Daniel Roger

Gabriel Vélu

Sonia Ait-Amar
email: sonia.aitamar@univ-artois.fr

Sylvain Babicz

HIGH TEMPERATURE MACHINES: A COMPARISON BETWEEN CERAMIC-COATED WIRES AND ANODIZED ALUMINUM STRIPS

Keywords: High temperature machine, Inorganic insulation, Thermal equivalent circuits

The paper proposes a comparative approach of two wire technologies for making compact coils able to operate in high temperature (HT°) machines. The first technology is based on ceramic-coated round wire associated with a HT° cement. The second one uses anodized aluminum strips. The advantages and drawbacks of the two technologies are compared, considering the machine global performances at high temperatures.

I. INTRODUCTION

Electrical machines are widely used in industry and transports; they perform efficient and accurate controls of complex mechanical systems. This advantage is however limited by their maximal running temperature, which is directly linked to the thermal limits of the polymers used in the electrical insulation system (EIS) and the expected lifetime [START_REF] Aymonino | Degradation and dielectrics measurements of rotating ma-chines insulation at high temperature (200-400°C)[END_REF][START_REF]Standard EIC 60216-1 "Matériaux isolants électrique, Propriétés d'endurance thermique[END_REF][START_REF] Amendola | Alumina filled silicone nanocomposites for electrical insulation of power rotating machines[END_REF][START_REF] Komeza | Calculations of heat transfer coefficient and equivalent thermal conductivity for induction motors thermal analysis[END_REF]. Consequently, classic electrical machines cannot work in very hot environments, where the temperature exceeds 200 °C as, for instance, near an aircraft turbine. Design of machines able to work permanently under high internal temperatures (over 250°C), is nevertheless possible with inorganic EIS made without any polymers [START_REF] Iosif | Assessment and improvements of inorganic insulation for high temperature low voltage motors[END_REF][START_REF] Iosif | An insulation solution for coils of high temperature motors (500 deg. c)[END_REF]. These high temperature machines are designed with rigid coils made with ceramic coated wires and HT°c ements used as potting materials. Such coils are able to withstand 500°C. For HT° machines, the design process is very different than for classical ones, because the inorganic coils are rigid objects. The magnetic core must be adapted to rigid coils. Distributed windings with complex end-winding connections are very difficult to build.

Generally speaking, the rated power of an electrical machine depends on the rotor speed, the flux density in the air-gap and the current density in active conductors [START_REF] Chatelain | Traité d'électricité, d'électronique et d'électrotechnique Machines électriques[END_REF][START_REF] Pyrhonen | Design of rotating electrical machine[END_REF]. The same principles apply for HT° machines, but with higher current densities because of the higher internal temperature gradients. The heat flows are more intense for the same motor sizes. The comparative study relies on a simplified thermal model, which computes the temperature of the critical parts of the machine.

II. COMPARISON PRINCIPLE OF THE WINDING TECHNOLOGIES

The assessment of the power density differences due to the two HT° insulation technologies is performed considering two identical Permanent Magnet Synchronous Machines (PMSM). The rotors are equipped with the same surface-mounted high-performance magnets. The only difference is the stator coil technology. Both machines are made using the widespread "24 teeth / 20 poles" structure for high power density applications [START_REF] Tovar-Barranco | Comparison of permanent magnet synchronous machines with concentrated windings and different rotor configurations[END_REF]. Each stator tooth receives a prefabricated coil. All coils have the same number of turns. The 24 stator coils form 3 phases of 8 coils connected in series. The winding directions are chosen to get a dominant 20-pole rotating field in the air-gap, when a balanced 3-phase system feeds the machine. Fig. 1 shows the stator of the machine made with ceramic-coated wire coils embedded in a HT° potting cement. The general aspect of the stator made with anodized aluminum strips is very similar. This figure shows also the details of two consecutive inorganic coils on stator teeth. The coils have a rectangular cross section. The slots are cuboid and the teeth faces are parallel. Consequently, the slots have a specific shape with a larger width in their bottom that cannot be used by the coils. The small additional teeth in the bottom of the slots yield a better thermal contact between the coils and the magnetic core. Another solution will be to make not cubic coils but with a trapezoidal section, to feel all the slot. In this case pair and unpair coils are different and more complexe to wind previously. Fig. 2 shows the details of the first tested technology for building inorganic HT° coil made with round ceramic-coated wire. The turn distribution presented in Fig. 2 is schematic; it represents the worst case. In a real coil, the external layer is wound with a tensile force on the wire. The turns apply a mechanical pressure that bends the inter-layer insulation mica film. Therefore, the real thermal contact between layers is slightly better than in the model. For this example, a two layer 19-turn coil is considered. The mica interlayer insulation must be added because of the poor electrical performances of the ceramic coating [START_REF] Roger | Concentrated winding machines fed by PWM inverters: Insulation design helped by simulations based on equivalent circuits[END_REF]. The ground insulation is also made of mica. A potting HT° cement immobilizes the turns and the mica. The hardening thermal cycles of the cement are made in a steel mold. Therefore, the coils are rigid objects with a good mechanical accuracy given by the mold and with a high mechanical hardness. They are placed on stator teeth with a small clearance of more or less 0.1mm. The slot is closed with a non-magnetic thin steel wedge. A HT° textile strip is placed between the rigid coil and the wedge for getting a mechanical clamping. The alternative HT° technology is presented in Fig. 3. The coil is made with anodized aluminum strip. The alumina layer obtained by the anodization process is 5 µm thick [START_REF] Babicz | Dielectric Characteristics of an Anodized Aluminum Strip[END_REF]. The position of each turn is very different; the voltage distribution between turns is much better [START_REF] Roger | Voltage distribution in inorganic insulation windings for high temperature motors[END_REF]. The mica ground insulations and the potting cement are identical.

III. BASIS OF THE COMPARISON

For comparing the two inorganic coil technologies, it is supposed that the coil external geometries and the number of turns are identical. Same stators are modeled with the same teeth and slot sizes. The internal temperatures are computed for identical external temperatures and the same global current. The reference is the round wire technology. The coil is made of 19 turns of ceramiccoated wire. For high temperatures, the copper must be protected by a nickel layer of 40µm. The metal diameter is 1.6mm. The coating thickness is in the range of 10-15µm. It is also supposed that an extra space between adjacent turns exists, because of the difficult winding with a brittle ceramic insulated wire. Consequently, the distance between the metal surfaces of two adjacent turns is estimated to 200µm. With these hypotheses the coil thickness is ℎ = 4.3

; the height of the coil is ℎ = 18.6 , taking into account the thickness of the mica ground insulation. The global cross section of this rectangular coil is 80 for an effective conducting section of 38.2

. The feeling ratio is estimated to 47%, which suppose a careful winding.

When the alternative anodized-aluminum technology is used to build the same coil, it requires a careful potting. Therefore, it is necessary to have a sufficient space between the mica insulation and the anodized-aluminum strip, which must be filled by the HT°c ement and is estimated to 200µm. Consequently, the strip height is 17 . The cumulated thickness of the 19 strips is 3.18 . Therefore, the anodized-aluminum strip thickness must be 167µm with the alumina insulation and 157µm without. The global conducting section is 50

, the feeling ratio of the coil is better (62,5%).

IV. THERMAL COMPARISON

The simplified thermal equivalent circuit of Fig. 4 is used for estimating the motor internal temperatures. The model is based on four simplifying hypotheses:

-The thermal flows between nodes are proportional to the temperature differences; -Only 4 temperatures in critical parts are considered: the rotor magnets (M), the windings (W), the stator core (Iron-I) and the motor frame (F); -The cooling system is a standard fan that creates an external airflow through the fins of the stator frame; -The direct heat exchange between coils is neglected.

The magnets are glued on a metallic rotor. Consequently, a part of the magnet losses (PM) flows directly outside the motor by the metallic shaft (GMA). The other part crosses the air-gap toward the stator (GMW and GMI). The only difference between both coil technologies is the red part of Fig. 4. The aluminum strip technology yields a radial thermal flow in aluminum, higher than the first technology, where the heat flow must cross the cement potting. The red part of the thermal equivalent circuit must be detailed at the turn level.

Generally speaking, for the classical polymer insulation technology, the rated current is obtained when the maximum temperature is reached at the hottest point of the winding insulation. This widespread reasoning is based on a simple fact: if the insulation breaks at the hottest point and a cumulative phenomenon destroys all of the insulation. However, the temperature of the hottest point depends on the life expectancy of the machine estimation are performed using the standards bases on Ahrenius law.

For inorganic insulation technologies, the problem is very different because the potting cement can withstand very high temperatures, over the Curie point of the iron core or aluminum melting point [13]. The rated current must be defined with new concepts. For permanent magnet machines, the rated value can be defined by the maximum temperature of magnets, which is more or less 350°C [START_REF] Liu | Thermal stability and performance data for smco 2:17 high-temperature magnets on ppm focusing structures[END_REF]. The rated value can also be defined considering the decrease of the machine efficiency. A more detailed analysis is proposed for comparing the two proposed organic technologies.

A. Equivalent circuit for round wire technology

The detailed thermal equivalent circuit of the coil is presented in Fig. 5. Each turn corresponds to a node associated to a power source defined by the corresponding joule losses. The node B correspond to the slot back and T the center of a tooth. Each turn is inside the HT° cement, the heat flow must cross this cement. The thermal model of a single turn considers the cuboid part of cement around the conducting wire, which is the source. Fig. 6 presents the temperature map in the cement and a schematic representation of the power flow for a single wire represented by eight thermal resistances, one per half a face. They have the same value, they are computed considering that the temperature of the copper wire is 1°C, while the border temperature is fixed to 0°C. The thermal flux presented in Fig. 7 is computed by a 2D finite element method, for the HT° cement and for the standard polymer technology. The 8 thermal resistances are computed by integrating the heat flow on half a face and for the average length of a turn considering an imposed temperature difference of 1°K for the simulation. The thermal resistances of the flat parts that correspond to the mica ground and inter-layer insulation are calculated and added for computing all the thermal resistances of Fig. 5; results are given in Table 1.

B. Equivalent circuit for the anodized aluminum strip technology

The heat flow toward the slot back in the aluminum coil is very different. The model divider each strip in three parts. The associated nodes are defined at the center of each part as shown in fig. 8. The thermal equivalent circuit is presented in Fig. 9. The horizontal thermal resistances R1 represent the thermal transfer through the Al2O3 insulating layer. The vertical ones correspond to the heat transfer inside the aluminum strip. Each node is associated to the corresponding joule loses. The heat flow crosses the tooth insulation represented by R T, for the tooth and the 19 conductances R B . Table 2 gives the thermal resistances.

C. Temperature computation

A PSpice simulator computes the temperature in each node of the equivalent circuits from the joule losses in each turn and the thermal resistances, using the algorithm of fig. 10. ) (1 = The current IT is the same for all the turns, but the turn resistances RT depend on their temperatures. The stator core temperature depends on the whole machine thermal balance, the comparison of coil technologies is not easy in this global context. For comparing easily the HT° coil technologies, the slot back temperature (node B) is arbitrary fixed to 100°C. The algorithm stops for a temperature difference 1 < °.

Results are given in Fig. 11. The horizontal axes represent the turn position and the vertical axes the temperatures or losses. Fig. 11 is dawn for 40 =

; current densities are 20A/mm 2 in the copper and 15A/mm 2 for the anodized aluminum strip because of the better volume filling. The larger temperatures of turns 11-19, corresponding to the external layer of the coil, shows that the heatflow crosses the inner layer. The temperature differences between turns are lower for the cement potting because of its better thermal conductivity. Despite higher joule losses in aluminum turns, the turn temperatures are lower with a negligible difference between turns. A more detailed analysis shows also a very small temperature difference inside aluminum strips, the difference between nodes L, M and H (fig. 8) are under 1°C, because of the high thermal conductivity of aluminum.

For 40A, the temperature at the hottest points remains compatible with standard class H polymer insulation systems. However, this technology cannot be used for higher currents. The same algorithm is used for computing temperatures and losses for 80A and for inorganic technologies, because the temperatures are too high for polymers. Results are given in Fig. 12. It can be seen that temperatures are much higher than for 40A but they remain compatible with the capabilities the potting cement and alumina. These results show that, despite of higher joule losses, the coils made with anodized-aluminum strips can be used for very high currents.

V. CONCLUSION

For prefabricated coils placed on rectangular teeth, the anodized aluminum technology offers a better filling than round wires. Consequently, the current density is lower for the same stator current. The thermal transfer between the turns and the stator core is better and, despite, the higher joule losses due to the higher resistivity, the average temperatures are similar for the two HT°t echnologies. With these technologies, it is possible to work with much higher currents, for the same coil volumes that increase strongly the power density when the magnetic core temperature remains at the same value by an efficient cooling system.

Fig. 1 .

 1 Fig. 1. Stator of a HT° PMSM made with 24 rigid inorganic coils. The picture was made before closing the slots with metallic wedges.

Fig. 2 .

 2 Fig. 2.First technology: ceramic-coated round wire and HT° potting cement.

Fig. 3 .

 3 Fig. 3. Alternative technology: anodized aluminum strip and HT° potting cement.

Fig. 4 .

 4 Fig. 4. Simplified thermal equivalent circuit of a PMSM at steady state (PM=magnet losses, PW=winding losses, PI=Iron losses).

Fig. 5 .

 5 Fig. 5. Detailed thermal equivalent circuit for the coil made with a round wire.

Fig. 6 .

 6 Fig. 6. Round wire thermal simulation for estimating the 8 thermal resistances characterizing the thermal flow.

Fig. 7 .Fig. 9 .

 79 Fig. 7. Power flow through a face of the cuboid-shaped cement around the round wire. The wire temperature is set to 1°C and the cuboid faces to 0°C.

Fig. 10 .

 10 Fig. 10. Computation algorithm with a PSpice simulator.

Fig. 12 .

 12 Fig. 12. Temperature and joule losses in every turn for 80A.

Table 1 .

 1 Thermal resistances for the coil made with round wire.

	Thermal resistances (°K/W)		Polymer potting	HT° Cement potting
	Turn-to-turn through the inter-layer insulation	R1	6.6	2.56
	Turn-to-turn in the same layer	R2	3.3	0.29
	Turn to tooth	R3	5.5	7.1
	Turn to slot-back	RB	5.5	7.1
	Tooth center -Slot-back	RT	0.51

Table 2 .

 2 Thermal resistances for the coil made with aluminum strip.

	Thermal resistances (°K/W)		HT° Cement potting
	Strip-to-strip for 1/3 of the strip	R1	3.15e-3
	Inside the strip between nodes	R2	1.17
	1/3 strip to tooth	RTL,M or H	1.03
	Strip to slot-back	RB	55.1
	Tooth center -Slot-back	RT	0.51

Fig. 8. Position of nodes for the coil made with anodized aluminum strip.

Fig. 11. Temperature and joule losses in every turn for 40A.


S Langlois
email: sabine.langlois@renault.com

Augmented reality versus classical HUD to take over from automated driving: an aid to smooth reactions and to anticipate maneuvers

Sabine Langlois, Soualmi Boussaad

I. INTRODUCTION

In the near future, technology advances will allow the realization of cars equipped with level 3 automation, named Limited Self-Driving Automation. The NHTSA defines this level as "enabling the driver to cede full control of all safetycritical functions under certain traffic or environmental conditions and in those conditions to rely heavily on the vehicle to monitor for changes in those conditions requiring transition back to driver control. The driver is expected to be available for occasional control, but with sufficiently comfortable transition time." [START_REF] Anhts | U.S. Department of Transportation Releases Policy on Automated Vehicle Development[END_REF]. Works on determining the necessary time speak of a minimum of 10s [START_REF] Merat | Transition to manual: Driver behaviour when resuming control from a highly automated vehicle[END_REF]. But it can be feared that 10s is too short a time for the driver to gain complete situation awareness [START_REF] Endsley | The out-of-the-loop performance problem and level of control in automation[END_REF], especially if the driving situation is complex [START_REF] Merat | Transition to manual: Driver behaviour when resuming control from a highly automated vehicle[END_REF] e.g. when the driver has to make a lane change in order to avoid an obstacle [START_REF] Hoc | Human-Machine cooperation in car driving for lateral safety : Delegation and mutual control[END_REF] [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF] or to reach a desired lane (e.g. highway exit). In an automated driving (AD) mode, the driver is out of the driving loop and may be distracted by another task [START_REF] Feldhütter | How the Duration of Automated Driving Influences Take-Over Performance and Gaze Behavior[END_REF], so that, at the takeover request (TOR), he has to, first, switch his attention towards this TOR, understand the current driving situation, choose the appropriate actions and finally act on the vehicle. It can be said that the transition phase from AD to MD is a critical phase for NHTSA level 3 systems from a human factors point of view, which is why we focus on this item.

Head-up displays (HUD) help the driver keep his eyes on the road [START_REF] Pauzié | Head up display in automotive: a new reality for the driver. Design, user experience, and usability: interactive experience design[END_REF]. Augmented reality-(AR) HUDs, also called contact analog HUDs, allow direct superimposition of the information onto the real spatiotemporal context, which helps the driver detect, analyze and react appropriately [START_REF] Pauzié | Head up display in automotive: a new reality for the driver. Design, user experience, and usability: interactive experience design[END_REF]. As such, we assume that AR can help the driver when he is taking over, to better rebuild his situational awareness and adopt a safer driving behavior. As it is observed that the driver's actions, when resuming the control of the vehicle, are brutal (there is over-compensation on steering and pedals [START_REF] Liang | Combining cognitive and visual distraction: Less than the sum of its parts[END_REF]), we also assume that AR could reduce this effect, and thus enhance driving comfort.

To check our hypotheses, we compare three conditions: manual mode (MD), transition from AD to MD with AR, transition from AD to MD with a reference HMI placed on a classical HUD.

We conduct a simulator study and prepare scenarios where the driver has to take over within 10s to make a lane change following navigation instructions. As driving is a highly dynamic activity, we consider that the driver gets information about his environment and is thus able to anticipate the evolution of the situation through his actions [START_REF] Chalandon | Conscience de la situation: invariants internes et invariants externes[END_REF]. We expect to get insights about the driver's situational awareness thanks to his driving and ocular behaviors, and thanks to verbatim collected by explicitation interviews [START_REF] Vermersch | L'entretien d'explicitation[END_REF].

We first present our testing method, then describe, analyze and discuss the results of driving behavior I. METHOD

A. Experimental setup

The study is conducted on a Renault driving simulator, CARDS. It is a full vehicle mock-up with a 240° field of view. The driver is seated at 2.2m from the main screen. CARDs has already been used for AR HUD studies [START_REF] Halit | Head motion parallax effect on driving performances using an AR-HUD: simulation study on Renault's CARDs simulator[END_REF]. Due to technical problems, it is not possible to use both eye tracker and stereoscopic projection at the beginning of the testing; we therefore use a monoscopic projection. SCANeR® studio software [START_REF] Oktal | SCANeR™studio[END_REF] is used to run the driving simulation.

We develop a driving supervisor able to perform high speed automated driving on the highway, without lane change [START_REF] Soualmi | Automationdriver cooperative driving in presence of undetected obstacles[END_REF]. Its level of automation corresponds to NHTSA level 3. To take over, the driver is required to push on button A located on the steering wheel (see Fig 1). As soon as button A is pushed, the driver is in MD. If the driver does not push on button A but places his hands on the steering wheel, the system will move on to MD at the end of the transition phase that lasts 10s; if not, it will perform the minimum risk B. Soualmi is with IRT SystemX, 8, Avenue de la Vauve -CS 90070, 91127 Palaiseau Cedex (e-mail: Boussaad.soualmi@irt-systemx.fr) Augmented reality versus classical HUD to take over from automated driving: an aid to smooth reactions and to anticipate maneuvers 1 * S.Langlois, B.Soualmi maneuver, which consists of braking the vehicle to a complete stop. During the transition phase, the system cruises as in AD mode.

In MD, the driver is assisted by two informative systems: a distance warning that measures the security distance from the vehicle in front in the same lane, and a blind spot warning that indicates the presence of a car in the blind spot.

The HMI supervisor receives information from the simulated sensors and from the driving supervisor. Its rules define what should be displayed to the driver, how and when.

The driver receives visual information from two HUDs: the "classical HUD" dedicated to classical information like on-going speed and TOR message, and one dedicated to AR ("AR HUD"). These HUDs have a surface respectively equal to 4*15° and to 9*15° (from 0 to -9° vertically, where 0° is the horizon). The classical HUD images are generated by a dedicated pico-projector (Optoma ML 1500e), chosen for its high luminosity and contrast. The AR-HUD is simulated by a virtual HUD, a module of SCANeR® especially developed for our project [START_REF] Langlois | Virtual head-up displays for augmented reality in cars[END_REF]. It simulates the image produced by a real HUD (field of view, projection distance, color, transparency).

The side mirrors are an additional way to provide information to the driver, to warn about a car present on the side of the car. Sounds are also emitted, especially one for takeover, that lasts during the whole transition phase and is designed to sound more and more urgent.

A touch screen placed in the middle of the dash board is used to play a game, Sonic Dash, during AD mode. This game was chosen as non-driving-related activity because it requires a constant visual and cognitive attention from the player who has to help a character run and jump along a tricky road.

We can collect data about the driver's behavior from an eye tracker, a hand sensor on the steering wheel, and from different vehicle performance sensors that will be described in chapter III.

Figure 1 shows the components of the configuration to be tested.

A. HMI design

Two HMI conditions are compared: with and without AR. The following table (table I) describes the objects highlighted by AR in both MD and AD modes. We follow Eyraud's recommendations [START_REF] Eyraud | Allocation of visual attention while driving with simulated augmented reality[END_REF] based on Wickens's model of the allocation of visual attention [START_REF] Wickens | Pilot task management: testing an attentional expected value model of visual scanning[END_REF]: as AR adds saliency, it should be associated only with task-related cues to avoid distraction.

In AD, all surrounding vehicles are highlighted to show the driver that the system detects and takes into account the traffic around him: the lead vehicle is differentiated so that the driver can understand on which vehicle the longitudinal control is carried out. A previous expert testing showed that the highlight of the car ahead should be thin in MD, so as not to interfere with the driving scene, and that the highlight in AD could be thicker, so as to be quickly detected when the driver briefly interrupts his non-driving-related activity to check that the system has a correct comprehension of the surrounding traffic, and also to increase the difference between AD and MD, thus limiting confusion between modes.

To highlight the lane to take, we decide to show the driver which constraint to take into account rather than impose a trajectory to follow. We choose the iconic representation of the signs used along roads to warn about dangerous curves (see Fig 4). One virtual sign is placed every 14m. This design respects the recommendations given by Pfannmüller et al. [START_REF] Pfannmüller | A comparison of display concepts for a navigation system in a contact analog headup display[END_REF] (better use a "boomerang" type design than arrows; limit animations). Lorenz [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF] shows that an AR design that highlights the place not to go, in red color (the obstacle forward in his study) produces inappropriate driving strategies (braking instead of steering action). Our highlight rather shows the envelope of the possible trajectories. Ng-Thow-Hing et al. in [START_REF] Ng-Thow-Hing | User-centered perspectives for automotive augmented reality[END_REF] also recommend providing drivers with better information to improve their driving decisions rather than explicitly telling them what to do. The AR signs are masked by vehicles (see Fig 4) because we consider their priority as lower.

The following picture (Fig 2 ) shows, in AD, the TOR phase with AR. The AR signs for the exit to take (chevronshaped blue and white signs) and for the lead vehicle (green trapezoid) can be seen. Vehicles on adjacent lanes would be highlighted with a white rectangle beneath. On the classical HUD, the current speed and speed limit, navigation and takeover messages can be seen.

As soon as the driver has pressed button A, he is in MD and HMI is the following (Fig 3 ), with an AR U-shaped line under the car ahead (here orange to warn the driver that he should decelerate).

Without AR, the whole information is located on the classical HUD. For AD, we developed a birds eye view ( Contrary to Lorenz [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF] whose baseline HMI was an icon in the instrument cluster and a warning sound, we want to compare AR to the "state of the art" technology, i.e. to a classical HUD, to see if the industrial effort to implement an AR-HUD inside the car is worth it. As a summary, we compared both following HMI conditions:

• With AR: speed, speed limit, navigation and AD messages are on the classical HUD, AR is on the AR-HUD and on the side mirrors (rectangle on the car).

• Without AR: speed, speed limit, navigation and AD messages, birds eye view in AD or distance warning icon in MD are on the classical HUD; an icon can appear on the side mirrors.

As both HMI conditions share the same modality (vision) and the same technology (HUD), we limit comparison bias.

B. Test procedure

To avoid testing the discovery phase of the system, we divided the testing into three phases: the first takes place in a real car and the next two in CARDs.

The first one consists of driving a Mini Cooper car for one hour under adaptive cruise control and a classical HUD, to allow the participant to gain experience of the longitudinal control managed by the car and of HUD displays in a real car.

The second phase lasts around one hour. The participant discovers the simulator, the simulated freeway and its traffic, the AD system, the HMI and the game. He exercises the TOR. It is the opportunity to study the driver's impressions while monitoring the system in AD.

In the third phase, the participant has to drive three times, in each experimental condition: 1-in MD, 2-in AD without AR, and 3-in AD with AR (within-subject design). The conditions are counterbalanced. Each runs lasts 11min, to allow the driver to be fully disconnected from the driving task in AD. It takes place on a three lane-highway with a 90km/h speed limit. At the end of the run, the driver is expected to make a lane change maneuver in MD and to slow down in this lane due to a braking vehicle ahead. We prepared three different scenarios sharing these characteristics to avoid participant habituation. The last scene of the first scenario (hereafter called "scene 1") consists of changing to the left lane due to a highway split and dealing with a braking vehicle in this new lane. The last scene of the second scenario (hereafter called "scene 2") consists of moving left towards a busy lane, also due to a highway split. The last scene of the third scenario (hereafter called "scene 3") consists of changing to the right lane to take the next exit and dealing with a braking vehicle ahead. The scenes are counterbalanced.

We planned the TOR message (hereafter called TOR) in AD to appear 546m before the hatched road markings that define the maneuver limit point: as described in Fig 6 . 264m before is the point where the vehicle should be stopped at the end of the minimum risk maneuver to still allow the driver to handle the lane change maneuver, and 282m is the distance required by the AD system to drive the car during the 10s transition phase and to stop it during the minimum risk maneuver (MRM on the next figure).

From the TOR to the end of the scenario, the driver usually drives around 30s.

In MD, the driver ends the scenario (navigation message and ending scene) without AR. To be as surprising as in AD, the navigation message also appears only 30s before the end of the scenario. We thus explore the comparison between MD and AD in the situation where the driver should perform an unexpected lane change maneuver, here artificially represented by a navigation task that should normally be planned by the system.

C. Participants

All participants are Renault employees who share the following characteristics: they drive at least three times a week, they use a cruise control, and are interested in AD cars.

Those who volunteer are all men, aged from 24 to 61 (mean=47). From the 36 people we recruit, due to simulator sickness and technical problems, 26 results are available for each condition.

D. Hypotheses to check

We presume that driving behavior is modified in the manual phase that follows TOR, compared to the same situation in MD, and that AR helps the driver in this phase. Our four hypotheses are the following:  Driver's reaction is sharper after TOR than in MD (H1). AR minimizes this effect (H2).  After TOR, the driver has a higher risk of missing the exit / lane to take (H3). AR helps reduce this risk (H4).

III. CONSIDERED VARIABLES

We focus our attention on the last part of the scenarios of the third phase, from TOR to the end of the run.

In order to check the hypotheses, we analyze the driver's reaction to TOR, the vehicle dynamics and the impact of AR on the driver's situation awareness. The driver's behavior is analyzed with regard to his actions to take over the driving; the way he handles the steering wheel and the car pedals. As he has to make a lane change, the correlation between the AR indication and the success of the maneuver is expected. We expect the distance at which the driver makes the lane change to be before the hatched road markings, this point being considered as the limit point maneuver (see Fig 6). In SCANeR [START_REF] Oktal | SCANeR™studio[END_REF] simulation environment, the lane change is triggered when the vehicle's center of gravity passes over the lane markings: we then consider that the driver has arrived in the destination lane. The comfort of the lane change maneuver is judged by looking at the lateral accelerations.

In MD the degree of risk of forward collision is measured by the time headway (THW) expressed as:

𝑇𝐻𝑊 = 𝐷 𝑖𝑛𝑡 𝑣 𝑒𝑔𝑜 (1)
Where 𝐷 𝑖𝑛𝑡 is the distance from the vehicle ahead and 𝑣 𝑒𝑔𝑜 is the ego vehicle speed. We summarize below the variables that we calculate:

• Hands on (s): duration between TOR and the time when the driver puts his hands on the steering wheel. • Press button (s): duration between TOR and the time when the driver presses button A deactivating the AD mode. • Pedal pressed (s): duration between TOR and the time when the driver presses one of the vehicle pedals for the first time; o Brake pedal: considered as pushed when the force applied is greater than 2N; this value is considered in order to avoid interpreting a touch of the pedal as a push. o Accelerator pedal: as for the brake pedal, we consider a value of 1%.

IV. RESULTS

In this chapter, we will first describe takeover processes and then check the hypotheses presented above.

A. Takeover processes (sequence)

No participant goes to minimum risk maneuver: without AR, all participants press button A; with AR, three participants forget this action, all three in the first run, but as these three persons have their hands on the wheel, they go to MD. Most of the participants follow the process we expected: they first put their hands on the wheel, then press button A and finally activate a pedal. Only one participant without AR does not follow the process (he presses button A before gripping the wheel). With AR, in addition to the 3 who forget to press button A, 2 press the brake pedal less than 1s before they grip the wheel. All participants press the brake pedal, 3 (1 without AR, 2 with) do not use the accelerator pedal, which is the pedal mostly used first (19 participants without AR, 15 with).

As soon as the TOR message appears (sound + iconic message on the classical HUD), the driver takes some time to put his hands on the steering wheel, press button A, depress a pedal, that is, to regain control over the commands. We describe the means (M) of these different reaction times and their standard deviations (SD) in table II:

For each reaction time, an ANOVA is calculated with the following factors: participant (to take account of individual variability), condition, scene, and interaction between condition*scene. The relevant level of significance is determined by α=0.05. No significant influence is revealed for the reaction times listed in table II, which also indicates the pvalue calculated by the ANOVAs for the "condition" factor.

B. Hypotheses 1) Hypotheses 1&2: "Driver's reaction is sharper after TOR than in MD (H1). AR minimizes this effect (H2)"

ANOVAs similar to those described above are calculated. Post-hoc t-tests with Bonferroni-correction are calculated for all significant main effects of the factor variation.

We first analyze the lateral control. The driver applies a noticeable movement on the steering wheel (more than 2°) sooner in MD after AD than in MD: the duration between the instant when the driver is back in MD and his action on the wheel is equal to 0.9s on average (AD with or without AR), compared to 4.8s in MD (duration between the navigation message and the noticeable effect on the wheel). The influence of the condition on this variable is significant (F(2,23)=15.1; p<.0001). The maximum steering rate is not influenced by the condition. Nevertheless the next figure shows that the spectrum of the steering rate has more energy at high frequency in MD after AD than in MD. In Figure 7. the average of spectra of the steering rate for all participants are represented; in red the participants are back in MD after AD and MD driving is represented in blue. To analyze longitudinal control, we first consider the accelerator pedal. The instant of the first action on this pedal appears much sooner in MD (0.3s compared to 8s on average in AD, with and without AR), which is obvious because the scenario on a highway with free traffic requires the driver constantly to accelerate in MD. The influence of the condition on this variable is very significant (F(2,23)=46.7; p<.0001). The intensity of this first action, the instant and the intensity of the maximum action on the gas pedal are not influenced by the condition.

We secondly consider the brake pedal. There is no influence of the condition on the instant and the intensity of the first action, whereas the instant of the maximum action (pedal speed) is influenced (F(2,23)=7.88; p=.001): it is delayed in AD, with (25.4s) or without AD (27.5s), compared to MD (15.6s). Note that this action is mostly carried out after the lane change, in all conditions (except for 13% of the drivers on average), which means it is presumably performed to adapt to the slowing traffic in the destination lane. As the interaction condition*scene has an influence on the intensity of the maximum action on the brake pedal (F(4,21)=3.14; p=0.024), we have to consider each scene separately: conditions only differ in scene 1 where AD without AR (pedal speed=1237N/s) is significantly higher than MD (654N/s; p<.0001), and AD with AR (977N/s) is similar to AD without AR and to MD. We finally analyze the maximum vehicle speed: it is influenced by the condition (F(2,23)=7.63; p=.001), is higher in MD (96.2km/h) than in AD, where both with and without AR conditions are not significantly different (respectively 87. [START_REF] Feldhütter | How the Duration of Automated Driving Influences Take-Over Performance and Gaze Behavior[END_REF]

and 89.3 km/h).

We analyze the effect of the driver's control of vehicle behavior by means of the following variables: maximum value of longitudinal, lateral and resulting acceleration. The condition influences neither the longitudinal (F(2,23)=2.51; p=.093) nor the lateral acceleration (F(2,23)=0.92; p=.404) but it slightly influences the resulting acceleration (F(2,23)=3.74; p=.032). MD presents the lowest value (8.0m/s 2 ), AD without AR the highest (8.6m/s 2 ), both conditions being different according to the post-hoc test (p=.009); AD with AR is in between (8.4m/s 2 ), not significantly different from MD and from AD without AR. The main component of resulting acceleration is the longitudinal one, the maximum usually appearing when the driver brakes hardest, i.e. to handle the slowing traffic in the destination lane, as already mentioned.

To understand how far the driver takes into account the surrounding traffic, we calculate the minimum time headway. It is not significantly different between conditions (1.97s in MD; 1.52s in AD without AR; 1.33s in AD with AR). This variable describes the driver's behavior in respect of the vehicle in front.

The following table (table III) summarizes the analyzed variables that are influenced by the conditions. A positive influence is marked in the column "MD vs. AD" when there is a significant difference between MD and AD with or / and without AR, that is between driving in full MD and driving in a similar situation in the MD phase that follows AD; "MD<AD" is written when the variable has a significantly lower value in MD than in AD with and without AR. A positive influence is marked in the column "with AR vs. without AR" when there is a significant difference between both HMI conditions in the MD phase that follows AD, or when one of these conditions is similar to MD whereas the other one is not. 2) Hypotheses 3&4: "After TOR, the driver has a higher risk of missing the exit / lane to take (H3). AR helps reduce this risk (H4)"

In this part, we only consider the participants who realized after TOR the lane change to the destination lane: 50% in MD, as many drivers were already in the middle lane when the navigation message is displayed, 96% in AD without AR, 92% in AD with AR.

We first analyze the distance between TOR and the maneuver limit point, with and without AR. The condition influences this variable (F(2,23)=3.65; p=.039). The distance with AR (147m) is significantly higher (p=.004) than that without (86m). There is no influence of the factor condition*scene; nevertheless, if we look at the means by scene, we can see that the greatest difference appears in scene 2 (224m with AR, 89 without). In scene 3, the difference is small (66m with AR, 64m without) because the distance available to perform the maneuver is limited by the exit size (85m). The following graph (Fig 8) summarizes these results, with means and 95% confidence intervals represented for each condition and scene. Confidence intervals appear as larger with AR, especially in scene1. This means that the trajectories differ amongst drivers more with than without AR. We also analyzed the duration between TOR and the instant when the driver activates the appropriate turn signal. The condition influences this variable (F(2,23)=10.53; p=.001). According to post-hoc tests, MD (4.7s) is significantly different from AD with (p<.0001) and AD without (p=.01), both last ones being similar. These results concern those drivers who activate the turn signal (85% in MD, 76% in AD without AR, 75% in AD with AR).

The duration between TOR and the lane change into the appropriate lane (third lane for scenes 1 and 2, exit lane for scene 3) is also influenced by the condition (F(2,23)=16.87; p<.0001) but also by the factor condition*scene (F(4,21)=2.93; p=.04). We thus have to analyze what appears in each scene. According to the Bonferroni test, in scene 1, there is no significant difference between the conditions (average=14.1s). In scene 2, the lane change takes more time in AD without AR (22.1s) than in MD (5.6s; p<.0001); it also takes more time than in AD with AR (12.8s; p=.001); neither MD nor AD with AR conditions are significantly different (p=.064). In scene 3, the lane change takes more time in AD with AR (19.6s) than in MD (10.2s; p=0.001); AD without AR (18.4s) is not significantly different from MD (p=.003) and from AD with AR (p=.596). The following graph (Fig 9) summarizes these results, with means and confidence intervals represented for each condition and scene: Lane change : distance to the maneuver limit point (m)

AD with AR AD without AR The following table (table IV) summarizes the analyzed variables that are influenced by the conditions:

A. Takeover

As presented earlier, the takeover process is similar in both cases using AR or not. The majority of participants put their hand on the steering wheel, first, then press button A and finally push one of the vehicle pedals. As, before the TOR happens, the vehicle is cruising at the appropriate speed and in a straight lane, in general, the drivers take their time pushing the gas pedal so that the vehicle slows down by itself and is then at a greater distance from vehicles ahead. Comparing the results obtained with those of Lorenz [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF] and Gold [START_REF] Gold | Take over!" How long does it take to get the driver back into the loop?[END_REF], the sequences of the takeover are similar, but the interval of time TOR-"hands on the wheel" is greater in our results: around 3.10s vs. [1.39, 1.85]s and [1.45, 1.79]s. This difference may be caused by the means used to distract the drivers when the vehicle is in AD or by the nature of the situation to handle in TOR: in our case there is no urgency, whereas there is an obstacle to avoid in Lorenz's and Gold's studies.

One of the major results is that most of the participants take between 1 and 4s to put their hands on the steering wheel and between 2 and 5s to push button A to resume control, so that 2s represents a minimum duration for the drivers to take over the driving.

B. Comparison MD -AD

The driver's actions on the pedals and steering wheel after resuming control of the vehicle are sharper when they come back to the driving than when they were in MD. Therefore H1 is validated. This is apparent from looking at the brake pedal and steering wheel speeds. The maximum brake pedal speed is increased. The vehicle dynamics is directly affected, so that the values of the accelerations, especially the resulting one, are greater than in MD, but the difference is not substantial. Both effects, on maximum braking speed and resulting acceleration, mostly occur when the driver has to take into account the slowing traffic in his destination lane, approximately 27s after TOR; this means that the influence of takeover on the driving behavior lasts quite a while.

The driver's behaviors can be interpreted thus: after resuming control, the drivers prefer to have a greater secured distance from the vehicles ahead and they react with more pressure on the brake pedal.

The fact that the drivers take less than one second to turn the steering wheel by a significant angle after takeover can be seen as though the drivers are checking on the steering wheel to ensure they have control of the vehicle.

The steering rate spectrum presents more energy at high frequencies (greater than 1Hz) in the case of MD after AD than in MD, which shows that, after resuming control, the drivers take moment to stabilize the lateral control of the vehicle.

The lane change maneuver (indicator usage included) is delayed by the takeover process. Therefore H3 is validated.

C. Influence of AR

AR has no influence on the takeover: the reaction times to regain control over the commands (steering wheel and pedals) are not modified. This result is similar to those of Lorenz [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF]. It could be expected that AR would help the driver take the time to look around and rebuild his situational awareness before he hands over, but it is not the case, at least in the first uses of the system. To know if some drivers develop the strategy to check mirrors and to analyze the environment, strategy being supported by AR, a longitudinal study has to be conducted. H2 is true for two variables, the resulting acceleration and the maximum braking intensity, as AR allows these variables to be reduced and to become not significantly different from MD. As such, AR seems to help the driver smooth out the control of his car, especially if the traffic slows down when he resumes control. To ascertain if this can be explained by the highlight on the vehicle in front, we have to analyze the verbatim that we collected during the interviews.

Our results show that AR has a positive influence on the operational level of driving.

To check if H4 is true, the variable "duration between TOR and lane change" does not seem to be relevant as two contradictory assumptions can be made: either AR could help the driver take time to understand the situation before making the lane change, or it could help him to perform the maneuver faster. The variable "distance to the maneuver limit point" is much more relevant. It is increased by AR, especially when the distance in which to make the lane change is not too constrained, for example to move to the appropriate highway lane at a highway split. As such, H4 is true: AR seems to help the driver become more aware of the lane change he must make and of the infrastructure constraints, by adding the Duration between TOR and lane change (s)

AD with AR AD without AR MD information directly within the driving scene. The fact that AR modifies the driver strategy after taking over has already been demonstrated by Lorenz [START_REF] Lorenz | Designing take over scenarios for automated driving: How does augmented reality support the driver to get back into the loop?[END_REF]. Other studies, conducted in MD, also show that AR allows the driver to better understand the direction to follow (cf. synthesis by Pauzié [START_REF] Pauzié | Head up display in automotive: a new reality for the driver. Design, user experience, and usability: interactive experience design[END_REF] or by Bark [20]). Lorenz shows that, in an emergency (obstacle avoidance), the driver's trajectories, with the AR that highlights the trajectory to follow to avoid the obstacle ahead ("AR green"), lie closer together than without. Our results indicate that, in a less urgent use case, drivers' distances to the maneuver limit points vary more with AR. As our objective was to warn about the constraint through our AR design, and not to suggest a trajectory to take, it is understandable that we get a different result from Lorenz and that our objective to give the driver free choice about the trajectory to take is fulfilled.

In conclusion our results confirm that the tactical level of driving described by Michon [21]is also supported by AR.

VI. CONCLUSION

Our experiment shows that, with AR, the lane change maneuver is more anticipated and the driver's action on the brake pedal is smoother, in the case where a lane change is needed to follow a navigation instruction and where attention is required to adapt to slowing traffic. We can consequently assume that AR helps the driver to rebuild his situation awareness when he has to take over quickly. The analysis of driving data reflects the driver's actions. It should be completed by the analysis of the eye tracking data to give clues about what the driver has possibly detected and analyzed. Data triangulation (driving and ocular data completed by verbatim, cf. [START_REF] Chauvin | Decision making and strategies in an interaction situation: Collision avoidance at sea[END_REF]), will give insights about the driver's intentions, decisions and strategies, and about how far the driver could understand and anticipate the situation.

Our results, obtained in a driving simulator with monoscopic projection, concern an AR that is perfectly superimposed on the environmental objects. In a real car, due to packaging constraints, AR images are usually projected at a fixed distance (e.g. 8 m) and so the superimposition is valid only in 2D. AR design should facilitate congruence [START_REF] Langlois | Virtual head-up displays for augmented reality in cars[END_REF] but will probably not be perfect [START_REF] Bark | Personal navi: benefits of an augmented reality navigational aid using see-thru 3D volumetric HUD[END_REF], and so AR efficiency could decrease in a real car. In-vehicle testing is needed to answer these questions.

Figure 1 .

 1 Figure 1. Components integrated into the simulator.

Fig 4 )

 4 that covers approximately the same spatial context as AR ahead, up to 75m). It shows the shape of the road and the cars around. The ego car is represented by a blue rectangle, the lead vehicle by a green rectangle and a vehicle on an adjacent lane by a white rectangle. AD duration is also indicated. In MD, a classical icon dedicated to the distance warning system is used (here in orange because the distance from the vehicle ahead is too short, seeFig 5).

Figure 2 .Figure 3 .

 23 Figure 2. TOR phase with AR (AD mode is on)

Figure 5 .

 5 Figure 5. Classical HUD with warning icon in MD

Figure 6 .

 6 Figure 6. The TOR message and the exit configuration (scene 3)

2 + 𝑎 𝑙𝑎𝑡 2 .

 22 Steering >2° (s): duration between the time when the driver puts his hand on the steering wheel and the time when he alters steering by at least 2°. • Indicator (s): duration between TOR and the time when the driver activates the indicator relative to the destination lane. • Lane change (s): duration between TOR and the time when the driver arrives in the destination lane. • Steering rate (°/s): measuring how smoothly the driver acts on the steering wheel. Maximum value and frequency spectrum are analyzed. • Depression speed of the gas and brake pedals (%/s and N/s respectively): measuring how the driver acts on the car pedals. The first and maximum pedal speeds are calculated. • Vehicle longitudinal acceleration (m/s 2 ). The maximum is calculated, it is observed in deceleration, generally when the driver is braking to avoid a collision with the vehicle ahead. • Vehicle lateral acceleration (m/s 2 ). The maximum is calculated, it is observed when the driver performs a sudden maneuver. It generally measures the comfort of the lateral displacement needed to make the lane change. • Vehicle resulting acceleration: this is the absolute acceleration produced in the center of gravity of the vehicle. Its expression is: 𝑎 𝑟𝑒𝑠 = √𝑎 𝑙𝑜𝑛𝑔 The maximum is calculated. • Distance of lane change to the maneuver limit point (m). • Vehicle speed (km/h). The maximum is calculated. In this work the oculometric and verbatim are not addressed.

Figure 7 .

 7 Figure 7. Average of spectrum of steering rate in MD and MD after AD

Figure 8 .

 8 Figure 8. Distance to the maneuver limit point

Figure 9 .

 9 Figure 9. Duration between TOR and lane change

TABLE I .

 I OBJECTS HIGHLIGHTED BY AR IN MD AND AD MODES

TABLE II .

 II

	TAKEOVER TIME SEQUENCE
	Variable	Without	With AR p-
		AR		value
	Duration between TOR and "hands on the wheel"	M=3.12s SD=1.24s	M=3.13s SD=1.42s	0.645
	Duration between TOR and pressing button A	M=4.63s SD=1.87s	M=5.09s SD=2.58s	0.24
	Duration between "hands on the wheel" and pressing button A	M=1.49s SD=1.63s	M=1.44s SD=1.36s	0.262
	Duration between TOR and the first action on a pedal	M=7.55s SD=4.47s	M=8.95s SD=7.83s	0.301
	Duration between "hands on the wheel" and the first action on the	M=4.63s SD=3.18s	M=5.12s SD=3.25s	0.872
	accelerator pedal
	Duration between "hands on the wheel" and the first action on the brake pedal	M=14.01s SD=10.65s	M=11.68s SD=9.25s	0.576

TABLE III .

 III

	VARIABLES INFLUENCED BY THE CONDITIONS
	Variable	MD vs. AD	With AR vs.
			without AR
	Instant of the first action	AD<MD	No influence
	on the steering wheel
	Instant of the first action	MD<AD	No influence
	on the accelerator pedal
	Instant of the maximum	AD>MD	No influence
	action on the brake pedal
	Intensity of the 1 st action	Influence in scene 1:	Influence in scene 1:
	of the maximum action on	AD without AR>MD	AD with AR=MD
	the brake pedal
	Maximum speed	MD>AD	No influence
	Maximum resulting	AD without AR>MD AD with AR=MD
	acceleration

TABLE IV .

 IV

				VARIABLES INFLUENCED BY THE CONDITIONS
	Variable			MD vs. AD	With AR vs. without AR
	Distance	to	the	Not available	with > without
	maneuver limit point
	Instant of indicator	MD<AD	No influence
	use
	Duration	between	Influence in scene 2:	Influence in scene 2:
	TOR and lane change	AD without AR>MD	without>with
				Influence in scene 3:	Influence in scene 3: AD
				AD with AR>MD	without AR=MD
				V. DISCUSSION

*Research supported by IRT System X, LRA project.


Mahdi Sellah
email: mahdi.sellah@auxel.com

Jean-François Wecxsteen

Sonia Ait-Amar

Daniel Roger

Partial discharge investigations in laminated busbars

Keywords: Laminated busbars (LBB), partial discharges (PD), triple junction area, Paschen's law, PDIV predicitons

Abstrac-The aim of the study is to predict the presence or absence of partial discharges (PDs), in a laminated busbar (LBB), for a given voltage. PDs appear in specific zones that are located using a representative sample of industrial LBBs. A numerical model based on Paschen's law, proposes an interpretation of the observed phenomena and an estimation of LBB Partial Discharge Inception Voltage (PDIV). A theoretical reasoning and simplifications, based on Paschen's theory, are proposed, for applying this well-known law in the case of non-uniform electric fiels existing in LBB's.

I. INTRODUCTION

Laminated busbars (LBBs) are used in power electronic convertors using basic or sophisticated structures [START_REF] Chen | Modeling and optimization of high power inverter three-layer laminated busbar[END_REF][START_REF] Kon | Development of a multiple series-connected IGBT converter for large-capacity STATCOM[END_REF]. Specific designs are developed for high powers [START_REF] Puigdellivol | Thermal Topology Optimization of a Three-Layer Laminated Busbar for Power Converters[END_REF]. Nowadays, the insulated gate bipolar transistors (IGBT) are widely used and faster SiC components appear in the market. These electronic switches have short commutation times that create high di/dt in the electric circuit during transients [START_REF] Khan | Laminated busbar design criteria in power converters for electrified powertrain applications[END_REF]. The inductance L of the switching loop may produce large overvoltages L di/dt. Consequently, the design of LBBs used in the switching loops of converters must be made for getting inductances as small as possible. This goal is reached using flat conductors insulated by a thin polymer layer [START_REF] Frey | Electric field investigation in high voltage power modules using finite element simulations and partial discharge measurements[END_REF]. Combined with a general trend to operate with higher voltages, the electric field stress in the LBB insulating layers becomes a critical parameter of their design [START_REF] Chang | Developing an experimental method for a cavity PD based life model[END_REF]. Therefore, a good knowledge of the mechanism of PD ignition in LBBs is becoming a major challenge because, when they exist, PDs cause local erosions of the polymer layer that reduce the LBB life times [START_REF] Tanaka | Internal partial discharge and material degradation[END_REF][START_REF] Allocco | Laminated bus bars for power system interconnects[END_REF].

In the current study, PDs location is explained using a representative sample of industrial LBBs. The paper proposes also a method able to predict the presence or absence of PDs in these areas, when the voltage increases. The suggested method is based on Paschen's law established from the electronic avalanche theory in gas and for uniform fields. The proposed 2D model is based on the actual geometry of LBBs. It shows that, for a voltage equal to PDIV measured at a standard pressure, Paschen's law can be used with a negligible error, by considering the field-line length in air rather than the interelectrode distance. The proposed 2D model needs several simplifications. The forces on moving charges due to the magnetic field, which are perpendicular to the charge trajectories, are neglected. It is also supposed that PD ignition phenomena are much faster than electric transients in the convertor. Therefore, the study is made considering a 2D model with a DC voltage equal to the actual maximum value of the convertor transients.

II. EXAMPLE OF LBB USED IN A MOTOR DRIVE

The LBB makes the critical electric connections between components of power electronic converters of the switching loops situated between the electronic switches and the DC bus capacitors. Fig. 1 is an example of industrial motor drive that uses a LBB for connecting the rectifier, the DC bus capacitors and three IGBT modules. For the output connections, the inductance are not critical parameters, they are made with classical copper bars.

III. REPRESENTATIVE SAMPLE OF INDUSTRIAL LBBS

Experiments are made on representative samples of industrial LBBs (Fig. 2). These samples are made of two conducting nickel-plated copper plates of 1mm thickness. A 190µm polyethylene terephthalate (PET) layer provides the electrical insulation between the conducting plates. Two 20µm adhesive layers give the mechanical fixing. The standard thermal bonding process used for industrial LLBs is also used for the samples. Indeed, a suitable thermal cycle is applied under a strong pressure for eliminating the air bubbles in the adhesive layers. The polymer sheet is 5mm larger than the copper plates, for avoiding surface discharges between conducting plates on the sample sides, as it is performed for industrial LBBs.

When a high magnitude sine voltage is imposed between the two copper plates of a representative sample, PDs appear. For locating PDs on the samples, pictures were made in a deep darkness with a night vision device called "Corona Finder" [9]. This optical system makes a visible image from the UV radiation of PDs. Fig. 3 is representative of most of pictures made for voltages over the PDIV. The green zones show the UV radiation emitted by many PDs during the camera opening time. It can be seen that PDs occur only near the boundaries of the copper plates, in a zone called "triple junction area", where the ambient air is in contact with a conducting plate border and the insulating layer. In this area, the electric field in air is stronger than in polymer, due to its lower permittivity. Fig. 3 shows that the emitted light is more intense on the bottom boundary, where the lower plate is present below the insulating layer. The geometry is not the same than on lateral sides, the electric field is stronger. Microscopic observations are made on cutting planes perpendicular to the conducting flat surfaces, in areas where the lower conducting plate exists. The purpose is the determination of the triple junction area geometry at the micrometre-scale. Ten microscopies were made; Fig. 4 is representative of most of microscopies. Small differences are observed, but the typical shape of the triple junction area is a vertical copper wall connected the horizontal polymer plane surface with a quarter-circle of 40!" radius. The punching process used for cutting the copper plates explains the conducting plates border shapes. During the manufacturing process, the orientation of the conducting plates is chosen according to the direction of the punching, to avoid sharp burrs in contact with the polymer thin film.

IV. ELECTRIC FIELD IN THE TRIPLE JUNCTION AREA

The finite element method (FEM) is used for building a 2D model of the triple junction area with a dense mesh (Fig. 5). It computes the electric field when the copper plates impose the 2D problem boundary conditions, which are the electric DC potentials (! = 1700! for the upper plate ! = 0! for the lower one). Fig. 6 presents the electric field magnitude. V. ADDITIONAL THEORETICAL CONSIDERATIONS For using Paschen's law, which defines the breakdown voltage in a gas as a function of the distance X pressure product, it is necessary to verify that the free electrons follow the lines as they do for the uniform fields of Paschen's experiences.

Let us remind that Paschen's works are based on Townsend's theory that considers that free electrons are accelerated by the uniform electric field between flat electrodes. If an accelerated free electron has enough kinetic energy when it collides a gas molecule, this latter is ionized and produced another free electron. This process initiates an electronic avalanche. This case corresponds to an external voltage slightly over the PDIV.

In the triple junction area of LBBs, the interesting parts of the field lines are situated in the air between the surface of the glue and the conducting plate border. Unlike Paschen's experiences, the inertia of electrons may have an influence on their trajectories. This difference with the general background of Paschen's experiences must be evaluated for determining whether it is negligible or not.

For igniting a PD in air, the energy acquired by a free electron must be high enough for ionizing a molecule of Oxygen or of Nitrogen. When the applied voltage is equal to the PDIV, it may be supposed that the collided gas molecule by a free electron absorbs the energy of the collision, by creating a new free electron, without any kinetic energy. This new electron is accelerated by the field and will collide another molecule, when it gets the ionization energy. The elastic collisions are not considered. With such simplifying hypotheses, it is possible to estimate trajectory of free electrons between collisions, by solving the mechanical equation of a solid object placed in the field force ! ! = !!. The computation is made with the electric field map in the triple junction area, determined by the FEM model, for a voltage equal to the experimental value of the PDIV at room temperature and standard pressure. Well-known values of electron charge and mass (! = ! -1.602!10 !!" !!; ! = !9.11!10 !!" !!") are used.

Figures 8 and9 show the simulation results of the mechanical problem considering an example of a free electron appearing at the origin of the field line 4 in Fig. 7. The computation is made with a geometric square mesh grid of 0.4µm and a time step equal to 0.01ps. The computations are made for two voltages: 1700V that corresponds to the PDIV measured at ground pressure and 850V that corresponds to the PDIV at a much lower pressure. In these figures, the small crosses correspond to the ionizing collisions with of a Nitrogen molecule, when the molecule absorbs the kinetic energy of the considered free electron for creating another one at zero speed. The results show that, for the field line 4, the free electron trajectories computed with these simplifying hypotheses follow the field lines. In Fig. 8, the curves are superimposed except at their very end. Additional simulations show negligible errors for the other field lines, for both pressures. It can be concluded that, in the triple junction areas of LBBs, the free electrons follow the field lines for a voltage equal to PDIV.

When a free electron is accelerated by the electric field over an infinitesimal distance dl by the Coulomb's force, it acquires an elementary energy:

!" = ! ! !"!! (1)
The relationship between electrostatic field vector !, generated by scalar potential V is given as: Considering a part of a field line between points a and b, (1) and ( 2) yield the energy accumulated by a free electron accelerated on the distance ab:

! = -!. V!! (2)
! = ! !. !" = ! ! !! ! ! -! ! (3)
Expression [START_REF] Puigdellivol | Thermal Topology Optimization of a Three-Layer Laminated Busbar for Power Converters[END_REF] shows that the energy acquired by a free electron following a field line depends only on the potential difference between two points b and a of the field line. It does not depend on the magnitude variations of the electric field between the considered points. Consequently, Paschen's curves can be used for estimating the PDIV, when the distance between the parallel electrodes is substituted to the field line length, in the triple junction area of LBBs.

VI. PDIV PREDICTION BY USING PASCHEN'S CURVE

Paschen's law gives the breakdown voltage ! !" in the gas between parallel conducting plates. Paschen used Townsend's model [START_REF] Carey | Characterization of Paschen curve anomolies at high P* D values[END_REF] that defines the second Townsend coefficient γ.

! !" = !"# ! + !"(!") ; !!!"#ℎ!!! = !" ! !" 1 + 1 ! (4)
In ( 4) p is the gas pressure, d the distance between the parallel electrodes of Paschen's experiences. The Paschen curve in Fig. 10 is computed with (4) and the well-known parameters for dry air at room temperature, taken in the literature [START_REF] Harris | Nitrogen and air Paschen curves for dielectric barrier discharges in µm-sized voids[END_REF]. The 10 red crosses correspond to the 10 field lines plotted in Fig. 7. For each cross, the length of the considered field line is the abscissa d and the potential difference between the end and the begining of the considered line is the ordinate. The results presented in Fig. 10, show that PDs in the triple junction area appears for points over the Paschen's curve, between lines 4 and 9. For short field lines (<10µm), the free electrons do not acquire enough kinetic energy on the whole field length for ionizing a gas molecule. No PD appears very near the contact point, although the electric field is the highest. For long field lines (>100µm), the electric field magnitude is low and the acceleration of free electrons is not high enough for getting the required ionization energy. For lower voltages, all the red crosses in Fig. 10 are moved downward and PDs disappear. For higher voltages all the red crosses are moved upward; PDs appear for longer field lines. Let us remind that the proposed 2D model is valid only for voltages close to the PDIV. The theory becomes much more complex for higher voltages corresponding to a permanent PD activity as in Fig. 3 Similar phenomena exist in triple junction area of other applications [START_REF] Tran Duy | Partial discharges at a triple junction metal/solid insulator/gas and simulation of inception voltage[END_REF][START_REF] Jae-Hyun | Evaluation of Discharge Characteristics on the Triple Junction for Development of the Gas-Insulated Switchgear[END_REF].

VII. CONCLUSION

In industrial LBB made following the state-of-the-art rules, no significant air-voids exist inside the insulating layers. For voltages slightly over the PDIV, PDs occur in the triple junction areas, where the ambient air is in contact with the conducting plate borders and the polymer layers. The theoretical investigations show that, associated with a FEM simulation, the Paschen's law can be used for determining the PDIV. This analysis opens perspectives for designing highperformance LBBs able to work at higher voltages.

Fig. 1 .

 1 Fig. 1. Industrial motor drive made with a LBB in critical zones.

Fig. 2 .

 2 Fig. 2. Representative sample of industrial LBBs used for electrical tests.

Fig. 3 :

 3 Fig. 3: Optical detection of PDs in the representative sample.

Fig. 4 :

 4 Fig. 4: Microscopic observation of a sample near the triple junction area.

Fig. 5 .

 5 Fig. 5. FEM mesh of the triple junction area and the polymer layers.

Fig. 6 :

 6 Fig. 6: Electric field magnitude in the triple junction area.

Fig. 7 :

 7 Fig. 7: Electric field lines in the Triple junction area.

Fig. 8 :

 8 Fig. 8: Trajectories of free electrons between ionizing collisions for two voltages corresponding to PDIVs at two pressures.

Fig. 10 :

 10 Fig. 10: Paschen curve and points corresponding to 10 field lines of fig 7.

The authors would like to express their gratitude to the French National Research and Technology Association (ANRT) and AUXELFTG who support this research work.978-1-5386-6389-9/18/$31.00 ©2018 IEEE