Adrien Gougeon
email: adrien.gougeon@irisa.fr

Benjamin Camus
email: benjamin.camus@irisa.fr

Anne Blavette
email: anne.blavette@ens-rennes.fr

Anne-Cécile Orgerie
email: anne-cecile.orgerie@irisa.fr

Impact of wired telecommunication network latency on demand-side management in smart grids

Demand-side management relies on the flexibility of consumers' load to avoid electrical network issues, including grid congestion. Recent advances in smart grid systems (also called Energy Internet) allow using demand-side management reactive strategies based on the dynamical shedding of residential consumers appliances. Both centralized and decentralized approaches are considered in literature, depending on the considered system size, but only few contributions consider the potential impact of the telecommunication network on their performance. In this paper, we conduct a comparative analysis on a realistic scenario based on representative power consumption time series of a residential power system. Our results show that latency may have a significant impact on energy management strategies in terms of performance for the smart grid, and that it should be considered when designing such strategies.

I. INTRODUCTION

The ever-increasing individual electricity consumption, the electrification of transport and the grid connection of variable, and somewhat uncertain, decentralized renewable energy sources (e.g. wind, solar) may raise congestion issues on the electrical network [START_REF] Verzijlbergh | Renewable Energy Sources and Responsive Demand. Do We Need Congestion Management in the Distribution Grid[END_REF]. Congestion occurs when the current flowing through a piece of electrical equipment (e.g. a transformer) exceeds its rated value, which would lead to thermal overloading: it must therefore be avoided. In the past, conservative sizing and reinforcement of the electrical network used to represent the sole option to prevent this issue. However, nowadays, the advent of the smart grid, a cyber-physical system based on a ubiquitous and fast communication network (also called the Energy Internet [START_REF] Wang | A Survey on Energy Internet Communications for Sustainability[END_REF]), renders demand-side management technically feasible. Demand-side management implies to adjust the power consumption of so-called "flexible loads" (e.g. smart heaters, electric vehicles) in order to prevent or mitigate grid issues in a considered area. This approach may represent a cost-effective alternative to expensive and timeconsuming grid reinforcement measures, and it is therefore enthusiastically considered by grid operators.

However, the large number of flexible loads to be controlled, as well as the short timescale at which they should be controlled, will render the traditional centralized approaches obsolete [START_REF] Shrestha | Peer-to-Peer Energy Trading in Micro/Mini-Grids for Local Energy Communities: A Review and Case Study of Nepal[END_REF], [START_REF] Ghorbanian | Communication in Smart Grids: A Comprehensive Review on the Existing and Future Communication and Information Infrastructures[END_REF]. Under such conditions, these approaches would indeed require a prohibitive computing effort, as well as raise potential privacy issues due to the transmission and centralization of short timescale, and therefore highly sensitive, consumers electricity consumption data.

Hence, decentralized management approaches are now considered [START_REF] Nimalsiri | A Survey of Algorithms for Distributed Charging Control of Electric Vehicles in Smart Grids[END_REF], [START_REF] Shrestha | Peer-to-Peer Energy Trading in Micro/Mini-Grids for Local Energy Communities: A Review and Case Study of Nepal[END_REF]. Among them, anticipatory and reactive approaches may be distinguished. The anticipatory approach is intended to generate a load power consumption schedule preventing grid issues, based on forecasts (e.g. of the power consumption and generation in the considered network) and on sufficient knowledge of the network characteristics such as topology and impedance for instance. However, forecasts inherently present a certain level of error, thus impacting the performance of such an approach, and sufficient information on the network characteristics may be unavailable. Contrary to the anticipatory approach, the reactive approach is envisaged as a mitigation measure once an issue in the grid (e.g. a congestion) is detected or is close to occur [START_REF] Singh | Simplified Algorithm for Dynamic Demand Response in Smart Homes Under Smart Grid Environment[END_REF], [START_REF] Zhang | Security-Based Load Shedding Strategy Considering the Load Frequency Dependency in Island Distribution System[END_REF], [START_REF] Meyn | Ancillary service to the grid using intelligent deferrable loads[END_REF]. Therefore, it does not require any knowledge on the future and needs only limited to no information on the electrical network characteristics. Such an approach relies on short period measurements in the problematic area (e.g. short period measurements of the electrical current in the potentially congested piece of equipment), and on equally short period flexible loads control.

This paper presents a comparative analysis of the performance between two such reactive energy management algorithms, one being decentralized and the other being centralized, both based on short frequency measurements and control, and both intended to mitigate congestion in a low-voltage electrical network, whose model is publicly available, and will be detailed later in the paper. The algorithms are based on the successive and repeated shedding (called "cascado-cyclic shedding" ) of a sufficiently important number of direct-acting smart electric heaters [START_REF] Vaubourg | Multi-agent multi-model simulation of smart grids in the MS4SG project[END_REF]. These loads can be reasonably shed during a short amount of time without impacting noticeably their owners' comfort due to the significant thermal inertia in typical households [START_REF] Vaubourg | Multi-agent multi-model simulation of smart grids in the MS4SG project[END_REF].

However, decentralized management approaches are expected to be more sensitive to communication delays, jitter and bottlenecks, as experienced in the Internet, than centralized ones [START_REF] Guo | Impact of Communication Delay on Asynchronous Distributed Optimal Power Flow Using ADMM[END_REF]. Hence, this comparative analysis, between a centralized and a decentralized approach, is performed for a range of communication latency values typical of local area networks. The impact of latency on the performance of demand-side management algorithms for congestion prevention/mitigation is generally not covered in papers dealing with this approach [START_REF] Nimalsiri | A Survey of Algorithms for Distributed Charging Control of Electric Vehicles in Smart Grids[END_REF]. Yet, this impact may have significant consequences even for small-sized power systems, as we will show in our study, notably in terms of performance and in terms of the necessary number of messages for each approach. The numerical simulations are performed based on an opensource co-simulation platform combining telecommunication network simulators (SimGrid, ns-3) and power system simulator pandapower [START_REF] Camus | Cosimulation of an electrical distribution network and its supervision communication network[END_REF]. The impact of wired telecommunication network latency between the centralized and the decentralized approaches is very significant, the latter being more affected than the former.

The paper is organized as follows. Section II details the state of the art. The studied use-case is presented in Section III and the validation framework is detailed in Section IV. The results are discussed in Section V. Section VI concludes this work and presents future work.

II. STATE OF THE ART A. Demand-side management

The emergence of smart grids renders more and more urgent the need for adopting a holistic view on the power system and on its supervision telecommunication network. Combining both systems aims at making the power system more flexible in order to integrate variable, less-dispatchable renewable energy sources into the grid [START_REF] Rehmani | Integrating Renewable Energy Resources Into the Smart Grid: Recent Developments in Information and Communication Technologies[END_REF]. It also aims at operating the power system in a more efficient way, increasingly closer to its physical limits, by adopting less conservative security margins [START_REF] Rte | Outlines of RTE's R&D programmefor 2017-2020[END_REF], [START_REF] Zhang | Security-Based Load Shedding Strategy Considering the Load Frequency Dependency in Island Distribution System[END_REF]. This should contribute in postponing, or even avoiding, the need for costly grid reinforcement.

However, this combination renders the power system performance dependent on the design and management of its telecommunication supervising infrastructure [START_REF] Ardiansyah | Latency Minimization for Energy Internet Communications with SDN Virtualization Infrastructure[END_REF]. The performance of the former can of course be enhanced by using the additional amount of information provided by the latter [START_REF] Vinot | Congestion Avoidance in Low-Voltage Networks by using the Advanced Metering Infrastructure[END_REF]. Energy Internet communications make use of various wired (Ethernet, DSL, Power Line Communications) and wireless (Wi-Fi, ZigBee, LoRaWAN, etc.) technologies [START_REF] Ghorbanian | Communication in Smart Grids: A Comprehensive Review on the Existing and Future Communication and Information Infrastructures[END_REF], [START_REF] Wang | A Survey on Energy Internet Communications for Sustainability[END_REF]. In particular, wired Ethernet-based networks are praised for their reliability and energy efficiency [START_REF] Ghorbanian | Communication in Smart Grids: A Comprehensive Review on the Existing and Future Communication and Information Infrastructures[END_REF], contrary to power line communications that present severe channel conditions and are unable to accommodate a massive number of clients [START_REF] Deng | CSMAand-NOMA-based Random Massive Access in Power Line Communication for Smart Gird Applications[END_REF]. Hence, this renders wired telecommunications particularly suitable to the requirements of residential demand-side management in terms of bandwidth, latency, reliability and coverage area [START_REF] Ardiansyah | Latency Minimization for Energy Internet Communications with SDN Virtualization Infrastructure[END_REF], [START_REF] Ghorbanian | Communication in Smart Grids: A Comprehensive Review on the Existing and Future Communication and Information Infrastructures[END_REF].

However, recent works have shown that communication delays, inherent to the transmission of information, could degrade dramatically the performance of a smart grid [START_REF] Guo | Impact of Communication Delay on Asynchronous Distributed Optimal Power Flow Using ADMM[END_REF]. Hence, communication latencies should be taken into account when designing control algorithms with a significant share of information transmission, such as distributed energy management strategies. Yet, many work consider perfect telecommunication conditions, without latency constraints [START_REF] Haider | A review of residential demand response of smart grid[END_REF], [START_REF] Safdarian | Optimal Residential Load Management in Smart Grids: A Decentralized Framework[END_REF], [START_REF] Singh | Simplified Algorithm for Dynamic Demand Response in Smart Homes Under Smart Grid Environment[END_REF], although the implied reaction time required for such a scenario is in the order of seconds or lower [START_REF] Ardiansyah | Latency Minimization for Energy Internet Communications with SDN Virtualization Infrastructure[END_REF], [START_REF] Ghorbanian | Communication in Smart Grids: A Comprehensive Review on the Existing and Future Communication and Information Infrastructures[END_REF], [START_REF] Zhang | Security-Based Load Shedding Strategy Considering the Load Frequency Dependency in Island Distribution System[END_REF].

Additionally, the need for integrating disparate, intermittent and widely geographically distributed energy sources (i.e. renewable sources) and flexible loads (i.e. heaters, electric vehicles) presenting individual constraints calls for a decentralization of the power system management [START_REF] Safdarian | Optimal Residential Load Management in Smart Grids: A Decentralized Framework[END_REF], [START_REF] Shrestha | Peer-to-Peer Energy Trading in Micro/Mini-Grids for Local Energy Communities: A Review and Case Study of Nepal[END_REF]. However, without centralization, demand-side management strategies may be even more sensitive to telecommunication latencies. To explore this assumption, we conduct a comparative analysis of two approaches, a centralized and a decentralized one, on a single realistic scenario representative of residential conditions. The benefits of residential demand-side management for reducing network congestion have been assessed in the literature [START_REF] Haider | A review of residential demand response of smart grid[END_REF], [START_REF] Safdarian | Optimal Residential Load Management in Smart Grids: A Decentralized Framework[END_REF].

B. Simulation of smart grid infrastructures

Electrical grid studies usually rely on power system simulators that numerically reproduce the dynamics of an electrical network and perform power flow calculations for a considered network. Such simulators represent the necessary alternative to performing tests on the actual network, which may cause disturbances detrimental to customers. Several tools exist for power system simulations, such as pandapower [START_REF] Pandapower | Official website[END_REF] and PowerFactory [START_REF] Digsilent | Official website[END_REF].

On the other hand, event-based packet-level simulators, such as ns-3 [START_REF] Henderson | NS-3 project goals[END_REF] and OMNeT++ [START_REF] Varga | An overview of the OMNeT++ simulation environment[END_REF], are widely used in the telecommunication network community. They implement a large range of communication protocols (e.g. TCP/IP, UDP, Wi-Fi) that may be deployed in smart grids, thus making them good candidates for simulating the smart grid supervision telecommunication network. The highly-efficient SimGrid platform [START_REF] Casanova | Versatile, Scalable, and Accurate Simulation of Distributed Applications and Platforms[END_REF] is dedicated to the simulation of large-scale distributed systems, which makes it perfectly suitable to simulate a smart grid control system.

Co-simulation consists in coupling different stand-alone simulation tools, so that they simulate together a whole cyber-physical system in a consistent way. In this work, we employ our own open-source co-simulation tool relying on pandapower on the power system side, ns-3 on the telecommunication side and SimGrid for the co-simulation framework. While our previous study using this framework [START_REF] Camus | Cosimulation of an electrical distribution network and its supervision communication network[END_REF] employed PowerFactory for the power system, we developed, for the study presented in this paper, an interface for pandapower as this simulation tool is not license-dependent and thus allows for multiple simulations to be launched at the same time on the same machine. Consequently, our co-simulation framework for cyber-physical systems based on SimGrid, ns-3 and pandapower greatly shortens the experimental campaign's duration, and as all the software pieces are freely available, it is easily reusable by others.

III. DEMAND-SIDE MANAGEMENT SCENARIO

Grid operators tend to operate their electrical networks increasingly closer to their physical limits [START_REF] Rte | Outlines of RTE's R&D programmefor 2017-2020[END_REF]. In particular, despite the fact that consumption is ever-increasing, grid operators are reluctant to carry out grid reinforcements, as they are costly, time-consuming and may give rise to strong public opposition. Hence, it is expected that intelligent load shedding strategies will be developed and applied in order to solve any congestion issues that may have arisen from the electrical current exceeding maximum allowed values in lines and transformers.

Such congestion issues may occur during peak period times, when consumption is at its highest, that is in the early evening in most countries, especially in winter times when electrical heaters are used. This type of appliance is power and energy intensive, but can be interrupted for a short period without disturbing the consumers. This is why we consider controllable electrical heaters in this case study in order to analyze the influence of the telecommunication network's performance on the smart management of the electrical grid.

A. Power system

Real data from existing power systems are scarce, especially when considering not only few isolated loads, but an entire network, its topology and its loads. We chose to base our study on the publicly available electrical network IEEE model "European Low Voltage Test Feeder" (ELVTF) [START_REF]European low voltage test feeder[END_REF]. This network includes a 3-phase, low voltage (230/400 V) distribution grid with multiple feeders connected to a 11 kV/416 V substation typical of the United Kingdom [START_REF] Schneider | Analytic Considerations and Design Basis for the IEEE Distribution Test Feeder[END_REF]. The model also provides time series of one-minute averaged consumption. Each time series corresponds to the consumption of a single household, for a total of 55 time series for 55 households. In this study, for the sake of simplicity and as a first step, it is assumed that the electrical network is ideally balanced over the three phases while future studies will consider a larger scale, unbalanced network. Our study focuses on the peak hour, between 5:30 pm and 6:45 pm for the ELVTF model, as it constitutes the most stressful hour for power system management.

Gas boilers and electric storage radiators are commonly used in the UK [START_REF] Ofgem | Insights paper on households with electric and other non-gas heating[END_REF]. So, we supposed that domestic directacting electric heating was not included in the ELVTF traces for the considered peak period. Nevertheless, our scenario considers a context where direct-acting electric heating is widely used, as it is the case in France [START_REF] Ademe | Les avis de l'ademe, modes de chauffage dans l'habitat individuel[END_REF], in order to provide flexibility to the power system management. Thus, for our scenario, 3 electric heaters are added in each household. Each heater power consumption is modeled as a cyclic profile alternating between typical values of 2 kW and 0 kW. Used values rely on an experiment performed on an electric radiator located in the Rennes region, France on Feb, 11 2019 between 7:15 pm and 8:30 pm, during the French consumption peak period (or more exactly to its second, descending part) [START_REF] Rte | French national daily load curves[END_REF]. Each radiator has a power profile based on real data on which random time-delays are applied. Each time-delay is equal to the sum of two random time-delays which represent respectively the dephasing between radiators belonging to the same household (arbitrarily-selected to be equal to 30 seconds maximum to illustrate variability within a single house) and the dephasing between two households (arbitrarily-selected to be equal to 15 minutes maximum to showcase the variability among the houses of the same district). It must be pointed out that a simple heater model is considered due to the absence of additional experimental data. In the considered model, the post-shedding rebound effect on the power consumption is not taken into account. It is assumed that the rebound effect due to a relatively short shedding duration is negligible.

B. Computing system

In this scenario, we consider that each household has a smart electricity meter that can send on/off instructions to the electrical heaters. A TCP/IP telecommunication network is considered in our scenario of automated and intelligent shedding in the electrical network. In order to be managed and monitored, the electric line Line1, feeding the 11 kV/416 V substation, and the households are equipped with computing devices. We assume that these devices belong to the same LAN (local area network), connected through Ethernet links following a star topology, each computing device being linked to a central switch that can be the district DSLAM (digital subscriber line access multiplexer). For the sake of simplicity, homogeneous bandwidths and latencies are considered for each link.

C. Smart grid management

In order to automate the shedding of the electric heaters in the different households, we consider the cascado-cyclic policy. In the cascado-cyclic policy, a shedding process is initiated when the current in Line1 goes above an upper threshold Θ. Then, several households are selected to be shed. We considered that, on average, at least one heater per household is in the on-duty part of its cycle. Assuming that the current I Line1 flowing in the considered line is mostly active (i.e. its reactive part is considered as negligible), then, it can be expressed as:

I Line1 ≈ i P H,i √ 3V Line (1)
where P H,i is the instantaneous power consumption of household i and V Line1 the line phase-to-phase voltage. Following this, the number n H of households to shed is approximated using Equation 2 according to the current in Line1 I Line1 , the maximum consumption P h of a single heater of an household and the phase-to-phase voltage V Line1 .

n H = (I Line1 -Θ) × √ 3 × V Line1 P h ( 2
)
where Θ is the maximum rated current that the line may transmit on a permanent basis. The shedding process stops when the current I Line1 in Line1 goes below a current threshold θ (lower than Θ) determined with Equation 3. In this equation, we consider the worst case scenario where all the households that stop shedding switch all their three heaters back on at the same time. The resulting power consumption increase would be then of 3 × P h per household. Hence, the lower threshold θ can be expressed as:

θ = Θ - n H × P h √ 3 V Line1 (3)
where the lower threshold θ is dynamically adapted during the cascado-cyclic process when the current number of shed households n H varies. During the shedding process, the group of shed households is regularly modified, avoiding an household being shed for too long consecutively. For the same reason, and also to balance the shedding among the different households, the selection of households to be shed is done in a cyclic way, described hereafter. Indeed, as we do not consider pricing mechanisms to incentivize users to accept shedding policies, we target a fair shedding policy balancing the shedding duration among the users. The cascado-cyclic policy may be implemented by multiple algorithms. In this work, we propose two representative and simple algorithms: a centralized and a decentralized one. Both rely on the telecommunication network among the households previously described to exchange information. We opted for simple algorithms to highlight the telecommunication network impact without hiding its effects over complex optimizations.

D. Centralized Cascado-cyclic approach

The major component of the centralized approach in the cascado-cyclic process consists in the master node. It is in charge of managing the households in order to keep the current below its upper threshold in Line1. It periodically receives information from the power and current probes positioned in each household. According to this data, it decides whether or not electric heaters should be shed. As a consequence, it sends commands to shutdown or switch on electric heaters in households. Taking advantage of the amount of information it receives, the master selects in priority the households that have the highest average power consumption over the last δ seconds, but still balances the shedding among the different households, as stated previously. The reactivity of the centralized approach strongly depends on the frequency at which it receives information when no prediction algorithm is used. Consequently, we employ in our scenario a high frequency to guarantee the performance of the power system management: one message per second for each household and for Line1 is sent to the master node. The master node can be located either near the Line1 substation or in a remote location connected through wired telecommunication networks.

In subsequent work, we explored various lower frequencies for information exchange and concluded that decreasing the frequency increases both the cumulative peak duration and its variability, thus leading to closer performance between centralized and decentralized approaches, as expected.

E. Decentralized cascado-cyclic approach

The decentralization of the cascado-cyclic shedding process removes the ability to sample and compare the power consumption of each household. Thus, the only value monitored is the current at the Line1 substation, which is periodically sampled by a probe. For this approach, the households are considered sorted in a predefined and arbitrary order. Whenever the current in Line1 goes above the upper threshold, shedding commands are sent to the first household. The first household Fig. 1: The proposed experimentation set-up. then decides whether or not it will handle the command. If it does, the household is shed for a specific duration, and it sends the command to the next household afterward. If it does not, the command is directly forwarded to the next household which will decide whether or not it will handle the command, and so on. A cycle is completed whenever the last household forwards the command to the Line1 probe. The probe keeps track of the number of completed cycles (i.e. a cycle is finished when all sheddable households have handled one command) and adds this information in the shedding commands. Each household may handle a command only if the command has a number of cycles equals to the number of times the household has been shed. This tokenbased strategy ensure that each household handles the same number of commands. Whenever the current in Line1 goes below the lower threshold a command is sent to stop the shedding process. This command goes through each household in a similar way than the shedding command. At the time the command reaches the Line1 probe, it ensures that the shedding process has stopped for each household. The cycle is resumed when a new cascado-cyclic process starts, thanks to this decentralized algorithm. This decentralized algorithm is a classical token-based algorithm whose main advantage consists in its simplicity. Indeed, it does not require complex computation or heavy data storage for each node: it simply requires each node to keep track of its number of executed shedding and to compare this number with the cycle number included in the shedding command.

IV. VALIDATION FRAMEWORK

A. Validation means

We propose to study the impact of ICT systems on smart grids operations by using the set-up of Figure 1. It makes SimGrid, ns-3 and pandapower co-evolve and interact to rigorously model and simulate a smart grid, while taking into account the electrical and telecommunication intertwined systems.

We use the programming interface of SimGrid to model the distributed control application of the smart grid and its computing infrastructure. We can use then the unique ICT performance models of SimGrid to simulate the execution of this distributed ICT system. Thanks to an ad-hoc coupling between SimGrid and ns-3, we use the telecommunication models of ns-3 to simulate message exchange in the smart grid. We benefit then from the high accuracy of ns-3 and from its various communication models.

As part of this work, we developed an open-source dedicated tool to export pandapower as an FMU, which is available online 1 . Thanks to the open-source SimGrid-FMI plug-in developed in our previous work [START_REF] Camus | Cosimulation of an electrical distribution network and its supervision communication network[END_REF] and officially certified by the FMI standard2 , these FMUs can be imported into SimGrid. During the simulation, the distributed control system modeled in SimGrid can then interact directly with the electric grid modeled in pandapower (e.g. get the current in a line, or set the consumption of a load) and the telecommunication network modeled in ns-3. For this study, we rely on SimGrid v3.24, pandapower v2.1.0 and ns-3 v3.29.

B. Experimental plan

We compare the two approaches for three metrics: 1) Cumulative overcurrent duration: cumulative duration during which the current in Line1 is above the upper threshold. It is computed by SimGrid and is a measure of our approach efficiency from the Distribution System Operator's perspective; 2) Cumulative household shedding duration: cumulative duration of shedding required to solve the congestion problem. It is computed by SimGrid and indicates the efficiency of the approach from the smart grid consumers perspective; 3) Total amount of data sent through the telecommunication network. It is computed by SimGrid and indicates the impact of the smart grid control system on the telecommunication network.

Table I summarizes the fixed parameters in our experiments: the network bandwidth (voluntarily oversized as its impact for wired network is not a limiting factor in our context), the sampling frequency at which the power and current values are monitored and sent to the master node in the case of the centralized approach, the duration of a single shedding if not interrupted by a switching on command, and the duration for averaging the household consumption in order to select in priority the highest consuming households. Table II summarizes the variable parameters: the number of sheddable households, the upper current threshold on Line1, the communication latency for each telecommunication link and the size of each command and monitoring message. During a simulation, only one parameter varies from the default parameters. The default parameters are indicated in the last column of Table II and their choice is explained throughout the simulation results.

To compare the approaches with a given parameters set, we run three simulations: (1) a co-simulation with the centralized approach, (2) a co-simulation with the decentralized one, and (3) a simulation of the electrical network without shedding, in order to build baseline results. When switching to a new set of parameters, a new electric heater power profile with random The simulations were run in parallel using several machines on the Grid'5000 [START_REF]Official website[END_REF] platform. We performed a total of 4,200 simulations to execute this experimental plan.

V. RESULTS

In this section, we explore the impact of:

• the upper current threshold, that is of uttermost importance for the electricity distribution system operator, and that can include a safety margin depending on the expected reactivity of the system; • the number of sheddable households, that depends on the consumers' willingness to help the electricity operator, and in our case, this effort is fairly shared among the voluntary users; • the communication latency and message sizes that are used for implementing the demand-side management and that depend on the telecommunication network topology and communication protocols.

A. Cascado-cyclic behavior assessment

Figure 2 shows the typical evolution of current in Line1 over time for a single simulation run with the centralized approach (the decentralized one follows a similar trajectory). From this figure, we can see that, during peak time, the current progressively increases to reach the upper current threshold of 440 A at 5.49 pm. Then, the cascado-cyclic process starts shedding household heaters to keep the current below the upper threshold. We can see from the variations of the lower current threshold that the cascado-cyclic process dynamically adapts the shedding effort to successfully remain below the upper threshold (i.e. the lower the threshold is, the more important the shedding effort needs to be).

B. Influence of the upper current threshold

We can see from Figure 3 that both cascado-cyclic approaches significantly reduce overcurrent duration. Considering the default value of 440 A for the upper current threshold, the centralized (resp. decentralized) approach reduces overcurrent duration of about 94 % (resp. 89 %) compared to the baseline scenario without any shedding.

We can observe that the two approaches perform even better with lower thresholds when there are more overcurrent peaks to reduce. With a threshold of 410 A, the overcurrent duration is reduced by about 96 % (resp. 94 %) with the centralized (resp. decentralized) approach. The required reactivity of the approaches is more important with higher thresholds when the number and the duration of the overcurrent peaks decrease. This explains why the centralized approach outperforms the decentralized one, in particular in this case. Indeed, the decentralized approach is less reactive because the shedding commands may have to be forwarded several times from household to household before being applied. At the opposite, the centralized implementation sends the shedding commands directly to the sheddable households. Nonetheless, even in this context, with a threshold of 450 A, the two approaches significantly reduces overcurrent duration of about 93 % (resp. 87 %) for the centralized (resp. decentralized) approach.

We can observe from Figure 4 that both approaches achieve such a performance with a similar amount of shedding for every considered threshold. As expected, the duration of the shedding decreases when there is less overcurrent peaks -i.e. with higher thresholds. Even in the worst considered case with a threshold of 410 A, the shedding remains significantly low with an average cumulative shedding duration per household of about 7 minutes during the considered period. With our threshold default value of 440 A, the shedding becomes negligible for the end-users with an average cumulative shedding time per household of about 2 minutes only.

As shown on Figure 5 and as expected, the upper threshold does not have a significant impact on the number of messages sent by the two approaches. We observe that, because of its power probes, the centralized approach sends about 27 times more messages through the telecommunication network than the decentralized one, no matter the upper threshold value. This may strongly limit the performance with wireless telecommunication technologies (e.g. Wi-Fi).

C. Influence of the number of sheddable households

Figure 6 shows that the gap between the number of sent messages increases linearly with the number of sheddable households (and therefore with the number of power probes in the centralized approach). With 55 households, the centralized approach sends about 50 times more messages than the decentralized one. This may limit the scalability of the centralized approach, which would be even more limited in a wireless context.

Figure 7 shows the decreasing standard deviation for the average per-household shedding duration when the number of sheddable households increases. It means that, in this case, both approaches efficiently share the shedding effort between the available households. As expected, the average shedding time per household decreases as the number of sheddable households increases: it goes from about 4.5 minutes with 15 households to about 1 minute with 55 households.

Figure 8 shows that the number of households does not impact significantly the cumulative overcurrent duration. This means that both approaches scale up in our context and do not require a high number of sheddable households for a reasonable upper current threshold. As expected, since the centralized approach is more reactive and takes advantage of more information, it achieves a lower overcurrent duration (about 40% lower) than the decentralized approach.

These results indicate that the telecommunication network size, which represents here the number of sheddable -and thus communicating -households, slightly impacts the cumulative overcurrent duration for both approaches. Yet, the better performance of the centralized approach comes with a strong increase in the required number of messages: 55.5 messages per second on average for 55 households, against 1.1 messages per second for the decentralized approach. Here also, relying on a wired network with a reliable transport protocol makes the scenario feasible for demand-side management.

D. Influence of the communication latency and message size

Figure 9 shows that the two approaches are not significantly impacted by the size of the messages. Although the centralized approach outperforms the decentralized approach in terms of overcurrent duration (45 seconds on average against 80 seconds), both equally distribute the shedding duration among the households and present a similar average shedding duration per household. Concerning the number of sent messages, the decentralized approach largely outperforms the centralized one as observed in Figures 5 and6. The negligible impact of message size is mainly due to the scenario conditions: packet losses are not considered in this scenario because the wired telecommunication network does not experience congestion, and the transport protocol is reliable (i.e. TCP). This behavior would significantly change in the context of power line communications or Wi-Fi networks.

Similarly, the telecommunication network latency does not significantly impact the number of sent messages for both approaches (results are similar to Figure 5). However, we observe from Figure 10 that the telecommunication latency has a non negligible impact on the approaches' performance. If we consider an unrealistic 0 ms latency (instantaneous data transfers and reactions), like many studies of the literature, the centralized approach decreases the cumulative overcurrent duration of about 75 % compared to the decentralized one. However, if we consider a 1 ms latency, the centralized approach reduces the overcurrent duration of only about 40 % compared to the decentralized one. With a 20 ms latency, the overcurrent duration is getting even closer in both approaches especially when taking into account the standard deviation. In addition, we observe on Figure 11 that the centralized approach also largely outperforms the decentralized one in terms of average overcurrent duration when considering a 0 ms latency, but this gap is tighter for latencies above 0 ms. We also note that results' variability grows faster in the decentralized management as the latency increases. Consequently, the centralized approach significantly outperforms the decentralized one only with low communication latencies, and the difference diminishes for larger latencies.

According to Figure 12, when considering low latencies, the average cumulative shedding time per household is comparable between both the decentralized and the centralized approaches. However, the gap between them increases with latency because it impacts the propagation delay of the shedding commands in the decentralized approach, which is then outperformed by the centralized one. Hence, with a 20 ms latency, the average shedding per household is about 140 s (resp. 250 s) in the centralized (resp. decentralized) approach. In this case, the decentralized approach overreacts and performs more shedding than required.

E. Discussion

The two proposed approaches greatly reduce the overcurrent peak duration (from about 96 % to 87 %) without a significant impact on the end-users: the average cumulative shedding per households ranges from about 7 to 1 minutes, corresponding respectively to 9% and 1% of the simulated time.

When disregarding the telecommunication network parameters, one may consider that the centralized approach is always better than the decentralized one because it decreases the overcurrent peak duration more with a similar impact for the end-users (i.e. (cumulative) shedding duration per household). However, the centralized approach requires a high number of messages to achieve this level of performance, even on a small-size network (up to 55 households). Since it significantly increases the traffic on the telecommunication network (up to more than 50 times), the centralized approach may not scale up well with the expected large number of households to be deployed on the smart grid (e.g. with the Wi-Fi technology). In addition, as the network latency increases, the overcurrent reductions achieved by the centralized approach get closer and even similar to ones obtained with the decentralized one. However, at higher latencies, the decentralized approach has significantly more impact on the end-users as it increases the cumulative shedding duration per household. It means that, although decentralized approaches should better scale with larger networks than centralized ones, they may be less accepted by electrical grid users since their performance in terms of shedding time per household is more impacted by latency. Thus, the approaches should be carefully chosen according to the telecommunication network features and the size of the considered power system. In this work, for both centralized and decentralized cases, we evaluated simple algorithms not requiring significant computation power in order to highlight the network latency influence on the performance of a smart grid. In the case of more complex algorithms, the computation duration adds time to the latency, and can consequently impact the shedding performance as well.

VI. CONCLUSION

Residential reactive demand-side management becomes feasible in the context of smart grids and Energy Internet. In this paper, we explore the cascado-cyclic shedding strategy with electrical heaters to avoid electrical network congestion. We compare the centralized and decentralized management versions of this strategy and study the impact of wired telecommunication network latency on the performance perceived by the power system manager and by the electricity consumers.

The evaluation exploits a realistic scenario of 55 households based on traces from a real electrical grid and numerical co-simulations, combining SimGrid, ns-3 and pandapower simulators, to faithfully reproduce the co-evolution of the power system and of its wired telecommunication network. We made available the open source co-simulation tools used in this paper.

Our results show that not considering any telecommunication network latency, as often assumed in literature, implies a strong overestimation of the performance achieved by the centralized approach from the power system operator's perspective. We also show that, for the power system operator, larger telecommunication network latency penalizes the centralized approach and favors the decentralized approach, although for the studied latency range, the centralized approach always performs better. As for the electricity consumer's point of view, larger telecommunication network latency has a strong negative impact for the decentralized approach, while it is negligible for the centralized one. Thus, for the decentralized approach, the latency affects negatively and heavily consumers. Considering the studied scenario and from the consumer point of view, the centralized approach is preferable for latencies above 10 ms.

Future work will consider larger scale, unbalanced smart grids, and exploring other telecommunication technologies, such as wireless networks.

Fig. 2 :

 2 Fig. 2: Evolution of the current in Line1 over time with the centralized implementation with 30 sheddable households, an upper threshold of 440 A, a communication latency of 5ms and 1024 kb messages.

Fig. 3 :

 3 Fig. 3: Overcurrent reduction in comparison to the baseline scenario (without any shedding) when varying the current threshold.

Fig. 4 :

 4 Fig. 4: Average cumulative shedding time per household versus current threshold.

Fig. 5 :

 5 Fig. 5: Number of messages sent versus current threshold.

Fig. 6 :

 6 Fig. 6: Number of messages sent versus number of sheddable households.

Fig. 7 :

 7 Fig. 7: Average cumulative shedding time per household versus number of sheddable households.

Fig. 8 :

 8 Fig. 8: Cumulative overcurrent duration versus number of sheddable households.

Fig. 9 :

 9 Fig. 9: Cumulative overcurrent duration versus messages size.

Fig. 10 :

 10 Fig. 10: Cumulative overcurrent duration versus telecommunication latency. Fig. 11: Average overcurrent duration versus telecommunication latency.

Fig. 12 :

 12 Fig. 12: Average cumulative shedding time per household versus latency.

TABLE I :

 I Co-simulations fixed-parameters.

	Network bandwidth	10Gb
	Power and current probes sampling frequency	1 sec
	Duration of a single shedding
	(if not interrupted)	60 sec
	Duration δ considered to average
	households consumption	300 sec

TABLE II :

 II Co-simulations variable-parameters.

		Range	Step	Default
	Number of sheddable
	households 3	15 to 55	5	30
	Upper current
	threshold	410 to 450 A	10 A	440 A
	Communication
	latency 4	0 to 20 ms	5 ms	5 ms
	Messages size	1024 to 10240 kb 1024 kb 1024 kb
	time-delays (as described on Section III-A) is generated for
	each household. Each set of parameters is simulated 50 times
	and the results present mean and standard deviation values.

https://framagit.org/Adrien.Gougeon/pandapower-fmu

https://fmi-standard.org/tools/

The number of households in the simulation stay the same, 55. However, the number of households that can be shedded varies.

The configuration with 1 ms latency was also explored.

ACKNOWLEDGMENT

This project is funded through RennesGrid project from the "Programme des Investissements d'Avenir" operated by the French Environment and Energy Management Agency (ADEME) and by the CNRS Momentum project RI/RE.


Adrien Gougeon

Benjamin Camus

Franc ¸ois Lemercier

Martin Quinson

Anne Blavette
email: anne.blavette@ens-rennes.fr

Anne-Cécile Orgerie

Co-Simulation of Power Systems and Computing Systems using the FMI Standard

Simulation-oriented research requires precise and validated simulators. Each community has its set of preferred and widely adopted software tools. Some works are multidomain and require the use of dedicated tools and semantic of each domain to produce largely accepted results. In this work, we demonstrate how to realize co-simulation between power system networks, telecommunication networks and distributed computing resources. The demo will show a basic scenario to explicit the relevance of such a combination.

I. INTRODUCTION

Several research fields rely on simulators to explore their hypotheses, and many are at the crossing of several domains. Smart grids constitute such an example of multi-domain requirements as they rely on computing and telecommunication network resources to pilot the underlying power system networks. This article presents a way to combine simulation tools for power system networks, telecommunication networks and distributed computing resources in a coherent co-simulation framework. The co-simulation idea consists in using triedand-tested simulators from the original communities. Such a combined tool will ease the study of complex smart grids scenarios where the performance of each part of the system impacts the rest of the system's functioning.

The vast majority of power network studies are based on power system simulators which mimic the behavior of actual power networks. These simulators allow researchers to perform experimentation campaigns without degrading the safe and reliable operation of actual power systems, while staying in a controllable, modular, and often reproducible environment. Some simulators are commonly used by the power system community like pandapower [START_REF] Pandapower | Official website[END_REF] or PowerFactory [START_REF] Digsilent | Official website[END_REF]. For similar reasons, the telecommunication network community also has its own set of preferred simulators, such as ns-3 [START_REF] Henderson | NS-3 project goals[END_REF] or OMNeT++ [START_REF] Varga | An overview of the OMNeT++ simulation environment[END_REF]. These simulators allow users to model and experiment several commonly used communication protocols, either wired or wireless, in packet-level simulations.

The SimGrid framework [START_REF] Casanova | Versatile, Scalable, and Accurate Simulation of Distributed Applications and Platforms[END_REF] is a toolbox to develop simulators of distributed platforms. SimGrid can either use its own communication system or a fully integrated ns-3 communication mode. In addition, SimGrid is part of the Functional Mock-up Interface (FMI) standard [START_REF] Camus | Co-simulation of FMUs and Distributed Applications with SimGrid[END_REF], making SimGrid an interface able to import Functional Mock-up Units (FMUs), i.e., simulation models from other simulators.

II. CONTRIBUTION

We developed a tool to generate pandapower networks FMUs1 . It allows users to build and export power networks models that can then be imported into SimGrid. Inside Sim-Grid, the power network inputs can be modified and the electrical network load flow problem is only solved when trying to access its outputs. We chose to rely on pandapower as it is part of the open source initiative and thus fully free to use. As every part of the co-simulation is license-free, the deployment of the simulations on distant testbed servers is facilitated and reproducible. Figure 1 shows a simplified view of how ns-3 and pandapower are interacting with SimGrid, which acts as a co-simulation engine for running multi-models of complex systems in this case.

III. CONSIDERED SCENARIO

We chose to use a basic, though realistic, scenario to present our co-simulation environment. In this scenario, there is a load and a generator connected through a power network to a transformer. The generator provides a part of the power demand of the load, while the other part comes from the external grid through the transformer. We simulate an unexpected shutdown of the generator, increasing the power flow through the transformer, due to the load consumption. When the power flow through the transformer exceeds its rated power, the transformer sends a request to the load asking it to reduce its power demand. The power network we chose to rely on is part of the first tutorial of pandapower2 , presented in Figure 4.

Interactions between pandapower and SimGrid are done using the SimGrid-FMI plugin. This plugin makes SimGrid compatible with every FMU meeting the FMI standards, including FMUs created using pandapower-fmu, developped for this project. The plugin allows users to read and / or modify variables of FMUs dynamically during the co-simulation.

On top of the power network, we consider a distributed management orchestrated by SimGrid. Three actors coexist during the simulation:

• The master actor samples the power demand at the transformer every second. If the demand is above the transformer rated power, 1.5 MW, it sends a message to the load asking it to reduce its power demand; • The generator crasher shuts down the generator after 15 hours of simulated time, changing its power generation to 0MW. This actor simulates an unexpected shutdown or disconnection of the generator; • The load manager changes the load power demand every 30 minutes following a normal distribution, in order to simulate a typical fluctuating load profile.

For the communication network, we considered a star topology presented in Figure 3, where each entity is connected to a common router. We fixed a wired latency of 10ms from one entity to the router. We performed two simulations : one with a reactive master shedding the load if needed, and one with a passive master. The total simulated time is 24 hours. The power demand at the transformer during the simulations is depicted in Figure 2. The horizontal green line shows the rated power of the transformer. The vertical red line shows the moment at which the generator shutdown is simulated. The orange line shows the power flow through the transformer in a simulation without the master reacting to the excessive power demand above its rated power, i.e., when the master actor does not perform load shedding. The blue line shows the power trough the transformer in a simulation with the master reacting to the excessive demand by sending a message to the load, i.e., performs load shedding. As expected, with the active master the power flow stay below the transformer rated power.

IV. CONCLUSION

In this work, we proposed a scenario at the crossing of several domains : distributed networks, power networks and telecommunication networks. The tools presented here allows coherent co-simulations between several dedicated, domainspecific simulators. The proposed tools are all open source, facilitating the deployment of the co-simulation and providing a better cross-checking of the produced results.

Fig. 1 :

 1 Fig. 1: Co-simulation framework.

Fig. 2 :

 2 Fig. 2: Power demand at the transformer.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Star communication network.

Tool available: https://framagit.org/Adrien.Gougeon/pandapower-fmu

Tutorial available: https://github.com/e2nIEE/pandapower/blob/develop/ tutorials/create simple.ipynb

ACKNOWLEDGMENT

This project is funded through the CNRS Momentum project RI/RE.


Florence Flaig

Caroline Faria Bellani

Özgün Uyumaz

Guy Schlatter
email: guy.schlatter@unistra.fr

Anne Hebraud
email: anne.hebraud@unistra.fr

Icpees

Anne Hébraud

Elaboration and mechanical properties of elastomeric fibrous scaffolds based on crosslinked

Introduction

Tissue engineering is a promising field for the regeneration of soft tissues, in particular for cardiac regeneration. 1 In this approach, cells are seeded on scaffolds designed to promote cell differentiation, growth and spreading, before in vivo implantation. Scaffold should mimic the extracellular matrix to influence the cells behavior and the use of biomaterials having mechanical properties matching the host tissue's properties is highly desirable. 2 The design of elastomeric scaffolds is thus of great interest for soft tissue engineering. Poly(glycerol sebacate) (PGS), a biodegradable elastomer prepared from two natural metabolites of the human body has been developed for this purpose. 3 Variation of its synthesis conditions allows to tune its mechanical properties and degradation kinetics. 4 Scaffolds with Young's moduli matching heart's stiffness have thus been prepared and used as patches for the delivery of embryonic stems cells to the heart. 5 They showed good compatibility in vitro as well as in vivo. Besides, the scaffolds therapeutic properties were improved by the structuration of the PGS constructs: for example, accordionlike honeycombs structures gave interesting results 6 as they mimic myocardium's anisotropy. The structuration of the scaffold in a nanofibrous mat, mimicking the extracellular matrix can also be obtained by electrospinning, and has shown to enhance tissue regeneration. 7 Electrospun scaffold have thus become promising candidates for tissue engineering.

7-10

However, as PGS is an insoluble thermoset elastomer, it is not possible to electrospin it directly. Thus, PGS scaffolds have to be prepared in at least 3 steps. In a first step, the polycondensation of glycerol and sebacic acid leads to a soluble low-molar mass prepolymer (pPGS). In the second step, pPGS should be melted or dissolved in order to process it by electrospinning. Finally, a curing step at 120°C-180°C under vacuum allows the crosslinking of pPGS into a 3D macromolecular elastomeric network. However, because of its low molar mass, pPGS does not provide the entanglements in solution, that are necessary to prevent the breaking of the jet into droplets during electrospinning 11 . Different carrier polymers able to provide entanglements have thus been added in the pPGS solution to produce continuous nanofibers by electrospinning. As examples, proteins, such as zein, gelatin or collagen, were used for their good biocompatibility. Zein 12 or gelatin 13,14 was blended with pPGS to prepare fibers with up to two thirds of pPGS in the case of gelatin, while collagen was used as shell material in the coaxial electrospinning of core-shell fibers containing pPGS in the core. 15 In both cases, pPGS was not crosslinked into the PGS elastomer because proteins are not heat resistant and the mats cannot therefore withstand thermal treatment. To reach relatively high strains, proteins were crosslinked with EDC/NHS solution for gelatin 13 or under glutaraldehyde vapors for collagen. 15 However, an additional toxicity is brought by these reactants, whereas the final material does not benefit from PGS elastomeric properties.

Several works are also focused on electrospinning of pPGS blended with the thermoplastic poly(ε-caprolactone) (PCL) to prepare cardiac patches, 16,17 However, although these scaffolds achieved excellent biological properties, PLA was not removed and the overall mechanical properties were not elastomeric. As a matter of fact, the chosen carrier polymer should have a glass transition temperature (T g ) or melting temperature (T m ) higher than the curing temperature in order to keep the fibers shape and prevent the low-viscous melted pPGS to leak out of the fibers during crosslinking. Moreover, after crosslinking, it should be possible to dissolve the carrier polymer to obtain pure crosslinked PGS fibers. In this context, You et al. 20,21 used PLA as carrier polymer in coaxial electrospinning. They electrospun a core solution of pPGS and a shell solution of PLA (T m =160°C). Polyethylene oxide (PEO, T m =60°C) was added to the shell in order to decrease the modulus of the final material. The PEO had to be removed by dissolution in water before curing at 120°C, and PLA was removed by dissolution in chloroform after crosslinking. The resultant fibrous mat had a Young's modulus of 0.47 MPa in dry state which is suitable for soft tissues. However, in this method, a toxic solvent is employed to purify the PGS fibers: a water-soluble carrier polymer would be a better choice. Poly(vinyl alcohol) (PVA) was chosen by Xu et al. 22 to electrospin coaxial fibers with PVA as the shell and pPGS as the core. After crosslinking, the PVA is partially removed by dissolution in water, leading to a material having a Young's modulus close to 35 MPa and a strain at break of 130% in wet state. The blend strategy was preferred by Jeffries et al.

23

whose work led, after curing and dissolution of PVA in water, to fibrous mats having a Young's modulus close to 1 MPa and strain at break potentially higher than 750% for the weakest crosslinking conditions. Nevertheless, in these last examples, it was not possible to entirely remove the carrier polymer. This could be explained by a chemical reaction occurring during curing between the alcohols on PVA and the carboxylic acids on PGS.

In the present study, polyvinylpyrrolidone (PVP) was chosen as carrier polymer for blend electrospinning as it has a T g of 180°C allowing thermal post-treatments, is water soluble and presents no reactive sites for PGS. Moreover, it is approved by the FDA for biomedical applications. PVP was also used with pPGS in blend electrospinning by Keirouz et al. 24 to prepare fibers with up to 40% of pPGS. But in this work, PGS was not totally crosslinked in the thermoset elastomer. Yet, uncrosslinked pPGS is known to possibly induce toxicity due to the acid groups.

25

In our work, in order to increase the content of PGS in the fibers while preventing the fibers to merge together during electrospinning or crosslinking, addition of hydroxypropyl-βcyclodextrin (HPβCD) in the processed mixture was proposed. Indeed, HPβCD has a high degradation temperature (278°C), is biocompatible and is known to have the ability to stabilize the electrospinning process. [26][27][28] Besides, its hydrophobic cavity can be exploited to encapsulate drugs by host-guest inclusion complexes. 29 Different blends of pPGS, PVP and HPβCD were electrospun to form materials with 50% of pPGS and various proportions of PVP and HPβCD. The minimal HPβCD content necessary to electrospin regular fibers in a stable way was identified. These fibers were cured following two different heating settings in order to tune their mechanical properties. Finally, they were washed in water to remove the PVP and unreacted HPβCD and obtain elastomeric mats. Their mechanical properties were compared to those of PGS-based scaffolds prepared with PVA as carrier polymer in order to evaluate their suitability for soft tissue engineering.

Experimental

Synthesis and characterization of the prepolymer (pPGS)

PGS synthesis was adapted from previous procedures.

30,31

Briefly, 6.987 g (75.9 mmol, 2 equivalents) of glycerol, 23.013 g (113.9 mmol, 3 equivalents) of sebacic acid and a stirrer bar were introduced in a 100 mL round-bottomed flask. An open glass extender tube was connected to the flask to let the water vapors leave the reactor. The flask was placed in a microwave oven (Discover SP, CEM) and heated at 150°C with a maximal power of 200 W. The reaction was stopped before complete crosslinking of PGS, otherwise neither the dissolution nor subsequent process could be envisaged. After 400 minutes at 150°C, a pale-yellow liquid is obtained. After cooling to room temperature, pPGS was pasty. The flask was placed under vacuum for 1 hour at room temperature to evaporate excess of water without important loss of potential remaining glycerol. Sample was taken for 1 H NMR (400 MHz, Bruker) analysis in d-DMSO. The degree of esterification was calculated from NMR analysis (Figure S1) according to the following equation:

𝐷𝐸 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑠𝑡𝑒𝑟𝑠 𝑐𝑟𝑒𝑎𝑡𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑂𝑂𝐻 𝑖𝑛𝑖𝑡𝑎𝑙 × 100 = 𝐼 𝑒𝑠𝑡𝑒𝑟𝑠 𝐼 𝑒𝑠𝑡𝑒𝑟𝑠 + 𝐼 𝑎𝑐𝑖𝑑𝑠 × 100
with 𝐼 𝑎𝑐𝑖𝑑𝑠 and 𝐼 𝑒𝑠𝑡𝑒𝑟𝑠 the integration of the peaks on the spectra obtained by 1 H NMR, respectively at 2.18 ppm for the carboxylic acids (-CH 2 -COOH) and 2.28 ppm for the esters (-CH 2 -COOR). The prepolymer used for the electrospinning process had a DE of 72%.

Electrospinning of pPGS/HPβCD/PVP blends and optimization

pPGS, PVP and HPβCD are all soluble in DMF and ethanol. Electrospinning solutions were thus prepared 24h prior to | 3

Please do not adjust margins Please do not adjust margins electrospinning, by dissolving the three components in DMF/ethanol 3/7 to reach 13 wt% of total solid in the solution. This total solid content was composed of 50% of pPGS, X% of HPβCD (X=0, 5, 10, 15, 20 or 25) and (50-X)% of PVP. The compositions of the solutions are summarized in Table 1. Samples are named CDX with X the percentage of HPβCD in the solid expressed in percentage of weight by weight of solid. A home-made vertical electrospinning set-up including a cylindrical rotating collector, covered by backing paper, and translating needles was used. Two metallic 18 gauge needles were fed with the solution at 2.4 mL/h by a syringe pump (PHD 2000, Harvard Apparatus). The collector was placed 15 cm above the tip of the needles and rotated at 150 rpm. High voltage was applied to the collector (-5 kV) and to the needles (14 kV) by two power supplies (SL10, Spellman). Large membranes (15 x 30 cm²) suitable for post-treatments were electrospun during 5h.

Electrospinning of pPGS/PVA blends

Fibrous mats with 50 wt% of pPGS and 50 wt% of PVA were prepared by blend electrospinning using HFIP as solvent. The solution, containing 3.2 wt% of pPGS and 3.2 wt% of PVA in HFIP, was prepared 24 h prior to electrospinning. The same electrospinning set-up was used as for pPGS/HPβCD/PVP samples. The distance between the needles and the collector was fixed at 18 cm and the applied voltage at 25 kV at the needles and -1 kV at the collector. The solution was infused at 2.0 mL/h at each syringe. Because of its low stability, the process was stopped after 1h but it was enough to obtain detachable and easy to handle samples. All other parameters were kept the same as for pPGS/HPβCD/PVP. These samples containing 50% of PVA were named PVA50.

Crosslinking of PGS and purification of the fibers

After peeling from the paper, the samples were cut in the appropriate shape and placed between two frames tightened together by clamps to limit membrane shrinkage during curing. They were put in a pre-heated vacuum oven (Vacutherm VT6025, Fisher Scientific) at 120°C. The curing step was then conducted under a pressure bellow 10 -2 mbar following different curing schemes: a short one with a maximal reached temperature of 140°C named C short (24h at 120°C followed by 48h at 140°C) and a long one with a maximal temperature of 170°C named C long (24h at 120°C followed by 48h at 140°C and 24h at 170°C).

After curing, CD25 and PVA50 samples were immersed in gently stirred osmosed water. After 1h, 2h30 and 19h of immersion, the water was changed and the membranes were rinsed. After 24h of washing, they were dried overnight under vacuum at ambient temperature.

Characterization of PGS-based mats

The surface of the samples was observed by scanning electron microscopy (SEM) after coating by a thin layer of gold. The SEM (Vega 3, Tescan) was used in high vacuum mode with a voltage of 5 kV. Mean diameter of fibers was calculated over 100 diameters measurements using ImageJ software. The mean values are given with the standard deviation.

The efficiency of the mat purification was first evaluated by measuring the mass loss after washing. Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopic analyses were also performed (Nicolet 380, Thermo Fisher) before and after washing to characterize the PVP and PVA removal. Results were compared to raw materials' spectra. The mechanical properties in dry state of as spun, cured, and washed mats were characterized by uniaxial tensile tests using the Linear Tension Geometry of a rheometer (Discovery HR3, TA Instruments). Rectangular samples were cut with 5 mm width and about 20 mm long. Purified samples were also characterized at wet state after two days of immersion in osmosed water. Width and thickness were then measured after hydration. The samples were fixed in the clamps with an initial gap of 10 mm and then pre-loaded with an axial force of about 0.01 N. The gap after preloading was set as the initial length. The tensile tests were conducted at 150 µm/s until breaking. 5 measurements were performed for each type of samples. Young's modulus was calculated as the slope of the curve in the initial (between 0 and 1% of deformation) linear part. Cyclic tests were conducted on cured and washed samples at dry and wet state to evaluate elastic recovery. Specimens were cut and their dimensions measured in the same way than for tensile tests. After pre-loading, they were stretched at 150 µm/s until a strain of 15%, 15% elongation being a typical value for cardiac muscle 32,33 . After stretching, samples were released at the same rate until 0% elongation to conclude one cycle, and a new cycle was started. The loading-release cycle was repeated 10 times.

Results and discussion

In the strategy presented here, fibrous scaffolds are prepared by blend electrospinning of pPGS with either PVP and HPβCD or PVA followed by a crosslinking and a washing step (Figure 1A). A pPGS prepolymer was first synthetized, with a degree of esterification (DE) equal to 72% prepared with a molar ratio glycerol/sebacic acid fixed at 2/3, corresponding to the stoichiometric ratio (Figure 1B). This ratio, favoring the reaction of the glycerol secondary alcohol during crosslinking, combined with a high DE leads to a pPGS very closed to its gel Please do not adjust margins Please do not adjust margins

Effect of cyclodextrin and PVP contents on the fiber morphology

In order to prepare elastomeric mats and investigate their properties depending on the crosslinking parameters, the materials content in the PGS/PVP/HPβCD fibers was first optimized. Consistently with the literature, 23 the amount of pPGS in the as spun dry fibers was fixed at 50%. Indeed, a high enough percentage of pPGS is required to have continuous fibers after curing and washing, and a sufficient amount of carrier polymer is needed to keep the fiber shape during thermal treatment. The objective was thus to find a formulation able to reach an amount of 50% of pPGS with the help of PVP and HPβCD as carrier materials while preserving a fibrous morphology of the final scaffold. Electrospinning of formulations with less than 1.95% of HPβCD in the solution (CD15) was not stable due to periodic breaking of the jet (several times a minute) leading to solution projections on the collector. It did not allow the formation of continuous fibers, as shown for CD0 in Figure 2. For CD5 and CD10, fibers could be seen on the collector but they tended to stick together and form an almost continuous film (Figure S4).

PVP alone was not able to stabilize the jet and form solid enough fibers with such a high proportion of pPGS. A minimum of 15% of HPβCD was necessary to obtain membranes made of continuous fibers. Moreover, an increase of HPβCD content combined with a decrease of PVP content, resulted in a decrease of the fibers diameters, from 511 ± 136 nm for CD15, 382 ± 144 nm for CD20 to 318 ± 143 nm for CD25. These materials were cured to crosslink the PGS. Figure 2 shows that 15% of HPβCD was not enough to avoid the melting of the fibers. Finally, 20% of HPβCD and more, it was possible to get fibers with crosslinked PGS and only few melted areas, mostly at the contact points between fibers and around the few beads.

Fabrication of elastomeric mats

In this work, the mechanical properties of the mats prepared from pPGS/HPβCD/PVP and pPGS/PVA blends are compared with an identical pPGS weight amount of 50%. For the strategy based on the use of HPβCD and PVP, contents of 25 wt% of HPβCD and 25 wt% of PVP were taken. This condition, with a solid content of 13%, allows the fabrication of regular fibers as shown above. Moreover, it was assumed that a higher content in cyclodextrin would increase the modulus of the final materials as HPβCD can create multiple crosslinking point due to its large number of -OH groups. The selected formulation led to the fabrication of thin fibers (CD25 having a mean diameter of 318 ± 143 nm) comprising some beads (Figure 3). In the case of 50/50 pPGS/PVA fibers, regular fibers were obtained from solutions containing a total concentration of solid of 6.4 wt%, while other values did not allow the formation of continuous fibers. It led to regular fibers being almost 5 times thicker than CD25 (PVA50 mean diameter: 1402 ± 503 nm, Figure 3B). CD25 fibers are less regular, but in any case, fibers morphology is more or less modified by the curing step. In addition, the preparation of PVA50 fibers requires the use of a costly and toxic solvent, HFIP, which is not the case for CD25. The mats were then crosslinked under vacuum following two different heating settings: C short (24h at 120°C followed by 48h at 140°C) or C long (24h at 120°C followed by 48h at 140°C and 24h at 170°C). The influence of the curing parameters on the morphology and the mechanical properties of the final scaffolds was investigated. After curing, crosslinked PGS/HPβCD/PVP fibers are fused together at the contact points and some melted spots are also visible. Figure 3 shows the result after C long , but the same observations can be done after C short curing conditions (Figure 2 andS5). The integrity of PVA/PGS fibers is better preserved after curing, even if fibers are also merged at contact points. After the washing step in water, cured CD25 partially lost their fibrous morphology. In particular, numerous continuous areas are observed on cured CD25 crosslinked with C short conditions, leading to a high density of less porous areas. In the case of C long crosslinking conditions, a higher porosity is observed. From these results, it can be concluded that if PGS is not enough crosslinked, some of the material can be dissolved or swollen out of the fibers and redeposit around them. In the case of washed crosslinked PVA50 fibers, the fibrous structure is well preserved thanks to the fact that the PVA50 fiber diameter is much larger than for CD25 fibers. This result can also be justified by strong interactions between PGS and PVA as -OH groups of PVA can react with -COOH groups of PGS. Yet, cured PVA50 fibers are slightly attached together by melted material too. Besides, it can be observed that PVA left a noticeable roughness or even small pores at the surface of the fibers after its removal (Figure 3C). In order to check the efficiency of the washing step, the membranes were weighed before and after washing and drying. In all cases, 65% to 80% of the initial mass remains after washing showing that pure PGS membranes are not obtained. However, the removal seems to be more efficient after the C short curing than after C long : 68% of CD25-C short remains after washing versus 72% for CD25-C long .The same tendency is observed in the case of PVA50: 75% of the initial weight remains after washing for PVA50-C short whereas a percentage of 78% is measured for PVA50-C long . Thus, the C long procedure leads to more "entrapment" of the carrier material in the fiber matrix. This "entrapment" can be the effect of covalent bonding, especially between PVA or HPβCD and PGS, or the effect of an entanglement of the carrier polymer (PVA for PVA50 or PVP for CD25) in the PGS network, both effects being increased for a higher reaction time or temperature and the resulting higher crosslinking density. It can be noticed that the removal is more efficient for CD25 than for PVA50, demonstrating stronger interactions between PVA and PGS.

Please do not adjust margins

Please do not adjust margins In order to get more insight into the efficiency of the fiber washing step, ATR-FTIR characterization was carried out. Spectra of cured CD25 and cured PVA50 before and after washing were compared to pPGS, PVP, HPβCD (Figures 4A-C, S6 and S7) and PVA spectra (Figures 4D-F, S8 and S9). Two areas of interest are considered. In the first one, corresponding to elongation of C=O bonds (1650-1730 cm -1

), pPGS spectrum shows characteristic bands for acids at 1710 cm -1 and for esters at 1730 cm -1 . In the fibers after curing, the shoulder at 1710 cm -1 is not visible anymore (Figure 4B), confirming the esterification. The PGS characteristic bands partially overlap the PVP band arising from amide C=O bond (1650 cm -1

) in CD25 sample (Figure 4B). In the same way, the C=O band of residual acetate groups of PVA (1724 cm -1

) is overlapped with the C=O bands of PGS in PVA50 (Figure 4E). The second interesting area includes the C-O of esters bonds (1160 cm ). Because of the overlapping of the bands, it was difficult to quantify the presence of each component, but the evolution of intensities was investigated. In CD25-C long , the intensity of the band at 1027 cm -1 clearly decreases relatively to PGS band after washing (Figure 4C). Indeed, the ratio of intensities of C-O in HPβCD over C-O in PGS decreases from 1.2 before washing to 0.7 after washing, showing that cyclodextrin was partially lost during the washing step. However, PVP band at 1287 cm -1 does not clearly decrease relatively to PGS band: the ratio of intensities remains stable at 0.6. Surprisingly, it seems that HPβCD was easier to wash away, despite the fact that cyclodextrin can be covalently bonded with PGS. Indeed, all HPβCD molecules are not bonded to PGS, because there are 3 to 4 times more -OH groups (primary and secondary alcohols) from cyclodextrin than -COOH groups from PGS. Moreover, it can be assumed that the long PVP macromolecules are actually trapped in the PGS network. In PVA50, the band at 845 cm -1 decreased relatively to PGS band after washing (Figure 4F): the ratio of intensities of C-C from PVA over C-O from PGS decreased from 0.7 to 0.4. This result highlights the partial removal of the PVA. The remaining PVA is bonded to the PGS or trapped in the network too.

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Mechanical properties

The objective of this work was to prepare a scaffold with mechanical properties matching soft tissues properties, especially the myocardium's one. It was shown that the left ventricular stiffness is about 10-20 kPa at the beginning of diastole and in the range of 200-500 kPa at the end of diastole 4 . Tensile tests were thus conducted to determine if the PGSbased membranes are suitable regarding such specifications. The effect of the curing and of the washing was evaluated, as well as the nature of the carrier material. Typical stress-strain curves are shown on Figure 5A (all curves are given in Figure S10 andS11). The mean Young's moduli (E), strain at break (ε break ) and ultimate tensile stress (UTS) are given on Figure 5B.

Comparison of the results of as spun and cured samples clearly shows that the curing step increases the modulus and the stress at break. Two explanations can be given about this observation. First, the curing step leads to the crosslinked elastomer network which obviously enhances the overall strength. However, the maximal strain is not significantly improved by cross-linking because heating the fibers leads to their fusion at the contact points and therefore to strong bonding between them. The relative movement of fibers along each other is thus inhibited, which is a reason for the increase of the modulus and UTS. The washing step decreases the Young's modulus and increases the strain at break. This result highlights the fact that the rigid carrier materials were at least partially removed, allowing the elastomer to have more impact on the overall mechanical properties of the scaffolds. After washing, it can be seen that the longest curing step leads to higher modulus and UTS and lower strain at break. Indeed, C long pushes further the reaction to a higher crosslinking density. Moreover, it has been shown by weighing that the rigid carrier materials are less efficiently washed away after C long than after C short curing step, what could also explain the modulus increase.

In addition, it should be noticed that cured and washed PVA50 and CD25 have different mechanical behaviors. PVA50 stressstrain curves show a clear first elastic domain with high modulus, before a region of irreversible deformations with lower modulus until breaking at higher strains. For cured and washed CD25, the first high modulus-domain is drastically reduced, and almost invisible. This difference can be explained by the structure and composition of the mats. PVA50 and CD25 can be compared to point-bonded PVC/TPU-based structures described by Lee et al. 34 . PVA50 still contains a large amount of rigid PVA but the density of bonding between its fibers is low; this case corresponds to fibers with high PVC/TPU ratio. When the mat is stretched, these bonds hinder the slipping of the fibers, while PVA phase endures the load until a critical stress is reached. Then, the elastomeric PGS phase governs the behavior. CD25 samples are more similar to PVC/TPU fibers with high TPU content, the density of bonding points being very high. Moreover, it can be considered that the PGS content is higher because it was shown that the mass loss after washing is higher for CD25 than for PVA50. In addition to that, a fraction of the remaining carrier material of CD25 is cyclodextrin, which is included in the elastomeric network as crosslink points and takes thus part to the elastomeric behavior. So, the mat is a quasi-continuous elastomeric phase, and behaves almost as such.

The values given in Figure 5B indicate that PVA50 has a higher modulus and UTS than CD25 regardless of the posttreatments. After curing and washing, PVA50 has a Young's modulus higher than 50 MPa for a strain at break close to 150% and an UTS close to 5 MPa. Washed CD25-C short and C long have Young's moduli of 2 and 6 MPa respectively and UTS below 2 MPa. After washing, the average strain at break reached 390% for C short and 111% for C long . In summary, the use of PVA as carrier polymer leads to stiffer materials than in the case of the use of HPβCD and PVP.

Please do not adjust margins Please do not adjust margins From Figure 5, it can be noticed that most of the samples do not show a linear elastic behavior for strains higher than 3%. Cyclic mechanical tests were thus conducted to study how the materials recover after several cycles of deformation. Figure 6 represents some typical stress-strain curves obtained with samples over 3 cycles of deformation varying from 0 to 15%. The maximal strain value of 15% was chosen to mimic the strain underwent by the heart tissue 32 . For all samples, during the first cycle, the stretching part of the curve is very different from the releasing part of the curve. But after the first deformation and release, all the following cycles overlap. This is visible on Figure 6 for cycle 2 and 3 (the 10 cycles can be seen for all samples in Figure S12 andS13). This overlapping illustrates a lower loss of energy than after the first cycle, suggesting that the membranes underwent an irreversible deformation during this first stretching-release. This can be justified be the relative movement of the fibers along each other. The energy recovery after stretching and release back to 0% of strain was calculated as the ratio of the area under the stressstrain curve during release over the area under the curve during stretching. The calculated values confirm the poor recovery during the first cycle (Figure 7 in grey). PVA50 recovery is close to 10% after C short and C long whereas the recovery of CD25 is slightly higher with values above 20%. An average value was calculated for cycle 2 to 10 as they are similar. The recovery reaches then nearly 40% for CD25 and 50% for PVA50 for samples after C short . After C long , the recovery is worse for PVA50 with 33% but stable for CD25. Mechanical properties were also measured on hydrated scaffolds (Figure 8). The results show a clear decrease in modulus, UTS and strain at break for all samples after hydration. Indeed, the material swells in water and behaves like a hydrogel. The water inside can plasticize the polymers and enhance the dissipation of the friction energy; the deformation is thus easier. It results in a wider elastic domain, the linear part reaching several tens of %. For all samples, the moduli of hydrated scaffolds are close to 100-200 kPa (Figure 8B), which is more suitable for soft tissue than the same dry samples. The maximal strains are lower than in the dry state but still high enough as the typical strain underwent by the heart tissue is 15%. Cyclic tensile tests show the reversibility of the deformation in the elastic domain below 15% (Figure 8C). Please do not adjust margins Please do not adjust margins Moreover, the mechanical properties in dry and wet state of our scaffolds were compared with the one found in the literature. They fall in the same range as the other developed PGS containing fibers. However, our PGS:PVP:CD system and the PGS:PVA one, first developed by Jeffries et al., 23 are the only systems for which the pPGS is cured after electrospinning and the carrier polymer washed, leaving almost pure PGS fibers, and without chemical crosslinking with toxic agents such as acrylate, EDC-NHS or glutaraldehyde.

Conclusions

In this work, PGS-based membranes were successfully prepared using a blend of PVP and HPβCD as carrier molecules.

Composite fibers with 50% of pPGS, 25% of PVP and 25% of HPβCD were electrospun, cured and washed. For comparison, fibers with 50% of pPGS and 50% of PVA were also electrospun and post-treated in the same way. The fibers obtained from pPGS/PVP/HPβCD are almost 5 times thinner than those obtained from pPGS/PVA. In both cases, the washing step did not lead to pure PGS fibers. Washing was however slightly more efficient for materials prepared with PVP and HPβCD. Mechanical characterization in dry state, showed that both types of membranes can be stretched at strains larger than 100% after washing but the moduli of pPGS/PVP/HPβCD scaffolds are lower than those prepared with PVA. In addition, cyclic mechanical tests showed that samples prepared with PVP/HPβCD have a good resilience, making them good candidates for soft tissue engineering. In wet state, the moduli and tensile strength decrease, reaching values suitable for soft tissue engineering and the elastic domains increases allowing real elastic deformation of the scaffolds. Finally, the presence of cyclodextrin in the material should offers the possibility to encapsulate and deliver molecules of therapeutic interest.

  point. It results in a fast crosslinking of PGS, leaving no time for the pPGS to flow outside of the fibers during thermal treatment. pPGS was then electrospun with the carrier material. Preliminary experiments have shown that PVP alone is not a good carrier for PGS as it does not allow to maintain the fibrous structure of the scaffold during thermal treatment (FigureS2-S3). HPβCD, with a high degradation temperature (278°C), is thus required to keep the fibrous structure during curing and to stabilize the electrospinning process.

Figure 1 .

 1 Figure 1. Strategy for the elaboration of the elastomeric PGS-based fibers. During thermal treatment, pPGS is crosslinked and reaction of -OH groups HPβCD with -COOH groups of pPGS (in red) occurs (A). Chemical scheme of pPGS synthesis by polycondensation of glycerol and sebacic acid (B).

Figure 2 .

 2 Figure 2. Influence of the proportion of HPβCD on the PGS/HPβCD/PVP fibers morphology before and after curing for various formulations. CD0 contains 50% of PGS and 50% of PVP; CD15 contains 50% of PGS, 15% of HPβCD and 35% of PVP; CD20 contains 50% of PGS, 20% of HPβCD and 30% of PVP. The morphology is shown after the following curing steps: 24h at 120°C followed by 48h at 140°C (Cshort) or 24h at 120°C, 48h at 140°C and 24h at 170°C (Clong).

Figure 3 .

 3 Figure 3. Morphology of the fibers as spun and after post-treatments. Low magnification SEM pictures (A), diameter distribution of diameters of as spun fibers (B) and high magnification pictures of cured PVA50-washed fibers (C). CD25 contains 50% of PGS, 25% of HPβCD and 25% of PVP; PVA contains 50% of PGS and 50% of PVA. The morphol ogy is shown here after Clong (24h at 120°C, 48h at 140°C and 24h at 170°C) and after 24h washing in water.

  C in PVA (845 cm -1

Figure 4 .

 4 Figure 4. ATR-FTIR spectra of CD25 (A-C) and PVA50 (D-E) after curing and after purification compared to HPβCD, PVP, PVA and corresponding pPGS spectra. (A) and (D) Full spectra. (B) and (E) C=O bands, absorbance normalized to the 1730 cm -1 band. (C) and (F) C-O, C-C and C-N bands, absorbance normalized to the 1160 cm -1 band.

Figure 5 .

 5 Figure 5. Influence of curing and washing on the mechanical properties of CD25 and PVA50. (A) Typical stress-strain curves. (B) Evolution of modulus, strain at break and UTS along curing and washing.

Figure 6 . 9

 69 Figure 6. Stress-strain curves obtained for cured and washed CD25 and PVA50 between 0 and 15% of strain for the three first cycles.

Figure 7 .

 7 Figure 7. Energy recovery after the first cycle and mean energy recovery during cycles 2 to 10. The given value is the average value for 3 samples with the standard deviation.

Figure 8 .

 8 Figure 8. Mechanical behavior of the scaffolds in wet state. (A). Typical stress-strain curves, (B) Evolution of modulus, strain at break and UTS with curing and washing. The given value is the average value for 3 samples with the standard deviation. (C) Stress-strain curves obtained for cured and washed CD25 samples between 0 and 15 % strain

Table 1 .

 1 Composition of electrospinning solutions in DMF/ethanol 3/7 (w/w). All percentage are expressed as weight of solid over total weight of solution.

	Sample name pPGS HPβCD	PVP
	CD0	6.5%	0%	6.5%
	CD5	6.5%	0.65%	5.85%
	CD10	6.5%	1.3%	5.2%
	CD15	6.5%	1.95%	4.55%
	CD20	6.5%	2.6%	3.9%
	CD25	6.5%	3.25%	3.25%

Table 1

 1 Mechanical properties of PGS containing fibrous scaffolds in dry or wet state

	Fibers composition	electrospinning	Carrier polymer		strain at break
	(%PGS)	solvent	removal	modulus (MPa)	(%)	UTS(MPa)	state	ref
	pPGS : Zein (20%)	acetic acid	No	6-14	5-7	0.3-13	dry	12
	PGS : PLA (30%)	DMF:DCM	No	55 -278	50 -120	0.2-7	dry	18
	PGS : PLLA (50%)	DMF:DCM	No	7 -336	13 -66	1-7	dry	19
	PGS : gelatin (77%) acrylate (UV)	HFIP	No	10	20-40	0.65	dry	14
	PGS : gelatin (30-60%) EDC-NHS	acetic acid	No	9-14	31-34	1.5-1.6	dry	13
	PGS :collagen (32%) glutaraldehyde	HFIP	No	4.2	84	2	dry	15
								this
	PGS : PVA (>90%)	HFIP	Yes (water)	50	150	4-6.5	dry	article
								this
	PGS:PVP:CD (>90%)	DMF:ethanol	Yes (water)	2-6	110-390	0.6-2	dry	article
	PGS : gelatin (30-60%) EDC-NHS	acetic acid	No	0.15-0.30	90-180	0.3	wet	13
	PGS : gelatin (77%) acrylate (UV)	HFIP	No	0.1-1	30-45	0.03	wet	14
			Yes
	PGS : PVA (>90%)	HFIP	(water/ethanol)	0.1-0.8	200-750	0.8-1.2	wet	23
								this
	PGS : PVA (>90%)	HFIP	Yes (water)	0.15	70	0.1	wet	article
								this
	PGS:PVP:CD (>90%)	DMF:ethanol	Yes (water)	0.12-0.17	50-70	0.08-0.09	wet	article

Acknowledgements

The authors thank the financial supports of University of Strasbourg and CNRS. This work was supported by the Agence Nationale de la Recherche (MimHeart project ANR-15-CE08-0010-02).

Conflicts of interest

There are no conflicts to declare.