Adil Aboulkas

H Hammani

M El Achaby

E Bilal

Abdellatif Barakat

K El Harfi

K El

M El Achaby

Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char

Keywords: Pyrolysis, Algal waste, Bio-oil, Bio-char, Characterization

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

Introduction

Biomass has attracted a great attention as a source for renewable and clean energy [START_REF] Chen | Pyrolysis of oilplant wastes in a TGA and a fixed-bed reactor: Thermochemical behaviors, kinetics, and products characterization[END_REF][START_REF] Ertaş | Pyrolysis of laurel (Laurus nobilis L.) extraction residues in a fixed-bed reactor: Characterization of bio-oil and bio-char[END_REF]. Biomass can be converted directly into liquid, gaseous and solid fuels, usable for transport, heat and power production [START_REF] Demiral | Bio-oil production from pyrolysis of corncob (Zea mays L.)[END_REF]. Among a large variety of biomass resources, marine biomass has been considered to be a precious material for the third generation bio-fuels feedstock [START_REF] Demirbas | Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char[END_REF][START_REF] Li | Preparation and characteristics of bio-oil from the marine brown alga Sargassum patens C. Agardh[END_REF]. The marine areas of Morocco include almost 3500 km of coastline [START_REF] Ainane | Valuation Algal biomass of Morocco :Potential pharmacological and Environmental Applications, case of the brown algae Cystoseira tamariscifolia and Bifurcaria bifurcate[END_REF]. Red macroalgae (Gelidium sesquipedale) are considered economically valuable resources due to their ability to produce high yields of commercially valuable biomass [START_REF] Hanif | The exploitation of red algae Gelidium in the region of El-Jadida : socio-economic aspects and perspectives[END_REF]. Morocco the third producer in the world [START_REF] Mouradi-Givernaud | Biology and agar composition of Gelidium sesquipedale harvested along the Atlantic coast of Morocco[END_REF]. The Gelidium represents 90% of the harvest of the marine algae treated locally and that generates an important quantity of waste (production of 870 tons/years) that cannot be treated very well [START_REF] Ennouali | Biotransformation of algal waste by biological fermentation[END_REF].

Biochemical and thermochemical processes are used for converting waste to bio-fuel and/or other products. Among these technologies, pyrolysis is a promising technology, more favorable and economical for converting algal biomass into energy fuels (Ferrera-Lorenzo et al., 2014a, 2014b;[START_REF] Francavilla | Cascade approach of red macroalgae Gracilaria gracilis sustainable valorization by extraction of phycobiliproteins and pyrolysis of residue[END_REF]Hui Zhao et al., 2013). The thermal decomposition in the absence of oxygen and at temperatures (400-600 °C)

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 results in liquid products (bio-oil or pyrolytic oil); carbon-rich solid residues (bio-char); and gaseous products [START_REF] Chaiwong | Characterizations of Bio-oil and Bio-char Products from Algae with Slow and Fast Pyrolysis[END_REF][START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF][START_REF] Francavilla | Cascade approach of red macroalgae Gracilaria gracilis sustainable valorization by extraction of phycobiliproteins and pyrolysis of residue[END_REF][START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF][START_REF] Ross | Classification of macroalgae as fuel and its thermochemical behaviour[END_REF][START_REF] Yanik | Pyrolysis of algal biomass[END_REF]. Bio-oil is considered to be a very promising biofuel and may be used as fuel for heat, power or combined heat and power, or as an intermediate feedstock for various chemicals and liquid transport fuels production. The bio-char is also a useful product that can be used for soil amendment and to sequester carbon in the soil, bio-energy (high calorific value) or environmental-contaminant removal. The Characteristics of pyrolysis products depend on the experimental parameters: final temperature, heating rate, residence time, type of pyrolysis reactor, type of biomass used...etc. The effects of each factor are closely interconnected, which requires more knowledge of the operating conditions of the pyrolysis process to produce bio-oil and bio-char with excellent fuel properties.

A number of studies regarding bio-oil and bio-char production from various sources of biomass have showen that liquid and solid fuels can be produced from biomass [START_REF] Hassen-Trabelsi | Pyrolysis of waste animal fats in a fixed-bed reactor: Production and characterization of bio-oil and bio-char[END_REF][START_REF] Chaiwong | Characterizations of Bio-oil and Bio-char Products from Algae with Slow and Fast Pyrolysis[END_REF][START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF][START_REF] Demiral | Bio-oil production from pyrolysis of corncob (Zea mays L.)[END_REF][START_REF] Ertaş | Pyrolysis of laurel (Laurus nobilis L.) extraction residues in a fixed-bed reactor: Characterization of bio-oil and bio-char[END_REF][START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF][START_REF] Kraiem | Characterization of the liquid products obtained from Tunisian waste fish fats using the pyrolysis process[END_REF][START_REF] Onay | Influence of pyrolysis temperature and heating rate on the production of bio-oil and char from safflower seed by pyrolysis, using a well-swept fixedbed reactor[END_REF][START_REF] Onay | Influence of pyrolysis temperature and heating rate on the production of bio-oil and char from safflower seed by pyrolysis, using a well-swept fixedbed reactor[END_REF]Koçkar, 2006, 2004;[START_REF] Ross | Classification of macroalgae as fuel and its thermochemical behaviour[END_REF][START_REF] Yanik | Pyrolysis of algal biomass[END_REF]. However, very little information is available on the process of pyrolysis of macroalgae into bio-oil and bio-char and analysis of the characteristics of these products [START_REF] Chaiwong | Characterizations of Bio-oil and Bio-char Products from Algae with Slow and Fast Pyrolysis[END_REF][START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF][START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF]H. Zhao et al., 2013). [START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF] have reported the properties of bio-oils produced by pyrolysis of blue-green algae blooms. The experiments were performed in a fixed-bed reactor and the effects of pyrolysis temperature, particle size and nitrogen flow rate on product yields were studied. The results showed that a maximum oil yield of 54.97% was obtained at a final Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 pyrolysis temperature of 500 °C, a particle size below 0.25 mm and a nitrogen flow rate of 100 mL min -1 . The bio-oil was characterized with a high heating value of 31.9 MJ kg - 1 and an O/C molar ratio of 0.16 at optimum conditions. The authors have shown that the pyrolysis of algal biomass is a promising process for both renewable fuel production and lake environment improvement. Zhao et al. (2013) also investigated the properties of bio-oil produced by fast pyrolysis of macroalgae in a Free-fall Reactor. The bio-oil obtained was analyzed by elemental, GC-MS, and FT-IR analysis. The results showed that the average heat value was 25.33 MJ kg -1 and the oxygen content was 30.27 wt%.

The results suggested that macroalgae presents as a good bio-oil feedstock candidate. [START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF] pyrolyzed Brown algae in a fixed bed reactor under pyrolysis temperature (430-530 °C) and holding time (4-10min). The maximum yields of bio-oil and bio-char were approximately 48.4 and 32.3wt%, respectively, when prepared at 450 °C for 8 min. The results showed that the bio-char has properties, including a comparatively high nutrient content (Ca, K, Mg, N, and P), that make it suitable for use as a soil additive, and for long-term soil carbon sequestration. [START_REF] Francavilla | Cascade approach of red macroalgae Gracilaria gracilis sustainable valorization by extraction of phycobiliproteins and pyrolysis of residue[END_REF] carried out pyrolysis of G.gracilis (macroalgae) residue in order to investigate the production of bio-oil and bio-char within a pyrolysis temperature range of 400-600 °C.

Results showed that the bio-oil yield is high (65 wt%) at a pyrolysis temperature 500 °C and a bio-char yield ranging between 33 wt% (400 °C) and 26.5 wt% (600 °C). [START_REF] Bae | The characteristics of bio-oil produced from the pyrolysis of three marine macroalgae[END_REF] studied the effect of pyrolysis temperature on production and characterization of bio-oil from three marine macroalgae, and they concluded that the bio-oil yield reached a maximum, within the range of 37.5-47.4 wt.%, at 500 °C. The compounds identified suggest that pyrolysis can be used to produce bio-oils for various uses, such as chemical feedstock, through further treatment. However, these studies only focused Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 on bio-oil analyses, a comprehensive characterization including both bio-oil and biochar is necessary.

In this study, algal waste after extraction of agar-agar was chosen as source of algal biomass because there is no study on the influence of operating conditions on production and characterization of bio-oil and bio-char from algal waste via pyrolysis.

The major challenge in the energy field is the search for process to convert biomass wastes into biofuel with excellent fuel properties. Aim of this study was (i) to investigate the influence of experimental parameters on the pyrolysis of algal waste; (ii) to determine the suitable experimental parameters to achieve maximum bio-oil yield; and (iii) to characterize the bio-oil produced under suitable pyrolysis conditions using elemental analysis, TGA, FTIR, 1 H-NMR, GC-MS is characterized. The use of chemical and physical Characteristics was also performed in order to investigate the proprieties of the produced bio-char.

Materials and methods

Algal waste used in this study as a feedstock was obtained from the industrial processing of red macroalgae to obtain Agar product (SETEXAM company, Kenitra-Morocco). Prior to use, algal waste was air dried, ground and sieved to obtain particles in the ranges of 0.5-1 mm. Thermogravimetric curves were obtained at four different heating rates (5, 10, 20 and 50 °C min -1 ) between 105 °C and 900 °C. Nitrogen gas was used as an inert purge gas to displace air in the pyrolysis zone, thus avoiding unwanted oxidation of the sample. A flow rate of around 60 ml min -1 was fed to the system from a point below the sample and a purge time of 60 min (to be sure the air was eliminated Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 from the system and the atmosphere is inert). The balance can hold a maximum of 45 mg; therefore, all sample amounts used in this study averaged approximately 20 mg.

Proximate analysis was conducted using a thermogravimetric analyser (METTLER TOLEDO-TGA/DSC 3+). The moisture content is determined by the mass loss after the sample is heated to 105 °C under N 2 . The volatile matter corresponds to the mass loss between 105 and 900 °C under N 2 . Fixed carbon is the solid combustible material that leads to the mass loss at 900 °C when the atmosphere is switched from N 2 to air [START_REF] Saldarriaga | Fast characterization of biomass fuels by thermogravimetric analysis[END_REF]; the residue left is the ash content. Ultimate analysis for C, H, N and S content was performed using an elemental analyzer (vario MICRO cube V4.0.2). The H/C, O/C molar ratios and empirical formula were calculated from elemental composition. Higher heating value (HHV) of samples was experimentally measured using a bomb calorimetric (Model 1261, Parr Instruments) according to ASTM D 5865-04.

Pyrolysis procedure

The pyrolysis experiments were performed using a stainless steel fixed-bed reactor. The experiments were carried out in two series. The first group of the pyrolysis experiments was performed to determine the effect of the pyrolysis temperature on the pyrolysis product yields and the pyrolysis conversion. A sample of 20 g of algal waste was placed in the reactor and nitrogen gas (flow rate of 0.1 L/min) was introduced for 15 min to remove air in the reactor. The sample was pyrolyzed from an initial temperature (25 °C) to a final temperature (350,400,450,500,550 or 600 °C) with a heating rate of 10 °C/min and held for 20 min at the final temperature. The liquid products were condensed in a trapping system and recovered by washing with dichloromethane Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 (DCM). The aqueous phase was separated from bio-oil by decantation. The anhydrous sodium sulphate was added into the bio-oil and the solvent mixture to remove any remaining water. After the solvent was separated from the bio-oil using a rotary evaporator, the bio-oil was weighed and its yield was determined. The bio-char in the reactor was weighed and the gas yield was calculated by determining the weight difference. The second group of experiments was performed with four heating rates, namely, 5, 10, 20 and 50 °C/min at the pyrolysis temperature of 500 °C. This was in order to examine the influence of heating rate on the pyrolysis product yields. In this study, the pyrolysis experiments were repeated three times to confirm the reproducibility. The products yields are mean values of three equivalent experiments.

Bio-oil and bio-char characterization

The bio-oil selected for the characterization was that which gave the maximum bio-oil yield at the temperature of 500 °C and heating rate of 10 °C/min. The bio-char obtained at the same conditions was also characterized.

Elemental composition and ash content

The elemental composition (CHN-O) and ash content of the bio-oil and bio-char were determined with the same methods used for raw material.

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

Fourier Transform Infrared Spectroscopy (FTIR)

FTIR spectroscopic analyses were performed to determine the distribution of functional groups present in pyrolysis products (bio-oil and bio-char). The FTIR spectra of the produced bio-oil and bio-char were recorded using a bruker tensor27 infrared spectrometer in the wavelength range of 400-4000 cm -1 with a resolution of 4 cm -1 and accumulation of 16 scans.

1 H-NMR spectroscopy

1 H-NMR spectra were recorded on 600 MHz Bruker spectrospin instruments. The biooil sample was diluted with CDCl 3 .

Gas Chromatography-Mass Spectrometry (GC-MS)

Gas Chromatography-Mass Spectrometry (Thermo scientific ISQ single quadrupole) was used to analyze the bio-oil fraction. By comparing the recorded mass spectra of compounds with those given in the NIST2008 c2.0/Xcalibur data system library, provided by the instrument software, compound identification was done.

Bio-oil were separated by silica capillary column, using helium as the carrier gas (1.2 mL/min). The injection volume was 1µL using a 20:1 split ratio and an injector temperature of 260 °C. The GC temperature sequence was 70 °C start, hold 2 min, ramp at 10 °C/min to 300 °C and hold at 300 °C for 5 min.

Scanning Electron Microscopy (SEM)

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

The morphology of raw waste and its bio-char was investigated by a scanning electron microscope (phenom Pro X). SEM was carried out using an electron acceleration of 15 kV. Images were taken at a magnification of 3000×.

Results and discussion

Algal waste characteristics

The main characteristics of algal waste including the results of proximate and ultimate analyses are given in Table 1, where composition analysis gave 35.27 wt% C, 4.71 wt% H, 4.44 wt% N, 0.73 wt% S, 54.85 wt% O. The heating value of the algal waste was 14.98 MJ/kg, which is relatively high compared to other agricultural residues [START_REF] Nanda | Gasification of fruit wastes and agro-food residues in supercritical water[END_REF]. It was observed that the algal waste contains a high ash content (12.09 %) which is consistent with previous observations of the high ash content in aquatic flora from natural ecosystems, including micro-and macro-algae. The presence of high ash content in the algal waste favors the formation of char since inorganic compounds in the ash are known to catalyze the formation of char during pyrolysis [START_REF] Maddi | Comparative study of pyrolysis of algal biomass from natural lake blooms with lignocellulosic biomass[END_REF].

Thermogravimetric analysis of algal waste

The thermogravmetric analysis was performed to determine the pyrolysis process temperature. The algal waste was heated from 105 ºC to 900 ºC at four heating rate of 5, 10, 20 and 50 ºC/min in a nitrogen atmosphere. Figure 1 shows the behavior of the algal waste under these conditions. The main mass change seen between 250 ºC and 600 ºC is attributed to de-volatilization stage in which the pyrolysis main process occurred. This mass loss represents the decomposition of carbohydrate and the protein content [START_REF] Kim | Thermogravimetric characteristics and pyrolysis kinetics of Alga Sagarssum sp. biomass[END_REF]. The maximum thermal degradation of the algal waste was at approximately Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 340-380 °C (depending on heating rate). Moreover, a significant proportion of inorganic materials in kelps decompose at 600 -800 °C, probably a consequence of metal carbonates [START_REF] Norouzi | Promotion of hydrogen-rich gas and phenolic-rich bio-oil production from green macroalgae Cladophora glomerata via pyrolysis over its bio-char[END_REF]. The TGA curve indicates that over 60wt% of the algal waste is thermally degraded when the reaction temperature is beyond 380 °C. It follows that the algal waste pyrolysis should be performed at temperatures higher than 380 °C.

For this reason, algal waste pyrolysis at the five reaction temperatures of 400, 450, 500, 550 and 600 °C were considered.

FTIR characterization of algal waste

The FTIR spectrum of algal waste is shown in Figure 2. The FTIR analysis was conducted to observe the organic functional groups. The wide band between 3500-3100 cm -1 assigned to O-H stretching vibrations. This band indicates the presence of polysaccharides and proteins in the algal waste. The absorption band located at 1640 сm -1 , originated from conjugated carbonyl groups (located at α-position). The C-H bending vibrations at 1370 cm -1 -1422 cm -1 , together with the C-O bending vibration at 1235 cm-1 were found in the spectra of algal waste, and this suggests the presence of fats and esters (Zou et al., 2009). The absorbance peak at around 1030 cm -1 was also observed and that was possibly from C-O stretching vibrations.

Effect of final temperature and heating rate on yields of pyrolysis products

Pyrolysis temperature is the most important parameter affecting the product yields. The distribution of pyrolysis products from pyrolysis of algal waste at various final pyrolysis temperatures such as 400, 450, 500, 550 and 600 °C is as shown in figure 3a. It can be seen that the conversion yield increased from 47.91 to 59.64 % when the pyrolysis Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 temperature was increased from 400 to 600 °C. The bio-oil yield was 19.90 % at the lowest temperature of 400 °C, this data reflects incomplete pyrolysis of algal waste. The peak yield of bio-oil was 24.10 % at 500 °C after which it decreased to 22.30 % at 600 °C. The increase in the yield of bio-oil from 400 °C to 500 °C is explained by the increase of the primary decomposition of the algal waste or the secondary decomposition of the bio-char residue, as the pyrolysis temperature increases. The decrease in the yield bio-oil from 500 °C to 600 °C may be due to the secondary cracking of the pyrolysis vapors at higher temperatures. The yield of bio-char markedly always decreased from 52.09 to 40.36 wt.%, while the yield of gaseous product gradually rose from 21.81 to 31.44 wt.% as the pyrolysis temperature rose from 400 to 600 °C. The decrease in the char yield may be attributed to either the greater primary decomposition of algal waste at higher temperature or the secondary thermal decomposition of the char formed before being entrained out of the reactor. The gas increase is speculated to be owing to the secondary cracking of the char and the pyrolysis vapors.

Due to the maximum oil yield obtained in the first set of experiments, the pyrolysis temperature was held constant at 500°C. Figure 3b shows the pyrolysis product yields were obtained at four heating rates of 5, 10, 20 and 50 °C/min with the final pyrolysis temperature being 500 °C. The bio-oil yield was 22.30 %, 24.10 %, 23.50 % and 22.70 % for the heating rates of 5, 10, 20 and 50 °C/min, respectively. The bio-char yield decreased from 45.23 % to 42.31 % and the gas yield increased from 26.67 % to 28.69 % with an increasing heating rate from 5 °C/min to 50 °C/min. The slight decrease in the bio-char yield and the little increase in the gas yield are due to secondary cracking of Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 the pyrolysis vapors and secondary decomposition of the bio-char at higher heating rates.

All experiments indicate that the pyrolysis temperature at 500 °C and the heating rate of 10 °C/min are the parameters that result in a maximum bio-oil yield of around 24.10%.

It is known that the final temperature has a significant effect on yield and composition of pyrolysis products [START_REF] Bae | The characteristics of bio-oil produced from the pyrolysis of three marine macroalgae[END_REF][START_REF] Hassen-Trabelsi | Pyrolysis of waste animal fats in a fixed-bed reactor: Production and characterization of bio-oil and bio-char[END_REF][START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF][START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF][START_REF] Onay | Influence of pyrolysis temperature and heating rate on the production of bio-oil and char from safflower seed by pyrolysis, using a well-swept fixedbed reactor[END_REF]. The increase of the final temperature is always followed by an important decrease of bio-char yield and an increase in the gases amounts. On the other hand, the bio-oil reaches a maximum in the temperature range of 500-550 °C. For example, [START_REF] Choi | Characterization of the bio-oil and bio-char produced by fixed bed pyrolysis of the brown alga Saccharina japonica[END_REF] studied the pyrolysis of brown alga and evaluated the effect of the final temperature (430-530 °C) on product distribution. They found that the bio-char yield steadily decreased from 34.50 to 25.5wt%, with rising temperature. This was the opposite of the gas yield, which increased from 20.30 to 27.2 wt%. The yield of bio-oil reached a maximum value of 48.40 wt% at 450 °C (48.40wt%), and then decreased as the temperature increased. [START_REF] Bae | The characteristics of bio-oil produced from the pyrolysis of three marine macroalgae[END_REF] investigated the effect of the pyrolysis temperature (300-600 °C) on the pyrolysis characteristics of bio-oil in a quartz U-tube reactor. They found that the maximum production of bio-oil was achieved at 500 °C. Furthermore, They Argued that this was due to the secondary tar reactions in the vapor phase since the liquid yields decreased while corresponding the gas yields increased at 600 °C. The pyrolysis of macroalgae offers a new opportunity for feedstock production; however, the utilization of bio-oil as a fuel product needs further assessment. [START_REF] Hu | Bio-oil production through pyrolysis of blue-green algae blooms (BGAB): Product distribution and bio-oil characterization[END_REF] studied the pyrolysis of bluegreen algae blooms in a fixed-bed reactor for bio-oil production. The effect of process parameters such as pyrolysis temperature, particle size and sweep gas flow rate on the Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 yields of pyrolysis products and their chemical compositions were investigated. When the temperature was increased from 300 °C to 700 °C in 50 °C increments, the char yield decreased sharply from 57.09% to 20.39%, while the gas yield rose dramatically from 16.25% to 41.33%. In particular, the bio-oil yield did not display monotonic trends with the increasing temperature. The bio-oil yield achieved the maximum of 54.97 % at the final pyrolysis temperature of 500 °C.

The decrease of the bio-oil yield at higher pyrolysis temperatures is due to the secondary reactions that, in parallel cause the increase in of the gas yield. The decrease of the bio-char yield with increasing temperature may be attributed to either a greater primary decomposition of the raw material at higher temperatures or to the secondary decomposition of the solid product, leading to an increase of the pyrolysis conversion.

The yield of non-condensable gas products increases due to the secondary decomposition of the bio-char at higher temperatures, which also contribute to the increasing of the gas products yield with increasing temperature [START_REF] Onay | Influence of pyrolysis temperature and heating rate on the production of bio-oil and char from safflower seed by pyrolysis, using a well-swept fixedbed reactor[END_REF][START_REF] Onay | Influence of pyrolysis temperature and heating rate on the production of bio-oil and char from safflower seed by pyrolysis, using a well-swept fixedbed reactor[END_REF]Koçkar, 2006, 2004;[START_REF] Rahman | Temperature effect on the characterization of pyrolysis products from oil palm fronds[END_REF].

The rest of this study, only bio-oil and bio-char that were obtained under the most suitable conditions, a temperature of 500 °C and a heating rate of 10 °C/min were retained for next characterization.

Bio-oil characterization

Elemental composition and ash content

The ultimate analysis, proximate analysis and calorific value of the bio-oil are shown in Table 1. As can be seen, the bio-oil has a high carbon (51.12%) content and a low oxygen content (37.20%) content, whereas there is a slight increase in the hydrogen Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

(5.81%) content compared to the raw algal waste (35.27 %, 54.85 % and 4.71 %, respectively). The results show an increase in HHV and a decrease of the H/C molar ratio of the bio-oil compared to the raw material. The average chemical composition of the bio-oil is CH 1,364 O 1,546 N 0,078 .

FTIR characterization

The bio-oil was analyzed by FTIR spectroscopy (Figure 2), the functional groups and related classification of compounds were listed in Table 2. The absorption peak at 3200-3600 cm -1 indicated the presence of oxygenated compounds (O-H group). The presence of methyl and methylene groups (alkanes, alkenes) is indicated by the intense peak of C-H stretching vibrations between 2800 and 3000 cm -1 (tree peat at 2852, 2925 and 2960 cm -1 ) and by C-H deformation vibrations between 1350 and 1475 cm -1 (tree peaks at 1376, 1411 and 1452 cm -1 ) [START_REF] Francavilla | Cascade approach of red macroalgae Gracilaria gracilis sustainable valorization by extraction of phycobiliproteins and pyrolysis of residue[END_REF]. The C=O deformation vibrations with absorbance at 1700 cm -1 indicate the presence of ketones, carboxylic acid or aldehydes groups. The intense peak 1656 cm -1 represents C=C stretching vibrations, which is indicative of alkenes. In addition, the absorbance peaks at 1730-1150 cm -1 , corresponding to the presence of heteroatoms (i.e. N and O) functionality, were also observed, which was consistent with results of the GC-MS analysis presented in Table 3. The peaks appear in the range of 1475-1525 cm -1 and 700 and 900 cm -1 , attributable to the aromatic stretching vibrations, indicating the presence of aromatic compounds in bio-oil. Moreover, the acid compounds are represented by the C-O stretching peaks observed between 1210 cm -1 and 1320 cm -1 . The peaks between 1000 and 1200 cm -1 are due to the presence of alcohols, phenols, ethers and esters showing the C-O stretching vibrations.

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

Chemical composition (GC/MS)

GC-MS analysis was carried out in order to determine the component of organic compounds in the bio-oil produced at the optimum pyrolysis conditions. As can be seen in Figure 4, bio-oil produced from algal waste is a very complex mixture, and more than 200 compounds were detected in the bio-oil. When mass spectra were compared to the NIST library data, 30 compounds with more than 1.5 % of the total area (defined by the percentage of the compound's chromatographic area out of the total area) were identified; the results is presented in Table 3. The bio-oil from algal waste pyrolysis was composed of a very complex mixture of organic compounds of 5-20 carbons. It can be seen that the bio-oil was mainly composed of phenols, acids, alkanes, furans, ketones, and alcohols and nitrogen-containing heterocycles (indoles and pyridines). The components of the bio-oil were similar to the liquid product obtained by other researchers (Ferrera-Lorenzo et al., 2014b;[START_REF] Ross | Classification of macroalgae as fuel and its thermochemical behaviour[END_REF]. The most abundant compound Phenols accounted for 24.79 %. These derivatives of phenolic fragments might be derived from the thermal decomposition of protein, which are known as the polyphenolic components in aquatic biomass [START_REF] Ross | Classification of macroalgae as fuel and its thermochemical behaviour[END_REF]. Different types of acids and alkanes were identified, and they mostly converted from carbohydrates degradation. The nitrogen-containing heterocyclic compounds in algal bio-oils, such as indoles and pyridines, were assumed to be derived from protein degradation (Zhou et al., 2010). Among the compositions of bio-oil, Phenol (8.82 area %), Phenol 4-methyl-(13.47 area %), Heptadecane (5.12 area %), n-Hexadecanoic acid (10.96 area %), Hexadecanamide (4.41 area %) showed the highest selectivity. This result is consistent with the FTIR result of bio-oil.

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

1 H-RMN characterization

To have a clearer understanding of the compound distribution of the whole bio-oil, an analysis was carried out using 1 H-NMR. NMR spectra provided complementary functional group information to the FTIR spectrum and the ability to quantify integration areas. The 1 H-NMR spectrum of the bio-oil is shown in Figure 5. The percentages of the proton types that were calculated on the basis of the chemical deviation values obtained from the 1 H-NMR spectra are in Table 4. The most up-field region from 0.5 to 1.5 ppm, represented aliphatic protons that were attached to carbon atoms, at least two bonds, removed from a C=C double bond or heteroatom (O or N). This region contains 32.31% of the protons in bio-oil. The next integral region from 1.5 to 3.0 ppm represents protons of aliphatic carbon atoms that may be bonded to a C=C double bond (aromatic or olefinic) or are two bonds away from a heteroatom (O or N).

These protons contribute with 29.61 % of the protons in the bio-oil. The typical compounds with these functional groups in the region 0.5-3.0 ppm were confirmed by GC/MS and FTIR. The region in 3.0-4.5 ppm contributes 5.99% of the protons in biooil, which represent protons on carbon atoms next to an aliphatic alcohol and nitrogen connected to methylene groups. The region 4.5 and 6.0 ppm represents aromatic ether proton and many of the hydrogen atoms of carbohydrate-like molecules. The value of proton percentage was 6.64 %. The region of the spectrum between 6.0 and 9.5 ppm corresponds to the aromatic portons, aldehyde protons, and also those in heteroaromatics containing oxygen and nitrogen and the content of this region was 25.45 %.

The bio-oil produced by pyrolysis cannot be used as fuel due to its high water and oxygen contents and the presence of unsaturated and phenolic compounds. As a result, Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 bio-oil need to be upgraded or pre-treated to improve their quality before being used as bio-fuel. The compounds identified in the bio-oil from waste algal suggest that pyrolysis can be used to produce bio-oil for various uses, such as in the petrochemical industry and as high added value chemicals, through further treatment.

Bio-char characterization

Elemental composition and ash content

The ultimate analysis, proximate analysis and calorific value of bio-char from the pyrolysis of algal waste are listed in Table 1. The bio-char have high carbon content (52.95 %), moderate oxygen content (38.00 %), low hydrogen content (2.83 %) and high nitrogen content (6.22 %). The ash content is high (around 31,52 %). In comparison to the raw algal waste, the O and H contents decrease in the bio-char due to dehydration, decarbonylation and decarboxylation reactions, which is consistent with the FTIR results. The hydrogen content decreases in the bio-char, probably due to the aromatization of the bio-char and evolution of H 2 , as light molecular hydrocarbons (CH 4 and C 2 ) were formed during the pyrolysis process. The carbon content and HHV make the bio-char from pyrolysis of algal waste acceptable for use as a renewable solid fuel.

FTIR characterization

The bio-char from pyrolysis of algal waste was also characterized by FTIR (figure 2).

Remarkable changes have been found for the FTIR spectra of Bio-char (Figure 2) compared to that of the raw material, which indicated an effective conversion of the waste algal under pyrolysis conditions (temperature of 500 °C and heating rate of 10 °C/min). The O-H stretching vibration at 3600-3100 cm -1 in the FTIR spectra of the bio-Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 char sharply decreased after pyrolysis, probably due to the dehydration of the waste algal together with the release of an amount of water. The bands occurring at 2860-2970 cm -1 , which can be assigned to the C-H alkyl functional groups, were almost absent in the bio-char. The peaks between 1900 and 2300 cm -1 indicate carboxyl and carbonyl groups. Strong peaks which are representative of aromatic C=O and C=C functional groups at 1400 cm -1 as well as a peak at 875 cm -1 which correlates with aromatic C-H stretching. A wide band from 900 to 1200 cm -1 shows aromatic C-O and phenolic O-H functional groups. The peaks between 700 and 900 cm -1 was assigned to aromatic C-H stretching vibrations that indicate the presence of adjacent aromatic hydrogens in biochar. Similar to the results obtained by the Zhou et al. (2010).

The spectrum of bio-char from waste algal suggests the presence of a variety of oxygen functional groups, as well as aromatic carbon groups (bio-char was mainly an aromatic polymer carbon atom). The spectrum correlates well with the elemental analysis, which also revealed a relatively high amount of retained oxygen content.

Scanning electron microscopy

The morphology of raw waste and its bio-char has been studied by scanning electron microscopy (SEM). The obtained photographs for raw waste and its bio-char are shown in Figure 6. From these micrographs, it is clear that the raw waste and its bio-char show different behaviours regarding their morphologies. The morphology of the bio-char shows more void space and higher porosity on its surface, confirming that the produced bio-char has a higher surface area than the raw waste material. This can be attributed to the fact that thermal treatment improves the porous structure of bio-char due to the loss of mass of part of volatiles from the starting algal waste leaving the skeletal structure.

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. ( 2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

Conclusion

In this study, the algal waste had been converted to bio-oil and bio-char by pyrolysis.

The maximum yields of bio-oil and bio-char were approximately 24.1 and 44.01wt%, respectively, at the pyrolysis temperature was 500 °C for heating rate of 10 °C/min. The bio-oil was composed of phenols, acids, alkanes, furans, ketones, and alcohols and nitrogen-containing heterocycles. This preliminary study has shown that the bio-oil cannot be used as bio-fuel, but can be potentially used as a source of value-added chemicals. In addition, the bio-char shows good properties as a solid fuel and as a carbon source for producing carbon materials. prolifera powder in a free-fall reactor. Energy Sources Part Recovery Util. Environ. Eff. 35, 859-867. Zhou, D., Zhang, L., Zhang, S., Fu, H., Chen, J., 2010. Hydrothermal liquefaction of macroalgae Enteromorpha prolifera to bio-oil. Energy Fuels 24, 4054-4061. Zou, S., Wu, Y., Yang, M., Li, C., Tong, J., 2009. Thermochemical

List of Figures:

List of Tables:

Table 1: Proximate and ultimate analysis of algal waste, bio-oil and bio-char.

Table 2: FTIR bands and functional groups of bio-oil obtained at 500°C for 10°C/min.  Waste algal was pyrolyzed to get value added materials: bio-oil and bio-char

Figure 1 :

 1 Figure 1: TGA/DTG of algal waste.

Figure 2 :

 2 Figure 2: FTIR spectrum of algal waste, its bio-oil and bio-char obtained at 500°C for

Figure 3 :

 3 Figure 3: a) The effect of final temperature on pyrolysis products distribution for a

Figure 4 :

 4 Figure 4: GC/MS spectrum of bio-oil obtained at 500°C for 10°C/min.

Figure 5

 5 Figure 5: 1 H-NMR spectrum of bio-oil obtained at 500°C for 10°C/min.

Figure 6 :

 6 Figure 6: SEM micrograph of the algal waste (a) and its bio-char (b).

  Figure 1

  Figure 3:

Figure 4

 4 Figure 4

  Figure 5

  ., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

  Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098 Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

  Catalytic Liquefaction of the Marine Microalgae Dunaliella tertiolecta and Characterization of Bio-oils. Energy Fuels 23, 3753-3758. citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

	Comment

Table 3 :

 3 Chemical composition of bio-oil obtained at 500°C for 10°C/min from GC/MS.

Table 4 :

 4 1 H-NMR analysis results of bio-oil obtained at 500°C for 10°C/min.

Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (

2017

). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

Table 1 :

 1

			algal waste	Bio-oil	Bio-char
	Proximate
	analysis	Moisture	5.04	14.22	4,05
	(wt.%)
		Volatile matter	68.91	86,75	24,70
		Ash	12.09	1,7	31,52
		Fixed carbon	19.00	11,55	43,78
	Ultimate
	analysis	C	35.27	51,12	52,95
	(wt.%)
		H	4.71	5,81	2,83
		N	4.44	4,68	6,22
		S	0.73	1,19	--
		O	54,85	37,2	38.00
	HHV (MJ/kg)		14.98	19.91	23.09
	Atomic	H/C	1,603	1.364	0.639
		O/C	1.166	0.546	0.538
	Empirical formula		CH 1,603 O 1,166 N 0,108	CH 1,364 O 1,546 N 0,078 CH 0,639 O 0,538 N 0,101

Table 2 :

 2 Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

	Frequency range, cm -1	Frequency, cm -1	Group	Class of Compound
	3300-3600	3230	O-H stretching	Polymeric O-H
	3050-2800	2852, 2925, 2960	C-H stretching	Alkanes
	1690-1750	1700	C=O stretching	Ketones, aldehydes, carboxylic acids
	1570-1680	1656	C=C stretching	Alkenes
	1475-1525	1515	C=Cring stretching	Aromatics
	1475-1330	1390, 1411, 1450	C-H deformation	Alkanes
	1280-1200	1260, 1240	C-H stretching	Aromatics
	1000-1200	1026, 1110, 1195	C-O stretching	Alcohols, esters, ethers
	885	885	C-H deformation	Aromatics
	750	750	Adjacent C-H deformation	Aromatics
	696	696	Out of plan =CH deformation	Alkenes
	615	615	Out of plan O-H deformation	Polymeric O-H

Table 3 :

 3 Comment citer ce document : Aboulkas, A., Hammani, H., El Achaby, Bilal, E., Barakat, A., El harfi, K. (2017). Valorization of algal waste via pyrolysis in a fixed-bed reactor: production and characterization of bio-oil and bio-char. Bioresource Technology, 243, 400-408. DOI : 10.1016/j.biortech.2017.06.098

	N°	Retention time (min)	Compounds	Molecular formula	Area (%)
	1	3,17	2-Furanmethanol	C 5 H 6 O 2	1,73
	2	3,94	Ethanone, 1-(2-furanyl)-	C 6 H 6 O 2	2,24
	3	4,91	Phenol	C 6 H 6 O	8,82
	4	5,65	2-Cyclopenten-1-one, 2-hydroxy-3-methyl-	C 6 H 8 O 2	3,2
	5	6,07	Phenol, 2-methyl-	C 7 H 8 O	3,67
			(3S,4R,5R,6R)-4,5-
	6	6,13	Bis(hydroxymethyl)-3,6-	C 10 H 18 O 2	1,66
			dimethylcyclohexene
	7	6,38	Phenol, 4-methyl-	C 7 H 8 O	13,47
	8	6,61	2,5-Pyrrolidinedione, 1-methyl-	C 5 H 7 NO 2	1,37
	9	6,88	2,4-Imidazolidinedione, 3,5,5-trimethyl-	C 6 H 10 N 2 O 2	1,51
	10	7	Maltol	C 6 H 6 O 3	2,97
	11	7,45	Glutarimide	C 5 H 7 NO 2	2,8
	12	7,52	Phenol, 2,4-dimethyl-	C 8 H 10 O	4,26
	13	7,8	Phenol, 4-ethyl-	C 8 H 10 O	3,39
	14	8,44	1,4:3,6-Dianhydro-à-d-glucopyranose	C 6 H 8 O 4	1,66
	15	8,61	3-phenyl-2-butenal	C 10 H 10 O	1,7
	16	8,71	Oxalic acid, 2-isopropylphenyl pentyl ester	C 16 H 22 O 4	1,51
	17	8,93	Benzenepropanenitrile	C 9 H 9 N	2,02
	18	9,25	1H-Indol-4-ol, 3-methyl-	C 9 H 9 NO	1,4
	19	9,71	Indole	C 8 H 7 N	3,08
	20	10,99	1H-Indole, 7-methyl-	C 9 H 9 N	2,27
	21	11,08	Benzeneacetic acid, 4-(1H-1,2,3,4-tetrazol-1-yl)-	C 9 H 8 N 4 O 2	1,66
	22	11,21	3-Isobutyldihydropyrazin-2-one	C 8 H 12 N 2 O	1,8
	23	12,28	4-(4-Methylphenyl)pyridine	C 12 H 11 N	1,4
	24	12,32	Pentadecane	C 15 H 32	1,54
	25	14,66	Heptadecane	C 17 H 36	5,12
	26	16,24	2-Pentadecanone, 6,10,14-trimethyl-	C 18 H 36 O	1,84
	27	16,81	Hexadecanenitrile	C 16 H 31 N	3,63
			5,10-Diethoxy-2,3,7,8-tetrahydro-
	28	17,29	1H,6H-dipyrrolo[1,2-a;1',2'-	C 14 H 22 N 2 O 2	2,9
			d]pyrazine
	29	17,4	n-Hexadecanoic acid	C 16 H 32 O 2	10,96
	30	19,44	Hexadecanamide	C 16 H 33 NO	4,41

Table 4 :

 4

Acknowledgements

The authors would like to thank Pr. Alami Jones, head of MSN department for his valuable assistance for improving the manuscript. The authors gratefully acknowledge the SETEXAM Company in Morocco for providing the algal waste. This work is the result of collaboration between the Faculté polydisciplinaire de Béni-Mellal (Université Sultan Moulay Slimane), INRA Montpellier and the Materials Science and Nanoengineering Department (Mohamed 6 Polytechnic University).


Charles-Henri Bonnard
email: charles-henri.bonnard@ens-rennes.fr

Anne Blavette

Salvy Bourguet

Adrien Charmetant

Modeling of a Wave Farm Export Cable for Electro-Thermal Sizing Studies

Keywords: Submarine export cable, electro-thermal model, wave energy farm

So far, only few studies have addressed the techno-economic optimization of an export cable sizing in the specific case of wave energy farms. However, in these works, the cable current rating is determined based on conservative steady-state conditions regarding the farm current output whereas considering dynamic conditions may be more relevant in the case of wave energy applications. However, this implies developing and using dedicated electro-thermal models, which poses a challenge regarding the determination of the modeling fineness level to be adopted for such studies. Hence, this paper presents several numerical models, the most refined of which is compared with experimental data, as well as well as preliminary cable sizing studies. Contrary to previous works in this field, the fluctuating nature of wave energy is considered here, thus allowing for more realistic results.

Introduction

Over the past decades, wave energy has been shown to have a great potential in terms of electricity generation. Hence, it constitutes a relevant alternative to non-renewable sources of energy. However, the levelized cost of energy (LCOE) is greater for wave energy than for more conventional power sources [START_REF] Kost | Levelized cost of electricity renewable energy techologies[END_REF], [START_REF]International levelised cost of energy for ocean energy technologies[END_REF].

Consequently, significant cost reductions are required for wave energy to become economically attractive and to allow its grid integration on a large-scale. Among the potential options available to reduce the wave energy LCOE, optimizing the electrical infrastructure of wave farms, and especially their cabling infrastructure, was identified as a relevant target in order to reduce capital expenditure.

Based on the experience of the offshore wind energy industry [START_REF]Wind turbine technology and operations factbook[END_REF][START_REF] Gasnier | Technical and economic assessment tool for offshore wind generation connection scheme: Application to comparing 33 kV and 66 kV ac collector grids[END_REF][START_REF] Macaskill | Offshore wind -an overview[END_REF], it is indeed interesting to note that the costs related to the electrical infrastructure, and composed mostly of cabling and substations costs (approx. 50% each), may represent up to 20 % of a wave farm capital expenditure. Hence, a reasonable percentage of cost reduction in this area may lead to a significant decrease in terms of capital expenditure [START_REF] Sharkey | Maximising value of electrical networks for wave energy converter arrays[END_REF][START_REF] Bull | Electrical cable utilization for wave energy converters[END_REF].

However, so far, and to the best of the authors' knowledge, only few studies have addressed the techno-economic optimization of the cabling infrastructure sizing in the specific case of wave energy farms [START_REF] Sharkey | Maximising value of electrical networks for wave energy converter arrays[END_REF][START_REF] Bull | Electrical cable utilization for wave energy converters[END_REF]. In both studies, the cable current rating is determined based on an approximation implying that a wave farm outputs its maximum current in the form of a constant profile, thus implying steady-state conditions. However, this may lead to a highly conservative estimation of a cable current rating in the specific case of wave energy. This power source is indeed highly fluctuating by nature and its variations are reflected in the power output of a wave farm. This can be explained by the fact that most wave energy converters (WECs) are oscillating bodies with limited storage capacities, thus generating a fluctuating current output. Consequently, a farm composed of such devices is also expected to output a fluctuating current profile, which is however potentially reduced thanks to the devices aggregation effect. Hence, determining the current rating of a cable based on more realistic, dynamic conditions could lead to a dramatic decrease regarding its sizing compared to the case where conservative, steady-state conditions are considered, as mentioned in preliminary works by the authors [START_REF] Blavette | Dimensioning the equipment of a wave farm: Energy storage and cables[END_REF][START_REF] Matine | Optimal sizing of submarine cables from an electrothermal perspective[END_REF].

In order to perform such techno-economic optimization studies focusing on the thermal response of a cable to a fluctuating current profile representative of wave energy conditions, dedicated electro-thermal models are required. However, developing such models presents challenges regarding the determination of the modeling fineness level to be adopted for the type of applications considered in this paper. There exist indeed several approaches to determine the thermal response of a cable, each of which presents different performance levels in terms of computational burden and of error level. The less computationally intensive approach is based on relatively simple models described in standards, such as IEC standard 60287-1-1 [START_REF]Electric cables Calculation of the current rating -Part 1-1: Current rating equations (100 % load factor) and calculation[END_REF]. In this document, the current rating is determined based on steady-state conditions where the amplitude of the current input to the cable is considered as constant over time. However, as explained earlier, using the maximum current output by the farm in such an approach is quite conservative in the case of wave energy applications. Although a complementary standard was developed to cover the case of a cycling load [START_REF]Calculation of the cyclic and emergency current rating of cables. Part 1: Cyclic rating[END_REF], it may not be relevant here. This standard includes indeed several approximations which do not allow to study a cable thermal response to a current profile fluctuating at the timescale of seconds.

Alternatively, the finite element method (FEM) is a far more computationallyintensive approach, but from which accurate results can be obtained with a userdefined level of approximation. For instance, a cable may be modeled in two or three dimensions (2D or 3D), and may include either linear or non-linear thermal characteristics for resistivity, specific heat and thermal conductivity. In this paper, the results obtained from different models, presenting different levels of modeling fineness (standard-based/FEM-based, 2D/3D and using linear/nonlinear thermal characteristics in the case of FEM-based models) will be presented. This study is intended to provide preliminary results regarding the level of error as a function of the level of modeling fineness. It is also important to mention that experiments, whose protocol will be described later in the paper, were carried out in order to validate the numerical results.

Beside providing preliminary guidance regarding the modeling fineness, this paper is also intended to present results on preliminary cable sizing studies focusing on two aspects. The first one regards the critical design conditions (either normal or short-circuit ones) for cable design. Both these studies are indeed usually performed at the planning stage for more conventional types of applications to determine which conditions constitute the critical design ones, therefore imposing a lower bound on the cable sizing. The second investigated aspect regards the potential room for improvement concerning the cable sizing when more realistic, dynamic conditions are considered, as opposed to conservative steady-state conditions.

Hence, in order to combine these two objectives, i.e. assess the error level as a function of the modeling fineness level, and carry out preliminary studies on cable sizing, the developed numerical models are used in two case studies which are presented in this paper. The obtained results are used to draw conclusions for each of the two topics considered here.

The rest of the paper is organized as follows: Section 2 presents the different numerical models developed as part of this study. Then, Section 3 details the experiments carried out on a real submarine cable to be used as a benchmark for the results obtained through numerical simulations. Following this, Section 4 describes the two case studies (considering either normal or short-circuit conditions) while Section 5 details the results. Finally, Section 6 concludes the paper.

Numerical models

This section presents in the first subsection the characteristics of the cable considered here. Then, it describes the developed numerical models, which are based either on IEC standards or on the finite element method (FEM).

Power cable characteristics

In this paper, numerical and experimental studies were carried out based on a real, 5.5 meter-long submarine cable sample. This sample was provided as a courtesy of École Centrale de Nantes (ECN). It corresponds to an unused part of the cable which ECN acquired for its SEM-REV offshore test site located off Le Croisic, France [12]. Twenty-four kilometers of this cable are currently installed at the SEM-REV test site and used as an export cable buried 1.5 meter deep in the soil. This export cable follows the green, dotted path shown in Fig. 1. The cable connects an onshore electrical substation (managed by French distribution system operator (DSO) "ENEDIS") to the hub of the SEM-REV test site where three devices (e.g. wave energy converters (WECs) and wind turbines) can be connected simultaneously. A cross-sectional view of a small sample of this 3-phase, 20-kV, 8-MVA cable, whose architecture is typical of static cables, is shown in Fig. 2. It is composed of 3×95 mm 2 copper conductors. For each phase, the conductor is surrounded by a semiconducting polymer screen, a cross-linked polyethylene (XLPE) insulation, a second semiconducting screen, a copper screen and finally an external sheath made of polyethylene (PE). The three phases are arranged in a twisted trefoil shape. The space between each phase and the inner sheath, also called "filler", is made of a combination of bulk PE tubes, PE yarn and air. Optical fibers are also present. The armour constitutes the last layer and is made of galvanized steel wires sheathed with PE. According to the electric insulation used in this cable, the maximum operating temperature of the copper cores is equal to 90 °C. However, it is allowed to reach 250 °C in case of a 5 s-long short-circuit, which is the longest short-circuit duration to be considered for cable design purposes, as recommended in IEC standard 60949 [START_REF]IEC standard 60949, Calculation of thermally permissible short-circuit currents[END_REF]. Finally, the cable current rating I R , based on steady-state conditions, is equal to 290 A. The following sections will present the numerical models (IEC standard-based and FEM-based) of the cable presented in the current section.

IEC standard-based model

IEC standard 60287-1-1 provides the following formula for calculating the temperature rise ∆T above ambient temperature of a three-phase buried cable:

∆T = (I 2 R + 0.5W d )R T 1 + [I 2 R(1 + λ 1 ) + W d ]nR T 2 (1)
+[I 2 R(1 + λ 1 + λ 2 ) + W d ]n(R T 3 + R T 4 )
where I is the current flowing in one conductor, R is the alternating current resistance per unit length of the conductor operating temperature, W d is the dielectric loss per unit length for the insulation surrounding the conductor, R T 1

is the thermal resistance per unit length of between one conductor and the sheath, R T 2 is the thermal resistance per unit length of the bedding between sheath and armour, R T 3 is the thermal resistance per unit length of the external serving of the cable, R T 4 is the thermal resistance per unit length between the cable surface and the surrounding medium, n is the number of load-carrying conductors in the cable, λ 1 is the ratio of losses in the metal sheath to total losses in all conductors, and λ 2 is the ratio of losses in the armouring to total losses in all conductors in the cable. Complementary formulae are provided in IEC standards 60287-1-1 and 60287-2-1 [START_REF]Electric cables Calculation of the current rating -Part 2-1: Thermal resistance -Calculation of thermal resistance[END_REF] to calculate parameters R to λ 2 , and were used for the numerical simulations presented in this paper. The thermal characteristics of the cable-soil system (resistivity, specific heat, and thermal conductivity) were modeled linearly, as proposed in the two standards.

Contrary to the previous works mentioned earlier, where current I was set to the maximum current output of a wave farm, current I is here set to the rootmean-square (RMS) over the simulation period of the RMS AC current profile.

For the sake of illustration, an RMS AC current profile is shown in Fig. 6: it is the RMS value of such a profile to which current I is set here. Considering the RMS value of the RMS current profile is envisaged to be more relevant in terms of temperature estimation than focusing on the maximum current. Hence, the relevance of such an approach will be investigated in the paper.

Finite Element Method models

Contrary to the previous approach based on IEC standards, simulating a model using the Finite Element Method (FEM) can be quite demanding in terms of computing resources, especially for 3D models combining several coupled physics. Hence, such 3D models are usually reduced to 2D models whenever possible. This strategy has been applied here, and two 2D models were developed: one includes linear thermal charateristics for the resistivity, specific heat and conductivity, as in our previous study [START_REF] Matine | Optimal sizing of submarine cables from an electrothermal perspective[END_REF], while the other includes more refined, non-linear characteristics. The non-linear characteristics for the second model were found in [14][15]. These two models are presented in this section and a comparative analysis with the experimental results, intended for validation purposes, is described in Section 5.2. It is important to note that the filler is a mix of air and PE yarn with a usually unknown mixing ratio, thus making more difficult the prediction of its thermal behavior. Hence, simulations were performed considering different values for the mixing ratio, from a filler solely made of PE to a filler composed exclusively of air.

The 2D cable models were developed using the well-known COMSOL Multiphysics ® simulation software [START_REF] Comsol | The COMSOL Multiphysics® website[END_REF]. The thermal problem was implemented using the general heat equation, i.e.

ρ m C p (T ) ∂T ∂t = ∇. (κ(T )∇T ) + Q J , (2)
where ρ m is the mass density of each material, C P is the specific heat, T is the temperature, t is the time, κ is the thermal conductivity and Q J = V ρ e J 2 dV is the total Joule losses inside the cable computed from the electromagnetic part of the model. Term J is the electric current density. The convection in free air was modeled by means of a non-linear law of cooling, and the cooling power Q c is defined as:

Q c = h(T s -T r ) • S • (T s -T r ) , (3)
where T s is the temperature of the cable external sheath surface, T r is the room temperature, S is the external sheath area, and h(T s -T r ) is an effective non-linear convection coefficient based on formulae given in [START_REF] Rohsenow | Handbook of heat transfer[END_REF] and taking into account a long horizontal circular cylinder. The radiative heat transfer Q r has also been considered and follows the Stefan-Boltzmann law, i.e.:

Q r = • σ T • S • T 4 s -T 4 r , (4)
where the emissivity factor was selected as equal to 0.9 in this study, and σ T is the Stefan-Boltzmann constant. The electromagnetic problem has been implemented using Maxwell's equations, i.e.

∇ × H = J , (5)
B = ∇ × A , (6)
E = - ∂A ∂t , (7)
J = σ e E , ( 8
)
where H is the magnetic field, B is the magnetic flux density, A is the vector potential, E is the electric field and σ e is the electrical conductivity.

Experimental setup and protocol

This section presents the experimental setup used as a benchmark for the numerical simulations carried out in this study. Then, the experimental protocol is described.

Experimental setup

As mentioned earlier, experiments were performed using a 5.5 meters-long sample of the SEM-REV export cable. In order to avoid any thermal effect from the ground during our experiments, the cable was installed in free air 1 m above the floor as presented in Fig. 3. A voltage-controlled current source was used to power the cable. It is designed to reach a maximum current of 900 A in steady-state (AC or DC) in a single-phase configuration [18][19]. Using it as a three-phase power source limits the maximum current value to 3 × 300 A.

Experimental protocol

The characteristics of the three cases considered for the experiments are shown in Table 1. In Cases 1 and 3, the amplitude of the current profile is constant. They were introduced to provide benchmark values for the numerical computation of the losses in DC and AC, as well as for the correct evaluation of the heat transfer from the conductor to the surrounding air. On the contrary, in Case 2, two variable, pulsed profiles, shown in Fig. 4, are used. The first one is used to power a single phase while in the second scenario of Case 2, all temperature of the powered phase(s) over time, using the temperature dependance of the copper core resistivity ρ e , which can be expressed as [START_REF]Electric cables Calculation of the current rating -Part 1-1: Current rating equations (100 % load factor) and calculation[END_REF]:

ρ e (T ) = ρ 0 × [1 + α (T c -T 0 )] , (9)
where ρ 0 = 1.724 × 10 -8 Ω.m, α = 3.93 × 10 -3 K -1 is the temperature coefficient of copper, T c is the core temperature in K and T 0 = 293.15 K is the reference temperature for which α is specified. The time-resistance R of the powered phase was evaluated using a classical four-point probes method with voltage and current measurements. The core cross-section, the twisting pitches of both strands and phases, directly impact the real length of the copper. Thus, using R and considering all the physical parameters that influence the core resistance, we were able to determine its resistivity ρ e . Once the value of ρ e is calculated, we were able to get back to the conductor core temperature by using Equation 9. It is also worth mentioning that the cable was powered during several hours prior to the experiments so that it had reached steadystate conditions when the monitoring phase started.

Case studies description

This section details the two case studies performed in order to evaluate which type of conditions (normal or short-circuit) constitutes the critical design In both case studies, and similarly to the physical installation at the SEM-REV test site, the cable is considered as buried 1.5 m deep under the sea bed.

The boundary conditions depicted in Fig. 5 were used in the thermal problem.

The ambient temperature for both the sea and the soil was selected as equal to 12 °C. This is typical of sea temperature conditions in wave energy abundant northwestern Europe [START_REF] Berx | Climatology of surface and near-bed temperature and salinity on the north-west European continental shelf for 1971-2000[END_REF].

Case study 1: normal conditions

A sea-state with a relatively high energy level is considered, as it presents a significant wave height H s equal to 6 m and a peak period

Case study 2: short-circuit conditions

Short-circuit conditions must be taken into account in cable design, and in particular regarding its sizing. Under such conditions, the core temperature increases rapidly during a short period of time. However, it must remain below a maximum allowed limit, e.g. 250 °C for XLPE electrical insulation [START_REF]IEC standard 60502, Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV)[END_REF] and a lower thermal limit of 160 °C for the sheaths that are mainly made of PE and PVC [START_REF] Pays | Câbles de transport d'énergie -Technologies, Caractéristiques[END_REF]. In this case study, short-circuits were considered to occur once an equilibrium state, corresponding to this of the 20 WECs scenario in Case study 1, has been reached.

Note that the electrical grid architecture of a WEC farm may be expected to be very similar to this of offshore windfarms equipped with Type 4 wind turbines using fully rated back-to-back AC/DC/AC converters [START_REF] Anaya-Lara | Offshore Wind Energy Technology[END_REF]. Such electronic interface allows to limit the fault current to a value that is barely above the rated current [START_REF] Walling | Current contributions from type 3 and type 4 wind turbine generators during faults[END_REF]. Based on this observation, the contribution of the WEC farm to the short-circuit current can be neglected. It is therefore assumed that the magnitude of the fault current I SC depends only on the characteristics of the upstream power network. The latter was modeled using a simple Thevenin equivalent circuit with a perfect voltage source, and with an impedance Z U = R U + jX U in series, where R U is the equivalent resistance of the grid and X U is its reactance. Simulations were performed for short-circuit current values I SC ranging from I SC = 5I R to I SC = 30I R , which correspond respectively to a weak grid and to a strong grid [START_REF] Glover | Power System Analysis and Design[END_REF]. The fault current I SC was calculated considering the steady-state fault current and the DC offset current, i.e.

I SC = E U √ 2 Z U sin(ωt -φ) + sin φ • e - R U L U t , (10)
where E U is the phase-to-phase voltage of the electrical network, φ is the phase shift between voltage and current such that φ = tan -1 X U R U . An X/R ratio equal to 3 is representative of a weak grid whereas a ratio equal to 20 can be considered as representative of a strong grid [START_REF] Glover | Power System Analysis and Design[END_REF][START_REF] Blavette | Grid integration of wave energy & generic modelling of ocean devices for power system studies[END_REF]. Although 3-phase short-circuits are usually the most critical cases, it is also important to consider single-phase short-circuits, as their consequences may, under certain conditions, be worse than for the former. For instance, an internal defect in the cable may lead the current to flow from the conductor directly to its copper screen which is grounded on its extremity. However, the cross-section of the core is greater than this of its copper screen (they are equal to 95 mm 2 and 16 mm 2 respectively for the cable considered in this study). Then, it is expected that the copper screen temperature increases faster than the core temperature for a given fault current. However, the copper screen temperature must still remain below the maximum allowed limit to prevent any excessive, global damage of the dielectric insulation. Thus, in this paper, two short-circuit scenarios were considered: a three-phase short-circuit scenario and a single-phase short-circuit scenario where a conductor is connected directly to its copper screen, as described previously.

Results

This section describes the results obtained for the two case studies performed for normal and short-circuit conditions. Then, it describes the results related to the modeling fineness analysis.

Case studies results

Case study 1 (i.e. considering normal conditions) was performed using the three different numerical models described in Section 2 while Case study 2 (i.e. considering short-circuit conditions) was performed using only the 2D FEM model including non-linear thermal characteristics. This model, as it will be detailed in Section 5.2.1, presents results similar to the experimental results and is therefore assumed as a relevant benchmark for the other two numerical models (i.e. IEC standard-based, and 2D FEM model including linear thermal characteristics) for the comparative analysis on modeling fineness described in Section 5.2.2.

Case study 1: normal conditions

The results corresponding to the core temperature simulations can be seen 320 in Fig. 7. In this section, only the results corresponding the non-linear 2D FEM model (referred to as "FEM + non-linear data" in the figure) will be discussed, and compared to the rated current I R . The results corresponding to the other two models will analyzed as part of the comparative analysis on modeling fineness in Section 5.2.2.

It can be observed that, despite the high current peaks generated by the WEC farm (e.g. up to 2.5 times the rated current I R when the 20 WECs farm is considered), the thermal inertia of the whole system composed by the cable and the soil acts as a strong, natural damper which reduces the amplitude of the cable core temperature fluctuations to 7 °C only. Besides, still in the 20 WECs farm case, it can be observed that the thermal constraints are still satisfied as the core temperature does not exceed the maximum operating temperature of 90 °C.

This confirms that significant current peaks may be injected in a submarine export cable without impacting the cable nor its environment, at least from a thermal perspective. However, it is also important that the surrounding shortcircuit protection system (e.g. circuit breakers) is also properly designed to avoid any undesired shedding.

The results also show that the operating maximum temperature of 90°C is reached for the 20 WECs farm, whose RMS current is equal to 315 A RM S , as mentioned in Section 4.1. This means that a current profile whose RMS value is 9% greater than the rated current I R can be safely injected into the cable while still satisfying the thermal constraints. This figure needs of course to be refined through an extensive analysis, including different sea-states for instance.

However, this study confirms that a wave farm export cable may be sized to a dramatically lower value than the maximum current output by the farm (as considered in other works), thus leading to potentially significant savings.

Case study 2: short-circuit conditions

As mentioned earlier, Case study 2 is composed of two studies: one deals with a three-phase short-circuit while the other focuses on a single-phase shortcircuit. Both studies were performed using the non-linear 2D FEM model.

Three-phase short-circuit. According to IEC standard 60949 [START_REF]IEC standard 60949, Calculation of thermally permissible short-circuit currents[END_REF], a fault duration of up to 5 seconds should be considered for cable design purposes. During this time, the cable cores and screens temperatures must remain below a maximum allowed limit to prevent any excessive damage of the dielectric insulation. The results of this study are shown in Fig. 8. It may be observed that the maximum fault current that the cable is able to withstand for the specified duration of 5 seconds is equal to 25 times the rated current I R . When the fault current is equal to 30 times the rated current, the cable temperature increases indeed to over 250 °C in about 3.5 seconds, thus failing to meet the requirements established in IEC standard 60949. However, it may be important to mention as well that not meeting this requirement does not lead automatically to an excessive cable damage, as it is expected that protection schemes would have triggered the breakers in a shorter amount of time. For instance, in the case where the short-circuit fault current is sufficiently high, the primary protection system can usually clear the corresponding fault in approximately 200 ms.

I SC /I R ratio Time to reach T (s) T =250 • C T =200 • C T =150 • C T =120 • C T =90 • C
Longer fault duration may be permitted if they are handled by the back-up protection system. According to [START_REF] Dorison | Modélisation et dimensionnement des liaisons souterraines. Tome 2 : Dimensionnement thermique[END_REF], fault durations range often between 0.5 s and 1 s, which is significantly shorter than the duration of 5 s recommended in IEC standard 60949 and which, therefore, may be considered as quite conservative. Single-phase short-circuit. The results corresponding to the single-phase short-circuit are shown in Fig. 9. They represent the copper screen temperatures, as opposed to the core temperatures which were presented in the previous section. The curves are similar to these presented in Fig. 8, which was expected since adiabatic conditions can almost be considered. It may be observed that, as expected, the copper screen is the weak point of the cable under the conditions considered in this study. This stems from a lower maximum allowed limit of 160 °C due to the neighboring sheath material (PE), and to the smaller cross-section of the copper screen. Under these conditions, the cable is only able to withstand single-phase fault currents of up to 6 times the rated current for the specified duration of 5 s. This may impose single-phase short-circuits as the critical design conditions if this scenario is to be included in the cable sizing requirements which, however, do not seem to be usually the case.

T =160 • C T =140 • C T =120 • C T =105 • C T =90 • C

Summary

As described in Sections 5.1.1 and 5.1.2, a single-phase short-circuit between a conductor and its copper screen would represent the critical design conditions for the cable sizing. However, this scenario does not seem to be usually taken into account in cable sizing requirements. If it is not, the results of the threephase short-circuit scenario showed that the cable could withstand up to 25 times its rated current I R . In terms of short-circuit level at 20 kV, this represents approximately 250 MVA and corresponds to a medium strength grid [START_REF] Blavette | Grid integration of wave energy & generic modelling of ocean devices for power system studies[END_REF]. Hence, the three-phase short-circuit may constitute the critical design conditions in terms of cable sizing for regions where the grid is relatively strong (e.g. in the WaveHub (UK) [START_REF]WaveHub test site[END_REF] and bimep (Spain) [START_REF]Bimep test site[END_REF] test sites areas), whereas for weaker grids (e.g. in the AMETS test site area (Ireland) [START_REF]AMETS test site[END_REF]), the cable sizing may be limited by the normal conditions. To conclude this section, it may, however, be important to mention as well that two other criteria, which were out of the scope of the presented study, namely the voltage drop along the cable and the Joule losses within the cable, must also be considered in the cable sizing requirements and may also constitute the critical design conditions. Hence, further work should be performed on the compliance to these criteria.

Numerical modeling fineness analysis

As described in the introduction, one of the objective of this paper is to present a quantitative assessment of the error level between the three different numerical models presented here. This comparative analysis is detailed in the second part of this section while the first part describes the comparative analysis between the non-linear 2D FEM model and the experimental results.

Comparison of the non-linear 2D FEM model with the experimental results

As mentioned previously, 3D FEM models are computationally-intensive, and especially those combining different physics, as it is the case here. Hence, they are reduced to 2D models whenever possible. In this section, the results of a comparative analysis between the experiments and the 2D FEM model including non-linear thermal characteristics are detailed. This analysis was intended to validate the relevance of using a 2D model instead of a more computationally intensive, 3D one. It may be recalled that the mixing ratio between the filler in the air being unknown, simulations had to be performed for several values of this ratio.

Case 1: steady-state DC current. The temperature results are shown in Table 2 (for the core temperature) and in Table 3 (minimum and maximum temperatures for the external sheath). As expected, a filler solely made of PE seems to slightly underestimate the conductor core temperature while a filler solely composed of air shows an overestimated temperature. Even if this has to be refined with additional experiments, the temperature simulated with the mixed filler matched with the expected results, i.e. the core temperature is only slightly higher than the measurements. Based on this observation, a mixed filler was retained in the 2D FEM models (linear and non-linear), with thermal conductivity κ f (T ) = 0.5 × κ P E (T ) and thermal capacity C f (T ) = 0.5 × C pP E (T ). The simulation results show nevertheless good agreement with the experiments. The slight observed error (less than 2 °C) is assumed due to be mainly due to the fact that the edge effects were neglected. # FEM simulation results.

The temperature distribution around the cable external sheath, where the thermocouples are positioned, as obtained from both the experimental data and from the numerical simulations, is presented in Fig. 10. Once again, good agreement is observed between the experimental and the simulated results. electrical and thermal problems. Regarding passive cooling, the FEM model is able to correctly reproduce the temperature decrease, which suggests that the heat transfer from the copper core to the external sheath is also well simulated.

Such observations, in addition to those already discussed, reinforce the validity of the non-linear 2D FEM model. This observation applies to the entire range of typical operating temperatures that should remain below 90°C under normal conditions (as opposed to short-circuit conditions). One can remark the slight differences which arise when the temperature reaches 80 °C. These can be explained by the physical properties of the XLPE insulation material that shows strong non-linearities of the thermal resistivity and of the heat capacity between 80 °C and 120 °C [START_REF] Qi | Thermal and mechanical properties of EPR and XLPE cable compounds[END_REF]. However, the temperature difference does not exceed 2.5 °C. Hence, it was not deemed necessary to adjust or to refine the thermal properties of XLPE using, for example, a differential scanning calorimeter (DSC) and a guarded hot plate (GHP) method.

Concerning the external sheath temperature presented in Fig. 13, it can be observed that the model seems to overestimate the temperature (up to 2 °C).

However, the overall temperature trend over time is very similar between the experiments and the simulations. Hence, these results suggest that the simulations do not fully reflect the measurements in terms of magnitude. As already 0.5 mentioned earlier, this error may stem from the fact the edge effects at each extremity of the cable were assumed negligible, thus resulting in an overestimation of the computed power per unit length compared to the experiments.

Case 3: steady-state AC current. This third study focuses on the characterization of the cable under AC steady-state conditions. The main objective of this test is to verify that the model accurately predicts the losses that, once again, are needed to compute the correct heat flux in the cable and its temperature evolution. This approach allows to evaluate the losses simulations due to the skin effect, as well as the screen and armour losses. In this case study, all the three phases were powered. Due to the rating limitations of the experimental current source, the injected current was approximately equal to 200 A RM S per phase. Such current level is obviously lower than the rated current I R but this does not prevent from performing a comparative study between the FEM simulations and the experimental measurements. Table 4 shows the results obtained with the non-linear 2D FEM model and the experimental measurements, as well as some available manufacturer data (referred to as MD). It can be observed that the differences between all these data types are reasonable.

Summary. Despite some inaccuracies that have been observed between the non-linear 2D FEM model and the experimental measurements, the results indicate that considering a 2D model is sufficiently precise for performing the electro-thermal analyses described earlier in this paper. For example, it was observed that the 2D FEM model provided good results for the core temperatures as well as for the external sheath temperature. It is worth mentioning that the differences between our simulations and the measurements on our short cable are assumed to be due to the fact that edge effects were neglected in the 2D FEM model. Note that such differences would have been drastically reduced considering a longer cable, which would be the case in a typical WEC farm installation, where cable lengths of few hundreds of meters to few tens of kilometers are used. Based on this assumption, we can neglect edge effects and axial heat flows and assume that the non-linear 2D FEM model is sufficiently accurate to estimate the cable electro-thermal behavior that could be installed in a WEC farm. Based on these observations, the model presented in this pa-

Comparison between the three cable numerical models

In Fig. 7, the IEC standard-based model is referred to as "IEC method", the linear 2D FEM model as "FEM + IEC data", as it may be recalled that it includes the linear thermal characteristics provided in IEC standards 60287-1-1 and 60287-2-1, and the non-linear 2D FEM model as "FEM + non-linear data".

Regarding the difference between the IEC standard-based model and the non-linear 2D FEM model, it is important to mention that the formulae proposed in the IEC standards considered here were identified as leading potentially to a significant underestimation of the cable temperature, even in the case where a constant current profile is considered [START_REF] Sedaghat | Thermal analysis of power cables in free air: Evaluation and improvement of the IEC standard ampacity calculations[END_REF]. In this paper, differences up to approximately 5°C could be observed. Hence, under the conditions considered in our case study, underestimations may have been expected, which is confirmed by our results. Quantitatively-speaking, the differences observed between the results obtained from IEC standard-based model and the average temperature obtained from the non-linear 2D FEM model are equal to approximately 6 °C, 10 °C and 5 °C when wave farms composed of 15, 20 and 25 WECs respectively are considered. This represents approximately 6% to 11% of the maximum operating temperature (90°C) and can therefore be qualified as very significant. In addition, this suggests that the margin of error identified in [START_REF] Sedaghat | Thermal analysis of power cables in free air: Evaluation and improvement of the IEC standard ampacity calculations[END_REF] might be further increased when other conditions, such as the ones considered in our study, are selected. Of course, even more important differences ranging from 9 °C to 15 °C can be observed when the maximum temperatures observed with the nonlinear 2D FEM model are considered. Hence, these results show that the IEC standard-based model focusing on the RMS value of the RMS current profile generally underestimates (very) significantly the core temperature: this error ranges between 10% and 17% of the maximum operating temperature (90°C).

Hence, such a model must be improved if it is intended to provide relevant results for cabling studies.

It can also be observed that the three temperature profiles show significant differences with discrepancies of up to 15 °C. The results of the FEM simulations show that using non-linear material properties (red dashed profile in Fig. 7) can have a very significant impact on the calculated core temperatures. This discrepancy may be as high as 7 °C if the targeted operating temperature lies in the zone where the cable thermal characteristics are highly non-linear, e.g.

between 80 °C and 120 °C in our case, which automatically reduces the heat transfer from the core to the external sheath. Otherwise, if the target operating temperature is outside the highly non-linear zone, the discrepancy between the linear and non-linear FEM models may almost become negligible and therefore, linear thermal characteristics may be used. It is also interesting to note that the simulated temperatures may be either under-or overestimated by the linear 2D FEM model, as shown in Fig. 7b and Fig. 7c respectively. In addition, compared to the IEC standard-based model, the 2D FEM models presented in this paper returned higher temperatures for the copper cores. For example, considering a 20 WECs farm, the maximum temperatures are equal to 76 °C when the IEC standard-based model is used, 84 °C when the linear 2D FEM model is used and 90 °C when the non-linear 2D FEM model is considered. This phenomenon may stem from the measure considered here (i.e. the RMS value of the RMS current profile), but also from the fact that, as already mentioned earlier, IEC standard 60287-1-1 generally underestimates temperature (very) significantly. In any case, adopting an approach which underestimates the core temperature is of course to be avoided to prevent any risks of overheating. It is therefore important to either develop an enhanced IEC model, or to use a FEM model. However, a FEM model is by nature much more computationally intensive which may raise computing time issues if an optimization algorithm requiring a large number of iterations using the electro-thermal model is selected.

Hence, further work will be undertaken regarding the level of modeling fineness required for such optimization studies, and especially on the development of a suitable electro-thermal cable model for computationally-intensive optimization studies.

Conclusion

This paper described preliminary cable sizing studies focusing on the electrothermal response of a submarine cable to be used as an export cable in a wave energy farm. It was shown that a current profile whose RMS value is 9% greater than the rated current I R , and whose maximum value is equal to approximately 2.5 times this rated current, may be safely injected in the cable without violating the thermal constraints. Conversely, this implies that a wave farm export cable can be safely sized to a dramatically lower value than the maximum current of the farm, thus leading to potentially significant savings. Hence, considering more realistic, dynamic conditions at the wave farm planning stage is recommended. It was also shown that short-circuit conditions may become the critical design conditions for areas with a short-circuit level of at least 250 MVA which, however, may not be the case for a large share of wave energy abundant regions such as the west of Ireland. As for the latter, normal conditions (i.e. without short-circuit) constitute the critical design conditions. The paper also focused on the level of numerical modeling fineness required for cable sizing studies.

A comparative analysis was carried out between three cable numerical models proposed in this study, the most refined of which was validated against experimental data. It was concluded that the proposed IEC standard-based model led to an important temperature underestimation ranging between 10% and 17% of the maximum allowed temperature (90°C) and needed to be enhanced to be fully relevant in wave energy applications. Hence, using a FEM-based model, including potentially non-linear thermal characteristics (if the targeted temperature is within the highly non-linear zone of these characteristics) seems to remain the safest option. However, the computational burden linked to using FEM-based models may represent an issue for certain optimization studies where a large number of iterations is required. Investigating further this issue, developing a suitable electro-thermal cable model, and testing its performances, both in terms of error level and computational burden, will be the focus of future work. Following this, detailed techno-economic optimization studies on the sizing of a wave farm export cable will be carried out.

Figure 1 :

 1 Figure 1: Map indicating the localization of SEM-REV test site. The export cable connects the SEM-REV offshore hub to an onshore substation and to the local network belonging to French DSO Enedis (red and dark green paths). Figure modified, courtesy of École Centrale de Nantes [12].

Figure 2 :

 2 Figure 2: Cross-sectional view of a small cable sample. Its architecture is typical of submarine export cables.

Figure 3 :

 3 Figure 3: Photograph of the instrumented cable installed in free air

Figure 4 :

 4 Figure 4: Pulsed DC current profiles applied in Case 2.

Figure 5 :

 5 Figure 5: Illustration of the boundary conditions

  T p equal to 9 s. A wave farm composed of 15, 20 or 25 WECs (three configurations are covered) is considered here. Its devices are identical heaving buoys controlled passively, as detailed in[START_REF] Kovaltchouk | Influence of control strategy on the global efficiency of a direct wave energy converter with electric power take-off[END_REF]. The current profile injected into the cable, when the 20

Figure 6 :

 6 Figure 6: Elementary sequence of the periodic current profile amplitude (RMS) for a 20 WECs farm used for Case study 1

  data FEM + non-linear data (a) 15 WECs.

  data FEM + non-linear data (b) 20 WECs.

Figure 7 :

 7 Figure 7: Core temperatures simulated with the three numerical different models and for three different numbers of WECs

Figure 8 :

 8 Figure 8: Core temperature profiles for different three-phase short-circuit levels.

5 I

 5 SC /I R ratio Time to reach T (s)

Figure 9 :

 9 Figure 9: Screen temperature profiles for different single phase short-circuit levels.

Figure 10 :

 10 Figure 10: External sheath temperature: experimental and numerical results

Case 2 :Figure 11 :

 211 Figure 11: Measured and simulated temperature profiles (Case 2, 1 powered phase)

Figure 12 :Figure 13 :FEM model and 3 )

 12133 Figure 12: Measured and simulated temperature profiles (Case 2, 3 powered phases)

Table 1 :

 1 Characteristics of the three cases considered for the experiments

	Case	Current profile	Amplitude	Number of powered phases
	1	Steady-state DC current	295 A	1
	2	Pulsed DC current	150-600 A	1, 3
	3	Steady-state AC current (50 Hz) 200 A RM S

Table 2 :

 2 Core temperature of the powered phase for Case 1

	Value (°C) Description
	54.1 *	Temp. derived from the 4-point probes method
	53.5 #	Temp. with full PE filler
	61.5 #	Temp. with full air filler
	54.8 #	Temp. with mixed filler

* Experimental measurements.

Table 3 :

 3 Maximum and minimum temperatures of the external sheath

	for Case 1
	Value MIN / MAX (°C) Description
	28 / 34 *	Temp from TCs measurements
	29 / 35 #	Temp. with full PE filler
	29 / 36 #	Temp. with full air filler
	29 / 35.5 #	Temp. with mixed filler

* Experimental measurements.

# FEM simulation results.

Table 4 :

 4 Experimental measurements, FEM simulation results and manu-

	facturer data (MD) (Case 3)
	Parameters	FEM Exp. * MD Description
	P (W/m)	25.04 24.68	-	Total power losses a
	R (µΩ/m)	195 201 b 196.4 Resistance of a phase c
	L (nH/m)	445	411	400 Inductance
	P cores (W/m)	24.55	-	-	Losses in copper cores c
	P armour (W/m) 0.07	-	-	Losses in the armour
	P screens (W/m) 0.46	-	-	Losses in copper screens

* Experimental measurements in steady-state. Mean value.

a The total power was divided by the cable length.

b Total equivalent resistance of one phase of the cable, including skin effects in the conductor cores, screens losses and armour losses. c Resistance values given for a temperature of 20 °C per is deemed valid, and it was considered as a benchmark for the two other numerical models, i.e. the IEC standard-based model and the linear 2D FEM model. It is however important to recall that the validity domain of the model, in terms of temperature, does not exceed 90°C: this model cannot thus be qualified as experimentally validated for short-circuit studies. Further experimental work focusing on high temperatures should therefore be carried out, which was however impossible to do as part of this study, due to the experimental means limitations.

Acknowledgment

The research work presented in this paper was conducted in the frame of the EMODI project (ANR-14-CE05-0032) funded by the French National Agency of Research (ANR), and continued in the frame of the BlueGrid project, funded

by the Brittany Regional Council. Complementary funding from ENS-Rennes was also provided. All these organizations are greatfully acknowleged. It is worth mentioning that this work would not have been possible without the help of École Centrale de Nantes that manages the SEM-REV test site and provided a sample of their export cable. The authors would also like to thank Thomas Soulard (LHEEA lab., École Centrale de Nantes), Didier Trichet, Guillaume Wasselynck, Jean-Christophe Olivier and Franck Judic (all with the IREENA lab., Université de Nantes) for valuable discussions and occasional assistance.