O Isnard

L Soulhac

G Dusserre

Numerical simulation of ammonia dispersion around a water curtain

Keywords: Water curtain, Ammonia, Dispersion

Water curtains have been suggested as a way of limiting the spread of ammonia in the event of an accidental release. Several field experiments have already been performed to investigate the interaction between a water curtain and a cloud of ammonia, most recently by Bara and Dusserre (1997, J. Loss Prev. Ind., 10(3), 179-183). Those experiments have been modelled numerically, using the computational code Mercure. The calculated velocities and concentrations agree reasonably well with the measurements.

Introduction

Ammonia is used in a wide range of industrial processes, and it is commonly stored, in liquid form, under pressure, on industrial sites. It is also frequently transported by road and rail in pressurised containers. There are therefore many opportunities for accidental releases of ammonia, and such release can have very serious consequences. Ammonia is a highly toxic gas, and for an accidental release in the atmosphere, the safe concentration limit is likely to occur too far away from the source to permit direct intervention at the source. It has been suggested that vertical water curtains might be used to create 'protected regions' within the ammonia cloud to permit emergency services to approach the source much more closely, and to protect vital installations.

The atmospheric dispersion of ammonia has been studied extensively using both experimental and numerical approaches. Recently Nielsen et al. (1997) published a review of field experiments set up during the CEC Environment project 'Fladis Field Experiments'. The main objective of these experiments was to study all stages in the dispersion of ammonia, over a flat terrain, from its release as liquified ammonia to a state of essentially passive dispersion. This study is particularly concerned with the use of a water curtain to modify the dispersion of ammonia. There have been several wind tunnel studies of the interaction between a dense gas cloud and an obstacle such as a fence (see Davies (1992) for an analysis of some of these experiments) and Papaspyros, Papanicolaou, Kastrinakis and Nychas (1996) report some wind tunnel studies of the effect of obstacles on the dispersion of ammonia. In particular, they concluded that the obstacle enhances the mixing and the dispersion of gas cloud. There have also been some field studies of the use of water curtains to limit the dispersion of various gases (e.g. [START_REF] Blewitt | Effectiveness of water sprays on mitigating anhydrous hydrofluoric-acid releases[END_REF], but as far as we are aware, the only field study of the use of water curtains with ammonia releases is that reported by Bara and Dusserre (1997). The aim of their experiments was to study the effect of a water curtain on the dispersion of a cloud of ammonia gas, released upstream of the water curtain. The water curtain modifies the dispersion in two major ways. Firstly, the airflow transporting the ammonia must pass around or over the water curtain. This creates a region in the wake of the water curtain which is largely protected from direct exposure to the gas cloud. Most of the transport into this region is by turbulent diffusion, although, as we shall see later, it is possible for the mean streamlines to penetrate the region. The pollutant which does enter the wake region is then mixed rather uniformly throughout the region, by the recirculating flow and the relatively high levels of turbulence, before leaving into the external flow. The droplets in the water curtain may contribute to a reduction in the ammonia concentration by absorbing ammonia vapour.

In order to assess the performance of the water curtain, we need to know the extent of the region protected by the water curtain, the likely ammonia concentration within the protected region, and the typical 'retention time' of the pollutant in the protected region. Such quantities are extremely difficult to measure in full-scale experiments, so a numerical model can provide a great deal of useful information. We have therefore used an existing computational code-Mercure-which was developed for the simulation of flow in the atmospheric boundary layer [START_REF] Buty | [END_REF] to simulate four of the field experiments reported by Bara and Dusserre (1997). As a first approach we have modelled the water curtain as a solid, rigid obstacle having approximatively the same dimensions as those reported for the water curtain. We have therefore ignored the possible absorption of ammonia by the water droplets in the spray, the semi-porous nature of the water curtain, and any dynamic interaction between the water curtain and the incident wind. So an important, additional question concerns whether such a simplified model can represent a non-rigid, semi-porous structure such as a water curtain. In Section 2, we review the field experiments briefly, and then, in Section 3 we describe the numerical simulations. The computational results for the wind velocities are presented and discussed in Section 4, followed by the concentrations in Section 5.

The field experiments

The field experiments were carried out at a test site at Champelauson (Gard, France), and they have been described in detail by Bara and Dusserre (1997), so they will only be summarised here. The test site is a large rectangular area, with a surface consisting principally of dirt and gravel, giving an average roughness height of about 1 cm.

The ammonia was stored as a liquid in a pressurised bottle, and was discharged through the outlet valve at the top of the bottle as a jet. The bottle was inclined so that the jet impacted on the ground; some of the ammonia formed a pool on the ground, and the rest dispersed immediately, either as vapour or as aerosol. The release rate was very low-about 20 kg of liquified ammonia in 2 min-so it can be assumed that the aerosol cloud did not have any significant initial momentum.

The water curtain was located 8 m downwind of the source, and consisted of a horizontal water jet (at pressure of about 10 bar) which impacted on a vertical, semielliptical plate which deflected and dispersed the jet. The resultant spray formed a water curtain in the shape of a peacock's tail.

The numerical simulations

The calculations have been performed using the atmospheric boundary layer code Mercure [START_REF] Buty | [END_REF], which is a 3-dimensional model, based on a classical Navier-Stokes solver, with a standard k-⑀ turbulence model. The program uses a structured grid; for these calculations we used a mesh with 65 points in the streamwise direction, 27 points in the vertical and 61 points in the transverse direction (see Fig. 1). This corresponds to a physical domain measuring 100 m long, 80 m wide and 40 m high. The ground is assumed to be flat, with an aerodynamic roughness height of 1 cm; the air temperature was fixed at 20°C. The inflow condition consists of a logarithmic velocity profile, with a turbulence intensity of 25%. The pressure at the outflow from the domain is imposed, and is set equal to the atmospheric pressure (pressure of the ambient air at 20°C which follows the ideal gas law).

An important, and rather general, problem in modelling this type of flow is the representation of the water curtain. In reality, this consists of a rather thin sheet containing water droplets moving at high speed, which therefore acts as a porous screen. It has two important functions; the upward momentum of droplets (and the air that they entrain) acts as a vertical barrier to the flow, deflecting most it around the edges of the water curtain. The water droplets also play an important role in removing ammonia from the atmosphere, through the coalesc- ence of droplets and the absorption of ammonia vapour. These processes are essentially small-scale and rather complicated, and it is not possible to model them directly in calculations of atmospheric boundary layer flows in realistic, complex geometries. So one of the objectives of this work is to begin to consider how to model the effects of the water curtain in this type of calculation. We have therefore begun with the simplest possible approach; the water curtain is modelled as an impermeable barrier, with a slip condition for the velocity on the faces. The experiments (Bara & Dusserre, 1997) showed that the water curtain resembled a peacock's tail; we have therefore represented it as a semi-cylinder, with a radius of 10 m and a thickness of 60 cm.

The velocity field

The flow around a bluff body in the surface boundary layer is very complicated, and the detailed structure of the flow can depend rather sensitively on parameters such as the shape, size, porosity and orientation of the object. [START_REF] Hosker | Methods for estimating wake flow and effluent dispersion near simple block-like buildings[END_REF] and [START_REF] Hunt | Flow round bluff obstacles[END_REF] provide comprehensive reviews of flow and dispersion round isolated obstacles. However, theoretical studies of dispersion in turbulent flows around bluff bodies (e.g. Puttock & Hunt, 1979;Puttock, 1979;Hunt & Mulhearn, 1973) suggest that the cross-sectional area of the pollutant cloud, and the concentrations, are determined mainly by the convergence and divergence of the mean streamlines, and do not depend too sensitively on the structure of the turbulence. Consequently, the quantities that are likely to be most important for a satisfactory prediction of pollutant concentrations will be the characteristic dimensions of the separation regions upstream and downstream of the water curtain.

Unfortunately, the velocity field around the water curtain was not measured during the field experiments-the only velocity that was measured was that of the incident wind upstream of the water curtain, at a height of 4 m. And since there do not seem to be any other published data sets of the velocity field around a water curtain, we have had to compare the results of our calculations with data for the flow around solid obstacles. This means that we have been unable to test our hypothesis that the water curtain can be modelled as a solid obstacle with a shearfree surface.

Most of the available data for the flow around bluff bodies are for objects for which the length (L) in the streamwise direction, is of the same order as the height (H) and width, (W). That is, the data have been obtained principally for objects with L/H Ն 1. We have modelled the water curtain as a rather thick 'plate', for which L/H ෂ 0.006. The ratio L/H is important in that it determines whether the flow which separates upstream of the obstacle reattaches on the top or the sides of the obstacle, or whether the obstacle is enclosed in a single recirculation 'bubble'. Most measurements (e.g. [START_REF] Hosker | Methods for estimating wake flow and effluent dispersion near simple block-like buildings[END_REF] suggest that there will be no reattachment on the surface of the obstacle if L/H Ͻ 1 and L/W Ͻ 1. So we have compared our numerical results with data obtained for obstacles with L/H Յ 1 and L/W Յ 1.

Upwind separation

As the main flow approaches the water curtain it decelerates in the streamwise direction and accelerates vertically and laterally, so as to pass round the curtain. A standing eddy forms in front of the water curtain. This is illustrated in Fig. 2 which shows some of the mean streamlines in a view looking downwind towards the water curtain. The spiralling pattern of the streamlines immediately upwind of the water curtain illustrates the rather complex structure of the upwind vortex, and suggests that the vortex plays an important role in dividing the oncoming flow into the fraction that passes round the obstacle, and the fraction that passes over.

Previous wind tunnel studies have shown that the size and strength of the upwind vortex depends on the incident velocity profile relative to the body height. [START_REF] Corke | Sensitivity of flow around and pressures on a building model to changes in simulated atmospheric surface layer characteristics[END_REF] conducted wind tunnel studies on block-like obstacles in boundary layers with a range of different power-law velocity profiles (uϰz n ). For the case closest to the one studied here (n ϭ 0.15) they found that the upwind vortex extended to a height of about 0.6 H. Our numerical computations give a height of about 0.65 R (where R is the radius of the water curtain) which agrees reasonably well with the experimental data, since we can assume that our results should scale on R in much the same way as those for a rectangular object scale on H.

Obstacle wake

The flow passing over and around the obstacle separates, creating a region of recirculating flow in the wake of the obstacle. If the obstacle is sufficiently short compared with its height and width (L/H Յ 1 and W/H Յ 1) then the length of the recirculation region (L r ) measured from the upwind face of the obstacle, should be relatively independent of L. [START_REF] Huber | Building wake effects on short stack effluents[END_REF] measured L r for a block-like structure (L/H ϭ 1 and W/H ϭ 2) and obtained L r /H ෂ 2.5. They also found that the maximum height (H r ) and half width (W r ) of the recirculating region were about 1.5 H, and occurred at a distance of about 1.5 H downwind of the upwind face of the obstacle. In these simulations, we obtain L r /R ෂ 2.8, and W r /R ෂ 1.3, which agree reasonably well with measured values.

The mean streamlines immediately downwind of the obstacle are rather complicated; Fig. 3 shows a view from downwind of the water curtain, looking upwind. Immediately behind the obstacle there is a large semitoroidal vortex, which is visualised here as a surface of constant low pressure. This is consistent with other results which show the formation of a parallel pair of vertical vortex tubes immediately behind sharp edged bluff bodies [START_REF] Woo | Wind-tunnel measurements in the wakes structures[END_REF]. Since such structures cannot terminate in the fluid, they are therefore probably connected. The vertical nature of this large structure is emphasised by the mean streamline that enters the recirculation region close to the ground, and spirals round the vortex tube before leaving close to the top. This also illustrates the fact that mean streamlines can enter the wake (e.g. Hunt, Abell, Peterka & Woo, 1978), and this can be an important factor in determining the average concentration behind the water curtain.

Vertical profiles

Vertical profiles of the streamwise velocity at several positions along the streamwise axis of symmetry are shown in Fig. 4. The profiles show clearly the region of reverse flow behind the water curtain, which extends to about L r /R ෂ 2.8 downwind of the upstream face of the obstacle. A rough estimate for the vertical extent of the recirculating region can be obtained from the heights at which the (positive) velocity gradient is a maximum. This defines a line, almost level with the top of the water curtain, which remains at this height until x/R ෂ 3, and then falls rapidly to the ground level at x/R ෂ 3.5. This also coincides with the peak in the production of turbulent energy (Fig. 5), presumably because this is where the mean shear is a maximum. The dissipation is a maximum along this line too (Fig. 6).

Concentration field

In order to compare the computed concentrations with those measured in the field experiments of Bara and Dusserre (1997), we have selected four of their tests that were performed in similar conditions. The relevant experimental conditions are given in Table 1. The concentration C will depend on the location of the measurement (x, y, z), the wind speed (say U r , the velocity at the top of the water curtain), the size of the water curtain (R), the mass flow of ammonia at the source (Q) and a coefficient of turbulent diffusion (K):

C ϭ f(x,y,z,U r ,R,Q,K).
(1)

Now using standard techniques of dimensional analysis, and taking R, U r and Q as our basic parameters, we obtain:

ϭ CU r R 2 Q ϭ f ͩ x R , y R , z R , K U r R ͪ (2)
The coefficient of diffusion, K, can be estimated as uЈ 2 T L where uЈ is the rms velocity and T L is the Lagrangian integral Time Scale, which can in turn be estimated as ᏸ/uЈ where ᏸ is the integral scale of the turbulence. From which:

K U r R ෂ uЈᏸ U r R (3)
and it is likely that uЈ/U r and ᏸ/R did not vary much over the four field experiments being used for a comparison here, because the size of curtain (R) was kept constant, and for any given type of flow uЈ/U r usually remains similar at similar points in the flow. This means that the data from the flow field experiments, expressed in the form

ϭ KCU r R 2 Q ϭ f ͩ x R , y R , z R ͪ (4)
ought to collapse into a single curve.

Transverse profiles of the measured dimensionless concentrations are plotted at three positions downwind of the source (x/R ϭ 1.3,2.5,3.5) in Fig. 7(a-c), together with the results from the numerical simulations. The experimental data do not collapse onto a single curve (Fig. 7(a)) although they exhibit the same tendencies; close to the curtain the concentration drops towards the centreline, but further away, the concentration actually shows a peak on the centreline (Figs. 7(b) and (c)). The biggest differences between the experimental data occur in the profile measured at x/R ϭ 2.5, which is about x/R ϭ 1.7 downstream of the upwind face of the water curtain. There are several possible reasons for the failure of the experimental data to collapse onto a single curve. Firstly, the wind direction and speed fluctuated during the field experiments, and the concentrations were only measured for a period of about 90 s, so the measured concentrations probably do not represent a 'long term' average. This probably also explains why the experimental profiles are rarely symmetrical about the centreline. Secondly, the presence of the water curtain will lead to the formation of large-scale unsteady structures in its wake. A simple calculation for a rigid plate of the same dimensions, in the same flow conditions, suggest that large scale vortices will be shed into the flow at intervals of 25-50 s. This means that the flow downstream of the water curtain is probably influenced rather strongly by large scale unsteady structures with time scales that are rather long compared with the 'averaging time' of the measurements. Once again, then, the measurements probably do not represent a true 'long time' average. (Of course, the question of whether the flow past a rigid plate is a good model for a water curtain in a cross wind remains an important question which we have not been able to investigate here.)

The computed concentration profiles clearly give dimensionless concentrations that are of the same order of magnitude as those measured in the field experiments, which is, in itself, encouraging, because there has been no adjustment of coefficients to force, or improve the agreement. However, it is difficult to go much beyond this 'general agreement'; the numerical model predicts a concentration minimum on the centreline, which might be reproduced in the experimental profiles closest to the water curtain, but is certainly not observed further downwind, where the data show a concentration maximum on the centreline! The numerical simulations predict very high concentration peaks at the edges of the recirculating region behind the water curtain, but this is not really confirmed by the measurements. Although the measurement positions do not extend outwards sufficiently to provide a definite conclusion, it seems very unlikely that such steep concentration gradients existed in the experiments. There are several possible explanations for this difference. Firstly, the edge of the recirculating region is a zone of very high shear, and the local lateral diffusion of material will be significantly enhanced. This will reduce the peak values and the gradients. Secondly, in the experiments, there was a gap between the ground and the bottom of the water curtain so some ammonia will have been transported into the wake directly, beneath the water curtain (particularly since the ammonia is heavier than air). Also, it is well-known that the phenomenon of 'base bleed' can modify the structure of wake regions significantly.

Another important difference between the experiments and the numerical simulations concerns the unsteadiness of the oncoming flow. Even a nominally 'steady' wind exhibits low frequency fluctuations in direction, so that the effective size of the wake is much larger than that in a truly steady flow. Consequently, the diffusion behind the obstacle is greater than in a steady flow. This may explain why the measured profiles of concentrations in the wake are much flatter than those predicted by the numerical simulations, particularly as the distance downstream of the water curtain increases.

The computed streamwise profile of agrees reasonably well with the measured values (Fig. 8). The differences between the computations and the data are gener-ally smaller than the variations between the four experiments, although it is clear that compared with all four experiments, the computations underestimate the concentration immediately downwind of the water curtain.

Another important parameter for defining the performance of the water curtain is the average retention time in the wake. [START_REF] Humphries | [END_REF] measured the retention time of smoke in the wake of circular discs, and defined a dimensionless residence time r ϭ t e U ϱ /H where t e is the time for the concentration in the wake to decay by 1/e, U ϱ is the free stream velocity and H is the characteristic length scale of the object. They found that if the incident flow is smooth r ෂ 7.4, and this decreases as the turbulence in the free stream increases. In this simulation, we obtain R ෂ 6.9, which is therefore in good agreement with their results. The residence time represents the characteristic time scale for large scale concentration fluctuations in the wake; on the basis of the numerical simulations we estimate that its value in the experiments was of the order of 60 s. Now in the experiments reported by Bara and Dusserre (1997), the measurements began 30 s after release of the ammonia, and lasted for 90 s in total. Thus it seems likely that steady state conditions had not been established in the wake at the start of the measurements, but, on the other hand, the measurement period exceeded the characteristic response time of the wake.

Conclusion

The present numerical study shows the capability of a CFD code like Mercure to accurately simulate an ambient ammonia dispersion over a water curtain. The aim of this study was to reproduce the main features of the experiments of Bara and Dusserre (1997). The aerodynamical characteristics of the simulated flow over the curtain are reasonable and we find good agreement between our simulation and other studies from the literature [START_REF] Corke | Sensitivity of flow around and pressures on a building model to changes in simulated atmospheric surface layer characteristics[END_REF][START_REF] Huber | Building wake effects on short stack effluents[END_REF]. The computed concentration field is also in good agreement with experiments. These results show that numerical simulations can appreciably complement experiments and provide interesting information to study the efficiency of water curtains.

Fig. 1 .

 1 Fig. 1. Schematic view of the water curtain and the computational mesh. For clarity only every other grid point is shown.

Fig. 2 .

 2 Fig. 2. Visualisation of the mean strearnlines. View downwind, towards the water curtain.

Fig. 3 .

 3 Fig. 3. Visualization of a low pressure iso-surface and streamline behind the curtain, showing the existence of a toroidal vortex structure.

Fig. 4 .

 4 Fig. 4. Profiles of the mean horizontal velocity at several positions downwind of the water curtain.

Fig. 5 .

 5 Fig. 5. Profiles of the kinetic energy at several positions downwind of the water curtain.

Fig. 6 .

 6 Fig. 6. Profiles of the dissipation at several positions downwind of the water curtain.

Fig. 7 .

 7 Fig. 7. Transverse profiles of concentration at a height of 0.2 m, at three positions downwind of the release (a) 13 m downwind of the release, (b) 25 m downwind of the release, (c) 35 m downwind of the release. ---, Numerical simulation; ᭺, Trial 1; ᮀ, Trial 2; ̃, Trial 3; ̅, Trial 4.

Fig. 8 .

 8 Fig. 8. Longitudinal profile of concentration, at a height of 20 cm. ---, Numerical simulation; ᭺, Trial 1; ᮀ, Trial 2; ̃, Trial 3; ̅, Trial 4.

Acknowledgements

O. Isnard is grateful to the Centre Lyonnais d'Inge ´nieurie d'E ´lectricite ´de France for research funding. The authors are also grateful to R.J. Perkins for useful discussions.


Sihem Mallek Daclin

Nicolas Daclin

Gilles Dusserre

Bruno Lhéritier

Jean Blanchard

Isabelle Arnaud

Maturity model-driven assessment of Field Hospitals

Keywords: maturity model, field hospital, maturity levels, maturity assessment, axis of interest, emergency

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The emergencies caused by disasters (wars, climate, epidemics. ) are characterized by a to al mess The suppor to the victims must be fast and effic ent, the first hours post disaster are generally the mos valuable. To respond to the emergencies, medical resources are deployed AMP (Advanced Medical Post civil security) or PSM (Post Sanitary Mobile), are referred to routinely as "field hospita s" [START_REF] Paho | WHO-PAHO Guidelines for the Use of Foreign Field Hospitals in the Aftermath of Sudden-Impact Disasters[END_REF] Their operators are multiple (civilian, military, NGOs) and their capabilities and functioning are somewhat standardized [START_REF] Canadian | The future of field hospitals in disaster response[END_REF].

Field hospitals aim to supply local health structures which can be insufficient in crisis conditions. A f eld hospital is primarily (1) a medical team (doctors experienced nurses) and (2) the conditioning of medical equipment to be easily transportable. Field h spitals target four main missions [START_REF] Paho | WHO-PAHO Guidelines for the Use of Foreign Field Hospitals in the Aftermath of Sudden-Impact Disasters[END_REF] (Nortan et al , 2003):

1. The triage of victims or serious related emergencies; 2. The identification of victims by developing a medical card called "forward ; 3. The care for serious victims; 4. The organization of evacuations according to priorities and availability of hospital.

However, in a real emergency situation, a field hospital faces up some limits such as: mismanagement of the organization, logistics, and lack of communication with the authorities of the disaster country… Faced with the many l m tations of these s ructures he HOP CAMP project at emp s to develop a set of innovative solutions to optimize emergency care and offer an integrated solution for a new g neration o fie d hospital. In this way, the objective of this research work is to propose good practices and ecommendations to improve the deployment of a field hospital thanks to the concept of maturity model. The here presented research is validated by the team of ESCRIM 1 , the field hospital deployed by France. I is managed by the Departmental Fire and Rescue Service of the Gard region (SDIS 2 30) and the Civil Security Instruction and Intervention Unit 7 (UIISC7 3 ). The effectiveness of its rollout depends not only on the medical services provided but also on other aspects such as, for instance, the logistic, the management of resources and its ability to work with other organizations.

After this brief introduction, the context of this research is pr ented through the prism of field hospitals in disaster response. The third section presents a short survey regarding to some matur ty models in health domain. Section four presents the proposed structure of the Field Hospital Maturity Model (FHMM). After, section five shows the way on which Abstract: Mobile field hospitals are set up urgently to respond to all types of emergencies and to meet the health needs of people. In this case, field hospital must be efficient and respond accurately to the emergency for which it is deployed However, this efficiency can be observed only when the field hospital is deployed during the emergency. Therefore, any deficiencies can not be corrected "on the fly" to fully respond to the emergency. As a consequence, it is interesting to assess the field hospitals before their deployment to ensure it is able to respond efficiently to the emergency. The triage of victims or serious related emergencies; 2

The identification of victims by developing a medical card called "forward ; 3 Th ar f r s ri us i tims 4

The organization of evacuations according to pri riti s and a ailabilit f h spital However, in a real emergency situation, a field hospital faces up s me limits su h as mismanag ment f th rganizati n logistics, and lack of communication with the authorities of the disaster country Faced with the many limitations of these structures, the H PI AMP project attempts to develop a s t f inn ati s luti ns t ptimiz m rg n ar and offer an integrated solution for a new generation of field h spital In this wa th bj ti f this r s ar h w rk is t propose good practices and recommendations to improve the deployment of a field hospital thanks to the c ncept of maturity model The here presented research is validated by the t am f ES RIM 1 , the field hospital deplo ed b France It is managed by the Departmental Fire and Rescue ervice f the G rd r gi n (SDIS 2 30) and th i il S urit Instruction and Intervention Unit 7 (UII 7 3 ) Th ff ti n ss f its r ll ut d p nds n t nl n th medical services provided but also on other aspects such as, for instance, the logistic, the management of resources and its abilit to work with other organi ations Aft r this bri f intr du ti n th nt xt f this r s ar h is presented through the prism of field hospitals in disaster r sp ns Th third s t n pr s nts a sh rt sur r garding to some maturit models in health domain ection four pr s nts th pr p s d stru tur f th Field H spital Maturit Model (FHMM) After, section five shows the way on which Abstract: Mob le fie hos itals are t up urge tly to respond o al ty e of em rgen ies an to meet the heal h needs of peop e In this case f ld hospita m st be efficient and esp nd accu tely to th emerge cy for wh ch it is deplo ed However thi e ficiency can be observed only when the field hosp tal is deploy d d ring h emerg ncy There o e an d ficien ies can not e co rected "on the fly" to fully respo d to the emergency As a co sequence it s interesting to assess the fie hosp tals before their ploym nt ensure it is ble to re pond f iently to th e genc T s p per foc es and illustrates the f r t development to a sess a f eld hospital a

Keywords:

The eme gencie caused y disast rs (wars clima e, epi emics . ) are character zed by a tota mes h supp rt to the vict ms must be ast and efficient, e irst hou s ost disaste are nerally t most val ble o respon o the emergencie medi l r ourc a e d pl yed AMP (Advanc d Medic P t, civil ec ity) or M (Post Sanita y Mobi e), re referr d to routinely as "field hospita (PAHO a , 00 ). T ir op a ors are m iple (ci ilian, mili ary, NGOs) and their capabilities an functi Fie d hospitals aim to supp local he h struc ures wh ch can be insu ic ent in c isis ondition A field ho pital is primari y ( ) a medica eam (doctors, experie ced urses) and ( 2 ). The eff ctiveness of its rollout dep nds ot only on the medical ser ice provid d but also on other a pect such as, for ins a ce, the l gistic, the manageme After this b ief in od ction, he context of this re earch is presente through the pri m of fi ld hos itals in disaster re ponse The third section pr sents short su ey reg ding to some maturity models in health domain Sec ion four presen s the prop sed s uc u e of the Field Ho pita aturity Elémen e S cu ité i ile apid Médicale : http //www.e crim.org/ 2 Service D partemental d ncendie e de cours this proposed maturity model is validated. Finally, a conclusion is given section six.

FIELD HOSPITALS IN DISASTER RESPONSE: STAKEHOLDERS' REQUIREMENTS

An emergency is a situation that poses an immediate risk to health, life, property, or environment. Most emergencies require urgent intervention to prevent a worsening of the situation (UK Government Advice, 2007). To face the emergency situation, some governmental and nongovernmental organizations offer medical solutions among which, the field hospitals. A Field hospital is defined as: "a mobile, self-contained, self-sufficient health care facility capable of rapid deployment and expansion or contraction to meet immediate emergency requirements for a specified period of time" [START_REF] Paho | WHO-PAHO Guidelines for the Use of Foreign Field Hospitals in the Aftermath of Sudden-Impact Disasters[END_REF]. These hospitals are deployed in few days and provide the services of a common hospital on the site of the emergency until local medical facilities are able to manage the patients flow. The decision to deploy is related to the context, the nature and the intensity of the emergency event. Hence, a rapid assessment of needs, capacities and vulnerabilities is critical for an appropriate and a customized response. Furthermore, disasters create chaos; therefore, to maximize efficiency and to provide the best emergency care to the local population, coordination and collaboration efforts are required. However, in a real situation, these goals are often partially or not reached [START_REF] Canadian | The future of field hospitals in disaster response[END_REF].

For instance, the earthquake in Haiti in 2010 caused many deaths and wounded. Due to the intensity of the event, several countries and organisations have sent aids to help the population and support local authorities. The most important support was coming from field hospitals. Indeed, a total of 44 foreign field hospitals were sent on an assignment from different countries (Nortan et al., 2003). However, problems have been highlighted in relation to the deployment of these field hospitals. One of these problems is related to the gap between the real needs, on the spot, and the needs assessed in terms of capacity and skills before deployment. A second problem to mention is related to the coordination mechanism between the various field hospitals which find difficulties with teams that are not accustomed with international emergency response systems and standards (Nortan et al., 2003).

Consequently, inexperienced teams can be unable to provide the best help for local population. The quality of preparedness strongly affects the response time and effectiveness. For these reasons, a field hospital must achieve a minimum standards and effective response to disasters. To support and guide the achievement of an optimal response to an emergency situation, the here proposed research aims to make available:

• A reference model (maturity model) that identifies and defines precisely the aspects that play a crucial part in the deployment of a field hospital namely "axes of interest".

• The means to measure each axis of interest to have precise vision of the strengths and weaknesses of the studied field hospital. • A set of recommendations that guide and give the best practices to improve each axis of interest.

At the end, an approach will also propose to guide end-users to use the proposed model. This approach will define: (1) steps to follow, (2) actors who lead the evaluation and (3) sequences between steps in order to implement the maturity model and get evaluation in coherent manner. The final purpose is to provide a full methodology allowing to use the model properly and to improve field hospitals (Fig. 1).

Maturity Model

Requirements Evolution Measure

Structured approach

Definition of steps

Definition of actors

Sequence (Ex. Feedback)

Fig. 1. Big picture of the methodology to support field hospital evaluation.

MATURITY MODELS IN HEALTH DOMAIN: STATE OF THE ART

A maturity model includes levels consisting of a predefined set of axes of interest. These levels are measured by the achievement of the specific and generic goals that apply to each predefined set of axes of interest. Furthermore, a maturity model provides recommendations and practices to evolve throughout maturity levels for continuous improvement and the achievement of full maturity regarding the axes of interest (adapted from [START_REF] Cmmi | CMMI for systems engineering, software engineering, integrated product and process development, and supplier sourcing[END_REF]. The maturity models were introduced in the 1980s with the development of Capability Maturity Model (CMM) [START_REF] Paulk | The capability maturity model: guidelines for improving the software process[END_REF]. Among numerous existing maturity models, let mention the popular Capability Maturity Model Integration [START_REF] Cmmi | CMMI for systems engineering, software engineering, integrated product and process development, and supplier sourcing[END_REF]. The starting point of the proposition of such maturity models was based on the need to know the status of multiple existing IT projects. Indeed, these maturity models are dedicated to evaluate project management through the control of processes in enterprises. From these initial models, numerous models was built up and, currently, maturity models are developed in different fields such as Information System Interoperability (C4ISR, 1998), Enterprise Interoperability [START_REF] Guédria | Maturity model for enterprise interoperability[END_REF], Enterprise

Architecture [START_REF] Nascio | NASCIO Enterprise Architecture Maturity Model[END_REF], and represent an accurate mean of evaluation with several advantages such as:

• Self-evaluation, a maturity model can be used directly by the end-users to assess their structures according to the considered point of view; • Easy to learn and to apply, a maturity model does not require specific training; • Reduced delay to get an accurate analysis of the considered system; • Precise recommendations and path to evolve progressively through the maturity levels.

Regarding maturity models dedicated to health, the Healthcare Data Quality Maturity focuses on the knowledge of the level of Data Quality within a hospital. It is considered that it is possible for the medical errors to be related, directly or indirectly, with the level of Data Quality (Pinto-Valverde et al., 2003). The Health Usability Maturity Model supports health leaders and individuals to assess their levels of usability and then move toward more advanced levels [START_REF] Staggers | Promoting Usability in Health Organizations:Initial Steps and Progress Toward a Healthcare Usability Maturity Model[END_REF]. It exists another model such as the Business Intelligence Maturity Model for Healthcare which contributes to information and knowledge management in healthcare [START_REF] Brooks | Towards a Business Intelligence Maturity Model for Healthcare[END_REF]. These maturity models are dedicated to health for organizations such as hospitals or clinics. However, they do not take into account the emergency aspect that characterizes the nature of a field hospital.

In this way, numerous works related to field hospitals are available. These works offer standards and applicable documents describing requirements that a field hospital must satisfy to respond efficiently to an emergency situation. The most known, is probably the Emergency Medical Team developed by the WHO (World Health Organization) (Nortan et al., 2003). The main goal of the WHO is the coordination of the international response to emergency situations. To this aim, this document classifies care on three levels using 21 criteria such as hospital accommodation capacity or else, the type of surgery carried out. It also gives general guidance on standards for logistics. Furthermore, the major NGOs (Non-Governmental Organizations) have their own guidelines regarding to some aspects of the organization of a field hospital [START_REF] Tertrais | La prise en compte de l'environnement dans l'action humanitaire médicale[END_REF]. For instance, the MSF 4 Guidelines [START_REF] Noorgate | Public Health Engineering in precarious situations[END_REF], Red Cross guidelines (CICR, 2011), WHO guidelines [START_REF] Chartier | Safe management of wastes from health-care activities -Second edition[END_REF] and the Sphere Project (The Sphere Project, 2011) provide guidance to manage, in particular, the medical and domestic wastes and the use of water. These works are related to a specific part of the deployment of a field hospital, especially on care area. Hence, these works do not lead the global organization regarding, for example, human resources management, equipment management, economic and environmental impacts, logistics… As a consequence, it is proposed to elaborate a maturity model and associated tools for field hospitals whose primary developments are given in the next section.

4 Médecins Sans Frontières 4. THE FIELD HOSPITAL MATURITY MODEL (FHMM)

Founding principles

Improving the proper functioning of a field hospital require to have a list of criteria that characterizes its functioning as complete as possible, sufficiently formalized to be evaluated and highlighting relevant axes of development to favour. In this way, developing a maturity model can be an efficient solution. In the case of the HOPICAMP project, the proposed maturity model for field hospital is based on several existing works/documents (Fig. 2.) that means:

• Existing documents describing Field hospital structure and organisation such as the ESCRIM [START_REF] Mailhac | Modélisation et évaluation des hôpitaux de campagne : Application au cas de l'Escrim[END_REF], French field hospital. • Existing guidance for field hospitals especially the EMT (Emergency Medical Team) developed by the WHO which offers a global classification of field hospital regarding care response [START_REF] Chartier | Safe management of wastes from health-care activities -Second edition[END_REF]. The EEMC (European Emergency Response Capacity) gives a grid for the certification of field hospital5 . INSARAG (International Search and Rescue Advisory Group) guidelines are intended as a reference guide for international urban search and rescue operations [START_REF] Insarag | International Search and Rescue Advisory Group, Guidelines and methodology. United Nations, Office for the coordination of the humanitarian affairs[END_REF]. These guides provide criteria to develop a maturity model. • Other existing related works such as maturity models (CMMI, 2012) that can be used for the logistic aspect of field hospital. Another document can be used to build the proposed maturity model: the Sphere Project (The Sphere Project, 2011) which frames a Humanitarian Charter and identifies a set of minimum standards in key lifesaving sectors. • The used and applied standards/norms in the country, in which the disaster occur as well as the standards/norms used and applied by the country in charge of the deployment of the field hospital must be considered to respond efficiently to emergency situation with techniques that are experienced. Lastly, the construction of the maturity model is based on the very first structure presented in [START_REF] Daclin | Towards a maturity model to assess field hospitals' rollout[END_REF]. Indeed, the structure of this first model is extended and reorganized, taking into consideration the structure of a field hospital for better consistency as indicated below. 4.2 Structure of the maturity model

The structure of a field hospital may differ from one country to another and from one organization to another. Nevertheless, whatever the structure and based on systemic theory -enabling to grasp a system under different points of view -(Le [START_REF] Moigne | La théorie du système générale -théorie de la modélisation[END_REF], a field hospital must consider the logistic (support aspects) medical (business aspects) and governance (decision-making aspects) facets (Fig. 3). • Governance: it refers to the decisional aspect of the field hospital during its mission with the consideration of critical point to consider during the whole lifecycle of the mission such as the situation assessment, the deployment, the operation and the withdrawal.

• Logistics: it refers to the supply, storage, transport and the collect after use on site of all means used by the field hospital (medical and non-medical). The logistic can be ensured by internal or external organizations.

• Care: it refers to the medical services (care) provided by the field hospital during its mission.

These 3 axes are composed of the set of key points. These key points were identified and placed on the maturity model after a bibliographic study, as shown in Fig. 2, and interviews with stakeholders (mainly SDIS 30). This granularity level allows (1) to gain in reading of the whole model (e.g. safety and security, waste management) and ( 2) to gain in precision for a future measurement. Indeed, the better the measurement, the better the identification of weak point and the recommendation Each axe presented previously is characterized by the 5 levels of progression enabling an accurate assessment of maturity and defined such as [START_REF] Daclin | Towards a maturity model to assess field hospitals' rollout[END_REF]:

• Unconsidered/unknown: this level represents a poor (or in worth cases no) consideration of the axis of interest. Intersection between axes of interest and maturity levels gives requirements to satisfy to achieve the desired maturity level. As a consequence, each intersection in the model has to be defined precisely in order to characterize the maturity levels. It is on the basis of the levels that maturity can be evaluated. Thus, the definition and the filling of the Field Hospital Maturity Model relies on the analysis of the documents such as guidelines, other models and standards related to the domain as presented previously in the construction process (See Fig. 2.).

Maturity measure and recommendations: first proposal

The assessment is essential at each maturity level to have an accurate view of the strengths and the weaknesses regarding to axes of interest. The measure provided by the Field Hospital Maturity Model is based on the satisfaction (or not or else partially) of requirements that define each level. However, the measure of a maturity level is not only related to the satisfaction of a set of requirements, it depends also on the context in which the mission is located. For instance, an interoperability requirement such as: "ability to work together with other modules and teams" will have no meaning in the case where there is only one field hospital deployed in the area. Therefore, interoperability with other teams is no longer required. In this case, some requirements may, for example, be neglected and their satisfaction is no longer required to achieve a certain maturity level. Thus, the local measure of maturity, in terms of Governance, Logistics and Care depends, first, on the satisfaction of requirements and, second, on the context in which the field hospital is deployed as shown (1).

( , )

L M f R C = ( 1 )
With: M L : the local maturity  Governance, Logistics, Care} R: Requirements of each level. C: Context of the mission.

In this sense, the evaluation is only considered at a local level (each axis of interest is evaluated independently) and it could be interesting to consider the maturity evaluation at a global level, i.e., to get a global maturity indicator coming from the aggregation of each local evaluation as in (2). Indeed, the maturity model provides a mean to evaluate each axis locally (each axis can evolve at different levels) but the impact on other axis must be considered and the mechanisms to know and to evaluate this impact must be also developed in order to develop the right and the better strategy of progression.

'( , , )

G M f Governance Logitics Care = (2)
With: M G : the Global maturity. Governance, Logistics and Care: the Local Maturity. Furthermore, the evolution of field hospital from each level to another is driven with some recommendations to define. In this case, it is necessary to define rules to formalize the transition from one maturity level to another. Most of maturity models in the literature, state that recommendations, practices and requirements proposed in each axis of interest at each maturity level must reach their goals before moving to the next level [START_REF] Cmmi | CMMI for systems engineering, software engineering, integrated product and process development, and supplier sourcing[END_REF]. These recommendations have to be clear and exploitable to enable a simple evolution and to make easier the achievement of changes.

VALIDATION OF FIELD HOSPITAL MATURITY MODEL

In order to get a relevant model and to provide proper recommendations, the proposed model is validated and tested with the support of the stakeholders (ESCRIM Team from SDIS 30), in the case of the HOPICAMP Project. Indeed, at each step of the development, the maturity model i.e., the axes of interest, the maturity levels and further the recommendations are improved and validated. This validation done through iterations with the stakeholders to validate (or not) each development or evolution of the model.

In this way, the first validation was related to the 3 axes of interest. The SDIS 30 considers that 3 axes facilitates the readiness of the maturity model and are fully related to the field hospital deployment. The second validation was related to the maturity levels. On this point, the issue was related to the number of level: why to propose five levels while the care aspect has three levels regarding the WHO model [START_REF] Norton | Classification and minimum standartds for Foreign Medical Teams in sudden onset disasters[END_REF]? In fact, the WHO model is widely used to evaluate a field hospital for all care aspects with three levels (outpatient emergency, inpatient surgical emergency and inpatient referral) that can be considered as maturity levels.

The general rule choosing the number of levels is that "the optimum level of maturity is recognized as being the level that delivers the organization's strategic objectives most effectively and efficiently which does not necessarily mean level five" (Jansson, 2011). As a consequence, five levels seem the most appropriate. This number is based on the fact that (1) a too small number of levels does not allow a precise evaluation (e.g. binary), (2) a too large number of levels bring details not necessarily useful for the users, (3) the evolution throughout levels has to be progressive to allow an effective progression (e.g. cost, human and materials means are engaged to evolve) and more marginal and (4), a common number of levels can allow to align different maturity models if it is useful [START_REF] Daclin | Towards a maturity model to assess field hospitals' rollout[END_REF].

CONCLUSION

To face up emergency situations and support impacted areas, some countries and non-governmental organizations set up temporary medical solutions such as the field hospitals. They are deployed in a few days and provide the standard hospital services on-site until local medical facilities are able to work properly. In this way, the assessment of the organization regarding to the deployment allowing to know their strengths and weaknesses and further to progress to be better is a key factor. To this purpose, the method presented is based on the use of a maturity model. The proposed maturity model is based on the study of (1) the structure and the organisation of field hospitals, (2) documents offering guidelines and recommendations for field hospitals, (3) other related models and maturity models and (4) standards and norms from countries in disaster as well as helping countries. The result is a structure of a maturity model providing the major axes to consider and to develop in a field hospital as well as different maturity levels and their definition allowing organizations to be positioned regarding to the axes of development.

Currently, the maturity model is continuously refined, populated and validated with the support of the ESCRIM Team. In this way, a first validation was occurred regarding the maturity levels and the axes of interest.

Next research works is the definition of the recommendations allowing users to evolve throughout the maturity levels according to the result of the maturity assessment, their own objectives and capabilities. . Other future works are related to the proposition of metrics to assess of field hospital.

1

  Elément de Sécurité Civile Rapide d'Intervention Médicale : http /www escrim.org/ 2 Service Départemental d'Incendie et de Secours 3 Unité d'Instruction et d'Intervention de la Sécurité Civile

  s aus d b disast rs (wars limat epidemics ) are characterized by a total mess The support to th i tims must b fast and ffi ient th first h rs p st disaster are generally the most valuable To respond to the m rgen i s medi al r s ur s ar d pl d AMP (Advanced Medical Post, civil security) or P M (Post Sanitar M bil ) ar r f rr d t r utin l as fi ld hospitals" (PAH et al 200 ) Their operators are multiple ( i ilian militar NG s) and th ir apabilities nd functioning are somewhat standardized ( anadian Red ross, 014) Field hospitals aim to supply local health structures which an b insufficient in risis nditi ns A field h spital is primaril (1) a medical team (doctors, experienced nurses) and ( ) th nditi ning f m di al quipm nt t asil transportable Field hospitals target four main missions (PAH et al 003) (N rtan et al 003) 1

  ) the c nditio ing of m dical e uipment to be easily transportable Field hospitals t get f id n ification o victim m i al ard cal ed forwa 3 The a e fo s rio ic s; The organization of vacuations Howeve in a eal eme gency situa ion, fi ld hospital face log stic , an ack o ommu icati n w t the authoritie f the disaster co ntr … Fac d wi h the many limit tions of t ese st uctures, th HOPICAMP projec attempts t dev lop a set nno ative olutions o o timize mergency car and offer an in egrated olution or a new generation of field hospital In th s way, the ob ective of this research wo k is to propose goo p a ices nd reco m nd o t mp o e e deployment of a fi ld hospital th nks to he concept of ma urity model The h re presented res arch is v li ated by th eam of E C IM , the field hospital dep oyed by France. It m aged by the epartm nta Fire and escu Service of the

  Fig. 2. Construction process of Field Hospital MaturityModel.

  Fig. 3. Overview of a field hospital structure. From this first structure, the maturity model proposed is based upon a global model including three main axes of interest themselves developed by 3 local models, as shown in Fig. 4.:

•Fig. 4 .

 4 Fig.4. Field Hospital Maturity model.

Sihem Mallek-Daclin*, Nicolas Daclin*, Gilles Dusserre**, Bruno Lhéritier***, Jean Blanchard***, Isabelle Arnaud***

  This paper focuses and illustrates the first development to assess a field hospital and based on maturity model. This work takes place within the collaborative research project "HOPICAMP", funded by the French Unique Interministerial Fund for a new generation of field hospitals

				* Laboratoire de Génie Informatique et d'Ingénierie de Production
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model-driven assessment of Field Hospitals

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ACKNOWLEDGEMENTS

This work is supported and performed within the project FUI 20 HOPICAMP -Hôpital de campagne nouvelle génération. The authors thank and acknowledge all the stakeholders from the SDIS 30, the two NGOs and the rally medical assistance for their support and contributions.


Guillaume Pellecuer
email: guillaumepellecuer@umontpellier.fr

Thierry Martiré

Mickael Petit

Benjamin Loyer

On-Board Power Management in a Marine Autonomous Surface Vehicle (ASV): Multi-Port Transformer Design

This paper deals with the design of the magnetic component of an isolated bidirectional multiportconverter. This converter is intended to be embedded in an autonomous surface marine vehicle with a power rating in the kilowatt range and is intended to exchange power between photovoltaic panels, a lithium battery and the propulsion system in which the motors can also be operated as a tidal turbine. This magnetic component is a three-port symmetrical three-phase transformer that allows to interface three three-phase inverters with a six-step control. The converter is galvanically isolated and can operate in a fully bi-directional way. Phase shifting of the inverters allows the power flow between them to be adjusted.

Introduction

The development of UAVs and ASVs is complicated by the amount and availability of onboard power, which is an essential element for the operation of the vehicle. The space available on these exploration vehicles is relatively limited and high power density converter architectures must be used to reliably and efficiently power the ASV.

A three-port power management system may enable the advantages of the photovoltaic source and storage to be intelligently combined to perfectly manage the redistribution of instantaneous power in the system or to use storage as a way of buffering the power flow from the primary source [START_REF] Liu | A Three-Port Three-Phase DC-DC Converter for Hybrid Low Voltage Fuel Cell and Ultracapacitor[END_REF][START_REF] Michon | A three-port bi-directional converter for hybrid fuel cell systems[END_REF].

The use of storage elements also makes it possible to size the primary source solely on the basis of the average power of the load and not only on the basis of the peak power draw of the load, as the storage can supply the difference very quickly and thus avoid oversizing the primary energy source [START_REF] Tao | High-Power Three-Port Three-Phase Bidirectional DC-DC Converter[END_REF][START_REF] Duarte | Three-Port Bidirectional Converter for Hybrid Fuel Cell Systems[END_REF][START_REF] Liu | A Three-Port Three-Phase DC-DC Converter for Hybrid Low Voltage Fuel Cell and Ultracapacitor[END_REF]. Finally, the storage can be used as a back-up energy source when the primary source is not available.

A three-phase, magnetically isolated three port converter in which the number of inductive elements that usually contribute significantly to the weight and volume of the converter is minima therefore appears to be well suited to power management in a small, autonomous on-board system. The magnetic component at the heart of the system is a three-port symmetrical three-phase transformer to interface three three-phase inverters with full-wave control, so the converter is galvanically isolated and can operate fully bi-directionally as shown in Fig. 1.

The phase shift of the converter commands allows the power flow to be directed between the converters and therefore to the DC sources if they allow it. The three three-phase systems are therefore slightly shifted according to the transfer requirements.

A power converter such as this one has already been described in [START_REF] Waltrich | Design of symmetrical highfrequency coaxial wound transformer for multiport converters[END_REF] but the magnetic component was a high frequency symmetrical transformer with coaxial windings which requires a large number of toroidal cores and a complicated winding to make up for the availability of cores with the right shape for the transformer.

In the following sections a more conventional transformer structure and a planar winding is presented. Fig. 2 shows an exploded view of the magnetic core of the transformer wich was made by sawing commercially available ETD cores with a diamond saw to recover the central cylindric leg. Then the resulting ferrite cylinders were glued onto type I cores.

Three port transformer model

As mentioned before, the converter consists of three inverters connected by a specially designed transformer whose primary and secondary can be connected in star or delta and as there is no interphase coupling the component study can be conducted on a per phase basis. As shown in Fig. 3, on one leg of the transformer there are three electrically independent phases but magnetically coupled to each other and to the other legs through various mutual inductances. In the following, the currents fed by the inverters are assumed to form a balanced three-phase sine system, we will have, for example, for inverter a: 𝑖 + 𝑖 + 𝑖 = 0.

For example, to write the magnetic flux through winding 1a (inverter a, phase 1), the self-inductance must be taken into account, as well as the mutuals linking this coil to the 8 others in the transformer (the mutual between winding 1a and 2b, for example, will be noted M1a2b). Fig. 4 shows how the mutuals related to phase 1 of inverter A and its winding are placed and as shown in Eq.

By doing the same for the other 8 windings, we can obtain the (9x9) matrix of inductances of this transformer.

(

) 2
This matrix only contains values that are easily accessible through the use of an impedance analyser.

The inter-leg mutual inductances of the same inverter (A here) are assumed to be the same and we note 𝑀 = 𝑀 = 𝑀 , we then obtain:

We define 𝐿𝑐 the cyclic inductance which takes into account the effect of the other two phases of the inverter a with 𝐿𝑐 = 𝐿 -𝑀 .

This result is possible provided that the currents are sinusoidal. However, the three-phase system prohibits the 3rd harmonic. The leakage inductances filter the currents as a 1st order, the impedance at harmonic 5 (1st non-zero harmonic) is 5 times larger than that of the fundamental. The amplitude of the voltage 5th harmonic is 5 times smaller than that of the fundamental. We can conclude that the amplitude of the current 5th harmonic is 25 times smaller than that of the fundamental and that the currents are sinusoidal.

Inter-leg and inter-inverter mutuals are also assumed to be identical (𝑀 = 𝑀 = 𝑀 ) with 𝑀 : Mutual inductance between legs and between two inverters. 𝑀 is the mutual on the same leg and between two inverters, then:

𝑀 . 𝑖 + 𝑀 . 𝑖 + 𝑀 . 𝑖 = (𝑀 -𝑀 ). 𝑖 (4)
Defining M𝑐 𝑎𝑏 the mutual cyclic inductance between converters A and B that reflects the impact of the windings fed by converter B on those of converter a we have M𝑐 = 𝑀 -𝑀 On the third part of 𝜙 , assuming again that the inter-leg and inter-inverter mutuals are identical (𝑀 = 𝑀 = 𝑀 ) we will have:

𝑀 . 𝑖 + 𝑀 . 𝑖 + 𝑀 . 𝑖 = (𝑀 -𝑀 ). 𝑖 (5)
The cyclic inductance between inverter C and inverter A is noted M𝑐 with 𝑀𝑐 = 𝑀 -𝑀 . And like the previous one, it reflects the impact of the windings fed by the C converter on those of the A converter. Finally, the magnetic flux of Eq. 1 can then be written:

𝜙 = 𝐿𝑐 . 𝑖 + 𝑀𝑐 . 𝑖 + 𝑀𝑐 . 𝑖 (6)
This expression is now equivalent to what we have for a single-phase transformer with 3 windings. The inductance matrix can now be written as Eq. 7 shows and allows the conversion of a threephase transformer to an equivalent single-phase transformer with three windings on the same core as shown in Fig. 5. By circular permutation, we find all the elements of the new inductance matrix (Eq.7):

𝑉
With the matrix in equation 7 and the definition of its elements, it will now be possible to relate the magnetizing inductance and leakage inductances of the single-phase 3-winding system [START_REF] Ganz | A Simple, Exact Equivalent Circuit for the Three-Winding Transformer[END_REF] (Fig. 6) to the matrix of inductances and thus to measurable quantities.

Using the diagram in Fig. 6 it is possible to relate the voltages across the windings to the magnetizing inductance and leakage inductances of the component and:

𝑉 = 𝐿
With 𝐾 = = and 𝐾 = = These equations can be represented as a matrix system which only contains quantities that can now be calculated using the inductance matrix of Eq. 2.

Using Eq. 7 and Eq. 9 we obtain a system of 6 equations with 6 unknowns: In [START_REF] Sun | General equivalent circuit of a multiwinding co-axial winding transformer[END_REF][START_REF] Tao | A Soft-Switched Three-Port Bidirectional Converter for Fuel Cell and Supercapacitor Applications[END_REF], it has been shown that an N branch transformer can be described with a so-called T model using N+1 branches of inductances.

In the case of the equivalent three-winding transformer presented in the previous calculations, the T-model can be used and the equivalent circuit has one leg for the magnetizing inductance, one for the primary leakage inductance and two for the secondary leakage inductance as shown in Fig. 7.

Theoretically, the magnetizing inductance is much greater than the leakage inductances

The equivalent source voltages at the B and C secondaries and the related leakage inductances are given by Eq. 12.

In generator convention (no conjugate current), we can write that:

𝑃 = 1 2 𝑅𝑒𝑎𝑙(𝑉 × 𝐼) (17) hence, 𝑃 = -𝑉 2𝐿 𝜔 3 + 𝐿 𝐿 [sin(𝜑 ) + sin(𝜑 )] (18)
The same thing can be applied to inverters B and C (𝜑 = -𝜑 , 𝜑 = -𝜑 , 𝜑 = -𝜑 = 𝜑 -𝜑 ). Hence, the total power expression for each inverter is: With the conventions used for these calculations, the power is negative if the source draws power and positive when it delivers power.

𝑃 = -3𝑉 2𝐿 𝜔 3 + 𝐿 𝐿 [sin(𝜑 ) + sin(𝜑 )] (19)
4 Transformer design

Finite elements simulation

In order to validate our assumptions about the design of the transformer, we have built a prototype and have characterised it, but first we have chosen to model it using the finite element method [START_REF] Buchau | Analysis of a Three-Phase Transformer using COMSOL Multiphysics and a Virtual Reality Environment[END_REF] with the COMSOL Multiphysics software.

The simulated geometry was created using the 3D building interface of comsol. The magnetic core is made with three 3 cylindric leg obtained from ETD59 cores in 3C90 material and PLT64/50/5. The windings were simulated by multiturn coils with 2 turn like in the prototype. The software's built-in SPICE simulator was used to simulate the inverters and the coils were supplied with sinusoidal voltages with an amplitude of 20V and a frequency of 50kHz.

The 3C90 magnetic material constituting the transformer has been described by a Jiles Artheton hysteresis model integrated in the software [START_REF] Saeed | Modeling of Magnetic Elements Including Losses-Application to Variable Inductor[END_REF] allowing to take into account the magnetic hysteresis characteristic of the ferrite material and thus to calculate the iron losses (eddy currents, magnetic losses).

The first results showed that the planned design would achieve the intended power and indeed allow power to be transferred between the inverters. As shown in the example illustrated in Fig. 8, inverters A and B should send about 300W equally to inverter C. The induction in the transformer shows that the operating point is far from saturation and that even more power can be transferred without significant losses. For this operating point, we have about 15W of losses or an efficiency of 95%.

Realization of the transformer

As previously mentioned, the transformer was made by sawing commercially available cores to match the dimensions used in the simulation.

(a) (

A struers secotom diamond saw was used to obtain the columns, which are in fact composed of two cylinders from ETD59 cores placed end to end. The flat parts of the transformer are made up of PLT64 flat rectangles and the junction between the flats was obtained by sawing a PLT64 to make an equilateral triangle whose side length is equal to the smallest length of the PLT64. All these elements were then glued together to form a half shell (Fig. 9a). Two half-transformers were manufactured and assembled using 3D printed parts (Fig. 9b). The windings are drawn directly onto the PCB of the inverter. This PCB is drilled with holes and plugged directly onto the transformer columns (Fig. 9c).

Inductance matrix measurement

To measure the inductance matrix, the windings were connected in star and an HP4194a impedance analyser was used. The measurement and connection diagram of the impedance analyser is given in Fig. 10. Although in principle the matrix is symmetrical, the 81 self and mutual inductances were measured (3 inverters with 3 phases per inverter and 3 transformer legs with 3 windings per leg) in order to highlight possible imbalances.

Hcur/Lcur are the current injection ports of the HP4194a and Lpot/Hpot are the measurement ports. The inductance matrix was measured for a frequency of 50kHz which is the intended switching frequency of the inverters. The resulting inductance matrix is given in Fig. 11. (All values in H).

From these measurements it appears that, as expected, the matrix is symmetrical, taking into account the geometry. Moreover, the inductance matrix must be block symmetrical and this is what we obtain with measurement errors that are not large (<1%).

The self-inductances of the same three-phase system are close and the mutual inductances on the same leg are close. Furthermore, they are close to the self-inductances, which indicates that there is little inter-phase leakage and that the component is close to a true transformer, and not to coupled inductances in the flyback sense. Finally, the mutual inductances of the same three-phase system are close to one third of the self-inductance, which means that there is little inter-leg leakage. Sawing ferrites, which are very hard ceramic materials, is difficult and without grinding the sawn surfaces it is impossible to obtain a perfect surface finish. Finally, the manufacturing tolerances of commercial ferrites are of the order of a millimeter and it is therefore difficult to perfectly align them thus explaining the dissymmetries that are finally obtained between the different inductances. Nevertheless, we have introduced the values obtained from the measurements into the PSIM simulation schematic in Fig. 12.

Experimental equivalent T-model

All the sources have a frequency of 50kHz and a peak voltage value of 25V. Vb has a phase shift of 8° with respect to Va and Vc an offset of 13° (chosen arbitrarily).

With the chosen conventions in the previous calculations, power is considered negative when the source is absorbing power and positive when it is delivering power. The simulation in Fig. 13 shows that inverter A absorbs 225.9W and that inverters B and C supply 51.5W and 175W respectively. There is therefore a transfer of power between the different inverters, which can be adjusted by modifying the phase shift between their respective controls. However, it can also be seen that the asymmetry in the leakage inductances strongly unbalances the transfer.

If, as in the simulation in Fig. 14, the phase shifts of Vb with respect to Va and Vc with respect to Va are identical, it can be seen that one of the two sources delivers much more power than the other (232.8W for B and 82.2W for C for total power of 314W in A), which can eventually lead to involuntary saturation of a part of the transformer. It is therefore very important that the construction be absolutely symmetrical so that the different inductances of the circuit are also symmetrical.

Conclusion

In this paper we have proposed a three-port system based on the use of three-phase inverters and a multi-port transformer to facilitate the exchange of energy between the converters. The system was modelled analytically. The component was produced by sawing and gluing commercial elements, then characterised with an impedance analyser to determine its inductance matrix and a socalled T-model whose elements were calculated from this matrix was proposed and simulated. In the light of the results obtained, it is clear that this type of component can be used in multi-port converters but that it must be made with particular care, so that it is as symmetrical as possible in order that the inductances themselves are symmetrical and the power transfer is easily adjustable without the need to significantly vary the phase shifts between the inverters.

Acknowledgment

The ASV research was supported supported by Occitanie region in a FEDER program N : ESR R&S DF-000035-2017-006565.

Fig. 1 :

 1 Fig. 1: Complete schematic of the converter

Fig. 2 :

 2 Fig. 2: Exploded view of the magnetic component (grey) and its plastic supports (red)

Fig. 3 :

 3 Fig. 3: Inverters phases and windings arrangement on the transformer

  𝑖 + 𝑀 . 𝑖 + 𝑀 . 𝑖 = (𝐿 -𝑀 ). 𝑖

Fig. 4 :

 4 Fig. 4: Self and mutual inductances related to phase a of inverter 1 and its winding

Fig. 5 :

 5 Fig. 5: Three phase to single phase transformer conversion

Fig. 6 :

 6 Fig. 6: Full model of the three windings transformer

3𝑖

  Calculation of the power delivered by the sourcesTo carry out this calculation, we will use the diagram in fig.7, the T-model. The power calculation is done for one leg of the inverters A, B, C. A multiplication by 3 will give the total power. Hereafter, VM is the midpoint voltage, Va is the phase origin and the voltages Vb and Vc are respectively phase shifted by an angle φab and φac with respect to Va. Using Kirchhoff's laws we have: 𝑉 -𝐿𝑓 . 𝑖 -𝑉 = 0 𝑉 -𝐿𝑓 . 𝑖 -𝑉 = 0 (13) 𝑉 -𝐿𝑓 . 𝑖 -𝑉 = 0 the complex voltage notation ( 𝑉 = [𝑉 ; 0°], 𝑉 = [𝑉 ; 𝜑 ], 𝑉 = [𝑉 ; 𝜑 ] ) into Eq. 14 it leads to: cos(𝜑 ) + cos(𝜑 ) + 𝑗 sin(𝜑 ) + 𝑗 sin(𝜑 ))

Fig. 7 :

 7 Fig. 7: T-model of the three windings transformer

Fig. 8 :Fig. 9 :

 89 Fig. 8: Simulation of a power exchange (A and B each send 150W to C), induction in the transformer

  Using this matrix of inductances experimentally measured with the HP4194a impedance analyser and using the relationships determined in the previous equations it is possible to calculate the elements of the matrix of equation 7 as shown in Eq. 20. (All values in H) have 2 turns and are made on PCB. We therefore have Kab = Kac = 1 and we can determine all the elements of the equivalent Tmodel. L = 3,93H, 𝐿 = 0,552H, Lfb' = 0,19H, Lfc' = 0,534H.

Fig. 10 :Fig. 12 :

 1012 Fig. 10: Measurement schematics

Fig. 14 :

 14 Fig. 14: Simulation for phase shifts of 8 degrees between Va and Vb and 13 degrees between Va and Vc.

Fig. 13 :

 13 Fig. 13: Simulation for identical phase shifts between Va and Vb and Vc.