A Miño

C Lancelot

P Blanchard

C Lamonier

L Rouleau

M Roy-Auberger

S Royer

E Payen

Strategy to produce highly loaded alumina supported CoMo-S catalyst for straight run gas oil hydrodesulfurization

Keywords: mesoporous alumina, hydrotreatment, mesostructuration, SRGO

A simple postmodification synthesis is proposed to produce large pore volume alumina, with addition of a porogen during the peptization step, which is an industrial process preceding alumina shaping. By adjusting the synthesis parameters, obtained alumina present improved textural properties compared to conventional ones: specific surface areas between 380 à 430 m 2 .g -1 , large pore diameters between 12 and 20 nm and consequently large pore volumes. This allowed to prepare highly loaded catalysts, at a density of 4 at Mo .nm -2 , without the formation of undesirable bulk molybdenum-cobalt oxide species despite the high molybdenum content.

Catalysts performance were evaluated in thiophene HDS, where the activity varied by a factor 1.5. The most performant solid of the series was then tested in the HDS of a straight run gas oil under industrial conditions: it showed significantly improved activity compared to that of a catalyst prepared from a commercial alumina with the same molybdenum density, with a temperature gain of 17°C at 100 ppm residual sulfur. Moreover, the catalyst activity remained stable after one week of testing. This work thus evidences that the development of alumina supports with enhanced textural properties is an efficient way to improve the performance of HDS CoMo catalysts.

Introduction

Due to the continuous evolution in regulations concerning the sulfur content in transportation fuels, actually limited to 10 ppm in European countries [1], a significant improvement of the hydrodesulfurization (HDS) process of petroleum feedstocks is needed. The development of more performant catalytic materials is an effective solution to limit significant evolution of the process conditions. Conventional HDS catalysts are composed of nanometric MoS 2 crystallites promoted by cobalt atoms and dispersed on porous supports [START_REF] Topsøe | Hydrotreating Catalysis[END_REF][START_REF] Prins | [END_REF][4], obtained by sulfidation of an oxide precursor [START_REF] Lepage | Catalyse de Contact: conception, préparation et mise en oeuvre des catalyseurs industriels[END_REF].

The morphostructural properties of the support are important parameters: large surface area is beneficial to the active phase dispersion, while pore volume conditions metal loadings that can be achieved [START_REF] Dzwigaj | [END_REF][7]. Large pore diameter is also researched for a better diffusion of reactants during reaction [8], an important issue if we consider that heavier petroleum cuts are going to be treated for further incorporation in transportation fuels.

Consequently, the development of mesostructured oxide synthesis offered new perspectives for catalyst preparation [9][10], as these supports exhibit particularly high surface area with tunable mesopore size. Since the first reports on the synthesis of silica based mesoporous molecular sieves, from the M-41S family [9] and further from the SBA family [11][12], adaptation of mesotructuration methodologies to the synthesis of other oxides [13][14][15][16][17], including Al 2 O 3 [18][19][20][21], was proposed. Mesoporous alumina syntheses are based on precursor hydrolysis or precipitation in the presence of structure directing agent (anionic, cationic or neutral) [22][23]. For silica, the pore size can be adjusted by a judicious choice of the templating agent and/or by the use of a swelling agent in addition to the template [9,12,[24][25][26][27]. Such control is however more difficult for alumina. Hydrolysis conditions (temperature, pH, agitation), composition of the gel/precipitate (water, structuring agent, solvent), hydrothermal and maturation conditions are however keys to control pore structure properties [21,28]. In addition, periodic mesostructure over alumina can be difficult to maintain during template extraction [29] and wormhole-like porosity is often obtained [19][20][21][22][23]. Evaporation Induced Self Assembly route is however reported as efficient to produce Organized Mesostructured Alumina (OMA) [30,31], with some flexibility on the inorganic network composition [32,33] and pore structure characteristics [33][34][35]. With pore sizes in the mesopore range and high surface areas, templated alumina are good candidates as support for catalytic applications.

While mesostructured silica-based materials were extensively studied as HDS catalyst supports [36][37][38][39][40][41][42][43][44][45][46], the use of non-siliceous mesostructured oxides for HDS reactions is, in contrast, scarce. Cejka et al. [47] and Kaluza et al. [48] prepared wormhole-like mesoporous alumina and due to support characteristics, well-dispersed molybdenum species were observed even at MoO 3 loading as high as 30 wt%.

Catalysts having up to two times higher activity than a commercial one (containing 15 wt% MoO 3 ) were obtained. Hicks et al. [49] also studied the preparation of mesostructured alumina supported CoMo catalysts. Limited catalytic performances were reported due to loss in surface area and pore volume of the support under sulfiding treatment and under HDS reaction conditions. Such lack in stability over mesoporous alumina was also observed by Bejenaru et al. [50]. Despite limited stability, some of the catalysts displayed high catalytic performances (in the HDS of thiophene), especially those obtained over alumina exhibiting large mesopores and fine fibrillar morphology. HDS performances were also dependent on the nature of molybdate species present in oxidic form on the support. Low activity catalysts initially presented monomolybdate species whereas polymolybdate species were identified before sulfidation over high activity samples. Other authors also related the observed better performance of Co(Ni)Mo catalysts supported on mesostructured alumina to higher reducibility of molybdenum over such supports [51][52][53].

The reported results showed the potential of mesostructured alumina as support for HDS catalysts, despite the absence of organized pore network for most of the catalysts. We then propose herein the use of a porosity modification method to design supports with improved textural properties. The approach presents the advantage to be simple and adaptable to conventional alumina: the process is established after boehmite precipitation during peptization, porosity of alumina being modified by addition of a porogen to generate large and adjustable porosity [54,55]. Peptization step is indeed required prior to material shaping in catalyst support industry. This step consists in reducing the size of the boehmite agglomerates by adsorption of protons on the surface of the particles causing electrostatic repulsion.

Peptization by the mean of various acids leads to metastable sols or homogeneous pastes that are used to prepare shaped supports, obtained after extrusion, drying and calcination [56,57].

In this work, we studied the influence of the different synthesis parameters on the textural properties of alumina, which were further used as supports for highly loaded CoMo HDS catalysts.

The solids were characterized and their performance evaluated in thiophene HDS.

The most efficient catalyst of the series was then tested in Straight Run Gasoil (SRGO) HDS and its desulfurization ability was compared to that of a catalyst prepared on a commercial alumina with the same molybdenum atom surface density (dMo).

Experimental methods

Support synthesis

Large porosity alumina supports were prepared using a modified two step synthesis approach [54]. The first step consisted in the precipitation of aluminum nitrate (Al(NO 3 ),9H 2 O Aldrich, >99%) by an ammoniac solution (NH 3(aq) , 25 wt%), with a precipitation media composition of 1 Al : 27.8 H 2 O : 103.4 NH 3 solution (expressed in mol). The aluminum hydroxide precipitate was recovered by filtration and washed.

Thereafter, the hydrate precipitate was dispersed in water and peptized with nitric acid 1 mol.L -1 at 80°C before maturation for 2h at 60°C. The porogen, the triblock copolymer Pluronic P123 (BASF, poly(ethyleneoxide)-block-poly(propyleneoxide)-block-poly(ethyleneoxide), EO 20 PO 70 EO 20 ), was then added at the selected concentration and the mixture was maintained under stirring at ambient temperature for 12h. The molar composition was, depending on the quantity of peptizing and porogen agents, 1 Al : 55.6 H 2 O : x P123 (x = 0, 0.011, 0.022 or 0.035) : y HNO 3 (y = 0.8, 1.3, 1.8 or 3.1). Alumina support was obtained after evaporation of the solvent at 120°C and calcination of the resulting powder under air at 550°C during 4h (temperature increase rate of 1 °C.min -1 ). Alumina supports were named Al-xP123-yHNO 3 , where x was the porogen to alumina molar ratio (P123/Al) and y the peptizing agent to alumina molar ratio (HNO 3 /Al).

Catalyst synthesis

CoMo oxidic precursors were prepared by incipient wetness impregnation of the alumina supports, using an aqueous solution obtained by dissolution of Co and Mo species present on the support were identified by Raman spectroscopy.

Spectra of the oxidic precursors were recorded at room temperature, using a Raman microprobe Infinity instrument from Jobin-Yvon, equipped with a N 2 cooled CCD detector. The exciting laser source was the 532 nm line of a Nd-YAG laser.

For X-ray photoelectron spectroscopy (XPS) analysis, samples were pressed on an indium foil attached to the sample holder and spectra were recorded using a VG ESCALAB 220 XL spectrometer equipped with a monochromatic AlKα (E = 1486.6

eV) X-ray source (without air exposure in the case of sulfided catalysts). The surface atomic ratios were calculated using the CASA software.

High resolution electron microscopy was performed on a TECNAI microscope (200kV) equipped with a LaB 6 crystal.

Catalytic activity

Thiophene was selected for evaluation and comparison of the catalysts properties, since it is the simplest molecule representative of the aromatic sulfur compounds present in the hydrotreatment feeds. Reaction was performed at atmospheric pressure in a flow-type reactor packed with 0.200 g of catalyst. Before reaction, the oxidic precursor was heated at 400°C under atmospheric pressure for 2 h (temperature increase rate of 6°C min -1 ), under a flow of 10 vol.% H 2 S in H 2 (60 mL min -1 ). The reactor was then cooled to the reaction temperature (300°C). Thiophene (previously purified by two successive vacuum distillations) was introduced in the reactor at a constant partial pressure of 6.65 kPa in a flow of hydrogen (total flow rate = 10 mL.min -1 ). Reactants and products (butane, but-1-ene, trans-but-2-ene, cis-but-2-ene)

were analysed using a gas chromatograph equipped with a flame ionization detector and a Plot-alumina column. The conversion was calculated taking into account the relative response factor of each compound.

In order to evaluate the potential of the solids in the HDS of real feedstock and in conditions close to the industrial ones, selected catalysts were tested on a Straight Run Gas Oil (SRGO) containing 1 wt%S, in a high pressure up-flow microreactor. 10 mL of catalyst pellets (with selected granulometry, between 0.3 and 0.5 mm) were diluted with 15 mL of carborundum (0.25 mm), before being loaded in the isothermal zone of the reactor. The catalysts were sulfided using a mixture of dimethyldisulfide (DMDS) and SRGO (2 wt% DMDS + SRGO) and H 2 . After sulfidation, the feed was switched to the test feed (same SRGO than for sulfidation step), and the operating conditions stabilized (pressure = 35 bar, H 2 /oil = 250 NL/L, LHSV= 2 h -1 ). During each run, the temperature was changed in the sequence 350-360-370°C. Two hydrotreated product samples were collected at each temperature after stabilization for 15 h. H 2 S dissolved in the hydrotreated product oil was removed by stripping with nitrogen gas after sample collection. The total sulfur contents in treated feed samples were measured using an Antek 9000S sulfur analyzer (Ultra-Violet fluorescence).

After one week of testing, the temperature was returned to 350°C to evaluate the stability of the system.

Results and discussion

Survey of synthesis parameters allowing alumina texture control

As presented in the experimental section, alumina supports were prepared using a simple two steps synthesis approach, consisting in precipitation followed by a peptization step with an acidic solution containing P123 porogen. Among the different ways to adjust porosity, the first one is to vary the amount of porogen added. Alumina were thus prepared by maintaining constant the conditions of precipitation and the pH of peptization step and varying the amount of porogen (Table 1). 12.9

13.9

The diffractograms of the three samples prepared with different P123 contents (Figure SI 1) confirmed the presence of a well crystallized γ-alumina phase whatever the P123 content (JCPDS No. 010-0425). The amount of porogen has no visible effect on the crystalline structure of the final solid, in the range of P123/Al ratio studied, with no significant changes in width and intensity of the reflections.

The N 2 adsorption-desorption isotherms obtained for the precipitated alumina and for the three modified alumina supports are presented in Figure 1. All modified samples display isotherms of type IV, with parallel adsorption and desorption branches (and H1 type hysteresis). For the precipitated alumina without porogen addition, while isotherm is of type IV, the hysteresis is of H2 type, characteristic of the presence of slit-shaped pores. The pore size distribution of the precipitated alumina is narrow, centered at 3.8 nm (Table 1). Larger pore sizes between 12 and 14 nm, increasing with the porogen content, are measured for the modified alumina (Table 1). As can be awaited from the pore size evolution, the pore volume also increases with the P123 content (Figure 1, Table 1), to reach 2 cm 3 .g -1 .

The porosity generated in the modified alumina occurs through the random rearrangement of elementary crystallites of alumina, with formation of pores not displaying regular shape and size, as can be concluded from the absence of small angle reflection on diffraction patterns over these materials (not shown). Consequently, the porogen role is to modify the aggregation of alumina particles, resulting in more airy aggregates with a decreased degree of connection between the elementary particles. The second possible way to adjust material textural properties is the control of peptization conditions. Indeed, the role of the peptization step is to separate large agglomerates to obtain a stable suspension. Acidic conditions are applied to ensure the dissolution of a small fraction of the aluminum, their modification impacting dissolution rate and thus indirectly modifying the effect of the porogen on the rearrangement of the particles during drying step. Modified alumina supports were prepared at HNO 3 /Al molar ratio varying from 0.8 to 3.1 while maintaining constant the P123/Al ratio equal to 0.022. These values of HNO 3 /Al are higher than those classically used in a peptization process, but are comparable or slightly higher than values reported in studies developing comparable approaches for alumina porosity modification using porogen ([H + ]/[Al 3+ ] = 0.3-3.0 [54]). However, preliminary experiments at lower ratio (below 0.8) indicated that the modification of porosity remained very limited with the precipitate synthesized in this study and that the 0.8 to 3.1 ratio is the range for which the largest modifications of porosities were achieved.

For all the supports, after thermal treatment at 550°C, XRD patterns are characteristic of the crystalline γ-alumina phase (not shown). 2a). A progressive shift of the hysteresis loops towards higher P/P 0 values is observed with the increase in HNO 3 content. The pore size distribution consequently shifts towards higher values with the increase in HNO 3 /Al molar ratio (Figure 2b). For the material prepared at the highest acidity, a mean pore size of 19.7 nm is measured. In parallel with the increase in mean pore size, a significant increase in pore volume is observed. While the precipitated alumina presents a pore volume as low as 0.30 cm 3 .g -1 , this value progressively increases to reach 2.12 cm 3 .g -1 for Al-0.022P123-3.1HNO 3 (Table 2).

Despite the significant changes in pore size and pore volume with the acidity of the peptization media, the surface area remains around 400 ± 20 m 2 .g -1 whatever the HNO 3 concentration used (Table 2). This suggests that the crystallite size of alumina is not significantly affected during the peptization step and that elementary particles will develop in all cases relatively constant surfaces after the modification step. Meanwhile, evolution in pore volume and pore size clearly shows changes in porogen efficiency with the acidity of the peptization medium. By playing on these two parameters of synthesis, it is then possible to stabilize large pore size and high pore volume in alumina materials, while maintaining specific surface areas around 400 m 2 .g -1 .

Characterization of the CoMo-supported oxidic precursors.

Three modified alumina were selected for catalysts preparation, together with a commercial alumina. Al-0.011P123-0.8HNO 3 , Al-0.035P123-0.8HNO 3 and Al-0.022P123-3.1HNO 3 , denoted respectively Al-A, Al-B and Al-C, were chosen to cover wide ranges of support pore volumes and pore sizes (1.26, 1.98 and 2.12 cm 3 .g -1 for pore volume; 11.9, 13.9 and 19.7 nm for pore size) while maintaining comparable specific surface areas (around 380 m 2 .g -1 ). The commercial alumina, industrially used for HDS catalyst preparation, was denoted Al-P (for PURAL SB3) and calcined at 500°C prior to impregnation. The catalysts were named CoMoxAl-y where x is the molybdenum loading expressed in MoO 3 wt% and y refers to the alumina support (A, B, C and P).

Textural properties of the catalysts

Upon impregnation, different behaviors were evidenced depending on the support:

• For the catalyst prepared using Al-A alumina, the isotherm shape remained of type IV, with minor modification in pore size distribution (Figure 3a, Table 3). The observed decrease in pore volume (∆V P ~ 20% ) can be related to some pore blocking by the Co-Mo phases. However, differences in pore size and surface area with the support, when normalized by the weight gain issued from active phase deposition, remained moderate (< 20%). Such values are characteristic of a support not significantly impacted by the active phase impregnation, such as in the case of the commercial Pural support (Table 3).

• For catalysts prepared over the supports presenting higher pore size and pore volume (Al-B and Al-C), significant changes were observed upon impregnation. The isotherms remained of type IV (shown for CoMo25.4/Al-B, Figure 3b), with a significant decrease in N 2 volume adsorbed. Hysteresis loops were observed to shift towards lower P/P 0 values. While the surface areas per gram of support remained almost constant upon catalyst preparation (∆S BET < 20%), a significant decrease in pore size value was measured for both solids (∆D P ~ 60% -Table 3). This limited surface area decrease, combined to the significant decrease in pore size and volume, indicates a modification of the crystallites organization in the aggregates. Several authors already reported important evolution of alumina support during impregnation process. In the case of mesoporous alumina, Hicks et al. [49] observed decreases between 24 and 59% of the surface area and between 6 and 45% of the pore volume of the carrier after impregnation and calcination steps, depending on b a molybdenum content. However, the materials initially presented lower pore size and pore volume than the materials studied here. Authors attributed the decreases in surface area and pore volume to a thickening of the walls of the support porous structure and to pore filling. Limited hydrolytic stability of mesoporous alumina was also reported by Zhang et al. [59,60]. The porous network quickly lost its ordering when in contact with water, even at room temperature [19,61]. Alternative preparation methods to wet impregnation are reported in the literature to circumvent this issue: thermal spreading [62], impregnation by a solution of molybdenum dioxide diacetylacetonate in methanol [63], methanol assisted spreading of MoO 3 [64].

In our work, pore collapse, due to a rearrangement of the elementary particles during aqueous impregnation step, was observed over alumina with the largest pore diameters. However, even in this case, the improved textural properties of the supports allowed increasing the loading in active phase up to 25 wt%, while the same dMo corresponds to a value of 14 wt% on the Pural commercial support. Moreover, despite the textural modifications, the catalysts always retained adequate properties for their use in heterogeneous catalysis process.

Raman analysis of oxidic supported CoMo phase

Raman spectra of the CoMo oxidic precursors are presented in Figure 4. For all solids, a broad line at 952 cm -1 corresponding to well dispersed polymolybdate species on the support surface was identified [START_REF] Payen | Handbook of Vibrational Spectroscopy[END_REF][START_REF] Blanchard | [END_REF]. Spectra recorded for CoMo25. CoMoO 4 phases (that do not lead to the formation of active CoMoS phase upon activation). This is not always the case over alumina supports. Mazurelle et al. [68] observed the formation of MoO 3 and CoMoO 4 over conventional alumina, for equivalent MoO 3 content as low as 16 wt%. The limited surface area and pore volume (200 m 2 .g -1 and 0.8 cm 3 .g -1 -with a molybdenum surface density of 4.3 at Mo .nm -2 ) displayed by γ-alumina extrudates used are at the origin of the poor Mo phase dispersion. In this last study, at the selected 16% MoO 3 loading and considering the pore volume, the impregnation solution is close to saturation. Such conditions are responsible for the precipitation of the entity during impregnation, leading to poor molybdenum phase dispersion. Over alumina synthesized in this work, the calculated Mo surface densities vary between 4.4 and 4.9 at Mo .nm -2 (Table 3). These values are higher than the 4.3 at Mo .nm -2 determined for the same precursor on conventional γalumina and is not far from the values of maximum densities deposited on γ-alumina using complexing agents (5.2 at Mo .nm -2 ) while maintaining acceptable Mo dispersion [76]. Accordingly, these results demonstrate the possibility to prepare modified alumina supported catalysts with high molybdenum loading while maintaining good dispersion at high Mo densities.

Catalysts surface analysis.

XPS spectra of Al2p, O1s, Mo3d, Co2p and C1s levels were recorded for the CoMo oxidic precursors. Figure SI2 shows typical Mo3d and Co2p levels spectra, presented for CoMo24.8/Al-C catalyst. For the entire series of solids, the Mo3d This surface carbon content is mainly attributed to contamination, but on these alumina, a fraction of residual carbon can originate from residues issued from the thermal decomposition of the triblock copolymer used as porogen.

Values of atomic surface ratios are gathered in Table 4, together with the theoretical bulk ratios. All modified alumina derived catalysts present n Mo /n Al ratios determined by XPS that are similar (0.15±0.01). This value is slightly higher than the theoretical bulk ratio, indicating a satisfying dispersion of the molybdenum species on the alumina surface, as expected from the Raman results. Similar values of theoretical and experimental data are obtained on the Pural based catalyst for the n Mo /n Al and also for n Co /n Al ratios, while experimental n Co /n Al is lower than the bulk ratio in the case of the materials prepared over the Al-B and Al-C supports. For CoMo25.0/Al-A, the experimental n Co /n Al is only slightly higher than the theoretical bulk ratio. These results confirm the conclusions drawn from Raman analysis. Indeed, as bulk Co

Catalytic properties in thiophene HDS

Table 5 presents the catalytic performance obtained in thiophene HDS for the series of solids prepared with modified alumina. The results show a wide variation in reaction rate, from 122.5 and 186.1 L.h -1 .kg -1 depending on the support used. The order of activity per mass unit is as follows:

CoMo24.8/Al-C>CoMo25.4/Al-B > CoMo25.0/Al-A Activity measured for the three catalysts prepared over the modified alumina varies by a factor ∼1.5, with in all cases molybdenum initially in a well dispersed phase with no loss in bulk unsulfidable phase such as MoO 3 or CoMoO 4 . The presence of Co 3 O 4 has been evidenced on the two most active materials (and especially on the most efficient one CoMo24.8/Al-C). The loss of a fraction of the initial cobalt in a poorly dispersed bulk oxide phase (that will not incorporate the CoMoS active phase) does not seem to be detrimental to the material catalytic performance.

On CoMo catalysts prepared on commercial stable alumina, it is well known that the Co/Mo ratio in the oxidic form of the solids must be comprised between 0.4 and 0.5 to ensure enough Co atoms to promote molybdenum disulfide slabs [69]. Indeed upon preparation a loss of cobalt is always evidenced at the different steps of the catalyst preparation especially during the drying and calcination steps [78]. During these thermal treatments a more or less important fraction of cobalt migrates inside the alumina lattice to form a pseudo CoAl 2 O 4 type species and thus cannot participate to the formation of the CoMoS phase [77]. This is probably the case on Al-A support, which textural properties do not evolve upon impregnation.

On Al-B and Al-C supports, the low stability during impregnation, and more precisely the pore collapse, induces a rearrangement of the porosity during the impregnation-drying sequence which leads to precipitation of cobalt species giving XPS results show different carbon content in the prepared materials (Table 4). The most active catalyst (CoMo24.8/Al-C) contains the highest carbon surface content (20%), while comparable carbon content were measured for the other less active solids (10-12%). The influence of carbon on the activity of CoMo catalysts has been widely studied, either when used as support or when a precursor of C is deposited on the support. The presence of carbon is reported to induce: (i) different sulfidation degrees of Co and Mo and (ii) different structures and/or morphologies for the generated active phase [79,80]. Different sulfidation degrees of Mo and Co may obviously lead to more or less promoted and dispersed active phases [81]. Moreover heat generated during the sulfidation reaction can be partially absorbed by these residues, resulting in different crystallite growth than over carbon free support [82], with positive effects on activity for HDS reactions. High HDS activities can be obtained over carbon supported Co(Ni)Mo-S active phase [84][85][86], with possible formation, during sulfidation, of active carbide phases [87]. Consequently, impact of carbon on final properties of prepared materials cannot be excluded.

These results in thiophene HDS thus show the possibility to produce efficient highly loaded catalysts, where good dispersion of molybdenum is preserved. In order to confirm the potential of the developed solids in conditions close to the industrial ones, the most efficient catalyst CoMo24.8/Al-C was selected for evaluation in the HDS of SRGO, its performance being compared to that of the commercial Pural based material.

Characterization of the active phase after sulfidation in liquid phase was also undertaken to better understand the catalytic behavior. By statistical analysis of the images, the distribution in slab length and stacking of the MoS 2 slabs were obtained and appeared to be similar on both solids, with respective average slab length of 2.7 and 2.5 nm and average stacking of 1.6 and 1.4 for CoMo24.8/Al-C and CoMo14.1/Al-P catalysts respectively. Morphology of the active phase is thus similar on both catalysts despite their difference in loading. These results confirmed that the quantity of cobalt involved in the formation of the active CoMoS phase after sulfidation in the liquid phase corresponds to approximately half of the edge and corner atoms of the MoS 2 slabs, as already suggested by Herry et al. [90] This also shows that only a small part of the cobalt atoms introduced during the preparation is used for promotion, thus the formation of Co 3 O 4 with the excess cobalt is not detrimental to promotion.

Catalytic properties in SRGO HDS

Catalytic performance of CoMo24.8/Al-C and CoMo14.1/Al-P were evaluated in the HDS of SRGO 10000 ppmS. For both solids, the residual sulfur content in the hydrotreated product was plotted as a function of the reactor temperature, as shown in Figure 6. The modified alumina derived catalyst appears significantly more efficient than the commercial alumina supported one (per volume of catalyst and per mass of catalyst, considering their similar apparent densities), with 181 versus 415 ppmS at 350°C and 34 versus 100 ppmS at 370°C. A substantial temperature gain, which is an important parameter in industrial applications, is thus evidenced for the CoMo24.8/Al-C (17°C for 100 ppm residual S). Moreover after one week of test, the performance measured again at 350°C was found identical to that obtained initially, showing the stability of the system.

Characterization of the sulfided phase has shown similar morphology for the active phase together with similar substitution degree. The better performance of the CoMo24.8/Al-C can then be attributed to the higher quantity of active phase that is introduced in the reactor, due to its higher Co and Mo loading.

These results confirm the potential of highly loaded CoMoS catalysts developed in this study as support for HDS catalyst, not only for the conversion of model molecules but more interestingly also for the desulfurization of real feedstocks. From our knowledge, this is the first time that such high loading, with well dispersed active phase, is reported over alumina in HDS of SRGO under experimental conditions representative of industrial ones. Due to the high active phase loading allowed by the improved textural properties, final material presents increased HDS catalytic properties.

Conclusions

Alumina porosity can be easily tuned using a post-modification approach involving the use of triblock copolymer structuring agent. Addition of porogen was performed during the peptization step, which is industrially performed prior to the alumina shaping. No extra step would thus be required in the industrial alumina preparation process. The amount of porogen and the acidic conditions of the peptization step were varied in this study as they are key parameters allowing to tune the final textural properties of the support. While maintaining high surface areas (close to 400 m 2 .g -1 ), large porosity were thus obtained: pore volume can exceed 2 cm 3 .g -1 , with pore diameters that can reach 20 nm. The role of the selected porogen, in our case the triblock copolymer P123, consists in the modification of the alumina particles agglomeration and the acidic conditions selected for the modification steps does not induce significant modification of the elementary particle size, as deduced from the preservation of almost constant surface area for all modified alumina.

The high surface areas and high pore volumes displayed by the modified alumina allowed to prepare highly loaded CoMo catalysts. Upon impregnation, slight decrease in specific surface was observed on all solids while some collapse of the porous structure was noted on solids with large pore size superior to 15 nm. Final textural properties remained however attractive, with specific surface areas and pore volumes higher than the values encountered for classical alumina support. On all solids, satisfying dispersion of molybdenum species is obtained with no formation of undesirable bulk species as usually observed at high loading. On the solids presenting pore collapse, the unusual presence of Co 3 O 4 was observed, which was explained by the precipitation of cobalt species due to limited interaction of the cobalt cations with support surface combined to decrease in pore volume. It is however suggested that in this case, the formation of CoAl 2 O 4 type species is not favoured, the amount of cobalt available for promotion remaining thus sufficient.

Catalysts displayed activities in the HDS of thiophene varying by a factor of 1.5 and the performance of the most efficient solid of the series was evaluated in the HDS of SRGO under industrial conditions. It was found significantly more active than a CoMo catalyst prepared on a commercial alumina with similar dMo (temperature gain of 17°C at 100 ppm residual sulfur content), with a preserved activity after one week of testing. The two solids presented similar morphologies of the active phase as well as similar substitution degree as determined from XPS and TEM characterization of the sulfided phase. The higher performance of the mesoporous alumina supported catalyst can then be attributed to its high Mo and Co loading. This work thus highlights the interest of developing alumina supports with improved textural properties in order to produce well-dispersed highly loaded catalysts with enhanced HDS ability.

Figure 1 .

 1 Figure 1. N 2 adsorption-desorption isotherms of alumina prepared by PSM using different P(123) contents; n(P123) = 0.011, 0.022, 0.035 mol.

Figure 2 .

 2 Figure 2. N 2 adsorption-desorption isotherms (a) and BJH pore size distributions (b) obtained for alumina supports prepared under different peptization acidic conditions; n(HNO 3 ) = 0.8, 1.3, 1.8, 3.1 mol. Isotherms are shifted vertically by 1 cm 3 .g -1 each to facilitate reading.

Figure 3 .

 3 Figure 3. N 2 adsorption-desorption isotherms of support Al-A and catalyst CoMo25.0/Al-A (a), of support Al-B and catalyst CoMo25.4/Al-B (b).

Figure 4 .

 4 Figure 4. Raman spectra of CoMo catalysts supported on Pural Al-P, Al-A, Al-B and Al-C supports.

  3 O 4 phase was not detected by Raman over CoMo25.0/Al-A, all cobalt atoms can be considered as observable by XPS, including those possibly located in tetrahedral sites of CoAl 2 O 4 phase [66,77]. For the CoMo25.4/Al-B and CoMo24.8/Al-C materials, Raman analysis evidenced the formation of Co 3 O 4 phase and the measured difference between the n Co /n Al (th) and n Co /n Al (XPS) ratios, even limited, supports this observation as less Co atoms are then visible by XPS.

Co 3 O

 3 4 after calcination. The precipitation of these cobalt species probably limits the interaction of Co with the support and thus the migration of cobalt inside the alumina lattice. Only the cobalt in the Co 3 O 4 phase is thus lost for promotion.We can then propose that upon impregnation of the various supports that we use, either the support is stable (Al-A) and some Co is lost by formation of CoAl 2 O 4 type species, either the support is not stable (Al-B and Al-C) and Co is lost by formation of Co 3 O 4 , insuring in all cases enough available Co for efficient promotion.

3. 4 .

 4 Characterization and evaluation in SRGO HDS of the CoMo-supported sulfided catalysts CoMo24.8/Al-C and CoMo14.1/Al-P.

3. 4 . 1 .

 41 Morphology of the active phase for CoMo24.8/Al-C and CoMo14.1/Al-P catalysts. Representative TEM images of CoMo24.8/Al-C and CoMo14.1/Al-P catalysts sulfided in liquid phase are shown in Fig. 5, exhibiting the typical structure of the layered MoS 2 phase.

Figure 5 .

 5 Figure 5. HRTEM images of CoMo24.8/Al-C (a) and CoMo14.1/Al-P (b) sulfided in liquid phase.

3. 4 . 2 .

 42 XPS analysis of the sulfided catalysts CoMo24.8/Al-C and CoMo14.1/Al-P. XPS spectra of the Mo3d and Co2p levels (Figure SI 3) were recorded for CoMo24.8/Al-C and CoMo14.1/Al-P sulfided catalysts. Mo spectra (Fig SI3a) exhibited three well-known contributions attributed to Mo VI oxide (Mo3d 5/2 BE = 232.6 eV), Mo V oxysulfide (Mo3d 5/2 BE = 230.5 eV) and Mo IV sulfide (Mo3d 5/2 BE = 229.0 eV). In Co spectra (Fig SI3b), the three identified contributions correspond to Co in oxidic environment (Co2p 3/2 BE = 781.5 eV), Co in sulfided environment (Co2p 3/2 BE = 778.2 eV) ad Co in the CoMoS phase (Co2p 3/2 BE = 779.0 eV). A decomposition of the XPS Mo3d and Co2p peaks was performed in a way similar to that already described in the literature [88]. All the solids showed a satisfactory and similar sulfidation extent of molybdenum with a percentage of MoS 2 phase of 74.7% for CoMo24.8/Al-C and 70.7% for CoMo14.1/Al-P. The percentage of cobalt atoms involved in 10 nm bthe CoMoS phase was calculated from the decomposition of the Co2p photopeaks and corresponded to 41.6% for CoMo24.8/Al-C and 28.9% for CoMo14.1/Al-P. From these XPS data, and taking into account the morphological parameters of the active phase determined by TEM, it is possible to calculate the substitution degree, that is the percentage of edge and corner atoms in the molybdenum disulfide slabs substituted by cobalt atoms[89]. Similar substitution degrees were obtained on the catalysts : 0.38 and 0.42 for CoMo24.8/Al-C and CoMo14.1/Al-P respectively.

Figure 6 .

 6 Figure 6. Catalytic performance of the CoMo24.8/Al-C (▲) and CoMo14.1/Al-P (■) catalysts in the HDS of SRGO. Residual sulfur content in the desulfurized feed versus the temperature of the reactor.

Figure SI 1 .

 1 Figure SI 1. XRD diffractograms of alumina supports obtained at different P123 contents and calcined at 550°C; n(P123) = 0.011, 0.022, 0.035 mol.

Figure SI 2 .

 2 Figure SI 2. XPS spectra of Mo3d (a) and Co2p (b) levels for CoMo24.8/Al-C.

Figure SI 3 .

 3 Figure SI 3. XPS spectra of Mo3d (a) and Co2p (b) levels for sulfided CoMo24.8/Al-C.

Table 1 .

 1 Effect of the amount of porogen on textural properties of alumina calcined at 550°C.

	Sample	n(P123)	S BET	V p	D p
		/mol	/m².g -1	/cm 3 .g -1	/nm
	Al-0P123-0HNO 3	0.000	293	0.30	3.8
	Al-nP123-0.8HNO 3	0.011	381	1.26	11.9
		0.022	411	1.63
		0.035	391	1.98

Table 2 .

 2 Effect of peptization media acidity on the textural properties of the calcined alumina.

	Sample	n(HNO 3 )	S BET	V p	D p

Table 3 .

 3 Textural properties of oxidic CoMo-containing catalysts.

		Catalyst			Variations
	Sample	S BET	V p	D p	dMo real	∆S BET	∆D p
		/ m 2 .g -1	/ cm 3 .g -1	/ nm	/at.nm -2	/%	/%
	CoMo25.0/Al-A 219/320 [a] 0.66/0.96 [a] 11.1	4.8	-16	-7
	CoMo25.4/Al-B 244/359 [a] 0.37/0.55 [a] 5.2	4.4	-8	-64
	CoMo24.8/Al-C 211/307 [a] 0.65/0.95 [a] 7.2	4.9	-19	-63
	CoMo14.1/Al-P 161/196 [a] 0.37/0.45 [a] 7.3	4.0	9	0
	[a] Values corrected by removing the contribution of the weight gain consecutive to the
	introduction of the active phase (expressed per gram of support).

  The formation of cobalt oxide on CoMo25.4/Al-B and CoMo24.8/Al-C can be attributed to the significant modifications of the pore structure upon impregnation for these two materials, since it was not observed over classical alumina and over the Al-A support that present better stability. During impregnation, Co 2 Mo 10 solution exhibits a slightly acidic pH (close to 4). Under these conditions, alumina surface is positively charged (alumina point of zero charge is expected to be around 8)[START_REF] Euzen | Alumina, Handbook of Porous Solids[END_REF]. [Co 2 Mo 10 O 38 H 4 ] 6- anions, stable in a wide range of pH[START_REF] Moreau | [END_REF], can thus adsorb on the support, while Co 2+ counter cations in solution cannot directly interact with the surface. Due to the

	4/Al-B and
	CoMo24.8/Al-C materials displayed additional sharp lines located at 690, 480 and 516
	cm -1 , revealing the presence of Co 3 O 4 phase [67]. The use of Co 2 Mo 10 as a precursor of
	CoMo phase, whatever the support nature (zirconium oxide, titanium oxide or γ-

alumina), generally ensures the formation of well dispersed and easily sulfided phase.

The formation of Co 3 O 4 is generally not observed using this approach

[68][69][70][71][72][73]

. significant decrease in pore volume of Al-B and Al-C supports, part of the impregnation solution can be expulsed outside of the pores. The premature precipitation of cobalt species due to limited interaction of the cobalt cations with support surface combined to decrease in pore volume can thus lead to the formation of bulk Co 3 O 4 phase upon thermal treatment. Concerning molybdenum phase, good dispersion is obtained for all materials, with no evidence of the presence of MoO 3 or

Table 4 .

 4 n Mo /n Al , n Co /n Al and n Co /n Mo atomic ratios. (th) theoretical values calculated from material composition; (XPS) experimental values issued from XPS analysis.

	Sample	n Mo /n Al (th)	n Mo /n Al (XPS)	n Co /n Al (th)	n Co /n Al (XPS)	n Co /n Mo (XPS)	C 1s /%
	CoMo25.0/Al-A	0.13	0.15	0.065	0.073	0.51	10.0
	CoMo25.4/Al-B	0.13	0.14	0.066	0.053	0.39	12.1

Table 5 .

 5 Reaction rates (per mass of catalyst and per mole of Mo) of the synthesized materials for thiophene HDS reaction at 300°C.

	Sample	Reaction rate / L.h -1 .kg -1	Normalized reaction rate / L.h -1 .mol Mo -1
	CoMo25.0/Al-A	122.5	70.5
	CoMo25.4/Al-B	147.1	83.4
	CoMo24.8/Al-C	186.1	108.1

Acknowledgements

This work was supported by the Equatorian Government and IFPEN. Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur et de la Recherche, Région Nord -Pas de Calais and FEDER are acknowledged for supporting and funding partially this work (XPS, TEM). M. Trentesaux is acknowledged for XPS analysis support.


Vincent Reinbold
email: vincent.reinbold@g2elab.grenoble-inp.fr

Laurent Gerbaud

Emmanuel Vinot
email: emmanel.vinot@ifsttar.fr

MULTI-OBJECTIVE OPTIMIZATION OF THE SIZING OF A HYBRID ELECTRICAL VEHICLE

Keywords: Electrical machine, hybrid electrical vehicle, magnetic equivalent circuit, sizing, energy management, multi-objectives optimization

Hybrid electrical vehicles involve two sources of energy, usually gasoline and electricity. The energy management determines the power sharing between the internal combustion engine and the electrical machine (EM). It is highly dependent on the driving cycle (i.e. the use of the vehicle). In this context, the optimal sizing of the EM is determined by: the driving cycle, the power-train characteristics (i.e. ratios and physical limitations e.g. maximum torque available) and the energy management. The key idea of this work is to involve the driving cycle and the environment of the electrical machine in a global multi-objective optimization process taking into account an optimal energy management and an accurate model of the EM based on magnetic circuit equivalent model.

Introduction

Hybrid electrical vehicles (HEV) represent an innovative solution to reduce pollutant emission and fuel consumption. A possible configuration of the HEV is a parallel two-clutch architecture (Fig. 1). In this architecture, both Internal Combustion Engine (ICE) and Electrical Machine (EM) provide power to the wheels.

The energy management is a key point of the operating of HEVs as it highly influences the fuel economy. In fact, it determines the propulsion mode (electric, hybrid or thermal) and the power sharing between the ICE and the EM.

On the other hand, the sizing of the electrical machine is probably one of the most common optimization problems in electromagnetic research [START_REF] Barba | Design of Hybrid Excited Synchronous Machine for Electrical Vehicles[END_REF] [2] [START_REF] Chau | Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles[END_REF]. Usually, the problem is to maximize the efficiency of the EM for given operating points subjected to external constraints such as weight, thermal, physical limitations, etc. In a dynamic system, where operating points of the EM are not a priori known, the problem is more complex.

In fact, in HEVs, the energy management highly influences the operating of the electrical machine.

And, the size and performances of the machines highly interfere with the management. Moreover, the sizing of the other components (ICE, gear, etc.) has a high impact on the operating of the machine. The classical design process usually performed for HEVs consists in sizing energetically the system using coarse models of components such as efficiency maps for the EM [START_REF] Bertram | Multi-objective optimization of a parallel hybrid electric drive train[END_REF] [START_REF] Buerger | Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[END_REF]. It fixes the constraints on the components (battery number of elements, engine and electrical machine minimum required torque, etc.) and the energy management REINBOLD, Vincent, VINOT, Emmanuel, 2016, Multi-objective optimization of the sizing of a hybrid electrical vehicle, International Journal of Applied Electromagnetics and Mechanics, IOS Press, pp. 1-12, DOI: 10.3233/JAE-140160 [START_REF] Chau | Overview of permanent-magnet brushless drives for electric and hybrid electric vehicles[END_REF]. Then, the components are sized (using fine model) independently of their interaction with the system and of their effect on the management laws. It is clear that this method can easily lead to sub-optimal global solution.

Thus, in this context, the authors proposed to develop a global optimization. The proposed method will consider the control problem (energy management) as a sub-problem embedded in a global sizing optimization.

In this work, the optimal control method using discrete dynamic programming DDP [START_REF] Bellman | Dynamic programming and Lagrange multipliers[END_REF] [6] is chosen (section 2.B). The proposed design uses a fine, but fast enough to compute, electrical machine model (section 2.A). This design leads to the optimization of the electrical machine and other component characteristics (gear ratio, battery size, ICE power, etc.) in one global optimal design taking into account the influences between components, energy management and mission of the vehicle.

The first section of this paper details the modeling of the electrical machine and its validation with finite element method (FEM). The optimization process is then presented in a second section. This section also includes the presentation of the vehicle model. The third section presents the global sizing method proposed in the paper. A brief remaining on the optimal control problem which can be seen as a sub-optimization problem is also presented. The last section presents the results obtained with such a method for different driving conditions in terms of fuel economy and electrical machine geometries.

Modeling of the HEV

2.A. Modeling of the electrical machine

Usually, in HEV system's design, the Electrical machine (EM) is modelled using efficiency maps and applying scaling factor on torque, losses, power, etc. [START_REF] Buerger | Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[END_REF] [2] [START_REF] Kirk | Optimal control theory: an introduction[END_REF]. Such approach leads to a lack of accuracy (efficiency and maximum torque) especially considering that in our application the power of the EM varies from 5 to 50 kW. Moreover, there is no degree of freedom on the "geometries" of the machine whereas it can highly change the efficiency area and thus the operating of the machine considering optimal management. Thus, in this work, authors proposed to use an EM model taking into account geometrical parameters (see section 3.A).

In this study, an internal permanent magnet synchronous motor is chosen as it is the most used machine in electrical power train. The EM is represented by a magnetic equivalent circuit model (i.e. a reluctance circuit) (MECM), using Reluctool software tool [START_REF] Du Peloux | Automatic generation of sizing static models based on reluctance networks for the optimization of electromagnetic devices[END_REF] [8] [START_REF] Delinchant | An optimizer using the software component paradigm for the optimization of engineering systems[END_REF]. In such a model, flux tubes are represented by reluctances.

For sizing, reluctance expressions depend on geometrical parameters, (e.g. air-gap length, magnet sizes, stator external radius…) and winding characteristics. A possible circuit model of one pole of the EM is presented in Fig. 2.

The MECM is fast to compute (around 100 ms), and takes into account non-linear phenomena, such as magnetic saturation. The magneto motive forces depend on the stator current and the magnetic reluctances depend on the geometrical parameters and the magnetic characteristics of materials. The resolution of this nonlinear circuit is based on the Hopkinson's law and uses Newton-Raphson algorithm. This leads to the flux linkage and the induction field (B) in each magnetic reluctances.

To dispose of the static torque of the machine for different internal electrical angles, the rotation of the machine rotor is simulated by a multi-static solving. To avoid a change of MECM at each position, the rotor is considered to be fixed and the stator currents are changed to simulate the rotation. This is equivalent to a rotor rotation with fixed stator currents. This allows fast solving of the MECM (which remains the same) and very lower model size (so need of RAM memory). The drawback of such a method is that the torque ripple cannot be considered. In fact, the reluctance scheme corresponds to those with magnetic pole aligned to stator teeth.

Intermediary positions have to be taken into account to simulated torque ripples. For that, reluctance schemes with almost two times more reluctances parameterized by the rotor position are needed.

In the Park's reference (rotating bidirectional reference), the knowledge of the direct and the quadratic flux linkage d and  q leads to the first harmonic of the direct and quadratic voltage v d and v q :

           d q s q q d s d i R v i R v   ( 1)
where i d and i q are respectively, the direct and the quadratic current,  is the electrical pulsation of the electrical machine and R s is the electrical resistance of one stator phase.

The calculation of the electrical power leads to the estimation of the mechanical mean torque  em , for an active sign convention, i.e.  em positive in the motor mode :

em f iron d q q d em P P i i p         ) ( 2 3 (2)
where P iron and P f are respectively, the iron losses and the mechanical losses. p is the number of pole pairs and  em is the rotation speed of the electrical machine. The iron losses are calculated thanks to a first harmonic Bertotti's model in each magnetic reluctance, taking into account hysteresis, excess and eddy-current losses [10] [11]. Mechanical losses are assumed to be proportional to the square of the external radius of the electrical machine and proportional to the rotation speed [START_REF] Hsu | Report on Toyota/Prius Motor Torque-Capability,Torque-Property,No-Load Back EMF[END_REF].

2.B. Validation of the electrical machine model

In order to estimate the validity of this model for a global sizing process, a model validation of the magnetic circuit model has been made using a finite element method (FEM) with Flux2D. The initial geometrical characteristics and manufacturing assessment come from pictures and measurements of the Toyota Prius 2004 EM [START_REF] Hsu | Report on Toyota/Prius Motor Torque-Capability,Torque-Property,No-Load Back EMF[END_REF]. This initial machine is simulated using a magneto static method. This model allows an accurate computation of flux linkage, torque and losses for different mechanical operating points. Fig. 3 presents a comparison between flux linkage computed with the MECM and the FEM models. The flux linkage is represented versus the internal electrical angle, i.e. the angle between the current and the q-axis in Park's reference. One can see the good agreement of the MECM with the fine model (FEM). The evaluation error is lower than 5% for all the internal electrical angle possible ranges. MECM presents a good accuracy to calculate flux linkages (Fig. 3). The torque is also in good accordance with those obtained with FEM method (Fig. 4) except for the torque ripple which is not simulated with our model (section 2.A). A MECM model appears then to be relevant for an optimal global sizing process. It is fast enough (100 ms) to be called thousands of times.

2.C. Modeling of the hybrid electrical vehicle

The vehicle model is based on a systemic approach. Schematic representation and notations are presented in Fig. 5.

The modeling of the HEV is based on the knowledge of the driving cycle (vehicle speed with respect to time). An upstream approach from wheel to components allows to calculate the ICE operating point in a backward manner. Knowing the vehicle weight and inertia, the vehicle acceleration leads to the required wheel torque   (t). Knowing the demanded wheel torque and speed, and the gear box ratio, the torque and the speed before the first clutch are given by the following equations:

) ( ) ( ) ( ) ( * t k t k t red bv t s red      (3)                   min * * min ) ( 1 2 ) ( else ) ( ) ( ) ( ) ( ) ( ) ( 1 )
) ( ) ) ( ( ) ( ) ( ) ( *           (5)
) ( ) ( * t t ice    (6)
where,  ice and  ice are respectively the engine torque and speed,  em ,  em, and J em are respectively the electrical machine torque, speed and inertia.  cpl and k cpl are the efficiency and ratio of the coupling device.

In electrical propulsion mode u 2 (t)=0 :

) ) ( ( ) ( 0 ) ( * dt d J t i k t em em bat em cpl t s cpl        (7) 0 ) (   t mt (8)
The model of the battery is a classical serial open circuit voltage source and resistance. The electromotive force E, depends on the state of charge, soc(t). The serial resistance depends on the battery state of charge and current.

The ICE model is made using a specific fuel consumption (SFC) map (Fig. 6). The colored lined represents the specific fuel consumption, i.e the fuel burned in grams to produce one kW/h of mechanical energy on the shaft of the engine. Up and low torque limits are represented with a solid black line. The low bound correspond to the engine breaking with zero fuel consumption.

During the sizing process, the maximal power of the ICE, P ICE is changed applying a scaling factor on the torque and the fuel consumption ( ICE =P ICE /P ICE_nom ). It is usually assumed that the power density is constant and lengths proportional to  ICE 1/3 [START_REF] Bertram | Multi-objective optimization of a parallel hybrid electric drive train[END_REF]. Mass moments of inertia have units of dimension M.L 2 , this leads to a mass proportional to  ICE and a moment of inertia proportional to  ICE 5/3

. The SFC remains thus the same.

Optimization of the sizing of the HEV

3.A. Optimization problems

The optimization parameters taken into account in the paper are the number of NiMh modules (N bat ), the continuous voltage of the converter (U bus ) the ratios (k cpl , k red ), the standard power of the ICE (P ICE ), and geometrical parameters of the EM (X em ). Fig. 7 presents the geometrical parameters of the EM. X is defined as the set of the 15 optimization variables. All of them are continuous.

    Depth MAGWID S W S H S H GAP LM RAD RHQ X X k k P U N X em em red cpl ice dc bat , , 3 , 4 , 3 , , , , 1 , , , , , ,    (9)
The objectives to minimize are the fuel consumption over a driving cycle (J 1 ) and the number of battery modules (N bat ):

dt X t u t i m J bat t t fuel f ) ), ( ), ( ( 2 1 0
   (10)
where

fuel m 
is the instantaneous fuel rate, u 2 (t) the state of clutch 2, i bat the battery current and X the optimization parameter set [START_REF] Delinchant | An optimizer using the software component paradigm for the optimization of engineering systems[END_REF].

The main constraints to be respected are:

-geometrical constraints on the electrical machine -battery state of charge (soc) at the end of the driving cycle (section 3.B) -dynamic performances of the vehicles, determined using the previously presented vehicle model; Table 1 presents the constraints used below.

Fig. 8 shows the optimization strategy of the sizing of the parallel-HEV. The control problem is considered as a sub-optimization problem embedded in the global optimization of the sizing of the vehicle. The global sizing optimization is performed using multi-objective NSGA-II algorithm [START_REF] Deb | Multi-objective optimization using evolutionary algorithms[END_REF]. This allows to perform a multi-objective optimization and to dispose of a Pareto front which allows to choose an architecture after the optimization process. The optimization has been carried out using NSGA-II implementation from Matlab.

Consequently, this problem involves 15 optimization variables and 10 constraints. The computation time of the objective for one set of parameters and a driving cycle of 556s (1s step time), is about 16s with an i7-2630 QM processor and 8Go RAM. The global optimization time, with 60 individuals and 500 generations is about 24h using a 6 cores parallel computation.

As said before, in the paper, the two objectives to be minimized are: the fuel consumption and the battery number. Nevertheless, with this approach, it becomes easy to add objectives representing the cost or the volume of raw material for example. In future works, this will be really useful to make a choice after sizing process regarding economic criteria.

3.B. Optimal control problem

The control problem is a key point of HEV operating and is even more critical in global design process.

For real time implementation in vehicle, a rule-based strategy is usually used. However, such a strategy highly depends on the sizing of the vehicle and on the efficiency of the components. Thus, it can be relevant for one sizing and not for another. To avoid this non monotonic effect in an optimization process, the authors chose to use the optimal energy management (OEM), based on optimization methods. This leads to the optimal fuel consumption of the vehicle for a given set of parameters and thus allows a fair comparison between different sizings. However, this strategy requires the knowledge of the driving cycle in advance.

In the proposed method, the discrete dynamic programming (DDP) [START_REF] Bellman | Dynamic programming and Lagrange multipliers[END_REF] [6] [14] is used and is solved at each step of the sizing optimization. A good representation of this optimization problem is a SOC versus time graph (Fig. 9) limited by maximum battery charge and discharge capabilities. The constraint on the final SOC is obviously respected by the building of the limits (Fig. 9).

This graph is regularly sampled in time and SOC. The points of two consecutive columns are linked by oriented edges associated to a fuel consumption. This fuel consumption depends on the drive cycle profile and the SOC variation between the two points of an edge. It is calculated using the previously presented vehicle model (section 2.C). The sum of fuel consumption of the edges on a trajectory provides the objectives to minimize. The DDP method is then applied to find the best trajectory in an efficient way [5] [6].

Results

This section presents the results obtained when using the previously proposed method. Different driving cycles representing urban road and highway conditions are used. A first initial sizing is described to provide a reference.

4.A. Initial sizing and performances of the hybrid electrical vehicle

The initial sizing (Table 2) is based on those of the Toyota Prius II. The number of battery elements is 28 leading to a global battery power of 30 kW. The initial geometry of the machine corresponds to those of the Prius and has a power of 50kW.

In our case of parallel architecture, the EM machine power is normally chosen equal to the standard power of the battery pack. The EM has thus been downsized using a scaling factor on every dimension (see

section 3.A).
The coupling ratio is chosen to be 0.7 so that the optimal rotation speed of the electrical machine matches with the optimal rotation speed of the internal combustion engine. Gear box ratios, ICE and reduction ratio are based on an existing conventional vehicle, which is the Renaud Clio. The initial ICE fuel consumption map is presented Fig. 6.

Initial fuel consumptions of the vehicle are shown in Table 3.

4.B. Result for several driving conditions

The global optimization process has been applied to three different driving cycles. About 27000 simulations are needed for each cycle. Computation time depends on the driving cycle length and varies from 16h to 24h. This optimization is performed using parallel computing (8 cores). One can see that there is a compromise between the battery pack size and the fuel consumption over the driving cycle. The fuel consumption logically decreases when the number of battery elements increase. In fact, the battery can be used in a more efficient manner and in particular regenerative braking energy can be completely recovered. However, over a certain number of battery elements, no improvement can be obtained.

The battery becomes more and more heavy and cannot be used in a more efficient manner.

Table 3 presents the optimal design obtained for 25 elements in the battery pack which seems a good trade off -fuel consumption versus battery numbers-in the Pareto front. It is compared to the initial sizing of the electrical machine and the component. Fig. 11 presents the corresponding obtained geometries of the electrical machine.

In Table 3, it clearly appears that the fuel consumption is reduced from 10% with the proposed optimal method compared to an initial design based on existing components. Going from urban driving conditions to highway conditions the power of the EM decreases when those of the ICE increases. This can be explained by considering that pure electrical modes (propulsion and regenerative braking) are more involved and efficient in urban conditions, whereas ICE is highly involved in highway condition.

Fig. 11 shows that, compared to the initial geometry, the volumes of magnet and copper increase. This probably allows improving the efficiency of the EM on its operating point; this, taking in mind that global optimization leads to the best trade-off between EM and ICE efficiency.

Efficiency maps of initial sizing and the optimal solution for the urban cycle and operating points over the urban driving cycle are presented in Fig. 12. First, we note that both EM are over-sized considering the operating points. This is due to a compromise between the standard powers of the ICE because the total installed power is mainly constrained to the dynamical performances. One can see the differences on the torque limits. It is mainly explained by the copper section difference and the maximal voltage available (c.f. Table 3).

Comparing both simulations, we can measure an improvement of 3.34% of the EM efficiency over the whole cycle. Over the urban driving cycle, the fuel consumption gain between the two sizings can be partly explained by a better use of the EM.

Conclusion

This paper proposes a new global optimization method to size the power train of a hybrid vehicle. The EM is sized at the same time as its surrounding components (gear, battery ...). For that, a fast but accurate model of the EM using magnetic circuit model has been developed. The energy management control problems, which highly interfere with the components size and efficiency is solved using DDP optimal method. This allows a fair comparison between the different sizings and avoids the non-monotonic effect of energy management in the sizing process.

DDP is embedded in a multi-objective genetic optimization with EM geometrical parameters and system parameters. This provides the Pareto front fuel consumption/battery number of elements. The time calculation (16 to 24h) proves the feasibility of such an approach (optimal control and fine EM model embedded in NSGA algorithm). The results shows an improvement on fuel consumption around 10% compared to an initial sizing based on decoupled approach.

Pareto front including economical consideration can easily be obtained adding a cost or volume of raw material objectives. This allows an a posteriori choice of the final architecture of the drive train considering the actual price of material and fuel.

This method is currently applied to more complex hybrid architectures containing two or more electrical machines.

Acknowledgments

Fig. 10

 10 Fig. 10 presents the Pareto front -number of battery elements versus fuel consumption-obtained for urban driving conditions. All the simulated individuals are plotted. The corresponding Pareto front is represented in bold.

Fig. 1 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8

 1345678 Fig. 1 Parallel HEV architecture Fig. 2 MECM circuit of the electrical machine using Reluctool Fig. 3 Validation of the flux linkage computing with finite element method (FE) and Ime = 200 A Fig. 4 Validation of the torque with finite element method Fig. 5 Modeling of the hybrid drive train Fig. 6 Specific fuel consumption (g/kW.h) map of ICE Fig. 7 Geometrical parameters of the EM Fig. 8 Optimization strategy Fig. 9 DDP principle Fig. 10 Pareto front battery versus fuel consumption for urban driving cycle Fig. 11 (a) Initial EM geometry, (b) urban driving cycle, (c) road driving cycle, (d) highway driving cycle Fig. 12 Comparison of operation points and efficiency map between the initial sizing and the urban optimal solution

Figure 1 .

 1 Figure 1. Parallel HEV architecture.

Fig. 3 Fig. 4 Fig. 5 Fig. 11

 34511 Fig. 3 Validation of the flux linkage computing with finite element method (FE) and Ime = 200 A

  k bv (t) is the gear box ratio at instant t, k red is the reduction gear ratio and

	If	u	( t	)	0	or	( u	( t	and	k	bv	t	k	red	t	w	t	ice
		t		k	bv	t	k	red	t	w	t							(4)
		t			ice
																				) red (t s	is the efficiency of the final
	gear with respect to the power flow direction : s(t)=sign(**). u 2 (t) represents the state of Clutch 2 (closed if
	u 2 (t)=1 and open if u 2 (t)=0).
	In hybrid propulsion mode (Clutch 2 closed), u 2 (t)=1 :
	ice	t			t				t cpl s k cpl	em	i bat	t		J	em	d	dt em	J	em	d	dt ICE	t

where

Table 1 .

 1 Dynamic performances constraints

	Acceleration time from 0 to 100 km/h (s)	Maximal vehicle speed (km/h)	Time to overpass a truck driving at 80 km/h (s)
	t 0100	V max	T pas
	12.0	160	9.0

Table 2 .

 2 Initial hybrid vehicle sizing

	Standard power of the EM	30	kW
	Base speed of the EM	1420	tr.min -1
	Maximal torque of the EM	200	N.m -1
	Continuous voltage : U bus	330	V
	Internal combustion power: P mt	50.6	kW
	NiMh module number : N bat	28
	Battery pack standard power	29.5	kW
	Coupling ration : k cpl	0.7
	Reduction gear ratio: k red	3.2941

Funding for this project was provided by a grant from la Région Rhône-Alpes.