David Ramsey

Alain Bouscayrol

Loic Boulon

Anatole Desreveaux

Alexandre Vaudrey

Flexible Simulation of an Electric Vehicle to Estimate the Impact of Thermal Comfort on the Energy Consumption

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1 Abstract-The energy consumption of electric vehicles depends on the traction energy but also on the thermal comfort energy. Some studies lead to the estimation of this energy consumption from real measurements on different driving and climatic conditions. However, those results rely on a large number of vehicle tests, which is time consuming. Moreover, the impacts of the different subsystems cannot be differentiated in such global studies. A flexible simulation tool can help to analyze the impact of the different parts of a vehicle. This paper proposes a multiphysical parametrized model of an electric vehicle including the traction and comfort subsystems. A flexible model of a Renault Zoe is developed thanks to the energetic macroscopic representation. This model is validated by experimental tests of the real vehicle. Then, the impact of the HVAC (heating, ventilation, and air conditioning) subsystem is studied for different driving cycles and climatic conditions. In very cold conditions, the use of the HVAC subsystem represents an increase of up to 248% of the total energy consumption, compared to summer conditions. Index Terms-air conditioning, cabin heating, climatic conditions, electric vehicle, energetic macroscopic representation, flexible simulation, HVAC system.

NOMENCLATURE

Main variables β

Recirculation ratio C Heat capacity (J/K) cp Specific heat capacity at constant pressure [J/(kg-

I. INTRODUCTION

ATTERY electric vehicles (BEVs) represent a solution to reduce emissions of greenhouse gasses due to the transport sector [START_REF] Belgin | Making the Case for Electrified Transportation[END_REF]. However, their driving range, initial cost and long charging time limit their widespread adoption [START_REF] Melliger | Anxiety vs Reality -Sufficiency of Battery Electric Vehicles Range in Switzerland and Finlad[END_REF]. Although driving ranges have increased in recent years, they can still be strongly affected when considering the use of the HVAC subsystem for thermal comfort [START_REF] Zhang | The solutions to electric vehicle air conditioning systems: A review[END_REF].

Recent research works on electrified vehicles have focused on their energy storage and management [START_REF] Du | Heuristic Energy Management Strategy of Hybrid Electric Vehicle Based on Deep Reinforcement Learning with Accelerated Gradient Optimization[END_REF], [START_REF] Ehsani | Modern Electric, Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory and Design[END_REF], the development of charging infrastructure [START_REF] Ucer | Modeling and Analysis of a Fast Charging Station and Evaluation of Service Quality for Electric Vehicles[END_REF], the interaction with the power grid (V2G) [START_REF] Ebrahimi | Stochastic Charging Optimization of V2G-Capable PEVs: A Comprehensive Model for Battery Aging and Customer Service Quality[END_REF], and the aging of their battery [START_REF] Jafari | Electric Vehicle Battery Cycle Aging Evaluation in Real-World Daily Driving and Vehicle-to-Grid Services[END_REF], [START_REF] Jaguemont | Lithium-Ion Battery Aging Experiments at Subzero Temperatures and Model Development for Capacity Fade Estimation[END_REF]. Most of these works consider only the traction subsystem in L. Boulon is with Institut de Recherche sur l'Hydrogène, Université du Québec à Trois-Rivières, Trois-Rivières, Québec, G9A 5H7, Canada (email: loic.boulon@uqtr.ca).

A. Vaudrey is with EIGSI La Rochelle, La Rochelle, France (e-mail: vaudrey@eigsi.fr).

Flexible Simulation of an Electric Vehicle to Estimate the Impact of Thermal Comfort on the Energy Consumption

David Ramsey, Alain Bouscayrol, Member, IEEE, Loïc Boulon, Member, IEEE, Anatole Desreveaux, and Alexandre Vaudrey B terms of energy consumption. However, the need for thermal comfort could entail a large variation of the overall energy consumption during the year, especially in regions with very cold winters [START_REF] Reyes | Winter Happens: The Effect of Ambient Temperature on the Travel Range of Electric Vehicles[END_REF]. This means that, for example, the performance of an energy management strategy, or the frequency of battery recharges would also vary during the year. Thus, the energy consumption of the HVAC subsystem should also be considered.

The impact of ambient conditions on the energy consumption has been studied under real driving conditions in [START_REF] Reyes | Winter Happens: The Effect of Ambient Temperature on the Travel Range of Electric Vehicles[END_REF], [START_REF] Al-Wreikat | Effects of ambient temperature and trip characteristics on the energy consumption of an electric vehicle[END_REF]. Results show reductions of 50% to 70% of the driving range under extreme cold conditions. Although the experimental approach highlights the overall impact of ambient conditions, the results are limited to the considered region and time of the study. Furthermore, they consider the combined effects of all factors related to the energy consumption (driving cycle, ambient conditions, desired cabin temperature, etc.), which may vary from one user to another. Finally, this approach requires a large amount of data, which is time consuming.

In contrast, numerical simulations, based on mathematical models, are flexible and enable repeatable and specific studies under various scenarios. Simulation is essential for the development and evaluation of new electrified vehicles [START_REF] Lajunen | Review of Cabin Thermal Management for Electrified Passenger Vehicles[END_REF]. However, an important modeling effort is required. In this context, a flexible simulation of a BEV in its environment will enable more complete studies on its performances under several scenarios and ambient conditions. For this, thermal models of the passenger cabin and the HVAC subsystem must be coupled with electrothermal models of the battery, and electromechanical models of the traction subsystem.

The traction subsystem has been widely studied in the literature [START_REF] Ehsani | Modern Electric, Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory and Design[END_REF]. Recent studies have focused on new powertrain architectures and control (e.g., four-wheel-independently actuated BEVs) [START_REF] Ding | Longitudinal Vehicle Speed Estimation for Four-Wheel-Independently-Actuated Electric Vehicles Based on Multi-Sensor Fusion[END_REF], [START_REF] Guo | Robust Adaptative Fault-Tolerant Control of Four-Wheel Indepdently Actuated Electric Vehicles[END_REF], on quantifying the overall energy consumption [START_REF] Fiori | Power-based electric vehicle energy consumption model: Model development and validation[END_REF], [START_REF] Desreveaux | Impact of the Velocity Profile on Energy Consumption of Electric Vehicles[END_REF], and on accurate driving range estimations [START_REF] Scheubner | A Stochastic Range Estimation Algorithm for Electric Vehicles Using Traffic Phase Classification[END_REF]. A review of trends on electric powertrains can be found in [START_REF] Ehsani | State of the Art and Trends in Electric and Hybrid Electric Vehicles[END_REF]. Regarding the battery pack, several studies have addressed the impact of low temperatures on their performances, as well as their thermal management [START_REF] Yang | Electrothermal Modeling of Lithium-Ion Batteries for Electric Vehicles[END_REF]- [START_REF] German | Dynamical Coupling of a Battery Electro-Thermal Model and the Traction Model of an EV for Driving Range Simulation[END_REF]. However, these studies have not considered thermal comfort.

Regarding the passenger cabin, the lumped-parameters approach has been used by [START_REF] Marcos | The development and validation of a thermal model for the cabin of a vehicle[END_REF]- [START_REF] Wu | Analysis and validation of transient thermal model for automobile cabin[END_REF] to model and validate the cabin of passenger cars, and by [START_REF] Torregrosa | Transient thermal model of a vehicle's cabin validated under variable ambient conditions[END_REF] for a minibus. This approach considers an average cabin temperature and the total heat flows at its boundaries. These models can describe accurately the evolution of the average cabin temperature under different ambient conditions. However, no interconnections with the models of the traction subsystem are presented.

Regarding the HVAC subsystem, the air ventilation circuit can be studied using classical air conditioning models [START_REF]ASHRAE Handbook -Fundamentals[END_REF], [START_REF] Çengel | Thermodynamics: An Engineering Approach[END_REF]. In addition, several studies have focused on the control and optimization of reversible heat pumps [START_REF] Zhang | Energy-Optimal Control of an Automotive Air Conditioning System for Ancillary Load Reduction[END_REF]- [START_REF] Schaut | Thermal Management for th Cabin of a Battery Electric Vehicle Considering Passengers' Comfort[END_REF]. Some include simplified lumped-parameters models to also describe the evolution of the cabin temperature. However, these studies do not consider the large yearly variation of the cabin thermal needs, nor the reduced performances of heat pumps at very low temperatures. Moreover, experimental studies have analyzed the performances of heat pumps and electric heaters of electrified vehicles under extreme cold conditions [START_REF] Kim | Experimental Studies on the Heating Performance of the PTC Heater and Heat Pump Combined System in Fuel Cells and Electric Vehicles[END_REF]- [START_REF] Park | Heating Performance Characteristics of High-Voltage PTC Heater for an Electric Vehicle[END_REF]. In particular, Kim et al. [START_REF] Kim | Experimental Studies on the Heating Performance of the PTC Heater and Heat Pump Combined System in Fuel Cells and Electric Vehicles[END_REF] quantified the variation of the performance of a heat pump as a function of the ambient temperature. In these studies, no interconnections with the models of the traction subsystem are presented.

Finally, regarding the system interconnection, Neubauer et al. [START_REF] Neubauer | Thru-life impacts of driver aggression, climate, cabin thermal management, and battery thermal management on battery electric vehicle utility[END_REF] from the National Renewable Energy Laboratory studied the performances of BEVs considering the ambient conditions of several cities in the United States, using an internally developed simulation tool. However, this study does not describe the modeling process, nor the experimental validations.

Despite the numerous existing models for the main subsystems of a BEV, an interconnection between them is rarely described. The development of a complete model is a challenging task, because it requires several complex models from different physical domains (i.e., thermal, electrical and mechanical), as well as their control and energy management (e.g., regenerative braking). Thus, an appropriate model organization is necessary. In this context, Horrein et al. [START_REF] Horrein | Influence of the heating system on the fuel consumption of a hybrid electric vehicle[END_REF] used the Energetic Macroscopic Representation (EMR) formalism [START_REF] Bouscayrol | Graphic formalisms for the control of multi-physical energetic system: COG and EMR[END_REF] to develop a simplified model of the cabin and the electric heater of a hybrid electric vehicle and coupled it with the traction subsystem. This work studied the impact of electric heating on the energy consumption for mild winter scenarios. Likewise, German et al. [START_REF] German | Dynamical Coupling of a Battery Electro-Thermal Model and the Traction Model of an EV for Driving Range Simulation[END_REF] coupled an EMR-based electrothermal battery model with that of a traction subsystem to study the evolution of the battery temperature during driving (the comfort subsystem is not considered). The EMR formalism is based on a systemic modeling approach and organizes models according to their energetic function in the system, rather than their physical structure [START_REF] Chan | Electric, Hybrid, and Fuel-Cell Vehicles: Architectures and Modeling[END_REF]. Thus, it considers the dynamic interactions between subsystems and facilitates the interconnection of multi-domain models into a unified simulator. In this paper, EMR is used to interconnect the models of the traction and comfort subsystem to develop a flexible simulation of a BEV.

Most simulation tools are based on a structural approach, where models strictly respect the physical topology of a system. These tools propose integrated libraries of predefined models, which facilitates the model interconnection for users. However, this approach could entail conflicts of association between variables, difficulties to modify the granularity of models and difficulties to define control schemes [START_REF] Chan | Electric, Hybrid, and Fuel-Cell Vehicles: Architectures and Modeling[END_REF]. On the contrary, a functional organization of models (based on physical causality) leads to a prior solving of association conflicts. This enables seamless modifications of subsystem models and a systematic deduction of control schemes [START_REF] Bouscayrol | Graphic formalisms for the control of multi-physical energetic system: COG and EMR[END_REF]. This functional-based simulation, organized through the EMR formalism, allows to estimate the energy consumption, and quantify the individual impacts of ambient conditions at a system and subsystem level. This flexibility is achieved by the unified organization approach, which allows to readily include, remove, or modify a model of a subsystem and adapt its control, without affecting the rest of the system.

The objective of this paper is to develop a flexible simulation of a BEV in its environment. This simulation tool will enable studies on the impact of thermal comfort on the energy consumption in various ambient conditions. The EMR formalism is used to organize and interconnect models of the main subsystems of a commercial BEV: a Renault Zoe (BEV of a French Automaker) [START_REF]Renault ZOE 2018 Datasheet[END_REF]. The ambient conditions considered are ambient and sky temperatures, solar irradiance, and relative humidity. The accuracy of the simulation is verified by experimental tests on the real BEV. Finally, an energy consumption study is performed using real data of ambient conditions in a Canadian region. The main contributions of this paper are the interconnection and the experimental validation of multi-domain models of the passenger cabin, the HVAC subsystem and the traction subsystem of a BEV. In a previous work, the traction subsystem of a Renault Zoe has been modeled and validated by driving tests on a real vehicle [START_REF] Desreveaux | Impact of the Velocity Profile on Energy Consumption of Electric Vehicles[END_REF]. Moreover, an EMR-based model describing the interaction between the cabin and ambient air has also been developed and validated in [START_REF] Ramsey | Simulation of an electric vehicle to study the impact of cabin heating on the driving range[END_REF]. The cabin model is now completed by considering the effects of solar and sky radiation. In addition, the model and control of an HVAC subsystem are included. Finally, all the models are interconnected. Section II deals with the models of the BEV subsystems. In Section III, the simulation is validated by experimental measurements on a real BEV. Finally, the energy consumption of the thermal comfort subsystem is studied in Section IV.

II. MODELING OF THE STUDIED ELECTRIC VEHICLE

The studied vehicle (Fig. 1) is composed of a Li-ion battery, the traction and HVAC subsystems, and the rest of ancillaries. All models are organized and interconnected with EMR [START_REF] Bouscayrol | Graphic formalisms for the control of multi-physical energetic system: COG and EMR[END_REF]. In EMR, all elements are represented by pictograms, according to their energetic behavior. Thus, regardless of their physical domain or their real structure, elements can only be depicted as energy sources (green ovals), energy accumulators (orange crossed rectangles), monodomain or multidomain energy converters (orange squares or circles), and energy distributors (overlapped orange squares or circles). This feature facilitates the organization and interconnection of models from complex multi-domain systems, as well as the development of their control structures. In addition, the interaction principle is considered by the 2 arrows connecting the pictograms. The product of the action and reaction variables always yields the instantaneous power being exchanged between elements. This feature facilitates the analysis of energy transfers within the system. By using the EMR formalism, a systemic approach is adopted [START_REF] Chan | Electric, Hybrid, and Fuel-Cell Vehicles: Architectures and Modeling[END_REF]. Thus, the dynamic interactions between subsystems and with the environment of the vehicle are considered.

+ - u b i b Anc i anc F total i trac i hvac v Q hvac Q cab T amb T cab

A. Model of the traction subsystem

The traction subsystem considers the battery, an electric drive, a mechanical transmission, the inertia of the vehicle and the rest of ancillaries. Since it has already been widely studied in the literature, a simplified quasi-static model is presented. Fig. 2 shows the EMR and control structure of this subsystem. The battery pack is depicted as an energy source imposing its terminal voltage ub to all the subsystems of the vehicle. This voltage is a function of the open-circuit voltage OCV, the state of charge SoC, the current ib, and an equivalent internal resistance Rb. The current ib is the sum of those absorbed by each subsystem. The current ihvac is obtained from the model of the HVAC subsystem, and the current ianc is obtained by considering a constant power demand from the rest of ancillaries. These parallel connections are described by an energy distribution element. Since this study is focused on the thermal comfort, the temperature effects on the battery are not considered. However, an EMR-based electrothermal battery model has already been developed in [START_REF] German | Dynamical Coupling of a Battery Electro-Thermal Model and the Traction Model of an EV for Driving Range Simulation[END_REF] and will also be considered in future works

u b = OCV(SoC) -R b i b () i b = i trac +i hvac +i anc ()
A static model describes the coupling of the electric drive (ED) and the mechanical transmission (MT) as a controlled electromechanical converter [START_REF] Dépature | Characterisation of the electric drive of EV: on-road vs off-road method[END_REF]. This converter imposes the traction force Ftrac, which is equal to its reference. Moreover, the current itrac is obtained from ub, Ftrac, the velocity v and a global efficiency η. This global efficiency is based on the efficiency map of the electric drive of the Renault Zoe [START_REF]Report on the virtual testing of the BEV[END_REF] and a constant efficiency for the mechanical transmission (Fig. 3).

{ i trac = F trac v u b ηk F trac =F trac-ref , with k=sign(F trac v) ()
Mechanical brakes are depicted by a controlled energy source imposing the braking force Fbk. The total force acting on the vehicle Ftotal is the sum of Ftrac and Fbk.

{ F total = F trac +F bk F bk =F bk-ref ()
The mechanical inertia of the vehicle is depicted as an energy accumulation element imposing its velocity v, which is obtained from the vehicle mass M, the total force Ftotal, and the driving resistance forces Fres.

d dt v= 1 M (F total -F res ) ()
Finally, the driving resistance force Fres is the sum of the rolling resistance Froll and the aerodynamic drag Fdrag [START_REF] Ehsani | Modern Electric, Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory and Design[END_REF]. The force Fdrag is a function of the air density, and thus is also influenced by ambient conditions (Tamb and ωamb) [START_REF] Heißing | Driving Dynamics[END_REF].

F res =F roll + F drag (T amb , ω amb ) ()
From the EMR, an inversion-based control is deduced. Moreover, a strategy imposes a coefficient kd-trac to distribute the braking effort during regenerative braking. The regenerative braking strategy considers the velocity, the braking effort distribution between both axles and the limits of the electric drive [START_REF] Ehsani | Modern Electric, Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory and Design[END_REF]. More details and the model validation using a real vehicle can be found in [START_REF] Desreveaux | Impact of the Velocity Profile on Energy Consumption of Electric Vehicles[END_REF]. Classical studies consider this type of model to estimate the energy consumption of BEVs. Some studies consider a constant power for the HVAC consumption, others neglect it. The rest of this section presents the modeling of the passenger cabin and HVAC subsystems.

B. Model of the passenger cabin

The passenger cabin model is based on the lumpedparameters approach: each body is considered as an equivalent thermal node and temperature gradients are neglected [START_REF] Torregrosa | Transient thermal model of a vehicle's cabin validated under variable ambient conditions[END_REF]. Fig. 4 shows the structure of the passenger cabin and the HVAC subsystem. The considered heat rates are internal and external convection (Q ̇conv), thermal radiation between internal surfaces (Q ̇rad), conduction through the roof (Q ̇cond), the heat produced by passengers (Q ̇pass), the heat supplied or removed by the HVAC subsystem (Q ̇hvac), and solar (Q ̇sol-abs) and sky (Q ̇rad-sky) radiation. Moreover, all heat rates into the cabin are considered positive and heat transfers through doors and floor panels are neglected.

Since heat rates Q ̇ are already rates of energy transfers (power), the property entropy S is included in the EMR-based modeling. Thus, entropy flows Ṡ at the boundaries of a body are a function of its temperature T and the heat rates

Q ̇. S = Q T ()
The EMR of the passenger cabin is shown in Fig. 5. The considered thermal nodes (and temperatures) are the cabin air (Tcab), the equivalent interior masses (i.e., dashboard, seats, etc.) (Tim), the ceiling (Tceil), the roof (Troof), and the windows (Tg). These nodes are represented as energy accumulation elements (orange crossed rectangle).

The temperature evolution of each node (i) depends on their equivalent thermal capacity Ci, and the total entropy flows entering Ṡi-in and exiting Ṡi-out [START_REF] Jafari | Electric Vehicle Battery Cycle Aging Evaluation in Real-World Daily Driving and Vehicle-to-Grid Services[END_REF]. These total entropy flows are obtained from entropy balances at the boundaries of each node [START_REF] Jaguemont | Lithium-Ion Battery Aging Experiments at Subzero Temperatures and Model Development for Capacity Fade Estimation[END_REF] and are depicted as energy distribution elements (overlapped orange squares). Moreover, vector notation (i.e., square brackets) is used to denote the temperatures of all windows [Tg], all internal surfaces [Tis], all external surfaces [Tes], and their corresponding entropy flows.

T i =T i 0 exp ( 1 C i ∫ (S i-in -S i-out )dt) () { S i-in = ∑ S in S i-out = ∑ S out ()
Heat rates Q ̇ between 2 nodes at different temperatures (Thot and Tcold) depend on the heat transfer mechanism: conduction Q ̇cond, convection Q ̇conv or radiation Q ̇rad [START_REF]ASHRAE Handbook -Fundamentals[END_REF], and are depicted by monodomain energy conversion elements (orange squares). The equivalent entropy flows are then obtained from [START_REF] Ebrahimi | Stochastic Charging Optimization of V2G-Capable PEVs: A Comprehensive Model for Battery Aging and Customer Service Quality[END_REF]. More modeling details can be found in [START_REF] Ramsey | Simulation of an electric vehicle to study the impact of cabin heating on the driving range[END_REF].

S cond-hot = Q cond T hot & S cond-cold = Q cond T cold () S conv-hot = Q conv T hot & S conv-cold = Q conv T cold () S rad-hot = Q rad T hot & S rad-cold = Q rad T cold ()
Passengers are considered as an energy source imposing their generated entropy flow Ṡpass, which is obtained from their generated sensible Q ̇sensible and latent Q ̇latent heat rates [START_REF]ASHRAE Handbook -Fundamentals[END_REF].

S pass = Q senible + Q latent T cab ()
For the absorbed solar irradiance, the entropy flow Ṡsol-i depends on the total incident irradiance on each surface Gi (W/m 2 ), the surface area Ai, and the absorptivity of the material αi. For interior masses, the entropy flow also depends on the transmissivity of windows τg. Solar irradiance (depicted as an energy source) can be either obtained from measures or estimated using an isotropic sky model, as described in [START_REF] Duffie | Solar Engineering of Thermal Processes[END_REF].

{ S sol i = α i G i A i T i
for external surfaces

S sol im =α im ∑ τ g i G i A i T im
for interior masses

()
Finally, ambient air and the sky are energy sources imposing their temperatures Tamb and Tsky. Sky temperatures can be estimated from correlations described in [START_REF] Berdahl | The Thermal Radiance of Clear Skies[END_REF] and [START_REF] Algarni | Survey of Sky Effective Temperature Models Applicable to Building Envelope Radiant Heat Transfer[END_REF].

C. Model of the HVAC subsystem

The HVAC subsystem (see Fig. 4) is composed of the air ducts, a recirculation flap, an air blower, the air vents and two heat sources: an electric heater and a reversible heat pump (HP). The reversible heat pump supplies heat during winter and absorbs it in summer.

To model this subsystem, a control volume (CV) is considered around the heat pump and the electric heater [START_REF] Çengel | Thermodynamics: An Engineering Approach[END_REF]. Thus, the blown air enters the cabin at a temperature Tcv. This approach is used to facilitate the control of the system and the experimental validation. Moreover, the condensation of water vapor in summer could represent an additional latent heat load on the heat pump [START_REF]ASHRAE Handbook -Fundamentals[END_REF]. This is considered by including the humidity ratios ω (ratio of the mass of water vapor to the mass of dry air) in the model. Humidity ratios are obtained from the ambient humidity, and from mass balances in the cabin and the control volume [START_REF]ASHRAE Handbook -Fundamentals[END_REF], [START_REF] Çengel | Thermodynamics: An Engineering Approach[END_REF].

The air vents are depicted by an energy conversion element. The heat flow leaving the control volume (and entering the cabin) Q ̇hvac depends on the mass rate of blown air ṁ, the humidity ratio in the control volume ωcv, the specific heat capacities of dry air cp-da and water vapor cp-vap and the temperature Tcv [START_REF]ASHRAE Handbook -Fundamentals[END_REF]. Only sea level pressure is considered. The corresponding entropy flows are obtained from [START_REF] Ebrahimi | Stochastic Charging Optimization of V2G-Capable PEVs: A Comprehensive Model for Battery Aging and Customer Service Quality[END_REF]. [START_REF] Guo | Robust Adaptative Fault-Tolerant Control of Four-Wheel Indepdently Actuated Electric Vehicles[END_REF] +ω cv (2.5e6 +c p-vap (T cv -273. [START_REF] Guo | Robust Adaptative Fault-Tolerant Control of Four-Wheel Indepdently Actuated Electric Vehicles[END_REF]) )]

{ Q hvac =m [c p-da (T cv -273.
S hvac = Q hvac T cab & S cv-out = Q hvac T cv ()
The total entropy flow entering the control volume Ṡcv-in is the sum of the entropy flow coming from the blown air Ṡair-in, and that generated by the electric heater Ṡheater and the reversible HP Ṡhp. The control volume is depicted by an accumulation element imposing its temperature Tcv, also obtained from ( 8)

S cv-in =S air-in +S heater +S hp ()
The net heat rate of blown air Q ̇air-in depends on that of fresh air Q ̇fresh and recirculated air Q ̇rec. These rates depend on the mass rate ṁ, the recirculation ratio β, and the ambient and cabin temperatures (Tamb and Tcab) and humidity ratios (ωamb and ωcab).

Q air-in = Q fresh + Q rec S air-in = Q air-in T cv ()
Likewise, the heat rate of the air leaving the vehicle Q ̇air-out when there is an input of fresh air depends on the recirculation ratio β, the mass rate ṁ, and the cabin conditions Tcab and ωcab. It is assumed that the mass rate of air leaving is equal to that of the fresh air entering. The corresponding entropy flow Ṡair-out is obtained from [START_REF] Ebrahimi | Stochastic Charging Optimization of V2G-Capable PEVs: A Comprehensive Model for Battery Aging and Customer Service Quality[END_REF].

{ Q air-out = (1-β)m [c p-da (T cab -273.15) +ω cab (2.5e6 +c p-vap (T cab -273.15))] S air-out = Q air-out T cab ()
The electric heater is considered as a controlled electrothermal converter and is depicted by a multidomain energy conversion element (orange circle). Thus, the generated entropy flow Ṡheater equals its reference Ṡheater-ref. The consumed electric current iheater is obtained from Ṡheater, the voltage ub, and the temperature Tcv. The total current absorbed by the whole HVAC subsystem ihvac is the sum of iheater and ihp. The power consumption of the blower is included with the rest of ancillary loads.

i hvac =i heater +i hp ()
From the EMR (see Fig. 5), a control scheme can be obtained by direct inversion of each block between the objective variable (the cabin temperature Tcab) and the control variables (the reference entropy flows Ṡhp-ref and Ṡheater-ref). It should be noted that the presented control structure is ideal and quite different from that used in real automotive HVAC systems. Indeed, the control of a heat pump is much more complex, because it is necessary to regulate the pressures of the heat exchangers, as well as the mass flow of the refrigerant [START_REF] Zhang | Energy-Optimal Control of an Automotive Air Conditioning System for Ancillary Load Reduction[END_REF]. However, the presented approach suffices from an energetic standpoint, because it allows to estimate the amount of heat required to regulate the temperature of the passenger cabin. This is verified with the experimental tests presented in Section III.

To consider the performance limitations of heat pumps at low temperatures, the maximal generated entropy Ṡhp and the COP are limited according to the experimental results presented in [START_REF] Kim | Experimental Studies on the Heating Performance of the PTC Heater and Heat Pump Combined System in Fuel Cells and Electric Vehicles[END_REF]. Moreover, a strategy imposes a coefficient kd-hvac to distribute the entropy flow generated by the heat pump and the electric heater. In this study, the heat pump is always prioritized. When it cannot supply all the heat needed in winter, the electric heater starts working. Further, the heat pump is considered to stop working at ambient temperatures below -15 °C [START_REF] Kim | Experimental Studies on the Heating Performance of the PTC Heater and Heat Pump Combined System in Fuel Cells and Electric Vehicles[END_REF]. Finally, a maximal heating power of 5 kW is considered for the electric heater.

III. VALIDATION OF THE MODELS

Three experimental tests have been performed on a commercial BEV, a Renault Zoe, to validate the developed models. The traction subsystem alone has already been validated experimentally in [START_REF] Desreveaux | Impact of the Velocity Profile on Energy Consumption of Electric Vehicles[END_REF]. Regarding the parameters needed for the thermal models, the large majority have been obtained from previous studies [START_REF] Marcos | The development and validation of a thermal model for the cabin of a vehicle[END_REF], [START_REF] Torregrosa | Transient thermal model of a vehicle's cabin validated under variable ambient conditions[END_REF], [START_REF] Rashid | Thermal management of Vehicle Interior Temperature for Improvement of Fuel Economy[END_REF], from tables of thermophysical properties for the materials used in automotive applications [START_REF]ASHRAE Handbook -Fundamentals[END_REF], [START_REF] Çengel | Thermodynamics: An Engineering Approach[END_REF], and from the datasheet of the Renault Zoe [START_REF]Renault ZOE 2018 Datasheet[END_REF]. Table I shows the main parameters used in the simulation. Fig. 6 shows the equipment used during the validation tests. The first test is performed to validate the passenger cabin model. In this test, the vehicle is parked outdoors for 10 hours. Solar irradiance, and the temperatures of the cabin and external air are recorded. Then, the same scenario is simulated, using the measured irradiance and external air temperature as inputs.

Fig. 7a shows the measured solar irradiance. The variations after 13:00 are due to cloud movements. Fig. 7b shows that the evolution of the measured and simulated cabin temperatures are similar. The maximal absolute error is 3.5 °C and the RMS error is 1.74 °C. Thus, the accuracy of the cabin model is verified. An indoors validation of this model (neglecting solar irradiance) can be found in [START_REF] Ramsey | Simulation of an electric vehicle to study the impact of cabin heating on the driving range[END_REF].

The second test is performed to validate the HVAC model and its control in cooling mode. For this, the vehicle is parked outdoors on a hot, partly cloudy day. The recorded measurements are solar irradiance, cabin and external air temperatures, and the air flow rate and temperature at the vents. The same scenario is simulated, using the measured irradiance, air flow rate and external air temperature as inputs. The desired cabin temperature is set to 21 °C. Fig. 8 shows the validation results. Simulated and measured temperatures evolve similarly. The maximal absolute error for the cabin temperature is ±3 °C, during the transient state.

During the steady state, the absolute error is less than 1 °C. The RMS error (considering the whole test) is 0.83 °C.

To control the temperature of the cabin air, the HVAC subsystem acts upon the air flowing into the cabin (Tcv in the model). Thus, a good accuracy for both temperatures (cabin and vents) also means a good estimation of the cabin thermal needs and a good control of the HVAC subsystem. Therefore, the accuracy of the global model is verified.

The third test is performed to validate the interconnection of the traction and passenger comfort models. In this test, the vehicle is driven on a cold morning (Tamb ≈ -5 °C); thus, the HVAC subsystem is in heating mode. Ambient, cabin and vents temperatures, as well as the air flow rate are recorded. In addition, battery current and voltage measurements are extracted from the CAN network of the vehicle. The velocity is recorded with a GPS device. Measured solar irradiance at the time of the test was ~100 W/m2.

The same scenario is simulated, using the measured velocity, ambient conditions, and air flow rate as inputs. Fig. 9 shows the validation results. Simulated and measured temperatures, as well as the battery power evolve similarly. The error for the total energy consumption is 2.7%. Thus, the interconnected model is also verified.

The presented experimental results firstly verify the accuracy of the model for the passenger cabin alone; then, of the coupling of the passenger cabin with the HVAC subsystem and its control; finally, of the interconnection of the 3 subsystems. The considered tests include summer and winter scenarios, and all the results show that the simulated temperatures evolve similarly to the measured ones. Finally, the small error between the simulated and measured energy consumption for the last test (interconnected system), shows that the developed simulation can be used to estimate the energy consumption considering thermal comfort and real ambient conditions.

IV. VARIATION OF THE OVERALL ENERGY CONSUMPTION DUE TO THERMAL COMFORT

The previous sections showed the development of an interconnected BEV model and its environment, as well as the validation tests. In this section, 2 energetic studies are performed. The first one is the contribution of the traction and HVAC subsystems to the overall energy consumption under different constant climatic scenarios. The second study is the yearly variation of the energy consumption using real data for ambient conditions in a cold region. For both studies, 3 types driving cycles are considered: urban, extra-urban and highway (the latter was obtained from real measures) (Fig. 10).

A. Distribution of the energy consumption per subsystem

The first study is the estimation of the distribution of the energy consumption under different climatic scenarios (summarized Table II). For all cases, the desired cabin temperature is 20 °C and all initial temperatures are equal to the ambient temperature (no preconditioning). Finally, all simulations consider the same driving time (1 hour) to ensure the same consumption time for the HVAC subsystem. [START_REF] Du | Heuristic Energy Management Strategy of Hybrid Electric Vehicle Based on Deep Reinforcement Learning with Accelerated Gradient Optimization[END_REF] 10 °C 50% Cloudy Sc. [START_REF] Ehsani | Modern Electric, Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory and Design[END_REF] 20 °C No thermal comfort (references) Sc. [START_REF] Ucer | Modeling and Analysis of a Fast Charging Station and Evaluation of Service Quality for Electric Vehicles[END_REF] 30 °C 50% Clear Sc. [START_REF] Ebrahimi | Stochastic Charging Optimization of V2G-Capable PEVs: A Comprehensive Model for Battery Aging and Customer Service Quality[END_REF] 40 °C 50% Clear Fig. 11 shows the results for the distribution of the total energy consumption for each considered case. As expected, the minimal energy consumption (for each driving cycle) is for scenario 5: Tamb = 20 °C and no HVAC. This scenario is taken as the reference. Thus, for each driving cycle, the variations of the energy consumption are calculated from the total energy consumption at each temperature (including the rest of ancillaries) and the energy consumption at 20 °C. As the climatic conditions change, the need for thermal comfort and the total energy consumption increase accordingly.

The results show that, besides climatic conditions, the impact of the HVAC subsystem on energy consumption strongly depends on the driving cycle. Urban cycles are characterized by short distances and a high number of stops (traffic lights, stop signs, etc.). This means that the HVAC subsystem and the rest of ancillaries continue to consume energy when the vehicle is not moving. This can result on a great increase of the overall energy consumption. For extreme cold scenarios, the HVAC subsystem can even become the main load on the battery.

Indeed, there is an inverse relationship between the energy consumption per kilometer of the traction and HVAC subsystems. Urban cycles have low average speeds and require low energy for traction. Thus, thermal comfort represents an important increase of total energy consumption (in Wh) over relatively short distances (km). Moreover, the power required for traction and the distance traveled increase with the extraurban and highway cycles (over the same driving time). Therefore, the impact of thermal comfort on the energy consumption per kilometer (in Wh/km) decreases, whereas that of the traction subsystem increases. This concept is summarized in Table III, using the results for scenario 2 (Tamb = -10 °C). This table shows that the total energy consumption (in Wh) of the traction subsystem increases from the urban cycle to the highway one, while that of the HVAC subsystem remains very similar. Since all simulations consider the same driving time, the average power and energy consumption of the HVAC subsystem is similar for all 3 driving cycles. Thus, the impact of the HVAC subsystem on the overall energy consumption depends not only on climatic conditions, but also on the average speed of the driving cycle. As the average speed increases, the impact of the HVAC subsystem decreases. This allows for an analysis of the benefits of a passive driving style. Traditionally, a passive driving style, with smooth accelerations and low speeds, is considered more energy efficient. However, when the need for thermal comfort becomes important, a shorter driving time (and therefore higher speeds) can become advantageous from an energetic point of view.

B. Variation of the energy consumption with real ambient conditions

The second study is the yearly variation of the energy consumption with ambient conditions and the driving profile. For this, the climate of Regina (Canada) is considered. This region is chosen for its wide variation of ambient temperatures, which can range from -30 °C to 30 °C over a year (Fig. 12). For this study, a simulation is performed for each day of the year at the same hour (11:00). Real data for ambient temperature and humidity, sky temperature and solar irradiance, obtained from [START_REF] Amelie | Baseline Surface Radiation Network (BSRN): structure and data description (1992-2017[END_REF], are used as inputs in the simulations. Moreover, the 3 driving cycles in Fig. 10 are considered. The desired cabin temperature is 20 °C for all cases, except when ambient temperature is between 18 °C and 23 °C (no need for thermal comfort). All simulations consider one passenger and no preconditioning. The driving time is still 1 hour. Fig. 13 presents the results of the simulations. First, we see that the energy consumption remains almost constant if only the traction subsystem is considered (classical energetic studies). In this case, the energy consumption just depends on the driving profile. For the highway profile, the slight increase at low temperatures is due to air density and the aerodynamic drag.

On the other hand, a large variation in consumption is obtained by considering the interconnection with the HVAC subsystem. In addition, we can still see that the impact of ambient conditions is much greater on the urban cycle. For this type of profile, the estimated energy consumption ranges from 120 Wh/km at 20 °C, up to 418 Wh/km at very low temperatures: an increase of 248%. For the extra-urban cycle, the overall energy consumption varies from 136 Wh/km at 20 °C, up to 266 Wh/km, an increase of 95%. The highway cycle is the least impacted by the ambient conditions, with an increase in consumption of 43%.

The results also show that a maximal value of the energy consumption is attained at very low ambient temperatures. As aforementioned, the developed model considers that the heat pump stops working when the ambient temperature drops below -15 °C [START_REF] Kim | Experimental Studies on the Heating Performance of the PTC Heater and Heat Pump Combined System in Fuel Cells and Electric Vehicles[END_REF]. At this point, only the electric heater is functional. However, the model also considers a maximal power of 5 kW for the electric heater. Thus, when the cabin thermal needs surpass this maximal heating power, the total energy consumption is capped by the maximal capacity of the HVAC subsystem. Finally, Fig. 14 shows the monthly variation of the energy consumption by considering the 3 types of cycles and the interconnected system. The results show the very sharp contrast of the energy consumption between November and March (cold months), and that between April and October. Depending on the driving profile, the estimated energy consumption in winter ranges from 160 to 418 Wh/km. In summer, it ranges from 120 to 200 Wh/km. V. CONCLUSION This paper presents the interconnection of thermal and electromechanical models for the passenger cabin, the HVAC subsystem and the electric powertrain of a BEV. From the interconnected models, a flexible simulation of a BEV and its environment is developed thanks to a functional graphical description. The simulation is validated by experimental measurements taken on a real vehicle. The simulation then is used to estimate the contributions of the traction and HVAC subsystems to the overall energy consumption by considering 3 types of driving cycles. Finally, the yearly variation of the energy consumption is quantified under a wide range of real ambient conditions.

The results show the strong impact of thermal comfort on the overall energy consumption, especially for urban driving profiles in very cold conditions. Indeed, in extreme temperatures, the HVAC subsystem can even outweigh the traction subsystem in terms of energy consumption. Furthermore, the results show a yearly variation of the overall energy consumption of 248% in a Canadian climate (due to their very cold winters).

The next step is to include a thermal model of the battery, such as the one developed using EMR in [START_REF] German | Dynamical Coupling of a Battery Electro-Thermal Model and the Traction Model of an EV for Driving Range Simulation[END_REF]. Indeed, the battery thermal behavior is a key factor in the performance of the vehicle. In addition, a more complex model of the traction parts can be included, such as the effect of temperature on the wheel-road contact. Likewise, an advanced model of the HVAC subsystem could also consider the dehumidifier operation mode. The global model will enable more complete studies on BEVs at different climates, including the analysis of performance-improving guidelines (e.g., cabin and battery preheating). Finally, the presented models for the cabin and ventilation subsystems can also be adapted to thermal and hybrid vehicles. Future work could explore this adaptation by also considering an EMR-based model of an internal combustion engine and the use of waste heat, such as in [START_REF] Horrein | Influence of the heating system on the fuel consumption of a hybrid electric vehicle[END_REF].

VI. ACKNOWLEDGMENTS

This paper has been achieved within the framework of the International ssociated Laboratory "e-C M US" of University of Lille (France) and University of Québec à Trois-Rivières Canada , and with the funding of the Region "Hautsde-France" The experimental tests have been done using the "electricity & Vehicles" platform of the L2EP of Lille, France.

Fig. 1 :

 1 Fig. 1: Simplified structure of the studied BEV.

Fig. 2 :

 2 Fig. 2: EMR and inversion-based control of the traction subsystem.

Fig. 3 :

 3 Fig. 3: Efficiency map considered for the electric powertrain.

Fig. 4 :

 4 Fig. 4: Structure of the HVAC subsystem and the passenger cabin.

{

  Q fresh = (1-β)m [c p-da(T amb -273.15) +ω amb (2.5e6 +c p-vap (T amb -273.15))] Q rec = βm [c p-da (T cab -273.15) +ω cab (2.5e6 +c p-vap (T cab -273.15))]

Fig. 5 :

 5 Fig. 5: EMR and inversion-based control of the HVAC subsystem and the passenger cabin.

Fig. 6 :

 6 Fig. 6: Equipment used to measure data in validation tests.

Fig. 8 :

 8 Fig. 8: HVAC model validation. a) Solar irradiance. b) Temperatures.

Fig. 7 :

 7 Fig. 7: Cabin model validation. a) Solar irradiance. b) Temperatures.

Fig. 9 :

 9 Fig. 9: Validation of the interconnected model. a) Velocity. b) Temperatures. c) Battery power.

Fig. 10 :

 10 Fig. 10: Considered driving cycles.

Fig. 11 :

 11 Fig. 11: Distribution of the energy consumption. a) Urban cycle. b) Extraurban cycle. c) Highway cycle.

Fig. 12 :

 12 Fig. 12: Monthly variation of the ambient temperature in Regina.

Fig. 13 :

 13 Fig. 13: Yearly variation of the energy consumption. a) Urban cycle. b) Extraurban cycle. c) Highway cycle.

Fig. 14 :

 14 Fig. 14: Monthly variation of the energy consumption of a BEV in Canada.

TABLE II CONSIDERED

 II AMBIENT SCENARIOS (CONSTANTS)

	Scenario	Temperature	Relative humidity	Sky conditions
	Sc. 1	-20 °C	50%	Cloudy
	Sc. 2	-10 °C	50%	Cloudy
	Sc. 3	0 °C	50%	Cloudy
	Sc.


Pascal Roblot

Franck Morelb

Eric Leli&reb

Marie-Hcl&ne Biais-Sauv&treb

Donat De Grootec

Jean-Louis Preud'hommeb

Jean-Claude Lecronb

Serum soluble CD23 levels in giant cell arteritis'

Keywords: Giant cell arteritis, Soluble CD23, Inflammation, Corticotherapy '

Lymphocytes

and monocytes express various levels of membrane-bound CD23, the low affinity receptor for IgE (FceRII), and in some cases release it as a soluble form. Soluble CD23 (sCD23) has been implicated in the regulation of many immunological functions of T and B lymphocytes, macrophages and myeloid cells in humans. To study serum sCD23 levels in inflammatory conditions, we selected a systemic disease sensitive to corticotherapy, the giant cell arteritis, which is characterized by an inflammation of the temporal artery. Serum sCD23 levels, as measured by a radioimmunoassay, were increased in these patients, and returned to normal values within the 24 h following initiation of corticotherapy. The data suggest that the increase in sCD23 levels in giant cell arteritis results from an overproduction.

Introduction

Giant cell arteritis (GCA) is a vasculitis syndrome affecting the blood vessels, the walls of which contain significant amounts of elastic tissue, as the superficial temporal, ophtalmic and posterior ciliary arteries. Arterial biopsies reveal a panarteritis with inflammatory infiltration by T lymphocytes, macrophages and giant cells. There is an important chronic inflammatory syndrome with increased levels of acute phase proteins, including haptoglobin, al acid glycoprotein and C-reactive protein (CRP). Glucocorticoids usually induce a dramatic and rapid improvement of clinical symptoms whereas pathological lesions may persist for several months. The etiology of GCA remains obscure. How-*Corresponding author. Tel.: + 33 49 444324; fax: + 33 49 444383. ever, it has been suggested that cell-mediated immunity might be involved in the disease [1,2].

The 45 kDa CD23 surface antigen was first described as a B cell restricted antigen expressed at high density by Epstein-Barr virus transformed lymphoblastoid cell lines and cells from chronic lymphocytic leukemia, and at a low density by normal B cells. CD23 was then identified as the low-affinity receptor for IgE (FccRII) and found to be also weakly expressed on monocytes/ macrophages, eosinophils, platelets, follicular dendritic cells, Langherans cells, thymic epithelial cells and T cells [3]. CD23 is a member of the superfamily of type C animal lectins and it is a type II glycosylated transmembranous protein [4]. On the other hand, a 25 kDa stable soluble form of the CD23 molecule (sCD23) is spontaneously shed from the surface of most CD23bearing cells such as lymphoblastoid or activated normal B cells [3]. Human sCD23 still reacts with anti-CD23 monoclonal antibodies and binds IgE. Interestingly, several biological activities have been ascribed to sCD23, such as the control of human IgE synthesis, the regulation of B and T lymphocyte differentiation and proliferation, the differentiation of myeloid precursors and germinal centers B cells, and the inhibition of monocyte migration [3]. Recently, sCD23 has been described as an enhancer of monokine release by purified monocytes [5,6] and indirectly a potent costimulator of IL-2 or IL-12 induced IFN-y production by resting T lymphocytes [6].

sCD23 is detectable in normal sera. High levels of serum CD23 have been reported in hematological malignancies such as chronic lymphocytic and hairy cell leukemias [7]. In allergy and inflammatory diseases involving a B cell response, such as rheumatoid arthritis, Sjogren's syndrome, systemic lupus erythematosus or Kawasaki disease, increased levels of sCD23 have been reported also [8-111. Serum sCD23 levels are also high in dialysed chronic uremic patients [12]. The aim of this study was to analyse serum levels of sCD23 in a chronic inflammatory disease before and during corticotherapy.

Materials and methods

Twenty-five patients with biopsy-proven GCA were included in this prospective study, after informed consent. They were given 1 mg . kg-'. day -' prednisone (two thirds of the dosage at 0800 h, one third at 1200 h, no more than 60 mg + day -') during the first month of therapy with a progressive reduction during the next months. Blood samples were obtained at 0800 h, before treatment and after 1, 7 and 30 + 2 days of treatment. For three patients, samples were also obtained 4, 8, 12 and 36 h after the initiation of steroid therapy. Sera were frozen and stored in aliquots at -20°C before assay. Control samples were obtained from 20 healthy volunteers, seven patients suffering from acute bacterial pneumonia before any treatment (acute inflammation controls) and 11 patients suffering from necroziting vasculitis.

In addition to regular biological investigations, serum CRP, haptoglobin and al acid glycoprotein levels were determined by nephelemetry (Behring, Rueil-Malmaison, France). Serum sCD23 levels were measured in duplicate using a radio-immunosorbent assay with monoclonal antibodies which recognize 25 to 37 kDa sCD23 fragments, with a detection threshold of 0.3 U/ml (1 U = 5 ng/ml, Biosource Europe SA, Fleurus, Belgium). Serum IL-6 levels were measured using ELISA kits, kindly provided by Dr. J. Wijdenes (IN-NOTEST, Besancon, France).

Results are shown as means&standard error of mean (S.E.M.). Normal ,values were defined as the ranges of mean + 2 standard deviations of normal control serum levels. Results were compared using the Student's t-test for paired and unpaired data. Correlation analysis were carried out using Spearman correlation coefficients.

Results and discussion

Serum sCD23 levels were elevated on DO in GCA patients by comparison with healthy volunteers (P < 0.01) (Fig. 1). In contrast, they were not significantly affected in the two other inflammatory states studied, infectious pneumopathy and necroziting vasculitis (Fig. l), despite a similar increase in CRP levels in all cases (data not shown). A marked inflammatory response Measurements performed prior to and 1. was observed on DO (day 0), with high serum CRP, haptoglobin and cl1 acid glycoprotein levels (Table 1). IL-6 levels were also elevated, as previously described [13]. Serum sCD23 levels correlated with IL-6 levels on DO (r= 0.81, PC 0.001) but not with cl1 acid glycoprotein, haptoglobin and CRP levels. Such a correlation between IL-6 and sCD23 has been previously reported in dialysed chronic renal failure patients [12]. It could be of interest since sCD23 enhances IL-6 production by human monocytes in vitro [5]. On the other hand, sCD23 levels and serum alkaline phosphatase activity did not correlate despite the moderate cholestasis observed in 2/3 of these patients with GCA. Interestingly, serum sCD23 and creatinin levels correlated on DO (r = 0.69, P = 0.0004), in spite of the absence of noticeable renal failure in these patients.

Within the first 24 h following the onset of prednisone therapy, sCD23 levels reached normal control values in all but one patient and the difference between values recorded on DO and Dl was significant (P < 0.01) (Table 1). No further differences were observed between sCD23 levels on Dl (day I) and D7 (day 7) or between Dl and D7 compared to normal control values. In contrast, sCD23 levels on D30 (day 30) are significantly decreased (P < 0.05) when compared to normal control values. A decrease was also observed for IL-6 levels within the first 24 h but not for CRP. Short kinetic monitoring revealed that sCD23 sera levels decreased as soon as 4 h following initiation of corticosteroid therapy, suggesting a direct action of prednisone on CD23 synthesis or release and a short half-life for sCD23 in vivo (Fig. 2). Interestingly, we recently observed that lOme 5 M prednisolone in vitro decreases sCD23 release by a lymphoblastoid B cell line (data not shown), as previously shown for peripheral blood lymphocytes [14]. Taken together, these data suggest that high serum sCD23 levels in GCA patients results from an overproduction of the molecule rather than from a decrease in its clearance. Nevertheless, the cellular origin of sCD23 in GCA remains to be identified. We searched for but could not evidence differences of CD23 expression by peripheral blood mononuclear cells from healthy volunteers and GCA patients (data not shown). Since CD23 positive lymphocytes have been detected in the skin lesions from atopic dermatitis patients [15], it will be of interest to study sCD23 expression at the level of the arterial lesions. Interestingly, it has been recently suggested that sCD23, if produced locally, may participate in the initiation and in the maintenance of a non reactive inflammatory response triggered by foreign antigens [6] In other inflammatory diseases, high sCD23 levels have been found in autoimmune diseases involving a B cell response such as rheumatoid arthritis. systemic erythematosus lupus or primary Sjbgren's syndrome. In rheumatoid arthritis, sCD23 levels correlate with the titer of rheumatoid factors [9]. It has been suggested that the increase of sCD23 in these diseases reflects B lymphocyte activation. GCA is considered to be associated with a Thl response [2] and serum IgE levels are normal (data not shown). Hence, GCA seems to be an inflammatory disease mediated by T cells and associated with high serum sCD23 levels, a previously unreported situation. Whether increased serum sCD23 levels in GCA result from a lymphocyte or monocyte activation and the possible role of sCD23 in the physiopathology of the disease by modulating lymphocyte or monocyte functions remain opened questions. Interestingly, in type II collagen-induced arthritis in mice, a model for human rheumatoid arthritis, a successful disease modulation has been achieved by treatment with antibodies to murine sCD23 [16]

Fig. 1 .

 1 Fig. 1. Serum sCD23 levels (U/ml) in healthy volunteers (C), GCA patients before treatment, patients with acute pneumonia (P), and necroziting vasculitis (NV). Means are indicated as solid bars.

  Fig. 2. Evolutionof serum sCD23 levels (U/ml) in GCA patients before and 4, 8. 12, 24 and 36 h after initiation of corticosteroid therapy. Results are indicated as mean k S.E.M.

Table I

 I Effect of corticosteroid therapy on serum sCD23 levels and other serum parameters in 25 GCA patients

		NC	DO	Dl	D7	D30
	sCD23 (U/ml)	0.82 f 0.09	1.6 f 0.24	0.87 + 0.16	0.88 + 0.15	0.59 * 0.07
	IL-6 (pg/ml)	3.3 + 0.9	59.4 _+ 18	17.6 + 5.5	14 * 4.4	10.3 & 2.5
	CRP @g/ml)	12.3	91 k 9.6	54.4 _+ 9	8.7 & 2.6	7.9 + 3.2
	al GP (mg/ml)	0.441.2	2.28 f 0.13	2.23 + 0.2	1.63kO.12	1.46 + 0.09
	Haptoglobin (mg/ml)	0.5-3.2	6.65 + 0.29	6 + 0.35	5 + 0.27	3.72 + 0.33
	AP (mlU/ml)	53-120	318 ) 39	ND	325 & 54	177 * I2
	Creatinine (nmol/ml)	40-120	79 * 7	ND	99* II	83+4

This work was supported by CNRS, Poitiers University Hospital (clinical research grant), and Region Poitou-Charentes.


Hoang-Trung Ngo
email: hoang-trung.ngo@ec-nantes.fr

Bogdan Marinescu
email: bogdan.marinescu@ec-nantes.fr

Fast Frequency Support at a Wind Energy System Using Time-Varying Inertia and Droop Controls based on Globally Optimal H ∞ Control Design

Keywords: wind generation, H-infinity control, robustness, LMI, grid frequency support

The aim of this paper is to find an efficient strategy to provide local services for wind energy systems (i.e., regulate DC line voltage, active power, reactive power), frequency stability and support in both frequency deviation (using droop control) and rate of change of frequency (RoCoF) from generating units when it is used in an interconnected power as well as isolated ones. In order to achieve the research objectives, different strategies were studied. It's about the modeling of Permanent Magnet Synchronous Generator (PMSG) based on variable speed wind system connected grid using back to back converters and systems control. The aim of the present paper is that of analysing the possible contribution of variable speed wind generating units in frequency support, by means of the definition of dedicated control strategies to be implemented at power electronic level. Then, the paper also proposes the integration of inertial and droop frequency controller in order to define a control strategy capable of emulating the frequency response behaviour of a traditional generating unit. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov stability and are formulated in Linear Matrix Inequalities (LMIs). The performances and limits of the proposed controller are evaluated by means of dedicated simulations.

I. INTRODUCTION

W IT H the increasing level of Renewable Energy Sources (RES), frequency stability of power system has drawn considerable attentions from system operators [START_REF] Tsili | A review of grid code technical requirements for wind farms[END_REF]. This is due to the fact that these sources are systematically grid connected by power electronics which increases the Rate of Change of Frequency (RoCoF) and decreases the Frequency Nadir (FN) of the overall power system [START_REF] De Almeida | articipation of doubly fed induction wind generators in system frequency regulation[END_REF]. Moreover, the variable speed Wind Turbine Systems (WTS) are mostly operating in Maximum Power Point Tracking (MPPT) mode and thus do not regulate their active power to support the power grid when the grid frequency deviates Hoang-Trung NGO, Elkhatib KAMAL and Bogdan MARINESCU are with Ecole Centrale Nantes -LS2N (Laboratoire des sciences du numérique de Nantes), 1 Rue de la Noë, 44000 Nantes Cedex 3, France, Email: Hoang-Trung.Ngo@ec-nantes.fr, Elkhatib.Ibrahim@ecnantes.fr and Bogdan.Marinescu@ec-nantes.fr. Correspondence: Elkhatib KA-MAL (Elkhatib.Ibrahim@ec-nantes.fr)

This work is part of the H2020 European project POSYTYF (https://posytyf-h2020.eu/). from its nominal value.

Recently, there are many research works for power converter optimal control based on linear matrix inequalities (LMI), including H 2 and H ∞ for local services [START_REF] Sedghi | Robust voltage regulation in islanded microgrids: A LMI based mixed H 2 /H∞ control approach[END_REF]. Also, the research works for wind turbine system control are heavily investigated, both for Doubly Fed Induction Generator (DFIG) [START_REF] Kamal | Intelligent control of WECS subject to parameter uncertainties[END_REF] and Permanent Magnet Synchronous Generator (PMSG) [START_REF] Kamal | Converter Nonlinear Fuzzy Control of PMSG-Based for Wind Energy System in Network Context[END_REF]. However, there is no a comprehensive methodology which addresses both local services and frequency in terms of global control at the same time.

Frequency support for renewable in general, and for wind turbine in particular, is the ability of frequency regulation by adjusting the produced power from the generators [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Kundur | Power system stability[END_REF]. This is not only acting on frequency deviation using droop control [START_REF] Kundur | Power system stability[END_REF], but also taking into account of RoCoF behavior to ensure the stability of considered system and its neighbor [START_REF] Entso-E | Frequency stability evaluation criteria for the synchronous zone of Continental Europe-requirements and impacting factors[END_REF]. The frequency regulation in renewable energy is heavily investigated, both in frequency deviation using classical droop control [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Kundur | Power system stability[END_REF], [START_REF] Chang-Chien | Enhancing frequency response control by DFIGs in the high wind penetrated power systems[END_REF] and in inertia control (or RoCoF regulation) using hidden inertia control [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Su | Influence of wind plant ancillary frequency control on system small signal stability[END_REF] and fast power reserve [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Itani | Short-term frequency support utilizing inertial response of DFIG wind turbines[END_REF]. This work is totally adequate in the view of frequency support, however, lack of a global control structure which should include the local services control. The control system model with frequency support for neighbor grid is introduced. To perform and evaluate the performance of the frequency support strategies, one must find a way to include the dynamic of neighbor grid frequency [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Kundur | Power system stability[END_REF] into the control system model. However, to globally achieve both objectives of frequency support and local services (i.e. regulate DC line voltage, active power, reactive power), not only the frequency dynamic is considered as in [START_REF] Kundur | Power system stability[END_REF] but also the relationship of frequency and terminal voltage of the grid has to be taken into account. In [START_REF] Chang-Chien | Enhancing frequency response control by DFIGs in the high wind penetrated power systems[END_REF], many methodologies are introduced and proven effective for the neighbor grid, but still, the lack of relationship of frequency and terminal voltage of the grid makes the mentioned strategies less practical.

The objective of this paper is to focus on the wind generators connected to a large scale grid, a sector in which profitability is far from certain and which therefore requires a degree of optimization of energy efficiency [START_REF] Hohm | Comparative study of maximum power point tracking algorithms[END_REF]. In this context, the production of these energy sources has to be optimized, that is to say extracting a maximum power under all conditions of operation, for which we have proposed a maximum power point tracking control [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF], [START_REF] Hohm | Comparative study of maximum power point tracking algorithms[END_REF]. Several combinations of controls based on pitch control, droop control [START_REF] Chang-Chien | Enhancing frequency response control by DFIGs in the high wind penetrated power systems[END_REF] and frequency control (for RoCoF improvement) using H ∞ optimization. The main control strategy used to emulate an inertial behavior of generators connected to the grid by power electronics was detailed, namely hidden inertia controller [START_REF] Su | Influence of wind plant ancillary frequency control on system small signal stability[END_REF] and fast power reserve emulation [START_REF] Itani | Short-term frequency support utilizing inertial response of DFIG wind turbines[END_REF] to obtain a frequency support. In addition, the local services [START_REF] Kamal | Converter Nonlinear Fuzzy Control of PMSG-Based for Wind Energy System in Network Context[END_REF] (DC voltage control, generator speed control, reactive current of grid side converter) as well as grid frequency support are studied using Matlab/Simulink to illustrate the effectiveness of the proposed methods.

The paper is organized as follows. In Section II, the gridconnected PMSG dynamics are modeled and the control problem is formulated. In Section III, the proposed Globally H ∞ Controller is constructed. Simulation results that illustrate the effectiveness of the proposed strategies are presented in Section IV. Finally, the conclusions and future prospects are presented in Section V.

II. NONLINEAR MODEL OF GRID CONNECTED PMSGS

Consider the PMSG structure, with LCL filter and two converters as in the Fig. 1:

The PMSG nonlinear system in the d-q synchronous reference frame is given in [START_REF] Kamal | Converter Nonlinear Fuzzy Control of PMSG-Based for Wind Energy System in Network Context[END_REF].

Consider now 2 PMSGs connected to the grid as in Fig. 2: The dynamics of pitch angles are totally decoupled from the other PMSGs dynamics [START_REF] Kamal | Robust control of wind energy conversion systems[END_REF]:

dβ P M SG1 dt = -1 τ C1 β P M SG1 + 1 τ C1 β P M SG1ref dβ P M SG2 dt = -1 τ C2 β P M SG2 + 1 τ C2 β P M SG2ref (1)
where

β min ≤ β P M SG1 , β P M SG2 ≤ β max dβ dt min ≤ dβ P M SG1 dt , dβ P M SG2 dt ≤ dβ dt max
Typically, as in [START_REF] Kamal | Robust control of wind energy conversion systems[END_REF], these limitations come from the servo motor:

     τ C1 = 0.2 (s) ; τ C2 = 0.2 (s) β min = 0 (deg) ; β max = 20 (deg) dβ dt min = -10 (deg) ; dβ dt max = 10 (deg)
As a consequence, the pitch angle will be controlled separately from the other PMSGs dynamics.

A. Droop control with deloading methods

From the deloading lookup values in Fig. 3, for frequency support, the wind generator has to run at deloading point (10%) rather than MPPT to reserve an amount of power. For example, consider the wind turbine is running at 17 (m/s) wind speed in Fig. 4 [6], the wind turbine will produce power at 10% deloading point A to reserve 10% of its power capacity. To utilize this reserved power for frequency support, a droop relationship is established [START_REF] Kundur | Power system stability[END_REF]:

∆P ref = - 1 R ∆f, (2)
where ∆P ref is the required amount of change in power when there is a change in frequency ∆f . An increase in grid load or shortage in power generation will generate a droop in the frequency of grid [START_REF] Kundur | Power system stability[END_REF]. To compensate Fig. 1. The VSC-HVDC power structure this frequency droop, there is a need to increase power production using the reserved power. As a consequence, following (2), the operating point of wind generator moves from A to B to increase the mechanical power. Following Fig. 4, this will result in increasing of the produced power. Thus, P mref will be used to determine the desired generator speed w ref as follows [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF]:

P mref = P mdel + ∆P ref (3)
and

P mref = P mdel + (P mopt -P mdel ) w del -w ref w del -w opt (4)
From equation ( 4), the value of w ref will be calculated as:

w ref = w del -(w del -w opt ) - 1 R ∆f P mopt -P mdel (5)
The relationship between desired produced power P mref and desired pitch angle β ref is:

P mref = P mdel + (P mopt -P mdel ) β del -β ref β del -β opt (6)
Thus, from droop control relationship (3) and ( 6), the desired pitch angle β ref is

β ref = β del -(β del -β opt ) - 1 R ∆f P mopt -P mdel (7)

B. Wind generator inertia control

The emulated inertia control methodology is given in Fig. 5 [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF]. From the RoCoF feedback, the converter controller is able to produce immediate active power according to the status of RoCoF. Fig. 5. The hidden inertia control structure [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF] The gain K is chosen based on the fact that the change of the power of the grid with respect to the variation of the grid frequency is

∆P L = 2H df dt , ( 8
)
where H is the global inertia of the AC grid, f is grid frequency and ∆P L is the total power change. The principle of inertia control is to immediately generate the same amount of total power change to keep the RoCoF as small as possible. Thus, the required power to be supplementary produced in order to compensate the fall in RoCoF is

∆P eref = K df dt (9)
∆P eref = -∆P L = -2H df dt . (10)
The generator speed is controlled by a reference generated from a predefined active power amount [START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF] ω r,ref = ω 2 r0 -2

P const J t, ( 11
)
where J is the inertia of the wind turbine, P const is the predefined active power. The produced power is controlled by the scheme in Fig. 6 [6]. C. Global structure for PMSGs control with frequency support All of the aforementioned levels, including rapid response (RoCoF), slow response (droop control), and local requirements, should all be ensured in frequency support. As a result, the suggested control (which is a novel H ∞ control detailed in the following section) includes a mix of deloading methods, inertia control, droop control, and converters control for local services, as described in Fig. 7 [14]: The deloading techniques (3) for droop control and the emulated inertia control (10), the desired power which meets the need of droop control and RoCoF (very fast frequency control) support is:

P mref = P mdel + ∆P ref droop + ∆P ref inertia = P mdel + - 1 R ∆f + (-2H) df dt (12)
From the desired power (12), K droop and K in fig. 7 are

K = -2H K droop = -1 R (13)
The steps for switching generator speed control and/or pitch angle control in the algorithm in Fig. 7 are (i) Regulate and stabilize the PMSG with produced power at deloaded point P mdel . (ii) Continuously calculate the produced power based on equation ( 12) from frequency and RoCoF status using state-space model. (iii) If P mref ≤ P opt : maintain the same pitch angle, determine the equivalent generator speed w ref from the desired generated power P mref using (4). (iv) If P mref > P opt : at this stage, the generator speed control alone cannot generate enough power for frequency regulation. Hence, set w ref = w opt and determine the desired pitch angle β ref from the desired produced power P mref using ( 6).

D. Augmented system for local services

After linearization using first order approximation of the nonlinear PMSGs and grid system of the Fig. 1, one obtains the state-space form with disturbance

Ẋ = AX + B 1 U + B 2 W Y = CX (14)
Consider the extended state X and output Ȳ for the purpose of step reference tracking along with output error e:

X = Ẋ e ; Ȳ = e; e = -CX + Y ref . ( 15
)
The extended system which corresponds to this extended state and output is:

Ẋ = Ā X + B1 U + B2 Ẇ Y = C X ( 16
)
where: 16) can be stabilized by the state-feedback control which, in original variables, results into a multivariable PI controller

Ā = A 0 -C 0 ; B1 = B 1 0 B2 = B 2 0 ; C = 0 I System (
U = K X ⇒ U = K X edt (17)

III. SYNTHESIS OF THE PROPOSED GLOBALLY H ∞

CONTROLLER

Consider the linear state-space system:

   Ẋ = AX + B 1 U + B 2 W Y = CX + D 1 U + D 2 W U = KX (18)
The transfer function from disturbance W to the output Y is

Y (s) = G (s) W (s) G (s) = (C + D 1 K)(sI -(A + B 1 K)) -1 B 2 + D 2 (19)
It is obvious that:

∥Y ∥ 2 ≤ ∥G∥ ∞ ∥W ∥ 2 . ( 20
)
Problem 1: For the above system, the H ∞ problem is to design a static state feedback control law such that:

∥G∥ ∞ < γ (21)
Hold for a given positive scalar γ. Theorem 1:

The H ∞ problem 1 has solution if and only if there exist a symmetric positive definite matrix X p ≥ 0 and a matrix W p , such that

  Ψ B 2 (CX p + D 1 W p ) T B T 2 -γI D T 2 CX p + D 1 W p D 2 -γI   < 0 (22)
where

Ψ = (AX p + B 1 W p ) T + AX p + B 1 W p . (23)
The solution of the problem can be given as

K = W p X -1 p . (24)
Proof 1:

It is well-known that with linear system:

Ẋ = AX + BU Y = CX + DU (25)
The H ∞ problem with this system:

Y = G (s) U G (s) = C(sI -A) -1 B + D (26)
Is solved by [START_REF] Kamal | Converter Nonlinear Fuzzy Control of PMSG-Based for Wind Energy System in Network Context[END_REF], [START_REF] Kamal | Robust fuzzy logic control of wind energy conversion systems with unknown inputs[END_REF]- [START_REF] Kamal | Maximum power control of hybrid wind-diesel-storage system[END_REF] if and only if there exist a symmetric positive definite matrix X p , such that:

  X P A T + AX P B X P C T B T -γI D T CX P D -γI   < 0 (27)
Apply this for the linear system with disturbance (equation ( 18)), where G (s) is in the form of equation ( 19), the problem 1 is solved if and only if:

     Ψ B2 CX P + D1 KX P T BT 2 -γI DT 2 CX P + D1 KX P D2 -γI < 0 Ψ = ĀX P + B1 KX P T + ĀX P + B1 KX P (28)
and by defining W P = KX P , the inequality turns into theorem 1.

IV. SIMULATION AND RESULTS

The proposed control methodologies are applied to the 2 PMSGs in Fig. 2. Several combinations of controls were considered: all controls simultaneously applied or only pitch and drop control without fast frequency control (for Ro-CoF improvement) or other combinations. In all situations, H ∞ control was used. The latter control was synthesized in a coordinated manner for the 2 PMSGs. The local services (DC voltage control, generator speed control (or, equivalently, produced power control), reactive current of grid side converter (or, equivalently, reactive power)) as well as grid frequency support are checked by the following simulations.

Consider the scenario of load change of the overall power system in Fig. 8. Fig. 9 and Fig. 10 show that pitch control and generator speed control provide a significant amount of power, which play an important role in frequency deviation regulation. At the same time, fast regulation (inertia control) provides a rapid impact on produced power, which has a positive impact on RoCoF (Fig. 11 and12). Due to the strong relationship between generator speed and produced power (which is shown in MPPT relationship), the H ∞ optimization on frequency w f provide no increase of power supply, which means that there will be no effect on frequency behavior.

From the comparison given in Fig. 11, one can also conculde that the RoCoF is greatly improved by using fast frequency control (inertia control in our case). The pitch angle control and generator speed control also help to improve RoCoF but with less impact.

Frequency deviation shown in Fig. 12 is less severe when speed and pitch angle controls are used.

From results in Fig. 9 and Fig. 10 one can also deduce that generator speed control alone also increases power supply, which in turn diminishes frequency deviation. This paper presents a control method applied to wind turbines mainly fall under primary frequency control. In order to find an efficient strategy to provide local services for wind energy systems (i.e., regulate DC line voltage, active power, reactive power), frequency stability and support in both frequency deviation (using droop control) and RoCoF from generating units when it is used in an interconnected power as well as isolated ones. Therefore, different control strategies were studied. It's about the modeling of two PMSGs based on variable speed wind system connected grid using dual converters and systems control. The proposed control methodologies are validated using this model. Several combinations of controls based on pitch control, drop control and frequency control (for RoCoF improvement) using H ∞ optimization. The effectiveness of the proposed methodologies are finally demonstrated through a wind energy system with two PMSGs to illustrate the effectiveness of the proposed methods. The local services (DC voltage control, generator speed control (or, equivalently, produced power control), reactive current of grid side converter (or, equivalently, reactive power)) as well as grid frequency support are studied using Matlab/Simulink. In future work, the performance of the proposed methods will be implemented and tested through Experimental Setup.

Fig. 2 .

 2 Fig. 2. The VSC-HVDC power structure

Fig. 3 .Fig. 4 .

 34 Fig. 3. The output power with different wind speeds at MPPT and at 10% deload

Fig. 6 .

 6 Fig.6. The fast power reserve control structure[START_REF] Dreidy | Inertia response and frequency control techniques for renewable energy sources: A review[END_REF]

Fig. 7 .

 7 Fig. 7. The global control for PMSG with local services and frequency support

  (v) The equivalent generator speed w ref and pitch angle β ref become the input of the global control along with local services to globally fulfill both goals of local control and frequency supports.

Fig. 8 .

 8 Fig. 8. The change on load (in [W]) of the grid

Fig. 11 .

 11 Fig. 11. RoCoF behavior (Hz/s) of the grid in different control strategies

Fig. 12 .

 12 Fig. 12. Frequency behavior (pu) of the grid in different control strategies