Egoï Ortego

Antoine Dazin

Frédéric Colas

Olivier Roussette

Olivier Coutier Delgosha

Guy Caignaert

Multistage radial flow pump -turbine for compressed air energy storage: experimental analysis and modeling

The increasing development of storage systems connected to electrical networks is stimulated by network management issues related to recent energetic landscape evolutions such as the increasing integration of renewable production sources. Hydro-pneumatic systems seem to offer a clean and cheap energy storage solution among the set of existing storage techniques. The present study analyses an air-water direct contact accumulation system, in closed cycle, using a rotodynamic reversible pump/turbine. The use of a unique energy conversion machine and easy-to-recycle materials could lead to cost-effective, environmentally friendly storage technique with long service life. The paper is focused on the experimental implementation and analysis of the system in a Lab environment, and the modeling of its multi-physic dynamic behavior. To deal with the variable operating conditions of the system, two different real time control strategies of the hydraulic machine were successfully tested. Finally, the global system efficiency is discussed. The efficiency control strategy was achieved with a 31% round trip efficiency and the power control strategy lead to 5% and 23% precision on exchanged power in charge and discharge modes respectively. The multi-physic dynamic model led to a 4% error of turbine mode acceleration prediction showing the interest of such a modeling method for such transient systems.

Several types of energy storage techniques are currently available. It includes Pumped Hydroelectric Storage (PHS), Compressed Air Energy Storage (CAES), electrochemical batteries,

and flywheels [START_REF] Agency | Tracking Energy Integration[END_REF]. Nowadays, the most widely developed technique is PHS. This technique is extremely mature in terms of life time and cost management and represents 98% of the grid connected storage systems installed power [START_REF] Robyns | Energy Storage in electric grids[END_REF] [START_REF] Hunt | Global resource potential of seasonal pumped hydropower storage for energy and water storage[END_REF]. However, its development is limited in Europe by the lack of new sites, because of the needed water level difference and volume. The large-scale CAES represents a serious alternative to PHS [START_REF] Robyns | Energy Storage in electric grids[END_REF] [START_REF] Budt | A review on compressed air energy storage: Basic principles, past, milestones and recent developments[END_REF], however the currently installed CAES stations present the disadvantage of gas burning requirement during the expansion period [START_REF] Finkenrath | Status and Technical Chalenges of Advanced Compressed Air Energy Storage Technology[END_REF]; besides the existing CAES stations use gas compressors and turbines with a limited number of stages and intercoolers avoiding any possibility of isothermal compression/expansion that lead to severe losses if the storage is not adiabatic. It is possible to recover a part of the compression generated heat to store it and use it for expansion; but it is quite challenging to extract and conserve the heat at high temperatures [START_REF] Wang | Experimental study of compressed air energy storage system withthermal energy storage[END_REF]. Adiabatic-CAES could be a solution to the heat management problem. Such a system was studied by RWE in Germany with the so called ADELE project [START_REF] Zunft | Electricity storage with adiabatic compressed air energy storage: Results of the BMWiproject ADELE-ING[END_REF]. The main difficulties for such adiabatic systems come from the high operation temperatures and pressures leading to challenging designs for the rotating parts and the heat storage systems operated at high pressure. The technology readiness level and affordability of the very specific components required needs still to be proven.

Hydro-pneumatic energy storage (HYPES) is a type of volumetric compressed air storage technique [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF]. It intends to combine the good efficiency and technological maturity of hydraulic energy conversion with the spatial flexibility and large energy densities of compressed air energy storage in vessels. The HYPES basic idea is to compress air in a closed volume by means of a liquid piston during storage phase thanks to a pump and use this potential energy when needed to drive a turbine. Furthermore, the liquid piston concept presents a strong potential for the heat management all along compression or expansion making possible isothermal cycles. Such cycles don't need any heat storage and present higher energy densities than adiabatic cycles [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF].

The idea of using liquids to compress air is quite old, as it has been firstly described by Mékarski at the end of 19 th century [START_REF]Louis Mékarski_1875[END_REF]. It is also interesting reading the humid compressor patent of Dubois-François, in the same period, where the use of liquid water is proposed to improve the compression efficiency [START_REF]The Project Gutenberg EBook of Scientific American Supplement[END_REF]. The concepts of liquid piston and spray cooling were new at that time. This air compression technique enables to perform a quasiisothermal storage cycle, which has various advantages such as avoiding high temperature thermal storage, or energy sources (gas burning) and also higher energy densities [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF].

For these reasons, closed or open volume hydro-pneumatic compression/expansion systems have been more recently studied by different teams. A team of the EPFL worked on a hybrid system based on oil hydraulic machines at pressures up to 200bar in a closed cycle [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF]. The use of oil in such systems requires a separation membrane. The achievement of isothermal cycles using heat exchanger would be expensive at such pressures and prays injecting in a membrane are not technically obvious regarding cooling stream circulation. Achievement of such oil based liquid piston systems without membrane would require compatibility studies between oil and air at high pressures and temperatures for safety reasons. In general, water based systems are preferred by most teams working on isothermal compressed air storage systems This is the case of Sustain-X start up which developed water foam cooling based compressed air systems [START_REF] Mcbride | Systems and method for energy storage and recovery using rapid isothermal gas expansion and compression[END_REF] and also the case of LightSail Energy start up which developed water spray assisted storage system [START_REF] Stahlkopf | Compressed air energy storage system utilizing two-phase flow to facilitate heat axchange[END_REF]. These two companies objective was to attain isothermal cycles with large mechanical compression reciprocating devices. Unfortunately they both stopped their activity probably because of the excessive cost associated with the complex compression devices. Regarding water based hydro-pneumatic systems; a nice example is the case of the GLIDES project team in which a Pelton turbine was used for energy release and a centrifugal pump for storage [START_REF] Odukomaiya | Experimental and analytical evaluation of a hydro-pneumatic compressed-air Ground-Level Integrated Diverse Energy Storage (GLIDES) system[END_REF]. This system was operating between 70bar and 100bar and needed a separated motor and generator.

In this context, a new concept for HYPES systems is presented in this paper. It is deliberately based on simple components like a centrifugal pump used as a turbine and water as fluid compression system. Both motor and generator functions are performed by a single asynchronous machine. At the best knowledge of the authors this is the first time this kind of hydraulic machine is used for HYPES. An illustration of the proposed system is presented in Figure 1.

Figure 1: HYPES system using a reversible pump-turbine

This approach is a promising cost-effective solution, compared to other systems, as the initial investment is limited while it may enable an efficient management of the energy storage and recovery steps. Indeed, the use of a centrifugal pump enables to minimize the development costs, since pumps are very usual components and a single electric machine is needed. Moreover, the use of water instead of oil lowers the environmental impact, and the materials are also easier to recycle. Working at lower pressure (maximum of 40bar in the present case) could also decrease the design cost of the system, since a large variety of components can be found for operation with water up to 63bar.

Nevertheless, using a radial flow open machine in conditions of variable pressure is a major challenge. Besides, the pneumatics, hydraulics and mechanics of the system are strongly coupled, which makes the estimation process of the characteristic times very challenging. However, this information is crucial for the assessment of the system performance and the comparison of various storage devices. Furthermore the strong coupling between the components make the control of the system quit challenging when trying to maintain a given power demand for example; this is related to the pressure dependent non-linear relation between machine's flow rate and angular velocity. In order to handle these challenges, the performance of the new system is investigated in this study by a combination of original simulations and validations on a test rig. The simulations are based on a dynamic multi-physics model that simulates the transient behavior of a lab scale proof of concept prototype, and eventually provides a fine prediction of the response time of the system. It has to be pointed out that to the authors' knowledge, whereas such systems always operate in transient conditions all the existing models are based on a quasi-steady assumption. The development of a dynamic model is thus necessary to predict accurately the behavior of the system.

St orage Delivery

The lab-scale prototype was specifically developed to provide the appropriate data for the validation of the model. Besides, a novel real time supervision algorithm was developed for the storagerecovery cycles using the multi-physic dynamic model in order to numerically test different control strategies. The algorithm was then implemented in real time operating conditions on the test bench. It was developed to control the HYPES device either in best operating point mode or in a power request mode with variable pressure operation. This framework paves the way to design future systems based on the proposed principles in this paper.

Besides, even if a lot of air based energy storage systems have been studied in literature, very few experimental research papers deal with compressed air energy storage. For example in a very recent research review [START_REF] Olabi | Compressed air energy storage systems: Components and operating parameters -A review[END_REF] only 2 referred papers deal with CAES end-to-end (i.e. round trip cycle) experimental results; one of them refers to Huntorf plant and the other is the heat storage assisted CEAS cited above in the introduction [START_REF] Wang | Experimental study of compressed air energy storage system withthermal energy storage[END_REF]. So the present paper aims to contribute in HYPES systems knowledge by the technical feasibility demonstration of a novel HYPES system, by a novel real time control technique and by a multi-physics dynamic model. The paper is organized as follows: the modeling of the system, based on dynamic mass, momentum and energy balances, is first detailed, then the test rig is presented, including the experimental calibration of the accumulation vessel heat transfer coefficient. Finally, the experimental and simulated data of two storage-recovery cycles with different control strategies are presented and discussed.

HYPES modeling

The proposed model aims to predict the dynamic behavior of the storage device. The components of the HYPES system studied here are presented in Figure 1: an accumulator, a pump-turbine, an electric motor/generator controlled by a frequency inverter, a valve and a feeding vessel.

The model is composed of sub-models for each component and a supervision algorithm. Three main physical domains are modeled: mechanical, hydraulic and thermodynamic domains. The coupling between these domains makes the model multi-physic.

The system modeling is performed with Matlab/Simulink that accepts only a low number of algebraic loops. That's why the equations are written in order to avoid them by using a causal modeling approach. This allows a fast and simple time integration to solve the system. Each sub-model describes the behavior of the considered part as an assembly of basic inertial, capacitive or resistive elements. The central sub-model is the hydraulic sub-model; many of others interact through this one. Pressures are applied on it and it computes the flow rate which is an input for other sub-models. The status of the valve is ordered by the supervision program based on the storage cycle requirements and is depending on the actual flow rate value (this aspect is discussed in section 2.5).

The rotating bodies sub-model was designed in order to model the dynamics of the shaft in conjunction of the frequency inverter controller dynamics. One of the design criteria was to allow the ''freewheel'' mode operation in which the supervision program reference velocity ( 5;< ) is omitted and the shaft velocity depends only on hydro-mechanic dynamics allowing to estimate the natural response time of the turbine mode. The mechanical sub-model interacts with the hydraulic sub-model through the pump-turbine model as show in Figure 2. Each sub-model is described in more in detail in the following paragraphs. The equations for each component dynamic behavior are provided and the relations between the components are presented in the form of transfer functions to lighten the way of presenting the global mathematical formulation of each subdomain.

Mechanical sub-domain

The aim of this sub-model is to predict the angular speed of the rotating solids i.e. the pump/turbine and the motor. The model for the mechanical system is based on two inertial elements (the motor and the pump/turbine) and a capacitive element representing the torque sensor, considered as an elastic component connecting the two rigid elements (see Figure 3). The time derivative of the angular speed ( ) of rotating masses is related to the torques applied on them, as expressed by equation (1).

= =1 > Σ @A (1)
Where @A is the angular inertia of the considered element and Σ the sum of the torques applied on it:

• The electromagnetic torque ( BC3C5 ) and the elastic torque ( ;D)+ ) for the motor shaft • The hydraulic torque received or applied by the pump/turbine ( E/F ) and the elastic one ( ;D)+ ) on the pump shaft.

The behavior of the elastic element used to estimate the elastic torque is described by equation (2).

= =1 > BC3C5 G H4BH (2)
Where is the torsional stiffness of the parts between the motor and the pump.

The overall transfer function of the mechanical sub-model is shown in Figure 4. The two ''input'' torques (thicker lines boxes in Figure 4) are deduced from:

• The pump/turbine model discussed hereafter • A PI (proportional integral) controller (see appendix 7.1) that compute a driving electromagnetic torque value as a function of a reference speed ( 5;< in Figure 2) and the configured dynamic response parameters.

The time integration of equations ( 1) and ( 2) from their initial states provides the values of the angular speed and the elastic torque.

Hydraulic sub-domain

The hydraulic sub model describes the dynamics of the fluid (water) contained in the pipes and the hydraulic machine. A simplified form of the momentum equation is used to predict the flow rate (equation ( 3)) as a function of the pressures applied on the equivalent water column. The initial derivation of the equation can be found in the work of Nicolet [START_REF] Nicolet | Hydroacoustics Modelling and Numerical Simulation of Unsteady Operation of Hydroelectric Systems[END_REF] on the unsteady behavior of hydroelectric systems.

The hydraulic inertia of this water column is named I J . We consider here water as incompressible and the pipes are assumed to be rigid.

=# $ =1 > 1 L M . ∆ 6)D)PQ; (3)
The balance of the pressures applied to the water column (∆ 6)D)PQ; ) is detailed by equation ( 4).

∆ 6)D)PQ; > 7P R ∆ E/F G )QQ4 G ∆ )D G ∆ <57Q (4)
The accumulator pressure ( )QQ4 ) is an input variable computed in the reservoir model. The pump/turbine pressure difference (∆ E/F ) is computed by its corresponding sub-model (see section 2.3). Frictional pressure losses (∆ <57Q ), on pipes, junctions and filter, depend on the flow rate, and they are derived from literature [START_REF] Idelcik | Memento des pertes de charge[END_REF] and experimental observations performed by the authors [START_REF] Sampedro | Étude d'un système hydropneumatique de stockage d'énergie utilisant une pompe/turbine rotodynamique[END_REF]. In the later reference, detailed information on the sub model used to compute the pressure at the suction pipe inlet ( 7P ) can also be found.

The isolation valve is modeled as a pressure source (∆ )D ) responsible for the flow rate stopping when needed. The value of the pressure applied by the valve is computed by a PI controller based on the dynamics of the hydraulic circuit. The main asset of this method is to avoid residual flow rate involved in classic valve models, for all stand-by and operating pressure conditions. See appendix 7.2.

The overall fluid inertia ( S ) is the sum of various elementary inertias. The pipes are modeled as cylinders of cross section area S and length L; their hydraulic inertia is equal to T . /0.

It can be noticed that the hydraulic inertia related to the flow rate is inversely proportional to the cross section area. That is why the inertia of the water contained in both vessels is very small.

For the pump/turbine, the inertia for a wheel is evaluated with equation ( 5) [START_REF] Dazin | Transient Behavior of Turbomachineries: Applicationsto Radial Flow Pump Startups[END_REF].

TU;;D > T 4W X 1 % Y%Z .&[ \ Y%Z =% ]\ ]^ (5)
12 wheels are accounted for the overall inertia. The impeller internal and external radii are denoted R1 and R2. The function Y%Z represents the blade width evolution; it was considered constant here. The blade angle Y%Z was supposed to be a linear function between the impeller inlet and outlet angles.

The global transfer function of the hydraulic model is described in Figure 5. The pump/turbine behavior is modeled by its steady operating charts shown in Figure 6 and Figure 7. The dimensionless pressure ( ), power ( ) and efficiency are drawn as functions of the dimensionless flow rate ( ) computed with the system of equations ( 6). Efficiency was plotted with dotted lines and values are in the right axis. The relations between the dimensionless parameters values are modeled using the two polynomial expressions ( 7) and [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF].

_ à b > # $ '2 c . ω > ∆ H/3 T . '2 \ . ω \ > BeQU) T . '2 f . ω c (6)
> g1 R g2 R g3 \ (7) > i1 R i2 R i3 \ (8)
For low rotation speed operating conditions viscous nonlinear effects become relatively more important and a deviation from the presented curves is observed due to Reynolds effects. For these conditions, the pressure and the torque coefficients could be better modeled by a series of curves (one per angular velocity sector) or by 2D tables of the form > Y , Z. Deviations could also be observed at higher pressure levels, because of lower volumetric efficiencies.

Accumulator model

The objective of this sub model is to predict the global thermodynamic behavior of the accumulator; the main parameters responsible for the energetic state of charge are the mean temperature and the pressure of the compressed air. The direct air-water contact leads to mass transfer phenomena. Interface transfer mechanisms were treated by local models detailed in [START_REF] Sampedro | Étude d'un système hydropneumatique de stockage d'énergie utilisant une pompe/turbine rotodynamique[END_REF]; the main conclusion is that the air mass variation, for a 20 bar initial pressure, is less than 4% after 80 days of standby with stagnant water in contact with air; the air mass was thus considered constant. At the same time, the distance between the interface and the reservoir connection pipe was found sufficient to avoid any turbine performance degradation by air intrusion.

Air was considered as an ideal gas because of the relatively low operating air densities (pressures are below 20bar and temperature between -20°C and 70 °C).

Energy conservation is applied to the air mass contained in the accumulation volume as expressed in equation ( 9).

. $ . =- =1 > ! " G . =: =1 (9)
Where is the air average pressure. The pressure )QQ is equal to plus the water column height. The air volume is denoted V. The work introduced in equation 9, last right-hand term, is a function of the air mean pressure and the volume variation rate of the air; this last term is equal to the water volume flow rate (with an opposite sign), since water is considered as incompressible. The heat transfer rate (! " ) is related to the thermal transfer between the air and its surrounding. Equation 9 will be used to predict the air mean temperature (-). The relation between the pressure, the volume and the temperature is obtained by the perfect gas equation [START_REF]The Project Gutenberg EBook of Scientific American Supplement[END_REF].

. : > . ' k . - (10)
Where is the mass of air and ' + the air specific gas constant.

Since the components in contact with air (the metallic walls of the reservoir and the water) are characterized by large heat capacities, the temperature of the interface between air and its surrounding is considered as constant and homogeneous. This assumption was compared to a situation where all the heat generated by the compression would contribute to the temperature increase of the metallic wall. The two situations gave the same heat transfer rate within a few percents. On top of that, the maximum measured variation of the wall external temperature was about 1.5K, i.e. less than 2% of the maximum air temperature.

The heat flow is thus calculated by equation [START_REF] Mcbride | Systems and method for energy storage and recovery using rapid isothermal gas expansion and compression[END_REF].

! " > . 0. Y-7 G -Z (11)
The internal convective heat transfer coefficient ( ) takes into account the flow through the water such as the one through the metallic wall; it was experimentally determined by a thermal time constant measurement method [START_REF] Pourmovahed | An experimental thermal time constant correlation for hydraulic accumulators[END_REF]. The detail of this method and the results for our specific vessel are presented in section 3.3.

Supervision algorithm

A storage cycle is composed of three periods: accumulation, standby and delivery.

The two active periods are characterized by variable operating conditions in the present configuration. It requires the control of the angular velocity of the pump/turbine in order to maintain the required flow rate and/or efficiency conditions. Two main configurations were tested for the angular speed control: best efficiency point (BEP) and power control (PCT) configuration. The first computes a BEP angular speed by using the instantaneous value of the pressure difference at the pump/turbine inlet and outlet and the BEP point dimensionless pressure value ( lmE ) (see BEP in Table 1). The lmE value is obtained from the pump and turbine performance tests.

PCT )DnC > Y 5;< , p E/F Z (13)
The second reference speed is based on a lookup table in which the inputs are the value of the required mechanical power and the pump/turbine pressure difference value (see PCT in Table 1). The look-up tables are presented in appendix 7.3.

The supervision program state machine is presented in Figure 8. The observed variables were the actual motor angular speed, the storage vessel pressure and the mass flow rate. The controlled variables were the reference angular speed and the valve state.

The main particularity of the presented supervision program is related to the velocity management during start-up periods. Before the main ''Pump operating'' step, the standby pressure in the accumulator can be superior to the one of the pump inlet. Therefore, to avoid a rapid discharge, the pump was activated before opening the valve in order to reach a sufficient pressure; this is the role of the ''Pump starting'' step. For that situation, the reference speed is named q r ~t ; its value is based on the dimensionless pressure observed in zero flow condition ( u~t ).

q r ~t > o Y +3 G )3B Z u~t . R2 \ . T
The increase of the angular speed of rotation is limited to 270tr/min per second.

The ''Stopping'' step activates when the maximal pressure is reached in the storage vessel. This step triggers a decrease of the pump velocity to set the flow rate to values close to 0 and when the flow rate reaches its minimum threshold value (0,1m 3 /h), the valve is closed.

In the case of the turbine mode start-up, in order to avoid energy consumption during discharging, an auto-start-up situation was favored: first, the turbine is only driven by the torque produced by the water flow subsequent to the valve opening. The electric generator torque is zero: freewheel is active. When the angular speed is sufficient (close to the one of the maximum efficiency point), the ''freewheel'' mode is turned to inactive; then the power supply begins. The turbine is stopped when the air volume gets back to its initial value.

Equipments and methods

In this section are presented the components of the test rig, the physical parameters used for the modeling of each component and an example of a component characterization: the identification of the storage vessel thermal behavior.

Equipments

A schematic view of the developed prototype is shown in Figure 9. A picture of the test rig during the assembly phase is shown in Figure 10.

The test rig is composed of a Siemens bipolar 70kW squirrel cage asynchronous machine and an inverter including an Active Front End module (AFE), a KSB Multitec A50/12A reversible 12 stages pump, a storage steel vessel (40bar i.e. 280Wh/m 3 max capacity), a feeding vessel and a pneumatic control ball valve. The inverter freewheel mode is controlled by a digital input and the reference velocity by an analog input.

The piping includes a DN100 pipe connecting the feeding vessel to the pump suction side, a DN40 pipe which connects the pump outlet to the storage vessel and an auxiliary return pipe. This last pipe is used only for steady pump performance characterization; the vane on this pipe is a variable section valve that allowed setting several steady operating conditions. The storage vessel can be fed with compressed air up to 8bar in order to achieve pre-charged compression/expansion cycles. The storage vessel had a 1m3 volume leading to maximum design storage energy of 280Wh. The sensors used on the test rig are presented in Table 2. Their positions and associated variables are presented in Figure 9: the pressure transducers ( D and U ), the flow meter (# ), the torque transducer (-), the water level transducer ( T ) and the encoder on the motor shaft ( ). Data acquisition and generation of the control signals was performed with a National Instruments PXIe system with various PXI slots. The inverter was configured on vector control mode including real angular velocity signal. The supervision program was implemented in Labview. The control algorithm was executed at a frequency of 60Hz and a complete cycle duration was of the order of 90s.

Components' physical parameters

The test rig was used for the empirical tuning of the simulation model parameters; the main experimental studies were focused on:

• The steady state performance in the pumping mode • The quasi steady performance in the turbine mode • Internal natural heat convection coefficient of the storage vessel • Motor/generator friction factor • Pump/turbine mechanical inertia • Low pressure vessel dynamic behavior

The tuning procedures for these parameters are detailed in [START_REF] Sampedro | Étude d'un système hydropneumatique de stockage d'énergie utilisant une pompe/turbine rotodynamique[END_REF]. The resulting characteristics of the different components are presented hereafter.

Regarding the mechanical components, the empirical relation obtained for the motor natural friction factor has this form:

> 0,336. yt,z{ (14)
The values obtained for the inertias and the torsional stiffness are the following: The values BC3 and were provided by the manufacturers. The constants of equation ( 14) and the value of H4BH were obtained by free deceleration tests.

Regarding the hydraulic components, the retained hydraulic inertias are given in Table 3: The pump was characterized for different fixed angular speeds at different pressure levels in purely steady situation in a closed loop test configuration as mentioned before.

The turbine mode was characterized during quasi-steady operating conditions driven by the slow expansion of pre-compressed air flowing water out of the high-pressure vessel. Quasi-steady condition means that the effects of the hydraulic and mechanical accelerations are small. These effects can increase during fast start-ups of pumps for example and may affect noticeably the performance curves [START_REF] Dazin | Transient Behavior of Turbomachineries: Applicationsto Radial Flow Pump Startups[END_REF]. In the present case, according to the observed flow rate and angular velocity accelerations, these transient effects result in less than 3% of variation of the steady torque and pressure difference.

The values obtained experimentally for the constants in equations ( 7) and ( 8) are given in Table 4. These values are valid within a range of 5% for rotational speeds higher than 750rpm for the pump and the turbine. The presented dimensionless curves ( §2.3) and associated constants are valid for pressure differences ranging from 5 to 25bar.

The presented numerical values are specific for the specific test bench used in the present study. Nevertheless, the majority of inertial terms are scalable and the main frictional parameters are easy to estimate. A change in power rate would need to introduce the constants of the new hydraulic machine and it is generally feasible with the manufacturer data. Regarding the storage vessel, the change in energy capacity would need to adapt the volume and heat transfer area. Regarding the heat transfer coefficient, a method to measure it and an example is presented below.

Accumulator heat transfer coefficient

Hereafter is presented an example of physical characterization of a component.

The accumulator is one of the key components of the HYPES system. In a closed system, the dynamics of compression, expansion and stand by periods depend on the state of the air in the accumulator.

After a compression period, if the air temperature is different from the one of its surroundings, during a workless period (dV > 0), the thermal equilibrium is reached at a rate depending on the thermal capacitance of the air mass ( )75 . ), assuming that the temperature variation of the metal and water is negligible, and on the global heat transfer capability ( .S), analogue to the inverse of the resistive element in a RC electric circuit. Assuming a perfect gas behavior, a constant exchange surface mean temperature (k ) the relaxation rate of the mean air pressure can be expressed with a decreasing exponential function given in equation ( 15).

)75 G < > ~ 7 G < •. / y 3 €• (15)
The final thermodynamic equilibrium state is defined by the final pressure ( < related to the final temperature supposed equal tok and supposed here equal to the initial air temperature). The time constant ( ) is expressed as follows:

′ > )75 n 0 (16)
The time constant can easily be measured by analyzing the mean pressure, or temperature, history after a compression or expansion period (Figure 11 b). This thermal time constant method to compute global heat transfer coefficients on pneumatic accumulators, used in hydraulic circuits, was developed by Purmovahed & al. [START_REF] Pourmovahed | An experimental thermal time constant correlation for hydraulic accumulators[END_REF].

The mean air pressure is calculated by measuring the accumulator pressure at its bottom part (see +3 Figure 11 a), from which a water column pressure is subtracted ( T T ).

The air mass is supposed to be constant, and it is calculated before the heating/cooling periods, in a thermal equilibrium situation, assuming a perfect gas behavior and using the measurement of the initial volume, pressure and temperature. The initial temperature is measured by a sensor located at the top of the accumulator (see -)75_ƒ Figure 11 a). The water vapor mass is neglected.

)75 > 7 : 7 ' k -7 (17)
The expression of the global internal natural convective heat transfer coefficient is given by equation ( 18) as a function of the thermal time constant computed from the time history of the pressure (Figure 1-b).

> )75 . Y-Z ′. 0 (18)
The global heat transfer coefficient is then computed in its dimensionless form, the Nusselt number (Nu, see eq. ( 19)), in order to obtain a general empirical expression related to the parameters representative of the system state: a modified Rayleigh number (Ra* see eq. ( 20)) [START_REF] Pourmovahed | An experimental thermal time constant correlation for hydraulic accumulators[END_REF], ratio between buoyancy and viscous forces acting on air, and a geometric form factor (F see eq. ( 21)), useful to describe the possible end effects on the thermal transfer pattern.

> . Y-Z ( 19
)
' * > )73 \ . . ′. Y-)75 G -k Z. c . Y-Z Y-Z. Y-Z (20)
≡ : 0. ( 21
)
The air average transport properties are computed at the mean air temperature calculated from the mass, volume and pressure information at time 1 > . The relations used to estimate these properties were those used at atmospheric pressure and only dependent on temperature since pressure variations remained relatively modest in the configured tests. Details of the pressure effects on the air properties can be found in the literature (see for example: [START_REF] Kadoya | Viscosity and Thermal Conductivity of Dry air in the Gaseous Phase[END_REF], [START_REF] Stephan | The Thermal Conductivity of Fluid Air[END_REF], [START_REF] Kallman | Thermodynamic properties of real gases for use in high pressure problems[END_REF]).

The empirical relation between Nu and the other parameters is obtained by a linear regression done on the logarithms of the variables using R programming language [START_REF] Rteam | R: A Language and Environment for Statistical Computing[END_REF]. The subsequent expression for the Nusselt number is given by equation [START_REF] Kallman | Thermodynamic properties of real gases for use in high pressure problems[END_REF].

> 3,25. ' * t,\ †\ . t, †zf (22)
Figure 12: measured Nu compared to the regression line for the three parameters used in the expression and based on the measurement and data processing method; details of this analysis are given in [START_REF] Sampedro | Étude d'un système hydropneumatique de stockage d'énergie utilisant une pompe/turbine rotodynamique[END_REF].

It can be noticed that the cooling and heating Nusselt number values are very similar. This agrees with natural convection behavior on vertical surface as presented in [START_REF] Incropera | Fundamentals of Heat and Mass Transfer-chap[END_REF] (section 9.4).

In the next section the experimental procedure and results are presented.

Storage performance tests

Various storage cycles were conducted in order to test different control strategies.

Analysis of BEP cycle

An example of results obtained in the case of a BEP cycle is first presented. The experiment was performed with the initial conditions and parameters indicated in Table 5. Note that the turbine start up is activated manually in the test bench, so the starting time is included as a parameter for the simulations.

Table 5: initial conditions for the BEP cycle

: )75 ‡ Y c Z )75 ‡ Y Z -)75 ‡ Y° Z ‰)Š Y Z 1 +3 ‹OE•Ž Y.Z 0.51
9.10 5 18 12.5.10 5 64.5

These initial conditions were used to run the model presented in section 2.

The evolutions of the key parameters during a cycle are analyzed hereafter.

The angular speed of the pump/turbine is an essential parameter of the system, since this is the only controlled continuous variable responsible for the operating conditions. It is also the parameter that defines the time response of the storage system in case of a sudden energy request. During open valve active periods, the difference between the observed and modeled reference velocity is lower than 3rpm (Figure 13). It implies a very good prediction of the pressure difference used as reference for efficiency control (eq. ( 12)) and thus a good hydraulic model quality. This can also be observed on Figure 14 where the measured and predicted flow rates are shown.

Figure 14: water flow rate Figure 14 shows a predicted flow rate higher than the measured one; the data analysis showed that it was produced by an erroneous gain on the velocity reference sent to the inverter (see the difference between the reference speed of Labview and the real velocity in Figure 13 a.). Since the effective angular speed is lower than it should, the resulting pump pressure is lower, so it induces a lower flow rate. As a consequence, the maximal pressure is prematurely attained in the simulation (second 25 in Figure 14). At the end of the pumping period and at the beginning of the turbining period, the flow rates variation rates are very similar to the observed ones; this was made possible by the elaborated valve model. Besides the valve closing in conjunction to pump velocity reduction during the ''Stopping step'' (see Figure 8) worked well since flow annulations was achieved at very low torque and with very small back flow inducing no visible pressure drop in the vessel and thus very small energy losses.

During freewheel turbine start period, the acceleration was correctly predicted. This is a result of a good hydraulic turbine torque prediction; certainly due to a relatively good prediction of the flow rate in terms of order of magnitude and acceleration.

For this particular system, it seems that the hydraulic acceleration is largely higher than the mechanical one; thus the main parameter responsible of the time response of the device are the mechanical inertia and the torques applied on it. This shows the interest of multi-physic dynamic model since in such a coupled transient system this kind of information would be completely missing in a basic model. The measured torque is compared to the modeled pump torque and to the elastic torque (see Figure 15).

Two main parameters act on the torque value: the angular speed variations and the power transfer. The effect of the first can be observed is the first seconds of each startup where the elastic torque model changes at rates similar to the ones observed by the torque meter.

The accumulator pressure is shown in Figure 16. The difference between the modeled and observed values is about 8500Pa at the end of recovery period (t=83s) (less than 1 % of the measured value). That means that the computed air mean temperature is very close to the real one. Thus it can be concluded that the heat flows (dependent on the heat transfer empirical correlation) and the air volume variation rate are well predicted. The correct air pressure prediction contributes to the good prediction of the turbine stat up flow rate and the subsequent angular response time discussed before.

Figure 16: storage pressure A slight pressure decrease is observed in simulation at the end of pumping period; that was related to the water backflow during the vane closing. This backflow was higher on simulation results than in the reality (see Figure 14, t≈25s) and produces an increase of the air volume.

A good evaluation of the pump/turbine's instantaneous efficiency can be obtained by expression 23.

E/F • min "| | ; |Δ #|- max" | | ; |Δ #|- 23
The torque M is the one of the pump/turbine in the simulation and the measured torque for the empirical efficiency. That means that instantaneous efficiency comparisons can only be done during quasi-steady operating periods.

The time evolution of this efficiency is presented in Figure 17 and compared to the computed values. The pump was better modeled than turbine for which an efficiency discrepancy of 5 percent is observed; that seems to be related to a turbine torque over estimation.

Furthermore, despite the continuous pressure variation, the efficiency is maintained close to its optimum by the management of the angular velocity. This optimization does not prevent the system from the main energetic loss produced by the hydro-mechanic conversion.

Figure 17: pump/turbine efficiency: BEP mode Electrical power was given by the frequency inverter. Electrical conversion was not modeled here, thus it was roughly estimated by multiplying the speed control loop generated torque (that should be similar to the electromechanical one) and the angular velocity computed by the motor inertial model. The modeled and observed electrical powers are show in Figure 18; the ratio between both gives the efficiency of the asynchronous machine. That is why in pumping mode the measured values are higher than the modeled ones and in turbine mode the opposite is observed. Its value is around 87%. steps is in red. The efficiency of each step is in blue. Energy was obtained by time integration of power.

The main energy losses occur during pumping and turbining. This could be improved choosing machines with better efficiencies than the ones used in the present studies. This could be certainly possible at higher design powers.

Figure 19: energy flow over a cycle (electric conversion not included)

The losses in the accumulator are small compared to the hydraulic conversion losses. However, these can be easily reduced by water injection in the vessel in order to get a process close to an isothermal cycle.

Table 6 gives a comparison between measured and modeled values of some important parameters of the system. It confirms the reliability of the prediction of the model, already observed on the instantaneous evolution of the parameters. For comparison purposes, some compressed air storage systems efficiency experimental values are reported here. The efficiency of the two well-known Huntorf and McIntosh CAES plants are respectively of 42% and 54% [START_REF] Budt | A review on compressed air energy storage: Basic principles, past, milestones and recent developments[END_REF]. They were open systems operating around 50bar to 70bar and they presented the particularity of using gas combustion before expansion to reheat the air. . A Chinese team did a very interesting experimental work on this CAES with 108°C thermal storage; the observed round trip efficiency was 22.6% [START_REF] Wang | Experimental study of compressed air energy storage system withthermal energy storage[END_REF]. The main discrepancy to the expected value was due to the poor heat recovery during compression. For the GLIDES project the shaft efficiency was 30% [START_REF] Odukomaiya | Experimental and analytical evaluation of a hydro-pneumatic compressed-air Ground-Level Integrated Diverse Energy Storage (GLIDES) system[END_REF]; this was a closed HYPES system operating between 70bar and 100bar. Lemofouet-Gatsi obtained an efficiency of about 43% [START_REF] Lemofouet-Gatsi | Investigation and optimisation of hybrid electricity storage systems based on compressed air and supercapacitors[END_REF] with a closed HYPES system operating between 100bar and 200bar and oil hydraulic machines. The only system using a reversible machine was the last one. Another recent research paper presents a 15% efficiency (including thermal power) for an open compressed air storage system operating at 300bar where a multistage compressor and an air motor were used [START_REF] Cheayb | Modelling and experimental validation of a small-scale trigenerative compressed air energy storage system[END_REF].

The efficiency of 30% of the present system thus appears rather correct especially in regard to its simplicity. If it has a lower efficiency than the best systems in the literature, it presents also the advantage of using a unique water hydraulic machine which is appreciable if high power systems are imagined. First because the water is a natural and neutral fluid for environment; then the power capacity cost (or investment) is much lower using a single hydraulic machine, specially compared to gas compressors and turbines. For example, the cost of compressors and turbines for Huntorf station was around 450€/kW (without including inline heat exchangers cost) [START_REF] Kaldemeyer | Compressed air energy storage in the German energy system-status quo & perspectives[END_REF], in our case, for a small power machine the cost was around 195€/kW. Nevertheless the price of the storage volume needs to be evaluated and minimized; for the cited two high capacity CAES combustion assisted stations, underground caverns were used leading to a very low energy capacity cost. The use of vessels presents a challenge regarding the cost of all the small and medium power storage systems; but it is necessary when no natural cavities are available. The use of a higher efficiency pump/turbine and operating at higher design powers could fill the gap in efficiency to the best CAES systems with advantage of using no gas combustion or high temperature heat storage systems. The typical pump efficiencies are around 80% and could be even higher for turbines. A higher power system, for the same operating pressure, would lead to higher specific speed machines and thus better efficiencies [START_REF] Jacobsen-Grundfos | The Centrifugal Pump[END_REF]. Thus, a 55% round trip efficiency seems clearly achievable.

Analysis of PCT cycle

A precise power demand situation was simulated here. Instead of controlling the angular speed of the machine at its best efficiency point, it was controlled to deliver a given prescribed power during the charge and discharge period despite the working pressure variation.

The charging mechanical power was set to 10kW and discharge power to 2.6kW. The initial settings were the same as the ones used for the BEP cycle.

The response of the system in terms of power is shown in Figure 20.

Figure 20: powers during a PCT test

The pump power was maintained almost constant with a maximum gap to the reference power of 5%. During the discharge, the maximum power difference was of 23%. The turbine operation is much more sensitive to the operating conditions and thus angular velocity. For example in the case of the sensitivity of the torque related to the flow rate variation, for the turbine mode the sensitivity is twice as great as for the pump mode (see chapter 7.5 in [START_REF] Sampedro | Étude d'un système hydropneumatique de stockage d'énergie utilisant une pompe/turbine rotodynamique[END_REF]). The power control error could be corrected with a closed loop regulation system operating in real time.

The efficiency of the machine is shown in Figure 21. The pump efficiency is maintained relatively high and is almost constant despite the PCT mode whereas the turbine observes a higher variation. The turbine behavior prediction was worse than was for the pump. The overall efficiency was 28% this case. It has to be underlined that this value is quite close to the one in the BEP case.

Conclusion

A prototype of a closed hydro-pneumatic energy storage device using a pump as a turbine has been presented. The pneumatic accumulation efficiency was 84% and the mechanical round-trip efficiency was 31%.. This is a relatively correct efficiency especially in regard to the simplicity of the system and compared to recent HYPES systems in literature. The use of a single reversible machine was demonstrated in a lab scale prototype. This shows the opportunity offered by such machines for ecological, long term and cheap storage solutions.

Two control strategies of the hydraulic machine for a variable operating pressure situation were successfully implemented: best efficiency point and power control strategies. In the first case, the machine efficiency was effectively maintained close to its optimum; in the second case the power was maintained close to the power set-point within a 5% deviation for charging and 23% for discharging. The power control appeared harder to achieve for turbine mode and would probably need to be improved using a closed loop control. Besides the pump mode end control and turbine mode start-up were successfully achieved thus minimizing the valve operation losses and proving the possibility of an off-grid rotodynamic turbine start-up.The dynamic behavior of the system was simulated. Specific parameters of the different modeling sub-domains were empirically calibrated thank to specific tests; the example of the global heat transfer coefficient of the storage vessel was presented. The transient behavior of the system was correctly simulated in various situations and the response time of the storage device was well computed thanks to the presented multi-physic dynamic model. This was made possible by the presented multiphysics dynamic model that considers the strong coupling between hydraulics and mechanics.

The system can be improved in various ways. First, the pneumatic accumulation efficiency and energy density could be increased by achieving quasi-isothermal compression and expansion; that could be achieved by water injections inside the vessel. Then the turbine sensitivity and flexibility can be improved by variable angle external vanes. This could be done in higher power machines. Furthermore, at higher powers, maintaining the maximum pressure, the efficiencies of both modes would be improved; this is related to the increase of the specific speed of the machine. This last point is the main improvement path for such systems.

Regarding the architecture of the system, in order to increase the power flexibility at high efficiency, the use of various staged vessels at various pressures would allow the hydraulic machine operating at the more adequate pressure in function of the appeal power. Also a modular series-parallel piping of various machines with a lower number of stages could help in this same purpose.

At last, an economic analysis should be conducted in order to identify the storage services this kind of systems could answer to. Especially the minimization of the cost of the storage vessels needs to be explored by the right choice of storage pressure and materials. Also the possibility of an open cycle needs to be studied in order to attain competitive energy densities.

Acknowledgement

This project was carried out thanks to the financial support of the French agency for environment and energy management (ADEME), which actively induces research on smart grids and storage solutions. Furthermore the technical staff of ENSAM Lille has to be thanked for the important role he played for this project to be realized.

Appendices

Motor PI controller

The required torque of the electric motor was computed by a PI controller; see Figure 22. It takes the reference speed set by the user or the control algorithm. This controller was implemented in the code. In the case of the test bench, this part is integrated to the inverter; the reference speed in that case was given by the Labview program. The signal named ''FW'' refers to freewheel mode (1: active, 0: inactive. The threshold of the switch was 0. When freewheel mode is active no torque is applied by the electric motor. The Ti constant was set to 0.2 and K to 40.

Valve modeling

The pressure applied to the liquid column is computed in a manner that it could achieve the flow rate stopping in almost any situation i.e. closed storage vessel start-up, standard flow closing and those for opening and closing situations. The Figure 23 shows the Simulink program implemented to compute the pressure applied by the valve. The ''CO'' variable is the closing order (1: close, 0: open). A reset of the integrator of the valve model is needed to enable free circulation after a closing period (grey line). The value of the characteristic time ''Ti'' was 120 and the gain ''K'' had a value of 10.10 6 . The value of # $ 5;< was always set to 0. The ''1 +3 %=/%'' block represents a first order filter; the integrator of the filter had as initial value the inverse value of its gain. The variable Δ C3 has the value of the Δ 6)D)PQ; before the subtraction of Δ )D ; in equation ( 4) of the transfer function of Figure 5.

Power control tables

The look up table values for the PCT mode are given here; pump mode in Figure 24 and turbine mode in Figure 25. For the turbine mode, for a given set of ( 5;< , Δ ), two angular speed values exist; the one presenting the highest efficiency was used here.

Figure 24: angular speed as function of required power and observed pressure; pump

Figure 2

 2 Figure 2 displays the structure of the global model. The input/output variables of each sub-model are represented by the

Figure 2 :

 2 Figure 2: global bloc diagram; sub-models input/output variables and control/controlled variables

Figure 3 :

 3 Figure 3: model of the mechanical system

Figure 4 :

 4 Figure 4: transfer function of the mechanical sub-model

Figure 5 :

 5 Figure 5: hydraulic model transfer function 2.3. Pump/turbine model

Figure 6 :

 6 Figure 6: pump characteristics

Figure 8 :

 8 Figure 8: supervision state diagram / observed and controlled variables

Figure 9 :

 9 Figure 9: test rig main components and instrumentations; 1electric motor/generator, 2-reversible pump turbine, 3-storage vessel, 4-feeding vessel, 5-control vane Figure 10: view of the test rig

  kg.m² 0.15 kg.m² 95 kN.m/rad

Figure 11 :

 11 Figure 11: a-storage vessel; b-pressure change during a compression -cool down period

Figure 12

 12 Figure12shows the measured Nusselt number as a function of the Nusselt number computed by the expression (22) using

Figure 13

 13 Figure 13 displays the angular velocity observed and calculated by the model. The reference velocities of the Simulink model supervision program and the one of the experimental supervision system are also provided.

Figure 13 :

 13 Figure 13: angular velocity

  Figure 15: various torques

Figure 18 :

 18 Figure 18: measured electrical power; modeled electromechanical power A summary of the cycle's energy flows is presented in Figure 19. The fraction of the initial energy still available at different cycle

Figure 21 :

 21 Figure 21: pump/turbine efficiency; PCT mode

Figure 22 :

 22 Figure 22: PI controller used to compute the electromagnetic torque

Figure 23 :

 23 Figure 23: the valve pressure management program

Figure 25 :

 25 Figure 25: angular speed as function of required power and observed pressure; turbine

Table 1

 1

		: angular speed reference configurations for the
		supervision program
	BEP	)DnC > o	p E/F lmE . '2 \ .

T

[START_REF] Stahlkopf | Compressed air energy storage system utilizing two-phase flow to facilitate heat axchange[END_REF]

Table 2 :

 2 list of measuring instruments

	Variable	Type of sensor/transducer	Conditioning	Uncertainty
	Flow rate	Bidirectional electromagnetic: Proline Promag 50W. Hendress & Hausser.	4-20mA	0.2%
	Absolute static pressure	Piezoresistive : PAA 33X. Keller.	RS-485	0.025%FS
	Torque	Torque transducer : T30FN/500 N.m + MD18N amplifier. HBM.	±10V	Error band <0.08%
	Angular speed	Motor integrated encoder: 1024 pulses per rotation.	±10V
	Internal temperature	PT100 sensor: HC2-IE102 + HF532 transducer. Rotronic.	4-20mA	±0.1K at 23°C
	Water level	Guided radar level meter: Optiflex1300. Krohne.	4-20mA	±3mm

Table 3 :

 3 hydraulic inertias in kg/m4

	Low pressure pipe	High pressure pipe	Pump wheels	Pump diffusers	Storage vessel	S (total)
	1.81.10 5	7.36.10 5	8.33.10 5	2.02.10 5	5.62.10 3	1.96.10 6
	9%	38%	43%	10%	0.3%

Table 4

 4

		: pump and turbine constants
		Pump			Turbine
	1	2	3	1	2	3
	A 6.89 25.4 -810	4.94	-46.29 1196
	B 0.21 6.6 -23.1 -0.188 -0.226 99.16

Table 6

 6

	: a comparison between model and measurements
		Measured	Modeled	Discrepancy
	Cycle shaft efficiency	31%	33%	+6%
	Turbine unconstrained
	start up acceleration	581	559	-4%
	(rpm/s)
	Turbine start pressure (bar)	12,06	12	-3% (referred to )75 ‡™ ‡‹ )


Denis Georgelin

Fabienne Jonqua

Katarzyna Makowiecka

Sydney Wheeler

Christophe Baudouin

Dominique Brémond-Gignac

Antoine Labbé
email: dr.antoinelabbe@gmail.com

Antoine Pr

Labbé

Dépistage des troubles visuels à l'âge scolaire: les données du projet pilote PlanVue®

Keywords: Dépistage, Projet pilote, Troubles visuels, Correction optique, Population pédiatrique Screening, Pilot project, Visual impairment, Optical correction, Pediatric population

Introduction :

Dans son rapport de 2010, l'Organisation Mondiale de la Santé (OMS) estimait à 285 millions le nombre d'individus dans le monde présentant des troubles visuels dont près de la moitié (43%) correspondaient à des anomalies réfractives [START_REF]Global Data on Visual Impairments[END_REF]. Chez les enfants européens, la prévalence des troubles réfractifs est dominée par la myopie (14,3%) suivie par l'astigmatisme (12,9%) puis l'hypermétropie (9%) [START_REF] Hashemi | Global and regional estimates of prevalence of refractive errors: Systematic review and metaanalysis[END_REF]. Au total, les troubles visuels concerneraient 1 enfant sur 5 à l'âge de 6 ans [START_REF]charge chez le jeune enfant[END_REF].

Une anomalie de la fonction visuelle non corrigée chez un enfant peut être une source de handicap visuel irréversible en cas d'amblyopie, mais aussi de difficultés d'apprentissages, émotionnelles et sociales [START_REF] Zaba | Social, Emotional and Educational Consequences of Undetected Children's Vision Problems[END_REF] (Caroline K. Impact des troubles visuels sur la performance scolaire. Thèse de doctorat en psychologie, Université Lumière Lyon 2, 2015). La présence de troubles visuels non dépistés constituerait ainsi un risque de développement défaillant des compétences de lecture chez les enfants de 4 à 5 ans [START_REF] Bruce | Impact of visual acuity on developing literacy at age 4-5 years: a cohort-nested cross-sectional study[END_REF] voire un risque d'illettrisme à l'âge adulte [START_REF] Zaba | Social, Emotional and Educational Consequences of Undetected Children's Vision Problems[END_REF]. Les enfants affichant une mauvaise réussite à l'école sont plus fréquemment atteints de troubles de l'acuité visuelle, de la vision binoculaire et de l'oculomotricité [START_REF] Alvarez-Peregrina | Visual Health and Academic Performance in School-Aged Children[END_REF].

Lorsqu'une gêne visuelle est spontanément exprimée par l'enfant, celui-ci aurait 52% de risque supplémentaire d'avoir de faibles performances scolaires. A l'inverse, le port de lunettes diminuerait cette même probabilité de 53%, d'où l'importance du port d'une correction optique adaptée chez l'enfant (Caroline K. Impact des troubles visuels sur la performance scolaire. Thèse de doctorat en psychologie, Université Lumière Lyon 2, 2015).

Une bonne acuité visuelle serait ainsi un facteur prédictif majeur de réussite scolaire, au moins aussi important que le niveau éducatif des parents [START_REF] Jan | Association of visual acuity with educational outcomes: a prospective cohort study[END_REF].

En France, en dehors des recommandations de dépistage des troubles visuels réalisé par le médecin traitant ou le pédiatre, il n'existe pas de programme de dépistage systématique des troubles visuels à grande échelle chez les enfants d'âge verbal. Le projet pilote PlanVue®, qui s'est inspiré du programme américain ChildSight [START_REF] Pizzarello | A new school-based program to provide eyeglasses: ChildSight[END_REF], coordonné par l'association Helen Keller International Europe, avait pour but de détecter et de prendre en charge les troubles visuels chez les enfants scolarisés dans les réseaux d'éducation prioritaire (REP) de la politique de la ville de Nanterre (92). Ce projet a été développé en cinq phases, 1-sensibiliser les enfants et des enseignants aux troubles visuels, 2-réaliser un repérage par des orthoptistes des enfants présentant un trouble visuel, 3-organiser l'adressage vers une consultation d'ophtalmologie, 4-fournir un équipement en lunettes lorsque celui-ci était nécessaire, et Sur les 232 élèves de CM2 et de 5 ème ayant répondu à la question «As-tu déjà fait un test pour les yeux», 6% déclaraient n'en avoir jamais fait, et plus les élèves étaient jeunes, moins ils en avaient réalisé auparavant -Test de Khi 2 , seuil de 5%-(Figure 1). Concernant le port de lunettes antérieur au dépistage, il apparaissait que parmi les 515 enfants étudiés, 116 étaient déjà porteurs de lunettes (23%) contre 399 qui n'en avaient pas (77%) (Figure 2). Cette proportion d'enfants porteurs de lunettes en phase de repérage était inversement proportionnelle à leur âge (Figure 3). En effet, sur les 116 enfants porteurs de lunettes et ayant participé au repérage, les 4-5 ans étaient le moins équipés de tous. Parmi les 142 enfants de classe de CM2 et 5 ème ayant participé au repérage et ayant répondu par oui ou non à la question « Penses-tu bien voir ? », 108 enfant affirmaient très bien voir, contre 34 qui disaient mal voir. Parmi les 34 enfants qui affirmaient mal voir, 10 (29%) ont été réorientés vers un ophtalmologiste et nécessitaient une correction optique, alors que seuls 10 (9%) enfants sur les 108 affirmant avoir une bonne vue ont été adressés à un ophtalmologiste, avec uniquement 50% d'entre eux nécessitant une correction optique.

Le repérage fondé sur la mesure de l'AV de loin non corrigée retrouvait une anomalie chez 103 enfants (20%), plus précisément 24 (18%) des 4-5 ans, 40 (27%) des 6-9 ans et 39 (17%) des 9-15 ans (Figure 4). De la même façon, la mesure de la réfraction objective a détecté une anomalie de réfraction chez 96 enfants (19%) sur les 515 examinés, alors que 405 (79%) présentaient des valeurs « normales » au PS. Enfin, chez 14 enfants (3%) aucune mesure fiable n'a été obtenue au PS. En recoupant les données de mesure de l'AV avec celles issues des mesures au PS (Tableau 1), celles-ci montraient une concordance pour 388 enfants (77%), avec une anomalie retrouvée à la fois à la mesure de l'AV et au PS pour 8% des élèves, et une absence d'anomalie à la mesure de l'AV et au PS chez 69%. Pour 113 élèves (23%), les 2 tests n'étaient pas concordants, retrouvant une anomalie à la mesure de l'AV mais pas au PS ou inversement. Les valeurs obtenues au PS mettaient en évidence une hypermétropie chez 413 enfants (80%), une myopie chez 67 enfants (13%), l'absence d'amétropie sphérique chez 13 enfants (3%), et une antimétropie (un oeil myope et un oeil hypermétrope) chez 22 enfants (4%). Un astigmatisme était retrouvé sur au moins 1 oeil chez 482 enfants (94%) et seuls 33 enfants (6%) n'avaient aucune amétropie cylindrique. Sur les 1020 yeux étudiés et dont les valeurs de puissance cylindrique étaient disponibles, 868 yeux (85%) présentaient un astigmatisme. Parmi ces derniers, 506 yeux (50%) avaient un astigmatisme inférieur ou égal à 0,50D, 179 (18%) un astigmatisme compris entre 0,75D et 1D, 67 (7%) entre 1,25D et 1,50D, et 116 yeux (11%) avaient un astigmatisme supérieur ou égal à 1,75D (Figure 5). enfants n'était actuellement pas recommandé [START_REF]Accréditation et d'Évaluation en Santé. Dépistage précoce des troubles de la fonction visuelle chez l'enfant pour prévenir l'amblyopie[END_REF]. Presque 20 ans plus tard, il n'existe toujours pas de programme national de dépistage systématique d'anomalie de la fonction visuelle chez l'enfant d'âge scolaire, alors même que les conseils généraux ont une obligation de dépistage de l'enfant. L'examen de la fonction visuelle réalisé par le médecin généraliste ou le pédiatre se fonde sur les recommandations de l'ANAES, confortées par celles de l'association du CADET [START_REF]ans)[END_REF]. Celles-ci consistent, en dehors de facteurs de risque, en un examen de l'enfant d'âge verbal entre 30 mois et 4 ans par le médecin traitant avec un examen global de l'oeil, une recherche du réflexe photomoteur, un dépistage du strabisme, une mesure de l'AV de loin, et une estimation de la vision stéréoscopique par un test de Lang. En cas d'anomalie à cet examen, le médecin traitant réoriente l'enfant vers un ophtalmologiste [START_REF]Accréditation et d'Évaluation en Santé. Dépistage précoce des troubles de la fonction visuelle chez l'enfant pour prévenir l'amblyopie[END_REF]. Bien que figurant spécifiquement dans le carnet de santé de l'enfant, avec des examens nécessaires à la troisième, quatrième, et sixième année puis entre 8-9 ans, 11-13 ans, et 15-16 ans, ces recommandations restent encore trop peu mises en oeuvre. Dans une étude réalisée en 2017, il a été mis en évidence que plus de la moitié des médecins généralistes ne réalisaient pas ce test de dépistage, principalement par manque de matériel, défaut de formation, ou par manque de temps [START_REF] Naudin | Dépistage des troubles de la vision, de l'audition et du langage à l'âge de 3-4 ans : état des lieux des pratiques des médecins généralistes franciliens[END_REF]. Ce défaut de formation et de matériel peut s'illustrer par le choix du test utilisé pour la mesure de l'acuité visuelle. En effet, afin d'obtenir une mesure fiable, le médecin généraliste doit être en mesure de choisir et de disposer au cabinet d'un test adapté à l'âge de l'enfant et à son développement. Ainsi, une mesure avec l'échelle de Monoyer pourra s'avérer trop difficile chez un enfant très jeune tandis qu'une mesure par Stycar-test risque d'être faussement rassurante en surestimant l'acuité visuelle après l'âge de 5 ans [START_REF] Bois | Dépistage des troubles visuels entre 3 et 5 ans : expérience du service départemental de la Protection Maternelle et Infantile dans les Hauts-de-Seine[END_REF].

Les autres pays n'ont pas non plus réussi à mettre au point de programme de dépistage des troubles visuels de l'enfant à grande échelle. Au Royaume-Uni, il n'existe pas de recommandation claire quant à la pratique du dépistage visuel chez l'enfant d'âge scolaire.

Néanmoins, le National Screening Committee (NSC) stipule que le dépistage des troubles visuels chez les enfants de 4-5 ans devrait être confié aux orthoptistes avec pour but de tester l'intégralité des enfants avant leur 5 ème année. Les enfants présentant un strabisme ou une AV anormale doivent être référés à un ophtalmologiste [START_REF] Rahi | Screening and surveillance for ophthalmic disorders and visual deficits in children in the United Kingdom[END_REF]. Aux États-Unis, les recommandations émises par l'American Academy of Pediatrics, l'American Association of Pediatric Ophthalmology and Strabismus et l'American Academy of Ophthalmology préconisent un dépistage des troubles visuels à partir de 3 ans avec mesure de l'AV de loin, un examen sous écran, une évaluation de la vision stéréoscopique et un test de Bruckner [START_REF]Eye examination in infants, children, and young adults by pediatricians[END_REF].

Les recommandations canadiennes quant à elles recommandent un examen global de l'oeil, une étude du reflet rétinien, une recherche de strabisme et une mesure de l'AV. Seuls les enfants présentant une anomalie dépistée doivent être orientés vers un ophtalmologiste, tandis que ceux ne présentant pas d'anomalie mais ayant des difficultés de lecture doivent être orientés vers un orthoptiste [START_REF]Le dépistage des troubles de la vue chez les nourrissons, les enfants et les adolescents[END_REF].

Il apparaît néanmoins capital de dépister le plus largement possible et de façon systématique les enfants d'âge scolaire étant donné la prévalence encore trop importante des troubles réfractifs non corrigés et de l'amblyopie, estimée à 2,9% de la population Européenne [START_REF] Fu | Global prevalence of amblyopia and disease burden projections through 2040: a systematic review and meta-analysis[END_REF]. L'amblyopie toucherait 99,2 millions de personnes dans le monde et constitue donc un enjeu majeur de santé publique avec une prévision de 221,9 millions d'individus touchés à l'horizon 2040 [START_REF] Fu | Global prevalence of amblyopia and disease burden projections through 2040: a systematic review and meta-analysis[END_REF]. En dehors de l'amblyopie, les troubles visuels chez l'enfant sont à l'origine d'un préjudice individuel avec notamment une diminution des performances scolaires (Caroline K. Impact des troubles visuels sur la performance scolaire.

Thèse de doctorat en psychologie, Université Lumière Lyon 2, 2015) ou de la qualité de vie [START_REF] Sabri | The VF-14 and Psychological Impact of Amblyopia and Strabismus[END_REF], alors qu'ils sont accessibles à un traitement simple, efficace et peu couteux. Une étude espagnole de 2020 menée sur 11 406 enfants a en effet montré que ceux qui affichaient de moins bons résultats scolaires présentaient plus fréquemment des troubles visuels [START_REF] Alvarez-Peregrina | Visual Health and Academic Performance in School-Aged Children[END_REF]. La correction de ces troubles visuels pourrait ainsi permettre d'améliorer les performances d'apprentissage de l'enfant, comme le montre par exemple une étude chinoise qui a mis en évidence que le fait de corriger une éventuelle myopie permettait une amélioration des résultats scolaires de l'enfant [START_REF] Ma | Effect of providing free glasses on children's educational outcomes in China: cluster randomized controlled trial[END_REF]. L'aide des professionnels paramédicaux, et en particulier des orthoptistes, est capitale dans la conception d'un programme de dépistage à grande échelle. Bien que l'examen sous cycloplégie demeure la référence pour établir une ordonnance de correction optique chez l'enfant, le simple repérage des enfants ayant besoin d'être référés à un ophtalmologiste devrait être réalisé par les orthoptistes, comme cela est recommandé au Royaume-Uni. En revanche, l'examen sous cycloplégie doit être impérativement réalisé chez les enfants présentant une anomalie visuelle dépistée. L'étude ChildSight, qui avait été menée dans les années 90 sur 5851 enfants de la ville de New York, ne référait pas systématiquement tous les enfants avec une anomalie visuelle, et fournissait dans l'heure, sur place, la correction optique. Cette démarche s'inscrit dans un système de soins différent du système Français, avec un accès à l'ophtalmologiste plus difficile, puisque seuls 58 enfants sur les 5851 dépistés ont consulté un médecin dans cette étude américaine.

Selon notre étude, 14% des enfants de 4 à 13 ans scolarisés en réseau d'éducation prioritaire avaient besoin de lunettes et 87% d'entre eux n'en portaient pas avant le dépistage.

La France comptait en 2020 environ 12 millions d'enfants de moins de 15 ans [START_REF]Population par sexe et groupe d'âges[END_REF]

enfin 5 -

 5 un suivi-évaluation des enfants. Le but de notre étude était d'évaluer rétrospectivement les données épidémiologiques issues du projet pilote PlanVue® concernant la santé visuelle des enfants en âge scolaire en réseau d'éducation prioritaire en France. Patients et méthodes : Le projet pilote PlanVue® a été réalisé auprès de 594 enfants d'âge scolaire répartis dans cinq établissements scolaires du réseau d'éducation prioritaire (REP) de la ville de Nanterre, en France, au cours de l'année scolaire 2018-2019. Tous les parents des enfants qui ont participé au projet pilote PlanVue® ont été préalablement informés de la conduite de cette étude et leur consentement écrit a été systématiquement recueilli avant la réalisation de cette étude. Les enseignants avaient également donné leur accord pour participer à ce projet pilote. Une première phase, dite de sensibilisation, permettait d'informer les élèves, parents et professeurs sur le fonctionnement de l'oeil et la nécessité du port de lunettes, sous forme d'informations par livrets et d'ateliers scolaires. Parallèlement, et par le biais des enseignants, un questionnaire individuel sous format papier, adapté selon l'âge de l'enfant, a été soumis en classe aux élèves afin d'évaluer, outre leurs connaissances de l'oeil, combien parmi eux portaient des lunettes et quelles en étaient leurs perceptions et usages par rapport aux troubles visuels, combien avaient déjà consulté un ophtalmologiste ou fait un examen de la fonction visuelle. Une seconde phase, dite de repérage, a été réalisée entre janvier et mars 2019 au sein des écoles concernées par des orthoptistes. Ce repérage consistait en la mesure de l'acuité visuelle (AV) non corrigée de chaque oeil avec l'échelle de Pigassou ou de Monoyer selon le niveau scolaire de l'enfant, une évaluation de la réfraction objective avec un photoscreener (PS) portable 2WIN® (Adaptica, Italie), la recherche d'un strabisme par réalisation d'un examen sous écran, et une évaluation globale du comportement visuel de l'enfant par l'orthoptiste. Les enfants étaient ensuite adressés pour une consultation d'ophtalmologie s'ils présentaient une anomalie à l'un de ces tests en fonction des critères suivants : L'anomalie à la mesure de l'AV de loin était définie pour les enfants de moins de 6 ans comme une AV décimale inférieure ou égale à 6/10 ème sur l'un des 2 yeux ou une différence supérieure ou égale à 2/10 ème entre les 2 yeux; une acuité visuelle inférieure ou égale à 7/10ème à l'un des 2 yeux pour les enfants âgés entre 6-9 ans; et inférieure ou égale à 8/10ème à l'un des 2 yeux pour les enfants entre 9-15 ans. Les valeurs du photoscreening étaient considérées comme anormales si elles étaient supérieures en valeur absolue à 1.00 D pour la myopie, 2.50D pour l'hypermétropie, 2.00D pour l'astigmatisme, et en cas de différence de réfraction entre les deux yeux, supérieure à 1.00D. Les résultats des examens ophtalmologiques des enfants ayant été adressés à un ophtalmologiste ont été également analysés pour la présence d'une amblyopie, d'une amétropie, d'un strabisme, d'une nécessité de port de lunettes ou de rééducation orthoptique. L'analyse descriptive des variables continues ont été exprimées en moyennes, écart-type ou médiane. Les variables catégoriques ont été exprimées en pourcentages. Pour les études d'association et de comparaison, le test du Chi2 a été utilisé. Résultats : La population initiale comptait 594 enfants, dont seuls 531 ont participé à la phase de repérage. Parmi ces 531 enfants, 12 enfants ont été exclus en raison d'informations manquantes concernant leur âge, ou le fait qu'ils étaient ou non porteurs de lunettes préalablement à l'étude, et 4 autres l'ont été en raison de données manquantes quant à la mesure de leur AV. Au total, ce sont les données de 515 enfants qui ont été étudiées, dont 272 garçons (53%) et 243 filles (47%) âgé de 4 ans à 13 ans. Parmi les 515 enfants, 259 (50%) avaient entre 4 et 6 ans, 164 (32%) entre 7 et 10 ans, 92 (18%) entre 11 et 13 ans, avec une moyenne de 8 ± 2,72 ans. Les enfants étaient pour 129 (25%) d'entre eux en classe de Grande Section, 149 (29%) en CP/CE1, 148 (29%) en CM1/CM2, et 89 (17%) en 5 ème .

  Parmi les 515 enfants étudiés, 112 (22%) ont été orientés vers une consultation spécialisée d'ophtalmologie. Parmi les 112 enfants orientés, 81 enfants (72%) ont été adressés à l'ophtalmologiste sur un critère basé sur la mesure de l'AV et/ou du PS. Enfin, 31 enfants (28%) ont été orientés en raison d'anomalies sur les autres critères comme une la motricité oculaire, l'aspect des pupilles, ou un comportement visuel suspect selon les orthoptistes. Sur les 112 enfants adressés, 85 se sont présentés en consultation d'ophtalmologie au sein du réseau établi par le projet PlanVue® et avaient des résultats disponibles, et les enfants restants ont pour la majorité bénéficié d'un examen chez un autre ophtalmologiste. L'examen médical a retrouvé que 71 d'entre eux avaient besoin de lunettes, soit 84% des enfants ayant consulté. Il était intéressant de noter que 86% des enfants présentant une anomalie à la mesure de l'AV réalisée lors du repérage avaient besoin de lunettes, 89% des enfants présentant une anomalie au PS avaient besoin de lunettes, et que 90% des enfants présentant une concordance d'anomalie entre l'AV et au PS en avaient besoin. Les enfants qui n'avaient pas d'anomalie à la mesure de l'AV et au PS mais qui avaient été adressés sur d'autres critères avaient quand même besoin de lunettes pour 82% d'entre eux. En moyenne, sur l'ensemble de la population étudiée, 71 enfants avaient besoin de lunettes, soit 14%. Parmi ces 71 enfants, 62 (87%) n'avaient jamais eu de correction optique (Tableau 2). Chez les 245 enfants de moins de 6 ans qui ont participé au repérage, 42 avaient besoin de lunettes, soit 17% des enfants de cette classe d'âge. Chez ces 42 enfants, seuls 6 en avaient déjà lors du repérage, et 36 enfants (15%) n'en avaient pas. Chez les 7-10 ans, 22 enfants avaient besoin de lunettes, soit 13% d'entre eux, et 7 enfants de 11 à 13 ans avaient besoin de lunettes soit 8% dans cette classe d'âge. Sur les 85 enfants examinés par un ophtalmologiste et dont les résultats étaient disponibles, 11 (13%) présentaient une amblyopie, soit 2% des 515 enfants ayant participé au repérage, 44 (52%) présentaient une hypermétropie, 18 (21%) présentaient une myopie, 2 (2%) présentaient un strabisme, 49 (57%) présentaient un astigmatisme, et 6 (7%) n'avaient aucun trouble visuel retrouvé (Figure 6). Discussion Dans ses recommandations de 2002, l'Agence Nationale d'Accréditation et d'Évaluation en Santé (ANAES) concluait qu'un programme national de dépistage systématique des

  et on peut donc estimer qu'environ 1,4 millions d'enfants dans le pays auraient besoin de lunettes sans le savoir, justifiant la nécessité d'un tel dépistage. L'école semble être un lieu idéal pour réaliser ce dépistage de masse, de par son caractère obligatoire et sa facilité d'accès aux professionnels de santé. Ce dépistage comme celui réalisé dans le projet pilote PlanVue®, devrait suivre les recommandations de 2019 de l'AFSOP[20] qui préconise un dépistage systématique idéalement avant l'âge de 4 ans, avec une analyse de l'AV, une mesure au PS et une recherche de strabisme. La méthode la plus efficace de dépistage des troubles visuels de l'enfant consiste en l'association de la mesure de l'AV à des tests objectifs, permettant d'augmenter significativement la sensibilité du dépistage [21]. Ainsi, pour une spécificité de 90%, la sensibilité obtenue en terme de dépistage de trouble réfractif varie autour de 60% pour les photoscreeners en fonction du modèle utilisé. L'examen sous écran quant à lui affiche une excellente spécificité de 98% mais une faible sensibilité de 16%, et ne peut donc pas être utilisé seul. L'intérêt de réaliser ce dépistage le plus précocement possible, idéalement à un âge où l'amblyopie reste réversible, est conforté dans notre étude par le fait que le nombre d'enfants ayant besoin d'une correction optique est d'autant plus important que ceux-ci sont jeunes, pour atteindre 17% des moins de 6 ans. En effet, équiper en lunettes les enfants qui présentent une anomalie réfractive potentiellement amblyogène sera d'autant plus efficace que cet équipement est fait précocement. Comme pour l'étude ChildSight®, les données issues du projet PlanVue®, confirment la prévalence importante des troubles visuels au sein de la population d'âge scolaire. Il apparaît dès lors que les simples recommandations d'examens visuels mentionnées sur le carnet de santé et réalisés par le médecin généraliste ne suffisent pas au vu du nombre important d'enfants présentant un trouble visuel non corrigé. Cet examen visuel peut aussi réaliser, de façon plus exceptionnelle, un dépistage de pathologies oculaires rares pour lesquelles le dépistage précoce est essentiel, permettant d'éviter un risque visuel majeur (cataracte congénitale, glaucome congénital…) voire vital (rétinoblastome). Ces données justifient ainsi la mise en place d'un programme national de dépistage de troubles visuels à grande échelle, aisément réalisable en milieu scolaire, et par des professionnels paramédicaux comme le préconisent les recommandations britanniques, afin de repérer tous les enfants nécessitant une correction optique, et ce idéalement avant leurs 6 ans. Une des principales limites des données présentées par le projet pilote PlanVue®, est le caractère imprécis des données médicales recueillies. Il conviendrait de réaliser d'autres études avec plus d'enfants dépistés afin de préciser sur un plan médical les troubles visuels. Il pourrait aussi être utile pour de futures études de dépistage visuel chez les enfants d'âge verbal, d'établir un système de classification du risque visuel en fonction de l'anomalie retrouvée, afin de repérer et prioriser les enfants devant être réorientés vers un ophtalmologiste, tout en composant avec la saturabilité du système de soins visuels. [21] Comparison of preschool vision screening tests as administered by licensed eye care professionals in the vision in preschoolers study*1. Ophthalmology 2004;111:637-50. Anomalie à la mesure de l'AV de loin Absence d'anomalie à la mesure de l'AV de loin

Figure 1 :Figure 2 :Figure 3 :Figure 4 :

 1234 Figure 1 : Répartition des réponses des élèves de 8 à 13 ans à la question « As-tu déjà fait un

Figure 5 :Figure 6 :Figure 7 :

 567 Figure 5 : Puissance de l'amétropie cylindrique mesurée au photoscreener (n=1020 yeux)

Figure 1 :Figure 2 :

 12 Figure 1 : Répartition des réponses des élèves de 8 à 13 ans à la question « As-tu déjà fait un

Figure 3 :

 3 Figure 3 : Pourcentage d'enfants porteurs de lunettes au sein de leur classe d'âge (n=116)

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4 : Pourcentage d'enfants présentant une anomalie à la mesure de l'AV de loin en

Figure 7 :

 7 Figure 7 : Proportion de troubles visuels retrouvés chez les enfants ayant consulté un

Remerciements :

Merci à l'association du CADET et à l'ensemble des orthoptistes qui ont procédé au recueil de données au sein des écoles, ainsi qu'à l'association Helen Keller International Europe, qui a permis la réalisation de ce travail en accordant l'accès aux données recueillies.

Déclaration de liens d'intérêts :

Les auteurs déclarent ne pas avoir de conflits d'intérêts.