Adela Marian

Stéphane Holé
email: stephane.hole@espci.fr

Frédéric Lesur

Matteo Tropeano

Christian E Bruzek

Validation of the Superconducting and Insulating Components of a High-Power HVDC Cable

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1.Introduction

Across the European continent, the integration of increasing numbers of renewable energy sources within the electricity grids has become a strategic objective, requiring the modernization and expansion of the grids. In particular, recent studies have emphasized the major role of bulk power lines with lengths of several hundred kilometers. These pan-European transmission corridors with capacities of 5 to 20 GW were shown to be necessary, no matter which energy scenario is explored [START_REF]Europe's future secure and sustainable electricity infrastructure[END_REF], [START_REF]Ten-Year Network Development Plan 2016 (TYNDP), prepared by the European Network of Transmission System Operators for Electricity (ENTSOE)[END_REF].

At present, the main technological options for transmitting power in the range 1 -8 GW include overhead lines, underground cables with extruded insulation (XLPE, i.e. cross-linked polyethylene) [START_REF] Worzyk | Submarine Power Cables[END_REF], [START_REF] Mazzanti | Extruded Cables for High Voltage Direct Current Transmission: Advances in Research and Development[END_REF], and gas-insulated lines (GIL) [START_REF] Koch | Gas-Insulated Transmission Lines[END_REF]. In the last few years, strong public opposition has led to the necessity to limit the visual impact of long-distance transmission lines, which in turn has resulted in the prevalence of partial or full undergrounding of power lines. Generally, this requires broad right-of-way corridors and considerable civil engineering, since most often several parallel circuits are needed for the highest power levels. For instance, for a power rating of 3 GW, the four parallel circuits of 380 kV AC cables in Raesfeld (Germany) and Stevin (Belgium) are installed in a 12-20 m wide trench. This results in a strip of land with a width of about 50 m in the construction phase.

In this context, superconducting power cables represent a recent innovative development for highcapacity underground transmission. As a reminder, superconducting materials display no electrical resistance below three critical parameters: temperature (less than ~ 70 K), current density (several thousands of amperes per square millimeter) and magnetic field (several tesla), which are all specific to each material. Superconductivity was discovered more than 100 years ago and has found widespread application in some fields, e.g., in medical imaging devices and particle accelerators [START_REF] Grant | Fantastic five -Top five applications of superconductivity[END_REF]. Nevertheless, its great potential for energy transmission has remained largely unexploited for decades, due to the very low operating temperature (below 5 K) required by the commercially available NbTi alloy wires. The cooling medium employed in this case is liquid helium, which is expensive and necessitates a very high energy to be kept in the liquid state. This situation changed with the discovery of high-temperature superconductors (HTS) thirty years ago.

HTS are based on rare-earth copper-oxide compounds called cuprates, and operate in the environmentally friendly liquid nitrogen (LN 2 ), a low-cost and commonly implemented cooling medium. They have opened new and interesting perspectives for superconducting power applications, in particular for cable manufacturing. A number of projects involving superconducting cables have emerged, with links of various lengths and capacities already in operation or under construction worldwide [START_REF]Superconducting Power Equipment: Technology Watch[END_REF]. However, widespread use of such superconducting systems for power transmission has been hampered by the high costs of the HTS, i.e., the constituent materials and the complex manufacturing process.

In 2001, a promising alternative was ushered in with the discovery of superconductivity at temperatures below 39 K (~ -230°C) in magnesium diboride (MgB 2 ) [START_REF] Nagamatsu | Superconductivity at 39 K in magnesium diboride[END_REF]. Magnesium and boron are low-cost elements that are abundant in nature, especially when compared to the rare-earth components of HTS materials or their silver matrix. In addition, the much simpler manufacturing process further decreases costs for MgB 2 superconducting wires. The combination of these two factors makes the cost of MgB 2 less than 10 % of the cost of any other HTS material. As a consequence, MgB 2 is already available at commercial level in kilometric lengths. However, the necessary cooling medium and associated cooling system are more expensive than liquid nitrogen but are significantly cheaper than liquid helium. The interplay of the various cost components needs to be carefully considered, preferably in an economic viability analysis. For these reasons, the study of a high-power superconducting link Thus Demo 5 aims to showcase a full-scale 3 GW class HVDC superconducting cable system operating at 320 kV and 10 kA [START_REF] Ballarino | The BEST PATHS project on MgB 2 superconducting cables for very high power transmission[END_REF]. Besides validating the MgB 2 superconductor for high-power electricity transfer, the project will also provide guidance on new technical aspects, economic viability and environmental impact of this innovative technology. This article focuses on the design and development activities for the Best Paths superconducting cable, which were carried out in the first half of the project. After a general presentation of the cable system in Section II, the main outcomes of the cable conductor design are summarized in Section III. A substantial part of the paper is dedicated to the novel liquid-nitrogen-impregnated high-voltage insulation, in particular the first space-charge measurements on that insulation, which are reported and discussed in detail in Section IV. A first strategy for the testing of the demonstrator is proposed in the concluding section.

2.Specification and cable structure

To maintain the operating conditions required in a superconducting cable circuit, a system approach including cooling and electrical systems is needed. Active and passive elements are specifically designed according to the application and the site requirement.

In general, a superconducting cable system includes the following main elements:  the cable conductor,  the cryogenic envelope,  the cooling fluid(s), stably maintained at the adequate cryogenic temperature by the cooling system(s),  the voltage insulation, and  the terminations providing the grid connection needed for operation in the electricity grid.

As some heat inleak (i.e. heat ingress) is unavoidable, the cooling fluid temperature will increase and will therefore need to be lowered using cooling machines. The heat load from the cable system should be as small as possible for a cost-competitive design. Moreover, the dedicated cooling systems should be optimized for efficient use and benefit from reduced size and complexity. As an aside, the electric power required to operate these machines represents the only power consumption of the superconducting cable system. If this technology is applied to kilometric HVDC cable systems, the power dissipated at room temperature by a superconducting cable is estimated to be less than 3 W/(kA m) for a 10 kA monopole system, while a resistive cable dissipates 23 W/(kA m) [START_REF] Bruzek | Superconducting DC cables to improve the efficiency of electricity transmission and distribution networks: an overview[END_REF].

In the case of the MgB 2 superconductor, the operating temperature needs to be maintained in the range 15 -25 K (~ -250°C), which can be achieved by using either gaseous helium or liquid hydrogen.

A sophisticated cryogenic line is therefore required for the fluid circulation, and includes vacuum thermal insulation and a thermal shield using liquid nitrogen in the temperature range 70 -80 K. Thus several concentric corrugated tubes make up the cryogenic envelope proposed for the Best Paths project. Figure 1 schematically presents the basic cable configuration, apart from the electrical terminations. The MgB 2 conductor is housed in an inner helium-cooled cryogenic envelope whose outer wall is lapped with high-voltage insulation. This assembly is inserted into an outer flexible cryogenic envelope, which is cooled by liquid nitrogen acting as a thermal shield. In this way thermal losses are limited to an acceptable level. The envisioned outer diameter of the cable is around 150 mm. Apart from the so-called cold dielectric configuration using liquid nitrogen described here, a warm dielectric configuration was investigated in a recent publication [START_REF] Morandi | Feasibility of High Voltage DC superconducting cables with extruded warm dielectric[END_REF]. Although more complicated, the selection of the cold dielectric design for the project is based on careful consideration of the overall system efficiency. The heat flux interception by the low-cost LN 2 cryogen reduces by a factor of 2 the power required to maintain the MgB 2 superconductor at its operating temperature [START_REF] Bruzek | Superconducting DC cables to improve the efficiency of electricity transmission and distribution networks: an overview[END_REF]. As the heat inleak should be kept as small as possible, the strategy is to benefit from this LN 2 shield by also using it as high-voltage electrical insulation. The helical corrugations of the tubes constituting the cryogenic envelope contribute to the mechanical flexibility of the cable. Long tube lengths of several hundreds of meters can be routinely manufactured and transported to the installation site on drums. Since the cryogenic envelope allows for bending deformations, the cable can be pulled into ducts or pipes for installation.

As the cryogenic envelope completely eliminates thermal dissipation to the surrounding area, superconducting power links can be laid underground in a confined environment. By contrast, mutual heating between adjacent circuits of resistive cables leads to a decrease in their current rating. The absence of heat dissipation combined with a very compact design enables the superconducting cable system to fit into a smaller area than a conventional system with the same power rating. This is a significant advantage in areas with high ambient temperature, or when crossing busy urban districts.

Thus the transmission footprint of the 3 GW conventional system mentioned in the Introduction would be reduced to a width of only 0.8 m when using the Best Paths superconducting cable. This represents a reduction in the right of way by more than a factor of 10.

It is also worth noting that the overall weight of the superconducting cable system, including the cryogenic envelope and cooling fluid, can be as small as 3 % of the weight of a conventional system with the same power rating. Consequently, the reduction of raw materials, energy and associated greenhouse gas emissions during the manufacturing process is a valuable benefit.

Lastly, for integration into the grid, the cable system holds promise from both a technical and an economic point of view. In addition to the very high power transmission, it should have an acceptable loss level, and a proven record of reliable operation in the grid, particularly under transient conditions.

Note that some superconducting AC cables have already been installed in the grid for long-term testing.

A district of the German city of Essen has been energized for more than three years without any interruption or reported problems, using a kilometer-long superconducting cable [START_REF] Stemmle | AmpaCity project -Worldwide first superconducting cable and fault current limiter installation in a German city center[END_REF]. The same cautious approach should also be implemented as proof of long-term performance for the HVDC cable.

The most important specifications of the Best Paths cable are reported in Table 1. The upper part of the table summarizes the main nominal parameters of the cable, and the lower part shows the requirements imposed by transmission system operators for successful integration into the electricity grid. The fulfillment of these requirements was one of the key considerations for the cable conductor design.

3.Cable conductor status A) MgB 2 wires

The superconducting material is the essential component of the cable conductor. In principle, the superconductor needs to be available in lengths of several kilometers, and ideally be flexible in order to maintain its performance after cabling, winding and installation operations. Both these conditions are fully met by the MgB 2 superconductor.

The MgB 2 wires were designed, optimized and manufactured by Columbus Superconductors using the so-called Powder-in-Tube fabrication process [START_REF] Grasso | Large transport critical currents in unsintered MgB 2 superconducting tapes[END_REF], [START_REF] Braccini | Development of ex situ processed MgB 2 wires and their applications to magnets[END_REF]. To begin with, already reacted MgB 2 powders were used to fill a metal tube, generally made out of nickel. The nickel tube was then cold worked to obtain monofilamentary wires that were restacked in a new outer tube. This multifilamentary assembly was cold worked again down to the desired shape and dimension. A final heat treatment at about 900°C was carried out at the end of the process to recover and optimize the superconducting The wire development process is highly iterative, involving many fine adjustments of the wire layout, diameter, composition, and superconducting filling factor. For Best Paths, one of the key design goals was to fulfill the electrical grid requirements while ensuring good mechanical properties of the wires. To this end, four wire topologies were optimized, fully characterized, and produced in kilometric lengths. A significant effort was devoted to maintaining and verifying the wire homogeneity along its full length. This was achieved by careful qualification of the finishing stage of the production process, involving a number of tests such as eddy-current defect detection and laser acquisition of the wire dimensions at various intermediate stages. Moreover, the homogeneity of the superconducting performance was confirmed by measurements of the wire critical current, which were conducted at CERN [START_REF] Bruzek | Cable conductor design for the high-power MgB 2 DC superconducting cable project of BEST PATHS[END_REF]. Once the current-carrying capability of the wires was successfully demonstrated, they were ready to be integrated into the cable conductor.

B) Cable conductor

The cable conductor is assembled by helically winding the required number of MgB 2 wires around a flexible copper core, as seen in the cross section displayed in Fig. 3. The positioning of the MgB 2 wires in the external layer facilitates the electrical connection to the cable terminations. The copper core acts as a low-resistance electrical shunt protecting the superconducting wires. In case of electrical faults, these resistive wires transport the current in excess of the superconducting critical current. Since the cable core has a very low resistance, it can accept high fault currents. However, during such a fault, the resistive current causes an increase in temperature. As a consequence, the cable must be rapidly disconnected to prevent any damage to the superconductor. The typical timescale is around 100 ms, and the acceptable temperature rise during and after fault was shown to be 100 K. As soon as the fault is cleared, the cooling system returns the operating temperature to 20 K.

The main characteristics of the 10 kA Best Paths cable conductor are summarized in Table 2.

Finite-element modeling was used to design, enhance, and validate the cable structure under the transient grid conditions listed in Table 1 [START_REF] Bruzek | Cable conductor design for the high-power MgB 2 DC superconducting cable project of BEST PATHS[END_REF], [START_REF] Escamez | 3-D numerical modeling of AC losses in multifilamentary MgB 2 wires[END_REF]. For instance, numerical simulations were employed to calculate the optimal amount of copper required for efficient protection of the cable conductor.

Several kilometers of the cable conductor shown in Fig. 3 were manufactured by Nexans using an upgraded industrial cabling machine. Columbus Superconductors provided several tens of kilometers of MgB 2 wires for this cabling operation. The electrical characteristics of the cable conductor were then carefully tested in the first experimental trials. The qualification strategy is based on two main activities: measurements at 20 K on extracted wires, and measurements at 4.3 K on the cable conductor in a high magnetic field. These testing conditions are more stringent than those expected during operation in the grid. In the measurements at 20 K, no degradation in performance was found for the wires extracted from the cable.

In the measurements at 4.3 K, the experimental data were in very good agreement with those expected from specifically developed numerical models. This indicates good mechanical performance of the cable conductor, which in turn proves the absence of defects in the MgB 2 wires and the ability to assemble and handle them on industrial cabling machines.

4.Insulation concept and testing system

As previously mentioned, the MgB 2 cable system requires simultaneous operation at both high current and high voltage. As the inner cryogenic envelope enclosing the superconducting conductor is under high voltage, an insulating material is required to prevent the current from flowing towards ground. This material is inserted into the outer cryogenic envelope and thus operates at liquid nitrogen temperature. Common synthetic materials are not appropriate at such low temperatures (about 75 K ≈ -200°C), since cracks may easily appear due to mechanical constraints and differential shrinkage, resulting in an irreversible degradation of the insulation. Consequently polypropylene lapped paper (PPLP) is often used [START_REF] Kim | The Fundamental Characteristics of PPLP as Insulating Material for HTS DC Cable[END_REF]. The lapping provides mechanical flexibility for the structure without causing cracks, and the polypropylene offers a high breakdown voltage. Liquid nitrogen then impregnates the insulating structure to avoid any gaseous regions and subsequent partial discharges. In addition, the liquid nitrogen pressure can be increased, raising its boiling temperature and preventing bubble formation.

Another possible choice for the low temperature insulation is liquid nitrogen impregnated Kraft paper (instead of liquid nitrogen impregnated PPLP). The paper provides only a geometrical structure, and the liquid nitrogen provides the dielectric strength. Though the breakdown voltage is reduced, the cost is significantly lower, and self-healing can be considered. Indeed, if a small initial breakdown occurs in the impregnated Kraft paper, the resulting hole in the paper is rapidly filled with liquid nitrogen, and the breakdown voltage is unchanged. Breakdown does not become more severe, and eventually ceases. By contrast, when using PPLP, the hole resulting from the initial breakdown reduces drastically the overall breakdown voltage threshold, as the insulating material changes from polypropylene to liquid nitrogen. Consequently, if the voltage is not rapidly decreased breakdown becomes more severe, and an avalanche of major breakdowns will occur.

A) Space Charge Measurement System

Working at cryogenic temperatures requires good temperature control. Thus, in the context of this study, thermal space charge measurement methods are less suitable than elastic methods, either PEA or PWP [START_REF] Holé | Non-destructive methods for space charge distribution measurements: What are the differences?[END_REF]. One sheet of PPLP has already been tested under voltage in liquid nitrogen [START_REF] Kim | The Fundamental Characteristics of PPLP as Insulating Material for HTS DC Cable[END_REF] using the PEA (Pulsed-Electro-Acoustic) method [START_REF] Holé | Non-destructive methods for space charge distribution measurements: What are the differences?[END_REF], [START_REF] Maeno | Pulsed electro-acoustic method for the measurement of volume charge in e-beam irradiated PMMA[END_REF], and the conduction properties of multilayers of PPLP and Kraft paper have been compared [START_REF] Kwon | Comparison of the Electrical Conductivity of Polypropylene Laminated Paper (PPLP) and Kraft in LN 2 According to the Number of Layers[END_REF]. However, for the purpose of the Best Paths study, the multilayer structure must be tested both at liquid nitrogen temperature and at high pressure (at least 5 bar). A dedicated measurement setup [START_REF] Holé | Space charge measurements at very low temperatures[END_REF] has been designed to test coaxial samples, which are at least 2-mm thick, at 60 kV. The PWP (Pressure-Wave-Propagation) method [START_REF] Holé | Non-destructive methods for space charge distribution measurements: What are the differences?[END_REF] was chosen in that study, instead of the PEA method [START_REF] Maeno | Pulsed electro-acoustic method for the measurement of volume charge in e-beam irradiated PMMA[END_REF], since it offers a much better signal-to-noise ratio. However, employing a pulsed laser to generate the pressure wave, as in the LIPP (Laser-Induced-Pressure-Pulse) technique [START_REF] Alquié | Stress wave probing of electric field distributions in dielectrics[END_REF], [START_REF] Sessler | Measurement of charge distribution in polymer electrets by a new pressure-pulse method[END_REF], is not appropriate because it would create nitrogen bubbles. The PIPP (Piezoelectric-Induced-Pressure-Pulse) technique was used instead. The piezoelectric generator [START_REF] Holé | Design and optimization of unipolar pressure pulse generators with a single transducer[END_REF] consists of an aluminum waveguide, a brass backing medium and a Pz24 piezoceramic from Meggitt. The latter has a diameter of 15 mm and a thickness of 200 µm. Fig. 4 illustrates the structure of the generator.

The aluminum waveguide is flat on the piezoelectric side and cylindrical on the sample side, in order to match the sample coaxial geometry. The pressure pulses are therefore generated with a planar wave front and are focused inside the sample by the cylindrical interface between the aluminum and the liquid nitrogen. The focal distance is inversely proportional to (1α), where α = ν LN2 / ν Al is the ratio between the speed of sound in liquid nitrogen and in aluminum. As this ratio is relatively small, on the order of 14 %, the focal point is close to the center of the cylinder.

Fig. 4: Structure of the pressure pulse generator. The cylindrical shape at the bottom of the waveguide focuses the generated pressure pulse inside the coaxial sample. To generate short pressure pulses, the piezoceramic is supplied through a coaxial cable and an adapted capacitor.

As piezoceramics have large capacitance, which is detrimental for their rapid excitation, a 1 nF capacitor is inserted in series with the piezoceramic, and a 10 Ω cable is used to supply the pressure pulse generator (see Fig. 4). Pulses with durations of 30 -40 ns are then generated. The entire measurement system, including the pressure pulse generator and the high-voltage decoupling, is inserted into a cryostat. Valves are used to fill the cryostat from a nitrogen tank, or to empty the cryostat into the tank. During measurements, the pressure inside the cryostat is maintained by acting directly on the nitrogen leakage valve. PVC and aluminum tubes are used for high-voltage insulation and shielding, respectively. Figure 5 shows the general structure of the cryostat.

B) Samples and Space Charge Measurement Protocol

All samples are mounted on a steel tube with a diameter of 26.9 mm and a length of 70 cm that mimics the inner cryostat. Carbon loaded paper is then lapped around this tube, covering its entire surface. Carbon paper is also lapped on the 2-mm-thick insulation along a 10 cm length in the middle of the sample. The electric field at the inner/outer electrodes of the samples is thus of order 32/28 kV/mm under an applied voltage of 60 kV. For comparison, the electric field at the inner/outer electrodes of the full-size cable is 19.8/7.65 kV/mm under an applied voltage of 320 kV, given inner/outer diameters of 34/88 mm. Thus the measured samples were subjected to higher electric fields than those expected for the full-size cable. Taking into account the resistivity and permittivity of the insulation [START_REF] Kwon | Comparison of the Electrical Conductivity of Polypropylene Laminated Paper (PPLP) and Kraft in LN 2 According to the Number of Layers[END_REF], its time constant is of the order of 30 minutes. Therefore charge buildup due to conductivity should be detected within two hours.

However preliminary measurements (with the field off) showed a residual electric field of similar amplitude for various durations of the applied voltage. This is an indication of a more rapid process. We therefore used a specific protocol to follow the residual electric field during voltage application, in order to see if the residual electric field was voltage dependent and to observe its short term stability. The samples were subjected to +40 kV for 1 hour, shorted for the next hour, subjected to +60 kV for another hour, and finally shorted for the last hour (see Fig. 7 (a)). During voltage application one measurement was performed under voltage, the voltage was switched off for less than 50 s and a measurement taken under short-circuit, and the voltage was then reapplied (see Fig. 7 (b)). We checked that this rapid shortcircuiting had no influence on the signal obtained after the stress, compared to the continuous applied voltage case. Another advantage of rapid short-circuiting is that it facilitates checking of the stability of the measurement setup throughout the duration of the test. When dealing with insulation which is a mixture of liquid and solid, interfaces are likely to move due to internal electrostatic forces, and since the speed of sound in liquid nitrogen is very sensitive to pressure and temperature [START_REF] Van Itterbeek | Velocity of sound in liquid nitrogen[END_REF], an unchecked initial calibration could yield misleading results. In the measurement protocol, the liquid nitrogen pressure is maintained at 5 bar. Measurements are carried out before and during applied voltage cycles, and during short-circuit cycles.

C) Space Charge Measurement Results and Discussion

The difference between a measurement under voltage and an immediately following measurement under short-circuit, shown in Fig. 8 for Sample 2 (0 min), and at three later times, does not vary significantly. (The negative peak around 2600 ns is due to reflection from the stainless steel tube inside the sample). The same behavior is observed for all samples over the complete measurement cycles.

Hence it can be concluded that the measurement setup is very stable and that comparisons of different measurements are reliable. Moreover, the uncomplicated shape of the signals indicates that the pressure wave travels easily through the complex laminated structure of the sample, without significant reflection. Therefore, all measurements (Figs. 9-11) can be calibrated according to the procedure described in [START_REF] Holé | Space charge behaviour in epoxy laminates under high constant electric field[END_REF] and adapted for coaxial geometry. In the calibrated signals of The charges under short-circuit correspond to injection from the electrodes, since they are of the same polarity as the peaks observed under voltage application. As they remain trapped near the interface, they probably originate from the carbon loaded paper. Confirmation of this suggestion is the effect of the gap between the strips, which influences the number of charges. Thus comparing Sample 1

and Sample 2, the smaller the gap between the strips of liquid nitrogen impregnated paper (1 mm in Sample 1 and 5 mm in Sample 2), the lower the number of injected charges. In addition, the charge buildup observed in short-circuit measurements indicates that the charges appear as soon as the voltage is applied. The surface charge density on the outer electrode, calculated from figures 9b, 9d, 9f, 10b, 10d and 10f, shows a large increase when the applied voltage is increased, as seen in Fig. 11. These charges are therefore likely to be trapped on isolated carbon particles at the interface between the electrode and the insulator, which are not in contact with other carbon particles in the electrode. When the voltage amplitude increases, charges transfer to the isolated carbon particles as a result of small partial discharges at the electrodes. When the voltage decreases, some of the charges on the isolated carbon particles return to the electrode, while the remainder are still trapped on the particles since the electric field is no longer sufficiently strong to ignite a discharge. It follows from Figure 11 Fig. 11: Amplitude of negative charge buildup at the cathode (0 mm) during measurement protocol (see Fig. 7).

It is also interesting to note that there is no significant difference in the behavior of PPLP and Kraft paper for applied voltages lower than 60 kV, corresponding to applied electric fields of about 30 kV/mm. PPLP can therefore be safely replaced by liquid nitrogen impregnated Kraft paper, at the electric field values discussed here.

5.Conclusions and outlook

Within the Best Paths European project, important validations have been achieved for a 3 GW class power cable system based on the MgB 2 superconductor.

We have developed robust and reproducible wire manufacturing and associated cabling technologies at industrial scale. We have also developed realistic modeling which accurately predicts the performance of the various cable components.

For the first time, an experimental setup has been designed, tested and employed for measuring the space-charge distribution in multilayer insulation immersed in liquid nitrogen under high voltage and hydrostatic pressure.

No significant difference was found between PPLP and Kraft paper for electric fields up to 30 kV/mm. In both cases, charge injection at the interface between the carbon black paper electrodes and the insulation was detected. These charges were probably trapped on isolated black carbon particles detached from the carbon electrodes. Most importantly, space charge was not detected in the bulk of the insulation in any of the measurements. This absence shows that, unlike XLPE, the lapped insulation structure impregnated with liquid nitrogen does not accumulate charge over time, and suggests that the insulation can very probably be successfully integrated into superconducting cables.

Based on these findings, a full-size demonstrator including two terminations and the associated cooling systems will be manufactured and tested under high voltage in 2018. The high-voltage test of the superconducting system will be carried out at the Nexans high-voltage cryogenic platform in Hanover, which is well equipped for such tasks. The size of this testing station limits the cable length to a maximum of 20 to 30 m. The high-current tests (up to 20 kA) will be conducted at CERN at an adhoc constructed cryogenic installation developed previously [START_REF] Ballarino | Development of superconducting links for the large hadron collider machine[END_REF].

So far no standard has been established for testing HVDC superconducting cables. However, the testing of a full AC superconducting cable system (including cable, joints, terminations and cryogenics) has been reviewed by a Cigré working group, which published a technical brochure in 2013 [START_REF]Recommendations for testing of superconducting cables[END_REF]. These tests are directed towards ensuring essential expected intrinsic performance during the cable system lifetime, not just providing commissioning certificates. The tests are widely based on requirements for resistive cables, to which new tests have been added in order to cope specifically with requirements for the superconducting material performance. New end users can also find guidance on problems related to cryogenic system performance, specifications and safety, which can be critical to successful cable system operation.

Although the recommendations given in [START_REF]Recommendations for testing of superconducting cables[END_REF] cover high-temperature superconducting materials at AC voltages up to 150 kV, they will be very useful for the development of MgB 2 DC cables operating at higher voltage level. The starting point for addressing the HVDC requirements is provided in another

Cigré brochure [START_REF]Recommendations for testing DC extruded cable systems for power transmission at a rated voltage up to 500 kV[END_REF], which presents recommendations for testing DC extruded cables operating at voltages up to 500 kV. The combination of these two sets of established international practices should constitute a solid basis for testing the Best Paths superconducting demonstrator. At the same time, the results and measurements carried out within Best Paths will be a significant step towards preparing a first set of recommendations for the superconducting HVDC standard of the future.

  based on MgB 2 has been included in one of the largest EU-funded demonstration projects on energy transmission, Best Paths [9]. The acronym BEST PATHS stands for "BEyond State-of-the-art Technologies for rePowering Ac corridors and multi-Terminal HVDC Systems". The four-year project was launched in October 2014 and is supported by the European Commission within its FP7 research framework. Best Paths encompasses nearly 40 leading European organizations from science and industry, which have joined forces with utilities and transmission system operators to advance five large-scale demonstration areas. These demonstrators span a multitude of research activities ranging from connecting offshore wind parks, to developing standardized solutions for multivendor converter technologies, upgrading multi-terminal high-voltage DC (HVDC) links, and repowering of existing AC corridors. Finally, the fifth demonstrator -Demo 5 -is focused on high-capacity links based on the MgB 2 superconductor.

Fig. 1 :

 1 Fig. 1: Conceptual design a) and cross section b) of the HVDC cable. In both figures lighter cyan represents liquid nitrogen and darker cyan represents helium gas.

  properties of the MgB 2 compound. Cross sections of two round MgB 2 wires produced in this fashion are shown in Fig.2.

Fig. 2 :

 2 Fig. 2: Cross sections of two MgB 2 wires with diameters of 1.3 mm (left) and 1 mm (right), composed of 36 (left) and 37 (right) superconducting filaments embedded in a matrix of nickel and monel (an alloy of nickel and copper).

Fig. 3 :

 3 Fig. 3: The MgB 2 cable conductor for the Best Paths project.

Fig. 5 :

 5 Fig. 5: Sketch of the cryostat. Valves are used to fill, empty and regulate the liquid nitrogen pressure inside the cryostat. PVC tubes are employed for high-voltage insulation, and aluminum tubes for signal shielding.

Sample 1 Fig. 6 :

 16 Fig. 6: Photograph of a Kraft paper sample with a 5-mm gap between its strips (Sample 2).

Fig. 7 :

 7 Fig. 7: Measurement protocol. The purple arrows indicate the space charge measurements. (a) General cycle. (b) An intermediate short-circuit measurement. The intermediate short-circuit measurements are used to ensure that the sample has not changed due to the electrical stresses, and to help detect small charge buildups during applied voltage cycles.

Fig. 8 :

 8 Fig. 8: The difference between the signal obtained under voltage and the signal obtained under shortcircuit immediately afterwards, and at three later times (Sample 2).

Fig. 9 -Fig. 9 :

 99 Fig. 9: Measurements under 40 kV (a, c, e) and under short-circuit (b, d, f) for sample 1 (a, b), sample 2 (c, d) and sample 3 (e, f). Measurements at 60 kV and under short-circuit for Samples 1, 2 and 3 are shown in Fig. 10. Similarly, though the signals show no significant evolution during voltage application, charges are clearly detected for all samples under short-circuit.

Fig. 10 :

 10 Fig. 10: Measurements under 60 kV (a, c, e) and under short-circuit (b, d, f) for sample 1 (a, b), sample 2 (c, d) and sample 3 (e, f).

  that a 1-mm gap between strips (Sample 1) decreases the residual interface field by a factor 1.35 at 40 kV and by a factor 1.15 at 60 kV, relative to a 5 mm gap between strips (Sample 2). Using PPLP (Sample 3) increases however the residual interface field by a factor 1.3 at both 40 and 60 kV, relative to using Kraft paper (Sample 2). The capability to detect these trapped charges demonstrates the high sensitivity of the measurement system. There is no other change in the signal in the insulating part of the sample, indicating zero or negligible charge buildup in the bulk, and confirming the Best Paths cable design.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Conceptual design a) and cross section b) of the HVDC cable. In both figures lighter cyan represents liquid nitrogen and darker cyan represents helium gas.

Fig. 3 :

 3 Fig. 3: The MgB 2 cable conductor for the Best Paths project.

Fig. 4 :Fig. 5 :Fig. 6 :

 456 Fig.4: Structure of the pressure pulse generator. The cylindrical shape at the bottom of the waveguide focuses the generated pressure pulse inside the coaxial sample. To generate short pressure pulses, the piezoceramic is supplied through a coaxial cable and an adapted capacitor.

Fig. 7 :

 7 Fig. 7: Measurement protocol. The purple arrows indicate the space charge measurements. (a) General cycle. (b) An intermediate short-circuit measurement. The intermediate short-circuit measurements are used to ensure that the sample has not changed due to the electrical stresses, and to help detect small charge buildups during applied voltage cycles.

Fig. 8 :

 8 Fig. 8: The difference between signals obtained under voltage and signals obtained under short-circuit immediately afterwards, for Sample 2 at three subsequent times.

Fig. 9 :

 9 Fig. 9: Measurements under 40 kV (a, c, e) and under short-circuit (b, d, f) for sample 1 (a, b), sample 2 (c, d) and sample 3 (e, f).

Fig. 10 :

 10 Fig. 10: Measurements under 60 kV (a, c, e) and under short-circuit (b, d, f) for sample 1 (a, b), sample 2 (c, d) and sample 3 (e, f).

Fig. 11 :

 11 Fig.11: Amplitude of negative charge buildup at the cathode (0 mm) during measurement protocol (see Fig.7).

Table 1 :

 1 Specification of the Best Paths Cable

	Parameters	Values
	Power	3.2 GW
	Voltage	320 kV
	Operating DC current	10 kA
	Cooling medium	He gas for MgB2 LN2 for insulation
	Cryogenic losses	< 0.1 W/m at 20 K in He gas < 1 W/m at 80 K in LN2
	Current ripple	1% amplitude at 50 Hz
	Fault current	35 kA during 100 ms
	Power reversal ramp	100 MW/s to 10 GW/s

Table 2 :

 2 Electrical Characteristics of the Cable Conductor

	Parameters	Values
	Cable diameter	9.5 mm
	Number of MgB2 wires	18 wires, 1.33 mm diameter
	Number of Cu wires	19 wires, 1.33 mm diameter
	MgB2 cable pitch	250 mm
	Self magnetic field	0.6 T
	Operating temperature range	18 -22 K
	Cable conductor critical current in self field at 20 K; 1 μV/cm	14 kA

Table Captions Table 1 :

 Captions1 Specification of the Best Paths Cable

Table 2 :

 2 Electrical Characteristics of the Cable Conductor

Frédéric Lesur is an expert engineer in power cable systems. After being a merchant marine officer for three years, he was graduated in power electronics. He worked for the cable manufacturer Silec as a research engineer, mainly involved in the development of XLPE 400 kV underground links, in modeling and simulation. He moved to EDF utility in 1999, and managed the cable system testing facility of Les Renardières. He worked for the engineering branch of RTE, the French transmission system operator, from 2007 on various topics as cable system design, current ratings or magnetic field management, with the development of models and tools, in order to contribute to major interconnection projects and to support the regional deployment of land and offshore cable systems. His background led him to innovative technologies for the network for the future such as super grids and transmission


Julien Haffner

Cédric Margo

Yacine Oussar
email: yacine.oussar@espci.fr

Jessie Casimiro

Philippe Mabire

Stéphane Holé

Philipe Mabire

A smart capacitive measurement system for fall detection

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Life expectancy is constantly increasing in populations of industrialized countries. In France, the proportion of people over 60-years old represents 20% of the total population at the present time. This rate is expected to reach 35% by 2050 [START_REF] Robert-Bobée | Projections de population pour la France métropolitaine à l'horizon 2050[END_REF]. Well-being and autonomy of seniors are major concerns for these societies. Falls represent 84% of daily living accidents occurring for people over 65-years old [START_REF] Ricard | Plusieurs centaines de milliers de chutes chez les personnes âgées chaque année en France[END_REF] and their consequences worsen as the time before being cared increases. The death rate within 6 months is 50% for people who stayed on the floor more than one hour after falling [START_REF] Wild | How dangerous are falls in old people at home?[END_REF]. The need for an efficient solution to detect falls is then crucial.

Fall alert systems commonly used are emergency buttons. A victim must press on a button to trigger an alarm. Such systems are called active systems because it has to be activated by the victim himself.

They are totally useless if the victim is unable to press on the button for various reasons such as loss of consciousness or pain. Many types of detectors were developed with the aim of automatically detecting falls, without human intervention. These devices can be divided into three categories: wearable devices, image processing and ambient sensors [START_REF] Mubashir | A survey on fall detection: Principles and approaches[END_REF]. Wearable devices are directly worn by the users. They consist of accelerometers attached to one or several parts of the body [START_REF] Yang | A review of accelerometry-based wearable motion detectors for physical activity monitoring[END_REF]. A fall generates a strong acceleration which makes it detectable and then separable from other daily living activities (DAL) [START_REF] Lindemann | Evaluation of a fall detector based on accelerometers: A pilot study[END_REF][START_REF] Li | Accurate, fast fall detection using gyroscopes and accelerometer-derived posture information[END_REF]. However these devices are prone to a high rate of false detection alarms [START_REF] Yu | Approaches and principles of fall detection for elderly and patient[END_REF], which represents an obstacle to their industrial deployment. Another common drawback of wearable devices is the high solicitation of the users since they always have to remind to wear them. A consequence is that wearable devices are felt very intrusive and thus strengthen the feeling of loss of independence [START_REF] Brownsell | Fall detectors : do they work or reduce the fear of falling?[END_REF]. To avoid these disadvantages, other systems directly integrated in the environment of the users were proposed. The aim of these systems is to disturb as less as possible the user's daily life. Compared to wearable devices, theses systems are efficient in the limited area of the installation [START_REF] Igual | Challenges, issues and trends in fall detection systems[END_REF]. One method consists in using cameras installed in several places of the room to be monitored [START_REF] Nait-Charif | Activity summarisation and fall detection in a supportive home environment[END_REF]. A fall then can be recognized by using appropriate image processing techniques. However, video based solutions are difficult to implement in real life conditions. In fact a great number of cameras are required in order to limit the problem of occlusions caused by objects such as chairs or sofas [START_REF] Rougier | Robust video surveillance for fall detection based on human shape deformation[END_REF]. Algorithms are then very complex. Moreover, this solution remains a trouble for user's privacy since the presence of cameras increases the feeling of being observed [START_REF] Sixsmith | A smart sensor to detect the falls of the elderly[END_REF][START_REF] Fleck | Smart camera based monitoring system and its application to assisted living[END_REF]. Thus, systems which are fully invisible to the users are then preferable. Most of these ambient systems contain pressure sensors inserted under the floor [START_REF] Tzeng | Design of fall detection system with floor pressure and infrared image[END_REF]. Pressure sensors are cost efficient. However they present the disadvantage of being deformable and are then subject to mechanical wear. Other solutions were proposed such as: (i) motion detection by using Doppler Radar Sensor installed in floor or ceiling [START_REF] Liang Liu | Doppler radar sensor positioning in a fall detection system[END_REF], (ii) vibration detection caused by a human above the floor with piezoelectric sensors coupled to the floor [START_REF] Alwan | A smart and passive floor-vibration based fall detector for elderly[END_REF][START_REF] Litvak | Fall detection of elderly through floor vibrations and sound[END_REF]. These systems were tested only in laboratory conditions so far. Their implementation in real environments must be adapted to the architecture of each instrumented room [START_REF] Alwan | A smart and passive floor-vibration based fall detector for elderly[END_REF]. The development of these systems at an industrial level seems difficult for this reason.

Capacitive sensors installed under the floor is another non intrusive solution to detect human activity above the floor [START_REF] Valtonen | Capacitive indoor positioning and contact sensing for activity recognition in smart homes[END_REF][START_REF] Valtonen | TileTrack: Capacitive human tracking using floor tiles[END_REF]. Capacitive sensing is the measurement of the influence of the electric field generated by an electrode on which a voltage is applied [START_REF] Smith | Electric Field Imaging[END_REF]. As this electric field is modified by a human presence close to the sensor [START_REF] Mazzeo | Paper-based, capacitive touch pads[END_REF], it is then possible to detect a human presence above the floor and follow its activity in order to detect abnormal situations such as a fall. Unlike pressure sensors, capacitive sensors have no deformable parts. They are then much more robust and adapted for being used as floor sensors. Several fall detection systems based on this method were proposed in the last few years. In [START_REF] Rimminen | Human tracking using near field imaging[END_REF], capacitive sensors are made up of aluminum sheets (36 cm × 30 cm). In [START_REF] Steinhage | Monitoring movement behavior by means of a large area proximity sensor array in the floor[END_REF], the capacitive sensors consist in a floor mat containing conductive textile layers acting as the sensor electrodes. Due to their architecture, maintenance is expensive and time-consuming for both systems. In fact, either electronic cards or electrical connections between sensors and cards are placed directly under the floor covering. These devices are therefore fragile and can be damaged. In [START_REF] Rimminen | Detection of human movement by near field imaging : development of a novel method and applications[END_REF], it has been reported that oxidation of sensor connectors is at the origin of many false alarms. In such cases, floor covering has to be removed in order to replace the damaged components.

To avoid these drawbacks, the capacitive system presented in this paper has all its electrical parts and contacts out of the floor. Two main experimental setups are presented. The fisrt system (system 1) is an instrumented room of about 15 m², equipped with sensors directly installed in the floor. The second system (system 2) is a transportable demonstrator which size is 2.50 m × 1 m. In section 3 the systems and experimental setups are described. In section 4, data acquisition and classification methods used for fall recognition are presented. Results are discussed in section 5 before conclusion.

3 Capacitive measurement system description

Sensors

The system for detecting human falls occurring above the floor is formed by capacitive sensors integrated in the floor. Thus, the measurement system is fully invisible and respect user's privacy. Moreover, all damageable parts, i.e. electronic cards and electrical connections, are placed outside the floor in order to make maintenance operations of these devices easier.

Our capacitive sensors are made up of coated electrical wires. Coating protects sensors from corrosion, thus they can be directly integrated in the self leveling compound. Such an instrumented floor is then very close to a traditional floor. This means that the system disturbs as less as possible common maintenance operations, such as the replacement of the floor covering. It represents an important issue for health institutions (hospitals, retirement homes). Indeed, regular floor covering replacements every few years are mandatory for these types of institutions.

Geometry of sensors is designed to allow the measurement of various capacitances which confers different sensitivity maps and thus different signals for the same event. One sensor includes two nearby electrodes, one enclosing the other, and a third distant electrode. An illustration of one sensor is given by Figure 1. If C ij is the capacitance between electrodes i and j, the capacitive tensor [START_REF] Lucas | Analytical capacitive sensor sensitivity distribution and applications[END_REF] of the sensor illsutrated in Figure 1 is

       C 11 -C 12 -C 13 -C 1G -C 12 C 22 -C 23 -C 2G -C 13 -C 23 C 33 -C 3G -C 1G -C 2G -C 3G C GG        (1)
with C ii = j =i C ij + C iG where C iG represents capacitance between electrode i and the ground. The ground is defined as every conductor or dielectric with high permittivity and high dimensions, whose electric potential is constant within the time of acquisition. The concrete floor for instance can be considered as an electrical ground in a common room [START_REF] Jonassen | Human body capacitance: static or dynamic concept?[END_REF]. For measuring the capacitive tensor, a voltage is first applied on electrode 1 while the two remaining electrodes are grounded. Then the amount of charges induced by the electric field is measured on each sensor electrode. Those amount of charges are directly proportional to capacitances. This operation is repeated three times by applying the voltage alternatively to each of the sensor electrode. Considering [START_REF] Robert-Bobée | Projections de population pour la France métropolitaine à l'horizon 2050[END_REF], two different types of capacitances are measured: self capacitances and mutual capacitances. Mutual capacitance C ij (i = j) represents the capacitance between electrodes i and j. It is obtained when measuring the amount of charges on electrode j, when i is held to a voltage while all the other electrodes are grounded. Self capacitance C ii is obtained when measuring the amount of charges on electrode i, when i is polarized while all the other electrodes are grounded. It is thus the sum of all capacitors attached to electrode i. Contrary to mutual capacitances, C ii contains thus an information on the electrode ground coupling.

Measurement unit

An electronic system dedicated to the measurement of the amount of charges on each electrode of the sensor has been developed. Charge-transfer technique is used in order to obtain a high sensitivity [START_REF] Huang | Design of sensor electronics for electrical capacitance tomography[END_REF][START_REF] Hu | Further analysis of charge/discharge capacitance measuring circuit used with tomography sensors[END_REF].

Figure 2 shows a schematic of the circuit. The circuit contains a compensating system with a known capacitance C 0 . Switches J 1 open and close alternatively at a frequency f . When switches J 1 are closed, the capacitance C ij is loaded to voltage V . At the same time C 0 is loaded to negative voltage V 0 . Depending on the values of C 0 and V 0 , the charges loading C ij and C 0 balance each other. It is thus possible to detect very small variation of C ij with respect to C 0 . The resulting voltages measured at output of integrators are

V s1 = -I 12 R ′ = -2f R ′ (C ij V -C 0 V 0 ) and V s2 = -I 34 R ′ = -2f R ′ (C 0 V 0 -C ij V ). (2)
The value of C 0 and V 0 are chosen during an automatic calibration phase. Thereby, a change of C ij , typically due to a human presence for instance, will induce a variation of charges flowing to integrators V s1 and V s2 . This compensating system is a crucial element of the circuit, as it allows to ensure a high sensitivity without any saturation of electronics. In order to evaluate the ability of the system to detect the presence of a person nearby the sensors, the signal to noise ratio has been evaluated. During this test, a person is standing up on the floor onto one sensor. Sensors are 1 cm underneath the top of floor, and the person was wearing sneakers with 2 cm thick soles. The person's feet are then 3 cm above the sensors. Signal variations measured on self capacitance C 11 are reported in Figure 3. During acquisitions 1 to 20, the floor is empty. The person stands up onto the sensor from acquisitions 21 to 40. Signal to noise ratio is

V V0 - - + + J1 J1 J1 J2 J2 J2 Cij C0 C ′ C ′ R ′ R ′ Vs2 Vs2 I34 I12
SN R = signal RM S noise , (3)
where signal corresponds to the average variation of the measured signal due to the presence of the person, and where the noise is

RM S noise = 1 n n i=1 x i - 1 n n i=1 x i 2 , (4)
with n the number of acquisitions and x i the value of the acquisition i.

RM S noise is 0.07 V (0.05 pF) for acquisitions 1 to 20. The average value of the signal when the floor is empty is 1.73 V, and it is 2.36 V when the person is present on the floor. So one obtains signal = 0.63 V (0.44 pF). Considering (3), the signal to noise ratio is about 9. property makes the measurement system more convenient and economical valuable compared to systems presented in [START_REF] Rimminen | Detection of human movement by near field imaging : development of a novel method and applications[END_REF][START_REF] Steinhage | Monitoring movement behavior by means of a large area proximity sensor array in the floor[END_REF]. Five sensors have been installed in the room.

System 1: Instrumented room

A variant of system 1 (system 1'), has been made in the same room with a distance between sensors of 25 cm instead of 40 cm.

System 2: Demonstrator

A transportable system equipped with the same type of capacitive sensors has been made. Three sensors, 25 cm from each other are integrated in a self leveling compound poured on a plasterboard. Dimensions of the system is 2.50 m × 1 m. The system is reinforced by a wood support to reduce bending as much as possible during transportation. Thereby the capacitive floor is about 10 cm above the room floor. A photography of the system is shown in Figure 5: Photography of the transportable system (system No. 2).

Typical measurements

The capacitive tensor of a sensor with N electrodes includes N (N -1)/2 independent capacitances. Since the ground is considered as an electrode, the measurement system proposed is formed by N = 4 electrodes for each sensor. Thus, we can measure at most 6 independent capacitances for each sensor. Figure 6 shows the variations of the measured capacitances for system 1 in response to a human presence. Each spike on the curves corresponds to a human presence above the sensor. One can see that C 23 is almost insensitive to human presence and remains constant. Indeed, C 23 is the capacitance between electrodes 2 and 3, when 2 is polarized and both electrodes 1 and 3 are grounded. In this configuration electrode 1 acts as a shield that shunts electric field lines between electrodes 1 and 2. As a result C 23 does not vary much. Finally there are 5 relevant capacitances. To evaluate the ability of the system to detect a fall, measurements were performed with a person in different postures. Figure 7 shows histograms of capacitance changes measured with the system 1 using the same person in two different postures: Standing up (55 measurements) and Lying down straight on the back (47 measurements). The person is 1.8-m tall and is wearing sneakers whose soles are about 2 cm thick.

The histograms suggest that the information provided by the measurements allows a good separability of the postures. In particular, for capacitances C 11 and C 12 , the two postures are fully separated.

Influence of the environment

The analysis of measurements obtained in the instrumented room (system 1) and with the demonstrator (system 2) show that the two systems have different behaviors.

A typical example can be observed on capacitance C 13 . Figure 8 shows histograms of capacitance changes for Lying down on the back measurements and Standing up measurements, obtained with system 1 (left) and with system 2 (right). Two main differences can be seen between the two systems. First, the amplitude of capacitance changes is much higher with the system 2. Variations range from -0.8 V up to 0.4 V with system 2, whereas they range from -0.05 V up to 0.15 V with system 1. This difference is mainly due to stronger ground couplings in system 1, as sensors are directly integrated inside the room floor. An important part of electric field lines between electrodes 1 and 3 is then shunted to ground.

Inversely in system 2, sensors are about 10 cm above the room floor, so much more electric field lines are generated between the electrodes. The second difference between the two systems concerns the distribution of Lying down on the back measurements and Standing up measurements. In system 2, the direction of the capacitance variation is clearly different in both situations: C 13 increases for Standing up measurements and it decreases for Lying down on the back measurements. This means that the polarity of C 13 variation is a crucial information to detect a person lying down on the floor. In system 1 the change of C 13 is very different, since there are negative and positive C 13 variations for both Lying down on the back measurements and Standing up measurements. These differences are explained by considering the capacitive couplings occurring in the system. When O is entering the vicinity of electrodes, two phenomena occur: (i) a part of the electric field lines between 1 and 3 is shunted by O, as a consequence C 13 decreases (shunt mode), (ii) coupling between O and electrodes is stronger, as a consequence C 13 increases (transmit mode). Thus, the polarity of C 13 variation depends on the relative importance of these two phenomena [START_REF] Paradiso | Musical applications of electric field sensing[END_REF]. In the system . 2, the shunt mode is always dominant for a person standing up. Conversely, the transmit mode is dominant for a person lying down. Consequently, the discrimination between these two situations is very efficient for system 2. Multiple parameters have an influence on capacitive couplings shown in Figure 9: distance between electrodes, conditions of ground coupling of the electrodes and the object, and distance between object and electrodes. In the case of the two systems studied, two main differences in their structures can explain the great differences observed. The first difference concerns ground couplings. In system 1, sensors are integrated directly inside the floor. Then ground couplings of electrodes and objects are much higher than in system 2, which is elevated few centimeters above the floor. The second difference concerns the distance between sensors. The distance between each sensor is respectively 40 cm and 25 cm for systems 1 and 2. As capacitive couplings exist between two distant sensors, this distance has an important role in the signal behavior.

The comparison between systems 1 and 1' gives information about the influence of the distance between sensors on the signal for the same ground coupling. Figure 10 shows that the behavior of C 13 strongly depends of the distance d between sensors. When d = 25 cm, the behavior of C 13 is closer to the one observed in system 2 (see Figure 8). This means in a general way, C 13 tends to increase for a person standing up and to decrease for a person lying down. However the discrimination is less clear than for system 2. Then a lower ground coupling improves again strongly the differentiation.All conditions are then favorable in system 2 for a good differentiation between a person standing up and Lying down. This is due to: (i) the elevation of the sensors with regard to the floor, which decreases all couplings with ground, (ii) a distance between sensors d = 25 cm, which improves the discrimination between situations.

Fall detection methods

The system must be able to recognize falls of people automatically. Classification techniques are used to separate measured signals and detect that someone fell on the floor.

Statistical classification

Statistical classification is used to sort objects into different categories called classes. An object i is defined as a vector of variables x i . In the case of our study, one coefficient of the measured capacitive tensor this database has been satisfying enough for using the system 2 as a demonstrator as explained in section 3.4.

Data separation

Two models of classifiers have been used for separating Falls and Non-falls situations: k-nearest neighbors method and least square method.

4.3.1 K-nearest-neighbor method (k-nn)

For an object to sort, k-nn method attributes the class which is the most represented amongst its k-nearest neighbors stored in the database. The euclidean distance is used to define the distance between an object and its neighbors. Two parameters have to be estimated with this method: the number k of the nearest neighbors and the number of variables to consider.

Least square method

Least square method is a linear classification method. This means that the defined classifier is under the form f (x i ,θ)=x i θ. A linear method is advantageous because the model is simple so it requires a small amount of calculation time. It facilitates real time applications such as fall detection. Least square method defines the vector θ which minimizes the least square error

E(θ) = 1 N (Xθ -Y) T (Xθ -Y)
where N is the number of learning examples X is the learning matrix (N rows × M columns with M the number of variables)

Y is the vector containing the label of each example (i.e. the value arbitrarily attributed to the corresponding class)

Variable selection

In order to proceed to variable selection, Gram-Schmidt process has been applied to the databases. This method selects the variable which is the most correlated with the vector of labels. The most relevant variable is the one which maximizes the following value:

cos 2 (x k ,y p ) = ( T x k y p ) 2 ( T x k x k )(y p y p )
where x k is the vector containing the N examples of the k-th variable and y p is the vector of labels.

Then the process is repeated with the remaining variables, in the susbspace orthogonal to the last selected variable.

Results and discussion

Each method presented above has been used for building up classifiers from the collected databases. For system 1 with the k-nn method, using only two variables gives a validation rate very close to the one obtained when using all variables. Using only one variable reduces however significantly the validation rate from 90.4% to 77.7%. By comparison, using all of the variables instead of two improves only the results by about 1%. For least square method, the difference between one, two or all variables is much smaller, about 2.5%. In the case of system 1 the most relevant variable for separating classes Falls and Non-Falls is the self capacitance C 11 . This capacitance depends directly on the area of the electrode 1 which is covered by a person. The second one is the mutual capacitance C 13 between the two distant electrodes 1 and 3.

The validation is 100% with system 1' with both classification methods. Having better results with system 1' was expected as we noticed in Figure 10 that having a distance of 25 cm instead of 40 cm between each sensor allows a better separation of Falls and Non-Falls situations.

For system 2 the validation is still 100% when using only the most relevant variable. This variable is the capacitance C 13 , selected by Gram-Schmidt process. This confirms that the polarity of C 13 variation is a sufficient relevant information for separating Falls and Non-Falls situations with system 2 (see section 3.6).

Conclusion

This paper presents a new fall detection system based on capacitive sensors integrated in the floor. Maintenance of the system is made easy by having all the electronic parts out of the floor. Databases were acquired on two experimental setups: an instrumented room and a transportable demonstrator. Two main environmental parameters showed significant influence on sensor signals: [START_REF] Robert-Bobée | Projections de population pour la France métropolitaine à l'horizon 2050[END_REF] the distance between sensors and (2) the strength of ground couplings. Appropriate statistical classification techniques were used to sort data. For both systems, validation rates of Falls and Non-Falls situations were better than 92%, by using the k-nearest-neighbor method or the least square method.

Two options are currently studied in order to make the system efficient independently of the environment. The first is by adjusting the geometry of the system, i.e. the distances between electrodes and between sensors. The second consists in doing on-line learning. This way the database is constantly updated and then adapted for each new environment.

The system has to be tested with more cases which are likely to cause false alarms, such as having several persons together in the same room, or cleaning the floor with water. Taking into account dynamical parameters of the signal will surely further improve the separation between Falls and Non-Falls situations.

Figure 1 :

 1 Figure 1: Arrangement of the electrodes of a capacitive sensor integrated in the floor.

Figure 2 :

 2 Figure 2: Schematic of the charge-transfer circuit used to measure small variations of C ij .

  Sensors described in section 3.1 have been integrated in a dedicated room which size is 5 m × 3 m. The equipped floor is illustrated in Figure4. It consists in longitudinal sensors separated from each other by 40 cm. This distance corresponds roughly to the width of a human body lying straight down on the floor.

Figure 3 :Figure 4 :

 34 Figure 3 : Signal measured on capacitance C 11 when a person goes on the sensor. The person is above the sensor from acquisition 21 to 40.

Figure 5 .

 5 photography of the system is shown in Figure 5. This system was used as a demonstrator in Bostik's Global Innovation Forum held in Paris (France) in November 2013, and during the Festival of Science held in Elite School of Industrial Physics and Chemistry (ESPCI) in October 2015. It is able to detect and display in real time different situations: (i) the presence or absence of a person on the demonstrator, (ii) the posture of the person, i.e. lying down or standing up, (iii) the movements of the person above the floor.

8 Figure 6 :

 86 Figure 6: Capacitance changes of system 1 in response to a human presence.

Figure 7 :

 7 Figure 7: Histograms of capacitance changes for system 1 with a person lying down on the back (in blue) or standing up (in red).

Figure 8 :

 8 Figure 8: Histograms of capacitance changes measured on C 13 for a person lying down on the back or standing up with the system 1 (left) and with the system 2 (right).

Figure 9

 9 Figure 9 shows capacitive couplings to be taken into account when an object O is coming close to electrodes 1 and 3. Represented couplings are: • C 1O , C 3O : couplings between each electrode and the object • C 1T , C 3T : couplings between each electrode and the ground • C OT : coupling between the object and the ground • C ′ 13 : coupling between the electrodes

Figure 9 :

 9 Figure 9: Schematic of capacitive couplings in presence of a nearby object.

Figure 10 :

 10 Figure10: Histograms of capacitance changes measured on C13 for a person lying down on the back and standing up with system 1 (left) and with system 1' (right).

  corresponds to one variable. Each one of the studied postures corresponds to one class. Classification methods are made out of mathematical functions called classifiers, which sort objects to the predefined classes. A classifier is build from a set of measurements containing several objects of each class. In our study the class of each object of the database is known during the building of the classifier. This type of classification is called supervised classification. The classifier consists in defining the function f (x i ,θ) and the set of parameters θ, which give an optimal separation between classes. These parameters are obtained by validation techniques. The simpliest way is to split the database into two subsets: a learning set and a validation set. Values of θ are then arbitrarily fixed. A classifier is defined during the learning phase, by using the objects contained in the learning set. Then this classifier is tested with all the objects of the validation set. The validation rate is the percentage of objects correctly sorted by the classifier during the validation phase. This process is repeated several times with new values of θ. Finally we keep the vector θ which gives the best validation rate. This method is strongly dependent on the composition of the training and validation sets. In fact the validation rate changes if the subsets are modified.

Table 2

 2 shows the validation rate for the separation of classes Falls and Non-Falls for both systems.All of the 5 measured capacitances were used for classification. Results were obtained by using cross validation with 3 folds.

		System No. 1:	System No. 2:
		Validation rate	Validation rate
		(Falls Vs	(Lying down on
		Non-Falls)	the back Vs
			Standing up with
			shoes)
	k-nearest neighbors 91.5% (3 nearest	100% (1 nearest
		neighbors)	neighbor)
	least square	92.6%	100%

Table 2 :

 2 Validation rate by using all of the five measured variables For system 1, the best validation rate is 92.6%, and is obtained with least square method. Results

		System 1: Validation rate	System 2: Validation rate	System 1': Validation rate
		(Falls Vs Non-Falls)	(Lying down on the back Vs	(Lying down on the back Vs
				Standing up with shoes)	Standing up with shoes)
		1 variable	2 variables	1 variable	2 variables	1 variable	2 variables
	K-NN 77.7% (K=3) 90.4% (K=3)	100% (K=1) 100% (K=1)	100% (K=1) 100% (K=1)
	LS	83.5%	89.9%	100%	100%	100%	100%

are much better on system . 2: the validation rate is 100% with each method for separating the two classes. System 2 is expected to give better results for two reasons: (i) the database comprises only the two situations which are easiest to separate (Lying down on the back Vs Standing up with shoes), (ii) the environment of the system No. 2 is more favorable for an efficient separation of signals, as explained in section 3.6. Despite the small size of the database, system 2 has shown very satisfying performances over a broad range of situations. Situations not contained in the database such as Standing up with socks or Several persons standing up at the same time were recognized as Non-Falls situations as well.

Table

3

shows validation rates by using only the most relevant variable selected by Gram-Schmidt process, then by adding the second one.

Table 3 :

 3 Validation rate by using only the most or the two most relevant variables

Acknowledgements

The authors wish to express their gratitude to the company Bostik for taking part into this project.

The authors want to thank specifically Bruno Charrière, former Research, Development and Innovation Director, and François Court, actual Research, Development and Innovation Director, for the financial support of this project intended to improve life quality of elderly people, as well as André Mayer, Chief Technology Officer, for his work for developing the project towards an industrial application.

Cross-validation is a validation technique in which each object of the database is used during both training and validation phases. The database is divided into L sets called folds. The learning and validation processes are repeated L times, using only 1 fold for the validation phase and the L -1 remaining folds for the learning phase. The validation fold changes each time. The global validation rate is the average of the validation rates of each iteration.

One set of measurements has been built up for each of the experimental setups presented in paragraphs 3.3 and 3.4. shoes while grounded have been chosen to simulate a human in contact with a grounded metallic object (such as a bed in hospitals), which has a strong influence on capacitive measurements. The database is composed of 510 measurements in total. Details of measurements are shown in Table 1.

Data generation

For system 1', the database is composed of 36 situations in the posture Standing up with shoes, and 15 situations in the posture Lying down on the back. Only capacitances corresponding to the polarization of electrode

System 2: transportable demonstrator

The database built up with system 2 contains two different postures: Lying down on the back and Standing up with shoes. Each situation contains 50 examples. This set of measurements is much reduced compared to the one collected with system 1. However it has been very efficient for defining a reliable classifier. So


A Penillard

L Beccacce

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A De Rossi

S Combrié

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E Géron

Infrared optical anisotropic properties and photocarriers lifetime in 2D black phosphorus by angle-resolved absorption and reflectometry

In this article, angle and polarization-resolved absorption and time-resolved pump-probe measurements have been carried out on multi-layer black phosphorus (BP) at infrared wavelength (around 1550 nm) which is an extension of the previous studies of the BP behavior done at higher frequency 1 . Exfoliated down to a few layer, BP reveals the properties of a 2D material with anisotropic response, high mobility (up to 10 000 cm 2 /V/s), and absorption which are very relevant to optoelectronics. BP bandgap is tunable according to the number of layers, allowing applications from UV to IR. The bandgap height of the single and thicker layers has been measured through absorption and reflection spectra. We report the first measurement of the ambipolar carrier lifetime, which has been determined to be about 15 ps. The structure-induced anisotropy is studied. The results confirm BP as a suitable material for ultrafast devices such as microwave photo-switches, samplers, THz antenna for instance.

I. INTRODUCTION

Black phosphorus (BP) recently triggered strong interest as a better alternative to communally used semiconductor materials like transition metal dichalcogenide (TMDs) and other compounds for ultrafast optoelectronic applications. Indeed, the discovery of its graphene-like electronic properties, associated with its tunable bandgap from 0.3 eV for its bulk state to 1.8-2 eV for the monolayer 2 , makes it a perfect candidate to overcome graphene Dirac point and thus enables optical switching of electronics components. In a previous article [START_REF] Penillard | Effective photoconductivity of exfoliated black phosphorus for optoelectronic switching under 1.55 µm optical excitation[END_REF] , we studied BP photoconductivity when the material is integrated in optically-controlled-microwave switches at 1.55 µm.

BP has orthorhombic structure with two main axis, armchair and zigzag, with a 90° angle between them. From its structure results a strong anisotropy for both electrical and optical properties which has to be considered for optoelectronic components realization. This anisotropy is experimentally verified by angle-resolved Raman measurements [START_REF] Ribeiro | Unusual Angular Dependence of the Raman Response in Black Phosphorus[END_REF] as well as angle-resolved direct-current (DC) measurements on a transistor [START_REF] Xia | Rediscovering Black Phosphorus : A Unique Anisotropic 2D Material for Optoelectronics and Electronics[END_REF] and by infrared (IR) spectroscopy. Photo-carrier dynamics have been little explored in BP. Knowing their dynamics is however essential for optoelectronics and ultrafast applications.

Here, we present experimental results for angle-resolved absorption measurements at infrared wavelengths as well as time-resolved and angle-resolved reflective pump-probe measurements performed at 1550 nm associated with Raman spectroscopy. Samples and experiment are described in section II, with both absorption and reflectivity measurements. Section III is devoted to the results and their analysis

II. EXPERIMENT

BP has a puckered structure where each layers are held by weak Van der Waals forces, allowing BP mechanical exfoliation down to a few layers. In the experiments presented in this paper the BP flakes were extracted by a modified and improved scotch-tape exfoliation method on a silica substrate, used on TMD materials and adapted for BP [START_REF] Desai | Gold-Mediated Exfoliation of Ultralarge Optoelectronically-Perfect Monolayers[END_REF] . We focused on Raman spectroscopy Ag 2 peak which is almost not thickness dependent since it corresponds to an in-plane interaction and thus can be used to determine flake-orientation [START_REF] Jiang | Optical Anisotropy of Few-Layer Black Phosphorus Visualized by Scanning Polarisation Modulation Microscopy[END_REF] . Raman spectroscopy studies on BP performed and published previously [START_REF] Penillard | Exploring the promising properties of 2D exfoliated black phosphorus for optoelectronic applications under 1.55 μm optical excitation[END_REF][START_REF] Kim | Anomalous polarization dependence of Raman scattering and crystallographic orientation of bP[END_REF] indeed show the Ag 2 phonon intensity Fourier-like evolution with the layer orientation, for a fixed polarization. When the maximum intensity is reached, the laser polarization is aligned with the BP armchair direction. Following this statement, the crystallographic axis armchair and zigzag are identified by Raman spectroscopy at 532 nm in each BP samples created for the experiments. A total of five samples with various thickness have been exfoliated: two (A1, A2) for absorption measurements and three others (S1, S2, S3) for pump-probe spectroscopy. The sample thickness is measured by atomic force microscopy (AFM) and reported in Table 1. The sample A1 is partially monolayer with a thickness of 0.53 nm, and partially bilayer with a thickness of 1.06 nm. All samples have been exfoliated on a silica substrate and have been encapsulated to prevent air degradation, with a thin layer (about 20 nm) of AlxOy, except for sample S1 which has been capped with PMMA which is also a good protection against air degradation for short term experiments. The samples were less than 5 minutes at ambient air then are kept under azote atmosphere before being tested. The measurements are performed in ambient air, and no degradation has been observed on samples during the tests. It is worth noting important to note that oxidation prevents immediately any signal detection in such thin layer samples.

Name

A. Absorption measurement

The absorption measurements have been realized at LPEM in ESPCI Paris. Each BP layer is first illuminated by a halogen lamp with an illumination radius of about 20 µm and the transmitted signal is then selected with a spectrometer at the wavelength range of interest. From the transmitted signal, the absorbance is deduced as the fraction intensity variation measured in percent. The reflected signal is neglected. Here the considered wavelengths range from 0.8 µm to 2.1 µm. A polarizer, adjusted 5° by 5°, allows to study diverse directions in BP. The substrate and passivation layer effects on absorption spectra are compensated using a reference measurement on a sample without BP layer.

B. Reflectivity measurement

Angular-resolved and temporal-resolved pump-probe measurements have been performed on different samples of black phosphorus to understand photo-dynamics under an optical excitation of 1550 nm. The pump and probe pulses are obtained by spectral filtering on the output of a 100-fs passively-modelocked fibered laser (Optisiv), We have studied the absorption dependency at 1.55 µm with the polarization and so with the flake orientation.

The absorption follows the same Fourier-like evolution than Ag 2 phonon intensity, and is up to 4 times stronger in the armchair direction than in the zigzag direction, as shown in FIG. 4. The normalized root-mean-square error between the model and experimental data is 13% which validate correctly the Fourier-like model used. This evolution is experimentally observed in visible range [START_REF] Li | Polarization and Thickness Dependent Absorption Properties of Black Phosphorus: New Saturable Absorber for Ultrafast Pulse Generation[END_REF] and simulated for infrared wavelength [START_REF] Low | Tunable optical properties of multilayers black phosphorus thin films[END_REF] . Optical polarization is a crucial factor for optical application. The modification of the reflectivity is stronger in the armchair direction (see FIG. 5 (c)), where the absorption and so the photo-carrier generation is larger. This dependency can be observed at every delays (up to 240 ps).

For thick layers, a negative variation of the reflectivity is observed when the laser polarization is aligned with the zigzag direction. The error on normalized reflectivity measurement is about 0.2 and on the angle orientation about 2 degrees.

The difference in the behavior of reflectivity between armchair and zigzag direction on a very short time scale, in thick layer, can be explained by the difference between the effective masses for electrons and holes in the two directions [START_REF] He | Exceptional and anisotropic transport properties of photocarriers in black phosphorus[END_REF] : in the armchair direction me * =0.0825m0 and mh * =0.0761m0 and in the zigzag direction me * =1.027m0 and mh * =0.648m0. Intrinsically, black phosphorus is p-doped, with both light and heavy holes. Polarized excitation along the armchair direction generates light electrons and holes and enhances reflectivity. In the zigzag direction, generated photocarriers are heavy, and heavy holes and electrons are more likely to recombine with their light counterparts than the heavy ones. The plasma becomes heavier, and the reflectivity decreases.

When the layer thickness decreases, effective masses decrease as well and so the negative effect disappears as it is shown in FIG. 6. In that figure, the reflection coefficient of samples S2 and S3 is measured in time which is the interesting aspect to compare. The effect is not observed on the 1.5 nm thick BP layer (see FIG. 6), but has to be taken into account for thicker layer. This phenomenon has been observed by another group [START_REF] Ge | Dynamical Evolution of Anisotropic Response in Black Phosphorus under Ultrafast Photoexcitation[END_REF] , but has not yet been explained. From these observations, reflectivity evolution with time is identified as a bi-exponential evolution with two characteristic time scales (FIG. 5 (b)). On a short time scale, electrons and holes recombine directly, and on a longer times scale they recombine through lattice relaxation. Carrier life-time can thus be extracted and one obtains 14.8±0.3 ps, for 25 measurements. This direct recombination lifetime is thickness independent and angle independent. A second lifetime corresponding to lattice relaxation is thickness dependent and angle dependent and is measured from 0.64 ns for the thinner layer up to several nanoseconds for thicker layers. It is important to note that other authors found a unique lifetime around 100 ps for BP [START_REF] He | Exceptional and anisotropic transport properties of photocarriers in black phosphorus[END_REF][START_REF] Suess | Carrier dynamics and transient photobleaching in thin layers of black phosphorus[END_REF] . It is because they treated the reflectivity decay as a single exponential evolution. If we follow the same logic, we also obtain about 100 ps lifetime.

Nevertheless, it is more accurate to treat this decay as a bi-exponential evolution and to identify the two lifetimes, as direct lifetime value is a major key parameter when designing ultra-fast devices.

All these measurements validate BP angular dependency absorption at infrared wavelength and give a good approximation of the BP photocarrier lifetime.

As a side note, direct recombination of photocarriers in BP is the same with or without ALD capping, thus encapsulation seems to have negligible effects on direct recombination speed.

IV. CONCLUSION

In this paper, angular response of black phosphorus to 1.55 µm optical excitation is studied as well as photocarrier evolution at short time scale. The orientation and thickness of the layer influence the absorption, and lattice thermalization. Moreover direct recombination life-time of photo-carrier in black phosphorus is measured to be about 15 ps, making this material a great candidate for ultrafast applications like electronic sampling and photoconductive switching.

  which is spectrally broadened to cover the full C band upon amplification in a chirped amplifier. The delay between pump and probe is controlled through a mechanical delay stage as shown in FIG.1. The plasma of free carriers excited by the pump in the BP layer results in a change of the refractive index, therefore the reflectance of the BP, which is detected by the probe pulse. The normalized change of reflectivity ΔR R 0 = R ON -R OFF R 0 is measured as a function of the pump-probe time delay with R ON the detected reflectivity when the pump is activated, R OFF the detected reflectivity without pump, and R 0 the maximal probe reflectivity detection. The time resolution is about 1 ps and the time range is 240 ps. A half-wave plate in the laser optical path allows to change the angular orientation of the polarization and to study the change in reflectivity for each crystallographic direction of the layer.

FIG. 1 FIG. 3

 13 FIG.1Pump-probe reflectometry experiment scheme.

FIG. 4

 4 FIG.4Absorption evolution with laser polarization orientation. At 0°, the polarization is arbitrarily taken along the horizontal direction H on the optical image.

FIG. 6

 6 FIG. 6 Evolution of reflectivity as a function of pump-probe delay for different laser polarizations for sample s (a) S2 and (b) S3.