Luca Rava

Audrey Wantier

Mathieu Vallée

Alain Ruby

Nicolas Lamaison

Assessment of Varying Coupling Levels between Electric & Thermal networks at District Level using Co-Simulation and Model-predictive Control

Keywords: FMI, co-simulation, Model Predictive Control, energy storage, thermoelectric coupling, flexibility, modeling, complex energy system, district heating

This study focuses on the co-simulation of the heating and electrical systems of a district. A heat pump, a gas boiler, a biomass cogeneration, a photovoltaic plant and the national electric grid provide electricity and heat consumed by thirteen residential buildings. Two storage units are present: a heat storage (hot water tank) and an electric storage (chemical battery). Architecture design and pre-sizing of components have previously been computed by MILP optimizations.

As part of the Trilogy platform, a co-simulation platform Pegase runs the grid control and the detailed physical models developed using Modelica (heat system) and Simulink (electric system). A model predictive control (MPC) based on sliding time window MILP optimisations manages the flexibility of the multi energy system and insures the balance between production and consumption. The objective of the optimizations is to minimise CO2 equivalent emission costs and operational costs of each component, including the purchase of gas, biomass and electricity.

A parametric study on the coupling strength between the electric and the heat system is performed by modifying the price of the electricity purchased from the national grid. Multiple scenarios with different thermoelectric coupling strength are analysed to show the dependency of the energy mix on the coupling strength. With increasing coupling, photovoltaic self-consumption increases and heat generation gradually shifts from the heat pump to the biomass cogeneration and to the gas boiler. This study also demonstrates how the Trilogy platform tools enable easy implementation of optimal control on cosimulations of multi energy detailed physical models.

Introduction 1.Context

In France and other countries, a large share of energy consumption is devoted to providing residential areas with space heating and domestic hot water preparation. While this demand has long been covered with fossil-fuels, it has to be quickly reduced in order to face challenges related to climate change, as well as for energy independence. Massive electrification of the residential sector, i.e., substituting fossil fuels with power-to-heat technologies, is one possible option for performing this shift, especially when considering renewable energy sources [START_REF] Rte | Energy pathways 2050 -Key results[END_REF]. This transition process must take into account three major constraints. First, increasing the overall residential electricity consumption is not desirable. Indeed, a prospective study in France [START_REF] Rte | Energy pathways 2050 -Key results[END_REF] recommends a slight decrease by 2050. Second, the temporal mismatch between renewable electricity production and consumption for residential purpose (especially at yearly scale) must be accounted for [START_REF] Clerjon | Matching intermittent electricity supply and demand with electricity storage -An optimization based on a time scale analysis[END_REF]. Third, thermal renovation of the existing building stock will take time and may not be phased with electrification and an increase of renewable production capacity. As a consequence, more realistic scenarios require not only electrification but also increased sector coupling, in particular between the electric and thermal networks, which can provide flexibility at different time scales (from instant to year) [START_REF] Vandermeulen | Controlling district heating and cooling networks to unlock flexibility: A review[END_REF].

State of the art

Many works study sector coupling and multi-energy systems in the recent years. A typical categorization distinguishes between simulation, optimization and equilibrium methods [START_REF] Ringkjøb | A review of modelling tools for energy and electricity systems with large shares of variable renewables[END_REF]- [START_REF] Cuisinier | Techno-economic planning of local energy systems through optimization models: a survey of current methods[END_REF]. Mavromatidis et al. [START_REF] Mavromatidis | Ten questions concerning modeling of distributed multi-energy systems[END_REF] highlight that optimization models, although they are more widely used, are also less validated than simulation models.

The importance of fine-grained simulation for validating higher-level solution has been pointed out by Lamaison et al. [START_REF] Lamaison | Storage influence in a combined biomass and power-to-heat district heating production plant[END_REF], i.e. approximate models used for optimization can lead to different results or even infeasible cases in simulation.

Fine grained simulation of multi-vector district energy system poses modeling and performance challenges. In particular, no simulation tool is able to simulate all the domains with optimal efficiency, and the co-simulation approach has been proposed to overcome this challenge. Co-simulation is particularly relevant in studying multi-energy networks [START_REF] Leitner | A method for technical assessment of power-toheat use cases to couple local district heating and electrical distribution grids[END_REF]- [START_REF] Descamps | Operational Control of a Multi-energy District Heating System: Comparison of Model-Predictive Control and Rule-Based Control[END_REF].

The choice of control strategies is also very important. It is very difficult to define rule-based control strategies that are capable to achieve the results obtained in optimization [START_REF] Descamps | Operational Control of a Multi-energy District Heating System: Comparison of Model-Predictive Control and Rule-Based Control[END_REF], [START_REF] Cuisinier | New rolling horizon optimization approaches to balance short-term and long-term decisions: An application to energy planning[END_REF], whereas Model-Predictive Control (MPC) control strategies for energy systems provide good results [START_REF] Vallée | An efficient co-simulation and control approach to tackle complex multi-domain energetic systems: concepts and applications of the PEGASE platform[END_REF], [START_REF] Leitner | Control assessment in coupled local district heating and electrical distribution grids: Model predictive control of electric booster heaters[END_REF], [START_REF] Saloux | Model-based predictive control to minimize primary energy use in a solar district heating system with seasonal thermal energy storage[END_REF].

Case study: the Grenoble's "Cambridge" district

This paper considers a case study inspired on a real district in the city of Grenoble (France). This district, called the "Cambridge" district, has been studied in previous research work [START_REF] Pajot | An Approach to Study District Thermal Flexibility Using Generative Modeling from Existing Data[END_REF]- [START_REF] Fitó | Robustness of District Heating versus Electricity-Driven Energy System at District Level: a Multi-Objective Optimization Study[END_REF]. A complete description of the case can be found in the aforementioned papers: we briefly recall it here for the sake of completeness.

Fig. 1. Schematic representation of the "Cambridge" district (and its buildings) in the city of

Grenoble, France. [START_REF] Fitó | Robustness of District Heating versus Electricity-Driven Energy System at District Level: a Multi-Objective Optimization Study[END_REF] Fig.

1 [START_REF] Fitó | Robustness of District Heating versus Electricity-Driven Energy System at District Level: a Multi-Objective Optimization Study[END_REF] illustrates the layout of the "Cambridge" district. In this work, we consider 13 of its residential buildings, with approximately 500 dwellings.

Generation of electric and thermal load profiles

Based on the available data for these buildings (surface area, number of dwellings, monthly consumption), we used a combination of available load profile generation tools to produce synthetic load profiles at the hourly time step. More precisely, we combined:

 The CREST demand tool [START_REF] Richardson | A high-resolution domestic building occupancy model for energy demand simulations[END_REF], [START_REF] Richardson | Domestic electricity use: A high-resolution energy demand model[END_REF], used for computing dynamic occupancy in each dwelling and for computing specific electricity demand profiles.  A modified version of the DHW Calc tool [START_REF] Jordan | DHWcalc: program to generate domestic hot water profiles with statistical means for user defined conditions[END_REF] for computing Domestic Hot Water demand while taking into account occupancy profiles.  A simplified dynamic thermal simulation model, defined in [START_REF] Aoun | Development and assessment of a reduced-order building model designed for model predictive control of space-heating demand in district heating systems[END_REF], for computing space heating profiles.

Hypotheses on energy and CO2 prices

The reference electricity price used in the simulations is based on the data available from the ENTSO-E Transparence platform [START_REF]Day Ahead Prices (hourly data for 2018[END_REF]. This data has been adjusted with a constant bias in order to take into account transportation and distribution costs as well as the non-residential final consumer subscription. This constant bias is calculated in function of the average 2013-2018 values for France, retrieved from the Eurostat database [START_REF] Eurostat | Electricity prices by type of user [TEN00117[END_REF]. The simulation's electricity price's yearly average value is 0.0758 €/kWh. The prices for gas, biomass (wood) and CO2 taxes are constant throughout the whole simulated year, as indicated in Table 1. The gas price is the maximum value retrieved from the Eurostat database [START_REF] Eurostat | Electricity prices by type of user [TEN00117[END_REF] between 2013 and 2018, for non-residential consumers. Wood biomass price is retrieved from the IRENA report on renewable energy in District Heating and Cooling [START_REF] Irena | ANNEX 4: FUEL COSTS[END_REF]. A CO2 tax of 100 €/tCO2 is assumed, although it has marginal impact on the results (only very high CO2 taxes above 250 €/tCO2 would change the results, however this is considered as an unrealistic value in the near future) Table 1: gas, wood and CO2 equivalent emissions costs.

CO2 equivalent emissions costs only apply to heat production with gas and electricity extraction from the grid. The CO2 emissions of burnt wood is considered zero because the same amount of CO2 is assumed to be absorbed by the growth of new trees. Gas CO2 emissions have been estimated to be 0.243 kgCO2/kWh. The CO2 content of the electricity extracted from the grid is calculated from data of ENTSO-E [START_REF]Actual Generation per Production Type (hourly data for 2018[END_REF] by applying CO2 content data of the IPCC [START_REF]Technology-specific Cost and Performance Parameters[END_REF] to instantaneous power production. The average value of the electricity CO2 content timeseries used in the simulations is 0.062 kgCO2/kWh. Fig. 2 gives a schematic representation of the multi-energy system architecture considered in this study. It features two energy distribution networks, the electricity distribution grid (in black) and the district heating network (in red and blue for supply and return lines). Note that the illustrated layout is not representative of the real district, and that the district heating network is not present in the actual district.

Multi-Energy System architecture

In this multi-energy system, various components can provide, convert or store energy either in electrical or thermal form. More specifically, we consider:

 Solar PV production and batteries at district level, as well as PV production at building level (rooftop)  Heat pump, biomass cogeneration unit, backup gas boiler and heat storage at the district level In particular, the heat pump and cogeneration units connected to the district heating network are two coupling points between the electric and thermal networks.

The photovoltaic production of the three plants included in the study is determined by data obtained from the PhotoVoltaic Geographical Information System (PVgis) online platform [START_REF]PhotoVoltaic Geographical Information System (PVgis), hourly data at the Cambridge's Grenoble neighbourhood[END_REF]. The panels' tilt was optimized by PVgis to the value of 36° in Grenoble's Cambridge neighbourhood. A perfect production forecast is used in the MPC control.

Sizing of production, conversion and storage components

The sizes of the production, conversion and storage components of the electrical and thermal parts of the district energy system were optimized from a techno-economic and environmental point of view using the PERSEE CEA software [START_REF] Cuisinier | New rolling horizon optimization approaches to balance short-term and long-term decisions: An application to energy planning[END_REF]. It provides a MILP library of models to write a classical unit commitment techno economical optimization problem, using a perfect one-year foresight assumption at hourly time-step.

The objective function is the Net Present Value of the system and accounts for Capex, Opex, purchase expenditures and carbon emission penalties for each component over 20 years of operation using a discount rate of 7%.

Besides technical and physical constraints, the installed power of the biomass cogeneration was limited at 360 kW to take into account the limited availability of wood and the regulations concerning the wood used for residential heating.

Another important constraint is the maximum limit of total yearly carbon emission mass, set at 20 tCO2. This resulted in the absence of gas boiler, but a gas boiler was reintroduced for the simulations of this study because the detailed non linear thermal model requires it for its correct operation (the gas boiler represents the degree of freedom allowing to regulate flow and temperature of the heating fluid in the supply and return lines).

The decision variables to be optimized are:

-maximum production and storage capacities of the components -hourly operating set points for each component The table below shows the installed powers of each component.

Table 2. Sizing results.

The optimal values determined during this step depend on the one-year perfect foresight assumption: by over-estimating the capacity to anticipate future time evolution of boundary conditions, the optimization can underestimate the need for storage or production capacity. Hence, the final performance of a finer representation of the system could be worse than the one expected from the sizing step. Moreover, the present sizing based on the MILP formalism uses simplified linear description of the component behaviours, which is another possible important bias. It is also important to notice that during this sizing step one optimization has been run on the whole horizon, while the moving shorter optimisation horizon used for the simulations ignores any event or data beyond its limited horizon.

Modelling

Methodological and Software frameworks

The TRILOGY platform is used to model the study case. It includes a simulation platform PEGASE that runs the different models: the electrical model developed with Simulink, the thermal model developed with Modelica and the control model called PERSEE. The electrical and thermal models are compiled as FMU models using the FMI-CS-2.0 standard [START_REF]Functional Mock-up Interface 2.0.3 specifications[END_REF].

Fig. 3. General coupling scheme within PEGASE

The control of the energy system is performed by the PERSEE module of PEGASE, which implements the Model Predictive Control (MPC) of the system.

Electrical model

The electrical part of the physical model is controlled by power setpoints calculated in the optimization (battery) or calculated by the thermal model (heat pump and cogeneration). The former drives the physical model of the battery, the latter are taken into account in the energy balance calculation in order to know the electrical power supplied to or extracted from the grid. This model is developed with Simulink.

The electric consumption of the 13 buildings of the Cambridge neighbourhood is modelled with 13 simple load models. Among the 13 buildings, two have a PV installation on the roof. Another ground mounted PV power plant is included. These three PV power plants are modelled with a photovoltaic production model based on the conversion of solar irradiation into electrical power. An electrochemical battery and its inverter represent the electricity storage systems available in the microgrid. The electric grid is represented by the electrical power balance of all components of the study case. The heat pump power consumption and the biomass cogeneration electricity production are outputs of the thermal model and inputs of the electrical model. These setpoints are taken into account in the electrical power balance and produce the coupling of the thermal and electrical systems.

PV

Battery Heat storage Heat Pump Cogeneration Gas boiler Sizing 7020 m 2 5600 kWh 11364 kWh 1268 kW 360 kW 1000 kW

Buildings

The electrical load model makes use of a timeseries of consumed power and applies it to the building as its electrical consumption. These timeseries have been calculated based on statistical models of apartments' occupation and consumption of electrical devices, as specified in 2.1.

PV plants

The photovoltaic energy production model is driven by a solar irradiation timeseries perpendicular to the modules surface and a timeseries of air temperatures. The model calculates the AC electrical power produced by simulating the plant's inverter and the photovoltaic modules taking into account their working temperature.

Electrical storage

The electrical storage system is composed by two different models: the electrochemical battery and the inverter. The active power setpoint is an input of the inverter, which converts it into a current setpoint for the battery. The battery model uses an equivalent circuit model to calculate the real current flowing through its cells, the voltage and the electrical power. The current and the voltage are fed back as inputs to the inverter model to calculate the real power at the inverter's terminals.

Battery: it is a Li-Ion battery model with multiple parallel and series connected cells. It includes a BMS (Battery Management System) which saturates the battery setpoint according to the battery parameters.

The cells physical model is based on an equivalent circuit model which simulates the electrical behaviour of the cells depending on the current setpoint and the working temperature.

Inverter: this model includes a control module which calculates the current setpoint for the battery and a physical module which calculates the AC power output of the inverter depending on the current and voltage information generated by the battery.

Electrical grid

The electrical grid is modelled with an electrical power balance of all the components included in the study case: this total is assumed to be balanced by the extraction or injection of power from or into the grid. Since the electrical losses of the grid and the time scale of its transients are negligible compared to the thermal system, this model is considered satisfactory for the study case of this paper.

Thermal model

The thermal model of the production plant is schematically illustrated in Fig. 4. The boundary conditions are the thermal output setpoints (𝑄) imposed to the generator by the controller (see Section 3.4) on one hand and the district heating network (DHN) setpoint departure temperature (𝑇𝑑 𝐷𝐻𝑁 ), return temperature (𝑇𝑟 𝐷𝐻𝑁 ) and flow rate (𝑚̇𝐷 𝐻𝑁 ) on the other hand. The latter boundary conditions account for DHW and space heating loads (see Section 2.1) and heat losses in the piping network (considered equal to 5%).

Fig. 4: Schematic representation of the model of the thermal network production plant

This generic model used for the present study is composed of 4 types of components, as highlighted in Fig. 4:

-Controllable generators (𝑃 𝑖 ) in which the output thermal power is controlled in order to satisfy the outlet setpoint temperature (𝑇 𝑝𝑟𝑜𝑑 ), the mass flow rate is controlled in order to satisfy the external controller setpoint in terms of output thermal power. The operation is bounded by maximum thermal output, flow rate and temperature. For the present study, the biomass cogeneration and the heat pump are operated in this way. -Non-controllable generators (𝑅 𝑗 ) in which the thermal power is not-controlled and the flow rate is controlled in order to satisfy the outlet setpoint temperature. The operation is bounded by maximum flow rate and temperature. For the present study, there is no generator operated in this way but future studies may address a solar thermal field. -Storages (𝑆 𝑘 ) in which the mass flow rate is controlled in order to satisfy the external controller setpoint in terms of thermal power. In case of charge, the flow rate is from top to bottom while in case of discharge, it is from bottom to top. The outlet temperature is floating and depending on the storage state. The operation is bounded by maximum flow rate. For the present study, the heat storage tank is operated in this way. -The load-tracking generator (𝐿𝑇) in which the flow rate depends on the overall plant mass balance. When the resulting flow rate is from return to supply line, the generator thermal output power is controlled so that the outlet temperature of the plant is equal to the desired DHN departure temperature (𝑇𝑑 𝐷𝐻𝑁 ). The operation is bounded by maximum thermal output, flow rate and temperature. For the present study, the gas boiler is operated in this way.

The physical models for all the components are based on static mass and momentum balances and dynamic energy balance. For the latter, input/output terms represent the convective transport, sources terms are heat loss and heat inputs, and accumulation terms represent the thermal inertia associated to fluid content and generator body. All the components are modelled without spatial discretization (0D modelling) except for storages in which 1D discretization along the fluid flow accounts for imperfect thermal stratification.

Control

The PEGASE tool allows to set up a Model-Predictive Control (MPC) managing the thermoelectric coupled energy system. The optimization problem is defined using a 24 hours horizon with perfect forecasts. Optimisations are performed with a timestep of 1 hour and are based on the same MILP models used during the sizing step (2.4). The differences between the optimization run during the sizing step and the moving horizon MPC optimizations included in the simulations of this study are:

-The optimisations are run at midnight every day with a horizon of 24 hours.

-The objective function is a pure operating cost function accounting for purchase expenditures (gas, wood, electricity) and carbon emission penalties. -The decision variables are the hourly operating set points for each component: sizing variables are set to the optimal values determined in 2.4.

Simulations

In order to study the thermoelectric coupling effect on the energetic system, several simulations have been run on a horizon of one year with different grid electricity prices.

These prices can be indicators of the coupling strength between the electrical and thermal systems. Usually, in the case of a pure thermal simulation, the electricity needs are fulfilled through an electric grid without energy limits. This electricity extraction from the grid is considered as an operational cost of the thermal system analysed.

Instead, in the case of a thermoelectric co-simulation, the impact of the grid electricity supply on the system operation can be managed through an intelligent control of electrical and thermal components and measured with the use of detailed physical models. The electricity needs can be modulated or moved back or forward in time taking into account the controllable loads, the availability of the intermittent renewable energy and the storage capacity of the system. Because of the thermoelectric coupling, the system control can chose innovative ways to manage energy resources. The optimizer leans towards these types of energy management rather than the ones that are more dependent on an always available electricity source proportionally to the electricity price. In fact, when the electricity price of the grid is zero, there is no interest in storing energy, neither there is in favouring the self-consumption over the extraction of electricity from the grid: the electricity is simply extracted from the grid when the need arises. But when the electricity price is non-zero, the optimizer gradually favours other solutions over a limitless grid extraction and adopts different strategies depending on the electricity price.

This price timeseries has been modulated with a coefficient in order to run several simulations with different price magnitudes. Twelve simulations were run with twelve different price coefficients.

Table 3: List of simulations with the respective electricity price coefficient.

It is important to notice that the electricity price used in the simulations is only a purchase price, while the sale price is set to zero in order to favour self consumption.

The same timeseries of solar irradiation and temperature are used for all the simulations. This data has been retrieved from the PVgis online platform [START_REF]PhotoVoltaic Geographical Information System (PVgis), hourly data at the Cambridge's Grenoble neighbourhood[END_REF].

Results

The simulation results analysed are timeseries of electrical and thermal power actually produced or consumed by each detailed physical model of the study case. An example of operation is shown in Fig. 5.

Fig. 5: Three days of operation of the electrical and thermal network of the Cambridge neighbourhood for an electricity price coefficient of 1 (original prices). Positive values are productions, negatives values are consumptions. "Heat Load" represents all thermal loads

including losses.

Fig. 5 shows that the battery is often charged at night extracting energy from the electricity grid when the electricity price is lower, and discharged during the evenings, when the electricity price is higher. The battery is also recharged in case of abundance of photovoltaic production.

During the morning of second day of Fig. 5 (11 th March) the photovoltaic production is enough to cover all electrical loads and is therefore stored into the battery. In the afternoon, the heat pump does not only satisfy the heat load, but recharges the heat storage too. This energy is then used during the evening, when both electrical and thermal loads are satisfied using stored energy.

It is worth noticing that the biomass cogeneration is only used during the day with low photovoltaic production (the first one of Fig. 5, 10 th March). Wood is in fact used as the alternative renewable energy compensating the weak solar irradiation.

The simulation results have been analysed by calculating the yearly energy balance of each component and plotting it against the electricity price coefficient (Fig. 6). Fig. 6: Plot of yearly energy production of each component against the electricity price coefficient.

An electricity price of zero generates important electricity extraction from the grid. The photovoltaic power is self consumed thanks to the penalisation of the CO2 emissions of the electricity extracted from the grid. It is only injected into the grid when all electrical and thermal charges are satisfied and when the storages are already charged. In all the cases where the photovoltaic power is not enough to supply the neighbourhood, remaining thermal and electrical needs are completely satisfied with electricity extraction from the grid. This electricity is either directly consumed, or stored in the battery or converted into heat with the heat pump. The generated heat is also either directly consumed either stored for later use. The flexibility provided by the electrical and thermal storages is used, in this case, to redistribute the photovoltaic production over the whole day and to buy the electricity when its CO2 content is low.

The biomass cogeneration and the gas boiler are never used.

At a normal electricity price (electricity price coefficient = 1) the biomass cogeneration allows to decrease the use of the heat pump and further decrease grid electricity extraction by providing both heat and electricity to the system. The cogeneration is often used during the winter, when the energy demand is higher, and only sometimes used in the summer, especially during the days when the photovoltaic production is low. Its installed power rarely covers all the energy demand, but it provides an often constant power output that helps reducing the electricity grid extraction through the use of storage systems and that allows the remaining electricity extractions to be limited to specific times when the electricity price is at a minimum.

At higher values of electricity prices a similar behaviour is observed, up to an electricity price coefficient of about 2.5. Another control strategy transition is observed between the electricity price coefficients 2.5 and 4. At these increasing values of the electricity price, heat production from gas becomes more and more viable. The heat pump production decreases according to the increase of heat produced by the gas boiler. At high electricity prices the heat pump is used most of the times with photovoltaic power. The flexibility provided by the electricity and heat storages is used to maximize self consumption and reduce electricity extraction from the grid. At even higher electricity prices (coefficient = 10) no significant deviation from the trend showed in Fig. 6 is observed: the energy mix tends to consolidate at constant values.

The electricity extracted from the grid between the two simulations with electricity price coefficients 0 and 0.5 seems to increase. This is the opposite phenomenon observed for higher electricity price coefficients and was not expected. However, an explanation can be found by looking at the total yearly battery losses of the two simulations in question. When the price coefficient is zero, extraction from the grid can happen at any time (except for the variable costs generated by the CO2 emission cost, which are on average small compared to half the electricity price: 0.0062 €/kWh versus 0.0379 €/kWh). Therefore, electrical loads can be satisfied with direct grid extraction most of the times and the use of the battery is very limited compared to all the other simulations. Instead, when all the variations of the electricity price create significant economic advantages to recharge the battery at very specific times, the battery is used more often and, more importantly, with a higher charging power. Since electrical losses of the battery depend on the charging speed, this generates more electrical losses that cause the increase of grid electricity extraction observed between the first two simulations of Fig. 6 (coefficients 0 and 0.5). In order to analyse this phenomenon, the total yearly battery losses and the total yearly charged energy for each simulation have been plotted in Fig. 7. The losses have been normalized to the total yearly charged energy.

Fig. 7: Battery losses normalized to total charged energy and total charged energy against the electricity price coefficient.

As expected, normalized losses and use of the battery (total charged energy) increase from price coefficient 0 to price coefficient 0.5. Normalized losses then decrease again (though not as much) up to price coefficient 1. This can be explained with the introduction of the electrical production of the biomass cogeneration (Fig. 6). This generation reduces the overall need for electrical storage since it contributes to satisfy electrical demand during load peaks. The battery has to supply less energy during the peaks occurring at the same time as high electricity prices. It is therefore less charged when the electricity price is low and generates lower losses. For simulations with electricity price coefficient higher than 1, the electrical contribution of the biomass cogeneration to the system saturates and the use of the battery shows a slightly decreasing trend. The normalised battery losses increase again due to the exasperation of price differences: the charges are progressively more localized (therefore they are more often fast charges) at the times when the electricity price is low.

Conclusion and outlook

This study shows the ability of the TRILOGY platform to carry out co-simulations of electrical and thermal components controlled in the frame of the Model Predictive Control approach. It enables the full coupling of simplified linear electrical and thermal models to operate more detailed non-linear simulation models.

Sensitivity computations have been performed to assess the impact of the coupling strength between electrical and thermal models. Different control choices have been observed at different magnitudes of the electricity price, which suggest different behaviours of the electrical and thermal networks depending on their coupling strength. Specifically, the energy mix of the neighbourhood has been confirmed to be tightly related to the thermoelectric coupling strength.

This study highlights the importance of thermoelectric co-simulations in order to optimise energy use at a district level. The co-simulation platform developed for this study can be the basis of more advanced thermoelectric co-simulations of the same type. In particular, a comparison between simulations with and without detailed non linear models might generate important insights into their use in thermal-electric co-simulations. This is especially true when the forecasts used in the MPC control are not perfect and the optimised setpoints cannot be fully applied to the detailed physical models.

The analysis of the battery losses showed in Fig. 7 already generates an interesting insight into the way the battery is used even in the case of perfect forecasts. This analysis have been made possible by the use of a detailed non linear battery model that takes into account variable energy losses related to the speed of charge. This kind of insights rely on the use of detailed non linear models and can lead to the evaluation of innovative control rules and objectives and to better state of the art thermoelectric cosimulation expertise and results.

Fig. 2 .

 2 Fig. 2. Schematic representation of the multi-energy system architecture.

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 7 JULY, 2022, COPENHAGEN, DENMARK


Impact of thermal inertia coupled to natural night ventilation. A Case study for a high performance building in continental climate

Keywords: Thermal inertia, Thermal behavior, Measurements, Simulations, Natural ventilation, case study

In summer time, thermal inertia appears as a passive solution to improve the thermal comfort in many part of Europe. The objective of this paper is in a first step to generate thermal comfort data from energy efficient houses in summer time with a focus on the impact of thermal inertia and natural night ventilation. In a second step, numerical simulation are run on these configurations to compare their construction systems. This work confirms the positive impact of both thermal inertia and natural night ventilation on the thermal comfort for energy efficient buildings in continental climate. It also allows to quantify the difference of indoor air temperature on this case study and to ensure the reliability of the numerical models. Finally, contrary to what is mentioned in many papers, no significant time lags between the heavy and the light weight envelope have been highlighted.

Introduction

Today energy issues are becoming increasingly important with a goal for 2050 to reduce by a factor four energy consumption in European countries [START_REF] Europe | Europe's buildings under the microscope, Buildings Performance Institute Europe[END_REF]. In Europe, building sector represents about 44% of the total energy consumption and produces around 36% of the CO2 emissions (Buildings, n.d.). This leads to a changing building sector with more and more energy efficient new buildings with high insulated and air-tightness buildings. This can unfortunately rise to overheating in summer and so discomfort for the inhabitants. At the opposite, cooling systems are also increasingly used worldwide with predictions that energy needs for cooling systems will be higher than for heating in residential buildings before the end of our century [START_REF] Isaac | Modeling global residential sector energy demand for heating and air conditioning in the context of climate change[END_REF]. In this context, passive cooling techniques are becoming more and more important.

Thermal inertia coupled to natural night ventilation appears as an interesting passive solution to improve the thermal comfort in summer time. Indeed, during the day thermal inertia absorbs the heat gains [START_REF] Gregory | Effect of thermal mass on the thermal performance of various Australian residential constructions systems[END_REF]. The amplitude of the indoor air temperature of the building is reduced [START_REF] Ogoli | Predicting indoor temperatures in closed buildings with high thermal mass[END_REF] and a time lag appears between the peaks of the outdoor and indoor temperatures [START_REF] Ulgen | Experimental and theoretical investigation of effects of wall's thermophysical properties on time lag and decrement factor[END_REF]. The heat gains absorbed during the day are released at night [START_REF] Tonelli | Timber buildings and thermal inertia: Open scientific problems for summer behavior in Mediterranean climate[END_REF]. Geetha et al. [START_REF] Geetha | Passive cooling methods for energy efficient buildings with and without thermal energy storage -A review[END_REF] said "natural ventilation is the most important passive cooling technique" for release the heat gains of a building. Natural ventilation has to be used with thermal inertia to release at night, when the outdoor air temperature is lower, the heat absorbed in the thermal mass during the day [START_REF] Pfafferott | Thermal building behaviour in summer: Longterm data evaluation using simplified models[END_REF], (Amos-Abanyie, Akuffo, & Kutin-Sanwu, 2013), [START_REF] Zhou | Coupling of thermal mass and natural ventilation in buildings[END_REF]. With the natural ventilation at night, the indoor air temperature is also more comfortable during the day [START_REF] Balaras | The role of thermal mass in the cooling load of buildings. An overview of computational methods[END_REF], [START_REF] Evola | Different Strategies for Improving Summer Thermal Comfort in Heavyweight Traditional Buildings[END_REF].

Many papers exist in the literature dealing with thermal mass, mainly based on simulation. Aste et al. [START_REF] Aste | The influence of the external walls thermal inertia on the energy performance of well insulated buildings[END_REF] showed, by dynamics simulations, a reduction of the cooling energy demand with the use of high thermal inertia walls. [START_REF] Gregory | Effect of thermal mass on the thermal performance of various Australian residential constructions systems[END_REF] used numerical simulation to assess the impact of the thermal inertia on the thermal behavior for different typical building construction techniques in Australia. They demonstrated that the use of high thermal inertia can minimize the power consumption and can maintain a comfortable indoor temperature. Němeček et al. [START_REF] Němeček | Influence of thermal storage mass on summer thermal stability in a passive wooden house in the Czech Republic[END_REF] examined the influence of the thermal storage mass of a building on the thermal behavior, also by using a numerical simulation methodology. The simulated house is a passive wooden house in the Czech Republic. They showed that, for a single day simulation period, the thermal storage capacity of a wooden house with a reasonable quantity of thermal mass never achieves the same level of thermal storage of a brick house. Di Perna et al. [START_REF] Di Perna | Influence of the internal inertia of the building envelope on summertime comfort in buildings with high internal heat loads[END_REF] realized a study in a school building with high internal heat loads in Italy. They showed a better comfort with the wall with high thermal inertia in summer and mid-season.

This study aims to qualify, based on real data and numerical simulation from an experimental case study, the impact of both thermal inertia and natural night ventilation on the summer thermal behavior of high efficient buildings in continental climate. For that some comparison of two different levels of thermal inertia are done thanks to both experimental houses and numerical simulations in summer time. The two experimental houses have different thermal inertia with similar geometries. Two scenarios are studied: with and without natural ventilation. Firstly, the indoor air temperature measurements are analyzed for these two buildings. Secondly, numerical models of these houses are completed with EnergyPlus software and compared to the measurements. Finally two scenarios are studied to evaluate the influence for identical geometry of the natural ventilation on the indoor air temperature of houses with different thermal mass.

Methodology

The first objective of this work is to compare the thermal behavior at summer time of two different construction system of high performance houses in continental climate. For this, the following methodology illustrated in Figure 1 has been developed.

Firstly, 2 experimental houses with simulated occupation under real weather conditions, described in the following section, has been used. These houses are similar in geometry and insulation performance with a main difference in there construction system (heavy (H-A-M) vs light weight envelop (L-B-M)) Thanks to extensive sensors, and continuous monitoring in August and September 2013, the thermal behavior of each house can be analysed (Step1). Even if, these two houses are similar, they have slight differences in there geometry, especially in the windows properties (geometry A correspond to the experimental high inertia house, and geometry B corresponds to the experimental light weight house). This does not allow to compare directly the experimental results and to conclude on the impact of the construction system on the thermal behavior. Thus, Building Energy Simulation has been used in the following steps. Step 2 consists to develop a numerical model for each house (H-A-S, L-B-S), and to compare numerical results with experimental data, step2a for the heavy weighted houses (H-A-M vs H-A-S), and step 2.b for the light weight house (L-B-M vs L-B-S). In these steps, it is shown that both numerical models reproduce correctly the thermal behavior of the real houses. The next step consists to develop identical numerical model, except from the construction system. For that, a second light weight model (L-A-S) has been develop for which the construction of the light weighted house (L) has been applied to the heavy weight geometry (A). Step 3 will compare the numerical results of a light-weight house with its original configuration (L-B-S) with the geometry of the heavy weight house (L-A-S).

Finally, step 4 will compare the construction system light weight (L-A-S) vs heavy (H-A-S) houses everything else identical. In this paper, only two of these buildings are studied: the house with a "pre-cast concrete" construction (that we will named H-A in this paper) and the timber frame house (L-B). H-A house has a high thermal inertia. The building is in pre-cast concrete with an exterior insulation. The building has double glazing on the South, East and West side and triple glazing on the North side. L-B is a timber frame house, which will represent a low thermal inertia building. The glazing is triple to the South and West side and quadruple to the East and North side.

Sensors

Each house contains approximatively 100 sensors. The sensors measure air temperature, radiant temperature, wall temperature, humidity, air speed, etc. The acquisition is continuous with a one minute time step. In this paper only the indoor air temperature is presented. For that PT100 temperature sensors (class A, precision ±0.35°C) have been used. These sensors are located in the middle of each room at different heights: 0.1m, 1.1m and 1.7m. They are protected from direct solar radiation by white metal cylindrical shields. The experimental platform has a weather station, 50 meters from the houses, with several sensors. These sensors measure outdoor temperature, solar radiation (direct global and diffuse), wind speed and direction, humidity, pressure, etc.

Scenarios

Two scenarios have been studied (Table 1): Table 1: The windows opening consists to some tilt and turn windows as shown in Figure 3 on the window in the middle.

Tool

For the dynamic thermal simulations of the buildings the EnergyPlus 8.1 software was used.

This tool was developed by the U.S. Department of Energy Building Technologies Office. It models, among other things, heat transfer through walls and windows, mechanical ventilation, natural ventilation, cooling and heating loads, and systems. The software is very used by the community of researchers [START_REF] Sptitz | Practical application of uncertainty analysis and sensitivity analysis on an experimental house[END_REF], [START_REF] Boyano | Energy demands and potential savings in European office buildings: Case studies based on EnergyPlus simulations[END_REF], [START_REF] Royuela | Comparison of Energy Performance Rating of Dwellings in Malta Software (Eprdm) with Designbuilder: EnergyPlus Simulation Programme[END_REF], [START_REF] Mateus | Validation of EnergyPlus thermal simulation of a double skin naturally and mechanically ventilated test cell[END_REF]. It has been tested and validated by empirical results, analytical solutions and other tools [START_REF] Henninger | Analytical and comparative testing of EnergyPlus using IEA HVAC BESTEST E100-E200 test suite[END_REF], [START_REF] Tronchin | A Round Robin Test for buildings energy performance in Italy[END_REF]) [START_REF] Manz | Series of experiment for empirical validation of solar gain modeling in building energy codes experimental setup, test cell, characterization, specifications and uncertainty analysis[END_REF].

Numerical model

The houses are modeled with four thermal zones: the crawl space, the ground floor, the first Regarding the ventilation, without natural ventilation, the ventilation flow rate is assumed at 0.5 vol/h for the ground floor and first floor. When natural ventilation is "ON", , the Wind and Stack Open Area model in EnergyPlus is used. In this configuration, the ventilation air flow rate is determined from the wind speed and the thermal stack effect, along with the area of the opening being modeled (EnergyPlus Documentation).

Results and Discussion

Step 1: Measurements

In this paper, only the indoor air temperature of the ground floor is presented.

Weather conditions

Measurements of the outdoor daily temperature and global horizontal irradiance are presented in Figure 4 from 25/08 to 05/09. Le Bourget du Lac climate is continental. These figures shows that maximum daytime temperature vary from 23 to 35°C and from 9°C to 21°C for its minimum at night. The daily temperature amplitude vary from 9°C to 21°C.

Discrepancy of indoor air temperature in one floor

As mentioned previously, many sensors are set in each house, especially for the air-temperature.

Figure 5 shows the air temperature in different points of H-A ground floor. Most of sensors are located at 1.1m height except two in the living room: one at 0.1m and the other one at 1.7m

height. It illustrates that the air temperature is not uniform throughout the same level. Higher temperatures are recorded at positions near the south windows (living room, eating area) at daytime. Relatively lower temperatures are recorded at positions away from the windows (WC, entrance). This is predictable due to the effect of the solar gains passing through the large south windows and heating mainly the floor part that is near these windows. The discrepancy between all the sensors can reach around 1°C. L-B house ground floor air temperature is not presented in this study but results are similar on the discrepancy of the measurements.

For the following parts, when only one measurement is displayed, the sensor in the living room at 1.1m height is chosen. This sensor is chosen because it's located in the middle of the ground floor.

Figure 5: H-A air temperature measurements in ground floor

Air temperature in each houses

Measurements of the indoor air temperature in the living room at 1.1m height for H-A and L-B are presented in Figure 6.

From 25/08 to the 30/08, the same scenario, number 1 with natural night ventilation (see Figure 6), is in both houses. At 7 AM shutters (except South) and windows are closed, there is a direct increase of the air temperature because of the windows closed. The increase of the air temperature in the morning is faster in the H-A than in the L-B which is mainly due to the windows differences. Indeed, solar heat gains are around 40% lower in L-B than in H-A. At 9 PM, a significant decrease of the air temperature appear, when windows are opened, due to the natural ventilation. For this scenario and external condition, these houses have a similar behavior.

From 30/08 noon, the two houses do not follow the same scenario. H-A house follows the scenario 2 (without natural night ventilation) while L-B continues to follow scenario 1 (with natural night ventilation). Step

2: Comparison measurements / simulations

In this part, the comparison of the air temperature between the measurements and the simulations is done separately for each house (steps 2a and 2b respectively the heavy and lightweight house). Simulations are carry out with a one minute time step as described in 0. In this study, only the ground floor is presented, the results on first floor are similar.

Step 2a: Heavy weight House Scenario 1: With natural night ventilation First the measurements and the simulation of the H-A house for the scenario 1 is compared.

As illustrated in Figure 7, and taking into account the uncertainty range of the sensors measurements, an acceptable agreement is obtained between the measured and the simulated temperatures. The maximum discrepancy between a measure and the simulation is around 1°C and appears at daytime. The day peaks are more pronounced for the numerical model.

The reason may that the model is overestimating the amount of solar radiation entering the house and/or underestimating the thermal inertia of the house. We also observe that the peaks are in phase between the measurements and the simulation.

Scenario 2: without natural night ventilation Then, the air temperature measured and simulated for the scenario 2 are compared. Figure 7 shows a satisfactory agreement between the measurements and the numerical model. The maximum discrepancy is about 1°C between a measurement and the simulation and around 2°C just between the measurements due to sensors positions. In this part we can conclude that the numerical model of the H-A house represents correctly the thermal behavior in agreement with the measurements.

Step 2b: Light weight House

Figure 8 shows the L-B ground floor air temperature measured and simulated for the August period. There is a good agreement between the numerical model and the measurements.

During the day and the night the simulated air temperatures are very close to the measurements (difference lower than 0.5°C). Furthermore, peaks are in phase between the measurements and the simulation. In this part we have compared the indoor air temperatures between the measurements and the simulations for these two houses. The results showed an acceptable agreement between the numerical model and the measurements.

In the next part the objective is to estimate the impact of the type of construction on the thermal performance based on these numerical models. But as we have seen before differences exist between them: the geometry, the windows, the internal heat gains, and the infiltrations air flow rate.

Step 3: Impact of the geometrical differences of the experimental houses -Numerical comparison based on light weight models

A new numerical model of the light weight house has been defined. The model has the type of construction of the L-B house. But geometry, windows, thermal bridges and infiltrations air flow rate are the same as the H-A house. The new model is named L-A. Figure 9 shows the simulated air temperature for the L-B house and the L-A house. During the day time the L-A indoor air temperature is higher than L-B (around 2°C for the day peaks) due to larger solar heat gains as explained before. Indeed, the geometry A has double glazing windows and the surface of glazing is more important (+2.2m² for the ground floor) and the balcony is smaller for the geometry A, so the solar irradiance in this house is more important. At night the indoor air temperature is close between the buildings (differences is lower than 0.5°C).

Figure 9: Simulated ground floor air temperature

Step 4: Impact of thermal inertia and natural night ventilation on the thermal behavior

The objective of this final step is to compare the type of construction of the two experimental houses. For this, H-A and L-A numerical models are used. Figure 10 represents the H-A and L-A air temperature simulated in August. As mentioned above, the numerical model used for L-A has the characteristics of H-A, in order to only compare the type of construction of these two houses. The day peaks for the L-A temperature are higher than H-A (up to 2°C for August 28)

because the H-A house has more inertia so the heat gains are absorbed by the thermal mass and the air temperature increases less. At night, the L-A temperature decreases more than H-A (around 2°C). Indeed the natural ventilation releases the heat gains and the H-A house stores more heat gains than L-A during the day so at night the H-A temperature is higher. The amplitude day/night is smaller (around 3°C) for the H-A house because of the inertia, but allow to keep the H-A in a smaller range of temperature between 19 and 25°C most of the time for these weather conditions.

This confirms the impact of thermal inertia in a continental climate on the decrement factor with the reduction of the temperature daily amplitude and the maximum temperature to improve the thermal comfort. However, contrary to what is mentioned in many papers, no significant time lags between the two types of construction have been highlighted. (scenario 1), one without (scenario 2). Each simulation has the same scenario applied until the 30/08, with natural night ventilation (scenario1), as described in Table 3. Figure 12 shows the simulated ground floor air temperature for these 4 configurations. This confirms the combined positive effect of natural night ventilation and thermal inertia.

Natural night ventilation has a positive effect for both construction systems. For the light weight building, it allows to decrease the maximum of temperature up to 2°C and the minimum of temperature at night time up to 6°C. For the high thermal inertia house, there is a slight drift of the maximum temperature higher without natural night ventilation in this configuration which rises to 1°C after 5 days. The major difference appears at night where the minimum of temperature is higher of 4°C without natural night ventilation. As shown previously, the high thermal inertia is more comfortable than the light weight house with or without natural night ventilation. The difference between the light and the high thermal inertia house rises if the buildings don't have a strategy of natural ventilation during the night for this weather conditions. In this case, the high thermal inertia house is more robust to guarantee the thermal comfort for a few days of hot wave without a control strategy to benefit from the cool nights.

Conclusion

The objective of this paper is in a first step to generate thermal comfort data from energy efficient houses in summer time with a focus on the impact of thermal inertia and natural night ventilation. In a second step, numerical simulation are run on these configurations to compare their construction systems. For this, the thermal behavior of two energy efficient houses with different thermal mass is studied in summer time. These two experimental houses are located on the Building Energy platform at INES in the French Alps. The heavyweight building is built with a "pre-cast concrete" construction and the lightweight house has a timber frame construction. They are unoccupied and are equipped with many sensors (around 100). Two scenarios are studied during one month: one with natural ventilation at night and the other one without. Firstly, the indoor air temperature measurements of these two houses on the ground floor are presented. The impact of natural night ventilation is quantify for this configuration.

Indeed the daily amplitude in this configuration is reduced from a value of around 6°C with natural night ventilation to only 2°C without, and the daily maximum of indoor air temperature is kept globally constant with natural night ventilation while it is increasing day after day without. However, differences between the two houses exist and so it is not possible to compare directly their thermal behavior. This is why numerical models have been developed with the EnergyPlus 8.1 software. First step, ensures that these models represents correctly the thermal behavior of each house, and so numerical results are compared to the measures. Finally, an additional model has been built to compare the two construction systems on the same geometry and characteristics (except from the wall materials).

This work confirms the positive impact of both thermal inertia and natural night ventilation on the thermal comfort for energy efficient buildings in continental climate. Thermal inertia reduces the peaks of temperature during the day and the amplitude day/night of the temperature.

The difference between the case 'light weight and without natural night ventilation' and 'heavy weight and with natural night ventilation' is up to 5 to 6°C on the indoor air temperature during a whole day. It also highlights that internal mass permits to have a building less dependent of the natural ventilation scenario for energy efficient buildings. However, contrary to what is mentioned in many papers, no significant time lags between the heavy and the light weight envelope have been seen.

As a perspective, a new experimental house has been built in a Mediterranean climate in which, specific sensors has been implemented to follow the impact of the thermal inertia on the building thermal behaviours. Indeed, temperature and heat flux sensors have been implemented

in the concrete slabs and in a massive concrete wall at different depths. This will allow first to better know the heat flux between the massive elements of the house and the air, to have another type of climate, and to continue in the comparison with numerical models and improve them.

Figure

  Figure 1: methodology used

Figure 2 :

 2 Figure 2: INCAS houses picture

Figure 3 :

 3 Figure 3: Tilt and turn window of woodframe House (L-B) South face, ground floor.

  floor and the attic. The algorithm TARP is used for all zones to calculate the indoor and outside surface heat transfer convection. The door between the ground floor and the first floor was closed but not sealed. Although, it is assumed in the simulation that there is no airflow between the two zones. No air infiltrations are considered between the ground floor and the first floor.Thermal bridges of the ground floor are taken into account with a thermal resistance of 0.0625 m².K/W for H-A and 0.0883 m².K/W for L-B. The infiltrations was measured with a blower door. Infiltrations was defined in the model at 0.0156 vol/h for the H-A house and 0.0324 vol/h for L-B. Data loggers in the houses produced internal heat gains. Regarding the number of data loggers and their position in the houses, the internal heat gains was set to 160W for the ground floor and 40W for the first floor of the H-A house and 70W for the ground floor and 40W for the first floor of the L-B house. The internal heat gains are defined as 70% by convection and 30% by radiation.

Figure 4 :

 4 Figure 4: Weather station measurements -Zoom from 25/08 to 05/09

Figure 6

 6 Figure6highlights the large impact of the natural night ventilation on the thermal behavior for both construction typologies. Indeed, L-B keep the same thermal behavior contrary to H-A. Without natural ventilation the H-A air temperature average increases day after day and the daily amplitude is reduced at around 2°C (compared to an amplitude from 5 to 6°C for the scenario 1). In the morning, H-A temperature without natural night ventilation, starts to

Figure 6 :

 6 Figure 6: Air temperature measurements in living room from 25/08 to 06/09 (Top) -Zoom on Air temperature in Living Room with Weather conditions (Down)

Figure 7 :

 7 Figure 7: H-A air temperature: ground floor

Figure 8 :

 8 Figure 8: L-B air temperature: ground floor

Figure 10 :

 10 Figure 10: Simulated L-A and H-A ground floor air temperature In this configuration, the air exchange rate vary from one night to another and is really

Figure 11 :

 11 Figure 11: Simulated Air flow rate in ground floor of H-A-S, and wind speed at night In order to qualify the impact of both natural night ventilation and thermal inertia, 4 simulations

Figure 12 :

 12 Figure 12: Impact of thermal inertia and natural night ventilation on thermal comfort

Table 2 :

 2 Scenarios applied

		Week 1: 25/08  30/08	Week 2: 30/08 05/09
	H-A-M	Scenario 1: With	Scenario 2: Without
		natural night ventilation	natural night ventilation
	L-B-M	Scenario 1 : With natural night ventilation

Table 3 :

 3 Scenarios applied

		Configurations	01/08 30/08	31/0808/09
	Heavy	H-A with nnv	Scenario 1	Scenario 1
		H-A without nnv	With natural	Scenario 2 -withtout
	Light	L-A with nnv	night ventilation	Scenario 1
		L-A without nnv		Scenario 2 -withtout


Van-Sang Nguyen
email: van-sang.nguyen@cea.fr&rene.escoffier@cea.fr

René Escoffier

Stéphane Catellani

Murielle Fayolle-Lecocq

Jérémy Martin

Design, implementation and characterization of an integrated current sensing in GaN HEMT device by using the current-mirroring technique

Fast fault detection», «Gallium Nitride (GaN)», «HEMT», «Measurement», «Over-current protection», «Power die», «Power integrated circuit», «Test bench», «Wide bandgap devices»,

Introduction

Nowadays WBG semiconductors facilitate high efficient / compact energy conversion systems design [START_REF]Yole report on Power SiC 2020: Materials, Devices and Applications[END_REF][START_REF]Yole report GaN power 2021: epitaxy, devices, applications and technology trends[END_REF]. Given their high switching speed, their dynamic characterization requires high bandwidth and low intrusive probes. Current measurement is made difficult by the intrusiveness of the probes, which modify the power switching loop impedance. In general, the measurement of switched currents can be performed by using a coaxial shunt, a current transformer or Rogowski-coil. However, these current sensors implementation introduce significant undesired parasitic inductance in the power loop of the device under test [START_REF] Wang | Infinity Sensor: Temperature Sensing in GaN Power Devices using Peak di/dt[END_REF][START_REF] Zhang | Methodology for Wide Band-Gap Device Dynamic Characterization[END_REF]. This article presents an integrated current sensor inside a monolithic GaN HEMT device allowing eliminating any intrusive current sensor. Thanks to its dynamic response, this current sensor can be employed with an integrated gate driver as a high-speed protection against short circuits responding within several tens nanoseconds. . The authors present a high temperature DPT (Double-Pulse-Tester) in which the sensitivity and the responses of the integrated current sensor in different temperatures is characterized. Thanks to an infrared beam, the device under test is heated up locally while all the auxiliary circuits are at room temperature.

Current sensing by integrating a current mirror

The current-sense technique principle is based on current mirroring in integrated MOSFET at electronic circuits level [START_REF] Biglarbegian | Characterization of SenseGaN current-mirroring for power GaN with the virtual grounding in a boost converter[END_REF]. A 100V-10A GaN HEMTs has been designed on a single die prototype as Fig. 1. In this prototype, the drains of the power and sensing devices are separated allowing to verify each device independently. The work ongoing is dedicate to optimize the die's dimensions and implement additional functions by using the current sensor such as short-circuit protection in a new monolithic design. The gates of the power HEMT and the sense HEMTs share the same control signal. The current in the sense HEMT copies the current in the power HEMT with the ratio of the ON-state resistances and the value of the sense resistor as in equation [START_REF]Yole report on Power SiC 2020: Materials, Devices and Applications[END_REF].

_ _ _ _ (1)
The ON-state resistance of the power HEMT equals several tens of mΩ, the ON-state resistance of the sense HEMT is 50 times higher and the value of RSENSE equals several Ω in order to obtain a high sensitivity of the sensor. In addition, compared to the shunt-based approach [START_REF] Moench | Integrated Current Sensing in GaN Power ICs[END_REF], for which high temperature calibration can be tedious; the power/sense HEMTs share a similar thermal behavior and the selected RSENSE has a very low tolerance (0.1%) corresponding to a temperature coefficient of resistance of 10 ppm/°C for the high temperature operation. A DFN (Dual-Flat No-leads) package is used for the implementation of the die; on which can be found three electrodes connected to the power drain and two electrodes to the power source. One electrode is connected to the drain sense and another to the source sense. As mention, a single control electrode is common to the two power/sense transistors. This packaged die is implemented in a DPT circuit Fig. 2. The selected RSENSE is very closely to the source sense pad and source power pad in order to avoid the parasitic inductance. Base on the current ratio in these two devices, the measurement of the voltage drop across RSENSE is calibrated to demonstrate the current on the power device.

The experimental results

As in a recent work on the high temperature dynamic characterization of GaN HEMT [START_REF] Nguyen | A high precision dynamic characterization bench with a current collapse measurement circuit for GaN HEMT operating at 175[END_REF], the left side of Fig. 3 shows a high temperature test bench in which a specific profile of the infrared beam is applied on the device under test, heated-up to 175°C while avoiding overheating of the auxiliary components. The main difference in this work compared to [START_REF] Nguyen | A high precision dynamic characterization bench with a current collapse measurement circuit for GaN HEMT operating at 175[END_REF], is that the Fraunhofer-IZM [START_REF] Klein | Comprehensive AC Performance Analysis of Ceramic Capacitors for DC link usage[END_REF][START_REF] Klein | Power module design for utilizing of WBG switching performance[END_REF] sensor allowing to measure the drain-source pulsed current of the DUT is not implemented. The drain source current in this setup is measured by using the current mirror connected to RSENSE (Fig. 3). Fig. 3: High temperature set-up with a local heating-up on device under test by using an infrared beam Fig. 4 shows the experimental results of the sensitivity of the integrated current mirror for three different temperatures (25°C, 125°C and 175°C). The integrated sensor responses with a sensitivity between 60mV/A and 45mV/A for a switched current between 3 A and 8 A. Due to the different temperature coefficients of the GaN HEMT device and RSENSE with a very low temperature variation (10 ppm/°C) the sensitivities depend widely on the temperatures. As the observations under the infrared beam station, the device is auto-heat up when the characterized currents are applied; the higher the applied current is the higher of the ON-state resistance of DUT appears. In the next generations of this integrated current sensor, RSENSE will be integrated inside the device to give a homogeneous behavior to the temperatures. Fig. 4: High temperature characterizations of the sensor's sensitivity Fig. 5 shows the main waveforms of an experiment in a typical DPT when DUT is heated up to 175°C. As mentioned in Fig. 3, the current on the inductance is on Chanel 1, the drain-source voltage VDS is on Chanel 2, the control signal on the gate VGS is on Chanel 3. With a pre-defined sensitivity, the drain-source current of GaN power device is measured by the integrated sensor on Chanel 4, this current is extrapolated from the measured voltage on RSENSE. In this experiment, the current in the inductance were configured at the value of 8A, the sensor's sensitivity is took at 175°C/8A. Fig. 6 presents the DPT currents in power GaN device by its integrated sensor at six different temperatures from 25°C to 175°C, the current in the inductor (see Fig. 3) is measured separately by a commercial current probe (TCP0030A). In this typical DPT, there are three interval T1, T2 and T3 in order to turn-ON and turn-OFF the DUT at a pre-configured current value. To reach the configured current for the first turn-OFF during T1, the current in inductance is charged by a constant input DC voltage (VDC in Fig. 3); these first parts of all the measured currents are zoomed in Fig. 7. As we can see, the measure at 175°C is closest to the current by TCP0030A. In this figure, a current probe (TCP0030A) with another corrected gain gives the dash line. For these measurements, a smallest error deviation at each point by adjusting precisely the gain of the oscilloscope probe (dash line) can be obtained. In this way, the final measurement gain could be slightly corrected for the needs of the experiment by a third gain, so called Gain3 with a value close to 1, the final gain of the sensor (dash line in Fig. 8) can be written as:

%& '( ) 0,005 10 !/# 0.99 49.5 $!/# Follow up the experimental results, the linearity of the current sensor is much better as the temperature increases, the tests at 150°C and 175°C giving the best results.

With this approach, the auto-heatup phenomena is slightly different between the sensor part behavior and the power part behavior on this die that explains the changes of the sensitivity of the sensor in function of the level of measured currents at a fixed temperature. However further studies must be undertaken in order to understand the evolution of self-heating as a function of current levels, and in particular if the improvement in linearity of the sensor at 150°C and 175°C comes from the fact that the contribution of self-heating decreases as the temperature levels increase.

In the next version of this integrated sensor, RSENSE should be integrated and the corrected coefficient must be given at different temperature and current values (by adding a small external electronic correction circuit for example) in order to get the most linear response possible at any configuration. Fig. 9 zooms in the first turn-ON and the second turn-OFF of the measured current at 8 A by the integrated sensor as the second pulse of the DPT, after the calibrations, these observed edges on the sense device share similar behaviors of the power device. These experimental results show full functions of the integrated current sensor in a monolithic GaN HEMT device. By using this sensor, we can remove the high-speed current sensor that add the parasitic inductance in the power loop. The current-mirroring technique makes the behavior of the measured current similar to the current on the power devices.

In other hand, with a gate driver, this current sensor can use for protect very quickly the GaN device against the short-circuit in a specific application. However, this integrated device show its limitation on the stability of the sensitivity with the temperature and the characterized value of the current. Authors are going to make a new version of this current sensor with integrated RSENSE, in order to mitigate the dependent of the measures on the temperatures and the currents.

Conclusion

This work presents a full-integrated current sensor inside a GaN power device. The current sensing approach is current mirroring, measuring a copy of the current in a smaller device with similar thermal behavior, making this approach very stable even in high temperature, up to 175°C. The details of the calibration circuit at different temperature and current were demonstrated. And the high temperature characterizations were given. This sensor need to be improved to have a linear response at any value of the temperature. In a dynamic characterization, this sensor could be used to measure the rising and falling edges of the current through the GaN power devices. Moreover, the integrated sensor could be implemented with a gate driver on a monolithic GaN device to protect the device against the shortcircuit event within several nanosecond.

Fig. 1 :

 1 Fig. 1: GaN die (4.6mm x 4.3mm) with integrated current sensor and its schematic. Sense HEMT : 50x smaller Vs power HEMT

Fig. 2 :

 2 Fig. 2: GaN device with integrated current sensor in the characterization bench

Fig. 5 :

 5 Fig. 5: Experimental waveforms of the DPT at 175°C

Fig. 6 :

 6 Fig. 6: Superimposed DPT currents by integrated sensor ISENSOR_GaN and inductor's current from 25°C to 175°C

Fig. 7 .Fig. 8 .

 78 Fig. 7. Zoom in the first parts of measured currents before the first turn-OFF of DPT at different temperatures

Fig. 9 .

 9 Fig. 9. The second pulse by the integrated sensor during the third interval T3 Fig. 10 and Fig. 11 show the rise times and fall time of the measured current by the integrated sensor at six different temperatures from 25°C to 175°C, the slew-rates of the current are 800 A/µs and 8200 A/µs for the rise time and fall time, respectively. The rise times tR of the current from 10% to 90% of the values are 8.045 ns at different temperature. The equivalent bandwidth of the current sensor for the solicitation at a positive step is therefore classically: -./ .0ℎ 23 )45 0.35 0 0.35 8.045 8 43.5 9:;

Fig. 12 .

 12 Fig. 12. Fall times at different temperatures from 25°C to 175°C (red line) and the unmeasurable zone

Acknowledgements