Maxime Hervy

Damien Remy

Anthony Dufour

Guillain Mauviel
email: guillain.mauviel@univ-lorraine.fr

Air-blown gasification of Solid Recovered Fuels (SRFs) in lab-scale bubbling fluidized-bed: Influence of the operating conditions and of the SRF composition

est destinée au dépôt

Introduction

Nowadays, the worldwide MSW generation is around 1.3 billion tons per year, and is expected to reach 2.2 billion tons per year by 2025 [1]. Despite the recent progresses in waste management, the collection, recycling and valorization of waste still have to be strongly improved. Indeed, around 47 % of the wastes generated in EU are disposed in landfill sites [2], leading to air and soil pollution. In order to manage the increasing worldwide generation of municipal solid wastes, new solutions must be developed. Thermal treatment plants, such as incineration, are essential for the management of municipal wastes [START_REF] Brunner | VI.3 -Thermal waste treatmenta necessary element for sustainable waste management[END_REF][START_REF] Porteous | Why energy from waste incineration is an essential component of environmentally responsible waste management[END_REF]. In a comprehensive review, Arena summarized the main advantages of thermal treatments, including: (a) the reduction of waste mass and volume leading to significant saving of land compared to landfilling, (b) the destruction of contaminants, or (c) the concentration of inorganic species in the ashes [START_REF] Arena | Process and technological aspects of municipal solid waste gasification. A review[END_REF]. Incineration is the most known and optimized thermal process as it is operated at industrial scale for many years. However, gasification process appears as a promising way for waste valorization due to the numerous applications existing for the gasification gas, named syngas. While flue gas from combustion can be valorized solely by transferring its thermal energy to heat carriers (typically steam), the syngas can be used as a fuel in high efficiency processes such as gas engine, gas turbine, fuel cell, or as a precursor for liquid fuel synthesis (via the Fischer-Tropsch reaction) and chemicals production (methanol). Another advantage of gasification is that the syngas can be valorized under different forms in other times and places, while the heat produced by combustion must be consumed directly.

Solid recovered fuels (SRFs) consist of a mixture of non-hazardous solid wastes, such as plastics, textiles, tires, paper and carton, biomass waste, or sludge. SRFs are very complex and heterogeneous materials, and the fraction of each component can vary significantly depending on the waste origin, the season, the waste separation plant, and the SRF production technique. SRFs represent a significant waste resource, estimated at 90 million tons per year in France. The production of energy from the nonrecyclable fraction of the SRF thus appears as an attractive solution for waste management. The high diversity of SRFs chemical composition does not allow to precisely define the nature of this fuel, which makes difficult the development of valorization processes. In an attempt of clarification, a classification was established by a French professional organization of recycling companies (FEDEREC). SRFs are classified into four classes depending on the standards defined for the following parameters: lower heating value; density; particle size; halogen compounds concentration; sulfur, nitrogen and ash contents. A better definition of SRF is expected to facilitate the development of specific valorization routes having better energy efficiency than the actual use of SRF as fuel in cement kiln.

Gasification consists of a partial oxidation of the solid fuel at high temperature (800-1000 °C) using an oxidizing agent (air, steam, O2 or CO2). The solid fuel is mainly decomposed into syngas, a mixture of partially oxidized species (H2, CO, CO2, CH4, CnHm) having high calorific value. Gasification process has been intensively investigated for biomass valorization, but the presence of pollutants in the syngas (such as tar, acid gases, and particulate matter) compromises its valorization [START_REF] Milne | Biomass Gasifier Tars: Their Nature, Formation and Conversion[END_REF].

Different gasification technologies have been developed. Among them, fluidized bed reactor appears as the most suitable for medium-size processes (1 to 100 MW), due to the efficient flow mixing between reactants, the carefully controlled temperature, the high heat transfer performance, and the large operating flexibility allowing to use different kinds of fuels, including biomass and solid wastes [START_REF] Ramos | Co-gasification and recent developments on waste-to-energy conversion: A review[END_REF][START_REF] Sansaniwal | Recent advances in the development of biomass gasification technology: A comprehensive review[END_REF][START_REF] Couto | From laboratorial to pilot fluidized bed reactors: Analysis of the scale-up phenomenon[END_REF].

Air-blown bubbling fluidized bed was proved to efficiently convert different wastes in syngas: meat waste and wastewater treatment sludge [START_REF] Campoy | Gasification of wastes in a pilot fluidized bed gasifier[END_REF][START_REF] Lee | Experimental investigation of sewage sludge solid waste conversion to syngas using high temperature steam gasification[END_REF], tires [START_REF] Karatas | Experimental results of gasification of waste tire with air in a bubbling fluidized bed gasifier[END_REF][START_REF] Xiao | Low-temperature gasification of waste tire in a fluidized bed[END_REF], poultry fuel [START_REF] Gregorio | The effect of ash composition on gasification of poultry wastes in a fluidized bed reactor[END_REF], plastic wastes [START_REF] Mastellone | Co-gasification of coal, plastic waste and wood in a bubbling fluidized bed reactor[END_REF][START_REF] Arena | Energy generation by air gasification of two industrial plastic wastes in a pilot scale fluidized bed reactor[END_REF], municipal solid waste [START_REF] Couto | Assessment on steam gasification of municipal solid waste against biomass substrates[END_REF][START_REF] Hu | Co-gasification of municipal solid waste with high alkali coal char in a three-stage gasifier[END_REF], biomass waste [START_REF] González-Vázquez | Comparison of the gasification performance of multiple biomass types in a bubbling fluidized bed[END_REF][START_REF] Silva | Combining a 2-D multiphase CFD model with a Response Surface Methodology to optimize the gasification of Portuguese biomasses[END_REF], and solid recovered fuels [START_REF] Dunnu | The solid recovered fuel Stabilat®: Characteristics and fluidised bed gasification tests[END_REF][START_REF] Pinto | Gasification improvement of a poor quality solid recovered fuel (SRF). Effect of using natural minerals and biomass wastes blends[END_REF]. Olivine, dolomite, and sand are the most frequently used bed materials in fluidized bed reactor. Sand can be used as bed material to ensure the fluidization, but has insignificant catalytic activity in tar cracking reaction.

To improve the gasification efficiency and the syngas quality, catalysts can be used as bed materials. Dolomite is the low-cost catalyst having the highest catalytic activity in tar reforming reactions [START_REF] Pinto | Gasification improvement of a poor quality solid recovered fuel (SRF). Effect of using natural minerals and biomass wastes blends[END_REF]. Dolomite can also prevent bed agglomeration when the fuel gasified is rich in alkaline and alkaline earth metals [START_REF] Corella | Olivine or Dolomite as In-Bed Additive in Biomass Gasification with Air in a Fluidized Bed: Which Is Better?[END_REF]. The main drawback of dolomite consists in its attrition tendency which significantly increases the dust pollution in syngas from fluidized bed. On the contrary, olivine presents strong mechanical properties despite relatively low catalytic activity in tar cracking reactions [START_REF] Pinto | Gasification improvement of a poor quality solid recovered fuel (SRF). Effect of using natural minerals and biomass wastes blends[END_REF][START_REF] Devi | Catalytic decomposition of biomass tars: use of dolomite and untreated olivine[END_REF]. Olivine is often used as bed material in fluidized bed reactors, which reduces the dust load in syngas, and slightly decreases the tar content. Other types of materials have been tested, and their pros and cons are reported in the comprehensive review of Shen et al. [START_REF] Shen | By-products recycling for syngas cleanup in biomass pyrolysis -An overview[END_REF].

At industrial scale, the gasifiers are autothermal, but it is not the case at lab-scale because the walls of small reactors must be heated to balance the heat loss. As a consequence, temperature and ER are independent conditions, whereas temperature depends on ER at industrial scale. In the past few years, SRFs gasification was increasingly studied in lab-scale fluidized beds, and the effect of the operating conditions on gasification behavior was investigated. Increasing equivalence ratio (ER) was proved to promote the oxidation reactions which increases both the syngas yield and the carbon conversion [START_REF] Recari | Gasification of two solid recovered fuels (SRFs) in a lab-scale fluidized bed reactor: Influence of experimental conditions on process performance and release of HCl, H2S, HCN and NH3[END_REF][START_REF] Berrueco | Experimental Investigation of Solid Recovered Fuel (SRF) Gasification: Effect of Temperature and Equivalence Ratio on Process Performance and Release of Minor Contaminants[END_REF]. Similar results were obtained with the gasification of other wastes [START_REF] Campoy | Gasification of wastes in a pilot fluidized bed gasifier[END_REF][START_REF] Arena | Fluidized bed gasification of industrial solid recovered fuels[END_REF]. Oxidation reactions decreased the content of H2, CO, CH4 and light hydrocarbon compounds [START_REF] Devi | A review of the primary measures for tar elimination in biomass gasification processes[END_REF][START_REF] Arena | Fluidized bed gasification of waste-derived fuels[END_REF][START_REF] Gómez-Barea | Optimization of char and tar conversion in fluidized bed biomass gasifiers[END_REF], resulting in a drop of the syngas LHV and of the CGE. The influence of the temperature has also been investigated. Rising gasification temperature at a fixed ER value increases the syngas yield and carbon conversion [START_REF] Arena | Fluidized bed gasification of industrial solid recovered fuels[END_REF].

Globally, the cold gas efficiency (CGE) decreased with increasing temperatures due to the drop in syngas LHV [START_REF] Recari | Gasification of two solid recovered fuels (SRFs) in a lab-scale fluidized bed reactor: Influence of experimental conditions on process performance and release of HCl, H2S, HCN and NH3[END_REF][START_REF] Berrueco | Experimental Investigation of Solid Recovered Fuel (SRF) Gasification: Effect of Temperature and Equivalence Ratio on Process Performance and Release of Minor Contaminants[END_REF]. Contradictory results were reported about the evolution of the CH4 content and of the LHV of the syngas. While Berrueco et al. found that they reached a maximum at 800 °C before to decrease with higher temperature [START_REF] Recari | Gasification of two solid recovered fuels (SRFs) in a lab-scale fluidized bed reactor: Influence of experimental conditions on process performance and release of HCl, H2S, HCN and NH3[END_REF][START_REF] Berrueco | Experimental Investigation of Solid Recovered Fuel (SRF) Gasification: Effect of Temperature and Equivalence Ratio on Process Performance and Release of Minor Contaminants[END_REF], Dunnu et al. reported that they increased with rising temperature from 800 to 850 °C [START_REF] Dunnu | The solid recovered fuel Stabilat®: Characteristics and fluidised bed gasification tests[END_REF]. These opposite trends can result from the different SRF composition, but a lack of study devoted to the influence of the SRF composition prevents to conclude this point.

Most of the already published articles mainly focused on "synthetic" SRF consisting in the mixture of well-known plastics and biomass, without taking into consideration the complexity of a real SRF composition. In the present paper, two industrial SRFs having different chemical compositions have been used to improve the understanding of the SRFs composition influence on the gasification efficiency. A detailed characterization of SRFs was performed. Gasification temperature and equivalence ratio (ER) have been sequentially varied in order to identify their separate contribution on the gasification efficiency. The syngas composition was measured on-line with a µ-GC allowing to analyze permanent gases and BTX. Gasification efficiency was analyzed based on four indicators: cold gas efficiency (CGE), carbon conversion (CC), syngas lower heating value (LHVsyngas), and the syngas yield (ηsyngas). The distribution of hydrogen and carbon atoms in the gaseous products was determined and discussed based on SRF composition and gasification conditions.

Materials and methods

Characterization of the Solid Recovered Fuels

The two SRFs samples were provided by different French companies. The elemental composition was measured according to the standard NF EN 15407. The ash content was measured at 550°C according to the standard NF EN 15403. The composition of the resulting ashes was measured by X-Ray Fluorescence Spectroscopy. This technique was chosen to cope with the problem of the silica mineralization required for ICP analysis. The Br, Cl, and F contents were specifically determined by ionic chromatography according to the standards NF EN 15408 and NF EN ISO 10304-1. The Lower Heating Value (LHV) of the SRF was measured with a calorimetric bomb (NF EN 15400). The proportion and composition of biomass, non-biomass, and inert materials were determined according to the French standard NF EN 15 440.

Gasification reactor

Gasification tests were performed in a bubbling fluidized-bed constructed in our laboratory and presented in a previous article [START_REF] Lardier | Gas and Bed Axial Composition in a Bubbling Fluidized Bed Gasifier: Results with Miscanthus and Olivine[END_REF]. The gasifier is divided into three zones: the plenum (d=100 mm, H=300 mm), the bed zone (d=100 mm, H=800 mm), and the freeboard zone (d=140 mm, H=800 mm) (Figure 1). The gasifying agent was air whose flowrate was controlled by a mass flow controller (Brooks 5850S). At the bottom of the gasifier, a 3mm thick inox grid was used as distributor plate to homogenize the air flow and insure an efficient fluidization. The gasifier is heated by eight electrical heater shells at a maximum temperature of 1000 °C.

SRFs were fed at the top of the reactor with a sloping screw. Around 3 kg of olivine was placed in the gasifier. The particle size distribution of this olivine is presented in Figure S.1 (in Supplementary Material). At 800°C, the minimum fluidization velocity (Umf) was measured at 0.15 m/s at 800 °C in the reactor by progressively increasing the air flowrate while measuring the pressure drop in the gasifier.

At the gasifier outlet, the syngas flowed through a cyclone to remove particles, before to be cooled with two air heat exchangers. A water Venturi scrubber was also used to remove tar and acid gases before flaring the syngas. The gasifier is equipped with 19 lateral tubes allowing to locally measure the bed and freeboard temperatures. Pressure was continuously measured below the grid and at the top of the freeboard zone. The syngas was sampled before the Venturi scrubber (see Figure 1) and analyzed on-line by a µ-GC (Varian micro-GC 490) every 3 minutes. Permanent gases N2, CO, CO2, H2, CH4, C2H2, C2H4, C2H6, C3H4, C3H6, and C6H6 were quantified with this technique.

At the end of the experiment, the bed material (olivine+ash+char) was recovered after being cooled under a pure N2 sweep gas. Its velocity was lower than the minimum fluidization velocity to avoid the mixing of the bed. A solid sampler was introduced through the top of the gasifier and its vertical position was set. This system allowed sampling 100 mm thick bed layers.

Gasification conditions

Before starting the gasification tests, the system was preheated at the desired temperature (750-900 °C) under air. When the temperature was close to the gasification temperature, the air flowrate was set at the desired value. The air velocity was 4 times the minimum fluidization velocity, corresponding to an air flowrate of 4.5 m 3 /h (STP). Once the temperatures were stable along the gasifier, the gasification started by feeding the SRF at a controlled flowrate, corresponding to the desired ER. When the gasification conditions were stable (gasifier temperature, and syngas composition analyzed by µ-GC), the permanent regime was maintained at least 40 minutes before to be modified (Figure 2). During the tests, either the temperature or the equivalence ratio (ER) was changed. ER is defined as the operating air flowrate divided by the air flowrate required for the stoichiometric SRF oxidation. In this study, the ER was varied between 0.21 and 0.35. The SRF tank was continuously flushed with 10 NL/min of pure N2 to avoid the degradation of the fuel in the feeding screw. This flowrate was taken into consideration for the results analysis by using N2 as a tracer for the calculation of the syngas flowrate.

Evaluation of the gasification performance

The gasification efficiency is mainly evaluated based on four indicators calculated from experimental results. As benzene is not a problematic compound for syngas valorization in gas engine [START_REF] Jenbacher | Fuel gas quality, special gases[END_REF], it is taken into account in these calculations. The lower heating value of the dry syngas (LHVsyngas) is calculated from a weighted average of the molar LHV of each gas (including benzene) and is expressed in MJ/m 3 (STP) of syngas (including N2), according to Eq.1:

LHV syngas = ∑ ( LHV i x i ) 𝑖 V m
Eq.1

Where Vm represents the molar volume of ideal gas at STP (22.4 L/mol), and xi the molar fraction of the gas species i.

The syngas yield (ηsyngas) corresponds to the volume of dry syngas produced (including N2) by kg of SRF (on dry ash free basis), and was calculated according to Eq.2:

η syngas = Qv syngas Qm SRF Eq.2
Where Qvsyngas is the volumetric syngas flowrate including N2 (m 3 /h STP) which is calculated using N2 as a tracer, and QmSRF the mass flowrate of SRF (kgdaf/h). and Xi and Mi are respectively the mass fraction of the gas i in the syngas and its molecular weight.

Finally, the last indicator is the Cold Gas Efficiency (CGE), expressed in %, reflecting the fraction of chemical energy transferred from SRF to syngas:

CGE = η syngas * LHV syngas
LHV SRF * 100 Eq.4

Results

Physico-chemical properties of the SRF

The two SRF studied were provided by two French companies and produced from distinct waste separation facilities managing different pristine types of wastes. Therefore, they represent interesting and complementary materials having different compositions (Table 1). SRF1 is ash-rich (>35 wt.%) and relatively poor in carbon (≈ 36 wt.%). On the contrary, the SRF2 is rich in carbon (52.6 wt.%) and contains relatively small amount of ash (18.5 wt.%). The oxygen content is almost similar for the two SRF (≈20 wt.%). SRF2 has a significantly higher LHV than SRF1 (Table 1), resulting from the lower ash content of SRF2.

The ash composition of the SRF was analyzed after combustion by XRF ( The SRF2 mainly consists in non-biomass materials (Table 2) predominantly composed of plastics.

Indeed, plastics represent 65 wt.% of SRF2. SRF2 was inert-free, and its biomass fraction was composed of textiles, paper/cartons, and wood. These characterizations demonstrate that the two selected SRFs have significantly different compositions.

Influence of the Equivalence Ratio

To study the separate influence of the Equivalence Ratio (ER) on the gasification efficiency, the SRFs were gasified at a temperature of 810-825 °C controlled by the electrical heater shells. The ER was adjusted from 0.21 to 0.35 by modifying the SRF flowrate (between 2.3 and 5.9 kg/h on dry basis) while keeping a constant air flowrate in order to maintain similar fluidization conditions.

The evolutions of the cold gas efficiency (CGE), carbon conversion (CC), syngas yield (ηsyngas), and lower heating value of the syngas (LHVsyngas) versus ER are presented in Figure 3. Whatever the SRF composition, it can be observed that increasing ER led to: (i) a slight decrease of the CGE; (ii) a significant increase in syngas yield; and (iii) a decrease of the LHVsyngas. These results are in agreement with previous studies [START_REF] Hu | Co-gasification of municipal solid waste with high alkali coal char in a three-stage gasifier[END_REF][START_REF] Arena | Fluidized bed gasification of waste-derived fuels[END_REF]. However, the carbon conversion evolution depended on the SRF composition. In the range 0.21<ER<0.35, the CC increased by 6.8% for SRF1, while it decreased by 5.6% for SRF2. This difference can be attributed to the large amount of ash in SRF1 (35 wt.%), especially to the inorganic species known for their catalytic activity in gasification reaction (such as Ca, Na, K or Fe) [START_REF] Dupont | How inorganic elements of biomass influence char steam gasification kinetics[END_REF], which could catalyze the carbonaceous matter conversion. In addition, the type of plastics presents in SRF significantly influence the carbon conversion. For example, interactions occurring during the co-gasification of black polycarbonate and polyethylene-terephthalate with biomass were found to increase the carbon conversion, while no interaction was observed with polypropylene [START_REF] Burra | Synergistic effects in steam gasification of combined biomass and plastic waste mixtures[END_REF]. Moreover, other interactions could occur between plastics and biomass to enhance the char yield by promoting secondary reactions (condensation, polymerization), which decrease the carbon conversion [START_REF] Ephraim | Co-pyrolysis of wood and plastics: Influence of plastic type and content on product yield, gas composition and quality[END_REF]. A precise analysis of the plastic fractions would be required to elucidate the evolution of carbon conversion. Part of the carbon initially contained in the SRF was present in tars and fly ash generated during the gasification test, which explains that the carbon conversion is lower than 100%. The increase in syngas yield with rising ER is explained by the higher ratio of air to SRF in the gasifier.

If one subtracts the nitrogen from the outlet gas flowrate, the syngas yield (i.e. the gas produced) slightly increased with rising ER (Figure 4). However, it can be observed that the syngas production was around 20% higher with SRF1. To better understand the relationships between the SRF composition and the gasification phenomenon, the syngas composition was also studied. Table S.1 (in Supplementary Material) presents the syngas composition at the gasifier outlet, while Figure 5 displays the composition of the gas produced by gasification (nitrogen free). Rising ER decreased the fraction of the produced gases, except for CO2.

This latter increased due to the syngas oxidation reactions promoted by increasing ER (R1): This reaction also contributed to the decrease of the LHVsyngas with increasing ER. Indeed, the LHV of the N2-free syngas was proved to decrease with increasing ER (Figure 6). Plastic-rich SRF2 presented higher LHVsyngas than biomass-rich SRF1, which is in agreement with a previous study [START_REF] Mastellone | Co-gasification of coal, plastic waste and wood in a bubbling fluidized bed reactor[END_REF]. For SRF2, H2 and CH4 display similar evolution and comparable concentration with rising ER (Figure 5). However, for SRF1, the H2 content was significantly higher than that of CH4, especially at low ER.

The H2/CH4 ratio was equal to 3.4 at ER=0.21, and to 1.9 at ER=0.35.

ER LHV of the N 2 -free syngas

To go further in the H-species composition, the distribution of H atoms in the gaseous products was calculated, according to Eq.( 5):

S 𝐻 𝑖 = 𝑛 𝐻 𝑖 * 𝐹 𝑖 ∑ (𝑛 𝐻 𝑘 * 𝐹 𝑘 ) 𝑘 Eq.5
Where S 𝐻 𝑖 is the molar selectivity representing the fraction of H atoms present in the syngas in the form of the molecule i, 𝑛 𝐻 𝑘 is the number of H atom in the molecule k, and F k is the molar flowrate of the gas k.

Figure 7: Molar distribution of hydrogen in H-containing gases depending on the ER at a temperature of 800-820 °C.

The results, presented in Figure 7, confirm that H2 was the main H-containing gas produced during the gasification of SRF1, with a selectivity ranging between 31 and 43%, followed by CH4 and C2H4. For SRF1, the selectivity in H2, C3H6, C2H6 and C3H4 decreased with rising ER, while that of CH4, C2H2, C2H4 and C6H6 displayed the reverse trend. For SRF2, the distribution of H-gaseous products was significantly different. Indeed, the main H-products were CH4>C2H4>H2. As SRF are very complex materials composed of a mixture of heterogeneous wastes, it is difficult to precisely discriminate the specific contribution of each component, or the interactions between each of them. However, based on the characterization performed and on the previous articles, these results tend to indicate that high plastic content in the SRF is likely responsible for the formation of stable light hydrocarbon species, while the H2 content in the syngas is low compared to syngas from biomass-rich SRF [START_REF] Arena | Energy generation by air gasification of two industrial plastic wastes in a pilot scale fluidized bed reactor[END_REF][START_REF] Gómez-Barea | Optimization of char and tar conversion in fluidized bed biomass gasifiers[END_REF][START_REF] Arena | Gasification of a solid recovered fuel in a pilot scale fluidized bed reactor[END_REF]. The significant content of CH4 and C2H4 in syngas from SRF2 results from the decomposition of the plastic polymer chains generating various types of hydrocarbon species. Contrary to the trend observed with SRF1, the selectivity in H2 did not decrease with rising ER for SRF2.

H 2 CH 4 C 2 H 4 C 2 H 6 C 2 H 2 C 3 H 6 C 3 H 4 C 6 H 6 H 2 CH 4 C 2 H 4 C 2 H 6 C 2 H 2 C 3 H 6 C 3 H 4 C 6 H 6 H 2 CH 4 C 2 H 4 C 2 H 6 C 2 H 2 C 3 H 6 C 3 H 4 C 6 H 6
Similarly, the distribution of C atoms in the gaseous products was calculated (Figure 8). For SRF1, the two most important C-gases were CO2 (43-54 %) and CO (22-26 %), followed by C2H4 (8-10 %). The selectivities in CH4 and C6H6 were comparable (6-8 %) while that of other hydrocarbon species was lower than 3.6 %. The carbon distribution in syngas from SRF2 was slightly different. Although CO2 and CO were also the main products, their selectivities were significantly lower (35-50 %, and 16-19 %, respectively). On the contrary, the selectivity in C2H4, CH4, C6H6, and C2H2 was substantially higher than that obtained with SRF1. These results confirm that SRFs having high plastic content generate syngas rich in hydrocarbon compared to syngas from biomass-rich SRF. Moreover, these results revealed that syngas oxidation reactions were promoted by rising ER, since the distribution of carbon atoms in syngas in the form of CO2 increased from 43 to 54% for SRF1, and from 35 to 50% for SRF2.

Influence of the Temperature

The separate influence of the temperature on the gasification efficiency was investigated by gasifying the SRFs at constant ER (0.25) while varying the reactor temperature between 750 and 905°C. The evolution of the cold gas efficiency (CGE), the carbon conversion (CC), the syngas yield (ηsyngas) and the lower heating value of the syngas (LHVsyngas) versus gasification temperature is presented in Figure 9. For the two SRFs, increasing temperature resulted in the enhancement of the gasification efficiency, as reflected by the increase in LHVsyngas, syngas production, CGE and CC.

However, a problem of ash melting was encountered during the gasification of SRF1 at 880 °C, leading to the defluidization and the agglomeration of the bed. The agglomerate formed is presented in Figure 10. The results of this test are not presented, as the experiment had to be stopped before to reach the steady state. This agglomeration phenomenon was not observed during the high temperature tests with the SRF2. The high content of Si and P in the SRF1 ashes (40.51 and 2.24 wt.%, respectively) could contribute to this behavior, as these species are known to melt under gasification conditions [START_REF] Dupont | How inorganic elements of biomass influence char steam gasification kinetics[END_REF][START_REF] Hognon | Comparison of steam gasification reactivity of algal and lignocellulosic biomass: Influence of inorganic elements[END_REF][START_REF] Nzihou | The fate of heavy metals during combustion and gasification of contaminated biomass-A brief review[END_REF]. To go further in the understanding of the relationships between the SRF composition and the gasification phenomenon, the syngas composition was also studied. Table S.2 (in Supplementary Material) presents syngas composition at the gasifier outlet, while Figure 11 displays the composition of the gas produced by gasification reactions (nitrogen free). Whatever the nature of the SRF, the CO and H2 contents increased with rising temperature (Figure 11). On the contrary, the CO2 content decreased at higher temperatures. These trends can be attributed to several phenomena. Indeed, high gasification temperature can promote: the kinetic of gasification reactions generating H2 and CO at the expense of CO2 (R2); steam and dry reforming reactions of tar and light hydrocarbons which consume H2O and CO2 to produce H2 and CO (R3 and R4); and tar cracking reactions, mainly generating H2 and CO [START_REF] Dunnu | The solid recovered fuel Stabilat®: Characteristics and fluidised bed gasification tests[END_REF][START_REF] Recari | Gasification of two solid recovered fuels (SRFs) in a lab-scale fluidized bed reactor: Influence of experimental conditions on process performance and release of HCl, H2S, HCN and NH3[END_REF][START_REF] Berrueco | Experimental Investigation of Solid Recovered Fuel (SRF) Gasification: Effect of Temperature and Equivalence Ratio on Process Performance and Release of Minor Contaminants[END_REF]. In addition to dry reforming reaction, the decrease in CO2 can also be attributed to Boudouard reaction (R5), and to the Reverse Water-Gas Shift Reaction (R6). All these reactions are expected to occur simultaneously, thus explaining the syngas composition as well as the increase in gasification efficiency with rising temperature.

C The influence of the temperature on the distribution of hydrogen atoms in the gaseous products is presented in Figure 12. For the two SRFs, rising temperature increased the selectivity in H2, especially at temperature higher than 850 °C. This increase in H2 was also observed for the SRF2 rich in plastics.

Simultaneously, the selectivity in light hydrocarbons (C2H4, C2H6, C3H4, and C3H6) significantly decreased. These evolutions together with the drop of CO2 strengthen the hypothesis of dry reforming reactions. The reduction of light hydrocarbon species counterbalances the increase of H2 and CO: as a result, the LHVsyngas is relatively stable (Figure 9). In addition, tar reforming reactions are known to be promoted by high temperature [START_REF] Recari | Gasification of two solid recovered fuels (SRFs) in a lab-scale fluidized bed reactor: Influence of experimental conditions on process performance and release of HCl, H2S, HCN and NH3[END_REF][START_REF] Berrueco | Experimental Investigation of Solid Recovered Fuel (SRF) Gasification: Effect of Temperature and Equivalence Ratio on Process Performance and Release of Minor Contaminants[END_REF] which can also explain the increase in H2 and benzene (which is a product of light aromatics reforming) [START_REF] Dufour | Synthesis gas production by biomass pyrolysis: Effect of reactor temperature on product distribution[END_REF].

Conclusion

This article studied the influence of the Solid Recovered Fuels (SRFs) composition and of the operating conditions on the gasification efficiency. Two industrial SRFs having different compositions were investigated. The gasification tests were performed at lab-scale in a bubbling fluidized bed using olivine as bed material, and air as gasifying agent. At industrial scale, the gasifiers are autothermal, but it is not the case at lab-scale because the wall of the small reactors must be heated to balance the heat loss. To better understand the gasification phenomena, the separate contribution of temperature and equivalence ratio (ER) on the gasification efficiency was investigated by sequentially varying these two parameters.

Gasification efficiency was analyzed based on the syngas quality and on four indicators: cold gas efficiency (CGE), carbon conversion (CC), syngas lower heating value (LHVsyngas), and the syngas yield (ηsyngas).

The SRFs characterization highlighted significant differences in terms of elemental and global composition. SRF1 was ash-rich (≈37 wt.%) while its carbon content was relatively low (≈35 wt.%).

On the contrary, SRF2 was carbon-rich (53 wt.%) and presented low ash content (18.5 wt.%). The global composition showed that SRF1 was composed of a high biomass fraction (55.2 wt.%) mainly consisting in paper/carton. On the contrary, SRF2 was mainly composed of plastics (65 wt.%).

Gasification tests revealed that the LHVsyngas and the CGE significantly decreased with rising equivalence ratio (ER). This evolution resulted from the oxidation reactions promoted by high ER which decreased the concentration of carbonaceous gases at the expense of CO2, thus decreasing the LHVsyngas. The syngas yield was proved to be almost constant with increasing ER. For these reasons, the CGE decreased with rising ER. The significant amount of inorganic species (such as Ca, Na, K or Fe) present in SRF1 was expected to catalyze the gasification reactions of the carbonaceous matter, thus explaining the higher carbon conversion of SRF1 over SRF2. In addition, synergistic effects between plastics and biomass in SRF2 could promote secondary reactions leading to char formation. The H atoms distribution in syngas demonstrated that high plastic content in the SRF2 was responsible for the formation of stable light hydrocarbon species, while the H2 content in the syngas is low compared to syngas from biomass-rich SRF1.

Increasing gasification temperature at constant ER strongly improved the gasification efficiency whatever the SRF composition. Indeed, CGE, carbon conversion, syngas production and LHVsyngas were significantly increased between 750 and 900°C. The main limitation to the use of high temperature was the melting of mineral species leading to bed agglomeration and defluidization. However, this behavior was only observed with SRF1 which contained large amount of Si and P, both known for their melting tendency under gasification conditions. Rising temperature resulted in the increase of H2 and CO concentration in the syngas, while the concentration of CO2 and light hydrocarbons decreased. This evolution can be attributed to the several simultaneous reactions: gasification, steam and dry reforming, tar cracking, Boudouard, and Reverse Water-Gas Shift. This study provides original data on the influence of SRFs composition and operating conditions on the gasification efficiency and syngas composition.

Figure 1 :

 1 Figure 1: Scheme of the gasification device.

Figure 2 :

 2 Figure 2: Example of permanent regime reached during the gasification of SRF1 at 800 °C with ER=0.30.

Figure 3 :

 3 Figure 3: Evolution of the syngas Lower Heating Value (LHVsyngas), the syngas production (ηsyngas), the carbon conversion (CC) and the Cold Gas Efficiency (CGE) with the ER at a temperature of 800-820°C.

Figure 4 :

 4 Figure 4: Evolution of the syngas yield free of nitrogen with ER.

Figure 5 :

 5 Figure 5: Evolution of the composition of the gas produced (without nitrogen) with ER for the different SRFs at a temperature of 800-820°C.

Figure 6 :

 6 Figure 6: Evolution of the Lower Heating Value of the N2-free syngas with (ER).

Figure 8 :

 8 Figure 8: Molar distribution of carbon in C-containing gases depending on the ER at a temperature of 800-820 °C.

Figure 9 :Figure 10 :

 910 Figure 9: Evolution of Cold Gas Efficiency (CGE), carbon conversion (CC), syngas yield, and syngas lower heating value versus gasification temperature.

Figure 11 :

 11 Figure 11: Evolution of the composition of the gas produced (without nitrogen) versus gasification temperature for the different SRFs.

Figure S. 1 :

 1 Figure S.1: Particle size distribution of fresh olivine. 513

  The carbon conversion (CC) expresses the percentage of carbon transferred from SRF to syngas, and is

					CO 2
	calculated by Eq.3:
	𝐶𝐶 = Qm 𝑠𝑦𝑛𝑔𝑎𝑠 * 𝑀 𝐶 *	∑ ( 𝑀 𝑖 𝑋 𝑖 𝑖 𝑄𝑚 𝑆𝑅𝐹 * 𝑋 𝐶 * 𝑛 𝑖 𝐶 ) 𝑆𝑅𝐹 * 100		CO	Eq.3
					H 2
	𝐶 is the Where Qmsyngas is the mass flowrate of syngas (kg/h), MC is the molecular weight of carbon, 𝑛 𝑖 CH 4 C 3 H 6 C 2 H 2 C 6 H 6 C 2 H 4 number of carbon atoms in the molecule i, 𝑋 𝐶 𝑆𝑅𝐹 is the mass fraction of carbon is SRF (on daf basis),
	H2		CO	C2H4	C3H6
	C2H2	Méthane	Benzène	CO2

Table 1 :

 1 Table1). The ashes of SRF2 have high Ca and Si contents (35 and 30 wt.%, respectively). It can be noted that SRF1 and SRF2 present a significant concentration of Al (18.53 and 17.44 wt.%). SRF1 contains the highest amount of Si (40.51 wt.%). Its CaO content is significant (25.86 wt.%) but remains lower than that of SRF2. The results also showed that the two SRF are Br-free, but contain both Cl and F (Table1). According to the French classification, SRF2 is in class 4 due to its significant Cl content, while SRF1 is in class 2. Elemental analysis,ash composition, and lower heating value of the SRF.

		SRF1	SRF2
	Elemental analysis (dry wt.%)
	C	36.3	52.6
	H	4.9	7.2
	N	1.4	1.3
	S	0.3	0.2
	O	20.0	20.3
	Ash	37.1	18.5

nd: lower than 0.002 wt.% Table

2

presents the proportion and composition of biomass, non-biomass, and inert materials composing the two SRFs. SRF1 contains the higher fractions of inert and biomass materials (10.6 and 55.2 wt.%, respectively). Its biomass fraction mainly consists in fines and paper/cartons, while glass roughly composes the inert fraction. This latter explains its significant SiO2 content measured by XRF.

Table 2 :

 2 Proportion and composition of biomass, non-biomass, and inert materials in the SRF.

	SRF1	SRF2

  Table S.1: Syngas composition (in mol.%) at the gasifier outlet depending on the SRF for different Equivalent Ratio at a temperature of 800-820°C. .64 64.63 65.86 63.70 67.19 69.62 73.60 Table S.2: Syngas composition at the gasifier outlet depending on the SRF for different temperatures.

	SRF			SRF1				SRF2
	ER		0.21	0.25	0.30	0.35	0.21	0.25	0.30	0.35
	H2		9.92	6.70	4.25	3.20	4.00	3.31	3.43	2.46
	O2		0.00	0.08	0.53	0.00	0.14	0.04	0.14	0.11
	CO		9.42	8.00	6.46	6.12	7.27	6.18	5.53	4.57
	CO2	15.85 15.60 15.13 14.98 14.46 14.08 14.57 13.87
	C2H4	1.76	1.55	1.34	1.13	3.31	2.55	2.06	1.44
	C2H6	0.21	0.14	0.09	0.05	0.16	0.11	0.07	0.04
	C2H2	0.06	0.09	0.13	0.16	0.41	0.41	0.37	0.33
	CH4		2.94	2.38	1.89	1.66	4.15	3.26	2.63	2.07
	C3H6	0.43	0.27	0.15	0.08	0.34	0.22	0.13	0.04
	C3H4	0.11	0.08	0.02	0.02	0.04	0.03	0.01	0.01
	C6H6	0.44	0.38	0.35	0.34	1.05	0.88	0.22	0.55
	N2	53.39 58SRF	SRF1			SRF2
	T (°C)	755	825	880		775	810	850	905
		H2		6.08	6.70	9.55		2.63	3.31	4.09	6.61
		O2		0.13	0.08	0.00		0.08	0.04	0.01	0.49
		CO		5.56	8.00	15.63	6.05	6.18	6.67	8.54
		CO2	16.48 15.60 11.96	14.37 14.08 13.63 13.38
	C2H4		1.31	1.55	1.75		2.50	2.55	2.264	1.45
	C2H6		0.19	0.14	0.11		0.14	0.11	0.06	0.04
	C2H2		0.04	0.09	0.15		0.35	0.41	0.48	0.02
		CH4		2.03	2.38	3.00		2.90	3.26	3.30	3.01
	C3H6		0.47	0.27	0.12		0.39	0.22	0.06	0.02
	C3H4		0.02	0.08	0.00		0.04	0.03	0.02	0.01
	C6H6		0.34	0.38	0.50		0.66	0.88	1.10	1.07
		N2	63.70 58.64 50.24	69.63 67.19 64.99 59.46

Acknowledgements

The authors acknowledge the financial support of ADEME to the Terracotta project (1606C0013).

The authors also thank the EDF Company, especially Emmanuel Thunin and Mathieu Insa for their support on material characterizations.

Supplementary information


Gain in battery RMS current  elim Elimination rate of battery power impulses

Gain in battery losses G_I RMS

I. INTRODUCTION

In many industrial sectors, high reliability power supply is required for critical loads. Uninterruptible Power Supplies (UPS) are used to improve power quality and guarantee the reliability of backup power. During voltage sags or complete interruptions of the power supply, the energy has to be supplied by local Energy Storage Systems (ESS). Conventional ESS for UPS is basically relying on the choice of good lead-acid batteries [START_REF] Chlodnicki | Hybrid UPS Based on Supercapacitor Energy Storage and Adjustable Speed Generator[END_REF]. However, there are many disadvantages associated with batteries such as low power density and limited charge/discharge cycles.

Moreover, extracting pulsed power instead of average power from the battery can decrease its lifespan [START_REF] Van Voorden | The Application of Super Capacitors to relieve Battery-storage systems in Autonomous Renewable Energy Systems[END_REF]. First, the current variations cause voltage transients that can be interpreted by the low voltage detection circuit as a discharged battery creating a premature shutdown. Second, the pulsed currents have a higher RMS value, which might cause increasing battery losses. Third, pulsating currents also reduce greatly the battery runtime [START_REF] Dougal | Power and Life Extension of Battery-Ultracapacitor Hybrids[END_REF].

A supercapacitor is a double-layer electrochemical capacitor that can store thousand times more energy than a typical capacitor. It shares the characteristics of both batteries and conventional capacitors and has an energy density about 20% of a battery. Moreover, they have almost negligible losses and long lifespan. They can process a large number of charge and discharge cycles (several hundred thousand cycles) compared to only a few thousand cycles for lead-acid batteries [START_REF] Rufer | A Supercapacitor-Based Energy-Storage System for Elevators With Soft Commutated Interface[END_REF], [START_REF] Mallika | Reniew on Ultracapacitor-Battery Interface for Energy Management System[END_REF] and can supply much higher currents than batteries [START_REF] Rafik | Frequency, thermal and voltage supercapacitor characterization and modeling[END_REF].

Batteries are mostly efficient when used to supply low, reasonably steady power levels. Supercapacitors are very effective in storing charge for later use. Their leakage rate and series resistance are quite small [START_REF] Krishna | Managing Battery and Supercapacitor Resources for Real-Time Sporadic Workloads[END_REF], [START_REF] Belhachemi | A physical based model of power electric double-layer supercapacitors[END_REF].

The power sharing between supercapacitors, fuel cells and batteries is a promising solution for improving the performance system due to the dynamic behavior of the SC's and their long life [START_REF] Camara | Polynomial Control Method of DC/DC Converters for DC-Bus Voltage and Currents Management-Battery and Supercapacitors[END_REF][START_REF] Haddoun | Modeling, analysis, and neural network control of an EV electrical differential[END_REF].

This combination was tested successfully in many applications like Pure Battery-Powered Electric Vehicle (EV) [START_REF] Burke | Batteries and Ultracapacitors for Electric, Hybrid, and Fuel Cell Vehicles[END_REF], [START_REF] Camara | Design and New Control of DC/DC Converters to Share Energy Between Supercapacitors and Batteries in Hybrid Vehicles[END_REF], [START_REF] Gao | Power Enhancement of an Actively Controlled Battery/Ultracapacitor Hybrid[END_REF], Hybrid Electric Vehicle (HEV) [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF], [START_REF] Schaltz | Investigation of Battery/Ultracapacitor Energy Storage Rating for a Fuel Cell Hybrid Electric Vehicle[END_REF], [START_REF] Khaligh | Battery, ultracapacitor, fuel cell, and hybrid energy storage systems for electric, hybrid electric, fuel cell, and plug-in hybrid electric vehicles: State of the art[END_REF], and Fuel Cell (FC) based UPS systems [START_REF] Zhang | Analysis and Design of a Bidirectional Isolated DC-DC Converter for Fuel Cells and Supercapacitors Hybrid System[END_REF], [START_REF] Jia | A dynamic discharge structure for ultracapacitor application in the fuel cell UPS[END_REF], [START_REF] Chellappan | Fuel Cell Based Battery-Less UPS System[END_REF], [START_REF] Li | A three-switch structure for PEMFC and ultracapacitor hybrid in backup power[END_REF].

In UPS applications, batteries usually provide 5 to 15 minutes of backup min backup time power before a generator starts and is ready to accept the full load. Supercapacitors can supply only 5 to 20 seconds of backup at full power. This means that SC's could be a good battery replacement only when long runtime is not required because of their high price, their high size and mass [START_REF] Esposito | PSO Based Energy Management Strategy for Pure Electric Vehicles with Dual Energy Storage Systems[END_REF], [START_REF] Peppel | Elimination of high power delivery rates by energy storage in supercapacitors[END_REF], [START_REF] Mars | A Survey of Supercapacitors, Their Applications, Power Design with Supercapacitors, and Future Directions[END_REF]. Nowadays it is better to combine traditional battery for higher energy UPS and SC's for higher power UPS. It is worth mentioning that supercapacitors are experiencing high development and becoming more and more competitive in price [START_REF] Stepanov | Implementation of supercapacitors in uninterruptible power supplies[END_REF].

In this paper we present a power sharing method between the supercapacitors and the lead acid battery in a 500 kVA rated Uninterruptible Power Supply. Combining supercapacitors with battery-based UPS system gives the best of high energy and high power configurations. The supercapacitors ensure the power impulses and reduce high power demands away from the battery during the 10 min backup time. They also deliver the whole load power during outages lasting less than 10 s. The lifetime of the batteries could then be extended.

We focus then our study of the reduction in battery stresses by the use of SC's. We aim at investigating the optimal SC's/battery combination with respect to the cost price of supercapacitors. This investigation is threefold; first, supercapacitors and battery models are developed then validated using Matlab/Simulink ® software.

In a second stage, the architecture and the simulation of the designed system combining the two types of storage devices are shown. The study emphasizes on UPS autonomous running for grid faults lasting few minutes, the supercapacitors supply the transient demand of power and the battery is responsible for the smoothness requirement for energy. By allowing the battery to charge up the supercapacitors pack at a suitable rate, the energy stored in the SC's would be available to satisfy the maximum of the pulsating load power demands.

Finally, extensive simulations are carried out to determine the gain in battery RMS current, the gain in energy losses, the energy efficiency and the elimination rate of surge load power. These four performance parameters are determined through simulations and then analyzed. They reflect the potential decrease in battery stresses due to the SC's. We carried out a thorough analysis involving optimal study. We propose to draw the optimal SC's number and filter constant from the variation of the aforementioned parameters versus the cost price of the supercapacitors

II. PRESENTATION OF THE STUDIED UPS

A. UPS specification

The main specifications of the 500 kVA UPS are: -Power factor: FP = 0.9, -Total efficiency:  = 95 %, -Nominal output voltage: V ac = 400 V, -Nominal battery power: P N = 480 kW, -Backup time: T = 10 min, -DC-bus voltage: V DC = 400 V, -Nominal battery voltage: U bat_nom = 480 V.

Fig. 1 shows a simplified electrical diagram of the UPS under consideration. Its topology is an Online/Double-Conversion system [START_REF] Gurrero | Uninterruptible power supply systems provide protection[END_REF]. Before adding the supercapacitors (without the dotted part), in the case of interruption of the power grid from "Input1", the battery supplies immediately the full power to the inverter during short and long outages. The period of backup time is 10 minutes and it is the required time for the generator to start up and to reach its rated operation.

Referring to Standard EN 50160 [START_REF] Markiewicz | Voltage Disturbances, Standard EN 50160 -Voltage Characteristics in Public Distribution Systems[END_REF], grid failures requirements are as follows:

-Short interruptions of voltage supply: (up to 3 minutes), few tens -few hundreds/year, duration 70% of them < 1 s -Long interruptions of voltage supply: (longer than 3 minutes), <10 -50/year We mention that in practice, these requirements are not particularly rigorous for the supplier. On the other hand, the consumer regards the limits given in EN 50160 as requirements that must be guaranteed by the supplier [START_REF] Markiewicz | Voltage Disturbances, Standard EN 50160 -Voltage Characteristics in Public Distribution Systems[END_REF].

B. Supercpacitors pack sizing and modeling

We have chosen that the supercapacitors, added as high power storage devices, must supply the full power P load = P N during t = 10 s, the delivered energy is then estimated to be around 4.8 MJ.

The energy E sc stored at the voltage U sc of the SC's pack voltage can be expressed as follows:

2 2 2 1 2 1 sc sc s_sc p_sc sc eq sc U C N N U C E   (1)
where C eq is the equivalent capacity of the SC's pack, N p_sc and N s_sc are the number of parallel branches and the number of SC's series connections, respectively, and C sc is the SC capacitance.

The supercapacitors considered in this paper are the Maxwell/BCAP3000 type, rated 3000 F, 2.7 V. having the parameters given in Table 1.

TABLE I PARAMETERS OF THE BCAP 3000 SUPERCAPACITORS l It is usually allowed to utilize 75 % of the energy stored in the SC's pack by discharging the pack from its rated voltage U M = 300 V (about 80% of the DC-bus voltage [START_REF] Choi | Fuel-cell powered uninterruptible power supply systems: Design considerations[END_REF]) to the half of that value equal to U m = 150 V. Every elementary SC in then discharged from an initial voltage V sci = 2.7 V to a final voltage V scf = 1.35 V. Further, the internal losses in the SC's may be taken into account through the efficiency coefficient k = 0.9 [START_REF] Choi | Fuel-cell powered uninterruptible power supply systems: Design considerations[END_REF]. The energy extracted from the SC's can then be written as:

) U C U C ( k Δt P m eq M eq N 2 2 2 1 2 1    (2)
This leads, by considering an energy of 4.8 MJ, to a SC's pack having an equivalent capacitance C eq = 158 F. Referring to the initial voltage of the SC's pack, we obtain N s_sc = 112 and N p_sc = 6.

To optimize the supercapacitors combination with the battery in UPS applications, we need to establish a model to describe the supercapacitor behavior during fast charge and discharge cycles. We consider the equivalent electric circuit with two RC branches proposed by [START_REF] Zubieta | Characterization of double-layer capacitors for power electronics applications[END_REF], [START_REF] Gualous | Experimental study of supercapacitor serial resistance and capacitance variations with temperature[END_REF] as shown in figure 2. The main capacitance C 1 (differential capacitance [START_REF] Zubieta | Characterization of double-layer capacitors for power electronics applications[END_REF]) depends on the voltage v 1 . It consists of a constant capacity C 0 (in F) and a constant parameter C v (in F/V) and it is written as

C 1 =C 0 + C v v 1 .
The R 1 C 1 branch determines the immediate behavior of the supercapacitor during rapid charge and discharge cycles in a few seconds.

The R 2 C 2 cell is the slow branch. It completes the first cell in longtime range in order of a few minutes and describes the internal energy distribution at the end of the charge (or discharge). The equivalent parallel resistance R f represents the leakage current and can be neglected during fast charge/discharge of the supercapacitor.

To identify the parameters of the proposed model, we carried out a single fast controlled charge/discharge test at constant current 250 A and -250 A, respectively. The experimental method which determines the parameters of the supercapacitor equivalent circuit is described in [START_REF] Zubieta | Characterization of double-layer capacitors for power electronics applications[END_REF].

The obtained values are:

-R 1 = 0.360 mΩ, -C 0 = 2100 F, -C v = 623 F/V, -R 2 = 1.92 Ω, -C 2 = 172 F,
The simulation circuit with Matlab\Simulink ® of the supercapacitors pack is illustrated in figure 3.

Fig. 3. Matlab simulation model of Supercapacitors pack

This circuit is based on the following equations (leakage current of supercapacitor is neglected):

) N I R v ( N ) i R v ( N v N U p_sc sc s_sc sc s_sc sc s_sc sc 1 1 1 1      (3)
with:

-U sc and I sc are the SC's pack voltage and current respectively,

Slow cell Main cell R 1 R 2 C 2 v 1 C 1 = C 0 +C v .v 1 R f Losses v 2 v sc i sc i 1 i 2
-v sc and i sc are the elementary supercapacitor voltage and current respectively. The voltage v 2 in the secondary capacity C 2 is given by:

     dt ) v v ( R C dt i C v 2 1 2 2 2 2 2 1 1 1 (4)
Let Q 2 the instantaneous charge of C 2 , we have:

  dt i Q 2 2 (5)
The current i 1 going in the main capacitor C 1 is expressed as:

2 1 i i i sc   (6)
On the other hand, i 1 is expressed in terms of the instantaneous charge Q 1 and C 1 as:

dt dv ) v . C C ( dt dQ dt dv C i v 1 1 0 1 1 1 1     (7)
where the charge Q 1 is:

2 1 1 0 1 2 1 v . C v C Q v   (8)
The one supercapacitor element is supposed initially to be fully charged at

V sci = v 1i = v 2i = 2.7 V.
The initial values are then:

i i v C Q 2 2 2  (9) 2 1 1 0 1 2 1 i v i i v . C v C Q   (10)
The equation [START_REF] Haddoun | Modeling, analysis, and neural network control of an EV electrical differential[END_REF] leads to the inverse relationship between v 1 and Q 1 that represents the function f(u) in Fig. 3 and it is given by:

v v C Q C C C v 1 2 0 0 1 2     (11)
In Fig. 4 we represent the experimental results compared to the simulation carried out using Matlab/Simulink ® for the charge/discharge test at constant current 250 A and -250 A. We observe that the SC's model is in very good agreement with the experimental results.

Fig. 4. Comparison between simulation and experimental results for a supercapacitor charge and discharge cycle

Finally, we verify that the sized supercapacitors pack fulfills the UPS specifications set before. In fact, the instantaneous energy W sc stored in the main branch of an elementary supercapacitor is given by:

  1 1 dQ v W sc ( 12
)
By neglecting the energy dissipated in R 1 and referring to Eq. ( 7), we obtain the energy W sc stored in one SC element: as follows:

) 3 1 2 1 ( 3 2 sc v sc 0 sc v C v C W   (13)
The total energy stored in the SC's pack is then given by:

) 3 1 2 1 ( 3 2 sc v sc 0 p_sc s_sc sc v C v C N N E     (14)
The SC's voltage element drops from an initial value V sci = 2.7 V to a final value V scf = 1.35 V, the difference between initial energy E sci and final energy E scf of the SC's pack multiplied by the efficiency coefficient k is equal to 5.6 MJ. This means that the SC's pack sizing is in good concordance with the energy P N t = 4.8 MJ specified previously.

C. Battery sizing and modeling

For the studied 500 kVA UPS, the battery chosen by the UPS manufacturer is made of 2226 elementary lead-acid batteries (type VISION rated 7Ah 12V CP1270), the number of series and parallel connections are N s_bat = 42 and N p_bat = 53, respectively.

We notice that for a full power P N = 480 kW extracted from the battery during the ten-minute autonomous operation, each elementary battery is discharged at P bat = 216 W. Since each battery is made of 6 cells, each cell is then discharged at P cell = 36 W.

Referring to the one cell discharge table of the 7Ah 12V battery (cf. table II, line 1, column 2), the end point voltage of every cell is about 1.6 V, which means that the total battery end voltage is almost equal to 400 V. In conclusion, the battery voltage drops during a constant power discharge at P N = 480 kW from 555 V (2.2 V per cell) to 400 V. As the DC-bus voltage is equal to 400 V, the battery is connected to the DC-bus via a buck DC/DC converter (cf. Fig. 1). In order to simulate the UPS nominal running, we need a model of the battery that represents accurately its behavior during charge and discharge cycles for few minutes.

Battery modeling is much more complicated than that of SC's for many reasons to name a few, internal temperature and State of Charge (SoC) of battery model's parameters are known to be hardly measured. Many analytical models have been studied and experimentally validated [START_REF] Rakhmatov | A model for battery lifetime analysis for organizing applications on a pocket computer[END_REF], [START_REF] Bhangu | Nonlinear Observers for Predicting Stateof-Charge and State-of-Health of Lead-Acid Batteries for Hybrid-Electric Vehicles[END_REF], [START_REF] Chiasson | Estimating the State of Charge of a Battery[END_REF]. The battery model used in this paper is based on the circuit proposed by [START_REF] Tremblay | Experimental Validation of a Battery Dynamic Model for EV Applications[END_REF]. All the model parameters are determined based on the discharge curve as shown in Fig. 5. Fig. 5. Typical discharge curve [START_REF] Tremblay | Experimental Validation of a Battery Dynamic Model for EV Applications[END_REF] The main feature of this model is the accuracy of the battery's behavior with respect to current variation and the battery's SoC. Furthermore, the open circuit voltage (OCV) is taken as a function of the SoC.

A term concerning the polarization voltage is added to better represent the OCV behavior and the term concerning the polarization resistance is slightly modified [START_REF] Tremblay | Experimental Validation of a Battery Dynamic Model for EV Applications[END_REF], [START_REF] Shepherd | Design of Primary and Secondary Cells -Part 2. An equation describing battery discharge[END_REF].

The battery voltage v bat is expressed as follows:

* bat bat i . it Q Q K ) it . B exp( . A i R ) it .( it Q Q K E v         0 ( 15
)
where:

-E 0 = battery constant voltage (V), -K = polarization constant (V/Ah) or polarization resistance (Ω), -Q = battery capacity (Ah),

-it =  idt = actual battery charge (Ah), -A = exponential zone amplitude (V), -B = exponential zone time constant inverse (Ah -1 ), -R bat = internal resistance (Ω), -i = battery current (A), -i * = filtered current at low frequency (A).

The main feature of this model is that only three points of the discharge curve are required to obtain all the parameters. The points are the fully charged voltage (V full ), the end of the exponential zone (V exp , Q exp ) and the end of the nominal zone (V nom , Q nom ), respectively.

We suppose that the battery is discharged at the nominal power P N = 480 kW, its voltage drops from 555 V to 400 V. The total battery current rises from 865 A to approximately 1200 A. So the current extracted from every element varies between 16 A and 23 A. For an operating power range between 0.2P N and 0.9P N , the current varies from 4.5 A to 20 A. The discharge curves used to perform the battery model are chosen in this discharge current range. Fig. 6 shows the simulation results superimposed on the discharge curves for currents I d = 4.56 A, I d = 7 A and I d = 21 A. We notice that the battery model elaborated with Matlab/Simulink ® draws with good accuracy the battery behavior at steady state discharge and at variable discharge currents.

A. Combination without control system

Firstly, the battery and the supercapacitors have been combined in parallel without control system as shown in Fig. 7. The DC/DC and the AC/DC converters are supposed to be ideal without losses. The DC bus voltage V DC is equal to 400 V. However, the battery and the SC's power waveforms represented in Fig. 9 (a) show that the power delivered by the battery has transient peaks during all the backup time. These instantaneous power demands applied to the battery affect dramatically its lifetime. We also remark in Fig. 9 (b) that the SC's power have charge/discharge phases that are not controlled and may cause the failure of the supercapacitors.

B. Controlled SC's-battery Combination

The control system presented in this section is designed to benefit the fast charge and discharge capability of the supercapacitors in order to reduce the battery stresses due to instantaneous power demands. The purpose of the combination between SC's and the battery is to make the SC's supply the power transients and to smooth the high power demands applied to the battery during autonomous operation [START_REF] Lahyani | Design of Power Sharing System Between Supercapacitors and Battery in an Uninterruptible Power Supply (UPS)[END_REF]. Fig. 10 shows the new UPS topology counting the control system for power sharing between SC's and the battery. Fig. 10. Topology of the controlled SC's/battery combination The DC/DC converters are supposed to be without losses and modeled as DC ideal bi-directional transformers. The input currents of the converters associated with the battery and the SC's pack, respectively i bat_bus and i sc_bus (cf. Fig. 10) are controlled by the power sharing system. This control system performs according to the state of charge of the SC's pack and to the shape of the load power. The load current i load and the load power P load are distributed to the battery and the SC's according to the principle represented in Fig. 11. -P load is the load power, -P bat is the battery power, -P sc is the SC's pack power, -P Lm is the limit load power.

-P IV is the initial value of the battery power. 1-At time t 1 , the battery is subjected to a rising power requested by the load. A low-pass filter is applied to the load current diverting sudden power variation to the supercapacitors. The equations of this first phase can be written as follows:

The SC's power is then given by: bat load sc

P P P   (16)
2-The constant T au characterizes the dynamic of the low-pass filter. It is adjustable and can act on the discharge time of the SC's especially on the smoothing degree of the peak power applied to the battery. 3-At time t 2 , P load < P bat , the battery supplies a full load power and the low-pass filter operation is canceled. 4-At time t 3 , the load power P load is less than a load power limit P Lm , the battery supplies both the load and the SC's pack with energy intended to recharge the supercapacitors. 5-At time t 4 , the SC's voltage reaches its maximal tolerated value, the deterioration of supercapacitors is avoided by stopping the recharge process. 6-At time t 5 , a new power demand occurs and the low-pass filter is applied again, the SC's pack is now fully charged and has sufficient energy to meet again the power impulses. 7-At time t 6 , the SC's are discharged at a rate of 75 % and their voltage has reached its minimum value of 150 V. The SC's pack is stopped and the full power is transferred to the battery. The flowchart in Fig. 12 summarizes the principle of power distribution between the battery and the supercapacitors.

A. Combination without SC's recharging

The SC's supply the transient power demands without being recharged through the battery. Firstly, we show in Fig. 14 the load power P load , the battery power P bat and SC's power P sc obtained by simulation for a filter constant T au = 2 s.

The total number of supercapacitors is 672 (N s_sc = 112 and N p_sc = 6). For a price of around 0.015 €/F considered (price usually found today for large quantities), the total cost of the SC's pack is about 30 k€. The SC's recharging through the battery is inhibited. We notice form Fig. 14 that the SC's ensure the sudden power demands but only for a period of about 200 s. Beyond that time, the battery supplies the full power until the end of the backup time of 10 minutes.

In fact, Fig. 15 showing the evolution of the battery voltage U bat and the SC's voltage U sc , confirms that the SC's are stopped at about 200 s since U sc has reached its minimum value of approximately 150 V. Fig. 15. Waveforms of U bat and U sc for N p_sc = 6 N s_sc = 112 and T au = 2 s Secondly, we observed the influence of the filter constant T au on the system performance, and the possibility to enhance the power extracted from the battery by varying the SC's pack number. A special attention is given to the cost of the SC's pack.

The system simulation was performed for different values of filter constant (T au = 1 s, 2 s, 5 s and 10 s) and for a number of parallel SC's branches varying from 6 to 60. The total cost of the SC's pack varies then from 30 k€ (kEuros) to 300 k€ (about 0.015 €/Farad).

The battery/SC's hybrid systems have experimentally demonstrated longer operating times compared to systems without supercapacitors [START_REF] Miller | Battery-capacitor power source for digital communication applications: Simulations using advanced electrochemical capacitors[END_REF], [START_REF] Jarvis | Fuel cell/electrochemical capacitor hybrid for intermittent high power applications[END_REF], [START_REF] Jarvis | Hybrid power sources for land warrior scenario[END_REF]. In order to examine the effect of the designed SC'sbattery combination on the system performance versus T au and N p_sc , we based our study on four performance indicators that are [START_REF] Dougal | Power and Life Extension of Battery-Ultracapacitor Hybrids[END_REF], [START_REF] Andersson | Alternative Energy Storage System for Hybrid Electric[END_REF]: -Gain in battery RMS current, -Gain in battery energy losses, -Total energy efficiency, -Elimination rate of the power peaks.

The optimal combination is then investigated taking into account the total cost of the SC's.

Gain in battery RMS current

The RMS battery current gives an approximate image of the relative ohmic losses of the battery internal resistance where we neglect the chemical processes. This parameter is only used as a first step in the evaluation, where the actual battery current (I RMS ) is compared to the battery current for the system without SC's pack (I RMS_ref ). The gain ratio is given in percent as follows: We notice from Fig. 16 (a) that the RMS current-gain increases according to the number of parallel SC's branches and to the filter constant. We also remark that the gain reaches an upper limit versus increasing parallel connections after which there is no enhancement for the RMS current-gain. On the other side, Fig. 16

100 I I - I (%) Gain_I RMS_ref RMS RMS_ref RMS   (17)

Gain in battery energy losses

The reduction of the battery stresses are an important issue of this work. The total loss of energy in the battery is obtained from the Tremblay model [START_REF] Tremblay | Experimental Validation of a Battery Dynamic Model for EV Applications[END_REF]. The actual battery losses (W losses ) are compared to the battery losses for the system without SC's pack (W losses_ref ). The gain ratio is given in percent and it is calculated as:

100 W W - W (%) Gain_W f lossess_re losses losses_ref losses   (18)
Fig. 17 As for RMS current-gain, the gain in battery energy losses is enhanced with increasing constant filter and SC's parallel branches until an upper limit beyond which no improvement occurs. Contrariwise, the gain divided by the cost reaches a maximum of 220 for increasing T au and N p_sc well-marked for T au = 1 s and N p_sc = 6 branches.

Total energy efficiency

All the UPS components undergo losses, for example energy losses in battery, balancing circuitry of the SC's pack, DC/DC converter, cables and switching losses. Even though the reducing of the battery losses is emphasized in this work, the overall efficiency is also an important parameter since all losses in the system generate heat and, consequently, demand proper cooling.

The total energy efficiency is calculated as the ratio between the energy absorbed by the load and the energy extracted from the battery added to the energy absorbed/supplied from the SC's. Only the losses in the battery and the SC's are considered. They are included in the calculations. The energy efficiency is written as follows:

dt )] E E ( i ). i . R u [( dt P E E E (%) 0 0 100  (19)
where: -E load : total energy supplied/absorbed by the load during backup time T = 10 min, -E bat : energy extracted from the battery added to the losses in battery resistance R bat , -E sc : energy spplied/absorbed from the SC's added to the losses in the pack internal resistance, -E scf , E sci : initial and final stored energies in the main capacitive elements of the SC's (cf. Fig. 2). Fig. 18 shows the evolution of the energy efficiency versus T au and N p_sc . We note a very good overall efficiency of the system. The calculation of the efficiency would be more accurate if the losses in the DC/DC converters were taken into account. which leads to the battery failure [START_REF] Sauer | Comparison of different approaches for lifetime prediction of electrochemical -using lead acid batteries as example[END_REF], [START_REF] Lam | Failure mode of valve-regulated lead-acid batteries under high-rate partial-state-of-charge operation[END_REF].

We consider that for the lead acid batteries used in the UPS, the high currents needed during fast changing load power can be supplied/absorbed by the SC's, potentially increasing the battery lifetime. The most important parameter is then the rate of the transient power applied to the battery that can be eliminated.

Therefore, the stopping time of supercapacitors is the best indicator of the elimination rate ( elim ) of the power peaks required by the load. For example, if the SC's voltage reaches the minimum value of 150 V at time 300 s, for the total backup time (T = 600 s), 50 % of the power surges applied to the battery are eliminated.

We define the peak power elimination rate ( elim ) by:

100   T T (%) stop elim  (20)
where:

-T stop is the final time at which the SC's pack reaches its minimum voltage, -T is the duration of the autonomous running equal to 10 min.

As shown in Fig 19 (a), for a given parallel branches N p_sc , the elimination rate increases according to the filter constant T au . In fact, supercapacitors energy is switched and supplied by small parts. So, the SC's overcome greater number of peak power during the backup time. By dividing  elim by the SC's cost, we observe that the cost efficiency decreases for increasing N p_sc (cf. In conclusion, by comparing the evolution of all these indicators, we notice a trade-off between the peak power elimination rate and the other performance indicators. In fact, unlike the RMS current-gain, the gain in battery energy losses and the global efficiency,  elim increases for decreasing filter constant for a given number of parallel branches.

However, the evolution of the performance parameters is in good concordance while divided by the cost of the SC's pack. The maximum point is obtained for T au = 1 s and N p_sc = 6.

If we look at figures 16 (b), 17 (b) and 18 (b) showing the first three parameters G_I RMS , W losses and  global returned to the cost, we notice that for T au = 1 s and T au = 2 s, and for N p_sc = 8, the system performance are almost equal.

On the other side, taking  elim as the primary basic indicator, we have a clear advantage for T au = 1 s. In fact, we show in the next paragraph that by planning SC's recharge through the battery, T au = 2 s becomes better than T au = 1 s for N p_sc = 8 since 100 % of the power inrushes are eliminated and the three other performance parameters are improved.

B. Combination with SC's recharging

In this section, the influence of the SC's recharging via the battery on the performance parameters is analyzed. The system is designed to extract from the battery a power used simultaneously to supply the load and to recharge the SC's pack whenever the load power P load drops below a power limit denoted P Lm . The power load limit is set to P Lm = 80 kW and the power supplied by the battery is fixed at two levels.

A first recharge type consists in delivering 80 kW by the battery split between the load and the SC's (I bat_charge = 200 A at V DC = 400 V). In the second recharge type, the battery supplies 160 kW (I bat_charge = 400 A at V DC = 400 V).

It should be noted that the elimination rate as defined in Eq. ( 19) is minimally affected by the recharge of the SC's via the battery, since only rising power demand applied to the battery is considered.

We set the filter constant at T au = 2 s and we planned SC's recharge through the battery in order to inspect if the performance indicators can exceed those obtained for T au = 1 s.

In Fig. 20 (a), (b), (c), (d), (e), (f), (g) and (h), we show the results of this investigation for T au = 2 s and N p_sc between 6 and 15 branches. We notice a clear improvement of all performance parameters for increasing I bat_charge . This improvement is limited for N p_sc between 6 and 8 branches and more noticeable for I bat_charge = 400 A.

The best configuration is then explored. It consists in finding a compromise between: -Minimum of parallel branches for cost considerations, -Maximum constant filter T au for a better damping of power surges inflicted to the battery, -Maximum gain in battery power losses, -Maximum elimination rate of peak power. We consider that the last criterion consisting in the potential gain in peak power is the most important one since it traduces peak stresses relief on battery and therefore the positive influence on the system performance [START_REF] Dougal | Power and Life Extension of Battery-Ultracapacitor Hybrids[END_REF], [START_REF] Casadei | A supercapacitor-based power conditioning system for power quality improvement and uninterruptible power supply[END_REF], [START_REF] Schneuwly | Ultracapacitors revolutionize the power electronic world[END_REF].

We demonstrate in Fig. 21 that SC's recharge via the battery for I bat_charge = 400 A and N p_sc = 8 makes the system performances better for T au = 2 s than for T au = 1 s. Moreover, T au = 2 s leads to better smoothing of the power extracted from the battery and implies better stresses reduction. The total cost of the SC's pack is then about 40 k€. 22 shows the P load , P bat and P sc profiles at the end of the backup time of 600 s for the optimal combination (T au = 2s, N p_sc = 8 and I bat_charge = 400 A). We notice that the SC's overcome all the peak power during T = 10 min. thanks to the recharging operation through the battery. V. SIMULATION OF THE GLOBAL SYSTEM The system controlling the combination between the SC's and the battery in the 500 kVA rated UPS is designed so that the SC's supply the full load power during short failures of the power source lasting up 10 seconds. Furthermore, the reappearing intermittent grid permits to recharge the SC's between successive outages. The SC's pack is then ready to supply the transient power load during the backup operation in order to reduce the battery stresses. Fig. 23 illustrates the power waveforms of P load , P bat and P sc for the UPS operation during three 10 seconds brownouts and for the optimal combination previously found. At time t = 80 s, the system is switched to the 10 minutes autonomous operation. The full power is supplied by the SC's during the first intermittent functioning with fast charging through the power source. On the other side, during the backup time, only power impulses are covered by the SC's which are recharged through the battery. In Fig. 24 we represent the evolution of the battery voltage U bat and the SC's voltage U sc during the two operation modes. We notice that thanks to capability of fast recharging of the SC's, their energy can be extracted then restituted in few seconds. Therefore, SC's the voltage U sc is maintained in the range of [300 V -150 V] till the end of the backup time. VI. CONCLUSION In this paper, the design of a control system which optimizes the battery-supercapacitors combination in a 500 kVA rated UPS has been presented. The advantage of having a hybrid energy source for the UPS has been shown. The importance of supercapacitors in peak power smoothing has been elaborated on. The SC's pack and the battery are modeled using Matlab/Simulink software and then validated. The reduction in battery stresses has been discussed. The supercapacitors overcome the power surges and reduce high power demands away from the battery during the backup time. They also ensure the whole load power during outages lasting less than 10 s.

The study of some performance parameters with respect to the cost of the SC's pack has also been presented and an optimal configuration has been found for a filter constant T au = 2s, a number of SC's parallel branches N p_sc = 8 and battery recharge current I bat_charge = 400 A. The cost of this system is higher today than pure battery system however it should be pointed out that supercapacitors undergo intensive development and become more and more available in small-size and low price.

At the current state, the SC's pack cost is almost triple of the battery pack cost. The system we conceived would be efficient if the battery life time is enhanced at least 4 times. We are undertaking accelerated tests on lead acid batteries to observe the effect of pulsed loads and smoothed loads on battery wear-out process and reliability. Some extensions of this work are undertaken and experimental bench has been set up to carry accelerated tests on lead acid batteries. We aim to observe the effect of pulsed loads and smoothed loads on battery wear-out process and reliability in order to quantify the efficiency of the designed system.

Fig. 1 .

 1 Fig. 1. Topology of the 500 kVA UPS

Fig. 2 .

 2 Fig. 2. Supercapacitor simplified circuit: two branches model

Fig. 6 .

 6 Fig. 6. Experimental and simulated battery discharge curves

Fig. 7 .

 7 Fig. 7. Parallel combination between SC's and battery

Fig. 8 .

 8 Fig. 8. Battery voltage versus time

  Fig.9. P load , P bat and P sc without control system

Fig. 11 :

 11 Fig. 11: Principle of power sharing between SC's and the battery where:-P load is the load power, -P bat is the battery power, -P sc is the SC's pack power, -P Lm is the limit load power.-P IV is the initial value of the battery power. 1-At time t 1 , the battery is subjected to a rising power requested by the load. A low-pass filter is applied to the load current diverting sudden power variation to the supercapacitors. The equations of this first phase can be written as follows:

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Chart of the SC's/battery combination system

Fig. 14 .

 14 Fig. 14. Power waveforms with control system: P load , P bat and P sc

Fig. 16 (

 16 Fig.16(a) illustrates the RMS current-gain for a variable filter constant T au = 1 s, 2 s, 5 s and 10 s and for variable number of parallel SC's branches N p_sc from 6 to 60 branches. Fig.16 (b) shows the RMS current-gain divided by the cost of the SC's pack.We notice from Fig.16(a) that the RMS current-gain increases according to the number of parallel SC's branches and to the filter constant. We also remark that the gain reaches an upper limit versus increasing parallel connections after which there is no enhancement for the RMS current-gain. On the other side, Fig.16(b) shows a maximum value of gain/cost of about 120 for increasing T au and N p_sc .

Fig. 16 .

 16 Fig.16(a) illustrates the RMS current-gain for a variable filter constant T au = 1 s, 2 s, 5 s and 10 s and for variable number of parallel SC's branches N p_sc from 6 to 60 branches. Fig.16 (b) shows the RMS current-gain divided by the cost of the SC's pack.We notice from Fig.16(a) that the RMS current-gain increases according to the number of parallel SC's branches and to the filter constant. We also remark that the gain reaches an upper limit versus increasing parallel connections after which there is no enhancement for the RMS current-gain. On the other side, Fig.16(b) shows a maximum value of gain/cost of about 120 for increasing T au and N p_sc .

  Fig.17(a) and Fig. 17(b) illustrate the evolution of the gain in battery energy losses and the gain per

Fig. 17 .

 17 Fig.17(a) and Fig. 17(b) illustrate the evolution of the gain in battery energy losses and the gain per

6 .Fig. 18 .

 618 Fig. 18. Energy efficiency versus T au and N p_sc

  Fig 19 (b)).

Fig. 19 .

 19 Fig. 19. Elimination rate of peak power versus T au and N p_sc

Fig. 20 .

 20 Fig. 20. System performances with SC's recharge through the battery

Fig. 21 .

 21 Fig. 21. Comparison between system performances for T au = 1 s and T au = 2 s (N p_sc = 8)

Fig. 22 .

 22 Fig. 22. Power waveforms with intermediary SC's recharging

Fig. 23 .

 23 Fig. 23. Power waveforms for successive brownout and autonomous operation

Fig. 24 .

 24 Fig. 24. Voltage waveforms for successive brownout and autonomous operation

TABLE II DISCHARGE

 II TABLE OF ONE CELL OF THE 7AH 12V CP1270 VISION BATTERY

ACKNOWLEDGMENTS

The authors would like to thank APC by Schneider Electric, Grenoble, France, for its technical assistance.