Vanessa Rakotoson
email: vanessa.rakotoson@univ-reunion.fr

Jean Philippe Praene

A life cycle assessment approach to the electricity generation of French overseas territories

Keywords: Electricity generation, Greenhouse gas emission, Life Cycle Assessment, French overseas territories

Due to the high reliance on fossil fuels in the electricity production and transport sectors, completing the energy transition holds a particular importance for non-interconnected territories. The environmental impacts from electricity generation are mainly imputed to fossil fuel based technologies, for instance in the case of French insular territories. This paper summarizes the present electricity situation in these territories and aims to determine their different emissions and environmental impacts through a life cycle assessment (LCA) approach. To deliver 1 kWh of electricity to the power grid from the studied regions, the electricity mix is defined as the functional unit. The results refer to a life cycle cradle-to-gate electricity production model. The impact categories discussed in this paper are related to global warming potential, acidification potential, tropospheric ozone precursor potential, and the cumulative energy used. Due to its high share of renewable energies sources, French Guyana has the lowest greenhouse gases (GHG) emissions per kilowatt-hour produced compared to the other islands (373 g CO2-eq/kWh, 4.29 g SO2-eq/kWh and 2.65 g NMVOC-eq/kWh). Combined with other social, economic and environmental parameters, these results will be also used to determine the typologies of islands in order to define a common energy strategy for each group.

Introduction

Electricity production in France shows variation: in 2013, the mainland electricity mix was dominated by 74% nuclear and 13% hydroelectric, while French overseas departments and territories have an average coal and oil contribution of 73% [START_REF] Soes | Key energy data in France -Edition 2014[END_REF]. This high share of fossil fuels in the energy mixes of these territories can be explained by the general disadvantages that insular areas face in relation to their remoteness and size [START_REF] Erdinc | Overview of insular power systems under increasing penetration of renewable energy sources: Opportunities and challenges[END_REF]. In order to overcome the environmental challenges in the current French energy transition policy, it is important to have an accurate overview of the existing production. This study seeks to analyze the individual electricity generation influence and the GHG emissions of each French department studied to define the path to Preprint submitted to Journal of Cleaner Production November 30, 2017

achieving a low environmental impact in future electricity demand. Section 2 presents the electricity mix for each of the studied territories. Section 3 provides an overview the LCA method and the hypothesis tested. The results of the evaluation of emissions by energy source, energy mix and infrastructure are presented and discussed in Section 4. A classification of the studied territory using socio-economic and environmental criteria is presented in the last section.

Overview of the electricity sector

In a previous study, Notton provided the geographical locations of power installations in French territories and the average annual generation in 2012 [START_REF] Notton | Importance of islands in renewable energy production and storage: The situation of the French islands[END_REF]. This paper focuses primarily on the following territories for the base year of 2013: Corsica, Guadeloupe, Martinique, Mayotte, French Guyana and Reunion Island. Remoteness implies an increase in the average supply distance of petroleum products. Fuel transportation is a major driving force for CO2 emissions in the global LCA evaluation. As can be seen in Fig. 1 and Table 1, only Corsica benefits from the network interconnection with Sardinia, which plays an important role in the supply/demand balance, particularly during high consumption periods. Martinique and Mayotte represent the French overseas territories (FOTs) that are the least developed in terms of renewable energy sources (RES) in the electricity mix, with 95% of fossil-fuel and 5% of RES. The difference between the two situations lies in the contribution of wind energy and biogas production in Martinique. Recognizing their high potential for RES, Guadeloupe and Reunion diversified their mixes by integrating hydropower, solar energy, geothermal energy, biogas and bagasse [START_REF] Praene | Renewable energy: Progressing towards a net zero energy island, the case of Reunion Island[END_REF][START_REF] Ademe | Emission factor documentation of the Base Carbone R -Version 11[END_REF]. However, the RES component of Guadeloupe's generation is half that of Reunion's. French Guyana is the only territory that has used 63% RES for its electricity production, mainly using hydroprower. Data in Table 1 will be used for the electricity generation GHG emissions assessment.

Materials and methods

To date, a significant number of LCA analyses examining electricity generation technologies (EGTs) at different levels are available in the literature. [START_REF] Asdrubali | Life cycle assessment of electricity production from renewable energies: Review and results harmonization[END_REF], [START_REF] Turconi | Life cycle assessment (LCA) of electricity generation technologies: Overview, comparability and limitations[END_REF] and [START_REF] Jacobson | Review of solutions to global warming, air pollution, and energy security[END_REF] proposed an overview and a harmonization of LCA results from EGTs in order to provide a range of values of GHG emissions for each technology. Studies provide range of values of GHG emission for different technology : [START_REF] Asdrubali | Life cycle assessment of electricity production from renewable energies: Review and results harmonization[END_REF] gives an overview of LCA results of renewable technologies (RETs), [START_REF] Turconi | Life cycle assessment (LCA) of electricity generation technologies: Overview, comparability and limitations[END_REF] focused on 167 studies to provide a basis for making choices on technology and methodology approach. A comparison of the environmental impacts of fossil fuel-based technologies (FFTs) are presented by [START_REF] Atilgan | Life cycle environmental impacts of electricity from fossil fuels in Turkey[END_REF] in Turkey and [START_REF] Tan | LCI (Life cycle inventory) analysis of fuels and electricity generation in Singapore[END_REF] in Singapore. [START_REF] Ramjeawon | Life cycle assessment of electricity generation from bagasse in Mauritius[END_REF] presents LCA results of electricity from bagasse in Mauritius, and [START_REF] Silva | LCA Application : The Case of the Sugar Cane Bagasse Electricity Generation in Brazil[END_REF] in Brazil.Comparisons between FFTs and RETs performed by [START_REF] Hondo | Life cycle GHG emission analysis of power generation systems: Japanese case[END_REF] in Japan or [START_REF] Smith | Comparative Life Cycle Assessment of a Thai Island's diesel/PV/wind hybrid microgrid[END_REF] in Singapore, can help select the most appropriate technologies for an electricity generation system.Papers also provide LCA results by country, as Mexico [START_REF] Santoyo-Castelazo | Life cycle assessment of electricity generation in Mexico[END_REF], Portugal [START_REF] Garcia | Life-cycle assessment of electricity in Portugal[END_REF] or

Greece [START_REF] Theodosiou | Environmental impacts of the Greek electricity generation sector[END_REF]. [START_REF] Herbert | A typology for world electricity mix: Application for inventories in Consequential LCA (CLCA)[END_REF] developed a series of GHG emissions assessments for selected countries, from which four types of countries were identified. However, few papers concern islands [START_REF] Brizmohun | Life cycle assessment of electricity generation in Mauritius[END_REF]. This study will provide an initial evaluation of the environmental burdens of electricity generation in these , 2015). However, the assessment methodology and the assumptions used are not explicitly mentioned.

Scope and system boundary

In this study, LCA is used to identify the environmental burdens and impacts throughout the electricity generation process. The LCA methodology applied here is regulated by ISO standards 14040 and 14044 (International

55
Standards Organisation, 2006a,b). The study boundaries are from cradle-to-gate, including acquisition, transportation, infrastructure construction and electricity production. Transportation concerns the port-to-port carriage of direct-use energy. Fig. 2 represents the boundaries considered in energy production. The functional unit (FU) is defined by 1 kilowatt-hour produced; in the rest of the document, we will denote an FU as 1 kWhe.

Figure 2: Cradle-to-gate life cycle stages of the electricity production system (modified from [START_REF] Gujba | Environmental and economic appraisal of power generation capacity expansion plan in Nigeria[END_REF] and [START_REF] Brizmohun | Life cycle assessment of electricity generation in Mauritius[END_REF])

Life-cycle inventories and modeling

To identify the potential impacts, standard LCA software GEMIS version 4.9 and its database have been used

and adapted here (Öko-Institut, 2015). Due to the lack of information about the efficiency of each power plant, the GEMIS database has been used. However, parameters such as transportation, scale, power generated have been adapted to the islands' conditions as a lack of information on islands' technologies has been identified as a limitation of the software. The proposed tool has been implemented in a MATLAB environment in order to link the LCA results from GEMIS software to an another energy scenario tool in a unique environment. Results can be treated as a method to highlight the most emissive life-cycle stage and also can be used as constraints in future scenario modeling research.

The MATLAB code was developed in two parts. First, GEMIS provides the data emissions of each electricity generation, through its life cycle: raw materials extraction and its necessary quantities to produce 1 kWh electricity, the existing means of transport, the infrastructure construction and the production. These data are then manipulated in MATLAB. Second, in line with the LCA methodology, several inputs are required: the total electricity production, the installed capacity, the distance of the raw material supply, and the mean of transport used. These data help to determine the quantity of the raw materials, the adapted emission factor (EF) related to the size of the installed power plant, and indicates the remoteness of the territory. The total emission ET ot of the electricity mix of the studied territory is obtained by Eq.1

ET ot = n i=1 Eext,i + Etrans,i + Econs,i + E prod,i (1)
where Eext is the emission of raw materials extraction, Etrans the emission of the raw materials transport, Econs the emission due to the construction plant, E prod the emission due to the production operation, and i represents each power plant. For each technology and life-cycle stage inventory, the calculation of emission is based on the Eq.2

principle :

E lcs = n i=1 EFi × qp,i (2)
where E represents the emission value of the life cycle stage (extraction, construction, transport and production),

EF the corresponding EF for 1 FU of the life-cycle stage and qp the quantity of the product expressed in the FU.

Fig. 3 illustrates the methodology used in this work and shows which parameters are considered in the power system to evaluate the different potential environmental impacts.

• • • • • • • • • • • • •

Global warming potential (GWP)

Regarding to the results in Fig. 4, Mayotte produces the highest amount of GWP emissions with 0.921 kg CO2-eq/kWhe, followed by Martinique (0.883 kg CO2-eq/kWhe) and Guadeloupe (0.846 kg CO2-eq/kWhe). These results are explained by the massive use of fossil-fuel sources in these territories (see Fig. 1). Reunion generated about 0.687 kg CO2-eq/kWh. Through the extensive use of RES and the network interconnection, Corsica and French Guyana emit fewer pollutants than the other territories, with 0.505 and 0.373 kg CO2-eq/kWhe, respectively.

The values obtained in this study are slightly below those on the energy balance report for Reunion (SPL Energies Réunion, 2015). This can be explained by the considered boundaries for the assessment that might not to be the same. In Fig. 5-a, we can see that the production phase contributes greatly to each 1 kWhe produced for each island, representing 95% of the total emissions for every 1 kWhe produced. In Fig. 5-b, it is apparent that the extraction and transportation phase are mostly generated by fossil energies. Mayotte recorded the highest value for the extraction phase due to its high share of petroleum products. We can also see that the most significant value for fossil fuel transportation is recorded by Reunion, followed by Mayotte, a result that is explained by these islands' coal and fossil fuel supplies. Thus, these transportation results show that these two islands are more isolated than the others with regard to the distance of energy supply. French Guyana's emission records the lowest value in each phase except in power plant construction. With the understanding that hydropower composes 57% of the electricity mix and more than 75% of the construction emissions, we can deduce that the construction of renewable energy infrastructure is more emissive than that of other power sources. For Mayotte, the construction of photovoltaic panels generates more emissions than the construction of conventional sources.

Other impacts

As with GWP, the operation of FFTs is mainly responsible for the majority of the other impacts (Fig. 5). This is briefly discussed in the following paragraphs.

Acidification potential (AP).

As presented in the preceding section, we discuss here the contribution of each power plant to the AP that it generates when producing 1 kWhe. It can be seen in Fig. 4 that Mayotte has the highest AP value, followed by Martinique and Guadeloupe. As can be seen in Fig. 5-d, the main contributor in Reunion is the operation of the coal power plant (67%). On the other islands, fuel oil power plants contribute at least 61%, as in Guadeloupe, followed by coal (35%). In general, hydropower and solar panels do not exceed 1% of the total contribution in acidification potential.

Tropospheric ozone precursor potential (TOPP). TOPP is the mass-based equivalent of the ozone formation rate from precursors, measured in ozone precursors equivalents. The TOPP represents the potential formation of nearground (tropospheric) O3, which can cause summer smog (Öko-Institut, 2015). The distribution of the contributions of each power plant to TOPP emissions is quite similar to that for AP emissions (see Fig. 5-e andf). However, Martinique recorded the highest value of TOPP emissions produced per 1 kWhe (0,0057 g NMVOC eq), followed by Guadeloupe and Reunion.

Cumulative energy use (CEU). The CEU represents the expenditure of energy resources (primary energies) for the production of 1 kWhe. As can be seen in Fig. 4 From the results above, the FOTs can be classified using the typology of countries proposed by [START_REF] Herbert | A typology for world electricity mix: Application for inventories in Consequential LCA (CLCA)[END_REF]. This study proposed 4 types of electricity mixes that differ from one another in the major energy production 130 type and GWP value. Considering the existing groups as presented in Table 2, Guyana and Corsica belong to the third group, characterized by average values of GHGs (300-600 g CO2-eq). The remainder of the territories belong to the fourth group, in which energy mix composition is mainly composed of FFTs. However, even if Reunion is assumed to be withingroup 4, Reunion lies within the transition zone between groups 3 and 4: its electricity mix is mainly composed of coal and oil, and the remaining production is diversified.

From a national overview, FOTs contribute at a low level in the national electricity consumption, about 1.9% of the total amount of electricity consumption, including mainland and overseas territories and region. However, the emission factor of electricity in France in 2013 is about 84 g CO2eq/kWh, according to ADEME's value (ADEME, 2013), and the other territories record an emission electricity factor about 4 to 11 times higher than those of mainland.

Principal component analysis (PCA)

The previous results allow us to establish the first classification of FOTs in the global context. A PCA has been performed to investigate these islands regarding the following key data: population, GDP per capita, annual electricity production, RES share in the electricity mix, total GWP emissions from electricity production, area and the insulation situation index (ISI), as obtained from [START_REF] Delaître | Caractériser l'énergie dans les îles[END_REF]. The objective was to identify the similarities between the overseas territories, particularly from the perspective of renewables. Table 3 gives an overview of the parameters considered in the PCA. Once the correlation matrix was calculated, it was shown that the chosen criteria are not correlated, except the RES proportion and the GWP value. The negative correlation between these two parameters is explained by the fact that GWP emissions levels decline with the increase of RES. Area is also negatively correlated to GWP. Indeed, if the island is too small, there are likely fewer opportunities to produce electricity cleanly. The bar plot of the 150 percentage of variance allows to assess the projection quality. Fig. 6 shows that Dimensions 1 and 2 explain 82% of the variance (see Table A.1), which is a sufficient quality projection for the analysis. Based on the PCA results obtained from the package FactoMineR in the R statistical package [START_REF] Lê | FactoMineR: A package for multivariate analysis[END_REF], Fig. 7 presents a combination of the individuals' and variables' factor maps. Considering the factorial design, the projection qualities of the individuals are assessed by the total value of the square cosine on the two axes. The higher the square cosine value is, the better the projection quality is. Table A.2 shows that all the individuals have a square cosine value on the two axes above 0.600, except for Martinique, which records a total square cosine of 0.531.

Considering Table A.3, all variables present a total square cosine above 0.600, including the individuals results.

The contribution to the construction of the axis is an another indicator of the projection quality. Based on the results, the electricity production contribution is the highest for the Dimension 1, followed by the ISI. The GWP emission and the percentage of RES in the mix contribute about 70% of Dimension 2 in the variable factor map.

The PCA projection shows high dependencies among the variables Production, Population, GDP and ISI. For the individual projections, French Guyana and Mayotte contribute highly to the construction of the second axis, 45%

and 30 % respectively. The negative correlation between GWP emission and RES contribution is well represented in Fig. 7 in the variable factor map, as is the case of the ISI parameter and electricity production. These results allow us to identify two types of territories and two singular cases:

-Corsica and Reunion Island represent islands that have a high electricity production with large populations and a high GDP, and their electricity mix involves a relatively high proportion of RES (> 30 %);

-Guadeloupe and Martinique represent islands with a high fossil-fuel electricity generation. This could be explained by the small area and the ISI of these islands. The lack of hydropower plants on both highlights the small area and topographical variability;

-French Guyana is a large territory with an electricity mix mainly based on hydropower and a high degree of isolation;

-Mayotte is a small remote island, which explains the high GWP value for its electricity generation.

The PCA highlighted that electricity generation and its production modes are significant parameters that help characterize an island's remoteness and its predisposition to using fossil fuels. The ISI factor is also very important in the understanding of fossil-fuel source use in place of RES in the electricity mix.

Conclusion

The present study was designed to determine the effects of insularity on the electricity production on islands.

Although this study focuses on environmental impact assessment using LCA methodology, it also allowed for the development of an evaluation tool based on LCA in the MATLAB environment that will be linked to an energy forecast and scenario tool in future works. The LCA results will be taken as constraints in energy scenarios or, alternatively, the developed scenario will be evaluated through LCA in one combined tool. In this study, the results obtained identify Mayotte and Martinique as the islands that generated the most emissions for each indicator, particularly for GWP and CEU. It was also shown that operation-production generates the most GHG emissions.

For each studied territory, we have identified which energy sources generates the most GHG emissions. This study shows that RES shares in GHG emissions are very low, and their contribution is only significant in infrastructure construction. According to their geographic location, territories like these islands should promote the use of RES in their electricity production in order to reduce GHG emissions. This study has also allowed us to identify, among the French overseas territories, two types of islands: for the two groups, one with Reunion and Corsica and the other with Guadeloupe and Martinique, similar energy transition scenarios can be designed in future works. Mayotte and French

Guyana will be studied individually. This study has also led to positioning the FOTs in an international context through their GWP values. The PCA also highlights the influence of electricity production types in the classification of these non-interconnected territories. It seems that integrating an environmental index like as gCO2-eq per kWh of electricity into scenario projections would be helpful. Such an index represents an encapsulation of information that was previously contained in two factors, electricity production and RES share. This study helps in understanding which factors must be observed for future energy planning investigations. These key factors could be integrated in scenario modeling as constraints.

Figure 1 :

 1 Figure 1: Overview of the energy sources in the studied departments' electricity mixes. HFO: Heavy fuel oil; LFO: Light fuel oil. Other RESs include bagasse, biogas, biomass, and wind energy production.

FOTs

  and will enrich the literature review on LCA studies on insular territories . This work is conducted within the framework of cleaner production, because it shows the current status of the production mode of electricity in the French overseas territories. It helps to understand which part of the life cycle stage contributes the most in the greenhouse gases emissions. The energy balance report for Reunion in 2014 provided a comparison of FOTs by in 50 the electricity and transport sectors (SPL Energies Réunion

Figure 3 :(Figure 4 :

 34 Figure 3: Methodology and data used to assess the potential environmental impacts combining GEMIS, the LCA methodology and MATLAB

  , Martinique and Mayotte require the highest values of CEU, which is explained by the high proportion of fossil energies in their electricity mixes. They are followed by Guadeloupe and Reunion, which show fairly diversified electricity mixes.

Figure 5 :

 5 Figure 5: Potential impacts generated per life-cycle stage per 1 kWhe produced: (a) GWP [kg CO2-eq], (c) AP [g SO2-eq], (e) TOPP [g NMVOC-eq]. Share of each technology at life cycle stage: (b) GWP, (d) AP, (f) TOPP

FigureFigure 7 :

 7 Figure 6: Scree plot of the eigenvalues

Table 1 :

 1 Data and assumptions for electricity generation in French insular territories in 2013

	Type of energy	Installed capacity Production Share of mix	Fuel origin Distance
		(MW)	(GWh)	(%)		(km)
	Corsica (EDF-SEI, 2013a, 2014a, Hellion et al., 2008)
	Biogas	1.7	11.1	0.50	Local
	Heavy Fuel	186.3	529.9	23.71 PACA Region	491.8
	Hydrodam	181.1	522.8	23.4	Local
	Hydro ROR	25.6	73.9	3.31	Local
	Interconnected	150	663.8	29.70 Italy, Sardinia
	network
	Light fuel oil	105	299.1	13.39	PACA region	491.8
	Photovoltaic	86	113.9	5.10	Local
	Wind energy	18	20.1	0.90	Local
	Guadeloupe (Observatoire Régional de l'énergie et du climat, 2014, EDF-SEI, 2014c)
					Continued on next page

Table 2 :

 2 Classification of the FOT using the world mix typology based on[START_REF] Herbert | A typology for world electricity mix: Application for inventories in Consequential LCA (CLCA)[END_REF]

	Group Territories	GHG	Bounds		Main characteristics
				(g CO2eq/kWh) Major production	Other production
	1		Very low 0-37	Hydroelectric and/or nuclear Predominantly renewables
	2	France	Low	37-300	Hydroelectric and/or nuclear Diversification
	3	French Guyana, Corsica	Average	300-600	Gas	Diversification
	4	Reunion, Guadeloupe,	High	>600	Coal, oil	Predominantly fossils
		Martinique, Mayotte

Table 3 :

 3 Geographical and economic situation, electricity production and the environmental burdens of the FOT

	Location	Population	GDP	Electricity	Share of RES	GWP	Area	ISI
			per capita	production	(SHREN)	[kg CO2-eq	[km 2 ]
			[e/capita]	[GWh]	[%]	/kWh]
	Corsica	319,780	25,523	2235	32.71	0.505	8680	0.55
	Guadeloupe	41,1507	20,072	1729	17.51	0.846	1704	61.2
	French Guyana	23,7550	15,820	858	63	0.373	86,504	100.32
	Martinique	381,326	22,266	1577	5.8	0.883	1128	83.1
	Mayotte	211,397	7896	261.90	5.29	0.921	374	71.5
	Reunion	840,974	19,340	2813.4	37.78	0.687	2512	20.6

  Table A.3: Results for the variables (coordinates, square cosine and contributions)

	Variables	Dim.1	ctr	cos2 Dim.2	ctr	cos2 Dim.3	ctr	cos2
	GWP	0.066	0.139 0.004 -0.975 35.078 0.951	0.130	2.355 0.017
	Population	0.775 19.483 0.601	0.076	0.215 0.006	0.610 51.770 0.372
	GDP	0.705 16.118 0.497	0.329	3.999 0.108 -0.511 36.358 0.261
	Production	0.952 29.357 0.906	0.272	2.727 0.074	0.062	0.533 0.004
	SHREN	-0.095	0.295 0.009	0.972 34.875 0.945	0.198	5.487 0.039
	Area	-0.603 11.805 0.364	0.785 22.766 0.617	0.067	0.622 0.004
	ISI	-0.839 22.804 0.703 -0.096	0.341 0.009	0.144	2.876 0.021

Development Fund, within the context of the Territorial Cooperation Operational Programme.

Acknowledgments

This research received financial support from Reunion Region and the European Union -The European Regional

Appendix

PCA results.


Vanessa Rakotoson
email: vanessa.rakotoson@univ-reunion.fr

Jean Philippe Praene

Long-term electricity mix planning towards low GHG emission: The case of Reunion Island

Keywords: Linear programming, Normative scenario, Electricity mix, GHG emission, Reunion Island

This study presents a linear programming model for an optimal long-term electricity mix planning of an insular territory. A prospective exercise on electricity generation is conducted over a period of 15-35 years. A general methodology is presented to determine an optimal generation mix that minimize greenhouse gas (GHG) emission by taking into account the environmental challenges of the territory. This methodology is applied to the case of Reunion Island. The main constraints considered here are the evolution of electricity emission factor and to meet the future electricity demand. Due to the long time-frame that we consider, a normative electricity mix scenario is presented, which aimed to reach the target by adjustments of the current electricity power system. The obtained results refer two scenarios: preserving and transforming structure. Referring to results, it is feasible to achieve environmental policy established by the energy transition act.

INTRODUCTION

Energy planning models help to identify the best compromise between various constraints the energy demand increase, investment in technology production and climate change. There are different types of scenario that could be implemented, according to the objective of the study. Bradfield et al. [START_REF] Bradfield | The origins and evolution of scenario techniques in long range business planning[END_REF] and Amer et al. [START_REF] Amer | A review of scenario planning[END_REF] established a classification of scenario planning methods, there are three schools of major approaches for scenario development which are the intuitive logics, the probabilistic modified trends methodology and the French approach of La prospective. The latter approach is based on the principle that the future is not predetermined, thus it can be adjusted in accordance with national views. In order to reach the national policy objective, it is necessary to determine the type of scenario that will be implemented. Authors in [START_REF] Börjeson | Scenario types 0876-7 and techniques: Towards a user's guide[END_REF] defined three typologies of scenarios: predictive scenarios which answer to the question "What will happen?", explorative scenarios respond to the question "What can happen?", and normative scenarios answer to the question "How can a specific target be reached?". Normative scenarios consist of two types, characterized by the system structures: preserving scenarios 0876-1 suggest solutions by adjustments to the current situation and transforming scenarios respond to the target by necessary changes in the current structure. In this work, the prospective normative scenario is considered, based on the goal of mitigation of greenhouse gas (GHG) emissions. [START_REF] Saiah | Prospective analysis for a long-term optimal energy mix planning in Algeria: Towards high electricity generation security in 2062[END_REF] presented a prospective analysis for a long-term energy mix planning in Algeria, where the scenarios are constructed from a forward-looking assumptions of economic (population, GDP) and energy variables (efficiency, capacity). They determined scenario trended and voluntarism scenarios for each variable, in order to highlight the benefits of the voluntarism scenario. Thangavelu et al. [START_REF] Thangavelu | Long-term optimal energy mix planning towards high energy security and low GHG emission[END_REF] propose a long-term optimal energy methodology, taking into account the risk associated in the energy planning due to the uncertainties in the projected variables. The optimal energy mix satisfied the renewable penetration and the fuel diversity constraints at each time periods for the input scenarios.

Saiah and Stambouli

TIMES model is one of the most widely used in energy planning. Garcia-Gusano et al. [START_REF] García-Gusano | Integration of life-cycle indicators into energy optimisation models: The case study of power generation in Norway[END_REF] present a soft-linking of LCA an TIMES-Norway model, with a time-frame from 2010 to 2050. They showed that the life-cycle indicators evolve in accordance with the integration of new power generation technologies. Krakowski et al. [START_REF] Krakowski | Reprint of Feasible path toward 40 -100 % renewable energy shares for power supply in France by 2050 : A prospective analysis q[END_REF] applied a long-term energy-planning model from TIMES family, by exploring different levels of renewable source penetration in the French power system. Drouineau et al. [START_REF] Drouineau | Increasing shares of intermittent sources in Reunion Island: Impacts on the future reliability of power supply[END_REF] analyze the capability of the Reunion Island's power system to reach electricity autonomy by 2030 through a TIMES-Reunion model, from a prospective analysis. They showed that this objective can be reached by integrating high levels of biomass and intermittent sources.

Given that small islands are heavily dependent on fossil fuels for energy, particularly for electricity generation. Energy planning will help the decision-makers in the right choice for the future electricity sector. In this work, we propose a linear programmation (LP) to find the best compromise electricity mix scenario, in which various parameters should be considered, as the emission costs, energy security, carbon emission limits targets, and renewable energy potential. A normative prospective scenario will be set out in this work. The structure of this document is as follows: first, a description of the adopted methodology. Then, we will introduce the case study of Reunion Island with an overview of the electricity sector and the assumptions considered. The different scenarios that will be compared with the corresponding results.

METHODS

Problem statement

The work addresses a long-term electricity planning of a country, taking into account the GHG emissions associated with the energy scenario. This long-term electricity planning is identifying the optimal combination of electricity generation, to satisfy the objective of GHG reduction by kilowatt-hour electricity produced. This method is based on the MARKAL principle [START_REF] Maizi | Energy mix planning for the French electricity production sector[END_REF] and [START_REF] Thangavelu | Long-term optimal energy mix planning towards high energy security and low GHG emission[END_REF]. Linear programming models are subject to bounds, linear equality and inequality constraints. The objective function is to define the best electricity mix repartition which minimizes the total emission cost of the proposed electricity mix, and allows to reach the GHG reduction targets, over a time period horizon.

   n i ctax i i i g C ef x E st EmissionCo 1 , : min , t  (1)
Eq(1) quantifies the expected cost of GHG emission for t time, where i represents each generation technology that enters into the electricity mix, 𝑥 𝑖 represents the share of the 0876-2 generation technology, Eg the electricity generation, ef the GWP emission from power generation technology and C ctax represents the carbon tax emission. This problem is subject to various constraints relative to energy security, carbon emission limits, potential capacity and renewable contribution in the electricity mix. These parameters will be converted into appropriate constraints of equalities or inequalities in Eq (2-4).

Energy security

Energy security considered in this study, quantifies the ability of the electricity mix to meet the future energy demand. Eq(2) forces the electricity generation Eg to meet the electricity demand d at time t.

t i i g d x E   (2)

Carbon emission limits

According to the environmental policy of the studied area, emissions through electricity generation should not exceed the targets established by the government. As carbon emission relies on the power technology type, Eq (3) will force the integration of renewable sources and limit the fossil fuels contribution. The carbon target CT represents the emission factor from one kilowatt-hour electricity produced.

t i i i CT ef x   (3)

Potential capacity

According to their availability or capacity Cap, renewable energy sources have to face clear limitations of electricity generation. Eq (4) illustrates this limitation, which can be the potentiality, or the limit integration of intermittent sources of energy.

t i r i g Cap x E , , 
, t  (4) Values of Cap can change over time, based on the adopted scenario. In line with the territory objectives, renewable share in electricity mix can be imposed over the time period.

ASSUMPTIONS Case study: Reunion Island

Reunion Island, a territory of 2520 km², is a French overseas department and an ultraperipheral European region located in the Indian Ocean, among the Mascarenes islands with Mauritius and Rodrigues islands. Reunion Island is characterized by a diversified electricity mix, thanks to local resources as biomass, hydropower, wind, sea and solar energy. Despite these resources, primary energy consumption is 86.1% dependent on fossil fuels and current electricity generation is 35% self-sufficient [START_REF]Bilan énergétique -Ile de La Réunion[END_REF]. Within the framework of the energy transition for green growth, decision-makers have to consider how Reunion can achieve the energy, or electricity autonomy since 2030. Due to its geographical location, numerous environmental policy can be applied to this territory, and consequently, various energy scenarios.

In the base year of 2015, the electricity mix of Reunion Island is composed by coal (40%), heavy fuel oil and gas oil (24%), hydropower (17%), bagasse (9%) and the remainder is provided by other renewable sources as solar, biogas and wind energy (10%). An overview of the potential of renewable energy sources in Reunion is well described in [START_REF] Praene | Renewable energy: Progressing towards a net zero energy island, the case of Reunion Island[END_REF]; Reunion has huge potential in promising renewable such as geothermal and ocean energy. However, these technologies can be exploited only after 2030.

0876-3

On the basis of the foregoing and the history of the electricity consumption, Reunion's future energy demand is expected to increase at least in one of four possible ways that the French electricity provider (EDF) established: low (0.2%), high (3.02%), baseline scenario energy-side management (ESM) (1.4%) and an enhanced ESM (0.7%) on average per year. EDF takes into account various parameters in the implementation of the energy demand of the population, as the demography, the economic growth through the gross domestic product (GDP), or the household equipment rate [START_REF] Edf-Sei | Bilan Previsionnel D E L ' Equilibre Systemes Energetiques Insulaires : La Réunion[END_REF]. In this study, we will consider the ESM enhanced scenario.

The environmental burdens of each power technology for a 1 kWh electric produced are defined by its lifecycle assessment (LCA). These values have been assessed with the LCA methodology, regarding the 'cradle-to-gate' boundary. The GHG emissions reduction targets are defined by different complementary policies. Within the framework of the energy transition for green growth, the national energy policy aims to reduce the GHG emission by 40% below 1990 levels by 2030, and to a quarter of those in 1990 for 2050. Emissions targets implying a major slope for the first 15 years of the scenario. Here, we consider the medium-term objective on 2030, as shown in Figure 1.

ENERGY SCENARIO

In order to reach the GHG emission targets explained in the previous section, a normative scenario has to be implemented for each scenario case in order to reach a specific target. Based on the previous assumptions, two scenarios are distinguished:

-Scenario A: This scenario reflects a normative preserving scenario, where the current energy structure is not modified, meaning that any other technology can be added to the existing one, but their capacity can be extended in order to meet energy demand. -Scenario B: This scenario will assume both preserving and transforming scenario.

Indeed, according to the potential of renewable, the effective use of geothermal and OTEC technology will be possible from 2030.

For both scenarios, the following assumptions will be implemented in the methodology described previously:

-Hydropower capacity cannot be extended. As hydropower generation is closely tied to the rainfall, we assume that the maximum Eg,hydro equals the maximum value observed for the capacity installed [START_REF]Bilan énergétique -Ile de La Réunion[END_REF].

0876-4 ]) 2015 : 2010 [ max( ,hydro g hydro g E x E 
, t  (5) -Electricity from bagasse depends essentially on the sugar campaign. For an agricultural area of 22,664 ha, the current variety of sugar cane produces about 569 kt of bagasse.

Authors in [START_REF] Khoodaruth | Use of higher fi bre cane for increasing cogenerated electricity : Policy implications for Mauritius[END_REF] presented the increase of electricity generated from bagasse by using a higher fiber cane, which allows to produce the same amount of sugar with a higher amount of bagasse. Assuming that this new variety is integrated progressively in the cultivation of sugar cane, the electricity production from bagasse will increase proportionally until 2050.

highfiber bag g norm bag g bagasse g E E x E . , , ,   , t  (6)
-Reunion Island is a volcanic island whose geothermal potential is not clearly defined. However, an expected potential of 30 MW capacity is anticipated for 2030. Assuming that this process is exploited, we have determined the potential electricity production based on the process in Guadeloupe. Among the overseas department, only Guadeloupe exploits the geothermal energy, and there are two geothermal facilities with a total capacity of 15 MW. Based on the effective efficiency of those of Guadeloupe, we have determined the maximum electricity production expected [START_REF]Observatoire Régional de l'énergie et du climat[END_REF]. -Ocean thermal energy conversion (OTEC) is one of the most promising technology of sea energy in Reunion. Studies are currently carried out in the south of the island, but others sites can be exploited [START_REF] Sinama | Etude de la production d électricité à partir de l ' Energie Thermique des Mers à l ' île de La Réunion : Modélisation et optimisation du procédé[END_REF]. However, a potential capacity of 130 MW is expected to be installed in 2030. -To ensure the network stability, electricity from intermittent resources cannot exceed the limit of 30%.

g ermittent ren g E x E 30 . 0 int ,  , t  (7)
-All renewable production is equal or greater to the baseline year 2015, 2015 , ,ren

g ren g E x E  , t  (8)
-Section 1 of the law of the energy transition for green growth defines the increase of the C ctax from 2020 to 2030 (56 EUR to 100EUR per carbon ton) [START_REF] Jorf | 992 du 17 août 2015 relative à la transition énergétique pour la croissance verte[END_REF]. We will consider the 2030 C ctax value until the end of the energy programming.

RESULTS AND DISCUSSIONS

The development of the methodology in order to find the best electricity mix and to minimize the emission cost is the main result obtained. The case study of Reunion Island has been considered. The linear programming result is presented in this section, which has been calculated by the Eq (1, 5-8). In this context, two main parameters have to be discussed: the renewable contribution and the final electricity produced from each technology. The optimal electricity mix of both scenario satisfies the emission target and renewable integration at each time period for the given assumptions.

Figure 2 illustrates the electricity production from 2015 to 2050 under the scenario A and B. The electricity production from each technology was calculated over a 5-year period within the given constraints. Bagasse production is the same in the two scenarios, which is defined in Eq [START_REF] García-Gusano | Integration of life-cycle indicators into energy optimisation models: The case study of power generation in Norway[END_REF]. Given that OTEC and geothermal energy production can be exploited only from 2030, the obtained electricity mix in both scenarios remains the same between 2020 and 2030, as the emission target is the same. However, owing to their limited potential, these two energies contribute at about 180 GWh in 2050. We observed that electricity from fossil fuel-based 0876-5

technologies decreases gradually until 2050. Biomass production increases significantly between the first-time period, and helps to meet energy demand since the fossil fuels contribution have to decrease in order to reduce GHG emission. This implies a high investment in biomass facilities. Solar and wind energy have also shown significant growth between the baseline scenario and the given horizon 2050. Scenario A shows that reducing GHG emission is feasible if the electrical structure is maintained in its current form. The potential of geothermal and OTEC electricity generation can be improved, according to future researches. Indeed, the potential value used in the implementation of this energy scenario at this stage remains in expectation. However, investment in biomass, solar and wind energy facilities is essential to that goal, whether for Scenario A or Scenario B. Figure 3 shows the contribution of all power technologies in the future electricity generation.

Renewable energies attain about 77% of the electricity production in 2050, thanks to fuel diversity. Future renewable electricity generation will be ensured by bagasse 8-12%, hydro 15.8-18.1%, biomass 0.5%-19%, geothermal 0-2.3%, OTEC 0-3%, solar 8.4-15.8% and wind 0.5 -14.7%. According to these results, investment in renewable facilities is necessary to reach these goals. These scenarios allow to reverse the current situation, and reduce the fossil fuel 0876-6

contribution. Coal contribution has to decrease by more than half in 35 years (40% to 16%). Thermal production based on oil derivatives also presents a gap in their contribution (23.5% to 6.8%). The total emissions cost during the planning horizon will amount to about 582 million EUR.

Figure 4. Variations of power technologies contribution in future electricity

Figure 4 shows the variation contribution of each technology at the end of the planning period. As can be observed, renewable contribution as biogas, hydro and geothermal energy is not significant over time. The coal contribution faced high variability, followed by wind and solar. The allowable contribution of each technology has been capped at 40% of the energy demand during the optimization.

CONCLUSION

A multi-period electricity planning linear model has been developed to find the optimal electricity combination for any region and at any horizon time. The optimal electricity mix of each scenario satisfies all the technological and environmental constraints, and minimizes cost associated with GHG emission. In this case study, we have considered the enhanced ESM scenario for the future energy demand, which implies that population has to consume less energy in the future. The main constraint considered in this study was to reach the different targets in reducing GHG emissions. The electricity mix planning shows that the current technologies allow to reach these goals, subject to the condition of increasing of the solar, biomass and wind capacity. In this study, energy planning has been implemented for 35 years with a 5-year interval. The obtained results can be used directly to assess more accurately the life cycle environmental burdens of each scenario. To complete the developed model, future works have to include economic aspects regarding to investment, operation and maintenance cost.

Figure 1 .

 1 Figure 1. Evolution of the GHG emissions targets

Figure 2 .Figure 3 .

 23 Figure 2. Evolution electricity production of scenarios A and B [GWh]


Michaël Dauge

Michaël Gauthier
email: michael.gauthier@ens2m.fr

Emmanuel Piat

Modelling of a Planar Magnetic Micropusher for Biological Cell Manipulations

Keywords: Area -Micromechanics Micromanipulation, magnetic actuation, modelling, scale effect, biological cell

The improving of the efficiency and the automation of biological cell technologies is currently of great importance. One way is to build biological micro-factories which are able to perform complete biotechnological processes automatically. This technology requires the development of new automatic cell transport system to feed work stations in microfactories. An original magnetic cell micropusher is described in this paper. The ferromagnetic pusher which is submerged in the biological medium follows the movement of a permanent magnet located in the air. This paper focuses on the modelling of the dynamic behaviour of the micropusher according to the magnet trajectory. The generic model proposed is able to determine pusher trajectory according to the micropusher magnetic properties and the permanent magnet shape and properties. This simulation tool will permit to optimize and to study cell trajectory control in further works.

I. Introduction

Although the In-Vitro Fertilization (IVF) process is usually used by physicians, the success rate remains particularly low. Thus, the improving of this biological process with new biological technologies and new microtechnologies is of great importance. Some microtechnology research groups are working towards a high efficiency IVF process [START_REF] Arai | Pinpoint injection of microtools for minimally invasive micromanipulation of microbe by laser trap[END_REF][START_REF] Frenea | Positioning living cells on a high-density electrode array by negative dielectrophoresis[END_REF][START_REF] Kim | Cellular force measurement for force reflected biomanipulation[END_REF][START_REF] Li | Manipulation of living cells by atomic force microscopy[END_REF][START_REF] Sun | Mems for cellular force measurements and molecular detection[END_REF][START_REF] Sun | Mechanical property characterization of the mouse zona pellucida[END_REF][START_REF] Gauthier | Control of a particular micro-macro positionning system applied to cell microdisplacement[END_REF]. The IVF process whose goal is to fertilize oocytes consists of several manually or teleoperated manipulation steps and requires a high pratical know-how. The major part of the full process time is needed to prepare the oocytes before the technical operations. The typical size of a human oocyte is around 150 µm diameter.

Since all steps of the current IVF process are manually made or teleoperated, the design of an automatic IVF microfactory is a solution to improve the ergonomics of current processes and to guarantee a better repeatability of manipulations and injections. In this way, the efficiency of IVF (around 30 % of pregnancies at the present time in Europe) should improve.

Furthermore automated manipulations and oocyte treatments will enable other biotechnologies like embryonic stem-cell research for therapeutic cloning to develop. Presently, the objective of the therapeutic cloning is to build organs from one stem cell. These processes require the culture of a large number of oocytes. In this way, an oocyte treatment microfactory could contribute to therapeutic cloning.

Our microfactory project is presented in figure 1. This bio-microfactory will contain modular microrobots and a cells transport system to move cells inside the microfactory. Each modular microrobot will have a specific function: Oocyte cumulus removal, oocytes properties measurements, fertilization. The oocytes are placed in the input zone after cumulus removal (see figure 1). Oocytes go down on the sloping face and stand motionless against the wall. The transfer of oocytes from the input zone to the output area through the processing modules is achieved by a cell micropusher. Some standard modules (test or treatment modules) are placed by the physicians along the cell trajectory. At the end of the process, injected oocytes are placed in the output area where physicians can catch them.

The conventional glass micropipette is a competitive tool for the manipulation of oocytes. However, complex trajectories, complex shunting, or manipulation of an oocyte placed behind another oocyte cannot be performed with conventional micropipettes. Consequently, we propose a new technology allowing complex oocyte trajectories. This article presents a two degree-of-freedom (DOF) magnetic cell transport system for automated IVF micromanipulation. Previous works on cell magnetic micropushers concerned a one DOF configuration which was not suitable with current inverted microscope used in biological micromanipulations [START_REF] Gauthier | Control of a particular micro-macro positionning system applied to cell microdisplacement[END_REF], [START_REF]An electromagnetic micromanipulation system for single cell manipulation[END_REF].

The following section deals with the description of the oocyte transport system and open-loop oocyte micromanipulations. The third section focuses on the modelling of the pusher magnetic behaviour and dynamic behaviour. Experimental trajectories and comparisons with the models are described in the last section.

II. Oocyte Transport System

The aim of our oocyte transport system is to enable cell transport in a channel through the different work stations. The channel volume is filled with a biological medium ( see figure 1). To move our actuator, we chose to use magnetic energy which is a suitable solution for micro-actuation [START_REF] Bae | Feasibility test of an electromagnetically driven valve actuator for glaucoma treatment[END_REF][START_REF] Bourouina | Integration of two degree-of-freedom magnetostrictive actuation and piezoresistive detection: application to a twodimensional optical scanner[END_REF][START_REF] Cugat | Magnetic micro-actuators and systems (magmas)[END_REF][START_REF] Guckel | Progress in magnetic microactuators[END_REF][START_REF] Guo | A new kind of microrobot in pipe using driving fin[END_REF][START_REF] Hatch | A ferrofluidic magnetic micropump[END_REF][START_REF] Lagorce | Magnetic microatuator based on polymer magnets[END_REF][START_REF] Liu | Micromachined magnetic actuators using electroplated permalloy[END_REF][START_REF] Park | Development of magnetic materials and processing techniques applicable to integrated micromagnetic devices[END_REF][START_REF] Yesin | Analysis and design of wireless magnetically guided microrobots in body fluids[END_REF]. Moreover static magnetic field has no effect on living cells unlike laser trapping systems [START_REF] Arai | Non-contact manipulation of biological cells[END_REF]. The original single cell transport system consists of a wireless micropusher which pushes a single cell Magnet Micro-object Micropusher Fig. 3. Example of Automatic Open-loop Micromanipulation: The micropusher comes near the micro-object (1), pushes it (2), stops its movement (3), goes back (4) and goes over the micro-object (5) to goes on the other side him [START_REF] Sun | Mechanical property characterization of the mouse zona pellucida[END_REF], comes near the micro-object [START_REF] Gauthier | Control of a particular micro-macro positionning system applied to cell microdisplacement[END_REF] and pushes it [START_REF]An electromagnetic micromanipulation system for single cell manipulation[END_REF] in the other direction without contact with the external medium. When the cells manipulated are oocytes, the micropusher is a ferromagnetic particle (240 × 240 × 25 µm 3 ) made in electroplated nickel [START_REF] Gauthier | Microfabrication and scale effect studies for a magnetic micromanipulation system[END_REF] and actuated with an external magnetic field. In our case , the external magnetic field is induced by a cylindrical magnet (NdFeB, φ 1.6 mm, h=0.74 mm) placed on the other side of a vertical wall. Contrary to microfluidic transfer [START_REF] Ichikawa | Single cell trap on a chip using in-situ microfabrication with photo-crosslinkable resin and thermal gelation[END_REF], our proposed micropusher is able to push each cell individually. In the future, micropushers will be encapsulated because nickel is embryotoxic. The micropusher and cell positions are measured through an optical microscope and a CCD camera. The displacements are made by two motorized micro-translation stages (PI c , M-111.1) controlled by a computer. Figure 2 describes an example of some micropusher trajectories used to position oocytes. It's a linear view of the in vitro fertilization microfactory presented in figure 1. The first degree of freedom (DOF) along x axis is used to push the micro-object (step 1 or 3). The second DOF along y axis is used to go over the micro-object (step 2). Micropusher placed against the wall is used to position oocytes in front of tools like injector, aspiration pipe, sensor, etc.

To test our system and its feasibility, we did some preliminary automatic open loop micromanipulations. Figure 3 presents a pushing operation on a micro-object (200 µm diameter sphere). This micromanipulation example proves the feasibility of our concept. To optimize this principle, a complete modelling of the link between the magnet trajectory and micropusher trajectory is needed. Moreover to perform cell displacements, the micropusher trajectory must be controlled and the study of the automatic control needs a complete dynamic model too. The behaviour modelling is presented in the following.

III. Behaviour Modelling

The modelling aims are to propose a complete model of the dynamic behaviour of the micropusher in function of the magnetic source movement where parameters are the shape of the micropusher, and the shape and the nature (permanent magnet, micro-coils) of the magnetic source.

Position between micropusher and magnet, presented in figure 4, is defined by two points: Center O of the magnet top plane and contact point I between the micropusher and the glass wall. The position of the micropusher in an inertial reference frame R m : (O m , -→ x , -→ y , -→ z ) is defined by x m , y m , and z m . Relative positions between the point O and the point I are defined as OI x ,OI y and OI z . Micropusher orientation is defined by two angles: α and β defined in figure 4. Angle α enables movements like step 2 in figure 2. Angle β is useful for accurate positioning [START_REF] Gauthier | Control of a particular micro-macro positionning system applied to cell microdisplacement[END_REF]. The micropusher is modelled by a plane surface S, with a normal -→ n and a thickness e. Micro-pusher reference frame is defined by vectors: -→ n , -→ b and -→ c described in figure 4.

The model describes the behaviour of a ferromagnetic particle (whatever its plane shape is) into a magnetic field (whatever its source is). Consequently the model outputs are the position and the orientation of the micropusher, the inputs are the position of the magnetic source and the parameters are magnetic micropusher properties and the magnetic field -→ B 0 induced by the permanent magnet. The model is composed of several blocks (see figure 5) where each block represents one calculation step. First the finite element model "Flux3D c " is used to obtain the magnetic field -→ B 0 according to the magnetic source shape and properties. The second step consists of the calculation of the magnetization -→ M of the micropusher. Magnetic torque --→ Γ m,I in point I and magnetic force -→ F m applied by the magnet on the micropusher are determined in function of the relative position -→ OI between the micropusher and the magnet. These first steps are performed off-line and efforts ( -→ F m , --→ Γ m,I ) are stored in a large numerical matrix.

The last step is the determination of the micropusher position (x m , y m and z m ) and orientation (α and β) behaviour using the efforts stored. Each block principle is detailed in the following.

A. Magnetic Block

The aim of this part is to describe the process done by the magnetic block. The block ouput is the micropusher internal magnetization -→ M according to the micropusher geometrical characteristic and magnetic field -→ B 0 . To build this function, we assume two hypotheses:

• the micropusher is a flat surface S: magnetization is constant according to the micropusher thickness, • edge effects are not taken into account: there is no magnetic leak. With the magnetostatic Maxwell equations, we can define the continuity relation between -→ B 0 and the internal micropusher magnetic field -→ B i , and the continuity relation between external magnetic excitation -→ H 0 and internal micropusher magnetic excitation -→ H i (relations (1) and ( 2)).

--→ B 0n = -→ B in (1) -→ H 0t = -→ H it (2)
where:

-→ B 0 = B 0n . -→ n + B 0t . -→ t -→ B i = B in . -→ n + B it . -→ t -→ H 0 = H 0n . -→ n + H 0t . -→ t -→ H i = H in . -→ n + H it . -→ t
As described in figure 6, -→ B 0 and -→ H 0 orientation are defined by θ 0 and ϕ 0 , and orientation of both -→ B i and -→ H i by θ i and ϕ i . Our aim is to obtain magnetization -→ M .

-→ M and -→ B i are colinear, so the vector -→ M is defined by its module -→ M and the angles ϕ i and θ i . We assume that the magnetization has reached the saturation M sat , thus it gives the following equation:

-→ M = M sat (3)
= 5.1 × 10 5 A.m -1 nickel saturation magnetization Moreover from relation (2), ϕ i satisfies:

ϕ i = ϕ 0 (4)
From equations (1,3,4), θ i satisfies:

B 0n = tan (θ i ) . (B 0t + µ 0 .M sat . cos (θ i )) (5)
The system (3,4,5) defines the vector -→ M as a function of the magnetic field -→ B 0 .

B. Strain Block

To present the mechanical action applied by the magnetic source on the micropusher, a small surface dS of the flat micropusher around the point P is considered. Classical magnetic efforts applied on this element are:

• An elementary surface magnetic force

--→ dF m : --→ dF m = -→ ∇ -→ M . -→ B 0 .dS (6)
• An elementary surface magnetic torque

--→ dΓ m : --→ dΓ m = -→ M ∧ -→ B 0 .dS (7)
The complete magnetic effort applied on the pusher in the point I is thus:

-→ F m = e × S --→ dF m (8)
--→ Γ m,I = e.

S

--→ dΓ m + e.

S -→

P I ∧ --→ dF m ( 9
)
where e is the thickness of the flat micropusher.

C. Dynamic Block

We assume that the friction force applied from the glass wall to the micropusher -→ F f is applied in point I, and consequently that friction torque is null in I. The dynamic behaviour is defined by the equilibrium between efforts and dynamic terms in point I:

-→

F f + -→ F m = m -→ Γ (10) --→ Γ m,I = J. -→ γ (11)
where -→ F f is the action of the glass wall on the micropusher applied in point I, m the micropusher mass, -→ Γ its acceleration, J its angular inertia, and -→ γ the angular acceleration.

The dynamic behaviour in translation is a function of the magnetic force -→ F m and of friction conditions -→ F f . The angular behaviour is only a function of magnetic effects --→ Γ m,I .

The dynamic behaviour is the superposition of three elementary dynamic behaviours described as:

• The angular behaviour α with axe (I, -→ z );

• The angular behaviour β with axe (I, -→ b ); • The translation behaviour (x m ,y m ). By computation of the dynamic equations ( 10), [START_REF] Cugat | Magnetic micro-actuators and systems (magmas)[END_REF] The time constants of the angular behaviour are negligible compared to the translation time constant. Moreover, these time constants are very small compared to the time constant of the controller (around 1 ms) or compared to the time constant of the camera (20 ms) used to measure the micropusher position. Consequently the general dynamic behaviour can be considered as a dynamic behaviour in translation and a quasi-static behaviour in rotation. Both behaviours are detailed in the following sections 1) Angular Behaviour: At each time t, we consider that the micro-pusher is reaching its angular static equilibrium. The angular behaviour presented in [START_REF] Cugat | Magnetic micro-actuators and systems (magmas)[END_REF] is consequently reduced as:

-→ 0 = --→ Γ m,I = e. S --→ dΓ m + e. S -→ P I ∧ --→ dF m (12)
The angular position is characterized by the equilibrium between both terms of the magnetic torque --→ Γ m,I . Consequently, its calculation in function of the relative position -→ OI can be determined in preprocessing. Thus, the dynamic block can be presented as described in figure 7. Angular positions are defined in function of the torque --→ Γ m,I and are stored in a large numerical matrix. Translation behaviour is simulated in function of the position of the magnet and the stored magnetic forces. At each time t, the angle of the micropusher is calculated by interpolation of the stored angular positions.

2) Translation behaviour: The micropusher translation behaviour ( 10) is a function of the friction force applied by the glass vertical wall. This force -→ F f can be divided into:

• A normal component --→ F f N .
-→ z perpendicular to the contact surface which is in equilibrium with the normal magnetic force:

--→

F f N . -→ z = - -→ F m . -→ z (13) • A tangential component --→ F f T sum of both components F f T x . -→ x and F f T y . -→ y .
To describe the translation behaviour of the micro-pusher, two cases are studied: When the micropusher contact point I is immobile, the friction tangential component --→ F f T is lower than the product of the static friction coefficient f s and the normal component

--→ F f N : --→ F f T < f s . --→ F f N (14)
In this case, the tangential component of the friction force and the tangential magnetic force stay in equilibrium:

--→ F f T . -→ x + -→ F m . -→ x = 0 --→ F f T . -→ y + -→ F m . -→ y = 0 (15)
When the norm of the tangential component reaches the product f s .

--→ F f N , the contact point I moves:

--→ F f T = f s . --→ F f N ⇒ -→ V I = 0 ( 16
)
where -→ V I is the velocity of point I.

When the micropusher is in movement with a velocity -→ V I , the modulus of the friction tangential force is the product of the dynamic friction coefficient

f d (f d ≤ f s ) and the normal component --→ F f N : --→ F f T = -f d × --→ F f N . -→ n v (17)
where -→ n v is the unit vector of the velocity -→ V I . The translation dynamic behaviour of the micropusher is defined by the projection of the equation [START_REF] Bourouina | Integration of two degree-of-freedom magnetostrictive actuation and piezoresistive detection: application to a twodimensional optical scanner[END_REF] in the wall plane ( -→ x , -→ y ), thus:

MFm

-

→ F m . -→ x + --→ F f T . -→ x = mẍ m -→ F m . -→ y + --→ F f T . -→ y = mÿ m (18)    -→ F m . -→ x -f d . --→ F f N . -→ n v . -→ x = mẍ m -→ F m . -→ y -f d . --→ F f N . -→ n v . -→ y = mÿ m (19)            x m = 1 m -→ F m . -→ x -f d . --→ F f N . -→ n v . -→ x .d 2 t
+ ẋm (0)t + x m (0)

y m = 1 m -→ F m . -→ y -f d . --→ F f N . -→ n v . -→ y .d 2 t + ẏm (0)t + y m (0) (20)
The equations ( 15) and ( 20) define respectively the behaviour of the micro-pusher when point I is immobile and when it is in movement. The equation ( 16) defines the transition condition.

Moreover when f d = f s , the stick-slip motion appears as presented in [START_REF]An electromagnetic micromanipulation system for single cell manipulation[END_REF]. When the magnet moves, the micro-pusher stays first immobile until the magnetic tangential force reaches the static friction condition (equation ( 16)). Thus, the micro-pusher is moving in function of the dynamic behaviour (equation ( 20)), and a large acceleration is applied to the micro-pusher until it reaches a new static equilibrium position ( -→ V I = -→ 0 ). This phenomenon increases the difficulties to control the final position of the micro-pusher or the pushed object position. Some original control strategies are proposed in [START_REF] Gauthier | Control of a particular micro-macro positionning system applied to cell microdisplacement[END_REF] to overcome stick-slip.

IV. Experimental and simulation results

A. Magnetic results comparison

Firstly we have compared the magnetic field with the presence of the micropusher given by our model and by Flux3D model. Results are presented in figure 10 which represents the magnetic field

-→ B z (projection of -→ B o into z axis)
given by Flux3D and our model magnetic model at point P as a function of the distance OP z between the point P and the magnet surface. The simulation conditions are the following:

• micropusher is placed at the magnet center OI x = 0, OI y = 0, OI z = 200µm; • consequently the micropusher edges are placed at OP z = 200µm and OP z = 400µm. The consequences of the hypotheses made (no magnetic leak) are visible on the edges of this micropusher, but their influences on forces computation is under 10% as presented in the next section.

B. Force results comparison

To validate force calculation and to observe the influence of magnetization errors on forces calculation, force -→ F m was computed with magnetization calculated by Flux3D and our model. Experimental conditions are the following:

• micropusher is placed up to the magnet center (OI x = OI y = 0 and 200µm < OI z < 1600µm),

• micropusher is placed in xOz plane

The figure 11 presents a comparison between both calculated forces and experimental forces measured with a microbalance, according to the distance OI z .

-→ F z is nearly the same with Flux3D and our model.

C. Angular Behaviour

The first experimental validation deals with the equilibrium angle of the micropusher (angle β in figure 4) versus the micropusher size and the relative position -→ OI. These tests enable to compare computed and measured values. The calculated angles α and β are determined by the numerical resolution of equilibrium equation [START_REF] Guckel | Progress in magnetic microactuators[END_REF]. As shown by equation ( 12), the angular position is done by the equilibrium of two physical phenomena: The magnetic torques --→ dΓ m and the torques in I induced by the magnetic force --→ dF m :

S --→ dΓ m = - S -→ P I ∧ --→ dF m (21)
These two strains induce two different micropusher behaviours:

The magnetic torques --→ dΓ m consequence are the alignment of the micropusher on the external magnetic field -→ B 0 (see equation 7). On the contrary, the torque induced by the magnetic force -→ P I ∧ --→ dF m makes the micropusher lie flat on the plane.

In fact the first term is function of l 3 and the second is function of l 4 where l is the micropusher characteristic size. Consequently, the smaller the micropusher, the greater is the magnetic torque --→ dΓ m compared to the magnetic force torque -→ P I ∧ --→ dF m . Physically, the smaller the micropusher, the closer is its orientation to the magnetic field line (see figure IV-C).

Simulations and experimental measurements are presented in figure IV-C for the following case: -500µm < OI x < +500µm; OI y =0; OI z =200 µm. The micropusher is not aligned on the magnetic field -→ B 0 . Actually, magnetic torque is not prominent compared to the magnetic force torque. Conversly, the micropusher is also not lying down on the glass slide because magnetic force torque is not prominent compared to the magnetic torque. Both phenomena have the same value order and the micropusher orientation is defined between these two extremum positions. Experimental measurements and our model are similar.

D. Dynamic Comparison

This section presents the comparison between the computed trajectories and experimental measurements. The simulation of the pusher trajectory is based on the magnetic force calculation (8) computed for each relative position -→ OI in preprocessing. Simulated trajectory is obtained by resolution of the equations ( 15), ( 16) and [START_REF] Gauthier | Microfabrication and scale effect studies for a magnetic micromanipulation system[END_REF] in Matlab Simulink. The experimental position of the micro-pusher is measured by a CCD Camera and a visual treatment.

The example presented in figure IV-D is obtained with a square trajectory of the magnet. A good correlation between both results is observed, and trajectories are relatively near. Moreover, the model permits to compute trajectories in function of the magnetic source shape. We present the differences observed between two permanent magnets:

• A cylindrical magnet 1.6 mm in diameter, 0.74 mm in thickness and axis z; The model build is designed to be generic and is able to determine the dynamic behaviour of the micropusher in function of the magnet movement for different magnet shapes, and micropusher shapes and properties. Moreover, as the model is only based on the magnet field induced by a magnetic source it can be generalized to micro-coils.

V. Discussion and Conclusion

We propose in this paper a new and original structure of IVF process. The displacement of the cells in the biological microfactory is induced by a micropusher which follows the movement of a permanent magnet. This method is more flexible than the current technologies which are using micropipettes. Some other methods are studied around the world to manipulate cells like laser trapping [START_REF] Arai | Pinpoint injection of microtools for minimally invasive micromanipulation of microbe by laser trap[END_REF] and dielectrophoresis micromanipulation [START_REF] Frenea | Positioning living cells on a high-density electrode array by negative dielectrophoresis[END_REF]. Both technologies can induce irreversible damages to cells. The pushing action is more safety and is usually used with micropipettes. However, our nickel micropusher remains embryo toxic and cannot be used without biocompatible coating. This encapsulation will not disturb the magnetic behavior of the nickel micropusher but will modify the friction conditions of the micropusher, and consequently the trajectory of the micropusher. The dynamic model proposed in this paper is able to determine the pusher trajectory in function of friction conditions. Based on this model, further works will be done to analyse the impact of the encapsulation on micropusher behavior.

A new approach to manipulate a cell by using a small micropusher was described. The submerged ferromagnetic micropusher follows the movement of a magnet located in the air. We show that the manipulation of oocyte is possible with this device. A complete generic model of the micropusher trajectory is proposed. It enables to predict the micropusher movement in function of the magnet position according to the micropusher shape and properties and magnetic field induced by the magnet. This generic model can be generalized to other magnetic sources like micro-coils. This simulation tool will be the base of further works on the optimization of the micropusher architecture and on the development of automatic pushing tasks.

Fig. 1 .

 1 Fig. 1. In Vitro Fertilization Microfactory Concept

Fig. 2 .

 2 Fig. 2. Example of Cells Treatment Micromanipulation Strategy: Micropusher places an oocyte in front of the first tool (step1). When the second tool operation is finished, the micropusher goes over the first oocyte (step 2) and evacuates the second oocyte (step 3).

Fig. 4 .

 4 Fig. 4. Magnet Micropusher Position and Orientation

Fig. 6 .

 6 Fig. 5. Micropusher Behaviour Model Diagram

Fig. 7 .

 7 Fig. 7. Dynamic Simulation Model Diagram

Fig. 8 .Fig. 9 .

 89 Fig. 8. Strains applied by the magnet on the micropusher

Fig. 10 .

 10 Fig. 10. Model and Flux3D results comparison

Fig. 11 .

 11 Fig. 11. Comparison between Fz measurement and simulations

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Micropusher height influence on the micropusher orientation β

  Fig. 15. Micro-pusher and Magnet Trajectories: Influence of the Magnet Shape on the Micro-pusher Trajectory.

  • A square magnet (1.6 × 1.6 × 0.74mm 3 ). Both magnets have a remanent magnetic field oriented along the z axis. Both trajectories are presented in figure IV-D.The second geometry induces a modification of the magnetic field -→ B 0 simulated by the software Flux 3D. This modification induces a new dynamic behaviour and a modification of the micro-pusher trajectory.

  the time constants of these behaviours are determined. These values are presented in table I.

	Elementary Dynamic Behaviours	Time Constant
	Rotation α	45 × 10 -6 s
	Rotation β	37 × 10 -6 s
	Translation (xm,ym)	930 × 10 -6 s
		TABLE I
	Time Constant of the Three Elementary Dynamic Behaviour

Acknowledgments

This research was supported by the LAB (Laboratory of Automation of Besançon -France). The authors thank Prof. C. Roux (research group on "genetic and reproduction", Besançon) for collaboration on human oocytes micromanipulations. The authors thank the LCEP-Besançon for the fabrication of the micropusher glass sample support.