PhD student Marwa Khouya

Abdelhay Benabdelhadi

The contribution of public communication on the good governance process: The case of public institutions in Morocco

Keywords: Public communication, good governance, public institutions, new public management, transparency. JEL Classification: D73, D83, H83, M00 Paper type: Empirical research

Good governance includes all the rules and collective processes by which the actors concerned participate in the decision-making and realization of public actions. Public communication with a strategic and well-structured vision of information exchange is part of this perspective. Despite the fact that studies have been devoted to the relationship between public communication and good governance in public institutions, few empirical studies have explained the nature of this relationship. As part of the new public management, public institutions in Morocco have moved towards a whole new way of managing through reforms and implementation of the good governance approach. The purpose of our qualitative study is to highlight the importance of public communication in the process of good governance, as well as to clarify the different components of public communication in order to understand its contribution to the process of good governance. The interviewees were managers and officials of various positions within public institutions operating in different sectors of activity. Ten semi-structured interviews were conducted and subjected to a thematic content analysis. The results identify the main elements that determine public communication: public service values, free access to information, digitization, interactivity, personal skills and behaviors, ethics and transparency. Especially since each component is taken into account both theoretically and empirically in the process of good governance, takes place in Moroccan institutions more and more. Thereby, this research provides valuable implications about the potential role of public communication in contributing to transparency, clarity in decision-making, ethical behavior, the rule of law, and strengthening the public interest in public institutions in Morocco.

Introduction

The new terminology of public action is visibly based on public management tools: monitoring by objectives, management by results, project-based work, performance indicators, and good governance practices. This study is part of the new public management approach [START_REF] Aktouf | Management and Theories of Organizations in the 1990s : Toward a Critical Radical Humanism?[END_REF][START_REF] Dickinson | From New Public Management to New Public Governance : The implications for a 'new public service[END_REF]Gnan et al., 2013;[START_REF] Huet | Vers un « new public management » pour les pays émergents[END_REF][START_REF] Pesqueux | Le « nouveau management public[END_REF][START_REF] Vartola | New Public Management and Decentralization An analysis in Bangladesh and Nepal[END_REF][START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF] which includes all of the actions in a public organization that respond to specific procedures and must achieve objectives with planning, control, and results-based management. Broadly, good governance concerns all the rules and collective processes, formalized or not, by which the actors concerned participate in the decision and realization of public actions [START_REF] Andrews | The Good Governance Agenda : Beyond Indicators without Theory[END_REF] ). These rules and processes, as well as the decisions that result from them, are the outcome of a constant exchange and discussion between the various actors involved. In this work, we focus on public communication, considered to be the main component of good governance. Indeed, the development of results-based management can raise questions about the essence of public service, which is based primarily on the general interest, and good governance [START_REF] Bessieres | L'évaluation de la communication publique, entre norme gestionnaire et légitimités, des enjeux difficilement conciliables ?[END_REF]. At this level, the reforms undertaken over the last few decades in public institutions in Morocco raise questions about the role of public communication in this good governance process. Public communication in Morocco has been progressively strengthened over the last few decades, taking an increasingly prominent place in the institution. The Good Management Pact developed by the government of Morocco is an example of this. Indeed, this Pact places public communication at the center of the administration's action. It specifies that communication will henceforth be an important springboard for the action of public services. Firstly, we will focus on the theoretical foundations of public communication. Specifically, we will explore the components of public communication in the context of good governance in public institutions. The second part will be consecrated to the methodological side of our research. Finally, we will analyze and discuss the results obtained.

Literature review 2.1 Theoretical background on public communication

Public communication refers to the institutional communication of public organizations. Therefore, it reflects a specific field of organizational communication, which is public organizations, and seems to be similar to it [START_REF] Bessieres | L'hybridité : Une composante ancienne mais aujourd'hui démultipliée de la communication publique[END_REF]. Its conceptualization is largely based on the pioneer works of Pierre Zemor, one of the founders of Public Communication, who considers it as formal communication that tends to promote the exchange and sharing of public utility information [START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF], as well as the maintenance of social connections, and for which public institutions are mainly responsible [START_REF] Lemaire | La communication publique en pratiques[END_REF]. Furthermore, public communication in public institutions can be defined as all the activities of public institutions and organizations aimed at transmitting and exchanging information with the main purpose of presenting and explaining public decisions and actions, promoting their legitimacy, defending the results obtained and the recognized values and helping to maintain social links [START_REF] Boucherville | Communication publique et société : Repères pour la réflexion et l'action[END_REF]Cobut, 2011;[START_REF] Pasquier | Chapitre 2. Communication publique : Définitions, fonctions et types[END_REF]. The theoretical development of public communication is generally presented as a response to an imperative of publicity in a Kantian sense of disseminating information about issues of general interest, and of proximity, or even transparency on the part of public institutions (Ollivier-Yaniv, 2014).

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Referring to a definition that aims to summarize the principal empirical research conducted from an organizational and managerial perspective, [START_REF] Sauvé | La communication publique en pratiques[END_REF] consider the public communication as a democratic requirement and an imperative of good governance [START_REF] Sauvé | La communication publique en pratiques[END_REF]. As a reminder, we mention the contribution of [START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF] who considers the open access to public information as a principal component of public communication. More precisely, the public service is determined by the relationship of the institution with the public, in particular the free access of the citizen, not only to the public places, therefore signaling, reception, consideration, but also to the public information [START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF]. Therefore, public communication managers manage communication services and service providers (e.g. communication agencies). They define communication plans and actions: public and press relations, websites, institutional magazines, posters, brochures, events, etc. Their widespread use in public organizations is quite recent, during the 1990s [START_REF] Bessieres | L'évaluation de la communication publique, entre norme gestionnaire et légitimités, des enjeux difficilement conciliables ?[END_REF].

Public Communication and Good Governance

It is commonly known that public communication takes on different forms linked to the missions of public institutions to make information available to the public, to establish relations and dialogue in order to provide an expected and precise service, to present the services offered and the projects carried out, to make the institutions themselves known, and finally to carry out information campaigns and communication actions of general interest [START_REF] Zemor | Les formes de la communication publique[END_REF]. This is an integral part of the process of good governance [START_REF] Zamoum | Transparence et communication publique : Étude du cas de la Ligue des États Arabes[END_REF]. Theoretically, good governance is presented as a new model for exercising authority in a society, which implies an orientation of collective participation in public management, and a vision of a unique rule of law ( [START_REF] Letourneau | Les théories de la gouvernance : Pluralité de discours et enjeux éthiques[END_REF]. According to several studies, the process of good governance aims to make the leaders of public institutions more aware of the shadow forces behind the used means of communication in order to develop both effective and rational public communication (Jarren, 2007a;[START_REF] Pløger | Public Participation and the Art of Governance[END_REF]. Nowadays, public communication must be transparent and citizen-oriented and not be reduced to sending out simple messages in the service of good news [START_REF] Megard | Chapitre 1. Spécificités et enjeux de la communication publique[END_REF]. However, like good governance itself, it must be attentive to the voice of citizens, not only to look at the opinion but also and above all to organize the ways and means to respond to their needs in terms of structuring projects and useful information. The Organization for Economic Cooperation and Development (OECD) defines public communication as "a culture of governance that promotes the principles of transparency, integrity, accountability and stakeholder participation, in the service of democracy and inclusive growth" (OECD, 2021). In practice, the relationship between public communication and good governance in the public area, has been examined by numerous researchers ( e.g, [START_REF] Gardère | Quelles communications pour la gouvernance des institutions publiques au XXIe siècle ? / What communication for the governance of public institutions in the 21st century?[END_REF]Jarren, 2007b;[START_REF] Zamoum | Transparence et communication publique : Étude du cas de la Ligue des États Arabes[END_REF]. They have affirmed that the two concepts are intrinsically related, especially since they are founded on the fundamentals of clarity of the decision-making process and transparency, as well as the right of access to information. The main purpose of the research is to determine the components of public communication and identify its main contributions in the process of good governance. This study will provide new insights to public communication specialists in management sciences and also to managers of public institutions about the effective utilization of this tool, and to invest in its different modes to achieve good governance. In this way, and based on the literature review, the following research questions will be answered: RQ1: What are the components that determine public communication? RQ2: In which ways are transparency and ethics both determinants of public communication and principles of good governance?

Methodology

The methodological approach adapted to our problematic is a qualitative approach. The purpose of a qualitative study is to understand in depth the perceptions of the different concepts and how they relate to each other, not to measure them (Giannelloni & Vernette, 2019). Furthermore, this work follows an inductive methodological reasoning, which is a bottom-up approach that proceeds from the specific to the general, and provides inputs from the field studied [START_REF] Thietard | Méthodes de recherche en Management[END_REF]. We consider that this method is the most appropriate, since the objective of our study is to understand how public communication contributes to good governance. This objective, which is exploratory in scope, focuses on the context of public institutions in Morocco and explains the perceptions of managers of these institutions.

Sampling and Investigation Instrument

Sample selection is not just a simple step in a research study [START_REF] Thietard | Méthodes de recherche en Management[END_REF]. To conduct this step, we have opted for the semi-structured interviews, which is the major and most used category of qualitative data collection techniques. It also allows for maximum interaction and discussion regarding the topics of the interview [START_REF] Gavard-Perret | Méthodologie de la recherche : Réussir son mémoire ou sa thèse en sciences de gestion[END_REF][START_REF] Grawitz | Méthodes des sciences sociales. 11ème édition (Dalloz)[END_REF][START_REF] Lancaster | Research Methods in Management[END_REF][START_REF] Roche | Rédiger et soutenir un mémoire avec succès[END_REF][START_REF] Thietard | Méthodes de recherche en Management[END_REF]. In fact, the constitution of a qualitative sample requires genuine rigor and must be precise in that it must meet predetermined selection criteria [START_REF] Keegan | Qualitative Research : Good Decision Making Through Understanding People, Cultures and Markets[END_REF]. In this way, we have interviewed managers from public institutions about general questions related to public communication, in order to understand their perception on the subject. But also on more detailed points about the determining elements of the public communication in the good governance process, its different forms and on how compatible and adequate it is with the quality of the services provided by their institution. These interviews focused on the public communication of public institutions since the adoption of good governance and the implementation of its mechanisms. Source: Author's processing www.ijafame.org

Data collection and analysis

All of the semi-structured interviews were conducted individually, after making an appointment in advance to discuss the subject of our research. The contact with the persons was conducted by sending a letter requesting an interview, in which we have introduced the general framework of this study, as well as a presentation of the authors and their scientific background. Subsequently, the interviews were conducted face-to-face, and each interview lasted an average of one and a half hour.

After conducting ten interviews with a diverse sample of respondents with different profiles, genders, sectors of activity, and years of seniority in their institutions (Table 1), we found that the interviews are mutually complementary and that the latter did not allow us to obtain new information that had not been concluded during the first interviews. We had therefore reached semantic saturation (Romelaer, 2005). The next step was to transcribe the different interviews in order to start the thematic content analysis. Indeed, thematic content analysis is a technique that relies on the principle of repeating units of discourse analysis (words, similar expressions or meanings, sentences, paragraphs) reveals the interests, concerns of the interviewees [START_REF] Thietard | Méthodes de recherche en Management[END_REF]. At this stage, all interviews were coded, i.e., all fragments of speech belonging to the same category, subcategory or meaning block were grouped together. We carried out this step using Nvivo software to develop an analysis grid that allowed us to extract our main results.

Results

Values of public service

In Of all the constituent elements that could be found, they highlight integrity and capability in general interest perspective as the most essential values of public service. In total, interviewees 1, 5 and 8 testified that in their institutions the public service provided is mainly focused on the general interest as a crucial value. This can be explained by the sector in which they operate. "Public communication is not distinguished from other types of communication by techniques and languages, i.e., from advertising to marketing, from the written word to audiovisual, including media and non-media, as well as digital in all its forms, but by its objectives and issues. Those of the general interest, of public service and of good governance." (Interviewee 1). This refers in fact to what [START_REF] Megard | Chapitre 1. Spécificités et enjeux de la communication publique[END_REF] and Box (2015) calls responsibility toward citizenusers, which includes all interests, values or objectives that are shared by all members of a society, and that are good for them all.

Open Access Information

As a result, all managers of public institutions interviewees consider open access to information as a component of public communication. In this regard, interviewee 3 said: "The administrative practices mystify the public service regarding the citizen-user who doesn't know what he is actually entitled to. Consequently, our first mission is to highlight the elements which he is entitled to, to be able to make him aware, and then to communicate to him the public information and ensure its free access". Indeed, citizens are of equal value in rights and aspirations to all public activities [START_REF] Demers | La communication publique, un concept pour repositionner le journalisme contemporain[END_REF]. By extension, they have the right of access to information which is granted by the supreme law of the country which is the constitution.

Interviewee 2 mentioned that this right allows following the news and the progress of the projects carried out by the public institutions, especially through the classic portal represented by their official website, "It must be admitted that very few citizens assimilate the information they are entitled to access, the public institution aware of this does not keep the citizen in this state of ignorance. How? by informing and training him, it proceeds rather by announcements of projects taken out of one does not know from where, which are never really or durably effective" (Interviewee2).

Digitalization

In addition to open access information, all the interviewees agree that it is necessary to capture the benefits of digital technology in favor of public communication. According to interviewee 9, "Digital technologies have made communication easier than ever, we must seize this opportunity and evolve to be in direct contact with citizen-users. And to achieve this goal, it is necessary to improve the accessibility of digital interfaces, content and messages and make them accessible to all". In the same directive, Interviewee (2023) also found similar results in their research which indicates that public communication relies primarily on ensuring access to information, and this through the various forms of communication and information dissemination, principally the digital ones.

"Moreover, the evolution of the digital world and the different media modalities have given new dynamism to public communication and opened up unprecedented perspectives of application and interaction. I would like to mention social networks, which are now a very powerful interactive channel between the institution and the citizens. A citizen can ask for useful information to his service by commenting or sending a private message, without necessarily using the platforms of the official website or physically moving to get a simple information." (Interviewee4

). Based on our results, we conclude that digitalization is a key factor for open access to information and a pioneer component of public communication. Therefore, the adoption of virtual platforms and social networks allows institutions to be in permanent and regular contact with citizens-users, but also with all those whose information would be useful.

Interactivity of Communication

For the majority of the interviewees (interviewees n°1,2,3,7 and 8) interactivity is not optional but rather required for public communication. This point is supported by the fact that it is imperative to understand the needs of users before communicating information to them. In this regard, interviewee 7 said: "I specify that communicating and informing are two different things. Informing is only one ingredient of public communication." By mentioning interactive communication, interviewee 3 also highlighted its importance in understanding the needs, as well as the closeness granted between the institution and the citizen. "Communication, especially in public institutions, is conditioned by interaction. It is necessary to listen to the needs of citizens to offer them a public service that responds to their own needs." (Interviewee1) This results corroborates with the claims of Elif (2020), [START_REF] Yeon | Interactive Communication Features on Nonprofit Organizations' Web Pages for the Practice of Excellence in Public Relations[END_REF] and Durkin et al. ( 2018), for whom interactive communication means transmitting and receiving information in a clear manner and actively communicating with others in a way that is effective and consistent with the institution's purpose.

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Personal Skills and Behaviors

Public communication does not neglect the classic rules imposed on public employees in their professional attitudes, including their skills and behaviors. Based on our findings, we conclude that ensuring free access to information cannot be achieved without accompanying employees and managers of public institutions in this direction. It is necessary for employees to develop their personal skills and orient their behaviors towards transparent public communication. Interviewee 3, explained that: "According to the law that came into effect in 2019 concerning access to information, Moroccan public institutions are now required to proactively disseminate their data, using all possible means of publication. In this context, the Ministry of Economy, Finance and Administration Reform of Morocco has issued a circular in 2020 encouraging administrations, both at the central and deconcentrated levels, to comply with the legal framework. As a result, training sessions were held for institutions developed by the lead ministries about a practical guidelines related to the application of the law, in order to help employees better understand the rights and remedies of citizens for open access to information, and to strengthen the skills required for proactive data dissemination...". This corroborates with the claims of [START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF] concerning the respect of competences, decisions and orders that given in their personal behavior and affect the image of the institution when exercising responsibilities [START_REF] Tsetsura | The U.S. capability framework for public relations and communication management : Results of a national three-stage study[END_REF][START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF]. Consequently, personal skills and behaviors required neutrality towards political involvement or personal convictions for achieving good public communication in Moroccan public institutions.

Ethics and Transparency

In our findings, transparency is important for successful public communication in public institutions, as a catalyst for good governance. Interviewee 6 said: "To improve the level of transparency, the managers use the public communication as a consistent way to increase the visibility of the institution's activities, results, and achievements". Moreover, the ethics of communication is often assessed by several authors in the context of media practice. Interviewee 10 confided that "It is obvious that ethics is an imperative, an essential factor for exercising public function. It is one of the principles of good governance, as it is the main driving factor of public communication, not only for managers and employees but also for the public institution as a homogeneous structure.". Thus, public communication, which constitutes only a part of the communication practiced in the public place, cannot be satisfied with satisfying the requirements, which are unfortunately very approximate, that the press and more generally the media assign to themselves [START_REF] Zampiccoli | le management public : Approches conceptuelles et enjeux de pilotage. Gestion et Management Publics[END_REF], whatever the nature of the information supports, governed for the most part by the rules of the public sector in the respect of the principles of governance such as transparency, and ethics in itself. «Ethics should be at the core of public communication in order to ensure the responsibility to inform and accomplish this public service mission towards citizens." (Interviewee5

Public Communication as a Condition of Good Governance

All interviewees agree that public communication through its various components in public is a condition and requirement of good governance. "Public communication constitutes a mechanism for good governance, especially since it allows free access to public information and the right to know. Therefore, the presence of institutions in the media has become a support and an unavoidable ally that pushes institutions to adopt a public communication strategy, which I perceive as a condition for good governance" (Interviwee8). In the same way, other www.ijafame.org interviewees mentioned the fact that the quality of public communication has an influence on the evolution of the implementation of good governance and insists on the effect of transparency in the management of information and the enhancement of the institution's image. He said: "I believe that the components or determinants of public communication are considered indispensable to good governance. It should be noted that in practice, there is an association between transparency and good governance essentially from the point of view of information management and the disclosure of information relating to the organization's image." (Interviwee4). These assertions corroborate the work of Jarren (2007) and [START_REF] Kemayou | La communication publique entre mythe et réalité au Cameroun : Une gouvernance de défiance vis-à-vis des citoyens-usagers ? Pyramides[END_REF], who finds that one of the stakes of public communication is precisely to maintain the social relationship and the living-together, from an open access public information sharing perspective in the process of good governance. Nevertheless, public information is supposed to give meaning to public action, to the effect of the participation of citizens-users, convinced of their common purposes, in the collective life. In this regard, interviewee 7 said: "Sharing information between public institutions and citizens and the dialogue that follows are essential components of good governance in the public field, and play a crucial role in improving public communication and public action." Regardless of the number of years of service or the sector of activity in which the interviewees exercise their functions, the importance of public communication is crucial, even indispensable, to good governance.

5.

Discussion: The contribution of public communication on good governance of Moroccan public institutions

Our findings revealed that good governance is intrinsically associated to the principles of transparency and communication ethics, especially in public institutions where serving the public interest is the main driver of performance. A general pragmatics, like Habermas, consists in the discourse mode itself, as deployed in public communication, whether the dialogue is based on the sincerity, comprehensibility, legitimacy and truthfulness of the arguments [START_REF] Hoch | A Pragmatic Inquiry about Planning and Power[END_REF]. Broadly, the public communication is performed as a condition of governance [START_REF] Gardère | Quelles communications pour la gouvernance des institutions publiques au XXIe siècle ? / What communication for the governance of public institutions in the 21st century?[END_REF]Jarren, 2007b;[START_REF] Zamoum | Transparence et communication publique : Étude du cas de la Ligue des États Arabes[END_REF]. This philosophy of good governance has ruled the organizational scene of public institutions and has anticipated the emergence of a culture of ethics and transparency ( ). The findings of our thematic content analysis reveal that the potentialities allowed by technical evolution come close to a vision borrowed from a certain technological determinism according to a classic framework of categorization of analysts' discourses on technological innovations. In such a perspective, it would be necessary to overcome the logic of unidirectional communication, in order to better take into consideration, the development of social media practices generating new and more horizontal ways of communication [START_REF] Durkin | Social Media and Interactive Communications : A service sector reflective on the challenges for practice and theory[END_REF]. The purpose is to build a community on social networks such as Twitter, LinkedIn, Facebook, Instagram, or even Tiktok to be in permanent contact with all the citizens, but also with potential partners. It is clear that despite the studies conducted in this direction, the literature remains insufficient to explain deeply the various relationship between public communication and good governance, www.ijafame.org especially in Morocco. Our qualitative study was conducted to resolve this insufficiency and brought results that stipulate that every component of public communication is crucial in the process of good governance to implement its principles and practices (figure 1). In its latest report about governance in Morocco, the OECD has highlighted the role that public communication has in addressing the gap in trust that existed between the institution and the citizen. The reasons are that innovations such as digital communication channels, massive data analytics and behavioral science insights have given public institutions an unprecedented arsenal to increase the reach and impact of their messages and to encourage positive behavior, but also to listen to citizens and understand their needs and expectations. This fact is proved by the findings of performed qualitative study. In summary, public communication is understood as a crucial function of public institutions to provide information, to listen and to respond to the needs of citizens and to ensure transparency required for the purpose of good governance.

  ; Ansell & Torfing, 2016; Anttiroiko et al., 2011; Assens & Lemeur, 2016; Aucoin, 1990; Charreaux, 2011; Foley et al., 2018; Grindle, 2007; Gross & Źróbek, 2015; Khouya & Benabdelhadi, 2020; Klusáček, 2018; Lacroix & St-Arnaud, 2012

  the practice of public communication, the values of public service are well taken into consideration. These values are mainly based on the general interest, whose legitimacy is opposed to personal wishes and opportunistic behavior and particular interests (Box, 2015;[START_REF] Megard | Chapitre 1. Spécificités et enjeux de la communication publique[END_REF]. This requires respect for the rule of law and the principles of equality[START_REF] Morrell | What is governance in the 'public interest' ? The case of the 1995 property forum in post-conflict Nicaragua[END_REF]. Nevertheless,[START_REF] Andersen | Public Values and Public Service Motivation : Conceptual and Empirical Relationships[END_REF] provided an overview of characteristics of public service.

Figure 1 :

 1 Figure 1: Framework of the components of public communication in good governance process

Table 1 : Characteristics of the sample

 1

	N° Interview	Post occupied	Sector	Gender	Seniority	Interview duration
	1	Professor	Higher education	Female	13	1h50
	2	Department head	Agriculture and rural development	Female	8	1h
	3	Chief executive officer	Investment	Male	13	50min
	4	Communication manager	Water and electricity	Male	2	1h15
	5	Department head	Higher education	Male	15	1h20
	6	Communication manager	Food Safety	Female	3	1h15
	7	Department head	Investment	Male	10	1h
	8	Professor	Higher education	Female	9	1h30
	9	Department head	Investment	Male	1	1h30
	10	Professor	Higher education	Female	11	2h

  ). Previous work has suggested that ethics and transparency are key to conducting public communication (Asdourian, 2015; Catellani & Crucifix, 2015; Ruppel & Harrington, 2000; Zamoum, 2014). This finding is reinforced by our results which indicate that in public communication, ethics and transparency are required elements within public institutions.

Marwa KHOUYA & Abdelhay BENABDELHADI. The contribution of public communication on the good governance process: The case of public institutions in Morocco

Volume 4, Issue 2-2 (2023), pp. 223-236. © Authors: CC BY-NC-ND


Moussa Boukhnifer
email: moussa.boukhnifer@univ-lorraine.fr

H Marzougui
email: marzougui.ensit@gmail.com

F Bacha

Energy Management Algorithm of Fuel Cell/Supercapacitor System

HAL is a

I. INTRODUCTION

In recent years the number of cars has shown a very significant increase which leads to a huge growth in the consumption of fossil fuels, thus, stimulating environmental pollution on a larger scale. For these reasons, the demand for vehicles that provide more or less fuel economy and less polluting solutions has increased. The use of clean and renewable energies in electrical systems becomes a necessity. Fuel cell (FC) can be considered, so, as a good solution which allows to reduce gases emissions, and consequently, environment pollution. We talk so about Fuel cell electric vehicle (FCEV) which is an electric vehicle. For a FC hybrid vehicle, it uses, in addition to the fuel cell, a secondary source of electrical energy which is reversible in power as storage systems (Super-capacitors and Batteries) [START_REF] Kascak | FOUR PHASE INTERLEAVED BOOST CONVERTER -ANALYSIS AND VERIFICATION[END_REF]. In order to satisfy the FCEV requirements in terms of stepup ratio, FC current ripple and fault tolerance [START_REF] Kascak | FOUR PHASE INTERLEAVED BOOST CONVERTER -ANALYSIS AND VERIFICATION[END_REF] Li [START_REF] Li | Controller design and fault tolerance analysis of 4-phase floating interleaved boost converter for fuel cell electric vehicles[END_REF] and Pang [START_REF] Pang | Fault-tolerant consideration and active stabilization for floating interleaved boost converter system[END_REF], the traditional boost converter is not a good solution because the converter with single switch has no fault tolerance and the voltage gain is limited. Compared to this topology, the Floating Interleaved Boost Converter (FIBC) is particularly suitable for fuel cell applications, due to the interleaving architecture of this topology that allows the converter to operate without any interruption in presence of open circuit fault (OCFs) occurred on one or two switches and the respective shift between the phases that allows reducing the input current ripple [START_REF] Barhoumi | Modelling and Control of Floating Interleaved Boost Converter for Electric Vehicle[END_REF] [START_REF] Guilbert | Power switch failures tolerance and remedial strategies of a 4-leg floating interleaved DC/DC boost converter for photovoltaic/fuel cell applications[END_REF]. Furthermore, Ref [START_REF] Guilbert | Power switch failures tolerance and remedial strategies of a 4-leg floating interleaved DC/DC boost converter for photovoltaic/fuel cell applications[END_REF][START_REF] Lute | Development of a four phase floating interleaved boost converter for photovoltaic systems[END_REF] has demonstrated that the 4phase FIBC is the best selection through discussing between the 2-phase, 4-phase and 6-phase FIBC from the different aspects (e.g. the input current ripple, efficiency, the volume of the inductors and fault tolerance). It is to mention, also, that for a hybrid vehicle which is powered by more than one source, a method of energy management between sources is necessary in order to evaluate the contribution of the hybridization of the source intended for the power supply of an electric vehicle compared to a traditional vehicle and its effect on fuel economy and reduction of pollutant emissions [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF]. There are several management methods that we can use. Among these methods, there rule-based energy management strategy has been frequently used for the simplicity of its implementation. Rules-based strategy can be, typically, applied on specific vehicle operation and states such: start, brake, accelerate, decelerate, climb and grade. In the energy management of FCHEVs, the operating modes mainly depend on the input parameters, such as the charging power, the vehicle speed or the state of charge of the storage system. A clear and beneficial explanation can be found in the previous research work [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF], who are among the researchers who applied the rule-based strategy for FCHEV. The paper is structured as follows: A thorough vehicle structure is executed in Section II. Section III is consecrated to develop modeling of DC/DC converters and present the propose control loops. Then, a rule-based energy management algorithm is developed in section IV. Then the numerical simulation results are given in Section V.

II. VEHICLE STRUCTURE

The energy chain of the studied hybrid electric vehicle is shown in figure 1. This chain is made up of:

-A fuel cell which is a unidirectional source: It plays the role of main source. This source consists on the heart cell associated with all auxiliaries which are necessary to the operation of a fuel cell for an embedded application.

-Supercapacitor is a bidirectional source: used as a storage system that presents the secondary source.

-A unidirectional floating interlaced DC/DC converter with four legs, its role is the interface between the main source and the DC bus.

-A bidirectional floating interleaved converter with four branches allowing to connect the storage system to the DC link while ensuring the transfer of energy between this device and the DC bus in both directions.

-An inverter whose role is to interface between the DC link and the propulsion motor.

In this work, we will limit ourselves only to the part before the DC link (from the sources to the DC link). o Constant frequency for phase shift. It should be mentioned that it is necessary to apply the adequate control to the proposed converter topology. This control must keep the output DC bus voltage constant to prevent load damage. However, the currents in all four legs must be equal in order to increase the efficiency of the converter and to avoid overloading any of the modules when energizing heavy loads. Furthermore, it is necessary to keep the intake current ripple low, as this latter can reduce the lifetime of the source [START_REF] Marzougui | Energy management of fuel cell/ battery/ ultracapacitor in electrical hybrid vehicle[END_REF]. Indeed, phases interleaving technology can be considered as an effective method to reduce input current ripple.

A. Bidirectional Floating Interleaved Converter Topology

The figure below shows the chosen bidirectional floating interleaved converter. S ,S ,S and S must be made. Interleaving two or more converter legs can reduce the input current ripple [START_REF] Marzougui | Energy management of fuel cell/ battery/ ultracapacitor in electrical hybrid vehicle[END_REF]. Moreover, this topology makes it possible to reduce the electrical constraints on the power semiconductors.

The number of phases of a floating DC/DC interlaced converter must always be even in order to maintain a balance between the non-floating part (i.e. the upper part) and the floating part (i.e. say the lower part). Moreover, in term of reliability, this architecture is more robust compared to the two-phase one [START_REF] Zhuo | Design and Control of a Floating Interleaved Boost DC-DC Converter for Fuel Cell Applications[END_REF]. It should also be noted that the loss of phase of a part (i.e. floating or non-floating part) for a 4-phase converter can be compensated by the other phase located on the defective part. However, by maintaining the balance of the converter, this leads to an excess of one phase, thus creating additional electrical stresses, in particular on the magnetic components.

All passive components are ideal elements without the parasitic parameters and they are also equal.

1 2 1 2 3 4 C C C & L L L L L       (1)
Regarding the duty cycle, we will build models and according to these models we will make control. Each leg is controlled by its proper Duty Cycle ( 1 2 3 4 d ,d ,d ,d )

A. Average model

The representation of the state space system is shown by the equation system (2).

x Ax Bu y Cx Du      U is the control or input vector, Y is the output, and X is the vector of state variables.

(2)

      1 2 3 4 1 2
, , , , ,

, t L L L L c c t SC Load DC x I I I I V V y V I u V t           (3)
CONFIDENTIAL. Limited circulation. For review only.

        (4)
During mode alternation, the operating mode of the FIBDC is forced conduction mode (FCM), and the FIBDC model contains both charging and discharging mode. These two models have a unified form, which means that the unified model ( 5) is also suitable for the alternating mode.

Discharging Mode

During high power demand or for high SOC cases, the FIBDC will operate in boost mode, and the Fuel cell will be dump. For the time being, the operating mode of the FIBDC will be in continuous conduction mode (CCM) or critical conduction mode (CRM). On the assumption that   are on, the inductors release energy to the capacities and the DC bus. Consequently, energy is transformed from the Supercapacitor side to the DC bus side so the FIBDC operates in boost mode.

The representation of the state space system on discharging mode is shown by the equation system (5).

1 1 2 2 1 2 3 3 3 4 4 4 1 1 2 1 2 3 4 2 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 L L L L L L L L C C C C dI d dt L dI d I dt L I dI d I dt L I d dI L dt V d d dV V C C dt d d dV C C dt                                                                                       1 0 1 0 1 0 1 0 1 0 1 0 Scc Load L L V L I L C C                                                       (5) 1 1 1 1 1 1 0 ; 0 ; 0 ; 0 ; 0 ; 0 B L L L L C C            1 1 1 1 0 0 C  (6)

B. Control in Discharging Mode

This type of controller is used for interleaved boost topologies (2), ( 3), ( 4), ( 5), [START_REF] Lute | Development of a four phase floating interleaved boost converter for photovoltaic systems[END_REF], and it makes it possible, in fact, to distribute the instantaneous currents between different phases.

Charging Mode

As shown in Fig. 2, the converter consists of two modules, when the load power demand is low or for low SOC case, the FIBDC will work in buck mode and the Supercapacitor must be loaded. At that moment, the mode of operation of the FIBDC was still CCM or CRM. Supposing that  

1 2 3 4 i U i , , ,  
is the signal control of the power switch 1 2 3 4 S , , , 

During the power state the switch

1 2 3 4 S , , , 
is on

1 i U   and 1 2 3 4 S , ,
, is off, the inductors store the DC bus energy, and the capacitors release the energy to the battery banks. During the state of the power switch

1 2 3 4 S , , ,  turn off   0 i U   and 1 2 3 4 S , ,
, turn off, the inductors release energy to the Supercapacitor. Energy is transformed from the DC bus on the Supercapacitor side so the FIBDC is in buck mode.

All math done for the charging mode, it can be modeled as follows:

1 1 2 2 1 2 3 3 3 4 4 4 1 1 2 1 2 3 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 L L L L L L L L C C C C dI d dt L dI d I dt L I dI d I dt L I d dI L dt V d d dV V C C dt d d dV C C dt                                                                                               1 0 1 0 1 0 1 0 1 0 1 0 sc Load L L V L I L C C                                                   (7)
Since the FIBDC is driven by complementary PWM, it is:

  1 1 2 3 4 i i U U i , , ,     (8)
Substitute ( 8) to [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF], the same pattern can be obtained as [START_REF] Guilbert | Power switch failures tolerance and remedial strategies of a 4-leg floating interleaved DC/DC boost converter for photovoltaic/fuel cell applications[END_REF], which proves that the two models of boost and buck actually have the unified form.

Control Model in Charging Mode

This type of controller is used for interleaved topologies, and it makes it possible to actually distribute the instantaneous currents between different phases. The control loops shown in Fig. 4 are applied, in this part, to the proposed 4-phase FIBC. In order to test the behavior of our system in this case, the same conditions (NEDC), used to test the performance of a single voltage regulation loop, and apply a regulation loop for each phase for the current.

IL3ref

B. Floating Interleaved Converter Topology (unidirectional)

A Bidirectional Converter circuit combines elements of a buck converter and a boost converter. As it is mentioned above, we can notice that the unidirectional floating interleaved boost converter has the same operation as the bidirectional in discharge mode, hence the same modeling and the same control

IV. ENERGY MANAGEMENT ALGORITHM
Since the vehicle is powered by more than one source, it is necessary to apply an energy management strategy which can distribute the power required by the motor traction between the two sources. Fig. 6 presents the energy management algorithm proposed to ensure the power sharing between fuel cell and supercapacitor. This algorithm allows to generate the reference of the fuel cell bower based on tests on the load power. So, the rules on which are based the algorithm, take into consideration the SOC of the supercapacitor and the power of the fuel cell. Rules guarantee, also, to keep these variables between their limit values [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF].

V. SIMULATION RESULTS

In order to evaluate the behavior of the studied system, the chosen converters and the proposed energy management strategy, we used the speed profile (NEDC), presented in Fig. Fig. 8 presents the evolution of different powers in the system (Load power, Fuel cell power and supercapacitor power). It can be seen that source powers satisfy the power required by the vehicle. The proposed energy management algorithm, allows to distribute the load power between the source elements respecting the limitation on the fuel cell power. It can be seen on Fig. 9, that the sum of the source currents is equal to the load current. Indeed, the currents evolution is the same seen on the powers evolution. From Fig. 10, we can see that the fuel cell voltage presents important drops when its power increases. As well for the supercapacitor voltage, this variable increases or decreases according to the operating mode (charging or discharging). For the SOC of the supercapacitor Fig. 11, its evolution present the same variations seen on the voltage of the same device. Thus it kept between the maximal and the minimal values imposed by the energy management algorithm. It can be proved from Fig. 12, Fig. 13 and Fig. 14 that the regulators used in these work present good performances. Indeed, the inductor currents and the capacitor voltages show perfectly their references obeying to the control loops presented in Fig. 4 and Fig. From the simulation results presented above, the major advantage of the strategy proposed in this paper is that it ensures stable operation of the fuel cell during long intervals as well as a limitation of the state of charge of the super-capacitor pack, which makes it possible to avoid the deep discharge of this storage device and, also, its overcharge.

VI. CONCLUSION

In this work, a rule-based power sharing strategy was developed and applied for a electrical vehicle supplied by a dual source power system which was consisting of a fuel cell, interfaced by a floating interleaved boost converter, and a supercapacitor connected to a floating interleaved bidirectional converter. The proposed converter topology and the energy management strategy were tested for the NEDC driving cycle. The adopted strategy was found to be effective in sharing the power flow between the main and the secondary source in order to satisfy the power required by the propulsion system taking into account constraints on the source powers and the supercapacitor SOC. The major advantage of the proposed converters topology in this paper, is that allows to reduce the input current ripple, increase efficiency, minimize the volume of the inductors and ensures operating in degraded mode.

Figure 1 .

 1 Figure 1. Energy chain of electric hybrid vehicle III. VEHICLE STRUCTURE DC/DC CONVERTERS The combination of two or more interleaved floating amplification architectures thus improves the voltage gain compared to the conventional amplification topology. Moreover, the presence of a non-floating and floating bus in the interleaved floating DC/DC boost converter nevertheless has a strong point of being fault-tolerant due to the presence of static redundancy [8]. Applying a Floating Interleaved Boost Converter at the source output can guarantee several advantages, the most important are: o Constant voltage at the output of the converter. o Equal leg currents.o Constant frequency for phase shift. It should be mentioned that it is necessary to apply the adequate control to the proposed converter topology. This control must keep the output DC bus voltage constant to prevent load damage. However, the currents in all four legs must be equal in order to increase the efficiency of the converter and to avoid overloading any of the modules when energizing heavy loads. Furthermore, it is necessary to keep the intake current ripple low, as this latter can reduce the lifetime of the source[START_REF] Marzougui | Energy management of fuel cell/ battery/ ultracapacitor in electrical hybrid vehicle[END_REF]. Indeed, phases interleaving technology can be considered as an effective method to reduce input current ripple.

Figure 2 . 4 -

 24 Figure 2. 4-leg Floating Interleaved buck-Boost Converter The concept of interleaving, used in the proposed topology is ensured by the paralleling of a non-floating version and a floating version of the DC/DC boost converter at the input. Thus, a delay between the control signals for the switches 1 2 3 4

Figure 3 .

 3 Figure 3. Control model

Figure 4 .

 4 Figure 4. Control model

Fig. 5 Figure 5 . 4 -

 554 Fig. 5 presents a 4-phase floating interleaved DC/DC Boost converter (Discharging mode on bidirectional) D1

Figure 6 .

 6 Figure 6. Rule-based energy management algorithm

7

 7

Figure 7 .

 7 Figure 7. New European Driving Cycle (NEDC)

Figure 8 .

 8 Figure 8. Powers of load, Fuel cell and supercapacitor

Figure 9 .

 9 Figure 9. Supercapacitor Fuel Cell Load Current

Figure 10 .

 10 Figure 10. FC Voltage

3

 3

Figure 12 .

 12 Figure 12. Ref and inductor Current (Unidirectional converter)

Figure 15 .

 15 Figure 15. DC link voltage

Manuscript 362 submitted to 8th International Conference on Control, Decision and Information Technologies (CODIT). Received February 25, 2022.


Nassira Barhoumi
email: nassira.barhoumi@gmail.com

Faouzi Bacha
email: faouzi.bacha@esstt.rnu.tn

Improved current Control of Floating Interleaved Boost Converter Dedicated to Vehicular Applications

Keywords: DC/DC Converter, floating interleaved boost converter, fuel cell, electrical vehicle

This paper investigates the performance of four-phase Floating Interleaved Boost Converter (FIBC) for vehicular applications. For such applications, current control is indispensable in order to ensure the vehicle power (eventually the current) requirement satisfaction. For this reason, two methods are applied in this work to control the current of the source associated to the studied converter which is a fuel cell in our case. This first method is based on using one current control loop which allows to maintain the total current in the output of the source equal to its reference. The second method consists on improving the first one by applying a current control loop for each converter leg (i.e using four control loops). This converter offers improved efficiency and voltage gain, while ensuring lower input current ripple than other DC-DC boost converter topologies.

In this paper, the proposed controls are evaluated for the same road conditions by applying the New European driving cycle (NEDC). Simulation results are presented to validate the effectiveness of the two adopted controls and prove the improvements presented by the technology using four control loops.

INTRODUCTION

A fuel cell is a device that converts chemical energy directly into electrical energy without any thermal or mechanical process. The stack at fuel is one of the most promising for power generation on-board applications, due to high energy density, high efficiency and low temperature of operation, allowing it to start faster compared to other types. However, some constraints are still pending, in particular its slow dynamics and its low voltage produced at the output. For these reasons, a DC / DC converter is not only necessary to raise this voltage up to the voltage level of the DC bus, but also for conditioning the output voltage of the fuel cell which varies greatly with load [START_REF] Kascak | FOUR PHASE INTERLEAVED BOOST CONVERTER -ANALYSIS AND VERIFICATION[END_REF].

Several topologies based on the basic architecture of the classic DC / DC boost converter has been proposed [START_REF] Kascak | FOUR PHASE INTERLEAVED BOOST CONVERTER -ANALYSIS AND VERIFICATION[END_REF], [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF], [START_REF] Marzougui | Energy management of fuel cell/ battery/ ultracapacitor in electrical hybrid vehicle[END_REF] in order to improve compactness, voltage gain and also energy efficiency. Basic changes to the DC / DC boost classical allow to build fault tolerant interleaved architectures to improve the gain of elevation and minimize the ripple current input [START_REF] Huangfu | Robust Voltage Control of Floating Interleaved Boost Converter for Fuel Cell Systems[END_REF]. The combination of two or more interleaved boost floating architecture improves, so, the voltage gain compared to the conventional boost topology because the voltages across the capacitors add up. In addition, with the presence of static redundancy [START_REF] Zhuo | Design and Control of a Floating Interleaved Boost DC-DC Converter for Fuel Cell Applications[END_REF], the converter is able to operate in degraded mode. For all these reasons, floating boost interleaved architectures are ideally suited to the expectations of Fuel cell electric vehicle applications [START_REF] Marzougui | Implementation of energy management strategy of hybrid power source for electrical vehicle[END_REF], [START_REF] Guilbert | Power switch failures tolerance and remedial strategies of a 4-leg floating interleaved DC/DC boost converter for photovoltaic/fuel cell applications[END_REF]. This is due to several advantages that presented the mentioned topology. Indeed, its size and volume of passive components are reduced compared to other topologies. Thus, input current ripple and DC bus ripple are reduced depending on the number of legs used in the floating converter. Besides, this converter is modular. It improves the reliability of the system owing to the presence of degrees of freedom and increases the power of this converter thanks to the parallel connection of legs. The interleaved floating DC / DC boost converter is of particular interest due to the presence of a non-floating and floating bus, it is fault tolerant due to the presence of static redundancy [START_REF] Li | Controller design and fault tolerance analysis of 4-phase floating interleaved boost converter for fuel cell electric vehicles[END_REF]. This redundancy is opposed to dynamic redundancy, which is often used to make a topology tolerant to faults. In this context, the objective of our work is to improve the current control of a four phase-floating interleaved boost DC / DC converter used to interface a PEMFC dedicated to vehicular application. Two control strategies are developed; a single-loop control for the total current of the four inductances. In the second strategy, four current loops are applied, one for each leg, in order to guarantee a balanced current in the four phases of the converter [4.8]. Simulation results are presented in order to validate the chosen topology and prove the effectiveness of the developed control strategies.

II. FLOATING INTERLEAVED BOOST CONVERTER TOPOLGY

The concept of interleaving, on which the proposed topology is based, is ensured by the parallel connection of a non-floating and a floating version of the DC / DC boost converter at the input. Thus, a delay between control signals for switches S1, S2, S3 and S4 should be performed.

Interleaving two or more converter legs allows to reduce the input current ripple [START_REF] Pang | Fault-tolerant consideration and active stabilization for floating interleaved boost converter system[END_REF]. In addition, this topology makes it possible to reduce the electrical constraints (i.e. voltage and current) on power semiconductors.

The number of phases of a DC / DC floating interleaved boost converter must be always even in order to keep a balance between the non-floating part (i.e. top part) and the floating part (i.e. bottom part). Moreover, in terms of reliability, this architecture is more robust compared to that with two phases [START_REF] Barhoumi | Modelling and Control of Floating Interleaved Boost Converter for Electric Vehicle[END_REF]. It is to note, also, that the loss of a phase of a part (i.e. floating or non-floating part) for a 4-phases converter could be compensated by the other phase located on the defective part. However, by keeping the balance of the converter, this leads to the excess of one phase, thus creating additional electrical stresses, in particular on the magnetic components.

All the passive components are ideal elements without the parasitic parameters and they are also equal.

1 2 1 2 3 4 C C C L L L L L     
Regarding the duty cycle, we will build two models and according to these models we will make two controls, one control for each model: For the first one:

1 2 3 4 d d d d d    
For the second one:

(1)

1 2 3 4 d d d d    (2)

III. FLOATING INTERLEAVED BOOST CONVERTER

A. MODELING WITH A SINGLE CONTROL LOOP 1. Equations

In order to ensure the adequate control of the converter, the performance goals needed for the appropriate dynamic models of used topology are needed. In the first stage of the converter, equations Fig. 2 given two operating sequences. For the sequence of operation (0 <t <DTs) and (DTs <t <Ts), the equations are given as follows:

d t L1 L1 C1 Bus d t L2 L2 C1 Bus L3 d t L3 C2 in L4 d t L4 C2 in C1 L1 L2 C1 C2 in C (r (1-d)-dr ) dI d-1 1 = I + V + I dt L L L (r (1-d)-dr ) dI d-1 1 = I + V + V dt L L L dI (r (1-d)-dr ) d-1 1 = I + V + V dt L L L dI (r (1-d)-dr ) d-1 1 = I + V + V dt L L L dV 1-d 1-d 1 1 1 = I + I - V - V + V dt L L RC RC RC dV 2 L3 L4 C1 C2 in 1-d 1-d 1 1 1 = I + I - V - V + V dt L L RC RC RC (3)
where Lx I (x=1,2,3,4) is the inductor current, Cy V (y=1,2)

is the capacitor voltage, in I and in V are respectively the input current and the input voltage while Bus I and Bus V are the output current and the output voltage, respectively. The input current and the DC-bus voltage dynamic are given by equation system (4). 2. Average model The average model was applied, known as average circuits on equations (3) and ( 4). The average model of the investigated converter given, so by equation system [START_REF] Zhuo | Design and Control of a Floating Interleaved Boost DC-DC Converter for Fuel Cell Applications[END_REF]. Where X is the state vector, while U presents the control vector.

          t L1 L2 L3 L4 C1 C2 X= I I I I V V FC U=V (6) A= d t d t d t d t (r (1-d)-dr ) d-1 0 0 0 0 L L (r (1-d)-dr ) d-1 0 0 0 0 L L (r (1-d)-dr ) d-1 0 0 0 0 L L (r (1-d)-dr ) d-1 0 0 0 0 L L 1-d 1-d 1 1 0 0 - - L L RC RC 1-d 1-d 1 1 0 0 - - L L RC RC                                   (7) t 1 1 1 1 1 1 B= L L L L RC RC         1 1 1 1 0 0 C  (8)

Conventional current control

To correctly select and design correctors, it is essential to establish control purposes that can be formulated as follows:

The fuel cell flow should be divided equally between the different phases of the conversions to avoid overloading one of the phases, especially for high load values. In addition, the phase currents should be advisable to compensate each other to reduce the input current ripple, which is undesirable in FC applications. Stability and dynamic performance should always be guaranteed when the system works in a closed loop. In the first proposal, the used PI controller will make possible to obtain the reference of the current in the phases from the difference between the reference of the current in the inductors and the current of the measured inductors. In the second, it will make it possible to obtain the reference of the current in each phase from the difference between the current reference in each inductor and the current measured in each inductor. To ensure the validity of the current output control loop, the controller parameters (KP and Ki) can be determined by Ziegler Nichols method. The output current of the converter is limited and compared with the desired reference current. The PI regulator output signal makes it possible to make available the work cycle d which guarantees that the total current of the four inductances in the desired reference value.

a. Simulation results for a variable load

To test the behavior of our converter when it is associated to fuel cell in order to satisfy the power requirement in vehicular application, we applied the speed profile (NEDC: New European Driving Cycle) which is presented in Fig. 3 For this speed profile, the power required by the vehicle is shown in Fig. 4. A proportional integral controller was used, as mentioned above, to control the current in the input of the proposed converter. The corresponding responses in relation to the various electrical variables are presented in this part. Figure .5 shows the load current. Its waveform shows the same evolution of the power required by the load which is presented by a traction motor in an electric vehicle. By exploiting evolution of the total current of the four inductances and its reference shown in Fig. 7, we can confirm that their evolutions satisfy that is imposed by the control loop applied in this work. For Fig. 8, it shows the current of a single phase of the converter. This current presents the quarter of the total current of the four inductances. The duty cycle obtained from the current control loop is illustrated by Fig. 10. This variable is used to control the IGBTs used in the adopted converter. By exploiting results shown in this section, it should be mentioned that the duty cycle used to control the converter operating presents important peaks which can influence on the converter performances. Thus, using a single control loop can present a lot of problems in the event of a fault occurring. The control adopted should be so improved by controlling each phase independently of other phases.

B. MODELING WITH A CONTROL LOOP FOR EACH LEG

1. Equations

1 1 1 1 1 1 2 2 2 2 2 1 3 3 3 3 3 2 4 4 4 4 4 2 1 1 2 1 2 2 ( ( 1) ) 1 1 ( ( 1) ) 1 1 ( ( 1) ) 1 1 ( ( 1) ) 1 1 1 1
d t L L C FC d t L L C FC L d t L C FC d t L L C FC C ch L L C r d d r dI d I V V dt L L L r d d r dI d I V V dt L L L dI r d d r d I V V dt L L L r d d r dI d I V V dt L L L dV I d d I I dt C C C dV dt                            3 4 3 4 1 1 ch L L d I d I I C C C     (9)
2. Average model The representation of the state space system is shown by the equation system [START_REF] Pang | Fault-tolerant consideration and active stabilization for floating interleaved boost converter system[END_REF].

x Ax Bu y Cx Du        (10)
U the control or input vector, Y is the output, and X is the vector of state variables.

      1 2 3 4 1 2
, , , , ,

, t L L L L c c t FC ch Bus x I I I I V V y V I u V t           (11)
With:

t dI dV dV dI dI dI L3 C1 C2 L1 L2 L4 X= dt dt dt dt dt dt         1 1 1 1 2 2 2 2
                                                     1 2 3 4 1 2 1 0 1 0 1 0 1 0 1 0 1 0 0 L L L FC L ch C C L I L I I V L I I L V V C C                                                                                                   
In the rest of our work we will neglect the two resistances r d and r t :

(12)

L I d dI L dt V d d dV V C C dt d d dV C C dt                                                                                       1 0 1 0 1 0 1 0 1 0 1 0 FC ch L L V L I L C C                                                       (13) 1 1 1 1 1 1 0 ; 0 ; 0 ; 0 ; 0 ; 0 B L L L L C C          (14)   1 1 1 1 0 0 C  (15)

CURRENT CONTROL PER PHASE

This type of controller is used for interleaved boost topologies (12), (13), (15), (16), and it makes it possible to actually distribute the instantaneous currents between different phases. The control loops shown in Fig. 11 are applied, in this part, to the proposed 4-phase FIBC. In order to test the behavior of our system in this case, the same conditions (NEDC), used to test the performances of a single control loop, are now applied to prove the effectiveness of using a control loop for each phase.

For the driving cycle (NEDC) presented in Fig. 3, we present the obtained results in Fig. 12-16. We can observe from the results presented in this section, that the studied system operates obeying to that is imposed by the proposed control loops. We can see that the duty cycle does not present the peaks seen when only a single current control loop is applied. The improvement of results can be proved also by exploiting the results presented in Fig. 14 which shows the waveform of the current of one phase and its reference. This figure proves good performances guaranteed by the proposed control.

I. Conclusion

The purpose of this paper was to modeling and to propose a control loop for a floating DC/DC boost converter. The proposed control is based on the regulation of the output current by a PI regulator. Indeed, the floating DC/DC converters composed of four legs are shifted relatively to each other by a 90 ° angle which causes a difference on the phase currents and the output voltage in the event of a failure one of these legs. Some tests were made using Matlab-Simulink to show the robustness of our system and simulation results validated the chosen control. Thus, the obtained results demonstrated the performance of the system when one of the two parameters is varied: Load and DC bus voltage in order to improve the reliability of the converter.

Fig. 1 Fig. 1 .

 11 Fig. 1. Four-phase Floating Interleaved Boost Converter topology

Fig. 2 .

 2 Fig. 2. Current control loop

Fig. 3 .Fig. 6 .Fig. 9 .

 369 Fig. 3. New European Driving Cycle (NEDC)

  Fig. 11.Control model

Fig. 12 .

 12 Fig. 12.Fuel Cell Current

TABLE I

 I

		. 4-PHASE FIBC SPECIFICATIONS
	Parameter	Value
	Rated input voltage	24V
	Output voltage	100V
	Switching frequency	20KHz
	Inductance	120µH
	Capacitor	470µF