Emmanuel Vinot
email: emmanuel.vinot@ifsttar.fr

Rochdi Trigui

Yuan Cheng
email: chengyuan_hit@yaho.com.cn

Christophe Espanet
email: christophe.espanet@univ-fcomte.fr

Alain Bouscayrol
email: alain.bouscayrol@univ-lille1.fr

Vincent Reinbold

Improvement of an EVT-based HEV using dynamic programming

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Improvement of an EVT-based HEV using dynamic programming

Emmanuel Vinot , Rochdi Trigui, Member, IEEE, Yuan Cheng, Christophe Espanet, Member, IEEE, Alain Bouscayrol, Member, IEEE, Vincent Reinbold.

Abstract-Automotive engineers and researchers have proposed different Series-Parallel Hybrid Electric Vehicle SP-HEV topologies. The Toyota Hybrid System (THS) is the most known SP-HEV based vehicle, but alternative solutions such as Electric Variable Transmission (EVT) have been also proposed. Efficient comparison between these different solutions is a key point in order to estimate the added value of each topology. This paper presents the application of optimal control to two seriesparallel hybrid architectures for efficiency assessment purpose. The dynamic programming method is applied to the THS as well as to a virtual hybrid vehicle with an EVT. The way to take into account the supplementary degree of freedom provided by the decoupling of wheels and engine in both topologies is presented. The optimal fuel consumptions are then compared on different driving cycles and bring out an over consumption of the EVT topology. Then, a parametric study shows that inserting an appropriate gear ratio on the ICE shaft can improve the EVT efficiency that becomes close to the THS efficiency.

Index Termsseries-parallel, hybrid vehicle, dynamic programming, electrical variable transmission

I. INTRODUCTION

Hybrid Electric Vehicles (HEVs) are one of the effective solutions chosen by the automotive industry to reduce CO 2 and pollutant emissions. By using a combination of an ICE and electrical machines supplied by batteries, the efficiency of the vehicle is enhanced. Among the different hybrid power-train architectures, full hybrid series-parallel architectures (SP-HEVs) are one of the more advanced solutions to reduce fuel consumption [START_REF] Cc | The state of the art of electric and hybrid vehicles[END_REF]- [START_REF] Ehsani | Hybrid Electric Vehicles: Architecture and Motor Drives[END_REF]. Such architectures allow splitting the power flow in a combined series and parallel way.

Moreover, this kind of topology provides a possible decoupling of the wheel and the engine speed. Therefore a supplementary degree of freedom can be used to optimize the engine operating points.

The series-parallel power split vehicle Toyota Prius was the first SP-HEV with worldwide diffusion and remains until now a reference for automotive hybridization [START_REF] Vinot | HEVs Comparison and Components Sizing Using Dynamic Programming[END_REF], [START_REF] Muta | Development of New Generation Hybrid System THS II -Drastic Improvement of Power Performance and Fuel Economy[END_REF]. However other advanced SP-HEVs like the Electric Variable Transmission (EVT) have been proposed in the literature but without efficiency comparison with the existing SP-HEVs. This topology enables theoretically the same functionalities as the THS but in a more compact way [START_REF] Miller | Hybrid electric vehicle propulsion system architectures of the e-CVT type[END_REF]- [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF].

The EVT has been studied and documented especially in a design purpose [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF]- [START_REF] Xizheng | Comparison of two different structure of permanent magnet dual mechanical port machine[END_REF]. Two main topologies are usually described using two electrical machines or one double rotor integrated machine. A sizing and design approach aiming to replace the THS transmission by an EVT has been proposed in [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF]. This study showed that the specifications of the maximum torque and power of the electrical machines are more or less the same in both SP-HEVs, namely THS and EVT.

The efficiency assessment of such complex systems is not an easy task. One of the key issues is the energy management because it has an important impact on the fuel economy results. The rule-based THS management has been discussed in previous publications [START_REF] Vinot | Model simulation, validation and case study of the 2004 THS of Toyota Prius[END_REF], [START_REF] Kimura | Drive force control of a parallel-series hybrid system[END_REF]. The same kind of strategy has been adapted to EVT [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF], [START_REF] Cheng | Global modelling and control strategy simulation for a Hybrid Electric Vehicle using Electrical Variable Transmission[END_REF]. However, in order to compare the HEVs in their best fuel consumption it is not appropriate to apply rule based control methods because the results strongly depend on the control tuning [START_REF] Kim | Power Management and Design Optimization of Fuel Cell/Batterry Hybrid Vehicle[END_REF].

An optimal control method has been developed to perform a comparison of both topologies [START_REF] Vinot | Optimal Management and Comparison of SP-HEV vehicles using the dynamic programming method[END_REF]. Using a system modelling approach, the dynamic programming method already applied to THS [START_REF] Vinot | HEVs Comparison and Components Sizing Using Dynamic Programming[END_REF], [START_REF] Scordia | Global Optimisation of Energy Management Laws in Hybrid Vehicles Using Dynamic Programming[END_REF], [START_REF] Koot | Energy Management Strategies for Vehicular Electric Power Systems[END_REF] has been extended to EVT. It shows that under the assumption of using the same components, EVT fuel consumption is 10 % higher than THS's. An energetic analysis has been performed and shows that the main difference appears in the losses of the electrical machine EM2. It shows that the EM2 linked to the engine in EVT mainly operates in a high torque and low speed area with low efficiency. This paper investigates the possibility of inserting a gear on the engine shaft to change the EM2 operating area.

First the SP-HEV principle is presented in section II. A reminder on dynamic programming and its application on SP-HEVs is then presented in section III. The method to choose the engine operating point is detailed for each topology. In 2 section IV, the comparison between THS and EVT is then presented. Finally a new EVT solution with gear shows that the fuel consumption of this architecture can be reduced to the level of THS.

II. SERIES PARALLEL HEV

A. General principle

In conventional vehicles it is of high importance to have a device that enables the change of the ratio between engine and wheel speed. This is generally performed by a gearbox and a clutch, and sometimes, a mechanical Continuous Variable Transmission is used in order to choose the engine operating point independently of the wheel speed.

In hybrid vehicles the use of electrical machines, by transmitting the power flow electromagnetically allows to decouple the engine and wheel speeds. A part of the power flow is thus an electrical series flow (Fig. 1). A well known way to split the engine flow is a mechanical coupling using a planetary gear as in the Toyota Hybrid Systems (section II.B).

Another solution called Electrical Variable Transmission (EVT) is to split the power flow using an electrical machine with rotating stator and rotor (section II.C).

ICE

B. Mechanical variable solution : the Toyota hybrid system

The Toyota hybrid system is the most known SP-HEV architecture. It is composed of one electrical machine EM1 linked to the wheel (Fig. 2) allowing the electrical mode. A planetary gear linked to the engine and the second electrical machine EM2 insures the splitting functionality. It is a relatively simple transmission considering that no gear box and no clutch are used. One drawback is that in electrical mode the planetary gear ring and thus the EM2 has to be in rotation. Moreover the EM2 speed can frequently be high (near 10000 rpm [START_REF] Vinot | HEVs Comparison and Components Sizing Using Dynamic Programming[END_REF]). This implies high losses in the machine, and sometimes, it can constrain the engine operation [START_REF] Vinot | HEVs Comparison and Components Sizing Using Dynamic Programming[END_REF].

C. Electrical variable transmission

The EVT (Fig. 3) is an interesting solution as it only uses electrical machines to split the engine power flow. A solution is to link the external armature of the EM2 machine to the engine shaft and its rotor to the wheel. Thus a rotating external armature has to be used and fed by power electronics. The EM2 speed (difference between engine and wheel speed) will determine the amount of energy split from the electrical network.

As in THS the EM1 machine is linked to the final gear and will insure the electrical mode.

A more compact topology (Fig. 4) can be made with only one double rotor electrical machine [START_REF] Cheng | Global modelling and control strategy simulation for a Hybrid Electric Vehicle using Electrical Variable Transmission[END_REF] to ensure the split functionality. In a functional point of view the two topologies behave exactly in the same way. Optimal management methods are a good way to compare the fuel consumption of hybrid architectures [START_REF] Koot | Energy Management Strategies for Vehicular Electric Power Systems[END_REF], [START_REF] Liu | Modeling and control of a power-Split Hybrid Vehicle[END_REF] and thus improve the systems. In this paper the Dynamic Programming method has been used to compare the optimal fuel consumption of THS and EVT.

A. The Dynamic Programming applied to hybrid vehicles

Dynamic Programming is frequently applied to hybrid vehicles to minimize the off-line fuel consumption (or more complex criterion) on an a priori known driving cycle [START_REF] Scordia | Global Optimisation of Energy Management Laws in Hybrid Vehicles Using Dynamic Programming[END_REF], [START_REF] Koot | Energy Management Strategies for Vehicular Electric Power Systems[END_REF].

In general, the optimization is based on a systemic approach and energetic models of different subsystems (section III.B).

In our study, optimization methods are applied using a backward approach [START_REF] Vinot | HEVs Comparison and Components Sizing Using Dynamic Programming[END_REF] which needs the knowledge of the driving cycle and the vehicle characteristics (inertia and 3 resistant forces) and goes upstream from the wheels to battery and engine.

In the case of SP-HEVs the optimal control has to determine:

-the share of power between batteries and engine, i.e the electric or hybrid mode and the amount of electric power in hybrid mode (section II.A.1) -the engine operating point, i.e. the engine speed and torque to maximize the overall system efficiency (section II.B.2). To apply the dynamic programming method to hybrid vehicles, a battery state of charge (SOC) vs. time area is considered (Fig. 5). The SOC is the state variable and the battery current (I bat ) is the control variable. The area is meshed in time and SOC samples. The time is sampled in N steps of t e , the SOC is sample in M steps between minimum and maximum SOC value, SOC min and SOC max .

The principle is to find the optimal battery state of charge trajectory which minimizes the fuel consumption along a known in advance driving cycle.

The points of two consecutive columns are linked by oriented edges associated with a fuel consumption. This fuel consumption depends on the driving cycle conditions and the SOC variation between the two points of an edge.

A fuel consumption objective J can be considered during a driving cycle of N samples of time t e :

N SOC k J J 1 ) , ( (1)
where J(k, soc ) is the instantaneous fuel rate for a given battery current and a given speed and torque of the wheels.

The minimum of J is obtained for the optimal trajectory of SOC using Bellman principle [START_REF] Kirk | Optimal Control Theory, An Introduction[END_REF].

Considering a given battery current from one SOC point to another, the fuel consumption on the edge between these two points has to be calculated using the vehicle model (section III.B). The battery current is easily calculated (2) using the SOC variation between the beginning and the end of the edge soc, where C bat is the battery capacity in Amps.hours, and f is the faradic efficiency.

The SOC constraint imposing the final SOC is respected by the graph construction (Fig. 5). Using the maximum battery charge and discharge possibilities, the studying area is built to bring the SOC from its initial value to its final desire value.

The maximum charge and discharge current is calculated using the system's model. For example, in all electric mode, the battery current is calculated in a backward direction from wheels to battery. If the necessary current is too high, electric mode is not possible and maximum battery continuous current limits the discharge current.

To solve this problem recurrent iterative methods using Bellman principle [START_REF] Kirk | Optimal Control Theory, An Introduction[END_REF] are currently used (Fig. 6).

At each point of a column i 2 , the following equation is solved iteratively, starting at point (1, i 0 ) with a fuel consumption 0

* ) , 1 ( 0 i J : ) 1 ( ) 1 ( ] [ min ] , [ max lim_ min lim_ 2 * ) , ( ) , 1 ( ) , ( ) ( ) ( 1 * ) , 1 ( 1 2 2 max 1 2 min 1 1 2 k i k i i for J J i J i k i k i k i i i i i i k i (3)
where J((k,i 1 ) (k+1,i 2 )) is the instantaneous fuel consumption from a point of index (k,i 1 ) to a point of index (k+1,i 2 ). For instance, we assume that it depends only on the SOC variation and vehicle speed (section II.B).

* ) , ( 1 i k J
is the minimum fuel consumption from the beginning (time 0) to point (k,i 1 ) i.e at time k for a state SOC(i 1 ). Knowing the best trajectory, the control variable (I bat ) is easily deduced from the SOC evolution (2) and other variables (engine torque and speed, electrical motor torque and speed…) are then deduced from the system model.

i 1 i 2 i lim_min (k+1) i lim_max (k+1) i lim_max (k) i lim_min (k) soc i 0 ) , 1 ( ) , ( 2 1 i k i k J * ) , ( 1 i k J ] [ min ) , 1 ( ) , ( * ) , ( * ) , 1 ( 2 1 1 1 2 i k i k i k i i k J J J i 1min (i 2 ) i 1max (i 2 )
Fig. 6 : Dynamic programming solving method The dynamic programming method described above can be applied to any HEV topology. In the case of SP-HEVs, an additional degree of freedom has to be considered. For a given battery current I bat and wheel torque and speed (T r and r ), a choice has to be previously done on the engine operating point to maximize the overall system efficiency as presented in the following section.

B. Case of SP-HEV 1. Mechanical and electrical relations in THS and EVT

This section presents the cost calculation on a given edge in the case of the THS (Fig. 7) and the EVT (Fig. 8).

The vehicle model is based on the VEHLIB library model [START_REF] Vinot | Model simulation, validation and case study of the 2004 THS of Toyota Prius[END_REF]. The electrical machines and the inverters are modelled with efficiency maps and the engine with fuel consumption maps. The battery model consists of an equivalent electric circuit with an open circuit voltage E bat , an internal serial resistance R bat , and a faradic efficiency f. E bat depends on the SOC and the temperature, f depends on the SOC and the current sign and R bat depends on the SOC, the temperature and the current sign, all using look up tables obtained by experiments.

The temperature is fixed for all the driving cycle but is chosen at the beginning of the cycle. Nevertheless, no thermal model is used, and the parameters remain constant vs. temperature during all the driving cycle. On each edge of the graph, I bat , T r and r are known. The equation of each components of the system has then to be used to calculate the engine operating point and thus its fuel consumption on a backward manner.

From the wheel torque and speed constraints (T r , r ), one can easily deduce that

f r veh r T dt d J T ( 4
)
where T r is the wheel torque, T f is the load torque calculated from the resistant forces, J veh is the overall inertia of the vehicle brought back to the wheels and r is the wheel speed. TABLE 1 presents the equations for the two architectures. T ring is the torque on the planetary gear ring, T em1 is the torque on the EM1 shaft, is the efficiency of the transmission (axle plus gear), R trans is the transmission ratio, Sign(T r , r ) is the sign of the wheel power. Thus the wheel torque is divided or multiplied by the gear efficiency depending on the direction of the wheel power. T ice is the ICE torque and PG is the efficiency of the planetary gear. T em2 is the torque on the EM2 machine shaft. em1 , em2, ring and ice are respectively the speeds of the electrical machines EM1 and EM2, planetary ring and engine.

R PG is the planetary gear ratio (R PG =-N teeth _ ring /N teeth_sun ), with N teeth _ ring and N teeth_sun the teeth number of the ring and sun gears.

The splitting power functionality is performed by the EM2 machine and the planetary gear in THS ( 7) to [START_REF] Hoeijmakers | The electric variable transmission[END_REF].

In EVT, EM2 torque strikes ICE torque [START_REF] Shu-Mei | Research on power density improvement design of an HEV using induction machine based electrical variable transmission[END_REF]. The EM2 rotor speed is the same as EM1 speed and the stator speed corresponds to the ICE speed. The difference between this two speeds (12) imposes the power derived by electrical network. Willis and torque Relationships in the planetary gear (Fig. 9): [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF] Relationships in the EM2 machines :

ice PG ring PG em R R ) 1 ( 2 (7) ) 1 ( 2 PG ice em R T T ( 8
1 2 em ice em [START_REF] Cheng | Design of a Permanent Magnet Electric Variable Transmission for HEV Application[END_REF] ice em T T 2 [START_REF] Shu-Mei | Research on power density improvement design of an HEV using induction machine based electrical variable transmission[END_REF] The electrical network is the same in both architectures. The electrical node between the electrical machines and the battery gives:

. 0 where I em1 , I em2, I acc and I bat are respectively the DC current in electrical inverters of the EM1 and EM2 electrical machines (considered as receptors), in the accessories and in battery (considered as a generator). Note the current in the accessories corresponds to a constant value of power consumed in accessories and is fixed to 250 W.

Pt em1 and Pt em2 are the losses in the electrical machines and inverters, E is the open battery voltage and R is the internal battery resistance which depends only on SOC and the battery current.

The problem is then to solve the SP-HEV systems equations.

Choice of engine operating point

In THS considering (6) to ( 9) and ( 14) to [START_REF] Kimura | Drive force control of a parallel-series hybrid system[END_REF], and I bat imposed by the strategy we obtain 7 equations and 8 unknown variables ( em2 , ice , T em2 , T ice , T ring , T em1 , I em2 , I em1 ). That means that there is one degree of freedom. This degree of freedom allows choosing, for example, the engine speed to minimize the fuel consumption for a given edge (I bat , T r and r imposed).

In EVT the system is described by 6 equations ( 11) to ( 13) and ( 14) to ( 16) and 7 unknown variables ( em2 , ice , T ice , T em2 , T em1 , I em2 , I em1 ), it means that, as in the THS, there is also one degree of freedom.

In both architectures, the engine speed is chosen as the variable to be fixed.

A possible solution to fix this degree of freedom is to use a pre-determined engine torque versus speed curve [START_REF] Liu | Modeling and control of a power-Split Hybrid Vehicle[END_REF]. This is the way used to develop the online rule-based management of the Prius-II [START_REF] Vinot | Model simulation, validation and case study of the 2004 THS of Toyota Prius[END_REF] and the used curve is presented in (Fig. 10), which allows operating the engine in an efficient specific area. Nevertheless, the best engine specific consumption is not obviously the best system operating point taking into account the electrical machine losses [START_REF] Vinot | Optimal Management and Comparison of SP-HEV vehicles using the dynamic programming method[END_REF]. Thus it does not correspond to the minimum possible fuel consumption. Moreover a pre-defined curve may be a good solution for THS but not for EVT. Taking the previous remarks into consideration, it is proposed to search in each edge the engine operating point which minimizes the fuel consumption. In fact, the electrical machines operations, and thus their efficiency, is highly dependant on the engine torque and speed. Thus the best system global efficiency has to be found.

To achieve that, in the simulation algorithm, ice is sampled from 0 to its maximum value. For each value of ice the non-linear systems (4) to [START_REF] Zheng | Magnetic coupling analysis of four-quadrant transducer used for hybrid electric vehicles[END_REF] are solved to find the engine torque T ice and thus the fuel consumption. It means that on each edge of the graph for each value of ice the engine torque which solves the systems has to be calculated.

A good way to solve the system with a minimum computer effort is to sample the engine torque between 0 and its maximum value for a given speed. Then the battery power P bat_syst obtained for each engine torque and speed couple is calculated and compared to the battery power P bat calculated using the edge soc variation: acc em em syst bat P P P P 2 1 _ [START_REF] Cheng | Global modelling and control strategy simulation for a Hybrid Electric Vehicle using Electrical Variable Transmission[END_REF] where P em1 and P em2 are the electrical power of the electrical machines and inverters, and P acc the accessories power.

Knowing that the electrical machine power is the sum of mechanical power and losses, it leads to: . ) , ( ) , ( Thus using ( 5) to ( 13) T em1 , em1 ,T em2 and em2 , can be expressed depending on T ice , ice and known parameters ( r and T r ), TABLE 2. Then P bat_syst can be expressed as in TABLE 3. ) ( _ [START_REF] Bertram | Multi-objective optimization of a parallel hybrid electric drive train[END_REF] On a given edge, soc and thus I bat are known. U bat is easily calculated using battery model. Solving the system consists then in finding T ice such as P bat_syst = P bat =I bat U bat .

Looking at the evolution of the battery power balance P bat_syst -P bat versus T ice (Fig. 11), a linear interpolation is performed between the nearest positive and negative value to zero. Thus the engine torque value is calculated for each engine speed and the corresponding fuel consumption is deduced. The engine speed with the lowest fuel consumption is finally selected as the final cost of the edge.

It has been observed that sampling the ICE Torque by step of 5 N.m gives good results. No significant changes have been observed in the global fuel consumption or strategy by increasing this precision.

IV. COMPARISON BETWEEN THS AND EVT

The purpose of this section is to present a comparison between THS and EVT. A first comparison is focused on the weight and volume of both topologies. A second comparison is focused on the fuel consumption for the same drive cycle. It should be noticed that THS-II is an existing optimized system implemented on commercial vehicles. On the opposite EVT characteristics are issued from a preliminary study which could be improve in future developments.

The data for the THS comes from different characterizations studies [START_REF] Vinot | Model simulation, validation and case study of the 2004 THS of Toyota Prius[END_REF], [START_REF] Olszewski | Evaluation of 2004 Toyota Prius Hybrid Electric Drive[END_REF], [START_REF] Hsu | Report on Toyota/prius motor design and manufacturing assessment[END_REF]. The data from the EVT is issued from previous works using the Finite Element method software [START_REF] Cheng | Design of a Permanent Magnet Electric Variable Transmission for HEV Application[END_REF]. The component specifications of the Prius-II are presented in TABLE 4.

A. Comparison elements on weight and volume

Fig. 12 and Fig. 13 present the cross sections of the two machines of THS and of the EVT. Fig. 14 and Fig. 15 present axial cross sections of the two systems in order to compare the overall occupied volume. TABLE 5 presents elements of weight and volume neglecting the housing of the systems. The planetary gear volume and weight have been approximately estimated.

Previous studies show that the specifications of the maximum torque and the power of the electrical machine are more or less the same in the two topologies [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF]. The length of EM1 of THS and EVT are the same as well as linear current density. To provide the same maximum torque on EM1 (400 Nm) the EVT external diameter is bigger as it uses surface mounted magnets instead of buried magnets as in THS. The THS air-gap field is thus higher. It also presents a high reluctant torque in addition to the electromagnetic torque. The length of the EVT EM2 machine is higher than that of THS as it is inside the EM1 machine. It is also noted that the slot of the inside EM2 machine, and consequently the copper volume, is high to avoid cooling problems of the inner rotor.

The work reported in [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF] concentrates on the design of a functional EVT that fits the needed specifications. The optimization of this device is in the perspective of the study. However, the designed EVT already presents relatively good characteristics compared to those of the THS in terms of weight and volume. For the moment, the results give an advantage of approximately 8 % of weight to the THS while the volume of THS is 20 % higher than the EVT system.

The EVT can be improved and become more compact. For example, buried magnets can be used instead of surfacemounted magnets. Also, the copper volume may be reduced especially in the inner rotor. The global design of the system can also be improved using a more global sizing approach [START_REF] Desai | Optimal Design of a Parallel Hybrid Electric Vehicle using Multi-Objective Genetic Algorithms[END_REF].This approach has to optimize the size of the different components with different gear ratios, together with the optimization of the energy management parameters [START_REF] Buerger | Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[END_REF], [START_REF] Bertram | Multi-objective optimization of a parallel hybrid electric drive train[END_REF]. A global optimization algorithm, including optimal energy management, can be used to calculate the fuel consumption objective. This approach is already in progress on another kind of HEV in the laboratories of the authors [START_REF] Reinbold | Global Optimization of a parallel hybrid vehicle using optimal energy management[END_REF].

B. Fuel consumption comparison

A comparison between the simulated optimal fuel consumption obtained using the dynamic programming method is presented in TABLE 6. The fuel consumption on a normalized driving cycle and more representative driving cycles, i.e. urban, road and highway conditions [START_REF] André | The ARTEMIS European driving cycles for measuring car pollutant emissions[END_REF] are presented. Charge sustaining operation is considered meaning that the battery energy variation over the cycle is zero in every case. Using the same characteristics for the machines in both architectures, it is clear that the EVT fuel consumption is much higher than that of a THS. TABLE 6 shows that it is around 10 % higher, whatever the driving cycle is. A study on components operating points and global comparative energy balance is then a good way to understand such an over consumption (see section II.B).

A. Analysis on the EVT efficiency

To explain the higher fuel consumption of EVT topology compared to THS, an energetic study has been performed [START_REF] Vinot | Optimal Management and Comparison of SP-HEV vehicles using the dynamic programming method[END_REF]. Considering a charge-sustaining operating mode, the total amount of energy is provided by the engine. The major section of this energy goes to the wheel and propels the vehicle. The rest is used in the vehicle auxiliaries and burned in losses.

Fig. 16 presents the energy balance of the two architectures. As the same driving cycle is followed by both vehicles, the energy going to the wheel is strictly the same. For the same reason the auxiliary and final gear losses are exactly the same. Note that this energy is coming from the global balance including traction and regenerative phases.

This energy balance shows that the main difference appears in the EM2 machine losses. Energy burned in electric EM1 and battery losses are not significantly different. The planetary gear losses in the THS (efficiency =0.97) remains small compared to the difference in EM2 losses.

To explain the higher losses in EM2 in the EVT cases, the operating point of the machine has been represented in road condition driving cycle (Fig. 17). This figure is the efficiency maps of the EM2 machine plus INV2 inverter. Efficiency is represented by coloured lines in torque versus speed area. Operating points of the machine appear in blue.

EVT EM2 machine operates at relatively high torques and the speed of EM2 remains low due to the differences between engine speed and drive-shaft speed. Thus, even if the optimal control chooses the best system efficiency operation, the machine operates mainly in an area with low efficiency.

Moreover, the ICE operates in a worse area with EVT than with THS [START_REF] Vinot | Optimal Management and Comparison of SP-HEV vehicles using the dynamic programming method[END_REF]. The mean specific consumption in road condition is 225 g/kW.h with THS compared to 229 in the case of the EVT architecture.

To improve the EVT system and reduce EM2 losses many solutions can be proposed. The EM2 design may be changed trying to improve the efficiency of the operating area. This could be performed using an iterative design process aiming to optimize the systems efficiency. Nevertheless the electrical machines keep a low efficiency at low speed. The EM2 can be scaled and oversized but it is not desirable for cost and size consideration and will be difficult in the case of a double rotor integrated machine [START_REF] Cheng | Specifications and Design of a PM Electric Variable Transmission for Toyota Prius II[END_REF]. The final gear ratio can be changed but this will also change the EM1 operating points and the global dynamic performances of the vehicle. For these reasons we consider in this paper the insertion of a gear between the engine and the EM2 electrical machine (section IV.B) that shifts the operating points of EM2 to a better efficiency region. As in the previous section, an energetic comparison is performed between THS and EVT with ICE gear. Fig. 20 is the comparative energy balance in real use condition for the two architectures. It clearly appears that using an additional gear the EM2 losses are drastically reduced compared to the original architecture (Fig. 16). This can be explained looking at the operating points of the ICE and EM2 which have been really shifted to join efficiency areas close to those of THS (Fig. 21 and Fig. 22) when adding a gear. The mean specific consumption in the road driving conditions becomes 222 g/kW.h with EVT against 225 g/kW.h with THS. It is noted that in urban conditions the consumption remains 5% higher. This is mainly due to EM1 losses which increase as the management chooses the best compromise between EM2 and EM1 efficiency. The off-line optimal control based on dynamic programming has been developed and applied to two SP-HEVs topologies. It has been applied to the well known Prius-II and to a virtual EVT based HEV built with the same components. A comparative study on different driving cycles shows that the EVT fuel consumption is approximately 10 % higher than that of the Prius-II.

The benefit of including a gear between the engine and the EVT has then been proven. Choosing a gear ratio around 1/2.75 reduces the EVT fuel consumption which reaches the level of the Prius-II consumption.

Concerning weight and volume of the two systems, the first results show values of the same order. Nevertheless, there are many EVT improvement possibilities: burying the magnet, adopting a V magnet structure, improving the slot shape, reducing the rotor thickness... The EVT may then be a good alternative to the THS systems. However, the use of a rotating armature fed by power electronics should be carefully studied.

To compare more precisely the performances of both topologies, a more global sizing approach is necessary, and the comparison has to be made with an optimized EVT. Continuing this work, this approach is currently in progress.

Fig. 1 :

 1 Fig. 1 : global scheme of SP-HEVs

Fig. 2 :

 2 Fig. 2 : THS architecture

Fig. 3 Fig. 4 :

 34 Fig. 3 : EVT architecture

Fig. 5 :

 5 Fig. 5 : Dynamic programming applied to HEVs Battery SOC

Fig. 7 :Fig. 8 :Fig. 9

 789 Fig. 7 : Backward approach of THS architecture

Fig. 10 :

 10 Fig. 10 : Pre-defined engine operating curve in Toyota Prius-II.

Fig. 11 :

 11 Fig. 11 : Battery power balance.

Fig. 13 .

 13 Fig. 12. EM1 of THS characteristics

Fig. 16 :

 16 Fig. 16 : Energy balance on road driving cycle.

Fig. 18 :Fig. 19 :

 1819 Fig. 18 : EVT architecture with gear between Engine and EM2

Fig. 20 :Fig. 22 :

 2022 Fig. 20 : Energy balance on different driving cycles.

TABLE 1 :

 1 Mechanical equations of THS and EVTTHSEVT

TABLE 3 :

 3 Pbat_syst for the two architectures

TABLE 4 :

 4 TOYOTA PRIUS-II CHARACTERISTICS Prius 2004

	Vehicle weight		1360 kg
		displacement	1497 cc
		max power	57 kW@5000rpm
	Planetary gear	ratio(ring,planet,sun)	2.6 (78/23/30)
	Gear	ratio	4.113
		max power	50 kW
		maximum speed	6000 rpm
		maximum voltage in use	500 V
		maximum torque	400 Nm (0 à 1200 rpm)
		max power	30 kW
		maximum speed	10000 rpm
		maximum voltage in use	500 V
		maximum torque	160 Nm(0 à 1800 tr/min)
		NiMh module number	28
		nominal energy	1.3 kWh
		nominal voltage	201.6 V
		electric mode	60 km/h
		hybrid mode	160 km/h

Electrical Motor Electrical Generator NiMh battery maximum vehicle speed Engine

TABLE 5 :

 5 This is the author's version of an article that has been published in this journal. Changes were made to version by the publisher prior to publication. The final version of record is available at http://dx.doi.org/10.1109/TVT.2013.2271646 Comparative weight and volume

		EM2	26 mm			EM1
					2.8 cm 83.6 mm
				30 mm	28 mm
							41 mm
	117 mm				71 mm
	270 mm
	67 mm		Chain		134.6 mm
			107 mm
		27 mm
			Planetary
			gear
		38 mm
		310 mm Fig. 14 THS dimensions 7.1 cm 30.6 cm 166 mm EM1 EM2 160 mm 86 mm 130 mm 80 mm 122 mm 41 cm 83.6 mm	320 mm
		Fig. 15. EVT dimensions
			EVT			THS
		global	EM1	EM2	global	EM1	EM2	PG
	global weight in kg	48.9	27.9	21.0	45.6	34.3	11.3	1.4
	copper weight in kg	10.9	5.6	5.3	7.0	4.5	2.5
	magnet weight in kg	2.7	1.8	0.9	1.4	1.1	0.3
	volume in l	13.3	7.7	5.6	15.7	9.4	4.7	0.3
								7

TABLE 6 :

 6 FUEL CONSUMPTION ON DIFFERENT DRIVING CYCLE

	drive cycle NEDC urban road highway	THS fuel consumption (l/100 km) 3.73 4.54 3.86 5.59	EVT fuel consumption (l/100 km) 4.13 5.04 4.16 6.17
	V. IMPROVEMENT OF THE EVT-BASED SOLUTION

TABLE 7 :

 7 FUEL CONSUMPTION ON DIFFERENT DRIVING CYCLE THS AND EVT WITH GEAR

	drive cycle	THS fuel consumption	EVT fuel consumption
		(l/100 km)	(l/100 km)
	NEDC	3.73	3.73
	urban	4.54	4.73
	road	3.86	3.82
	highway	5.59	5.63

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2013.2271646Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

215 225

B. Result for the new EVT-based solution

Considering that in the case of EVT, the EM2 operates in a low efficiency area, a gear (named ICE-G) can be inserted between engine and EM2 to increase the EM2 speed (Fig. 18). Note that, using a planetary gear with fixed ring, the volume of this gear can be equivalent to the THS' one. No supplementary space is thus required.

A parametric study has been performed to find the best gear ratio.

It is supposed that the gear efficiency equals 0.97 which is the same value as the planetary gear efficiency of THS.

Fig. 19 shows the optimal fuel consumption obtained with backward model and dynamic programming vs. gear ratio. It is presented for different driving cycles. The diamond-shaped points represent the THS fuel consumption. Looking at different driving cycles a good trade-off seems to select a gear ratio of 1/2.75. For such ratio the fuel consumption of both architectures may be quite the same (TABLE 7). His research interests include design and control of electric machines, modeling and control of electric (EVs) and hybrid electric vehicles (HEVs). From 2009 to 2011, he carried out the research of Permanent-Magnet EVT and its applications in HEVs in the frame of MEGEVH network, France.

In 2012, he joined PSA Peugeot Citroën in Paris, where he is responsible for the research of novel energetic conversion systems for automotive applications and the development of powertrain simulation tools.

Vincent

Reinbold received the engineering degree of Ecole National Supérieure d'Electricité de Grenoble (2011). He is currently a Ph.D student.

His research interests include the optimal design of electrical machine for hybrid vehicle.


Paul Mignon

Philippe Poignet

Jocelyne Troccaz

Using Rotation for Steerable Needle Detection in 3D Color-Doppler Ultrasound Images*

This paper demonstrates a new way to detect needles in 3D color-Doppler volumes of biological tissues. It uses rotation to generate vibrations of a needle using an existing robotic brachytherapy system. The results of our detection for color-Doppler and B-Mode ultrasound are compared to a needle location reference given by robot odometry and robot ultrasound calibration. Average errors between detection and reference are 5.8 mm on needle tip for B-Mode images and 2.17 mm for color-Doppler images. These results show that color-Doppler imaging leads to more robust needle detection in noisy environment with poor needle visibility or when needle interacts with other objects.

I. INTRODUCTION

Accuracy during needle based clinical procedures may be critical for both patient safety and operation success. Unfortunately, needle flexibility and variable stiffness of biological tissue intrinsically limit this accuracy. Handling capabilities and visual feedback issues faced by clinicians also make the gesture potentially inaccurate and/or unsuccessful. This has motivated a large amount of research about robotized needle insertion. Among them, needle steering -i.e. the fine control of needle curvature for the execution of curved trajectories toward a target -has received increasing interest. Indeed, needle steering also provides other clinical benefits in needle-involved procedures like obstacle avoidance or target movement compensation. Some prototypes (see [START_REF] Webster | Design considerations for robotic needle steering[END_REF] and [START_REF] Jahya | Observations of threedimensional needle deflection during insertion into soft tissue[END_REF]) use two degrees of freedom (DoFs) robots to insert and rotate the needle. They are efficient to steer needles but are not designed to fit clinical needs yet. In [START_REF] Wei | Robot-assisted 3d-trus guided prostate brachytherapy: system integration and validation[END_REF], a more complex brachytherapy robotic system was developed but did not integrate needle steering. Robotic devices are generally assisted by medical imaging, mainly ultrasound (US) [START_REF] Wei | Robot-assisted 3d-trus guided prostate brachytherapy: system integration and validation[END_REF], CT-scan [START_REF] Fichtinger | System for robotically assisted prostate biopsy and therapy with intraoperative ct guidance[END_REF] or MRI [START_REF] Fischer | Mri-compatible pneumatic robot for transperineal prostate needle placement[END_REF].

We previously developed a brachytherapy robot prototype called PROSPER [START_REF] Hungr | A 3-d ultrasound robotic prostate brachytherapy system with prostate motion tracking[END_REF] used for needle insertion and seed positioning under 3D US guidance. The robot offers six DoFs for the end-effector provided by seven motors : five of them, arranged in the positioning module, are used to orient the needle and to position its tip on a plane outside the patient. The two others, corresponding to the insertion module, are used to insert and rotate the needle inside tissue toward a predefined target. Once the needle is positioned, surgeons can easily insert seeds thanks to the needle hollow as usually *This work was partly supported by the French ANR within the Investissements d'Avenir program (Labex CAMI) under reference ANR-11-LABX-0004.

1 UJF-Grenoble 1 / CNRS / TIMC-IMAG UMR 5525, Grenoble, F-38041, France.

2 University Montpellier II, LIRMM, 161 rue Ada, 34095 Montpellier, France done in brachytherapy. To compensate for target movements due to prostate motion and deformation, the needle can move forward or backward based on 3D US image registration [START_REF] Baumann | Prostate biopsy tracking with deformation estimation[END_REF]. Experimental data showed that the average error between target and seed position was reduced to approximately 3 mm [START_REF] Hungr | A 3-d ultrasound robotic prostate brachytherapy system with prostate motion tracking[END_REF]. In order to improve its accuracy, the next step is to give this robot needle steering capabilities. This requires the capacity to accurately detect the needle from images.

US imaging has several benefits such as low-cost, simplicity of use, safety for both patients and clinicians. However, US imaging suffers from a lack of quality intrinsically due to the acoustic properties causing different types of image artifacts and speckle noise. This makes US images difficult to be processed.

In [START_REF] Okazawa | Methods for segmenting curved needles in ultrasound images[END_REF], a curved needle was segmented in 2D US imaging. In the context of 3D images, two main types of techniques exist. The first one involves processing 3D volume projections on several planes using as instance Radon transform [START_REF] Ding | Automatic needle segmentation in three-dimensional ultrasound images using two orthogonal two-dimensional image projections[END_REF]. Projections are then processed with 2D algorithms. The second type of methods consists in scanning directly the entire volume. In [START_REF] Qiu | Needle segmentation using 3d hough transform in 3d trus guided prostate transperineal therapy[END_REF], they suggested to use 3D Hough transform to detect straight lines in a volume. In [START_REF] Uhercik | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF], Uhercik used a Random Sample Consensus (RANSAC) algorithm to find 3D polynomial shapes. This method seems to be robust to noise or artifacts and can achieve relatively fast detection.

This paper focuses on the evaluation of needle segmentation in 3D color-Doppler volumes compared to the segmentation in 3D B-Mode volumes. We consider two biological tissues : beef liver and pork tenderloins. Let us stress the fact that the aim of this paper is to analyze segmentation accuracy, not to compute needle curvature. Thus, it concentrates on straight trajectories.

We propose to apply a RANSAC algorithm to color-Doppler imaging in order to make it more robust to image noise and artifacts. Color-Doppler is mostly used to detect blood flow and is visualized by coloring B-Mode images. Needle vibrations are necessary to make the needle visible on color-Doppler imaging. In our system the vibrations simply result from needle rotation.

II. MATERIALS AND METHODS

A. Color-Doppler and needle rotation

Very often, needles are difficult to detect in US images. This may come from large echogenicity of biological tissue around the needle, poor acoustic transmission, bad needle orientation with respect to transmitters or presence of objects (other needles, seeds, anatomical structures, etc. As mentioned before, color-Doppler imaging associated with needle rotation can be used to get a useful visual feedback. For that purpose, we used an Ultrasonix RP with endorectal endfire probe with a convex mechanical 3D transducer and a central frequency of 6 MHz. The 3D volume results from 115 sweeps captured at angular increment of approximately 0.8°and leads to a voxel size of 0.4 mm 3 .

The objective being to isolate the needle from other objects, Fronheiser in [START_REF] Fronheiser | Vibrating interventional device detection using real-time 3-d color doppler[END_REF] uses a low frequency ultrasound buzzer to create these vibrations. This configuration needs either to instrument the needle or to equip the robot, increasing the difficulty to sterilize the device for clinical use. Another complication with needle base instrumentation is the damping of vibration magnitude along the needle. The needle is therefore more visible near the entrance but less at the tip, specially in deeper insertions, as discussed in [START_REF] Adebar | 3-d ultrasound-guided robotic needle steering in biological tissue[END_REF].

To prevent those limitations, we used intrinsic vibrations based on needle rotation in tissue to make the needle visible in color-Doppler images. We assume that the vibrations are caused by the needle's slight asymmetry and the needle/robot connection slight eccentricity. Thus, they spread through the entire needle and are not only localized at its base.

B. Needle segmentation

Needle detection was achieved with a random sample consensus algorithm as described in [START_REF] Uhercik | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF]. It is based on four main steps. The first step is a fast thresholding of the image in order to keep only a specific percentage of the brightest voxels (needle is mostly brighter than the rest of the image). This percentage depends on tissue echogenicity. In the experiments (see III), a value of 1 % was used for all B-Mode images. It permitted, in our imaging conditions, to keep the entire needle shape while rejecting the maximum of medium artifacts. In the second step, a specific number of voxels are randomly selected from the voxel cloud resulting from the image thresholding. A polynomial Bezier curve is fitted to these random voxels. The random voxel number is limited by a lowest value depending on Bezier curve order. In our experiments, first order Bezier curves were used, thus the number of random voxels was set to 2. Finally, all the thresholded voxels are separated in inliers (supposed to belong to the fitted curve) and outliers. The separation criterion is a threshold on an approximation of the distance between voxels and the curve according to [START_REF] Uhercik | Model fitting using ransac for surgical tool localization in 3-d ultrasound images[END_REF]. The three last steps are repeated and the best result in terms of number of inliers is returned. Fifty iterations were computed to optimize both computation time and result accuracy. This algorithm can be applied to 2D or 3D images as well as grey scale or RGB images by adapting the first thresholding step. To segment color-Doppler volume, we transform RGB channels to HSV and use only the hue channel to compute RANSAC. As color-Doppler may create a blob around the needle, a morphological erosion is applied on the acquired volumes. The operator also reduces artifacts that can interfere with the needle shape. The image processing pipeline is shown in fig. 1. This segmentation process was applied on four B-Mode 3D US images and four 3D color-Doppler images. For each modality, two images correspond to bovine liver and the two others correspond to pork tenderloin. These configurations give several interesting conditions in terms of needle visibility and artifact interaction. For each image, the segmentation algorithm was run 100 times in order to test its repeatability and accuracy.

C. Needle reference

As needle position is robotically planned, a priori knowledge is available to limit the region of interest, allowing to reduce computation and improve segmentation precision. We computed a volume of interest using robot odometry and robot US calibration [START_REF] Hungr | A 3-d ultrasound robotic prostate brachytherapy system with prostate motion tracking[END_REF]. It consists of a box of 40 × 40 × L ins mm 3 where L ins is the insertion distance plus an arbitrary margin of 10 mm. It also permitted to keep an uncertainty on the needle location to test our algorithm.

The calibration between the US probe and the robot allows to compute the theoretical location of the needle in US images. It supposes that the needle did not bend during the insertion.

A standard non-beveled brachytherapy needle (diameter = 17 gauges = 1.15 mm) was inserted in the meat pieces with 5 rotations per second (rps) rotation speed and 1 mm/s insertion speed. The needle diameter and the rotation/insertion ratio imply that the resulting needle location is a straight line. Thus the segmentation detects 1 st order Bezier curves. Indeed having a curved needle would make the reference measurement inaccurate since it would rely on manual segmentation.

The errors presented in III were the average error along the axis, the error at needle tip, and the angular error in needle orientation. The first error corresponds to the mean of the distances between segmented needle points and their projections on the needle reference. The second error is the distance between segmented tip and reference tip. The last error is the angle between the segmented needle axis and the reference axis.

III. RESULTS

A. 3D B-Mode

As mentioned in II, the results of the hundred segmentations on two different volumes of each biological tissue (beef and pork, leading to a total of four hundred segmentations) were compared to the reference needle locations. Fig. 2 represents liver and pork B-Mode volumes. Needle references are displayed in 2a and 2c .

In fig. 2a the needle is not clearly discernible and in fig. 2b or 2d, as the needle was inserted twice, trace of previous insertion is also visible in the volume. It leads to many false detections for these three volumes. In the first pork image (fig. 2c) the needle appears distinctly and was inserted once, providing better results. All detections (false and correct) are presented in table I.

A detection is said "false" if the error between the reference and the segmented needle is greater than 3 mm at needle tip and 10 °in needle orientation. These values were selected based on expert advice.

False detections are reported in table I and occurred in 44 % and 48 % of the segmentations in beef volumes (2a, 2b) and in 26 % in pork volume with previous needle trace (2d). No false detections occurred in the other pork volume (2c). This results in an average error around 7 mm along needle axis and a very large average error (18 °or 12°) in needle orientation in three of the four images. This shows that segmentation accuracy is influenced by image quality or presence of other objects. In the first pork volume, the needle is clearly visible and undisturbed by previous insertions traces. The needle is thus accurately segmented, leading to an average error along the needle of 0.8 mm, 1.5 mm at the needle tip and only 2.9 °in needle orientation.

B. 3D color-Doppler

The needle appearance in color-Doppler images depends on the needle rotation speed. We tested different speeds between 0 and 13 rps (robot maximum rotation speed). We noticed that the needle becomes visible at 3-4 rps and is not visible at lower speed. Its visibility increases from 4 to 8 rps and seems to be stable above 8 rps. In fig. 3 the needle is more apparent at the tip and at tissue interface than at its middle. This could be due to needle rotation and its slight asymmetry causing a non-homogeneous distribution of vibration magnitude. (pork and beef). The low ratio of false detections shows that color-Doppler imaging significantly improves needle detection in beef (0 %) and pork with needle previous trace (5%). These percentages must be compared with those in B-Mode for beef (44%-48%) and for pork with previous trace (26%). The average error along the needle decreases to 2.1 mm and the angular error in needle orientation to 5 °. For the color-Doppler image represented fig. 3c, the results are slightly superior to those found in the B-Mode image represented in fig. 2c. This is probably due to the uncertainty provided by the color blob thickness surrounding the needle.

IV. DISCUSSIONS

Color-Doppler segmentation is done with a non-specific detection algorithm, able to segment either B-Mode or color-Doppler 2D and 3D images only by adapting thresholding step to the image type (RGB or grey scale). We may still improve the color-Doppler segmentation by applying a threshold/filtering step more specific to color-Doppler data. The error found at the needle tip in color-Doppler is relatively small compared to US volume's poor quality and resolution (0.4 mm 3 ).

As brightest voxel percentage used in B-Mode segmentations was defined manually, it must be adapted according to US image echogenicity. Furthermore, the iteration number was set intentionally to a low value in order to keep fast detections. Increasing this value may improve the algorithm robustness in B-Mode but will increase computation time.

We chose to compare only straight insertions in order to keep an objective reference given by robot odometry, not by a potentially imprecise manual segmentation on B-Mode images. However, in [START_REF] Adebar | 3-d ultrasound-guided robotic needle steering in biological tissue[END_REF], Adebar found similar errors for straight and curved needle (around 1 or 2 mm) compared to a manual segmentation. These errors are approximately equivalent to the ones presented in this paper. However, they resulted from a slice to slice segmentation assuming that the needle is orthogonal to the slices and thus is sensible to needle orientation with respect to the transducer.

V. CONCLUSIONS

We used needle rotation in color-Doppler ultrasound imaging to increase needle visibility thus facilitate its segmentation. Our method does not require any material modifications of our robotic device and uses needle's slight asymmetry to induce vibrations in the whole needle. We selected a RANSAC-based algorithm to segment needles in both B-Mode and color-Doppler 3D volumes. We tested our algorithm in these two types of imaging and compared the resulting segmentation to a calibrated reference.

The use of color-Doppler imaging results in more robust needle segmentations in case of poor visibility or interaction with bright objects in the image like acoustic artifacts or previous needle traces. This property can be useful in brachytherapy, where several objects can appear in the US image.

In the future, the developed color-Doppler segmentation may provide a useful feedback for robot needle steering.

Fig. 1 .

 1 Fig. 1. Steps of color-Doppler segmentation in a 2D image: (a) initial image, (b) extracted hue channel, (c) morphological erosion, (d) RANSAC needle location result.

Fig. 2 .

 2 Fig. 2. Needle in B-Mode US images in (a), (b) beef liver and (c), (d) pork tenderloin. The needle reference position given by robot odometry is displayed with a dotted line.

Fig. 3 .

 3 Fig. 3. Needle in color-Doppler US images in (a), (b) beef liver and (c), (d) pork tenderloin. The needle reference position given by robot odometry is displayed with a dotted line and a rotation of 8 RPS.

Table

  II summarizes the result of a hundred segmentations in two color-Doppler US volumes for the two conditions

TABLE II RESULTS

 II OF 100 SEGMENTATIONS ON TWO COLOR-DOPPLER US IMAGES IN PORK TENDERLOIN AND BEEF LIVER. AVERAGE DISTANCE ERROR ALONG THE NEEDLE, ERROR ON NEEDLE TIP, ANGULAR ERROR ON NEEDLE ORIENTATION AND PERCENTAGE OF FALSE DETECTION IN RELATION TO REFERENCE NEEDLE LOCATIONS ARE DISPLAYED.

			Along	Needle		False
	Error		needle	tip	Orientation	detection
			(mm)	(mm)	(°)	(%)
	Beef	3a	1.88	1.82	4.68	0
		3b	2.05	1.75	5.11	0
	Pork	3c	1.71	2.19	5.94	5
		3d	2.24	2.92	5.68	0


L Gauchia
email: lgauchia@ing.uc3m.es

A Bouscayrol
email: alain.bouscayrol@univ-lille1.fr

J Sanz
email: jsanz@ing.uc3m.es

R Trigui

P Barrade

Fuel Cell, Battery and Supercapacitor Hybrid System for Electric Vehicle: Modeling and Control via Energetic Macroscopic Representation

Nowadays, no electrochemical energy system presents a competitive operation if compared with internal combustion engine, which is the reason for combining electrochemical energy systems to obtain a hybrid energy storage system. This paper presents a fuel cell-battery-ultracapacitor system for vehicle application. The objective of this paper is to present the Energetic Macroscopic Representation (EMR) of the multisource power system. I.

INTRODUCTION

Current fossil fuel vehicles present a high energy and power density operation which still cannot be matched by any electrochemical energy system on its own. However, reducing oil reserves and environmental concerns due to pollutant emissions have activated the research for electrochemical energy systems. One of the current research lines is the hybridization of energy storage systems (ESS), in order to obtain competitive vehicle operation.

Electric vehicles (EVs) allow a wide range of topologies, depending on the energy systems involved [START_REF] Chan | The state-of-the-art of electric, hybrid, and fuel cell vehicles[END_REF]. The high energy density needed to compete with ICE can be obtained from high energy density batteries or fuel cells. Fuel cells, especially PEM (Proton Exchange Membrane) fuel cells present a particularly high energy density if compared to the rest of electrochemical energy systems. This is due to the fact that the fuel is stored in a separate tank, just the opposite to batteries. However, they present a poor ramp up capability, due to mass transport phenomena [START_REF] Ceraolo | Modelling static and dynamic behaviour of PEM fuel cells on the basis of electrochemical description[END_REF] related to the protons concentration on the cathode side.

Therefore, PEM fuel cells can be complemented with high power energy storage systems which are capable of both generating and absorbing high power peaks. The ESS can be supercapacitors or batteries or non electrochemical systems, such as flywheels.

These electrochemical systems admit a varied combination between the fuel cell, battery and supercapacitor. Depending on the topology, the power management will change. For example, for the FC-B case, the battery will be under severe power bursts [START_REF] Kim | Power management and design optimization of fuel cell/battery hybrid vehicles[END_REF] which could shorten the battery life time. The FC-SC combination could improve this, as supercapacitors present higher power, ramp capability and life cycle than batteries [START_REF] Bourke | Ultracapacitors: why, how and where is the technology[END_REF], but supercapacitors present much lower energy density than batteries [START_REF] Bauman | A comparative study of fuel cell-battery, fuel cell-ultracapacitor and fuel cell-battery-ultracapacitor vehicles[END_REF]. Moreover, it could present problems during vehicle start-up [START_REF] Gao | Performance comparison of a fuel cell-battery hybrid powertrain and a fuel cell-ultracapacitor hybrid powertrain[END_REF]. The B-SC combination could solve this last aspect, but it will reduce the total energy density due to the fact that batteries still have a lower energy density than fuel cells [START_REF] Dell | Energy storage technology for global energy sustainability[END_REF][START_REF] Miller | Energy storage system technology challenges facing strong hybrid, plug-in and battery electric vehicles[END_REF]. Therefore, the FC-B-SC combination keeps the high energy density due to the fuel cell, the high power density and ramp capability due to supercapacitors and batteries, as studied by Thounthong [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF] and Schaltz [START_REF] Shaltz | Investigation of battery/ultracapacitor energy storage rating for a fuel cell hybrid electric vehicle[END_REF].

The objective of this work is to present a fuel cell-batterysupercapacitor electric vehicle, from modeling to control. This is done using Energetic Macroscopic Representation, which allows representation of multiphysical system and its strategy and control.

II. EMR OF THE ELECTRIC VEHICLE

A. Energetic Macroscopic Representation

The FC-B-SC hybrid electric vehicle will be modelled in Energetic Macroscopic Representation (EMR). This is a graphical tool developed in 2000 [START_REF] Bouscayrol | Multimachine multiconverter system: application for electromechanical drives[END_REF], very helpful when studying complex systems and its energy management. The elements are connected considering the action-reaction principle and respecting physical causality. Physical causality is respected by considering only integral operations, discarding derivative operations. In physical systems the output is always delayed with respect to the input. In EMR each element is represented by a pictogram which internally includes the mathematical equations which describes the relationships between action and reaction inputs and outputs. Moreover, EMR does not only consider the representation of each element, but also complex control schemes and strategies. EMR has already proved to be useful in, e.g. vehicle [START_REF] Chen | Global modeling of different vehicles[END_REF] and fuel cell [START_REF] Boulon | From modelling to control of a PEM fuel cell using energetic macroscopic representation[END_REF] applications, among others.

The vehicle simulated is a 32 kW fuel cell-batterysupercapacitor (Fig. 1). The power converter arrangement can be varied due to the multiple power energy systems, and have been studied in [START_REF] Bauman | A comparative study of fuel cell-battery, fuel cell-ultracapacitor and fuel cell-battery-ultracapacitor vehicles[END_REF]. The complete system has three converters: one for the electric machine and two for the power sources. The number of power converters for the power sources can vary from none to three [START_REF] Bauman | A comparative study of fuel cell-battery, fuel cell-ultracapacitor and fuel cell-battery-ultracapacitor vehicles[END_REF]. No converters imply a necessary oversizing of supercapacitors to allow its charge and discharge, as well as negative long term effects on fuel cell and battery due to excessive cycling. On the other hand, three converters allow a greater control [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF], but it also increases weight, volume, costs and losses. An intermediate solution is the use of two converters for three power sources, leaving the third as a slack element. In this work we have chosen to interface fuel cell and supercapacitors with power converters, leaving the battery directly connected to the electric machine converter. This choice allows the voltage variation needed for the fuel cell and for, especially, the supercapacitors operation.

B. Fuel Cell System

Due to particularities in vehicle applications, such as fast start-up due to low temperature operation, PEM fuel cell (Proton Exchange Membrane) are commonly used in road transport applications.

Fuel cells include a stack, responsible for the power generation, and a number of ancillary systems, such as compressor, cooling system, humidification, etc. Therefore, it is a multiphysical and complex system. There is a wide range of modeling approaches to fuel cells. It can vary from stack centered models [START_REF] Pathapati | A new dynamical model for predicting transient phenomena in a PEM fuel cell[END_REF], to others which include auxiliary systems, such as [START_REF] Boulon | From modelling to control of a PEM fuel cell using energetic macroscopic representation[END_REF]. or control oriented [START_REF] Bordons | Constrained predictive control strategies for PEM fuel cells[END_REF]. Equivalent models obtained by impedance spectroscopy enable easy interaction with other electric models. The topology of the circuit can present slight variations, depending on the author [START_REF] Yuan | AC impedance diagnosis of a 500 W PEM fuel cell stack. Part I: stack impedance[END_REF].

The PEM fuel cell model used in this work is an equivalent circuit (see Fig. 2) obtained by impedance spectroscopy and experimentally validated [START_REF] Gauchia | A per-unit hardware-in-the-loop simulation of a fuel cell/battery hybrid energy system[END_REF]. The tests were carried out on a Nexa Ballard fuel cell, which is a 1.2 kW, 22-50 V system with a maximum current of 50 A. The model obtained has been scaled to represent a 300 cell stack with a voltage range of 138 -318 V.

The PEM fuel cell system EMR pictogram is a voltage source, represented by an oval block, as seen in Fig. 2. The output is the voltage computed by the fuel cell equations.

1 1 1 ) ( R U dt d C I I R E V U C fc fc ohm fc ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - - - = (1)
The voltage E depends on the stack temperature, the Faraday constant and hydrogen, oxygen and water partial pressures and the fuel cell standard voltage. The resistances and capacitor voltages represent the ohmic and double layer capacitance phenomena which take places in the stack.

The fuel cell is connected to the rest of the system via an inductance, to smooth the current ripple, and a dc-dc converter. Equations for both systems are presented.

) ( ) ( ) ( ) ( _ t Ri t i dt d L t u t u fc fc fc ind fc + = - (2) ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ = = ) ( ) ( ) ( ) ( ) ( ) ( 2 _ 2 _ t u t m t u t i t m t i bat fc ind fc fc chop (3)
C. Batteries Battery modeling has been deeply studied due to the complex phenomena which take place, both in the short and long term. A widely accepted test procedure to model batteries is the electrochemical impedance spectroscopy [START_REF] Karden | A method for measurement and interpretation of impedance spectra for industrial batteries[END_REF], [START_REF] Thele | Development of a voltage behavior model for NiMh batteries using an impedance based modeling concept[END_REF]. Ni-Mh, have already been successfully been used in Toyota Prius, and is the technology chosen for this work.

The battery model used is based on the model available in the Matlab/Simulink library. It is a 300 V 10 Ah Ni-Mh battery. The battery EMR pictogram is an oval element, with voltage as output and current as input, as depicted in Fig. 3. For the correct computation of the battery model, it is necessary to estimate the battery state-of-charge (SoC). The estimation of the SoC can be a complex task. Especially in nonflooded batteries, as the acid concentration of the electrolyte, which is normally a good indication of the battery SoC, cannot be directly measured. The different methods can be consulted in [START_REF] Piller | Methods for state-of-charge determination and their applications[END_REF]. The method chosen for this work is the ampere hour count, taking into account the ampere hour efficiency.

∫

- = - dt t i C SoC SoC n t t ) ( 100 (%) (%) 1 η (4)
D. Supercapacitors Supercapacitors enable high power delivery or braking, which is an attractive characteristic for transport applications. Supercapacitor modeling can yield a variety of equivalent circuits. Different authors present equivalent circuits with different topology, as [START_REF] Buller | Modeling the dynamic behaviour of supercapacitors using impedance spectroscopy[END_REF] and voltage equalization [START_REF] Barrade | Series Connection of Supercapacitors: Comparative Study of Solutions for the Active equalization of the Voltages, 7th International Conference on Modeling and Simulation of Electric Machines[END_REF].

The supercapacitor model used in this work is based on an previous experimentally validated work [START_REF] Gauchia | New approach to supercapacitor testing and dynamic modelling[END_REF] for a 3000 F 2.5 V Maxwell Boostcap element. The model has been scaled to a 120 series connected cell pack. The EMR pictogram for a supercapacitor is also a voltage source, represented again by an oval element (Fig. 4).

∫ ∫ ∫

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - + + = dt R t u i C dt R t u t i C dt t i C t u t u C uc C uc uc L uc 3 3 3 2 2 2 1 ) ( 1 ... ) ( ) ( 1 ) ( 1 ) ( ) ( (5)
Supercapacitors are connected to the dc bus through an inductance and a boost dc-dc converter.

E. Mechanical part and environment

The mechanical part of a hybrid electric vehicle can present different topologies [START_REF] Chen | Global modeling of different vehicles[END_REF].

The machine used for this simulation is a permanentmagnet DC machine. This implies that no external excitation system needs to be controlled. The electric machine is not directly coupled to the wheels, but needs to be interfaced by a differential in order to reduce the shaft speed, increase the torque and distribute it to both driven wheels. The gear multiplies the torque to be transmitted to the differential by a factor of 5. The differential will transmit the torque to left and right wheels, allowing a different speed for each if necessary. All the mechanical part has been included in an electric source at the dc bus, as seen in Fig. 5.

F. Parallel coupling

At the dc bus the voltage will be imposed by the battery, whilst the currents will be distributed in a parallel node. To facilitate later control schemes, the parallel connection is separated in two.

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + = + = ) ( ) ( ) ( ) ( ) ( ) ( _ _ 1 1 t i t i t i t i t i t i sc chop fc chop bat load (8)

III. INVERSION BASED CONTROL THROUGH EMR

Once the complete system is represented in EMR, it is necessary to be able to control it. The ability to do so is one of the interesting characteristics of EMR.

The control is done by firstly defining the control loops in the system. For this purpose it is important to define which are the system tuning and objective variables. In this case there are two control loops. One is related to the mechanical part of the system and the other one to the power generation system.

The control loop for the mechanical part has the speed as the objective variable and the power converter of the electric machine as the tuning variable. This loop is included in the electric source which simulates the mechanical part.

) ( ) ( ) ( ) ( _ t Ri t i dt d L t u t u sc sc sc ind sc + = - (6) ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ = = ) ( ) ( ) ( ) ( ) ( ) ( 3 _ 3 _ t u t m t u t i t m t i bat sc ind sc sc chop
U ind_fc i fc m 3 U fc i fc U sc i chop_sc U batt BAT FC i chop_fc U batt i batt SC i sc m 2 U batt U batt i 1 Mechanical part i load ES i sc U ind_sc U batt

Energy generation

Parallel coupling

U ind_fc i fc m 3 U fc i fc U sc i chop_sc U batt BAT FC i chop_fc U batt i batt SC i sc m 2 U batt U batt i 1
Mechanical part Fig. 5. EMR for the fuel cell-battery-supercapacitor vehicle

The power generation control loop has as objective the control of the current distribution in the dc bus. The current distribution is related to the first Kirchhoff law [START_REF] Miller | Energy storage system technology challenges facing strong hybrid, plug-in and battery electric vehicles[END_REF], where the current on the dc bus (i total ) is imposed by the dc machine. Therefore, only two currents need to be controlled to obtain the three currents. The choice of which of the two currents must be controlled will depend on the strategy, as seen in Fig. 6. This work will present the example of controlling the fuel cell current and battery current. Fuel cell current control equations: [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF] Battery current control loop related to the inversion based control equations are presented.

[ ] ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ = - - = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( _ _ _ _ 2 _ _ _ _ _ t u t u
[ ] [START_REF] Shaltz | Investigation of battery/ultracapacitor energy storage rating for a fuel cell hybrid electric vehicle[END_REF] The advantage is that fuel cell and battery are the elements that suffer more severe aging processes, so it is important to avoid excessive cycling. Known the tuning and objective variables, it is possible to define the control system using the inversion principle. This principle is based on the idea of inverting each block until the objective variable is obtained. This objective should follow the reference generated by the strategy.

⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ = - - = = - = - = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( _ _ _ _ 3 _ _ _ _ _ _ 3 _ _ _ _ _ _ 1 _ _ _ _ _ 1 t u t u

IV. SIMULATION RESULTS

The simulation results present the hybridization of a fuel cell-battery-supercapacitor system under a NEDC cycle (New European Driving Cycle), as shown in Fig. 7. A first strategy based on frequency selection is presented.

To avoid oxygen starvation on fuel cell systems, it is usual to avoid subjecting the fuel cell system to power bursts. This can be achieved by assigning as reference load currents with a frequency lower than 100 Hz. On the other hand, supercapacitors are specially designed to endure sudden power bursts, both during supply or regenerative braking. Therefore, high frequency loads, above 10 Hz will be supplied or absorbed by the supercapacitor. This implies that intermediate frequencies will be the reference for battery current. Results are presented in Fig. 8 and9.

i total = i bat + i chop _ fc + i chop _ sc [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF] The strategy must include limitations in each of the electrochemical energy sources. Limitations for maximum fuel cell current (50 A) are included. This limitation is due to the stack cross section. Any limitations for stack environment to guarantee correct operation is already carried out by the fuel cell system control. This control will make sure temperature, gas pressure and water content are the expected value for each operation point. The battery state-of-charge (SoC), is limited to 60-80%, to avoid deep discharges. Maximum voltage for supercapacitors must also be limited to 2.5 V per element. Supercapacitor voltage range is taken from 0 to 2.5 V per element, which is a wider range than the normally used 1.25-2.5 V range. This will allow a deeper discharge of the supercapacitors, which will enable a higher power recharge during regenerative braking.

V. CONCLUSIONS

In this paper we have obtained the energetic macroscopic representation of a fuel cell-battery-supercapacitor hybrid electric vehicle. The electrochemical energy systems models used were previously experimentally validated and adapted to the case power levels. An initial energy storage strategy was simulated, demonstrating EMR is a powerful tool for this issue. The next step will be to study how other energy management strategies affect each of the electrochemical energy systems involved.

Fig. 1 .

 1 Fig. 1. Fuel cell-battery-supercapacitor hybrid electric vehicle

Fig. 2 .

 2 Fig. 2. Fuel cell EMR (left) and equivalent circuit (right)

Fig. 3 .Fig. 4 .

 34 Fig. 3. Battery EMR (left) and equivalent circuit (right)

Fig. 6 .Fig. 7 .

 67 Fig. 6. EMR of the fuel cell-battery-supercapacitor system with inversion based control

ACKNOWLEDGMENT

  Authors acknowledge financial support from the LEESS research group of the University Carlos III of Madrid (UC3M), from the scholarships for mobility of researchers of UC3M 2011 and the L2EP of the University of Lille.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Current distribution on the parallel coupling


Houssam Arbess

Karine Isoird

Moustafa Zerarka

Henri Schneider

Marie-Laure Locatelli

Dominique Planson

Marie- Laure Locatelli

High termination efficiency using polyimide trench for high voltage diamond Schottky diode

Keywords: Diamond, TCAD Simulation, Field plate, Termination, Schottky, Polyimide

come

High termination efficiency using polyimide trench for high voltage diamond Schottky diode

Introduction

Due to its super properties such as high breakdown field, high saturation velocity, high carrier mobility and the highest thermal conductivity of all materials, diamond becomes the best material for the power devices [START_REF] Sussmann | CVD Diamond for Electronic Devices and Sensors[END_REF]. At high temperature, the conventional semiconductors cannot be used because of intrinsic carrier generation across the band gap. For these cases wide band gap semiconductor materials like SiC, GaN, and diamond are promising candidates. For example, due to a band-gap energy of 5.45 eV the diamond intrinsic carrier concentration at 1000°C is in the range of 10 10 cm -3 , which is similar to that of Silicon at room temperature and similar device performance may be expected [START_REF] Vescan | Very high temperature operation of diamond Schottky diode[END_REF]. Therefore, diamond is a very attractive material for high temperature, high-voltage and high-power switching applications in future power electronics.

The device under study in this paper is a diamond P type Schottky diode. As all power devices, a junction termination is needed in order to spread the equipotential lines, to reduce the electric field at the edge of devices and to reach the theoretical breakdown voltage. Several junction terminations have been explored for the Schottky diode in wide-band-gap semiconductors. Some of the more common ones are the guard ring [START_REF] Gupta S K, Pradhan | Design, Fabrication, and Characterization of Ni/4H-SiC (0001) Schottky Diodes Array Equipped With Field Plate and Floating Guard Ring Edge Termination Structures[END_REF][START_REF] Ueno | The guard-ring termination for the high-voltage SiC Schottky barrier diodes[END_REF], the metal field plates extending over an insulating surface layer [START_REF] Ikeda | Fabrication of a field plate structure for diamond Schottky barrier diodes[END_REF], [START_REF] Tarplee | Design rules for field plate edge termination in SiC Schottky diodes[END_REF], resistive Schottky barrier field plate (RESP) [START_REF] Bhatnagar | Edge terminations for SiC high voltage Schottky rectifiers[END_REF], and junction-termination extension (JTE) [START_REF] Alok | SiC device edge termination using finite area argon implantation[END_REF].

Due to difficulties associated with donor atom doping in diamond and destructive effects of ion implantation on the diamond crystal, N-type region is not yet optimized. Therefore, techniques commonly used for terminating Si or SiC devices, such as field rings or junction termination extensions, cannot be employed for diamond. That's why the field plate termination is chosen for this study.

Several materials and architectures have been used in order to optimize the efficiency of the field plate termination. Due to its high dielectric permittivity, Ikeda [START_REF] Ikeda | Fabrication of a field plate structure for diamond Schottky barrier diodes[END_REF][START_REF] Ikeda | Edge termination techniques for p-type diamond Schottky barrier diodes[END_REF] used the aluminum oxide (Ɛ ≈ 9) as a dielectric under the field plate. His results show an increasing of breakdown voltage from 200 V without termination to 700 V with field plate. Brezeanu [START_REF] Brezeanu | Termination Structures for Diamond Schottky Barrier Diodes[END_REF][START_REF] Brezeanu | Ramp oxide termination structure using high-k dielectrics for high voltage diamond Schottky diodes[END_REF] used the graduated, ramp dielectric form and high K dielectric under field plate in order to increase the breakdown voltage. Thion [START_REF] Thion | Simulation and design of junction termination structures for diamond Schottky diodes[END_REF] used semi-resistive material upon a layer of silicon nitride in order to diffuse the equipotential lines and therefore decrease the maximum electric field and increase the breakdown voltage.

The results of Thion [START_REF] Thion | Conception de protections périphériques applicables aux diodes Schottky réalisées sur diamant monocristallin[END_REF] show a difference between simulated and experimental results. One of the reasons can be the electric field peak at the edge of the termination. This peak is probably higher than the crictical field of the dielectric used under the field plate.

The principal goal of this study is to decrease the maximum electric field peak in the structure, which is normally localized at the edge of termination, using polyimide trench under field plate.

An architecture using a polyimide trench under field plate has been studied in this paper. Several architecture with many geometrical parameters have been tried in order to extract the optimum values and geometry.

Diamond Schottky diode simulation parameters

The structure under study is a diamond pseudo vertical Schottky diode. The technological and geometrical parameters were chosen using TCAD (Technology Computer-Aided Design) simulation to have a breakdown voltage equal to 1700 V at room temperature. One dimension simulations with Sentaurus have been made in order to extract these parameters. Assuming that, the termination efficiency is around 85%, that means, the insures a breakdown voltage equals 85% of the breakdown voltage of the ideal component (one dimension simulation), the thickness of P -layer should be equal to 11 or 12 µm with boron doping concentration equal to 2x10 15 or 4x10 15 cm -3 successively. The second parameters set (12µm ; 4x10 15 cm -3 ) have been chosen because simulation results show a forward current density greater than for the first parameters set (11µm ; 2x10 15 cm -3 ) at ON state. So, the structure consists of two diamond layer (Fig. 1), the first is a 7 µm P + doped diamond with a doping concentration of 3x10 20 cm -3 and the other is a 12 µm P --doped diamond with doping concentration of 4x10 15 cm -3 .The physical model used to calculate the breakdown voltage is the default Van Overstraeten model [START_REF]Sentaurus user guide A[END_REF][START_REF] Chynoweth | Ionization Rates for Electrons and Holes in Silicon[END_REF][START_REF] Van Overstraeten | Measurement of the ionization rates in diffused silicon p-n junctions[END_REF] with parameters value given in the paper of Rashid et al [START_REF] Rashid | Modelling of single-crystal diamond Schottky diodes for high-voltage applications[END_REF]. The carrier mobility, maximum electric field and other parameters are detailed in the thesis report of Thion [START_REF] Thion | Conception de protections périphériques applicables aux diodes Schottky réalisées sur diamant monocristallin[END_REF]. Due to convergence problem at low temperature, all simulations in this paper have been made at 800K. The electrical characterizations of this Schottky diode have been extracted by extrapolation after simulations at different temperatures. Other simulations have been made in order to evaluate the variation of the electric field with temperature shown a negligible difference.

The polyimide dielectric material has been used for all simulations as a secondary passivation.

New termination architecture

Many field plate termination architectures have been used in majority of simulations in order to increase the breakdown voltage without noticing of the electric field peak at the end of field plate. Indeed, the case of diamond is specific, and due to its high critical field, which is much larger than that of the dielectrics frequently used in power devices, the electric field peak in the termination is very high. So, it is necessary to design new termination architectures that reduce drastically the electric field in the dielectrics.

In previous papers [START_REF] Arbess | New termination architecture for 1700 V diamond Schottky diode[END_REF][START_REF] Nawawi | Design and optimization of planar mesa termination for diamond Schottky barrier diodes[END_REF] an idea has been proposed to increase the efficiency of the field plate by eliminating the electric field peak in the diamond (Fig. 2 -structure B). It is to keep the whole electrode flat, with no corners, and replace the diamond below the field plate region, with an optimized thickness of a dielectric material. This idea is not used to decrease the electric field peak value at the end of the field plate (almost 60 MV/cm at 1700 V). Several termination architecture (pillars dielectric form, graduated dielectric form and mixed dielectric form) with different dielectric materials (silicon oxide and aluminum oxide) [START_REF] Arbess | New termination architecture for 1700 V diamond Schottky diode[END_REF][START_REF] Arbess | Field plate termination for high voltage diamond Schottky diode[END_REF] have been proposed in order to decrease the electric field peak at the end of the field plate.

The electric field by definition is the potential variation in a given distance. If the potential lines in the structure can be displaced away the field plate, the maximum electric which located at the edge of field plate decreases. To achieve the spread of equipotential lines, it is necessary to use a dielectric with a value of permittivity smaller than the diamond in the lower part of the termination structure. An idea consists to make polyimide trench under the field plate (Fig. 2 -structure C). The used dielectric in this paper is the silicon oxide. Theolier [START_REF] Theolier | Deep trench MOSFET structures study for a 1200 Volts application[END_REF][START_REF] Théolier | A new junction termination technique: The Deep Trench Termination (DT²)[END_REF] has used this technique to design efficiency termination of superjunction silicon MOSFET (Deep Trench Termination DT²), but by using the BCB (Benzo-Cyclo-Butene) as a dielectric in place of polyimide. The polyimide is a sort of polymer [START_REF] Chiang | The synthesis and morphology characteristic study of BAO-ODPA polyimide/TiO2 nano hybrid films[END_REF][START_REF] Ghosh | Polyimides: Fundamentals and Applications[END_REF]. Its critical field is around 5 MV/cm. One of its use is for second passivation in the microelectronic devices and particularly for high voltage and high temperature SiC devices [START_REF] Zelmat | Investigations on high temperature polyimide potentialities for silicon carbide power device passivation[END_REF], which encourages the use of this material is the facility of the deposit and its permittivity very close to the silicon oxide (≈ 3) that's mean, smaller than that of diamond (≈ 5.7).

Technological process

Due to several reasons, the necessary technological processes to make diamond components are specifics. The small wafer dimension (3mm x 3mm) and the difficulty to make a local doping are some of the more reason. In this case, the technological process which is able to make the diamond Schottky diode with the new termination, are describe in Fig. 3. The anode contacts of the all diodes is the wafer are interconnected. After etching until the P + layer, ohmic contacts must be made before the deposit of the polyimide layer. After the polymerization of the polyimide and the CMP (Chemical Mechanical Polish) process, the time of the silicon oxide deposit layer becomes. The final processes are the deposit of the Schottky contact and the etching of the polyimide at the edge of the wafer in order to have an access to the anode contacts.

Architecture parameters and results

The depth of the polyimide in this structure equals the diamond P -one. The field plate on the polyimide, as Fig. 2 (c) shows, is in the classic form. Three interest parameters can be effective in this architecture: the dielectric thickness, the field plate extension length and the position of the dielectric (Fig. 4).

Parameters effect on the breakdown voltage

The dielectric (silicon oxide) thickness was varied from 0 to 2 µm, the field plate extension length from 0.5 to 15 µm and the position of the dielectric from 0 to 10 µm. The variation of these parameters shows a negligible effect on the breakdown voltage. The obtained efficiency with all these parameters was equal to 97%. Indeed, the polyimide trench make the electric field homogeneous along horizontal axis passing through the diamond (Fig. 5), and as a result, the impact ionization is homogenous in the structure and there is not a weak point. Fig. 6 shows the impact ionization at breakdown for the three architectures respectively for the structure A, B and C at 2780 V, 3300 V and 4000 V. The impact ionization in Fig. 6-c is almost homogeneous in the diamond and does not have a weak point as the architecture of Fig. 6-a and b. In some cases, the efficiency of the termination is smaller than 97 % : If the position of the dielectric (under extension field plate) is close to the beginning of the polyimide (smaller than 3 µm), the efficiency decreases down to 88 % if the position of the dielectric equals 0 and its thickness equal 2 µm. Indeed, the variation of the direction of the equipotential lines increases the electric field at this edge (begin of the field plate). This punctual increasing has a result of premature breakdown.

The polyimide trench has a positive effect to the maximum electric field peak. Indeed, Fig. 7 shows the equipotential lines at 1700 V for the structures B and C successively Fig. 7-a and Fig. 7-b. For the first case (a), the electrostatic potential lines have a direction to the up there are very tight. That means high potential variation in small distance and as a result, high electric field. In the second case (b), the electrostatic potential lines change their direction downward after entering the polyimide trench. This variation of direction makes the potential variation smaller than for the first case in the same distance and as a result the electric field decreases. This structure is simulated with a polyimide as a second passivation which has a negligible effect on the breakdown voltage.

Parameters effect on the maximum electric field peak

Since the Schottky diode is designed to operate at 1700 V, the maximum electric field values have been extracted at 1700 V. The node-to-node distance in the simulation mesh has a great effect to the electric field peak value in the dielectric. Therefore, all comparisons in this paper have been made in the same node-to-node distance (10 nm).

The variation of geometrical parameters has now an enormous effect. The electric field peak at the edge of field plate decreases when increasing the thickness of the dielectric under field plate extension 1x10 -30 cm -3 s -1 1x10 -30 cm -3 s -1 7.2x10 24 cm -3 s -1

1.03x10 26 cm -3 s -1 5.2x10 23 cm -3 s -1 1x10 -30 cm -3 s -1

(a) (b) (c) 0 V 1700 V 1700 V 0 V (a) (b)
from 20 MV/cm with 1.2 µm of dielectric thickness down to 17 MV/cm with 2.2 µm of dielectric thickness (Fig. 8). The position of the dielectric in this case equals 11 µm and the extension field plate length equals 1µm. Note that, the increase in dielectric thickness has a minor negative effect on the breakdown voltage. Increasing the extension field plate length, the maximum electric field peak increases. For example passing from 0.5 µm to 4 µm, the maximum electric field peak increases from 13.3 MV/cm up to 20.5 MV/cm (Fig. 9). With this variation, the minimum feasible value of the extension field plate length is the best. The diamond cheap dimensions equal to (3 mm * 3mm), so, the classic photolithography machine has been used to make the mask. For this machine, the precision is equal to 1 µm.

Fig. 9: Variation of the maximum electric field peak in terms of extension field plate length

The position of the dielectric has a small effect while it's far from the beginning of the polyimide trench. Passing from 1 µm to 15 µm the maximum electric field peak decrease from 18.5 down to 17 MV/cm (Fig. 10). As shown before, this variation has an impact on the breakdown voltage. Indeed, the presence of a corner close the semiconductor (diamond) increases the impact ionization and as a conclusion the breakdown voltage decreases. With this architecture the maximum field peak is around 25 MV/cm. If the pillars dielectric form or the graduated dielectric form replaces the simple field plate [START_REF] Arbess | New termination architecture for 1700 V diamond Schottky diode[END_REF], the maximum electric field can be decreases to 18 MV/cm with 4 pillars and 2 µm of thickness and 20 MV/cm with 3 graduations and 2 µm for each graduation.

Conclusion

In this paper, new termination architecture has been applied for 1700 V diamond Schottky diode. The termination efficiency has been increased from 67% for a simple field plate with optimum parameters to 97 % for new topology with polyimide trench under the field plate. The maximum electric field problem at the end of the field plate has been studied also. Several parameters of the new architecture have been simulated in order to obtain the minimum of the electric field peak. It can be arrived to 13MV/cm of this peak with high precision of the photolithography process. This value remains greater than the critical field of silicon oxide, but ten times smaller than for the classical field plate.

Fig. 1 :

 1 Fig. 1: One dimension simulation structure for diamond Schottky diode.

Fig. 2 :

 2 Fig. 2: Field plate architectures. From (a) to (c), classic architecture, advanced architecture [18] and with polyimide trench

Fig. 3 :

 3 Fig. 3: Technological steps for diamond Schottky diode

Fig. 4 :

 4 Fig. 4: Termination architecture with polyimide trench

Fig. 5 :Fig. 6 :

 56 Fig. 5: Electric field along horizontal axis passes at the diamond surface (0.1 µm of depth) at breakdown

Fig. 7 :

 7 Fig. 7: Equipotential lines at 1700 V for the structures of Fig. 2 b and c respectively from left to right

Fig. 8 :

 8 Fig. 8: Variation of the maximum electric field peak in terms of dielectric thickness under extension field plate

Fig. 10 :

 10 Fig. 10: Variation of the maximum electric field peak in terms of extension field plate length

  extension field plate (µm)

Acknowledgements

This study was conducted in the framework of the topic "simulation, design and realization of high voltage and high temperature power devices" of the LIA (International Laboratory) WIDE-Lab (Wide bandgap technologies for Integration of energy efficient Devices), composed by two French laboratories LAAS and Ampere affiliated at CNRS, and IBM/CNM CSIC laboratory. This work was supported by French FUI project DIAMONIX2