Laneyrie Elsa
email: elsa.laneyrie@univ-lyon2.fr

Aurélie Landry
email: aurelie.landry@univ-grenoble-alpes.fr

Identifying Management Styles of Chefs: How Staff Well-Being and Work Performance Are Linked to and Depend on the Way Chefs View Their Managerial Role Authors

Keywords: chef, management, prevention, projective cards, activity analysis

In this study, we sought to analyze the determinants of the chef's management of the kitchen staff in relation to constraints and resources, in particular those dictated by working conditions. We specifically sought to identify management styles that focus on the well-being of the staff and their work performance. To that end, we interviewed 20 chefs individually, using projective cards from the card game DIXIT. Qualitative analysis identified several common characteristics shared by the chefs in management of their staff, including managerial skills, importance of the "team" concept, a desire to give their profession a new and more positive image, and business constraints. We also found that they needed training in managing both their job and their staff. We discuss our findings on the collective activity of the kitchen staff and its effect on professional identity.

Introduction

The food service industry has been facing significant difficulties in recruiting qualified labour, especially since the COVID-19 crisis. It is now classified as being "in crisis" (Boulevard et al., 2021). Several studies have revealed the drudgery of working conditions: manual handling of materials; strenuous physical positions; night work; and temperatures over 30 °C (CNAMTS, 2021). Nonetheless, very few cooks have a compte pénibilité (a "hardship account" that entitles employees with arduous working conditions to early retirement). Cooks belong to one of the 15 occupations most exposed to intense physical demands [START_REF] Dares | L'exposition des salaries aux facteurs de pénibilité dans le travail[END_REF]. They are also exposed to musculoskeletal problems and psychosocial risks (PSR) due to situations with physical, psychological and sexual violence (Laneyrie, Kennicker, Cuvillier, 2022). The media have also reported on many cases of alleged outbursts by Michelin-starred chefs (see the Cagna report) against their kitchen staff.

Middle management skills appear to be a way to deal with some occupational health issues [START_REF] Laborie | Le soutien social du manager direct : Une solution pour limiter l'épuisement professionnel pendant la crise sanitaire liée à la COVID-19?[END_REF] through prevention, work organization and promotion of health and safety in the workplace [START_REF] Grosjean | Comment favoriser chez les chefs d'entreprise une plus large prise en compte de la prévention[END_REF] . We think that one of the industry's difficulties lies in the forms of management used by chefs. Because few social science researchers have investigated the managerial activity of restaurant chefs, we decided to do such investigation in line with the work of [START_REF] Pelletier-Bosshard | Strategies Used by Middle Managers to Support Employees Carrying Out Emotionally Demanding Work : Which Strategies and Why Those Ones?[END_REF] in health and social services and [START_REF] Racine | Un encadrement de proximité en recomposition : Les « managers de rayon » dans la grande distribution[END_REF] in the retail sector. In our study, which is part of a larger research program on the work of chefs, we propose to examine how chefs view their managerial role. We will examine the main concerns of these managers for the well-being of their staff in particularly difficult working conditions. To understand the role of management skills in their work, we will use two approaches from O'Leary and Sandberg (2016): defining their professional identity and defining their management skills.

Defining the Professional Identity of Chefs and Their Management Skills 2.1 A Professional Identity Shaped by Recognition

While covered widely by the media, the professional identity of chefs seems to lie between the image of French gastronomy (a part of French heritage declared "intangible" by UNESCO) and the day-to-day management of a restaurant, particularly to manage resources (raw materials, financial) and manage staff. In theory, professional identity is a triptych of 'I, we, others' [START_REF] Dubar | La socialisation. Construction des identités sociales et professionnelles[END_REF]. For this study, the term "others" refers to "the client," "the image of French cuisine," and the commis chefs assigned to the kitchen staff. The term "we" refers to all the chefs in the same industry, particularly the rules of the trade shared by industry professionals and the implicit obligations shared collectively by the profession, i.e., the professional genre as defined by [START_REF] Clot | La fonction psychologique du travail[END_REF]. The term "I" refers to the chef's style [START_REF] Clot | La fonction psychologique du travail[END_REF], i.e., how each chef adopts and adapts the rules of the professional genre, thus using the technical and psychological instruments of the trade in a unique and innovative manner [START_REF] Clot | Travail et pouvoir d'agir[END_REF]. In this way, personal style develops the professional genre. "Identity represents an individual's answer to the question 'who am I?' or a collective's answer to the question 'who are we?'" (Pratt &Foreman, 2000, Horton, Bayerl, and[START_REF] Horton | Identity conflicts at work: An integrative framework[END_REF].

According to Fray and Picouleau (2010, p.75), professional identity hinges on three key points:

• the lived experience at work: the objective situation of work and its meaning to the individual;

• work relationships: the subjective perception of interpersonal relationships and the sense of belonging to informal groups;

• career paths and perceptions of the future: description of the different stages and changes of professional activity.

Chefs are strongly attached to their professional image. The significant constraints of their work nonetheless push many to leave their profession. Others, however, remain because their work is recognized (by society, by other chefs, by their kitchen staff) [START_REF] Healy | The Reprofessionalization of Social Work: Collaborative Approaches for Achieving Professional Recognition[END_REF], and also because they gain personal satisfaction from doing a good job. In fact, a sense of recognition enables chefs to acquire resources that help them find their place in society. Chefs therefore show their personal skills through day-to-day experiences in the workplace and through the ways they meet routine challenges [START_REF] Flottes | Les sortilèges du virtuel[END_REF]. In this study, we will seek to understand how they view their relationships with their kitchen staff both as a way to achieve meaning and construct their identity and as a source of recognition at work.

A Professional Identity Oriented toward Teamwork: Management Skills

To serve food requires teamwork and, in the best case scenario, a work team [START_REF] Caroly | L'activité collective et la réélaboration des règles : des enjeux pour la santé au travail (Habilitation à diriger des recherches[END_REF]. Teamwork is a way of working together (Avila-Assuncão, 1998;[START_REF] De La Garza | Régulations horizontales et verticales du risque[END_REF][START_REF] Caroly | A conceptual framework of collective activity in Constructive Ergonomics[END_REF] to distribute tasks, exchange knowledge, and formulate common rules. In fact, it is inconceivable to imagine a kitchen staff meeting their primary objective of providing service without the associated teamwork. [START_REF] Karsenty | Le management par la confiance[END_REF] defines such activities as "trust management." Indeed, the kitchen staff include several trades. Staff size generally depends on the establishment's seating capacity and prestige (Table 1).

Head chef

Manages the kitchen staff, organizes the kitchen and manages the work Sous or second chef Assists the head chef and manages the chefs de partie

Chef de partie

Depending on the size of the establishment, is either a general cook or a specialized one ("fish chef," "sauce chef," etc.). Manages the commis chefs.

Commis chef

Executes the orders given by the chef de partie.

Dishwasher

Washes the kitchen equipment and dishes.

Intern, apprentice, kitchen assistant Helps the commis chefs with simple tasks. to the quality of life of kitchen staff members. Also, the practices used to manage a team often reflect the ideology of the "good professional" [START_REF] Clot | Travail et pouvoir d'agir[END_REF], which in this industry traditionally means an authoritarian style of management.

Managing a team means showing leadership, i.e., influencing the behaviour of one's employees so that they voluntarily strive to achieve the objectives of the organization and the group [START_REF] Hackman | Leading groups in organizations[END_REF][START_REF] Bergeron | Le leadership : traits personnels et comportements des leaders[END_REF]. A chef is thus expected to direct, inspect, organize, empower, encourage and manage change among the kitchen staff [START_REF] Dejeux | Management et leadership[END_REF]. Conversely, the kitchen staff need to understand the chef's instructions: "It is not just a matter of giving an instruction but also to do so in such a way that the team understands what it means and reappropriates the instruction as required by the situation" (ANACT, 2015, p. 4). The chef's place in the kitchen is complex because it is at the intersection of three needs: those of the restaurant's finance manager; those of the customers; and those of the staff. It is thus necessary to juggle financial, hygienic and quality goals, as well as those relating to the health of the chef and the team. Some goals may often be perceived as contradicting others.

In this study we will explore the nature of staff management activities from the chef's point of view by identifying management resources and constraints and by understanding how the activities determine professional identity. We will further aim to develop the concepts of personal style and professional genre and contribute to understanding of middle management skills and activities.

Methodology to Identify the Determinants of the Chef's Management Style

We used a qualitative method to collect data on how chefs perceive their style of management. Data collection is difficult in licensed restaurants, especially because chefs are often unavailable and because of the diverse range of restaurants. Interviews were used to collect data on management style and skills.

Data Collection

We conducted twenty 45-minute interviews with the chefs. Each interview was recorded and transcribed. The researcher travelled to the chef's workplace at the end of the lunchtime service. The semi-structured interview covered six points:

• The chef's activity: resources, constraints, targets, etc.

• How the public views the job of chef.

• Managing as a chef: how a chef manages employees or a group and the related skills.

• Teamwork and, where appropriate, the work team that brings together the staff and/or co-workers.

• How the chef's activities affect his/her well-being.

• The chef's demographic characteristics.

To help answer the questions, we provided the chef with playing cards (cf.

Figure 1) from the card game DIXIT (Roubira, 2016). These coloured cards are printed with illustrations (no text) that depict impossible situations. An interviewee interprets each card and is thus led to more subjective answers. Several projective techniques are used in psychology [START_REF] Guelfand | Les études qualitatives. Fondamentaux, méthodes, analyse et techniques[END_REF]. The one we used consisted of presenting the interviewee with ambiguous pictorial stimuli [START_REF] Tartaglia | Les Méthodes projectives[END_REF]. "The images are also keys for entering into what is real; they translate what we feel and enable us to talk about it. The images function as mediators between, on the one hand, the body's state and, on the other hand, language" (Guelfand, 2013, p. 44). We thus used them to help the interviewees speak more freely. For Guelfand (op. cit.,p. 46), the images serve six purposes:

1. Involvement, by evoking a profound past experience emotions" (Guelfand, 2013, p. 206).

That method enables users to construct meaning from their experiences after the fact by attributing details and properties to the cards they choose. In our study, we asked the interviewees to express the subjective emotion or sentiment they felt when making a choice. The illustration on the card helped them elaborate on their personal and subjective experiences. It also provided touchstones and milestones to help the interviewee relive the situation and thus help us better "understand the complex behaviours or put knowledge modelling into practice to access the cognitive procedures and processes which underlie these behaviours.

The method can then be used to identify the reasons for acting a certain way, the goals sought and the motivations that guide the action" (Brangier, Lancry & Louche, 2006, p. 24). Individually and collectively, the interviewees could better put their thoughts into words and express their interpretations of a theme or subject. This method, therefore, promotes active participation. Use of the cards "invokes relational, bodily, spatial and emotional intelligence, as well as linguistic and conceptual/logical intelligence" (Bélisle, 2014, p. 21).

Pre-Test of Cards

We made an initial selection from the 86 playing cards. Working in a group (two researchers in social sciences, a manager and a chef), we chose those cards that had a link to the job of chef. Finally, we chose five about management (cards 5, 6, 7, 8 and9) andfour about occupational constraints (cards 1, 2, 3 and4). The initial selection left us with 12 of the 86 cards. We then pre-tested the 12 cards with 10 chefs and kept 9 that were chosen at least seven times by those chefs. Table 2 presents the meanings of the selected cards. 1 The meanings were co-formulated with the members of the group who had preselected the cards. Card 2: Competition This card represents competition. A chef who always needs to be at the top of the game. A chef who therefore needs to excel every day. Card 7: Labour

This card represents the effort to do an arduous job.

Card 8: Appeal

This card represents the chef's appeal to the staff and also to customers. A chef needs to ensure not only that the staff believe in him/her and follow orders but also that the customers come back to eat at the restaurant.

1 The titles of the cards were not given to the interviewees.

Card 9: Controlling

This card represents a chef who is positioned at the centre of the kitchen and who wants to control everything that happens in it. The chef delegates tasks while keeping control over everything.

Actual Use of Cards during Interviews

As a prompt during the interview, we asked the chef three questions: "Which

Study Sample

Sample Characteristics

We booked the interview appointments directly (by visiting restaurants) or by phone, explaining that we wanted to understand the chef's working conditions.

To place the management activities within the broader context of all the chef's activities, we intentionally did not present our research as being about the management practices of chefs with their kitchen staff. About 20 of the chefs we approached did not wish to take part in our study. Finally, we received consent from 20 male chefs of French origin working in the Rhône-Alpes Auvergne region, none of whom was an owner-manager. The chefs we interviewed were mostly hired on permanent contracts (except for interviewees #9 and #16, who were managers). They worked in café/bistro restaurants that specialized in French cuisine (ranging from 20 to 300 customers per day). The restaurants were small businesses (fewer than 15 employees). To be included in the sample, the chef had to oversee at least one employee on a daily basis (in our sample, the number of employees ranged from 1 to 10). The interviewees' demographic characteristics are given in Table 3 below. Table 3 shows a variety of educational backgrounds , ranging from selftaught (4) to a CAP (6) and to a BEP (6). Two of the chefs had even attended the Institut Paul Bocuse. The chefs we interviewed had been mostly trained in how to prepare food rather than in how to manage employees. Furthermore, the sample was relatively young with a mean age of 34.6 years. The mean length of time in their current job was 4.9 years, as a chef 6.3 years and as a worker in a kitchen 13.35 years. They had not recently joined the profession and were thus probably better able to think objectively and have a better idea about not only the specific constraints of their line of work but also the resources needed to overcome them.

The mean wage hovered around 1,850 euros for a mean work week of 48 hours (39 hours reported). Table 3 shows that the chef's wage was not contingent on the number of working hours per week or even the number of customers, the skill level or the status within the company. There does not seem to be an industry standard, although the collective agreement specifies minimum wages for the different positions. Lastly, five of the chefs we interviewed were living with a partner, and eight had children.

In the sample, ten of the chefs worked in the industry out of love for cooking:

"It's a vocation. It's the profession that chose us. It's a hard job, physically, the family business, and two had gotten into that line of work by chance. Fourteen said

they wanted to open their own food-service business in the next five to ten years.

Data Analysis

We analyzed the interview data by theme [START_REF] Bardin | L'analyse de contenu[END_REF]. In particular, we wanted to study how the chefs perceived their management activities. We will focus here on such activities and not on all the data we collected (cf. themes in section 2.1). Our focus will be on the profession's resources and constraints with respect to teamwork and the chef's style of management, as shown in Figure 2. 3 Cards chosen at least four times by the interviewees. For each question we asked during the semi-structured interview we transcribed the verbal responses into Excel spreadsheets. For example, for the question on the chef's management approach we created a three-column table

showing (1) the number of people, (2) the management style described and (3) the verbal responses. To know in which box to put the verbal response, we used the classification presented by [START_REF] Bergeron | Le leadership : traits personnels et comportements des leaders[END_REF] and [START_REF] Dejeux | Management et leadership[END_REF].

How Chefs Perceived Their Management Activities

First, we will describe how they perceived their work and management activities. Second, we will present their professional identities by analyzing their answers about the "ideal" job. Third, we will report how they perceived the ability to build a cohesive team as a valuable resource in their skillset.

Differences in Perception between Imagined, Performed and Idealized Work of Chefs

A Chef's Job on a Daily Basis

To describe their tasks on a daily basis, the chefs chose four images: card #1 TIME (7); card #4 MULTI-TASKING (5); card #5 PROTECTION (5); and card #2 COMPETITION (4). Their perceptions varied. Most of the chefs were concerned about either their kitchen staff (i.e., concern for their well-being) or their work constraints (e.g., deadlines and unpredictable environmental factors), while striving to maintain high standards. Cards #6 AUTHORITARIAN and #9

CONTROLLING were not chosen to represent their profession; in fact, the vision of our chefs veered more toward a protective style rather than an authoritarian one, unlike the style of previous generations: "Let's be honest. There is a new generation of chefs, and practices are changing. Chucking waitresses into the washing machine is a thing of the past" (chef #1).

Being a Chef in Today's Workplace: Emergence of Management Styles

Several management styles emerged from our thematic analysis. We categorized them as follows, in line with Racine (2022) :

Robin Hood

Fourteen of the chefs felt that they were equitable leaders who did not distinguish between the different ranks of staff members: "Each job is important.

We form a team" (chef #5). We call this management style Robin Hoodism. To achieve a common goal efficiently and to ensure quality service, they felt it was important to take part in all the tasks: "I've always mopped the floor with my guys"

(chef #1). The role of each staff member was valued.

Sports Coach

Seven of the chefs perceived their role as akin to that of sports coaches.

Team members should be constantly motivated to surpass their limits: "When I'm managing early on, I get to know them, and then I push them to their limits until they snap, and when I've seen their limits, I stop and adjust" (chef #2); "I don't see myself as a shrink, but I listen a lot and try to draw the best out of the person" (chef #17).'

Paternalism

Six of the chefs had a more paternalistic style: "I look after my chefs as if they were my children" (chef #2). Some identified the daily sacrifices made for their team: "Me, I was always last in line, especially when it came to scheduling days off" (chef #1). An affectionate, or even paternalistic, dimension is significant in their activity: "You form emotional attachments. Given the constraints, we cannot offer amazing salaries, so we make up for it by forming emotional ties" (chef #11). Nine interviewees saw their position as an important link in the chain of preventing occupational risks: "Someone who protects their team, never doubts it, ensures that everyone is confident, someone who needs to calm everyone and have a solution for everything" (chef #17). They also provided their staff with a safe environment: "You need to know how to reassure others and make them feel secure. That they feel they can count on you. If the guys know they can count on you, and you have a solution to all their problems, then the guys will trust you, and you manage best in an environment of trust" (chef #10). The chefs thus identified occupational health and safety as an integral and daily part of their job. They were aware of the benefits of working with a healthy team.

Training Style

Twelve of the chefs explained that they were particularly attentive to training their staff. Several methods can be identified. Eight of the chefs tried to provide their commis chefs with the freedom to manoeuvre in their day-to-day work and thus challenge themselves and come up with new recipes: "The goal is to give them the wherewithal to create their own recipes. I try to help them grow as fast as possible. No one did that for me, and that really hindered my development" (chef #2). Seven of the twelve chefs devoted time to kitchen or debrief meetings: "I hold debrief meetings at the end of service to see how we can avoid committing certain mistakes or wasting time" (chef #3). Unsurprisingly, the same seven chefs described themselves as very rigorous and demanding (7). On the other hand, nine chefs averred that they lacked the time to train their team as they would like:

"I repeat it once, twice after I shouted at them. You try to start from their level but after a while you give up if they don't understand. You need to be efficient quickly'

(chef #9). There is, therefore, an ambiguity between the fundamental value of work and the actions the chefs managed to implement.

Professional Identity of Chef and the 'Ideal Job'

To represent their ideal job, none of the chefs chose cards referring to occupational risks (TIME, LABOUR and SOLITUDE). They could thus truly cast their minds to an ideal job without all the constraints of their profession, an idealized vision that implies they had succeeded in managing the associated difficulties. Once the work had been organized and under control (TIME/LABOUR) by performing multiple skills (MULTI-TASKING) or by withdrawing from the group (SOLITUDE), they imagined their ideal job as one that would focus on team management (PROTECTION) and success (COMPETITION, APPEAL).

The chefs would thus like to nurture their teams while upholding a high standard of performance. It was important to be not only the best on the team but also acknowledged by one's customers and peers. That need for recognition corresponds to the dimension of "others" in professional identity.

How Chefs Perceive Their Managerial Skills

Are Chefs Good Managers?

Twelve of the chefs considered themselves to be good managers: "I've never had any problem; generally we keep in touch, and I get to see them outside of work. If they end up being good, I will have succeeded" (chef #6). Five of them, however, said there was still much work to be done: "For me it's the hardest thing in the kitchen. It's the thorn in our side... You don't become a chef in a day either"

(chef #2); "I think I'm too nice. I avoid conflict too often. I don't come back quick enough to put people in their place" (chef #3). Overall, the chefs gave conflicting answers on how they could improve their management approaches (ranging from insecurity to the need to trust their team more readily). The general lack of management training was all the more frustrating when there was no clear management model to follow. The chefs we interviewed asserted that they did not wish to reproduce the management style of the chefs who had managed them (16). "Sometimes he would give you a chance: you would make a dish, but then he'd throw it at you and say you're useless" (chef #1); "If I shout, that stresses people out and creates palpable tension. That's exhausting for everybody" (chef #10). Consequently, they tended to construct their own management models that deliberately ran counter to the approaches of the chefs they had worked under.

Lack of Management Training Highlights a Need for Interpersonal Skills

Several 'generic' skills were identified as necessary for a competent chef (cf.

Figure 3). Most of the chefs used their image of a good manager to define the desired qualities they wished to be taught (14 of the chefs): "It's someone who knows how to help others develop, make them grow by bringing them together" (chef #11). The other skills they mentioned can be grouped under the heading of "soft skills": openness and capacity for listening (11); sociability (10); and rigorousness and honesty (6). Lastly, of the skills related directly to a particular management style (authoritarian) and the work of the profession, "being an excellent cook" was mentioned as a requirement for being a good chef.

4.3

The Team: A Resource for the Chef?

Developing the Team by Delegating Tasks in a Climate of Trust

Working as a chef requires knowing how to delegate in order to achieve the common team goal, i.e., ensuring quality service: 'I don't know why but it's like the army... You're all together, you have a goal, and you feel more united than you ever have been" (chef #17). This is possible only if the chef trusts the team: "It's a tough job with few staff members you can trust. You give your trust just once.

Because if it's destroyed, it gets complicated afterwards" (chef #3). In this respect, most of the chefs explained that they had learned to depend on their team and to delegate: "Over time, I realized it wouldn't work if it were just me" (chef #11). This did not keep them from wanting to inspect the work done by their team: "From A to Z, after that I'm always there to check. That's my job. I demonstrate and then I delegate-that's the point of a chef-and then I check" (chef #12). The chefs saw a strong sense of team spirit among their kitchen staff. On several occasions, the chefs confessed they regarded some of them as family because they worked with them for so much of the week (7): "I've known teams where you had the impression of being part of a family... You spend so much time with these people that it creates a sense of family. You trust one another, and you try to help each other outside work" (chef #10). The chef assumes the role of "protector" within the team: "You work so much that you need to like working together; you need a bond between the staff and managers. It's paternal to be close to one's team, to be the protector" (chef #7). There was a genuine devotion to the team, mostly seen in the fluid boundary between professional and personal life. Some chefs even felt guilty about going on a holiday or taking a few days off because they were passing on the workload to their colleagues: "We're a team, and if I don't come in, it's my team who suffers, not the customers" (chef #5).

The Job of Chef: between Being a Manager and Building an Identity

Analysis of the interviews revealed a number of management styles and the perceived benefits and constraints of management activities.

When Perceptions of Work Develop Professional Identity

Constraints Identified by Chefs for Management Activities

The chefs were unable to develop their management style with the knowledge learned during their training. In fact, only five of them had received management training. Similarly, they were seldom able to draw on their own career path or experiences to develop their management style, since they had worked under an authoritarian style of management that they were determined not to repeat. A possible reason may be the range of career paths before they went into the food-service industry. Lastly, although they attached much importance to staff training in their day-to-day work, they also regarded it as a source of frustration because they often lacked the time to train their staff properly. "Experience at work" had a strong impact on their profession's identity [START_REF] Fray | Le diagnostic de l'identité professionnelle : une dimension essentielle pour la qualité au travail[END_REF]. Indeed, the chefs mainly chose the cards TIME (1) and MULTI-TASKING (4) as components of their profession's image. They perceived their profession in terms of the "objective situation of work" [START_REF] Fray | Le diagnostic de l'identité professionnelle : une dimension essentielle pour la qualité au travail[END_REF] more than in terms of their relationships with their staff or their career path. How the chefs entered the profession differed considerably from one chef to another, a possible reason why their professional identity as a chef was not formed by their career path. Managerstaff relations were valued mainly in the reality of their job and in the ideal of their profession. Those relationships were, therefore, less foundational for professional identity, but they did represent resources for performance, on the one hand, and for continuity in the profession, on the other. Another reason was the generational turnover mentioned by several interviewees: the more traditional authoritarian styles of the past are giving way to a more protective style of management.

Resources Identified by Chefs for Management Activities

The main resource of the chefs was their sense of belonging to a team; they regarded themselves as part of the team and sought to treat each member equitably. The other resource was their role as trainer. Twelve of the chefs told us they were enthusiastic about passing on their vocation and giving their staff members one-on-one training. Such training requires two skills: being an effective teacher, and being a good listener.

Between Teamwork and Workplace Identity

Teamwork, like the work team, seems to be a leading resource of chefs.

Once a food service has been organized, and its components brought under control, the head chef's activities are geared toward managing relationships within the team. Teamwork is prioritized and directed toward a common goal of providing a service that meets a high standard. The chefs seek the most efficient way of working, which appears to tend toward cooperation [START_REF] De La Garza | Gestion individuelle et collective du danger et du risque de la maintenance d'infrastructure ferroviaire[END_REF]. Help and assistance seem to rest mainly on the chefs' shoulders. In this respect, they did not view the work climate among staff members as being competitive. A manager can thus contribute to the work team's wellbeing by giving meaning to their work [START_REF] Weick | The Collapse of Sensemaking in Organizations: The Mann Gulch Disaster[END_REF] and by helping strengthen their commitment to work [START_REF] Desgourdes | Mesure de l'influence du sensegiving sur l'engagement au travail des salariés en période de changement organisationnel[END_REF].

Lastly, the chefs mentioned the importance of holding debriefs to solve any problems that might occur during service and to find possible solutions rapidly. An immediate response not only helped protect the team members' sense of wellbeing but also united the team and strengthened its team spirit. Here we are entering a virtuous circle: strong team cohesion contributes to the health of individual members, which further strengthens team cohesion. The debriefs mostly happened when the teams ate together. They took place most often on the company's premises and provided the employees with an opportunity to come together and discuss any problems on the job, the different ways of working among staff members and the conditions for implementing group rules. The employees might even talk about and anticipate problems that could arise before the start of service. This forum was therefore an important space not only for working together but also for creating a work team as a foundation for teamwork [START_REF] Caroly | L'activité collective et la réélaboration des règles : des enjeux pour la santé au travail (Habilitation à diriger des recherches[END_REF].

The chefs told us they would speak about their job with friends in the same profession but rarely with members of their kitchen staff because of the difference in hierarchical level. The chefs mentioned the importance of visiting at least one culinary trade fair a year. Such events provided an opportunity not only to find new products and business partners but also to share "quality time" with colleagues and construct the "us" dimension of the profession.

Avenues for Future Research

We identified several limitations while conducting our research, in particular the sample size (20 chefs), the gender of the participants, and the absence of interviews with the entire kitchen staff.

It would be interesting to interview the staff members and observe the chefs at work in order to identify the times when they assisted each other. It would also be interesting to examine the locations where a chef would meet with the staff to determine how they were supposed to relate to each other.

Current data could be analyzed to determine how the chef's perceptions were affected by personal variables (age, experience, initial training) and organizational variables (size of staff, size of meal service).

It would be interesting to determine how the image of the food-service establishment affected how chefs built their identity and how that image affected the "race to get the Michelin star," where relevant, and the related management style. Indeed, Mériot (2002) showed that cooks who work in canteens are less satisfied than those who work in restaurants despite generally better working conditions. The type and image of the restaurant in which a chef works could indeed affect the chef's well-being and level of job satisfaction.

It would also be interesting to identify the different chef profiles and their related characteristics in order to identify the "tips and tricks" of the profession and pass them on to future generations. The aim should be to keep as much in touch as possible with current practices in the profession [START_REF] Boccara | L'analyse des travails pour la conception en formation[END_REF].

As shown by France's 2018 bill to reform continuing vocational training, such training should not be reduced to simply learning "on the job." Nor should it be kept separate from work. The reform has therefore brought an end to a long tradition of mistrust, the aim being to relieve the employee of production obligations and facilitate learning of knowledge and transferable skills.

Other avenues of research could include interactions between chefs from different food-service establishments. Future researchers might want to explore different forms and criteria of peer-related work recognition. One could also investigate potential meeting places for chefs, such as culinary trade fairs and the like (but not those designed to pit chefs against each other in competition, as in cooking contests). Finally, one could identify any existing controversies within the profession.

Conclusion

As we mentioned, the profession of chef is one of the most arduous to perform both physically and psychologically. This reality is seen in the absenteeism rate, the staff turnover and the difficulty in recruiting competent staff. The food-service industry is in crisis at a time when demand is rising. Also, paradoxically, it is being fantasized in the media, and more and more students are choosing careers

  The variety of positions means that the style of management should be adapted to the different needs, positions and times of service. No compulsory training is required to become a chef. Some hold a CAP (Certificat d'aptitudes professionnelles), a BEP (Brevet d'études professionnelles), and/or a management degree, while others are self-taught. Because the profession offers opportunities for rapid advancement, it is not always possible to anticipate the training needs of new chefs. Each chef creates basically his or her own personal management style. The absence of formal management training can be prejudicial

Figure

  Figure 1 -Projective Cards

  2. Motivation, by motivating the interviewee to participate 3. Representation, by providing a concrete portrayal 4. Mediation, by promoting "essential mediation between the body and language" 5. Reflection, by contributing to reasoning and problem resolution 6. Anticipation, by portraying the goal to be achieved This type of method puts "the interviewees in a new position in relation to the subject of what they are saying, inviting them to transpose it by means of analogical terms, to speak about it by means of imagery, to constantly break it down and put it back together until it is exhausted of all meaning and all possible

  solitude. A head chef who is at the centre of the kitchen and has a hard time relying on others. versatility. A chef who wears different hats and needs to look in all directions to make sure everything is perfect.Card 5: ProtectionThis card represents the head chef's protection of the staff, like a loving father. The chef strives to protect the entire staff and looks out for each of them.Card6:AuthoritarianThis card represents authority. A chef who has a hard time delegating and is at the centre of the kitchen.

Figure 2 -

 2 Figure 2 -Resources and Constraints of the Chef's Management Activities

Managerial

  Skills Acquired on the Job Eleven of the chefs explained that they had never received any management training and had essentially learned on the job: "You learn day by day how to manage a team; sometimes I think I've gone too far, and I'd question myself" (chef #4). Five of them had been trained on various management tools (orders, schedules), while another five had been fully trained: "Managing relationships with others, how to speak to them, what to say to them, holding briefings and debriefs. Setting goals, setting your own targets... Learning how to be fair in evaluations…" (chef #11). For those who had received it, management training had taken place at cooking school or during work for a large restaurant chain.

Figure 3 :

 3 Figure 3: Skills Required for Being a Good Chef

  therein. Measures are needed to keep them interested, particularly by protecting occupational health and safety. One measure would be to promote a horizontal style of management and develop collective intelligence (authors, 2021). Our study shows that managers of small teams experience a gap between ideal work and real day-to-day work, with the result that they may become demotivated and fall back on an authoritarian style of management. A more horizontal style is shown by our study and byPelletier-Bochard et al. (2022): the manager provides emotional support, facilitates team cohesion, adopts supportive attitudes and gives recognition, even in a hostile and turbulent work environment.

Table 1 : Main Positions of Kitchen Staff

 1

Table 2 : Meanings of Pre-Tested Cards

 2

Card 1: Time This card represents time, a chef's main enemy: the chef spends long hours in the kitchen and is always in a rush.

Table 3 : Sample Characteristics N Ag e Training Customers 2 Staf f Exp. in cooking Exp. in position Exp. as chef Wage Hours

 3

	/ week


A Nouviaire
email: anouviai@univ-lr.fr

R Lancien

Z Maache-Rezzoug

INFLUENCE OF HYDROTHERMAL TREATMENT ON RHEOLOGICAL AND COOKING CHARACTERISTICS OF FRESH EGG PASTA

Keywords: D.I.C. Hydrothermal treatment, Fresh egg pasta, Mechanical properties, Apparent density, Cooking quality

Abstract.

The effect of D.I.C. processing conditions on rheological and cooking properties of commercial fresh egg pasta was studied. The mechanical properties of pasta before and after cooking were evaluated by empirical test and characterized by maximal apparent force (F max ) and apparent relaxation coefficient (ARC). Structural (apparent density) and cooking quality were evaluated by determining mass ratio (W/Wo), optimal cooking time (OCT), swelling index (SI), solid, soluble and total cooking losses (TCL) and compared to untreated pasta. The hydrothermal treatment caused a reduction in firmness and relaxation capacity of treated pasta. The increase of processing conditions induced a decrease of F max and the processing time has an influence when it is associated to the low pressures. The values of ARC vary from 51% (untreated pasta) to 37% (D.I.C. treated pasta). The increase of processing time from 30 to 60 s does not seem to have a significant influence on ARC. The apparent density of treated pasta is function o f processing pressure and time but it is always lower than untreated pasta density. Treated pasta had a higher quality score based on water sorption and SI and matter losses (TCL values and solid and soluble losses) as compared to untreated pasta.

Introduction

Pasta, is one of the most consumed foods in the whole world, and it is a traditional product obtained from semolina. The most appropriate cereal for the production of high quality pasta products is durum wheat (Triticum durum) [START_REF] Feillet | Quality requirements of durum wheat for semolina milling and pasta production. Pasta and moodle technology[END_REF]. The commercial fresh pasta is most often made with durum wheat, pasteurised fresh egg and water, about 35% on a wet basis, and therefore is called fresh pasta to distinguish it from the dry pasta (11.5% w.b.). The eggs in the pasta brighten its color, add flavour, and give more nutritional value to pasta [START_REF] Iametti | Characterization of high pressure treated egg albumen[END_REF].

Quality of dried pasta has been improved by some hydrothermal treatment and several studies have been made on dried pasta treated by thermal process. [START_REF] Abecassis | Amélioration de la qualité des pâtes alimentaires par traitement thermique des produits secs[END_REF] noted that pasta previously dried at 37 °C, had an improved cooking quality and color after a short hydrothermal treatment at 90 °C. According to many authors, [START_REF] Baiano | Influence of drying temperature on the spaghetti cooking quality[END_REF][START_REF] Güler | Effects of industrial pasta drying temperatures on starch properties and pasta quality[END_REF][START_REF] Zweifel | Thermal modifications of starch during high-temperature drying of pasta[END_REF][START_REF] Abecassis | Improvement of cooking quality of maize pasta products by heat treatments[END_REF][START_REF] Dexter | Spaghetti stickiness: some factors influencing stickiness and relationship to other cooking quality characteristics[END_REF] high temperature drying improved cooking quality of dried pasta.

This quality has been shown to be highly influenced by starch gelatinization and protein network formation [START_REF] Riva | Starch retrogradation in cooked pasta and rice[END_REF][START_REF] Yue | Effect of Drying Temperature on Physicochemical Properties of Starch Isolated from Pasta[END_REF][START_REF] Fardet | Influence of technological modifications of the protein Network from pasta on in vitro starch degradation[END_REF][START_REF] Resmini | Ultrastructure studies of pasta : a review[END_REF]. The structure of cooked pasta is largely governed by the presence of a structured protein network [START_REF] Walsh | The influence of protein composition on spaghetti quality[END_REF]. [START_REF] Zweifel | Thermal modifications of starch during high-temperature drying of pasta[END_REF] showed that the high temperature dried pasta exhibited a smoother and more compact surface and a higher breaking strength than low temperature dried pasta. According to these authors, the formation of a tight protein network improves the embedding of the starch granules on the surface and it results in a stronger structure.

However, these studies were made on dried pasta and only few published papers exist on the application of hydrothermal treatment of fresh pasta. Alamprese et al. (2005a) have studied the influence of egg pasteurisation and the thermal treatment of fresh egg pasta on the protein network. The authors found that the industrial pasteurization of eggs does not affect the rheological and functional characteristics of pasta, but the double thermal pasteurisation of egg pasta deeply influenced its structural characteristics. The study carried out by Alamprese et al. (2005b) showed a great variability in rheological and functional characteristics of commercial fresh egg pasta. The authors attributed it to the difference of the intensity of heat treatments undergone by pasta during the production process. Maache- [START_REF] Maache-Rezzoug | Study of the effect of hydrothermal process conditions on pasta quality[END_REF] have studied the effect of a hydrothermal treatment called D.I.C. (Instantaneous Controlled Pressure Drop) on fresh pasta. This recent process has been developed and patented by [START_REF] Allaf | Procédé de traitement de produits biologiques en vue de la modification de leur texture, installations pour la mise en oeuvre d'un tel procédé et produits ainsi réalisés[END_REF] and consists in a short pressurisation of product followed by a sudden pressure drop towards vacuum pressure. This treatment was used in a first time to obtain puffed dried vegetables or fruits with quick rehydration [START_REF] Louka | Maîtrise de la qualité des produits agro-alimentaires séchés; modification texturale et réduction du coût énergétique par détente instantanée contrôlée « DIC » vers le vide[END_REF][START_REF] Nouviaire | Drying and texturization of strawberry by controlled instantaneous pressure drop and air drying[END_REF]. Indeed, the decompression towards vacuum during D.I.C. treatment induces a rapid modification of the thermodynamic equilibrium reached during the pressurisation (P 1 ,T 1 ) towards an other equilibrium state (P 2 ,T 2 ). This change of thermodynamic equilibrium state can create a complex process of micro-alveolation within the matrix.

The effect of D.I.C. treatment was also studied on hydration of various materials as schleroglucan [START_REF] Rezzoug | Effect of Instantaneous Controlled Pressure Drop Process on the hydration capacity of schleroglucan: Optimization of operating conditions by response surface methodology[END_REF]. Applied on fresh egg pasta, it has shown some great modifications on their quality: the water absorption, cooking time and colour quality were improved and a modification of their internal structure was observed (Maache- [START_REF] Maache-Rezzoug | Study of the effect of hydrothermal process conditions on pasta quality[END_REF].

The cooking behaviour, which is a critical step for quality perception is an essential stage of follow-up of pasta cooking quality and the most important characteristics include several parameters. The weight of cooked pasta indicates the water uptake and corresponds to a macroscopic event involving a complex molecular modification of starch and proteins [START_REF] Del Nobile | Modelling of water sorption kinetics in spaghetti during overcooking[END_REF][START_REF] Piazza | Modelling pasta cooking processes[END_REF]. The cooking loss, related to solid leaching during cooking is widely used as an indicator of the overall cooking performance [START_REF] D'egidio | Standardisation of cooking quality analysis in macaroni and pasta products[END_REF][START_REF] Dexter | Spaghetti stickiness: some factors influencing stickiness and relationship to other cooking quality characteristics[END_REF]. The texture of the cooked product has also an essential role in the final acceptance by consumers [START_REF] D'egidio | Textural measurment of cooked spaghetti[END_REF][START_REF] Oh | Noodles. I. Measuring the textural characteristics of cooked noodles[END_REF] and it is characterized by its firmness and resilience.

Firmness of cooked pasta represents the degree of resistance to the first bite and is sensorially defined as the force required to penetrate pasta with the teeth (D' Egidio and Nardi, 1996). Many testing instruments have been developed to measure pasta textural characteristics. [START_REF] Walsh | Measuring spaghetti firmness[END_REF] measured the firmness of cooked spaghetti with the Instron Universal Testing Instrument. Using the same testing machine, [START_REF] Edwards | Cooked Pasta Texture: Comparison of Dynamic Viscoelastic Properties to Instrumental Assessment of Firmness[END_REF] compared the texture of cooked noodles pasta prepared from durum wheat semolina of variable protein content, to provide samples with a different cooking quality. The Instron peak force measurement was found to be a more precise indicator of noodle firmness than was peak energy. The effect of cooking time on the textural properties has been studied by [START_REF] Gonzalez | Textural and structural changes in lasagna after cooking[END_REF]. The peak force which characterized firmness, decrease with increase cooking and holding time. [START_REF] Oh | Noodles. I. Measuring the textural characteristics of cooked noodles[END_REF] showed that the maximum cutting stress and resistance to compression of cooked noodles measured on the Intsron Universal Testing Instrument were well correlated with sensory evaluation of firmness and chewiness of noodles. [START_REF] Cuq | Effects of moisture content and temperature of spaghetti on their mechanical properties[END_REF] describe the mechanical properties of spaghetti pasta as a function of water content at different temperatures. The authors showed that an increase in temperature or in water content induces a plasticizing effect on mechanical properties of pasta, which is controlled by a phenomenon based on molecular mobility.

The objective of the present study was to complete previous study on D.I.C. treated pasta with mechanical, structural and cooking quality measurements. Fresh pasta (30% humidity) were treated with saturated steam (1 to 4 bar) during short time (30 and 60 s) followed by an abrupt decompression toward the vacuum (50 mbar). The effect of the two selected process parameters (steam pressure level and processing time) on the mechanical characteristics of pasta before and after cooking, and on the structural and cooking quality properties was studied.

Materials and methods

Raw material

Commercial fresh egg pasta (1.3 mm thickness) from a single commercial source (LUSTUCRU) was used in all experiments. The "tagliatelle" pasta shape was composed from semolina of durum wheat, water, fresh eggs at a rate of 140 g/kg of semolina, and salt (0.8%). The average moisture content of fresh egg pasta was 33.5±0.5 g/100 g. The tagliatelles pasta were cut into 50 mm length pieces and conditioned in sealed bags at 4 °C. The delay between the pasta processing and experiments was about 2 days.

Methods

Analyses of mechanical and functional characteristics of treated pasta were made according to the following diagram (Fig. 1).

D.I.C. hydrothermal treatment

The equipment and procedure of D.I.C. hydrothermal treatment for pasta were described previously by Maache- [START_REF] Maache-Rezzoug | Study of the effect of hydrothermal process conditions on pasta quality[END_REF]. During D.I.C. treatment, pasta was placed on treatment reactor in a single layer without superposition.

A vacuum of 50 mbar is established. This initial vacuum facilitates the diffusion of steam into product and allows its rapid heating [START_REF] Zarguili | Etude de l'effet de l'hydrotraitement DIC sur les modifications structurales et fonctionnelles des amidons de différentes origines botaniques[END_REF]. During a determinate processing time, saturated water steam is then introduced until a fixed pressure level.

The pressurisation is followed by a sudden decompression towards the vacuum that induces a rapid cooling and a micro-texturation of the product.

It's the difference between the high pressure level and the vacuum which determines the amount of steam generated by flash vaporization and thus the intensity of the mechanical constraints responsible for the micro-alveolation phenomenon. After D.I.C. treatment, pasta moisture content slightly increased due to absorption of condensed steam on the surface of product during the treatment. Typical pressure and temperature-time profiles in the D.I.C reactor and the pressure in the vacuum tank are presented in Fig. 2. The applied conditions were: processing pressure of 1.5, vacuum pressure of 50 mbar and processing time of 30 s. The temperature was measured on-line during DIC treatment by a thermocouple. In this study, the processing pressure was varied from 1 to 4 bar (corresponding at 99.93 °C to 143.63 °C) at two processing time conditions (30 and 60 s).

Moisture content

Moisture content of pasta was determined according to the AACC (1995) method adapted for pasta (i.e., weight measurements after drying at 105 °C for 10 h, milling and drying at 105 °C for 1h). The moisture content of pasta was measured for each sample after D.I.C. treatment, before and after mechanical analysis, after oven drying. Results are the average of three determinations and are expressed as % w.b.

Mechanical properties of pasta after D.I.C. treatment.

Mechanical properties of D.I.C. treated pasta was determined as a function of processing conditions by using an empirical test described by [START_REF] Cuq | Effects of moisture content and temperature of spaghetti on their mechanical properties[END_REF] and using an Instron Universal Testing Machine 5543 (Instron, France). The measures were carried out at room temperature using a 10 N compression cell for treated pasta and 1 kN for untreated pasta. Five samples of pasta (cut into 50 mm length pieces) were placed in a parallel position onto the measurement plate of the Instron. A Plexiglas straight probe (Fig. 3) was moved perpendicularly to the plate. To avoid perturbation of measure due to irregular form of pasta (side deformation principally), numeric acquisition started at yield force of 0.6 N. The apparent force was determined at constant speed of 0.1 mm/s until 0.5 mm compression, the probe was stopped and maintained at constant deformation during 35 s to measure the relaxation force.

The mechanical properties of pasta were estimated by maximal apparent force F max (i.e. force at 0.5 mm compression).The viscoelastic properties of pasta were evaluated by an apparent relaxation coefficient (ARC): ARC = (F max -F 30 )/F max , where F 30 is the force (N) recorded after 30 s relaxation. Standard deviation was evaluated from 3 measurements on each sample.

Drying stage

After D.I.C. treatment, all samples were dried by natural heat convection in a laboratory oven (Airlabo, AC 240) at 35 °C until reaching a constant weight. The moisture content of pasta was reduced fewer than 10% w.b. The samples were then stored at room temperature in hermetic bags.

Measurement of structure properties

Measure of apparent density of treated and untreated pasta is made after the oven drying. Because of hydrophilic characteristic of products, we used pycnometer with fine powder (80 µm diameter) at fixed density (0.96 g/cm 3 ). About 3 g (M 1 ) of pasta are placed in the pycnometer which is then tapped down mechanically (Autotap, Quantachrome) during the filling of the powder until a volume of 29.35 cm 3 before being weighed (M 2 ). Pasta apparent density is calculated as: ρ×M 1 /(M 2 -ρV+M 1 ). Three measurements were made for each sample.

Cooking properties

2.5 g of DIC treated pasta were placed in perforated box and cooked in 100 ml of distilled water at 100°C during 20 min. Each minute, the perforated box is taken out of boiled water and weighed (time of weighing is not taken into account). The same protocol is repeated for all samples to compare their rehydration rate. The water absorption for each sample is determinate as the mass ratio between cooked and uncooked pasta (W i /W 0 ). W i is the weight of cooked pasta at various cooking time and W 0 the weight of uncooked pasta. OCT (Optimal cooking time) is graphically determinate for each sample as the time when W i /Wo=2.27 (Maache- [START_REF] Maache-Rezzoug | Influence of instantaneous controlled decompression treatment on texturation and cooking time of the pasta[END_REF].

OCT of untreated pasta corresponds to 5 min of cooking time. This time is then taken as reference and all cooking properties of pasta were measured at this time. Mass ratio (W/W 0 ) where W is the weight of 5 min cooking pasta is determinate for each sample.

Swelling index (SI) was evaluated by drying the 5 min cooked pasta to constant weight at 105 °C [START_REF] Fardet | Caractéristiques physiques et physico-chimiques des aliments en relation avec leur digestion[END_REF]. SI was expressed as (g of water/g of dry pasta). Total cooking losses (TCL) were calculated as (DM uncooked pasta -DM cooked pasta)/DM cooked pasta; where DM is the dry matter ratio (g of matter / 100g). At 5 min of cooking, the cooking water was centrifuged at 5400 rpm for 15 min and dried at 105 °C until reaching a constant weight. The residue was weighed and reported as a percentage of dry matter of original pasta to calculate solid loss. The supernatant was diluted until 200 ml with distilled water and 2 ml of this solution was dried during 2 hours at 130 °C. The residue was weighed and reported as a percentage of dry matter of original pasta to calculate soluble losses.

Mechanical properties of pasta during cooking

Mechanical properties of pasta (D.I.C. treated and untreated) are measured as a function of cooking time. 2.5 g of pasta were cooked in boiling distilled water (100 ml) at fixed cooking time (3, 4, 6, 8 and 10 min). Pasta was rapidly cooled during 1 min in fresh water, drained during 2 min on filter paper to equilibrate, weighed and placed on Instron measurement table. The mechanical properties were measured according to described method in paragraph 2.2.3. F max (i.e. force at 0.5 mm compression) and ARC (Apparent Relaxation Coefficient) were determined as function of cooking time and processing pressure. After rheological tests, samples were weighed again to verify that water content did not change during analyses. Three independent replications were made for each test.

Results and discussion

Mechanical properties of D.I.C treated pasta.

The effect of hydrothermal treatment on mechanical properties of fresh egg pasta is illustrated by the differences between the experimental force-time curves of treated pasta, at specific processing conditions, by comparison with curve of untreated pasta (Fig. 4). Pasta was characterized by apparent "force-time" curves performed at crosshead speed. The first part of curves shows the increase of force value during the compression of pasta. Strength increases until a maximum value (F max ), then the deformation is suddenly stopped and the change of force as a function of time is recorded. A typical relaxation curve was obtained, the force decreases gradually until reaching an equilibrium value. These relaxation curves are characteristic of solid viscoelastic behaviour, and the relaxation of materials depends on their molecular structure.

The maximal apparent force F max is represented as a function of processing pressure for the 30 s and 60 s treatments in Fig. 5. The results show that the increase of pressure conditions induces a decrease of maximal apparent force (F max ). For untreated pasta, F max was of 16 N whereas for treated pasta F max ranged between 3 and 6 N. Although the processing time were very short (30 and 60 s) the effect of D.I.C. treatment on F max was important, and mainly at the time it was associated to low pressures levels. The reduction is very drastic even when the pressures applied were about 1 bar. The consequence of D.I.C. treatment is the reduction of firmness of treated pasta which behaves as soft materials especially when pressure is higher.

In the same way, the apparent relaxation coefficient is represented as a function of processing pressure for 30 s and 60 s treatments in Fig. 6. The fresh and hydrothermal treated pasta behave as a viscoelastic material. The ARC of fresh egg pasta was of 51%. This value is close to that obtained by [START_REF] Cuq | Effects of moisture content and temperature of spaghetti on their mechanical properties[END_REF] on spaghetti at 30% of moisture content (close to 50%). For DIC treated pasta, ARC values vary from 46% to 37%.

These results show that D.I.C. treatment reduces apparent relaxation coefficient. The same tendency is observed at 30s and 60 s treatments: increase of processing pressure involves a decrease of ARC until a pressure value where ARC is minimal and above which, ARC tendency is inverse (increase with pressure increase). However, increase processing time to 60 s has an impact on the ARC of pasta that becomes lower than for 30 s treatment.

Statistical analysis have been realised with Statgraphics software without taken into account results for untreated pasta. The multifactor variance analysis shows that parameters (pressure and time) have significant effect on maximal force changes (Pvalue of 0.0005 and 0.0163 respectively) and on ARC (P-value of 0.0051 and 0.0185 respectively for pressure and processing time). The relationship between mechanical properties (maximal force or apparent relaxation coefficient) and processing pressure can be described with a second degree polynomial model. Coefficients of the model are resumed in Table 1. The model fitted well experimental data. The model shows that minimal values of force and apparent relaxation coefficient are obtained at the same pressure, 3.6 and 2.8 bar for the processing time of 30 and 60 s, respectively (Fig. 5 and Fig. 6).

In order to make sure that observed variation on F max and ARC are only due to the effect of D.I.C. processing conditions (pressure and time), we have verified that moisture content was not modified by the hydrothermal treatment. Moisture content was carried out just before Instron analysis and the results showed that D.I.C. treatment modified moisture content of pasta but only in low proportion (from 33.16% to 36% w.b.) (data not shown). This increase is due to absorption of condensed steam on the product surface during the treatment. However, no tendency seems to be apparent between moisture content and the evolution of F max or ARC. According to [START_REF] Cuq | Effects of moisture content and temperature of spaghetti on their mechanical properties[END_REF], this interval of moisture contents variation does not have a significant effect on these two parameters.

It is known that pasta firmness is based on protein structure (Alamprese et al., 2005b) and composition formed during pasta production [START_REF] Gianibelli | Effect of source and proportion of waxy starches on pasta cooking quality[END_REF]. The hydrothermal treatment involves a decrease of firmness and elasticity when the D.I.C. conditions were intense. The high DIC conditions associated to high moisture content cause an excessive swelling of starch granules [START_REF] Loisel | Effect of hydrothermal treatment on the physical and rheological properties of maize starches[END_REF]. According to [START_REF] Resmini | The influence of raw material characteristics and of pasta-processing conditions on quality of pasta products[END_REF] the excessive swelling of starch granules has a consequence on the break down of the protein network and a decrease in the cooking performance. We can suppose that network protein is modified by swelling starch granules during D.I.C.

treatment.

The D.I.C. is a thermal treatment at high pressure but it's also associated to a mechanical effect obtained by a sudden decompression towards vacuum. This mechanical effect could induce a mechanical distortion of protein network that is not present with classic thermal treatment, it would be more important than the pressure level is high.

Structural properties of D.I.C. treated pasta.

In Fig. 7, the apparent densities are presented as function of processing pressure for 30 and 60 s of processing time and the value of untreated sample is used as reference.

For all D.I.C. conditions, treated pasta, even for the lighter conditions (1 bar and 30 s), has lower density than untreated pasta (1.2 g/cm 3 ). These results show that a micro-alveolation was created during decompression. The tendency for 30 s and 60 s treatments are the same until 3 bar: the apparent density decreased slightly as processing pressure increased. Above a certain pressure (3 bar), results of apparent density are opposite for 30 s and 60 s treatment. Whereas apparent density increase for 4 bar 30 s (0.92 g/cm 3 ), it seems to stabilize at lower value (0.73 g/cm 3 ) for 4 bar 60 s. The structure of pasta treated at 4 seems to be more sensitive to the treatment time.

Effect of processing pressure and processing time on this micro-alveolation was studied by a statistical analysis. The results show that processing pressure has a significant effect on apparent density (P-value of 0.0297) whereas processing time has no significant effect (P-value of 0.2083). Fitting of curves was made with a mathematical model of second degree polynomial type without taken into account untreated pasta. Equations of model and regression coefficients are given in figure 7 for 30 s and 60 s treatments.

This phenomenon of alveolation is due to the pressure drop involving a thermodynamic disequilibrium. This phenomenon is more important when the difference between high and vacuum pressures is important. For 4 bar of processing pressure, mechanical effect could have more impact than thermodynamic effect of alveolation, all the more that short processing time (30 s) is not sufficient to allow to the product to reach the equilibrium temperature before pressure drop. The nonhomogeneous heating of the product can create a collapse of the structure instead of its expansion. This time to reach the equilibrium temperature was estimated in a previous study by [START_REF] Zarguili | Influence of DIC hydrothermal process conditions on the gelatinization properties of standard maize starch[END_REF] on standard maize starch at 80, 70 and 60 seconds for respectively, 1, 2 and 3 bar, for a thickness of 0.5 cm. Then, at the opposite, for 60 s treatment, temperature equilibrium is reached and pressure drop has an expansion effect. [START_REF] Thymi | Structural properties of extruded corn starch[END_REF] showed in the same way that the increase of temperature can cause the decrease of the density of extruded corn's grits, resulting higher porosity.

As density increase, firmness and ARC of pasta decrease. The modification of apparent density during D.I.C. treatment can have an impact on maximal force and apparent relaxation coefficient. The increase of density is due to the creation of alveolation. The presence of cavity and little air bubbles involve a structure less compact and lead to a decrease of firmness. The apparent relaxation coefficient seems to evaluate as density: it decrease until 2.8 bar and increase for 3 and 4 bar for 30 s treatment. Air within pores created during D.I.C. treatment could improve elasticity of product. A study of porosity (distribution, size, type) is necessary to determinate direct impact of density on mechanical properties.

Cooking quality of D.I.C. treated pasta

The results of cooking performance of D.I.C. treated pasta compared to the control using the optimal cooking time (OCT) and pasta characteristics at 5 min cooking: mass ratio (W/Wo), swelling index (SI), solid and soluble losses, total cooking losses (TCL) are presented in Table 2. The mass ratio (W/W 0 ) represents the capacity of pasta to increase its global mass at 5 min cooking. W/W 0 takes into account of water absorption but also the total cooking losses. We can observe that, for 60 s treatment, W/W 0 increases when the processing pressure increases until 2 bar, and for higher pressures an opposite effect occurred. These results confirm a previous study reported by [START_REF] Maache-Rezzoug | Study of the effect of hydrothermal process conditions on pasta quality[END_REF] who explains this decrease by the disruption of protein network when high pressure is applied. As matter loss does not increase with increase of processing pressure whereas mass ratio decreases for pressures higher than 2 bar, that can signify that beyond the pressure of 2 bar the water sorption capacity was reduced for treated pasta.

A recent study [START_REF] Zarguili | Etude de l'effet de l'hydrotraitement DIC sur les modifications structurales et fonctionnelles des amidons de différentes origines botaniques[END_REF] on DIC treatment of standard maize starch showed a reduction in the sorption capacity of treated starch for 2 bar and 30 min of treatment time. According to [START_REF] Mazza | Dehydration of onion: some theoretical and practical considerations[END_REF], cited by [START_REF] Al-Muhtaseb | Water sorption isotherms of starch powders. Part 1: mathematical description of experimental data[END_REF] the decrease of sorption capacity is due to a reduction in the total number of active sites for water binding, consequences to the physicochemical modifications induced by temperature.

For the two studied processing times (30 and 60 s), the optimal cooking time (OCT)

follows the same tendency. OCT of treated pasta was reduced as processing pressure increases until 2 bar for 30 s and 3 bar for 60 s of treatment time. Beyond these pressures, OCT increases but its value remains below that of untreated sample that is equal to 5 min corresponding to a ratio of 2.27. [START_REF] Baiano | Influence of drying temperature on the spaghetti cooking quality[END_REF] has showed that quality characteristics of pasta during cooking were improved as drying temperature increased. These authors suggest that pasta dried at high temperature (90 °C) absorbs at the optimal cooking time less water than those dried at low (60 °C) and medium temperature (75 °C) thanks to the gluten network that made less available to imbibitions.

The values of swelling index (SI) of treated pasta at 30 s showed a slight difference with untreated pasta. If we take account of mean absolute error, the pressure level associated with a processing time of 30 s does not affect SI, but at 60 s, SI decreases with increasing pressure until 4 bar. From this pressure value, SI becomes constant and almost identical to SI values obtained at 30 s. The determination of pasta cooking quality is more dependent on a continuous protein network than the physicochemical properties of gelatinized starch [START_REF] Riva | Starch retrogradation in cooked pasta and rice[END_REF]. Swelling of cooked pasta is mainly due to the hydration of protein. During the cooking, the protein network is impacted by starch swelling. Few studies exist on the protein network changes of fresh pasta during cooking.

Globally, matter losses of treated pasta are lower than raw pasta. In contrast to the previous study carried by [START_REF] Maache-Rezzoug | Study of the effect of hydrothermal process conditions on pasta quality[END_REF], the matter losses (solid and soluble losses) are not more important at high pressures, but they decrease regularly as a function of pressure. According to Alamprese et al. (2005a), the heat treatment of pasta causes denaturation of proteins, leading to a stiffening of pasta structure, with a consequent reduction in the matter loss during cooking. The influence of treatment time is effective on solid and soluble losses (Table 2). At the same pressure values, these losses are more important at 60 s than 30 s of treatment time.

At the two treatment times, the increase of pressure leads to a decrease of total losses.

When SI increases or stabilizes with the increase of pressure whereas total losses decrease, this signifies that pasta absorb more water and lose less dry matter.

Mechanical characteristics of D.I.C treated pasta during cooking

Study of mechanical properties as a function of cooking time was primary carried out on fresh pasta. Fig. 8 for 10 min cooking. The influence of D.I.C. treatment on mechanical properties can be linked to the modification of water kinetics absorption. As treated pasta rehydrate faster than untreated pasta, at the same cooking time, water content of D.IC. pasta are higher and have "overcooked" mechanical properties (lower firmness and ARC) compared to untreated pasta. The influence of processing pressure is not the same for F max and ARC.

Whereas processing pressure is significant for F max variation (Pvalue at 0.004), it is not really significant for ARC variation. For short cooking time, F max seems to be lower for low processing pressure than for high pressure. We have seen that increase of pressure at 60s involves an increase of alveolation, but also a decrease of swelling index (SI) and total cooking looses (table2) probably du to the stiffness of pasta under highest pressure.

This tendency seems to be confirmed with the highest values of firmness obtained generally at 2 and 3 bar.

Conclusion

The analyses carried out on D.I.C. treated pasta showed that the rheological, structural and cooking properties of fresh egg pasta were modified considerably after hydrothermal treatment. Rheological measurements on treated pasta indicated a decrease in firmness and relaxation capacity of pasta when the processing pressure increases in comparison with untreated pasta. As expected the processing pressure had the greatest effect on mechanical, structural and cooking characteristics. Maache-Rezzoug and Allaf (2005) already showed by using response surface methodology that this parameter had a significant effect on all the response variables investigated. Under studied pressure conditions, the fresh pasta was undergoing physical modifications resulting in improvement of water absorption, and thus cooking time and colour quality. Increasing of pressure level induces a high apparent viscosity. Microscopic observations showed that the DIC treatment affects the internal structure and the state of starch granules.

After cooking, treated pasta behaved differently than untreated pasta. They had a high rehydration capacity and at same cooking time, their firmness was lower than raw pasta.

Matter losses were reduced whereas absorption capacity and swelling coefficient were improved. In addition to pasta mechanical and functional changes, structural modifications were observed with powder pycnometer analysis. Micro-alveolation is created in the pasta and density is function of processing conditions.

Figure Captions

  Abbreviations:

Fig. 1 .Fig. 2 .

 12 Fig. 1. Diagram of the different characterisation steps applied to the pasta after DIC treatment.

Fig. 6 .

 6 Fig. 6. Influence of D.I.C. treatment on apparent relaxation coefficient (ARC).

Fig. 7 .

 7 Fig. 7. Apparent density of untreated and D.I.C. treated pasta for two processing time(30 and 60 s). Model regression for 30 s: y = 0,1115x2 -0,6051x + 1,5648 (R 2 = 0.98), and for 60 s: y = 0,054x2 -0,3545x + 1,3065 (R 2 = 0.88)

  Figure 1.

Table 1 :

 1 Model parameters and regression coefficients of a second degree equation calculated to fit the experimental data in maximal force and apparent relaxation coefficient as a function of processing pressure. (Eq. (1))

	Processing time (s)		Model parameters		R 2
		a	b	c
	F max
	30	8.588	-2.671	0.371	99.96
	60	7.546	-2.204	0.305	98.07
	ARC
	30	54.367	-10.532	1.870	91.36
	60	54.030	-11.911	2.143	98.33
	F max , maximal apparent force at 0.5 mm compression; ARC, Apparent Relaxation
	Coefficient.

Table 2 .

 2 Cooking characteristics of D.I.C. treated pasta as function of processing Wo, mass ratio; SI, swelling index; TCL, total cooking losses;* mean absolute error calculated with 4 repetitions at 2 bar and 30 s.

	conditions.
	D.I.C. processing		Rehydration characteristics at 5 min of cooking time
	conditions
					SI
	Pressure		OCT	W/W 0	(g water/g dry	Solid loss	Soluble loss	TCL
	(bar)	Time (s)	(min)		matter)	(%)	(%)	(%)
	1		3.7	2.38	2.16	1.21	4.24	10.38
	1.5		2.7	2.78	2.19	0.95	3.16	9.89
	2	30	3.0	2.68	2.24	0.86	2.02	9.89
	3		3.3	2.64	2.24	0.85	1.79	9.63
	4		3.6	2.55	2.16	0.58	0.69	8.64
	1		2.8	2.75	2.63	1.64	4.62	11.33
	1.5		2.2	2.90	2.52	1.63	4.23	10.35
	2	60	2.1	2.96	2.47	1.50	3.83	8.70
	3		3.0	2.70	2.22	1.44	3.28	7.76
	4		4.2	2.42	2.21	1.44	2.58	7.30
	Untreated pasta	5.0	2.27	2.09	1.45	4.61	13.33
	Mean absolute error*	0.1	0.08	0.07	0.06	0.14	0.41
	OCT, optimal cooking time; W/

Table 3 .

 3 Mechanical properties as a function of cooking time of treated pasta at different pressures and at 60 s of treatment time.

					Mechanical properties of cooked pasta
				Fmax (N)			Apparent relaxation coefficient (%)
			Cooking time (min)			Cooking time (min)
	Processing	3	4	6	8	10	3	4	6	8	10
	pressure (bar)
	1	4.03	2.82	2.77	2.53	2.54	42.51	39.10	33.12	31.27	29.19
	1.5	3.98	3.48	2.90	3.14	2.83	34.80	34.20	30.66	30.63	29.68
	2	4.36	3.25	3.53	2.83	2.62	34.63	35.38	32.86	34.98	31.68
	3	4.42	3.94	3.33	3.22	3.05	34.88	33.54	31.96	35.76	34.82
	Untreated	5.13	4.39	3.71	3.29	3.19	44.94	41.17	36.80	33.60	31.62
	pasta
	Mean	0.01	0.21	0.23	0.47	0.11	1.41	1.54	1.32	2.19	0.52
	absolute
	error*

* mean absolute error calculated with 2 repetitions for untreated pasta


Sabine Vieira

Reinert Frello

Victor Lavaud

Romain Trimbur

David Frey

Marie-Cécile Alvarez-Herault

Yvon Besanger

Nouredine Hadjsaid

Michel Cordonnier

Guillaume Langlet
email: guillaume.langlet@enedis.fr

Leonard Bacaud
email: ⁴leonard.bacaud@enedis.fr

Sizing of a power electronics-based voltage regulating device to support the integration of photovoltaics and electric vehicles in LV grids

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

INTRODUCTION

The massive arrival of electric vehicle charging stations (EVs) and the increase in photovoltaic (PV) production connected to the low voltage (LV) distribution grids are likely to cause the appearance of local voltage issues requiring potentially costly grid reinforcements [START_REF] Hashemi | Methods and strategies for overvoltage prevention in low voltage distribution systems with PV[END_REF]. Among the alternatives to grid reinforcement, the Distribution System Operator (DSO) seeks efficient and less expensive voltage regulation solutions through devices such as On-Load Tap Changers (OLTC) [START_REF] Christian | Study of new Smart technical solutions for voltage control of LV distribution networks in France: Tests and performance analysis of LV regulators and MV/LV transformers with OLTC[END_REF] and power electronics-based structures. These are most commonly connected to the grid at the extreme points of the lines [START_REF] Rigo-Mariani | Voltage Regulation in Distribution Grid Using PV Smart Inverters[END_REF], far from the transformer and close to the loads under the most severe voltage constraints, while the application of OLTCs requires the replacement of the more traditional MV/LV transformers, with fixed tap-changer. In summary, LV grid voltage regulation can be performed at different points of the grid and different power electronic structures can be used, from capacitor banks to inverters connected to batteries. And although there are different structures capable of regulating the voltage, the connection of these devices is usually made in parallel with the loads and the MV/LV transformer, because it is easier to connect and disconnect for maintenance purposes and because it is safer from the point of view of grid protection triggering. Within this context, the addition of power electronicsbased converter devices (PED) at the secondary side of the transformer has been identified as an interesting emerging smart solution for downstream voltage regulation, as illustrated by Figure 1. This solution could be a cheaper alternative to an OLTC or to conventional grid reinforcement solutions. The PED presented in this paper regulates the grid voltage by manipulating its reactive power while connected in parallel downstream of the MV/LV transformer. This compensator injects and absorbs reactive power to increase or decrease the voltage, respectively. The goal of this paper is therefore to assess its sizing considering uncertainties related to the future development of EVs and PVs of the french LV distribution grid. To do this, we propose a Monte Carlo based simulation where different scenarios are modelled, representing the evolution of residential PVs and home charging stations for EVs in future LV grids. We believe that the proposed approach of placing the voltage regulating element right next to the MV/LV transformer is a pertinent way to expand its effectiveness in supplying energy to consumers without having to intervene either in the consumer's end or in the internal connections and structure of the transformer.

METHODOLOGY

For voltage regulation on the LV side, the European standard EN50160 is considered, which stipulates that the voltage at all points of the LV grid must be within ±10% of the nominal voltage value (400V phase-to-phase, 230V phase-to-neutral). Given these limits and the analysis of the LV grid behaviour downstream the MV/LV transformer, we developed a method to size the PED considering the steps presented in Figure 2 and detailed as follows:

-Elaboration of case studies using scenarios described in Enedis [START_REF] Enedis | Eléments de prospective du réseau public de distribution d'électricité à l'horizon 2050[END_REF] and RTE [START_REF] Rte | Futurs énergétiques 2050[END_REF] reports about the behaviour of LV grids in the foreseeable future. These case studies are detailed in the next subsection. -Application of a Monte Carlo-based simulation that considers various grid topologies with load and generation profiles inspired by the aforementioned scenarios. -Analysis of the results of the voltage variations that must be compensated and the reactive power that can be injected in parallel beside the MV/LV transformer by a PED responsible for the compensation.

Case Studies

In order to build the simulation models, the following case studies described in Table 1 were created based on the referenced documents. Three case studies are selected, named stagnation, intermediary and rupture, representing different levels of PV and EV penetration in the These case studies consider:

-Various real LV grid topologies provided by the french project SMAP [START_REF] Bernier | Comprehensive framework for PV integration with an OLTC in a rural distribution grid within the SMAP project[END_REF], responsible for the development of the first French rural smart grid. In these rural grids the lines are longer and customers are more sparsely connected to the grid. We believe that this choice depicts situations where voltage problems may arise more frequently in the LV distribution system. -LV grid voltage behaviour over a 24-hour period.

-Diverse residential consumption profiles [START_REF] Quoilin | Quantifying self-consumption linked to solar home battery systems: statistical analysis and economic assessment[END_REF] (common peak consumption in the morning and evening). -Most consumer units have a single phase profile, with a power factor cos()= 0.928, corresponding to a limit of tan()≤0.4 imposed by the french DSO. -Various electric vehicle charging profiles (recharging terminal power limits between 3kW and 7kW, with charging profiles for both daytime and evening). -Various rooftop PV generation profiles (single phase between 6kW and 12kW). -The percentages attributed to the stagnation and rupture cases were extracted directly from the Enedis report [START_REF] Enedis | Eléments de prospective du réseau public de distribution d'électricité à l'horizon 2050[END_REF], while the percentages for the intermediate scenario were obtained using the midpoint between the extreme scenarios.

Table 1: Features of the proposed case studies.

LV Grid Analysis Algorithm

First, the grid topology is selected and then the loads, PVs and EVs are randomly distributed throughout the grid according to the percentages determined for each case study. The consumption and production profiles are mapped throughout one day (24 hours) and a load-flow analysis is performed in order to estimate the voltage values at the secondary side of the MV/LV transformer for that period at a 30 minutes time step. This method yields an estimation of the voltage value downstream of the transformer.

The load-flow algorithm applied in this context, of an unbalanced three-phase power distribution system, was based on the Backward-Forward approach [START_REF] Kawambwa | An improved backward/forward sweep power flow method based on network tree depth for radial distribution systems[END_REF] to evaluate the voltage at each node, the current in each line and the losses. The result is an overview of the state of the electrical parameters of the grid at each time step.

Once the load-flow algorithm traverses the 24-hour period, a new random distribution of consumption and production profiles is performed throughout the nodes of the grid. This process is repeated for the number of iterations fixed at 100 for the Monte Carlo simulation. This number is chosen as a trade-off between computation time and robustness of the results. By increasing the number of iterations, we ensure that we cover a large representative panel of possible occurrences. Thus, it is possible to determine what is the absolute value of the voltage that needs to be compensated in order to comply with the EN50160 standard, and also the frequency of required actions of the PED.

Optimization of the PED Sizing

From a load-flow algorithm point of view, the modelling of the PED means adding an inductive or capacitive load depending on the desired action. When a voltage constraint is identified at a given moment, an optimization algorithm will calculate the minimum reactive power that the voltage regulation system must inject or absorb to stay within the tolerated voltage range. The optimization algorithm is formulated based on the minimization of the variable corresponding to the injected or consumed reactive power in each phase, according to the following equation:

𝑓(𝑥 1 , 𝑥 2 , 𝑥 3 ) = min (𝑥 1 2 + 𝑥 2 2 + 𝑥 3 2 )
This equation is subject to the condition that the voltage in each phase across all nodes of the grid is comprised between 0.9 p.u. and 1.1 p.u.. The optimization problem is then solved using a MATLAB optimization toolbox.

RESULTS

As a result of the complete algorithm presented on the diagram in Figure 2, it is thus possible to observe the voltage constraints, the frequency with which they occur in a day and the corresponding reactive power required for the PED action to be effective, illustrated by the boxplots of Figures 3, 4 and5. The grid employed in this analysis has 58 nodes and an MV/LV transformer with a rated apparent power of 250kVA. The boxplot graphs shown in Figure 3 represent the voltage behavior for a heavily loaded grid (rupture case) and show how much the voltage downstream the transformer exceeds the limits (± 10%) of the nominal grid voltage.

The voltage values to be compensated are expressed as a percentage of the nominal voltage of the grid (230V phaseto-neutral), while the reactive power values of the PED are expressed as a percentage of the transformer's rated power. The evaluation of the parameters in percentage is interesting in this analysis to estimate the size of the PED in relation to the size of the transformer, since overloading the transformer is unwanted.

The voltage that crosses the limits and needs to be compensated is called ∆𝑉 and the blue boxes (quartiles) express how often, for 100 Monte Carlo iterations, a given ∆𝑉 needs to be compensated at a certain time of the day.

In the case of this simulation result, it is possible to see voltage constraints occurring at the beginning of the day (around 6 a.m.), in the middle of the day (between 10 a.m. and 3 p.m.) and at the end of the day (around 8 p.m.). The early and late day constraints require the injection of a positive ∆𝑉 voltage to increase the voltage downstream the transformer. This means that there is an increase in the consumer load that causes this voltage decrease, while the mid-day constraint requires a voltage decrease in the LV grid. This is due to the power production by the PVs, which has its peak in the middle of the day, where the incidence of sunlight is usually greater. As for the reactive power equivalent to the ∆𝑉 to be compensated, the positive reactive power percentage indicates reactive power injection to increase the voltage, while the negative reactive power injection percentage indicates reactive power consumption to help lower the voltage.

Considering these plots, a PED capable of injecting and consuming around 75kVar (30% of the transformer's rated power) would be able to cover approximately 100% of the occurrences of voltage constraints in this LV grid in a year 2050 scenario for the rupture case. Figures 4 and5 show the behaviour of the same parameters as in Figure 3, but for the intermediary and stagnation cases for the same LV grid topology. In these cases, the grid is less loaded with PVs than in the rupture case and it is even possible to see that they do not produce overvoltages for this specific grid. However, undervoltages still occur at times of peak consumption as in the rupture case.

Besides the purpose of sizing the PED, these analyses also compose a tool to support the LV grid operator in the face of future difficulties in managing the voltage of the LV distribution grid up to the year 2050. This is due to the fact that, by integrating any real grid topology to the algorithm, it is possible to assess its robustness to the arrival of residential PVs and EVs by quantifying the voltage disturbances on the LV grid and the effectiveness of the DSO intervention if done locally only on the secondary side of the MV/LV transformer.

CONCLUSION AND NEXT STEPS

In this article, we have proposed a new methodology for the sizing of a PED used to regulate the voltage at the secondary side of MV/LV transformers under heavy penetration of renewable energy sources and EV charging stations. Different case studies were chosen to represent these conditions. Through a Monte Carlo approach, we are able to identify the reactive power injection and absorption capabilities of a parallel-connected PED that complies with current European standards. The next step in the development of the PED sizing algorithm is to analyse its behaviour when the device is connected in series with the grid.

Figure 1 :

 1 Figure 1: Suggested positioning of the PED in the LV grid.

Figure 2 :

 2 Figure 2: Flow chart of the PED sizing algorithm.

Figure 3 :

 3 Figure 3: Occurrence of voltage constraints in a 24-hour periodrupture case study.

Figure 4 :

 4 Figure 4: Occurrence of voltage constraints in a 24-hour periodintermediary case study.

Figure 5 :

 5 Figure 5: Occurrence of voltage constraints in a 24-hour periodstagnation case study.

∆𝑉]

  to be compensated on the LV side of the transformer ∆Q to be injected/consumed in parallel on the LV side of the transformer ∆𝑉 to be compensated on the LV side of the transformer ∆Q to be injected/consumed in parallel on the LV side of the transformer

ACKNOWLEDGMENTS

We thank Frédéric Wurtz and Nana Kofi Baabu Twum-Duah, from G2Elab, for their contribution with characteristic electric car charging profiles obtained within their research conducted on the PREDIS platform in the GreEn-ER building of Grenoble INP.