 °C. At this high temperature, we observe clearly a drastic increase in the permittivity (De'r >10) at low frequencies accompanied by a very significant increase in the conductivity which becomes frequency independent (slope of 0). These evolutions represent the electrical signature of the polarization at the electrodes (EP) also reported in the literature for polyimides [START_REF] Khazaka | Broadband dielectric spectroscopy of BPDA/ODA polyimide films[END_REF][START_REF] Diaham | Dielectric properties of polyamideimide[END_REF]. This phenomena results from the accumulation of thermally excited charge carriers in the vicinity of the polymer/electrode interface.

Moreover, we observe that the curves of εr' and sAC are shifted towards higher frequencies when the applied field increases at 260 °C as indicated by blue arrow in Fig. 4 (a). Hence, it is important to point out that EP phenomenon can be also electrically activated by high electric field values (>32 kV.mm -1 ) when the temperature is sufficiently high as found in this study. In other words, the mobile charge carriers have more energy to move rapidly toward the vicinity of the electrodes under enhanced electric fields.

As far as PEEK is concerned, Fig. 5 shows the evolution of εr' and sAC versus the different measuring parameters (E, T, and f). We found that the obtained permittivity values are relatively high compared to those reported elsewhere (3.1< εr'<4.5) [START_REF] Wei | High dielectric constant dipolar glass polymer based on sulfonylated poly(ether ether ketone)[END_REF]. This can be attributed to the process of the chemical synthesis of PEEK and to the nature of fillers injected into the polymer matrix [START_REF] Wei | High dielectric constant dipolar glass polymer based on sulfonylated poly(ether ether ketone)[END_REF].

Given the thickness of the samples (400 µm), the applied electric field here remains relatively low (maximum value of 3.3 kV.mm -1 ). Consequently, no significant impact of the electric field has been found here on PEEK properties. However, we can clearly distinguish the influence of temperatures higher than 150 °C which corresponds practically to the glass transition temperature. Below 150 °C, the dielectric behavior of PEEK as a function of frequency is typical involving a linear increasing of the conductivity and a quasi-constant permittivity attributed to the to the efficient rotation of highly polar side groups such as COOH and SO2 [START_REF] Wei | High dielectric constant dipolar glass polymer based on sulfonylated poly(ether ether ketone)[END_REF].

On the other hand, εr' and sAC begin to increase at low frequencies at 150 °C. The origin of this evolution is probably attributable to an intrinsic MWS interfacial polarization. This increase with temperature continues up to 200 °C where we can notice a variation in permittivity Dεr' > 1 (+15 to 30 % of values obtained at 20 °C, depending on the frequency) and an increase in conductivity of half a decade with respect to that measured at 20 °C. In addition, plateau region independent of frequency start to appear above 150 °C at low frequencies indicating the activation of DC conduction.

B. Electric Field Computation Results

At atmospheric pressure of 1 bar (750 Torr), the Paschen's minimum for air is about 325 Vpeak for a distance of about 10 µm (pressure-distance product of 0.75 Torr.cm) [START_REF] Sili | Polyimide lifetime under partial discharge aging: effects of temperature, pressure and humidity[END_REF]. For this reason, we are interested in the area where air gaps between the needle and the material have values at the same order of magnitude that the Paschen's minimum. In this section, Fig. 6 and7 present the distribution of the computed electric field in the case of PI/FEP and PEEK respectively as the temperature changes.

Contour plots with 9 levels are used for better visualization of the electric field changes. Indeed, contour plots display the maximum electric field results on a series of colored regions where each contour interface indicates a surface where the stress is at a constant level (specified by the color legend in V.m -1 ). For the simulation, an electric potential of 700 Vpeak at 50 Hz was applied on the needle electrode. Comparing the temperature dependence of the dielectric response of both materials (Fig. 4 and5) with results shown is Fig. 6 and7, the changing of the electric field distribution with temperature can be assigned to the significant changes of the insulation properties. It seems that the electric field in the polyimide bulk becomes more localized in the vicinity of the needle tip as the temperature rises (as indicated by the blue arrow). Besides, the enlargement of the red region (as highlighted by the red arrow in Fig. 6 and7) implies the enhancement of the electric field in the air and thus the acceleration of free electrons. Consequently, PDIV becomes lower for the same field line length.

C. Comparaison Between Experiments and Simulations

This section provides a comparison between experimental PDIV values and those obtained with numerical models. The first model (Model A) is based on extensive dielectric measurements on PI/FEP and PEEK. A second model (Model B) was implemented for the same geometry by defining dielectric properties as given in suppliers' datasheet (Table I). The PDIV values obtained by both models are plotted as a function of the temperature and compared with experimental results as shown in Fig. 8. In the case of PI/FEP material, a great agreement is found between computed and measured PDIV. The maximum deviations between average experimental and computed PDIV can be found in Table II. It can be seen that the deviation with experiments are slightly lower in the Model A based on dielectric measurements. Besides, results found by both models A and B are practically similar up to 210 °C, which is in agreement with dielectric measurements results shown in Fig. 4. In fact, we have found that PI/FEP properties changes under 50 Hz are not significant with temperatures up to 210 °C. Also, the drastic variations of εr' and sAC were assessed above this temperature essentially at low frequencies.

On the other hand, the simulated PDIV of Model A is kept with a variation below 6.9 % compared to experimental values in the case of PEEK. Moreover, the computed PDIV values in this Model are always found below measured ones, close to the minimum experimental values. However, the predicted results with Model B (based on values given in Table I) are significantly higher than measured ones. This can be explained by the important difference between dielectric characterizations values presented in this work and those can be extracted from the literature and datasheets.

IV. CONCLUSION

This work presents a robust numerical estimation of PDIV for aeronautical applications using FEM models linked with a numerical solver. The proposed approach is based on HV dielectric spectroscopy characterizations under various voltages, temperatures and frequencies on PI/FEP and PEEK. Spectroscopy results show that dielectric properties of PI/FEP are significantly affected at 260 °C where a conduction process and space charge accumulations in the vicinity of electrodes occur simultaneously with a large effect on the dielectric response. It has been found that this process can be enhanced as well by high electric field values. Concerning PEEK material, properties changes begin to take place in the temperature range from 150 to 200 °C, mainly due to intrinsic MWS interfacial polarization process. The integration of those results in our model led us to obtain more precise predictions of PDIV as a function of temperature for a needle-plane configuration compared to a second model based on fixed values extracted from the literature or datasheets.

The approach presented in this work can be the groundwork to study more complex geometries of real aeronautical components such as cables and connectors with multiple materials. Also, the changes of dielectric properties at high temperature, eventually under HV, could modify the electric field distribution in the component leading to more PD risks.

Fig. 1 .

 1 Fig. 1. Schematic diagram of the PD experimental setup.

Fig. 2 .

 2 Fig. 2. Geometry of the needle-plane model.

Fig. 3 .

 3 Fig. 3. Meshing strategy represented in the 2D-axisymetrical format.

  the variations of the dielectric constant εr' and the AC conductivity sAC of PI/FEP versus frequency and electric field at different temperatures. For temperatures below 210 °C, no significant change in the two properties was observed as a function of temperature. Besides, Fig.4(b) shows the quasilinear evolution of the conductivity as a function of frequency following a slope close to unity. This last result indicates that the dielectric behavior of the PI/FEP is mainly related to the mechanism of dipolar polarization[START_REF] Khazaka | Broadband dielectric spectroscopy of BPDA/ODA polyimide films[END_REF]. On the other hand, we can observe that both properties are affected by the increase of the electric field at all temperatures. This effect is more noticeable in sAC curves as shown in Fig.4(b).

Fig. 4 .

 4 Fig. 4. (a) Dielectric constant and (b) AC conductivity of PI/FEP as a function of electric field, temperature and frequency.

Fig. 5 .

 5 Fig. 5. (a) Dielectric constant and (b) AC conductivity of PEEK as a function of electric field, temperature and frequency.

Fig. 6 .

 6 Fig. 6. Contour plot of the electric field in needle-PI/FEP case study under a 50 Hz voltage of 700 Vmax : comparaison between 20 and 260 °C results.

Fig. 7 .

 7 Fig. 7. Contour plot of the electric field in needle-PEEK case study under a 50 Hz voltage of 700 Vmax : comparaison between 20 and 200 °C results.

Fig. 8 .

 8 Fig. 8. PDIV variation with temperature and comparaison between Model A, Model B and experiments.

TABLE I .

 I MATERIALS PROPERTIES GIVEN IN DATASHEETS

	Material	Dielectric constant	Conductivity (S.m -1 )
	PI/FEP	3.1	3.5 x 10 -12
	PEEK	3.9 at 1 MHz	2.8 x 10 -12

ACKNOWLEDGMENT

This work has been carried out in the framework of HYBELEC project at IRT Saint Exupéry with the financial support of the French Agence Nationale de la Recherche (ANR), Safran SEP, Airbus, Nexans and Souriau. The authors would like to thank Patrick RYBSKI (Nexans), Kossi BAYODA (Souriau), Thomas HÄHNER (Nexans), and Alain PHILIPPE (Souriau) for the provision of study materials and associated data.


Trung Trong

Le1

Rabih Khazaka1

Zarel Valdez Nava2

Guillaume Belijar1

Lionel Laudebat2

Sombel Diaham2

Process optimization for heterogeneous capacitive grading materials by voltage and time monitoring

In the aerospace field, transportation electrification is considered as one of the main solutions that allow the reduction of greenhouse gas levels in the air and slow down the climate change. One of the ways that can allow to reach this goal for electrified systems is the voltage increase and reduce the volume of system onboard. This approach induces consequently induce very high electrical constraints on the insulation materials used in the power conversion systems. These local high electric fields can cause premature failure, by partial discharge activity and insulation breakdown. In order to efficiently reduce the electrical stresses, the design of new system of stress-control encapsulation seem be promising it does not impact the volume of the power module and has a negligible impact on the overall mass.

An approach based on the use of low filler ratio composites and the monitoring of the particles (SrTiO3, BaTiO) density by the electric potential to tailor around critical areas where the electric field is high has been validated on simple configuration between two adjacent electrodes

Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable.. In addition, this approach has been used successfully to apply the FGM on various substrate electrodes of a power module by using a removable electrode in front of the substrate Erreur ! Source du renvoi introuvable.. In this paper, the impact of the applied electric potential and its duration will be presented in order to evaluate and optimize the process to allow apply an electrodeposition with a homogenous thinness of stress-control layer.

I. INTRODUCTION

The trend toward higher power density has been present in all electrical domain, for decades and it projected to continue faster because of asking of reduction of greenhouse gas levels in the air and slow down the climate change. Especially in aerospace field, all systems are much more constrained by their mass. In the development of the more electrical aircraft (total electrical aircraft, hybrid aircraft and hydrogen aircraft), one of main challenge is to increase the voltage and/or reduce the volume of converters. Among increase of power density, also higher voltage semi-conductor devices are becoming readily available, such as Si-based Insulated Gate Bipolar Transistor (IGBT) or SiC-based Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable. and the voltage of available active components keeps increasing steadily over time. These devices are asking a new system of encapsulation material with a superior electrical insulation property could be working stable.

However, this approach will induce extremely high electrical constraints on the insulating materials used in the electrical systems, including the ones closest to the active semiconductors in the power modules. At the heart of the power module, these high electrical fields are strengthen by the geometry imposed by the design, parts fabrication, assembly and packaging methods. One of the most critical regions will be at the junction of two insulating materials, namely the ceramic substrate and the encapsulation, with the metallic track on top of the ceramic substrate. This region is known as the "triple point", and since the metallization has a sharp geometry, the local electric fields are non-homogeneous and divergent Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable.. Treeing can propagate within the encapsulation or along the interface with the DBC substrate towards the grounded counter electrode Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable.. This triple point acts as a fringing electrical field region where discharges can incept, then progressively electrically degrade the encapsulation material Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable.as like partial discharge activity, up to finally breakdown of insulation in power modules and shutdown the system. The Fig. 1 shows a schematic cross section view of that type of power module with number of respective triple points highlighted in red circles. In the later strategy, beside finding new materials formulations, it is possible to lower local electrical fields at the triple point by modifying locally the electrical properties. This is known as electrical stress-control or field-grading. This can be achieved by applying different layers of materials with different intrinsic properties or by building a Functionally Graded Material (FGM). In latest publication, our method with using of electrodeposition phenomena allows to build FGM in high electric field regions of power module. Firstly, the described method was success cover on the high positive potential of two copper electrodes on top of a DBC. The results show an increasing of withstand voltage on track-totrack surface breakdown by at least 70% when compared to a neat epoxy encapsulation Erreur ! Source du renvoi introuvable.Erreur ! Source du renvoi introuvable.. To more nearly the real power module, two methods was proposed to cover the main triple points in a more complex tested DBC structured and one was validated Erreur ! Source du renvoi introuvable.. One removable electrode was added on top of DBC substrate with distance de 5mm during the FGM application by electrodeposition. This external electrode could be removed prior to the curing process of the polymer composite. All of electrode was cover by a homogenous thickness of accumulation layer. Evolution of thickness was observed qua-similar with the case of using two parallel electrodes. In order to evaluate and optimize this process, the main aim of this paper will present our experimental of electrodeposition with various of applied voltage. Then the results allow us not only to optimize the process but also understand more the mechanic and phenomenal of electrodeposition.

III. EXPERIMENTAL

Our process of electrodeposition is based on applying an electrical field on two parallel electrodes with the mixture of particles and epoxy resin is poured between. For process optimization, two copper parallels electrodes placed by 1mm using insulating spacer are used. The two electrodes are attached on a glass by using a transparent epoxy resin. (Photo For all experiments, a di-glycidyl ether of bisphenol F (DGEBF) thermosetting epoxy resin system (EP 630, Polytec PT GmbH) was used. The hardener is an amine type with a ratio of 10:1 (resin: hardener). After curing, the epoxy has a density of 1.23 g/cm3. Strontium titanate (SrTiO3) particles with a density of 5.11 g/cm3 were added at 10 vol% and mixed in a planetary mixer. The polyhedral-shaped particles have an average diameter of 600 nm. Microscopic observations during the electric field application are done from the transparent glass side using Keyence digital microscope and the current is measured between the two electrodes with a Keithley 2410 Sourcemeter. The impact of the applied electric potential on the composite with filler ration fix was evaluated under various voltages of 67V, 125V, 250V and 500V. In other hand, a higher tension of 1500V was tested with the two parallel electrodes and in a real substrate DBC.

III. VARIOUS EVOLUTION OF FILLED RESIN AND OPTIMAZATION PROCESS A. Various evolution of composite resin under various field.

For composites with low particle concentration (10 %), the fluid "turbulence" takes place at early time after the polarization in almost all the regions between the two electrodes. The electrostatic force attracts the particles (negatively charged) at the high voltage electrode to form a dense particles layer. The shear stress induced at the interface between the dense layer and the fluid in motion can remove some particles from the dense layer and hence acts in an opposite way to the electrostatic forces. This limits the electrodeposited layer growth rate and its final thickness. During the time, the horizontal limit of the turbulent motion region (green bars) is decreased gradually in an opposite way to the dense layer thickness where no turbulent flow appears (red bars) until reaching a quasi-equilibrium after about 1400s. The impact of applied electric field on the evolution of gradient material was evaluated and the recorded mages under after 1200s and 2700ss are presented in Fig. 3. Thus, the thickness of the dense layer increases faster for higher applied electric potential indicating that electrostatic forces became more dominant at higher voltages. Oppositely, the horizontal limit of the turbulent motion region in green bars is decrease faster with higher applied potential and inversion. We also noted as the higher external field as the particles concentration in the accumulated layer (red bars) is higher and in the resin in motion (green bars) is lower. The resin in motion after 2700s applying of 500V/mm shows an extremely low particles concentration as figure 3.d. The results show that the same behavior with all levels of potential is observed in the composite for the various applied electric potentials. In all cases, the fluid turbulence takes place at early time after the polarization in almost all the regions between the two electrodes. The thickness of the dense layer increases faster for higher applied electric potential indicating that electrostatic forces dominate the shear stress induced by the liquid motion at higher voltages and inversion.

Otherwise, the faster turbulent under higher field than 500V/mm applied potential seems cannot achieve a homogeneous layer.

B. Quasi-stabilization at interface of electrodeposited layer.

In the latest publication, the accumulation of particles on the higher potential was explicated because of influence of some phenomenal of electrophoresis, electrophoresis, electroosmosis and electrohydrodynamic (EHD). This explication is not enough to explain the quasi-stabilization state after 25min.

Indeed, a layer of lower concentration of particles in comparison with homogenous filled resin at interface of accumulated layer was observed and get our attention. In this layer the particles were moving different without the turbulent.

A quasi-stabilization stage with some particles is pulled to accumulation layer and compacted when some other is teared to back the moving resin. This phase seems be an equilibrium between the accumulation and the dispersion by the two different forces, one is electrophoresis force and other is because of monodisperse concentration. In fact, the accumulation is due by electrophoresis where particles are displaced within a liquid medium under the application of an electrostatic force (i.e. the Coulomb force) on the compound. charged particles present an arrangement of charges in the interface called the electrical double layer (EDL). In other hand, at the accumulation layer with higher concentration particle crowding produces hydrodynamic interactions between particles, resulting in significant positive deviation.

Many models have been proposed to describe the concentration dependence of the relative viscosity of concentrated suspensions. One of the most useful expressions is the semi-empirical equation of Krieger and Dougherty for monodisperse suspensions. The relative viscosity variation as function of filler ratio according to Einstein and Krieger-Dougherty was presented in some Erreur ! Source du renvoi introuvable.. In fact, charged particles present an arrangement of charges in the interface called the Electrical Double Layer (EDL). As two particles approach each other, the overlapping of double layers leads to long-range, electrostatic repulsive forces. The distortion of the EDL by the shear field leads to an increase in the viscosity due to increased energy dissipation. This effect was first considered by Smoluchowski and is called the primary electroviscous effect Erreur ! Source du renvoi introuvable..

C. Influence of various field electrodeposion.

The normalized conductivity (conductivity/conductivity t0) and the dense electrodeposited layer thickness under the various extension are presented in Fig. 4. We can see that the normalized conductivity during the first minutes followed by an increase or a stabilization of the value. For the thickness of accumulation layer, the evolution shows an increase during the first minutes followed by a quasi-stablization of the layer thickness (from 14min to 25min) until the end of the process after 45min. In the applied electric potential evaluated range, the time to reach equilibrium is not dependent of the external applied field and the dense layer is thicker for higher potentials at the end of the process (45min). During the phase where thickness increases, the electrostatic force that attracts the particles to the high voltage electrode dominates the electro hydrodynamic shear stress induced by the motion of the fluid. On the other hand, the quasistabilization phase reflects a quasi-equilibrium between the two controversial forces. The quasi equilibrium between the two forces can be due to the decrease of the viscosity of the fluid once a part of the particles are deposited on the high voltage electrodes. Accordingly, the viscous forces in the liquid are reduced and the flow motion related to electro hydrodynamics mechanisms is promoted. Hence, shear stress at the interfaces due to the fluid motion became sufficiently high to remove particles that are attracted by electrostatic forces. A second assumption based on the decrease of the internal field in the region between the dense electrodeposited layer and the ground electrodes can also contribute to the explanation of the quasi-equilibrium between the two opposed forces. Since dense particle layer is more resistive than composite with low density and particles are negatively charged, the electric field in the region in motion is reduced during the increase of the thickness of the dense layer. Once a certain level is reached, the electrostatic attractive forces will be more significantly reduced than the shear stress induced by the liquid motions and an equilibrium between the two forces is reached.

Finally, the growth rate of the dense layer on the high voltage electrode as function of the external electric field for a composite with 10%vol filled ratio is presented in Fig. 5. The values fit well with a polynomial form: y=-4e-7x2+0.0006x. C. Process optimization.

The growth rate of the dense layer on the high voltage electrode increases as the voltage increases. Depending on the targeted final thickness of the dense layer and the process time constraint, the voltage can be choose in the range between 67V and 500V (for 1mm space between the two electrodes) and the time period between 60 and 1400s. However, in order to avoid sharp variation of the accululation layer in the composite, the use of high fields (>250V/mm) for long periods (> 1000s) is not recommended. The higher tension of 1500V AC isn't recommended to avoid danger of thermal runaway because of high injection current. This thermal runaway in the case of apply the electrodeposition for a DBC substrate is present in Fig. 6. IV. CONCLUSION Our process of electrodeposition allows to apply a homogenous layer of stress-control surrounding high field region around the triple point. This paper presented the mechanic and electrodeposition phenomenal principal of our process with a clear explication.

Depending on the targeted final thickness of the accumulation layer, the voltage can be choose in 67V and 500 during a period between of 60s and 1400s fit with the equation ; y=-4e-7x2+0.0006x. Futher works need to be carried out the evaluation of process using the removable electrode with optimization time and voltage, verify the gain in performance obtained these FGM in a real module power.

Fig. 1 .

 1 Fig. 1. Cross section of power electronic module with various triple junction of gel-ceramic-electrode

Fig

  Fig. 2: a) Test vehicle with two parallel electrodes for process optimization. The distance between the two electrodes is fixed to 1mm. b) Installation of camera to observe the electrodeposition.

  Fig 3:: Recorded images of evolution instants for composites with 10 vol% under 67V, 125V, 250V, 375V, 500V after 1200s and 2700s.

Fig. 4 :

 4 Fig. 4 : Normalized conductivity and dense layer thickness evolution as function of time for various applied electric potentials.

Fig. 5 :

 5 Fig.5: Growth rate of the dense layer during the first 10 min as function of external applied potentials.

Fig. 6 :

 6 Fig.6: Growth rate of the dense layer during the first 10 min as function of external applied potentials.