Dr Marie Mianowski
email: marie.mianowski@univ-nantes.fr

'The cottage by the lough in Colum McCann's TransAtlantic: between

Keywords: place, landscape, Colum McCann, life-world, space in-between, phenomenology

'The cottage by the lough in Colum McCann's TransAtlantic: between finite and infinite.' Lifeworlds : Space, Place and Irish Culture. Edited by Nessa Cronin and Tim Collins. (peerreviewed, to be published 2016).

In his last work The Crisis of European Sciences and Transcendental Phenomenology

Edmund Husserl introduced the concept of the life-world drawing a clear line between the subjective, immediate experience of everyday life and the objective 'worlds' of the sciences.

In his view, the 'life-world' included individual, social, perceptual and practical experiences. 1 The concept was further developed and reassessed by philosophers among whom, according to Taylor Carman, Merleau-Ponty's phenomenology stands out, amounting 'to a radical, if discreet, departure not only from Husserl's theory of intentionality generally, but more specifically from his account of the intentional constitution of the body and its role in perceptual experience.' 2 As Carman stresses in his discussion on the body in Husserl and Merleau-Ponty, the phenomenology of Merleau-Ponty engages the body in the task of perceiving and experiencing life: thought and sensation as such occur only against a background of perceptual activity that we always already understand in bodily terms, by engaging in it. Moreover, the body undercuts the supposed dichotomy between the transparency of consciousness and the opacity of objective reality. 3 In The Implications of Immanence: Towards a New Concept of Life Leonard Lawlor's central hypothesis is that Husserl (and phenomenology more generally) 'does not think the abyss in between the senses; he thinks the space of sense (or the space of meaning), but not the space 1 Husserl, Edmund. The Crisis of European Science and Transcendental Phenomenology : an introduction to phenomenological philosophy, Evanston : Northwestern University Press, 1970, 138. 2 Carman, Taylor. 'The Body in Husserl and Merleau-Ponty,' Philosophical Topics, vol. 27, No. 2, Fall 1999, 205. http://ist-socrates.berkeley.edu/~hdreyfus/188_s05/pdf/Carman_Body.pdf 3 Carman,206. that we would have to call nonsense.' 4 According to Lawlor, because Husserl thinks the 'space of sense' and not the 'space of nonsense,' not 'the hollowed-out space in the middle of the knot of the double senses of Vorhandenheit,' 5 the ambiguity between the psychological sphere of experience and the transcendental sphere of experience, he claims that Husserl's project is epistemological rather than ontological. Lawlor argues phenomenological thought needs now to address this ontological aspect of experience.

Drawing from those two critical viewpoints on phenomenology, the pre-eminence of the body in Merleau-Ponty's philosophy (Carman) on the one hand, and the lack of ontological questioning in phenomenology in general (Lawlor) on the other, how can the representations of place, space, landscape and movement in Colum McCann's recent novel TransAtlantic (published in 2013) be read as an illustration of what Lawlor calls 'life-ism?' For Lawlor, 'life-ism' lies in the completion of immanence and is defined by a non-place, a 'hiatus'. To define this non-place, this 'hiatus' in which life-ism lies, he starts from what he defines as an 'imperative from Merleau-Ponty': we must obey this imperative if we want to conceive an archë, an origin or a principle, such as the principle of life.' 6 Lawlor defines the non-place of life-ism as 'neither positive nor negative, as neither infinite nor finite, as neither internal nor external, as neither objective nor subjective; it can be thought through neither idealism nor realism, through neither finalism (or teleology) nor mechanism, through neither dterminism nor indeterminism, through neither humanism nor naturalism, through neither metaphysics nor physics. 7 Lawlor further explains how, for Merleau-Ponty there must be no separation between the two 4 Lawlor, Leonard. The Implications of Immanence : Toward a New Concept of Life. New York : Fordham University Press, 2006, 12.

5 Lawlor, Leonard. The Implications of Immanence : Toward a New Concept of Life. New York : Fordham University Press, 2006, p.12. 6 Lawlor, 3. 7 Lawlor, 3. poles, nor no coincidence, thus excluding Platonism (separation) and Aristotelianism (coincidence). Merleau-Ponty's imperative, Lawlor argues is that 'instead of either a separation or a coincidence, there must be a 'hiatus,' un écart, which mixes the two together,' 8 and that this hiatus, death itself, 'defines life-ism.' 9

In the wake of Merleau-Ponty's insistence on the role of the body in the perception and definition of life-worlds, I will argue in this chapter that in TransAtlantic, the recurrent place described as 'the cottage on the lough' can be interpreted both as a variation of the 'space in-between' which haunts McCann's entire work, but also as the embodiment of the one period to the next, and from one space to another. In Let the Great World Spin he introduces the in-between space as the funambulist's journey across the twin towers of the World Trade Center which is also woven in between the chapters and puzzles the readers as much as the onlookers gazing up at the minuscule silhouette high up in the air. In 8 Lawlor, 3. 9 Lawlor, 3.

TransAtlantic, however, while representing great transatlantic distances and emigrant spaces between generations, the narrative also reveals a deep reflection on place. In representing an attachment to place and the influence of heritage and history on the lives and actions of generations, the narrative also sheds new light on our contemporary world. In particular, there is a clear focus on a specific place referred to in the narrative as 'the cottage on the lough,' situated on Strangford Lough, south of Belfast in Northern Ireland. It lies at the intersection between the spatial, the historical and the narrative lines of the novel. Through the use of language in his fiction, how does McCann manage to embody the minuscule hiatus which ignites creation and life? The cottage on the lough embodies the notions of circulation and transmission at play in the narrative. What is the nature of the space in-between which

McCann relentlessly describes throughout his work, and to what extent does it correspond to

Lawlor's definition of life-ism as immanence, as that ontological question which he deemed was lacking in classical phenomenology? The cottage on the lough will first be critically examined as a life-world in itself, in the sense of a place of strong anchorage and attachment.

The contradictions at stake in this life-world will also be delved into. In her introduction to Irish Literature in the Celtic Tiger Years 1990 to 2008 : Gender, Bodies, Memory, Susan Cahill argues that McCann 'foreground[s] the materiality of the body; [his] writing is material in its interests and concerns.' 10 Although I agree with this statement I wish to show that McCann's writing is not only material nor concerned with notions of redemption 11 , but profoundly hints at the ontological status and meaning of life. How does the cottage on the lough blend local and global scales of perception, rendering the representation of the cottage as a somewhat paradoxical place, at once to be inhabited and embodied; at once finite and infinite, to echoe Merleau-Ponty's phenomenological imperative? 12 The unceasing criss- 10 Cahill, Susan. Irish Literature in the Celtic Tiger Years 1990[START_REF] Desmond | Being Between: Conditions of Irish Thought[END_REF]: Gender, Bodies, Memory New York : Bloomsbury, 2013, p.6. 11 The first is the persistence of a chronological progression in Book II and III, even if chapters referring to periods in-between have been dealt with in Book I. The second is that the general movement is circular. The pattern is not that of the perfect circle or loop, beginning in 2012 and ending in 2011, but it nevertheless leads the reader to open the novel again once the first reading is over. He is in fact made to resume his reading and read again the 2012 prologue, since this second reading, after the first reading is completed, is the only way of actually making sense of the 2012-section, that is the opening of the novel. All along the narrative the same characters return front stage from time to time, so that the reader in fact comes across Lily Duggan's descendants, Emily and Lottie, before Lily Duggan is actually introduced to him.

I The Life-world of the 'Cottage on the Lough' Alongside the crisscrossing of characters and the historical leaps the reader is forced to make from one period to the next and geographically from one continent to the other, the cottage on the lough becomes a place of anchoring, both at the level of the storyline over the generations of Lily Duggan's descendants, and at the level of the narrative as it becomes a spatial reference point to the reader. But as an element of stability over time, the 'cottage on the lough' is also open to the chaotic influence of outside events.

In that respect, the cottage is an excellent example of a life-world as a place lived in and experienced by various people over a long period of time. As it survived financial crashes (1929, 2008), a world war (1939-45) as well as the Troubles (1968-1998), the cottage is presented as a key witness to all these life changes and to the continuity of the place as a unique lived-space. The cottage was gifted to Lily Duggan's granddaughter Lottie and her husband Ambrose Tuttle by his family as a wedding present on the eve of the 1929 crash, and was then passed on from generation to generation until 2011 and the post Celtic-Tiger financial crash. In 1929 the cottage was transmitted in a continuity to its initial vocation as a second home, a place to relax, live moments of happiness whether on one's own in communion with nature or in a group with other members of the extended family and friends.

Stangford Lough being situated between County Donegal in the Republic of Ireland, and County London/Derry in Northern Ireland. As such it occupies an 'in-between' water-space and natural border between two counties, two jurisdictions, and two states. Moreover, as a home and a kind of anchor on an island in the middle of Strangford Lough, it is a place of shelter from the agitation of the times and one to which people have been returning regularly.

It is sheltered and yet not immune to the invasion of the outside world (Thomas is murdered there during the Troubles and the recession threatens the cottage directly). It is the epitome of lived-space and yet it lies in a sort of non-place, in-between political, geographic and administrative borders. The reader experiences much the same thing, since, although the narrative of TransAtlantic is not chronological, the story takes place at the cottage on the lough in half the sequences, giving the reader the impression that he is very familiar with the place. And yet, skipping from one period to the other as the narrative does, the reader is given -Ah, he said. I've heard of it. The lake.

-Indeed. The lough. You should come visit, Senator. You'd be most welcome.

We've a small cottage on the water. 13 Etymologically, the word 'peninsula' comes from a Greek word meaning 'almost an island'.

Lottie Tuttle therefore insists on the fact that the cottage is on the lough, off Strangford, itself not quite separated from the mainland, but nonetheless not quite like the mainland. She also insists on its being Irish (a lough and not a lake) as well as on its intimacy with the water ('on the water.' 14 ) The intimate nature of the place itself is underlined by the adjective 'small.' Therefore, just as it is embedded in the narrative while at the same time framing it, the cottage is a life-world of its own, both open and secluded, as Lottie's warm invitation to Senator Mitchell ('You'd be most welcome') illustrates. It is also wrought by various inner and exterior tensions and therefore corresponds perfectly to the phenomenological definition of a life-world as a place characterized by living habits, emotions, sounds and smells. It is a lived place in which sensorial perception is paramount, as the routines and rituals of seasons follow one another, waves lap up against the shore and the seagulls drop oyster shells on the roof.

Both the continuity and slight changes in the landscape from sequence to sequence, as the generations succeed one another, inscribe the world of the cottage on the lough in the long 13 McCann, Colum. TransAtlantic. New York City : Vintage, 2013, 120. 14 My emphasis term of life. Just as its thatched roof of 1929 is later replaced by slates, the same blue halfdoor welcomes visitors and the tidal lough gives the pace and beat of the place:

The lake was tidal. It seemed to stretch forever to the east, rising and falling like a breathing thing. A pair of geese went across the sky, their long necks craned. They soared in over the cottage and away. They looked as if they were pulling the colour out of the sky. The movement of clouds shaped out the wind. The waves came in and applauded against the shore. The languid kelp rose and fell with the swells. (McCann 2013, 220) In the same way as the cottage was transmitted as a family inheritance across the generations, this description, and in particular the reference to the birds, links it to other parts of the novel.

The geese across the sky are historically associated with ancient Irish heritage and mythology, the 'wild geese' of the Gaelic Ulster lords of the early modern period, and with a painting given by Jon Ehrlich to Lily Duggan during their lives as husband and wife in Missouri at the end of the nineteenth century. The long necks of the geese, described as 'craned', also link this text to McCann's other novels in which cranes are a recurrent motif, whether as animals or as engines 15 . The cottage on the lough is undoubtedly at the intersection of exchanges, meetings and reunions on different scales. It is a place where generations meet, but also where local and global issues converge sometimes in a conflicting way.

The cottage as a life-world is comprises of a complex network of tensions and contradictions. Geographically speaking, it is on an island cut off from the mainland on a lough itself separated from the sea only by a small arm of water. It is therefore neither 15 enclosed, nor open. It is a place where the dramas of family life (weddings, births, separations, deaths) have been played out over generations against a backdrop of historical events: the 1929 crash, WWII, the Troubles, the post Celtic-Tiger recession. At all times, the cottage has been a refuge but not a place unscathed by global events. Lottie's grandson was killed on the lough during the Troubles only yards away from the cottage. After 2008, Hannah is ruined and many want to buy the land to develop it. All those tensions portray the cottage by the lough not only as a stable, sheltering place but also as a space of becoming undergoing changes over time, adapting itself to history. In his book Being Alive: Essays on Movement, Knowledge and Description, Tim Ingold defines place as cut-through of myriads of stories in a way which befits the cottage on the lough particularly well:

[space is] a world of incessant movement and becoming, one that is never complete but continually under construction, woven from the countless lifelines of its manifold human and non-human constituents as they thread their ways through the tangle of relationships in which they are comprehensively enmeshed. 16 In other words, space is not a flat, abstract, two-dimensional surface deprived of temporality, nor is it a lived-in enclosed portion of abstract space. In place, time and space are intimately connected. This notion of place as a meshwork is also echoed in the works of geographer Doreen Massey 17 . Like Ingold, she criticizes a certain conception of Kantian? space seen 'as a static slice through time, as representation, as a closed system and so forth.' 18 Analyzing the static conception of space as a way of 'taming' and controlling space, she emphasizes what she calls its 'real import':

The coeval multiplicity of other trajectories and the necessary outward-lookingness of a spatialised subjectivity […]. If time is to be open to a future of the new then space 16 Ingold, Tim. Being Alive: Essays on Movement, Knowledge and Description. London: Routledge, 2012, 142. 17 Massey, Doreen. 'interview'. http://www.socialsciencespace.com/2013/02/podcastdoreen-massey-on-space/ http://www.socialsciencespace.com/wp-content/uploads/DoreenMassey.pdf (last consulted on Dec 18th 2014). 18 Massey Doreen. For Space. London : Routledge, 2005, 59. The painting opposes Ehrlich's representation of a 'typical' Irish landscape to Lily's experience of Ireland and her subjective perception of a lived place. On receiving the painting, she is asked to greet it as reliable memory of the landscape of her native country. But her comments betray memories of lived space, a subjectively perceived experience of a place 19 Massey Doreen (2005), 59.

impossible to tell about, and differing entirely from what the painting conventionally portrays.

When she eventually tells her own story of Ireland, it has nothing to do with the picture of a cottage and a bridge over a river, but it is the story of her relationships with the people she lived with. The place she remembers then is defined by those relationships and just as she remembers her parents as drunkards, it seems to her the whole place drank: She had been a child of deviants in Dublin, she said. Drunkards. She had never told a soul before. She had tried to forget it. She expected no judgment and wanted no pity.

Her father drank. Her mother drank. Sometimes it seemed that the rats drank, the doors drank, the lintels drank, the roof drank, too. […] No part of Ireland had ever vaguely resembled the canvas Jo Ehrlich had brought home. (McCann 2013, 172) However the description made by the narrator of the painting is crucial at another level because it links the conventional representation of Lily's Ireland to her granddaughter's future cottage by the lough. The same words 'geese gunnelling through the sky' are used to describe the cottage in the painting as well as, later, Lottie and Hannah's cottage on the lough: 'a flock of brent geese came gunneling over the lough, bringing with them their own mystery, low over the water.' (McCann 2013, 249) The archetypal Irish cottage landscape and the flying geese symbolically link all the female characters in the novel to Ireland, and more specifically Lily Duggan to Hannah and to the cottage on the lough Lily never got to know. It endows the cottage as a life-world, with the silent, subtle and symbolic heritage of an imposed vision of a framed Irish landscape, as well as with her own history in a poor family. By contrast the cottage on the lough appears as a life-world coming alive through relationships and movement, and becoming the meeting point of lifelines over the years. In the same vein, the letter which circulates from one end of the novel to the other emphasizes the role of the cottage as part of the 'meshwork' described by Massey?

As Hannah, Lottie's daughter, begins Book 3 as a narrator, the family saga nears its end. Hannah relates the fate of the cottage on the lough in those post Celtic Tiger years as she faces the dilemma of having to sell up the cottage. She tells how the cottage was saved both because she was open to the future and able to imagine a new life for it, and able to turn towards strangers outside the family. She also tells how this rescue was already inscribed in the past and in the history of the family. Hannah's story is a story interlacing the past and the future, the intimacy of a family and the openness to other stories and histories. Manyaki, the Kenyan academic who eventually buys and saves the cottage with his Irish wife Aoibheann, offering to Hannah to go on living on the premices, had become intimate with the cottage because of a letter which had been circulating in the Ehrlich family ever since Emily and Lottie witnessed the first transatlantic flight in 1919. At the time, the young Lottie had given the letter to one of the aviators to be delivered to a lady who had helped her grandmother Lily Duggan emigrate to America during the Famine. But the letter was never delivered, and Lottie comes in possession of the letter again, the same day as she meets her future husband with whom she will later inherit the cottage. The letter is then still unopened but very intimately linked to the cottage both at the level of the storyline and at the level of the narrative. Just as the cottage on the lough, passed on from generation to generation down to Hannah, The letter has been passed from daughter to daughter, and through a succession of lives. I am almost half the letter's age, and have no daughter to whom I can pass it along, and there are times I admit that I have sat at the kitchen table, looking out over the lough, and have rubbed the edges of the envelope and held it in the palm of my hand to try to divine what the contents might be, but, just as we are knotted by wars, so mystery holds us together. (McCann 2013, 248) The letter therefore links the cottage to the rest of the story in more than one sense. Sitting in the kitchen of the cottage, rubbing the edges of the envelope trying to guess what its contents are, Hannah decides to find an expert, in the hope that the letter is worth enough money to save the cottage from being sold. Just as the former black slave Frederick Douglass had opened a window into Lily Duggan's future, Manyaki the Kenyan thus brings about the possibility of a future for Lily Duggan's descendant and her cottage. The shape of the narrative and the motif of circulation and transmission from daughter to daughter, as well as the echoes between the two black men Frederick Douglass and the Kenyan academic Manyaki underline the status of the cottage on the lough as a place where lifelines and storylines meet, blend and then go on their independent ways. Much in the same way as the limits of the novel itself have spilled over the official frame of the narrative, the opening 2012-prologue being literally outside the page count, the cottage is a life-world able to expand with time, as it links generations and stretches towards others outside the first/initial circle of the family. Thus doing, it pinpoints the pre-eminence of movement as a key element to read The absence of the funambulist as in Let The Great World Spin, but also the illusion that the tennis ball is for one minuscule instant suspended in mid-air before starting on the second half 21 Ingold, Tim. (2012) of its journey, could be likened to the 'blind spot' that Lawlor identifies as the 'minuscule hiatus' in his book The Implications of Immanence: Toward a New Concept of Life. The 'minuscule hiatus' is what separates the present and signals the irreducible presence of death at the heart of life, the invincible zone of tension between opposites, the visible and the invisible, words and things. According to Lawlor, the minuscule hiatus identified as death itself and which takes the form of a 'spacing' (espacement) in texts by Derrida, is precisely what defines 'life-ism'. It implies an 'out of place-ness,' a 're-placing which is a mis-placing.' To Lawlor, this 'mis-placing' is life: 'and insofar as life is always mis-placed, it goes over the limit and includes death -or memory'. 24 This conception of life defined by Lawlor, drawing from a fresh reading of Derrida, Merleau-Ponty and Deleuze, fits McCann's representation of the cottage on the lough in TransAtlantic. Situated on an island on a lough between the mainland and a peninsula, the cottage is on the water but not in the sea, in a closed lough but open onto the north Atlantic, linked to the past of a now ruined family. But above all it is presented as utterly open to the creative possibilities of the future. Its geography of dozens of small islands which look connected when seen from above, recalls Ingold's drawings of the wayfarer's knot. 25 Just as the line of the funambulist in Let the Great World Spin has become invisible in TransAtlantic, the cottage by the lough can in a way be read as an embodiment and a metaphor of the funambulist. As the meeting point of myriads of stories and trajectories, it has been entered, inhabited and left by generations of 'wayfarers.' 26 Dense is the knot represented by the cottage by the lough, as inhabitants have met within its precincts and entwined their trails over decades and generations. Enriched with this dense meshing the cottage stands halfway between the land and the sea, the closed and the open, the intimate and the public, the finite and the infinite. It embodies the space in-between that so much fascinates McCann. Just like the funambulist, the cottage is not only the embodiment of the impetus and 24 Lawlor, 11. 25 Ingold, Tim. (2012),148. 26 Ingold, Tim. (2012),111. the step forward. In McCann's fiction, the cottage on the lough and the funambulist embody the space in-between that William Desmond questions for historical and geographical reasons, as the 'Irish condition' in his book Being Between: Conditions of the Irish Thought:

'By being thus outside in the between one becomes intimate to the irreducible intermediacy within oneself, within us all, and between us all, in the most intimate communications that bind us together and respect our singular solitudes.' 27 The in-between experience is the fate of any emigrant/migrant as well as of many people in a globalized/transnational world. As in Desmond's quote, the intermediacy inherent to the inbetween experience is the locus of creativity in our times and, as McCann claims, ought to be the pretext to stretch forward and engender more empathy between people and bring about more peaceful relationships at every level.

In TransAtlantic, Colum McCann's representations of space map out an ever-changing globalized world in which place is not any more defined by nostalgia or the weight of tradition.

Just as new places can be adopted by newcomers, old places can in turn welcome foreigners since at the end of TransAtlantic the cottage is bought and saved by a Kenyan academic married to an Irish woman. And yet this new definition of place does not sign the advent of placelessness or the absence of place attachment or any sense of belonging. As Ingold and Massey show, space and place exist through relationships and myriads of stories. Space is not an abstract, infinite mode of reference, nor is place strictly localized and an enclosed portion of space. Rather, places take shape at the crossroads of multiple lifelines. In drawing the attention of the reader towards embodied movement as the main architect of both space and place, Colum McCann, like the characters he depicts, appears as a contemporary of the times he lives in. In her book promoting the advent of a metascience of landscape entitled 'paysagétique,' French philosopher Catherine 27 Desmond, William. Being Between: Conditions of Irish Thought. Leabhar Breac, 2008, 13.

  'hiatus' described by Lawlor and represented in McCann's fiction as a tension between life and death and the urge to inhabit the present moment. McCann's fiction is known for the vast and ambitious representations of cosmopolitan space, depicting long-distance displacements across and, critically, beyond Europe over different chronological moments and historical periods. In all novels and short stories since 1998, McCann's characters have travelled long distances and often exiled themselves from their native homes to start new lives afresh in foreign lands. Whereas in Songdogs, Dancer or Zoli the main characters journeyed across Europe or even danced the world over, in This Side of Brightness and Let the Great World Spin the characters investigated the horizontal and vertical possibilities of New York city cosmopolitan space, both above and underground. In all of McCann's narratives, readers and characters alike leap from one narrative to another,

  crossing of lifelines and storylines, in McCann's writing echoes anthropologist Tim Ingold's conception of place as run through by incessant movement, hence assigning a fundamental role to movement in McCann's fiction. To what extent does the representation of the cottage on the lough as a life-world open up a new perspective on our contemporary world, transforming our relationship to time and place in a world governed by speed and global information? In TransAtlantic, McCann describes three historical journeys from America to Ireland: that of former slave Frederick Douglass in 1845 from Boston to Dublin; the air travel of aviators John Alcock and Arthur Brown on their first transatlantic flight from St John's Newfoundland to Galway in 1919; and finally the political passage of Senator George Mitchell one of the key architects of the 1998 Good Friday Agreement, who spent months commuting between Belfast and New York City where he lived during that time. For various reasons, those three dates (1845, 1919, 1998) are key moments in the history of Ireland and modern history, because all three journeys express a desire for peace: promoting emancipation from slavery in 1845, joining two worlds after World War I in 1919, and formalizing the Northern Ireland Peace Process in 1998. The singularity of McCann's narrative is that those three journeys are intermingled with the saga of one fictional family over five generations, starting with Lily Duggan who was a maid at Mr Webb's house when Frederick Douglass stayed there in Dublin in 1845. Very much influenced by his speeches on freedom and democracy, Lily emigrated to America that same year. The structure of the novel is therefore distinctive, all the more so as it induces a special mode of reading, which in turn informs the overall interpretation. The spatial construction of the narrative and the reading process the reader is embarked on when reading the novel mimic the journey back and forth across the Atlantic and the criss-crossing of lives and destinies. It is divided into three 'Books', where Books I and II are themselves divided into three distinct long chapters referred to by dates, Book III is entitled 'Garden of Remembrance' and only concerns/brings us up to 2011. As a historically-based novel, the chapters are not arranged in any strict chronological order, but start in 2012 and then continue in 1919 and 1845 before leaping to 1998, returning to 1979 and finally ending in 2011. Two major tendencies can be observed.

  a kaleidoscopic vision of the cottage, at once varied and constant, open and closed, completed and incomplete. The novel is framed overall by two contemporary sequences taking place in 2011 and 2012 at the cottage, emphasizing the function of the cottage as a fundamental place on a narrative as well as structural level. Handed down to Lottie and Ambrose Tuttle on their wedding day in 1929 in Book 2, the cottage logically stands as the point of reference in the subsequent chapters of Book 2 and is the object of Book 3. But the cottage is already described in the third sequence of Book 1 when Lottie Tuttle, then a very old woman, first meets Senator Mitchell on a tennis court where he relaxes during the 1998 Peace Talks. They introduce each other and the way Lottie insistes on the details of her address in Strangford Lough, are eloquent of how crucial the geographical nature of the place is: -I live out by the peninsula. Strangford.

  cannot be equated with the closures and horizontalities of representation. More generally, if time is to be open then space must be open too. Conceptualizing space as open, multiple and relational, unfinished and always becoming, is a prerequisite for history to be open and thus a prerequisite, too, for the possibility of politics. 19 McCann's representations of space in TransAtlantic brilliantly illustrate this conception of space as open, multiple and relational, unfinished and always becoming. To show this, we will focus on two precise examples: a painting and a letter. The cottage on the lough not only frames the novel structurally, weaving its presence along the decades in the life of the Tuttle family, it is also implicitly hinted at more subtly throughout the narrative. This silent presence contributes to the 'meshing' of the cottage on the lough as a life-world at deep narrative level. In the first sequence of Book 2, Lily Duggan is offered a painting by her husband Jon Ehrlich who bought it on one of his trips. This is the end of the 19 th century, the family lives in Missouri running an ice-making industry. The painting depicts a typically conventional landscape corresponding to the archetype of how Jon Ehrlich is supposed to have imagined Ireland: A riverside in Ireland. An arched bridge. A row of overhanging trees. A distant cottage. Lily did not know what to say. She reached out and touched the framed edge of the painting. Looking into it was like looking out another window. Clouds. Fast water. Geese gunneling through the sky. (McCann 2013, 171)

TransAtlantic

  and Colum McCann's work as a whole. Movement reshuffles the perception of what belonging to a place might mean. The cottage on the lough is not a life-world closed up upon itself within the confines of the peninsula and the mainland, but a place to which generations are attached differently. II Wayfaring and Journeying between Life-worlds The lifelines running through the cottage on the lough and all along the novel are intertwined with other lifelines and storylines over the Atlantic. As Ingold remarks 'The wayfarer is continually on the move. More strictly, he is movement' 20 and this conception of movement at the heart of place reconfigures the notion of inhabiting a place and belonging to it: I use the term wayfaring to describe the embodied experience of this perambulatory movement. It is as wayfarers, then, that human beings inhabit the earth. […] But by the same token, human existence is not fundamentally place-bound, as Christopher Tilley […] maintains, but place-binding. Where inhabitants meet, trails are entwined, as the life of each becomes bound up with the other. Every entwining is a knot, and the more that lifelines are entwined, the greater the density of the knot. 21 In McCann's fiction the wayfaring movement itself, whether along lifelines or storylines, is crucial and in TransAtlantic the cottage is conveyed a metaphorical function as embodiment. The wayfaring movement to, from and through the cottage is one form of movement coexisting in parallel with the transatlantic crossing in the novel. Movement is part of McCann's prose and of its rhythm. It creates in impulse and a singularity of pace in the very act of reading: at times, as in the quote above, or as in McCann's contemporary short story 'Aisling' 22 , it becomes breathtaking. The attention is drawn not so much to the aim of the journey, but to the present moment and the space in-between. The journeys across the Atlantic visually recall the funambulist Eric Petit's journey across the void between the two twin towers of the World Trade Centre in Let the Great World Spin. In TransAtlantic however, the rope has become invisible, but the funambulist remains and takes on various forms. As I have written elsewhere, the funambulist illustrates place as embodiment of the present moment and a search for balance. But in TransAtlantic the search for balance and the funambulist have become more abstract. The funambulist has vanished from the scene as a human body and there only remains the tension and the swerve from one end to the other.' 23

  Eóin Flannery. Colum McCann: The Aesthetics of redemption. Dublin: Irish Academic Press, 2013.

12

Lawlor, 3.

  , 148. 22 McCann, Colum. 'Aisling'. New Irish Short Stories. (ed.) Joseph O'Connor, London : faber, 2011, 182-186. 23 Mianowski, Marie. 'The poetics of the leap in Colum McCann's latest novel TransAtlantic (2013)' Etudes Britanniques Contemporaines. (2015) #47 ECB.

Ingold, Tim. Being Alive: Essays on Movement, Knowledge and Description. London: Routledge, 2012, 150.

Chomarat-Ruiz defends the notion that because early twenty-first century human beings are torn between what Augustin Berque called the media body (chora) and the animal body (topos), human beings have the ethical responsibility of being in-between ("d'être au milieu"): to be the living beings who will think and act depending on the relationships they have struck with their natural environment and their territory -in the legal and political sense of this originally natural gift -of being living beings of landscape.' 28 While the definition of landscape which gives Catherine Chomarat -Ruiz relies on man as a living being in the middle of a life-world and conscious of his ethical responsibility with regards to his fellow living beings and his environment, McCann's fiction captures the tension between opposites and paradoxes of man's position in the world. Through fiction and language McCann manages to embody the minuscule hiatus which ignites creation and life. The space in-between, which he relentlessly describes throughout his work, is not a place to inhabit, shut out from the world outside -it is a landscape to be co-built in relation with others. McCann's time is the time of imminence, a present moment already leaping forward into the future. At a round-table event 29 in Rennes in June 2014, to present his novel TransAtlantic McCann insisted that stories of peace should be told over and over again because peace was not an, easy thing to do. In McCann's fiction, spaces in-between are not empty voids. They are spaces in which perspectives are being constantly re-shuffled to become creative meeting places from self to self and teach us to swerve ahead towards the others and contribute to world peace: 'it is the job of literature to confront the terrible truths of what war has done and continues to do to us. It is also the job of literature to make sense of whatever small beauty we can rescue from the maelstrom.' 30


Nacer K M'sirdi
email: nacer.msirdi@lis-lab.fr

Mohamed Benabdellatif

Giuseppe Marco

Aziz Naamane

Dynamic Coupled Electrical and Thermal Model for PV-T Solar Energy Collectors

Keywords: T system modeling, analysis and optimization, Variable Structure Automatic System, PVT state space model, Maximum Lifespan Power Point, MLSPP

This paper proposes a nonlinear state space model of a hybrid Photo-Voltaic /Thermal (glazed and unglazed PV/T) system taking into account the coupling of the electrical and the hydraulic circuits. A real time behavioral model is presented as Variable Structure Automatic System (VSAS), for simulation analysis and PV/T design optimization. The proposed model is appropriate for prediction, monitoring, control and can be used for diagnosis and the system Remaining Useful Life span increase. The analysis of the energy balance of the PVT system in its environment, leads to propose a new Maximum Life Span Power Point (MLSPP) to be used instead of the simple MPP to increase the life cycle of the PVT system.

I. INTRODUCTION

The solar energies (Electrical and Thermal) are more and more used to exploit renewable energies. The hybrid photo voltaic and thermal (PV/T) systems are used in several applications like heating systems [START_REF] Garg | Transient simulation of conventional hybrid photovoltaic/thermal air heating collectors[END_REF], [START_REF] Tripanagnostopoulos | Hybridphotovoltaic thermal solar systems[END_REF], [START_REF] Tripanagnostopoulos | Hybrid PV/T System with Improved Air Heat Extraction Modification[END_REF], water heating [START_REF] Bergene | Model calculations on a flat-plate solar heat collector with integrated solar cells[END_REF], [START_REF] Garg | Photovoltaic-thermosyphon water heating system for residential application[END_REF] and the water pumping [START_REF] Huang | Performance evaluation of solar photovoltaic/thermal systems[END_REF], [START_REF] Orda | Low-tech solar thermal water pumps for use in developing countries[END_REF]. Integrated photo-voltaic and thermal systems have proved to have better performance and efficiency [START_REF] Tiwari | Performance evaluation of hybrid pv/thermal water/air heating system a parametric study[END_REF].

Several PVT structures have been considered and studied in literature [START_REF] Zondag | The yield of different combined pv-thermal collector designs[END_REF], [START_REF] Tina | Electrical and thermal model for pv module temperature evaluation[END_REF], [START_REF] Rosa-Clot | Tespi: thermal electric solar panel integration[END_REF]. Hybrid PVT panels combine several advantages:

• the covered surface allows more energy production (electrical and heat) compared to the classic PV panels • the PVT system ensures uniform architecture roof.

• possibility of reducing the cost of facilities [START_REF] Bhaskrab | Hybrid photovoltaic thermal system : A state-of the-art literature review[END_REF]. The hybrid photo-voltaic thermal energy collectors are, in general, constructed by placing photo-voltaic solar cells directly over an absorber plate with a fluid circulation as thermal collector or solar water heater.

The proposal of solutions by Hybrid Renewable Energy Systems (HyRES) namely solar collectors PVT systems is increasing and seems more promising as the proposed technologies are more and more efficient [START_REF] Bonsignore | Neuro-fuzzy fault detection method for photovoltaic systems[END_REF]. Intelligent EMS (Energy Management Systems) are then required for such systems to manage harnessed energy and then their behavior modeling becomes crucial [START_REF] Tiwari | Bhaskrab Hybrid Photovoltaic Thermal System : A State-of the-Art Literature Review[END_REF]. This clearly imposes the use of Information and Communication Technologies, by developing models, real time simulation, optimization, diagnosis,prediction and control [START_REF] Sirdi | The best mppt algorithms by vsas approach for renewable energy sources (res)[END_REF].

Many technological investigations reported in literature show that the efficiency increases with Hybrid systems [START_REF] Chow | Dynamic performance of hybrid photovoltaic thermal collector wall in hong kong[END_REF]. The electrical power output of the PV cell depends on its operating temperature. The temperature may be controlled by action on the thermal energy collector [START_REF] Garg | Transient simulation of conventional hybrid photovoltaic/thermal air heating collectors[END_REF].

A. Context and motivation

Despite the existence of numerous papers exploring PVT systems, only few of them are oriented for the design optimization taking into account all the transient behavior effects. The optimization must take into account, not only the efficiency but, also the lifespan for the economical purpose. They are focused on the experimental evaluation of the system performances and efficiency All the models, presented in literature, are interesting for some special purposes like evaluation of the efficiency of PVT types, or the structures, or the application performance. The models are often partial and extracted from data analysis and measurements to get efficiency representation and comparison.

None of the models is complete enough to give dynamic state space systems and transients behavior, for complete realistic dynamic simulation. The model required for real time simulation has to describe the complete non linear dynamics (including transient effects) [START_REF] Cristofari | Thermal behavior of a copolymer pvt solar system in low flow rate conditions[END_REF], [START_REF] Rosa-Clot | Tespi: thermal electric solar panel integration[END_REF]. It must allow real time feedback control with several objective functions, like power optimization with care to the process maintenance and Remaining Useful Life Time (RUL).

To obtain an accurate model of the PVT module and to study its real-time characteristic with the variation in temperature and irradiation, a dynamic model must be developed and analyzed. We propose a more detailed thermal model of PVT panels where we take into consideration the external heat sources, operating conditions, internal heat sources, and heat dissipation.

Our objective is that the model must allow to drive the system to an operational point (the Maximum Life Span Power Point: MLSPP) with maximum efficiency while keeping the process in healthy comfortable situation for the process.

B. Contribution

This work gives a complete PVT Non Linear model for glazed and unglazed PVT collectors, written in state space form, able to clarify the rationale behind the electricalhydraulic-thermal couplings. This, as the main objective of this paper, is useful for real time simulation, analysis, optimization, prediction and control.

The focus of this paper is to develop a nonlinear dynamic model which explicitly describes the PV, hydraulic, thermodynamic, electrical and thermal couplings in the system and gives realistic behavior and real time representation in control point of view.

The proposed model provides the system dynamic states evolution (for thermal, hydrodynamic and PV coupled effects) of the various system components and describes well the transient behavior to allow deep performance analysis (of thermal/electrical coupling) and robust control and diagnosis. It allows to understand and manage thermal and PV coupling. This allowed us to define an interesting operation point, the Maximum Life Span Power Point (MLSPP) which allows to increase the RUL (Remaining Useful Life) of the PVT system, by managing the PV cells heating and limiting the cells temperature to acceptable values regarding to their State of Health (SoH). The developed models for glazed and unglazed PVT are validated using actual data. They are then used for numerical prototyping and we have compared, in simulations, their efficiency and performance when varying the systems physical parameters.

II. BACKGROUND, ASSUMPTIONS AND FORMULATION

A. Background

In fact, the solar energy is converted into electrical as well as thermal energy from a PVT module. The thermal energy is transmitted through convection, conduction, and radiations, and this varies with the PVT design structure, the angle at which they are installed, speed of the wind, cooling technique, etc.

A PVT panel, from a thermal point of view, can be seen as a flat affected by several heat fluxes that affect its temperature. It receives solar irradiation, transfers one part to the circulating fluid and evacuates dissipated thermal power, to its environment. Thus, it is obvious that these changes will affect the output voltage and the Maximum Power supplied by the PV module.

Fact 1. As the temperature plays an important role in the PV behavior and degradation [START_REF] Nehme | Assessing the effect of temperature on degradation modes of pv panels[END_REF] it must be analyzed more deeply. Then it is necessary to develop a dynamic (time varying) model of PVT system avoiding use of rough fixed estimation of operation temperature and efficiency coefficients.

Developing a thermal model allows us to understand thermal behavior of the PV system and to use it with parsimony and increase its life time. A validation of such thermal model for a simple PV is given in [START_REF] Nehme | Assessing the effect of temperature on degradation modes of pv panels[END_REF].

All the literature models assume separability of thermal and photo-voltaic subsystems (thanks to the difference of their (rise) time constants). They give in general separate, partial effects modeling and analysis which are confirmed by experimental tests and / or evaluation of the efficiency (thermal or electric).

In the following section we summarize the considered heat transfer and conversion, then we will gather all the dynamics to propose a one dimension Nominal Dynamic Model. Doing this, we will avoid the use of roughly defined estimations and try to be as precise as possible without going trough excessive details. The used assumptions will be detailed in order to allow further extension of this model.

B. Operating Conditions and PVT

In what follows, we describe more or less the energy sources and the near environment effect on the panel temperatures considered in the literature PVT models. The hybrid PV/T system is, in general, composed by several layers (see figure II.1 for glazed PVT) on which we consider a node for temperature evaluation. The hybrid collector is composed by a transparent glass, a photo-voltaic module which converts radiation into electricity and a metal plate attached to the rear cells using a thin adhesive layer ' Tedlar ' for absorbing heat. A coil, fixed to the back of the plate allows the heat exchange with the coolant fluid. To reduce heat losses, one layer is used for insulation.

C. Some Modeling Assumptions

Assumptions

• The temperature is estimated in a point at the middle of the corresponding layer (node) and assumed to be homogeneous (the layer averaged temperature). The temperature gradient is not considered in the layers. T a is temperature of ambient air in o C , G the irradiation in W.m -2 and T c is estimated temperature of the cell in o C.

• The edges are well insulated; Thus the edge losses are negligible.

• The heat transfer coefficients depend on many parameters: The wind velocity, the air density, the panel tilt angle, humidity and the dimensions of the panel. Although these factors may substantially affect the loss coefficients, their effect on the resulting absolute cell temperature is assumed small. For simplicity, the loss coefficient is assumed constant, which neglects the effect of these factors, such as wind speed, humidity, and temperature.

• The heat conduction is neglected, in general, because the panel nearly presents no contact to solids. The heat convection occurs on the front, back, and edges panel surfaces. Let h ga be a heat transfer coefficient in W.m -2 K -1 . The heat convection losses, from the glass to ambient air, is Q hconv = h ga .A g .(T g -T a ). • The radiation occurs from the front and the back surfaces to ambient air. The thermal radiation flux is expressed, in average, by the following formula, where g is the glass emissivity, σ is the Stephan-Boltzmann constant 5.67.10 -8 W.m -2 .K -4 , and T g is the average Temperature of PV panel glass in K. The front surface emissivity is taken as 0.9 [START_REF] Armstrong | A thermal model for photovoltaic panels under varying atmospheric conditions[END_REF] the back surface emissivity is taken as 0.84 [START_REF] Jones | A thermal model for photovoltaic systems[END_REF]. Radiation from the glass to ambient air, is

Qrad = g .σ.A. T 4 a -T 4 g (1)
• The heat losses from the glass to ambient air, by convection Q hconv and radiation Q rad , are then cumulated:

Q Hloss = σ.ε g .(T g 4 -T a 4 ) + h ga .A g .(T g -T a ) • Q cg = h cg .A g .(T g -T c
) heat exchange from the glass to the PV cells. • h cp is the heat transfer factor from the cells to the plate.

h cg is the conduction thermal transfer coefficient from the glass to the cells.

Q cp = h cp .A p .(T c -T p )
heat exchange from the plate (temperature T p ) to the PV cells. h cp = λc ec conduction heat transfer coefficient between cells and the plate. h ca = 5.67 + 3.8v w conduction heat transfer coefficient between cells and the ambient air. Let m p , c p be the plate mass in kg and thermal specific heat respectively. The radiation coefficient from cells to glass cover is h rgc. . It can be considered as null if the cells are fixed on the glass.

• The thermal convection flux from the glass and from the back surface (insulation) to ambient air can be expressed by the following formula, where we note α g the absorption factor and h ia the coefficient of convection transfer from insolation layer to the ambient air.

Q gconv = h ga .A g .(T g -T a ) + h ia .A i .(T i -T a ) (2)
• Q ia describes the losses in contact of insulation to environment air.

Q ia = h ia .A i .(T i -T a ) (3)
• The power generated by the PV panel P elec depends on temperature and its operating voltage V and I the generated PV current. Several times, in literature, empirical formulas are considered to get an estimate of the cells temperature using the PV module temperature and some defined PVT operating temperature (as a reference value) [START_REF] Tripanagnostopoulos | Hybrid PV/T System with Improved Air Heat Extraction Modification[END_REF]. Definition 2. The NOCT is defined as the measured cell temperature for an ambient temperature of 20°C, an irradiation of 800W.m -2 and a wind speed of v w = 1m.s -1 . An empirical estimation of the cell temperature is

T c = T a + N OCT -20 800 × G (4)
Definition 3. The heat convection transfer coefficient (from the glass to ambient air) is correlated to the wind velocity (v w in m.s -1 ). The convection transfer to the ambient air h ia is very often estimated (using some approximation) by the following formula [START_REF] Mattei | Calculation of the polycrystalline {PV} module temperature using a simple method of energy balance[END_REF][22] h ia = h wind = 5.7 + 3.8 * v w .

Fact 4. The NOCT is only a roughly calculated estimation or approximation defined as a reference in laboratory evaluation tests. The PV module, in general, does not operate always under this (steady state) temperature value (NOCT) and under fixed temperature and irradiation.

This is because between sunrise and sunset, the ambient temperature T a and the solar irradiation G may vary over a wide range depending on the weather conditions. Although the cell temperature T c mainly depends on the ambient air temperature, the wind, and radiation. It is affected also by the near heat sources and transfer. All these variables and parameters have values that may vary over a wide range, depending on the atmospheric condition, geographic location, etc.

III. MODELS OF PVT SYSTEMS A. Inputs and Outputs of the PVT system

The system takes as input the Irradiance G, the ambient temperature T a , the relative humidity R H , and the cells operating voltage V P V . The operating conditions of the PV panel (operating voltage and temperature) directly affect the output generated power. Let us consider a glazed PVT system in the analysis.

Let us note the temperature of each layer at its node: T g is the glass temperature in K, T c the cell temperature, T p temperature of the plate and T f is the coolant fluid temperature (in K Kelvin). Let T i be the temperature insulation part. As output we can consider the cells and the fluids temperatures and may be some other one.

The incident irradiation is the main energy source (input) that contributes to heating the panel. The quantity Q abs = Qsun -Q loss is the incident solar energy wich can be absorbed. The energy source is assumed to be reduced by a factor, generally of 5%, the losses Q loss are mainly due to reflection by the glass (which receives Q glass = Q abs -Q Cabs ) and dissipation to ambient air. Note that A g is the total area of the panel in m 2 with α g (R H , G, T a ) 0.95 as absorption factor which may depend on G, T a , R H .

Q abs = Q sun -Q loss ( 5
)
Q abs = α 0 .α g (R H , G, T a ).A g .G (6)
The parameter 0 =< α 0 < 1 depends on the incident angle.

Q glass = Q abs -Q Cabs -Q glassoutput Q glass = m g .c g . dTg dt + Q cg + Q Hloss (7)
Because of temperature difference between panel and ambient air, heat dissipates from the panel glass to outside via convection, conduction and radiation (see figure II.1).

The cells layer recieves Q Cabs . At the cells layer the absorbed sun energy is received trough the glass (filtered) Q Cabs = τ g α c .A c .G, where τ g is the glass transmissivity factor. The recieved power is converted in a thermal storage part

Q T hermal = m c .c c dT C
dt which contributes to heating the cells layer and an electrical part Q Elect (electricity produced by the cells) with some losses noted Q Closs .

Q Cabs = Q Closs -Q glassoutput + Q T hermal + Q Elect (8)
The electricity produced by energy conversion Q Elect is made of two parts: -the joule dissipation in the cells resistances P j and -the produced electricalpower -P f . It is worthwhile to note that on the literature proposed models this part is neglected or not taken into account. In addition of this several assumptions are considered implicitly despite that they have consequences on the model precision and validity. We try to clarify this in the next section.

Q cp = Q p + Q pi + Q pf + Q glassoutput (9)
The plate receives

Q cp , consumes Q p = m p .c p dT C dt and transmit Q pi = h pi .A i .(T p -T i ) to insulation layer and Q pf = h pf .A f .(T p -T f ) to the coolant fluid.
Let h pf be the convection heat transfer from the plate to the fluid.

h pf = [(1/h p ) + (1/h f )] -1 with h f = N u.λeau Di and h p = λp ep
, where ν Nu is the Nussle number which is ν = 4.36 for a laminar flow, and l eau is the water thermal conductivity and D i the fluid pipe section diameter. l p and e p are the conductivity and thickness of the plate respectively. h pi is the conduction heat transfer factor from the plate to the insolation layer.

The joule heat generated by PV Cells is given by equation 10. The panel also heats due to internal Joule dissipation for the N cells of the panel (N = N s .N p is total cells number). One part of the incident solar energy is absorbed by the PV cells and transformed in electricalpower P plus a thermal dissipation (power losses P j ). Note that his power P is consumed outside the PV panel and that the power loss represents a heat sink P j to the thermal system.

P j = N R s I 2 + N (V + R s I) 2 R sh (10)
Pj = N Rs I ph -Is[e ( q(V +Rs.I) nkTc ) -1] - (V + RsI) R sh 2 + N (V + RsI) 2 R sh (11)
The internal heat sources of the panel is due to the Joule effect of the series and shunt resistors. In fact, current passing through the printed Ag fingers and through the Cu bus-bars will lead to a localized heat generation modeled by the series resistor R s . Besides, current passing through a path around the cell will lead to a localized heat generation modeled by the series resistor R sh . The power loss is dissipated by the cells resistors R s and R sh , of each cell. This will have influence on the cell layer temperature.

B. Thermal Model of the Glazed PVT collector

The thermal behavior may be described by the equations (5-9), gathering the fluxes imposed to the PVT system [START_REF] Bonsignore | Neuro-fuzzy fault detection method for photovoltaic systems[END_REF]. In what follows, use of averaged efficiency factor is avoided. Note that thermal and electrical efficiencies are defined only in a steady state operation mode (for averaged behavior) and not valid in the transient periods.

a) Glass Model: Let m g and c g be the glass mass in kg and thermal specific heat (thermal capacity in J.Kg -1 .K -1 ) respectively. The glass thermal behavior can be summarized by equation 12:

m g .c g . dT g dt + h cg .A g .(T g -T c ) + σ.ε g .(T g 4 -T a 4 ) (12) = -h ga .A g .(T g -T a ) + α g .A g .G -Q Cabs b)
PV Cells Thermal Model: The dynamic heat transfer in the cells is described by the following equation. The absorbed thermal energy in the cells layer is

Q P V cells = m c .c c . dT c dt = Q Cabs + Q cg + Q Elect -Q cp (13) Q Elect = P j -P (14) m.c c . dT c dt + h cg .A g .(T c -T g ) + h cp .A p .(T c -T p ) (15) = τ g α c .A c .G + Q Elect c) Plate thermal storage:
The plate is used to catch the heat flow coming from the PV cells and the sun trough the glass and transmit it to the fluid. The absorbing plate collects thermal energy dissipated by the sun and cells and transfers it to the coolant fluid. This leads to a decrease of the cells temperature and then increases the PV efficiency. Its dynamic equation Q P late = m p .c p . dTp dt can be written:

m p .C p .(dT p /dt) + h cp .A p .(T p -T c ) + h pi .A p .(T p -T i ) (16) = -h pf .A f .(T p -T f out ) d) Fluid Thermal Equation:
The fluid temperature behavior is governed by the following equation where the fluid output temperature T f out depends strongly on the plate temperature T p , the inlet fluid temperature T f in and the liquid flow ṁ. Where m f is the fluid mass (in the exchanger) and c f the specific heat of the coolant fluid. We have

Q pf = h pf .A f .(T p -T f ) and Q u = ṁ.c.(T f out -T f in ) . m f .C f . dT f dt + h pf .A f .(T f -T p ) = -ṁ.c.(T f -T f in ) (17)
e) Insulation layer Thermal Equation:

Q pi = h pi .A i .(T p -T i ), is the heat flow from the plate to the insolation with h pi = [(1/h p ) + (1/h i )] -1 Q Isto = m i .c i . dT i dt = Q pi -Q ia ( 18
)
m i .c i . dT i dt = h pi .A i .(T p -T i ) -h ia .A i .(T i -T a ) (19)
C. Thermal Model of the Unglazed PVT

In the case of an unglazed PVT panel, the first equation (Glass) is droped because there is no glass. The remaining equations are more or less the same mutadis mutandi.

mccc dTc dt = αcGAc + N RsI 2 + N (V +RsI)² R sh -N V I +hcpAc(Tc -Tp) -(hca -hcar)Ac(Tc -Tp) mpcp dTp dt = hcpAc(Tc -Tp) -h pf Ap(Tp -T f ) -h pi A i (Tp -T i ) m f c f dT f dt = h pf A f (Tp -T f ) -ṁf Ap(T f out -T f in ) m i c i dT i dt = h pi A i (Tp -T i ) -(h ia -h iar )A i (T i -Ta) (20)
Where h car = ε c σ(T c ² + T a ²)(T c + T a ) is the radiation heat loss coefficient. h pf = [ ec λc + Di NuKw ] -1 is the convective heat transfer coefficient between the plate and the fluid.

h ip = λi ei is the conduction heat transfer coefficient between cells and the plate and h pi = [ ec λc + ei λi ] -1 is the heat transfer coefficient between thermal plate and insulation.

D. Controlled part and State Space variables 1) Pump Control:

The fluid flow is given by a pump controlled by a voltage input u p . The liquid flowing in the PVT collector circulates with the flow rate ṁ which is in general controlled by a pump driven by an electrical motor which can be represented by the following equations where the pump rotation velocity is noted Ω. In general we can assume that the flow is proportional to the rotation velocity of the pump ṁ = kΩ. Then we get the mechanical equation of the pump rotation and its driving motor

J dΩ dt + f Ω = C em -C r (21)
The pump mechanical load imposed to the motor is considered to be proportional to the squarred velocity C r = k r Ω² then we get the state equation governing the flow rate as follows, where the current i pump is an input used to control the flow rate.

J m + (f + k r ṁ) ṁ = K pump u p (22) m = - (f + k r ṁ) J ṁ + K pump J .u p (23)
2) The electrical power: The serial resistance R S relative to one cell in open circuit voltage V OC is:

R S = dV dI V OC = nkT 1,ref q /   I 0 (T 1,ref )e V OC (T 1,ref ) nkT 1,ref q   (24)
The shunt resistance is considered inversely proportional to the absorbed solar radiation,

R sh = R shref G ref G ( 25
)
The Current generated by one PV cell is

I = I ph -I s .[e ( q(V +Rs.I) nkTc ) -1] - (V + R s .I) R sh (26)
The photo-current I ph and the reverse saturation diode current I s depends on the cell junction temperature T c [Ref 10],

I s = I s ref .( T c
T ref ) 3 .e (q.Eg.

(( 1 T ref )-( 1 Tc )) (n.k) ) (27)
I ph = [I ph ref -C i .(T c -T ref )]. G G ref ) (28)
Equation ( 28) shows that the electrical efficiency of the system decreases when the temperature of the junction of the cells increases. C i is a positive coefficient and T ref the reference temperature defined as 25°C in general. The circulation of the coolant in the PVT panel lowers the cells temperature and thus it improves the electrical performance of the PV system.

The produced electrical power model P elec = I.V is given by its time variation (V come from the N cells of the panel):

dP elec dt = I. dV dt + V. dI dt = I.u 1 + V.u 2 (29)
dP elec dt = I ph -I s [e ( q(V +Rs.I) nkTc ) -1] - (V + R s I) R sh u 1 +V u 2
(30) To reach the operating point (V optim , I optim ) giving the Maximum Power (MPP), we can use the control imputs u 1 or u 2 , or both alternatively. See for details [START_REF] Sirdi | The best mppt algorithms by vsas approach for renewable energy sources (res)[END_REF], [START_REF] Msirdi | The vsas approach gives the best mppt for solar energy sources (res)[END_REF]. In a first case, the current may be fixed constant and set u 2 = 0. The control will be u

1 (k) = f ( V (k))
The PV output current I goes through a boost converter to control the input voltage V. The current i L flowing from the boost converter output, in the load assumed to be Z L is .

V = Z L i L (31)
If the load Z L is an R -L equivalent circuit, for the sake of simplicity, we can write Ri L +L di L dt = v o and then we get an equation defining a new additional state variable, which can be considered in the system model.

di L dt + R L i L = V L (32)
E. System State Space Representations 1) Glazed PVT Model: Let us consider the state vector defined as

X = [T g , T c , T p , T f , T i , m, P elec , i L ] T and the input control vector U = [u p , u 1 , u 2 ] T
To get a state space representation of the process,

Ẋ = f (X, T a , G, R H ) + g(u p , u 1 , u 2 ) y = h(X) (33)
we gather the equations ( 12),( 15), ( 16), ( 17), ( 19), ( 22), (30) and (32).

2) Unglazed PVT Model: In the case of an unglazed PVT panel the state vector will be

X u = [T c , T p , T f , T i , m, P elec , i L ] T the same and the input control vector U = [u p , u 1 , u 2 ] T .
The model gathers the equations ( 20),( 22), ( 30) and (32).

IV. PV/T PERFORMANCE EVALUATION A. Unglazed PVT Model Validation

For validation of our models, we consider the unglazed PV/T Wave proposed by DualSun. This hybrid panel is unglazed and it has an area of 1.604 m². The mono-crystalline cells encapsulated in EVA (Ethylene -Vinyl -Acetate) and TPT (Tedlar -polyester -Tedlar). This encapsulation ensures protection for cells and electrical insulation with other constituent. The thermal plate made of aluminum is totally covered by cells and so the excess of heat generated by cells is the input of the thermal part. The cells are integrated with the thermal part by pasting it on the absorber plate. The fluid ducts are welded in the back surface of plate and arranged with equal spacing between the tubes. Insulation is used to limit the back thermal losses. The electrical data of the solar cells under standard test conditions (STC) are given in the following table (IV-A). The simulation results, using the proposed model, show very good agreement with the experimental results given by TUV Rheinland Lab as shown in the figure (IV-A).

B. Performance Evaluation

The main interest of this study is to find a good combination of materials that ensures the optimal performances and reduces the price of the actual device. Simulation tests were carried out to compare the thermal behavior of PV/T using different materials for the absorber plate, cells type and with or without a glass under the steady state conditions of G=1000W/m², Ta=25°C, and a flow rate equal to 0.05Kg/s. Varying the parameters is done, in simulations, to obtain an optimal design for the system.

Many studies in the literature led to consider that polymer is one of the most promising material used to reduce the cost and the weight of the device. We tested at first, under the steady state conditions, the PVT panel with additional glass cover and compare it performances to the Unglazed PVT wave. The electrical efficiency of the PV/T cells (see figure IV-B) may be calculated by:

η el = V I A c G (34)
The thermal efficiency (compared for glazed and unglazed PVT in figure IV-B) is defined as the ratio of the thermal yield and the total incident energy: The glazed PVT presents a remarkably higher thermal efficiency, thus due to the presence of glass layer that limits the convective losses (see figure IV-B). But the electrical efficiency deteriorates due to the higher operating cells temperature and to the additional optic losses. This is also may accelerae the cells aging.

η th = ṁc f (T f out -T f in ) A p G (35)
A second test was carried out under the steady state conditions to compare performances of unglazed PVT Dualsun using other materials for the thermal plate :(1) Copper, and (2) Polymer. (in the actual design Aluminum was used).

As it can be shown in the figure (IV-B) and (IV-B), materials with higher thermal conductivity (in this case copper and aluminum) can transfer heat easily from the cells to the fluid as a result the thermal efficiency is remarkably higher. Also the cells operating temperature is nearly 4 degrees higher in the case of polymer PPO, and this leads to have the electrical efficiency is slightly lower than copper and aluminum PVT.

A third test was carried out to study the cells type effect on system performances. For the actual Dualsun Panel, single crystalline cells are used with η o slightly higher than 15% but they are more sensible to operating temperature. A simulation As shown in figures IV-B, IV-B and IV-B, the efficiency of the amorphous cells is less sensible to temperature. Their electrical efficiency lower than the silicon cells, meaning less amount of absorbed energy is converted to electricity and so more available energy for heat production . As result thermal efficiency for thin film cells in three cases is higher It's possible also to notice that in three cases the electrical efficiency for a chosen type of cells is practically the same. The thermal efficiency is slightly lower for the PPO. Semitransparent Thin film cells can be used in order to improve the global efficiency of the system. Extra solar radiation with With the semi-transparent cells, the plate temperature is higher resulting from the extra absorbed infrared radiations. Since they are pasted directly on the plate, the cells have a higher temperature than the classic cells and slightly lower electrical efficiency fig. 13. The global efficiency of the PV/T using semi-transparent is higher than the PVT with classic cells.

C. Maximum Life Span Power Point

Let us consider again the figure (IV-C) comparing the cells temperature variation for PVTs with different materials. We then remark that near the Maximum Power Point (in brown) there is a minimum of the temperature. At this point the power produced is reduced by 5% to 10% which is not to penalizing. The cells temperature may decrease from some degrees (depending on the PV nature and fluid circulation) and this may be more comfortable situation for the cells operation. We have then defined this as the Maximum Life Span Power Point (MLSPP) to increase the PVT life time, by limiting cells heating regarding to their State of Health (SoH). The Maximum Life Span Power Point (MLSPP) allows to drive the system to an operational point with maximum efficiency while keeping the process in healthy comfortable situation. Doing this reduces the produced power of around 10% only. Anyway this feature can be interestingly used in advanced system control.

V. CONCLUSION

We have developed PVT models, in glazed and unglazed cases, for numerical systems prototyping, analysis and control. With those models, it was possible to study the effect of different key parameters on the system performance; with or without glass cover, cells type, and material used for thermal plate. The design and the structure of the PVT device depends mainly on the application for which it is intended: hot water is more important or electricity.

From the simulation results, it's possible to conclude that Polymer was as much efficient as aluminum and copper. It may be a good substitute for aluminum in the actual commercialized PVT: Reduces the weight of the device, and reduces manufacturing cost. Also, it's more suitable to keep using mono-crystalline cells for their low operating temperature.

The state space formulation of these models opens interesting perspectives for advanced non linear control and energy management. We have then defined this as the MLSPP which allows to increase the PVT life time, by limiting cells heating to acceptable values regarding to their State of Health (SoH).

Fig. II. 1 .

 1 Fig. II.1. The general structure of a glazed PV/T collector

  numerical model of the unglazed PVT was validated based on the Data -sheet of Dualsun [DualSun] (see figure IV-A). It presents a steady state indoor experimental results done by TUV Rheinland Lab-Germany under conditions prescribed by EN12975 standards: G = 850W/m 2 , v w = and T f in varying from 20 • C to 55 • C. Let us note T red = T f out /G.

Fig. IV. 1 .

 1 Fig. IV.1. Thermal efficiency for steady state conditions T red = T f out /G

Fig. IV. 2 .

 2 Fig. IV.2. Thermal efficiency for glazed and unglazed PV/T.

Fig. IV. 3 .

 3 Fig. IV.3. Thermal efficiency for different materials.

Fig. IV. 4 .

 4 Fig. IV.4. Electrical efficiency for different materials.

  test was carried out to compare the different kind of thermal plates seen previously combined with both single crystalline cells and thin film cells (see figures IV-B, IV-B and IV-B).

Fig. IV. 5 .

 5 Fig. IV.5. Electrical and thermal efficiency for Aluminum plate.

Fig. IV. 6 .

 6 Fig. IV.6. Electrical and thermal efficiency for Polymer plate

Fig. IV. 7 .

 7 Fig. IV.7. Electrical and thermal efficiency for copper plate.

Fig. IV. 8 .

 8 Fig. IV.8. Thermal efficiency for semitransparent cells against classic cells.

Fig. IV. 9 .

 9 Fig. IV.9. Electrical efficiency for transparent cells against classic cells.

Fig. IV. 10 .

 10 Fig. IV.10. Global efficiency for semitransparent cells.

Fig

  Fig. IV.11. Cells temperature for different materials.