Christine Abdel Nour

Anne Migan-Dubois

Jordi Badosa

Vincent Bourdin

Claude Marchand

Tilda Akiki

Evaluation of the plane of array irradiance for a photovoltaic installation equipped with flat reflectors in different geographical locations

Keywords: Geometrical optimization, photovoltaic systems, plane of array irradiance, PV-Reflector architecture

This work describes a plane of array irradiance (GPOA) estimation study performed for a PV system equipped with flat reflectors. In fact, adding planar reflectors in front of the PV arrays will result in an increased GPOA reaching the panel's surface. This paper focuses on the GPOA study for a PV-Reflector system architecture in six different geographical locations. The study was conducted over a five years period of time and under various weather conditions. An analytical model was developed and experimentally validated for that purpose allowing the estimation and assessment of the GPOA for such system. Therefore, the study was performed according to an architectural optimization approach considering several geometrical variations in order to achieve the highest plane of array irradiance. The highest annual gain in GPOA added by the reflectors was obtained for Athens (35%) and regions with close latitudes showed quite similar results.

I. INTRODUCTION

Within the climate change awareness nowadays, the renewable energies growth is accelerating significantly. For instance, photovoltaic energy sector is developing exponentially. The estimation of the irradiance incident on the PV modules plane occupies a high importance when studying a photovoltaic installation power generation. Several technologies were developed in order to increase the concentration of the irradiance flux on the PV modules in order to enhance the electrical power generation. We can cite parabolic sensor systems [START_REF] Feuermann | High-concentration photovoltaic designs based on miniature parabolic dishes[END_REF] and Fresnel reflector systems [START_REF] Sierra | High solar energy concentration with a fresnel lens[END_REF]. Nevertheless, these two technologies are not viable in areas with low direct irradiance and their manufacturing cost is considerably high. In addition, CPV technology based on curved lenses allowing the concentration of irradiance on small multi-junction solar cells allow high efficiency levels [START_REF]Technology Roadmap Solar Photovoltaic Energy -2014 Edition[END_REF]. However the latter technology requires a cooling system and accurate solar trackers which increases the complexity and cost of the system as well. Therefore, planar reflectors technology allowing the increase of the incident flux on a PV module with a low cost comparable to that of previous technologies at manufacturing and complexity levels comes as a promising solution and several studies are under development in order to evaluate its efficiency [START_REF] Pavlov | [END_REF] [START_REF] Gelegenis | Feasibility for the use of Flat Booster Reflectors in Various Photovoltaic Installations[END_REF]. The irradiance in the plane of array (GPOA) assessment is an approach requiring calculations based on several parameters and measurements and it becomes more complex when adding planar reflectors in front of the panels. Several optical, geometrical and solar data must be taken into account for that purpose. On the other hand, the plane of array irradiance of a PV-Reflector system will be highly affected by the longitude, latitude and weather conditions. In this work, six different locations will be studied in this paper: Athens, Oslo, Palaiseau, New Delhi, Ouarzazat and Chicago (Table I). The irradiance data ( horizontal beam and diffuse) were taken from PVGIS (Photovoltaic Geographical Information System) dataset over a five years period (2012-2016) providing geographical assessment of solar resource and performance of photovoltaic technology [START_REF]Photovoltaic Geographical Information System (PVGIS)[END_REF] [START_REF] Suri | Geographic aspects of photovoltaics in Europe: contribution of the PVGIS website[END_REF].

A. Analytical estimation model

The analytical model input parameters used in our calculations are:

• The latitude and longitude of each location (decimal degrees). • BHI: The beam horizontal irradiance (W/m²), from which the beam normal irradiance (BNI) is calculated. • DHI: The diffuse horizontal irradiance (W/m²).

• OSunEl: The solar elevation angle (°).

• Albedo: The ground reflectivity factor.

• The mirror's reflectivity factor.

• Lr: The planar reflector Length (m).

• Lpv: The photovoltaic panel length (m).

• ϴtilt: The inclination angle of the PV module to the horizontal plane (°). • ϴR: The angle between reflector and the horizontal plane (°). The analytical model allows the calculation of the sun profile and position (Azimuth and Zenith) [START_REF] Hughes | class and related class materials on Engineering Astronomy at Sandia National Laboratories[END_REF] , the global horizontal irradiance (GHI), the angle of incidence (AOI ) and the view factor (between PV module and reflectors) to finally compute the plane of array irradiance in both cases: presence (GPOAMir) (1) and absence (GPOA) (2) of reflectors. The detailed model and equations as well as the experimental validation were developed in a previous work [START_REF] Nour | Geometrical optimization for a photovoltaic installation equipped with flat reflectors based on plane of array estimations[END_REF]. In order to validate our model, experimental GPOA measurements were performed over one year, without mirror with ϴtilt = 27º as well as for a period with mirrors (ϴR = 15°) at SIRTA observatory [START_REF] Haeffelin | SIRTA, a ground-based atmospheric observatory for cloud and aerosol research[END_REF], a reference meteorological and climate observatory in Palaiseau (France) which is part of BSRN (see details in [START_REF] Nour | Geometrical optimization for a photovoltaic installation equipped with flat reflectors based on plane of array estimations[END_REF]).

The following equations summarize the calculation of GPOA without and with reflectors, respectively [START_REF] Gelegenis | Feasibility for the use of Flat Booster Reflectors in Various Photovoltaic Installations[END_REF]:

(1) (2)
With DRBI and DRSR represent the direct and diffuse radiations reaching the reflector to be then absorbed by the PV array (see the details in [START_REF] Pavlov | [END_REF] and [START_REF] Nour | Geometrical optimization for a photovoltaic installation equipped with flat reflectors based on plane of array estimations[END_REF]). The DRBI contribution was only considered if the reflected irradiance covered the whole Lpv length. The case in which the Sun would be behind the reflector was also considered, for which GPOA Mir would only have a diffuse irradiance contribution [START_REF] Nour | Geometrical optimization for a photovoltaic installation equipped with flat reflectors based on plane of array estimations[END_REF]. Both equations 1 and 2 assume that the sky diffuse radiation is isotropic and the ground reflected radiation is Lambertian.

B. Optimization strategy

The objective was to find the optimal parametrical combination (ϴtilt, ϴR) from which the maximum average gain in GPOA (added by the mirrors) was computed. For this, the following variations were considered :

• Three possibilities for the reflector's length (Lr) were considered according to the lenght of the PV panel (Lpv): Lpv/2, Lpv and 2Lpv.

• Three architectural possibilities, affecting ϴtilt and ϴR: a fixed configuration, a seasonal adjustment and a monthly adjustment. Figures 2 and 3 illustrate the optimal ϴtilt and ϴR angles combinations obtained for Athens: average result of each 5 same months over the period considered (5 years), and considering a monthly (Fig. 2a and3a) a seasonal (Fig. 2b and3b) variation of the angles or a fixed architecture (Fig. 2c and3c). Each figure shows the results for each reflector's length (Lr = Lpv/2, Lr = Lpv and Lr = 2Lpv). Fig. 2 and3 show that in winter, it is more efficient to straighten the PV array since the sun is lower. It is the opposite case during summer. ϴtilt and ϴR vary in opposite cycles. Regarding the reflector, it's seen that for the lowest length (Lpv/2), the optimum results are obtained for lower ϴR values compared to Lpv and 2Lpv. In an optical perspective, for small mirror's length, it's important to lower it in order to allow its reflected irradiance to reach the top of the PV panel and thus avoid non uniform irradiance resulting in critical losses on the power production level. On the other hand, when increasing the mirror's length exceeding the length of the PV panel, it becomes interesting to straighten the reflector (ϴR) as well as the PV module (ϴtilt) in order to avoid losing a part of the reflected irradiance that could outreach the module's height. Figure 4 illustrates the gain obtained for each month after the optimization process for monthly varied (Fig. 4a), seasonal varied (Fig. 4b) and fixed (Fig. 4c) architectures. For monthly variation, through the gain curve we can observe that the geometrical optimization satisfies (gives a positive gain) each month. With seasonal variation, some months are penalized through the geometrical optimization compared to the monthly variation, nevertheless, the gains stay positive for all reflector's lengths. However, for fixed architecture, some months are highly affected with negative gain. This phenomenon can be observed between November and February and it is due to a shading effect of the reflectors onto the PV plane when the Sun is low. In this way, for this months, it would be better to remove the reflector or lower it to the horizontal plane (ϴR=0) in order to avoid its shading effect and therefore avoid PV power production losses. Finally, with a high reflector's length the higher gains achieved for fixed architectures are around spring and autumn equinoxes (around March and September) as illustrated in figure 4c. The same process was repeated for all locations and the optimization results were retrieved.

III. RESULTS AND DISCUSSIONS

The same architectural optimization strategy was conducted for all the geographical locations (Table I). Table II presents the optimal average gain in GPOA results added by the reflectors calculated over a five years period. Monthly and seasonal varied as well as fixed architectures were considered with different reflector's length. Table II presents the Gain in GPOA added by the reflectors over the entire period (5 years). This gain was obtained by computing the added GPOA in a PV-reflector system compared to a classical PV system (without reflector). Lowest gain is found for small reflectors and fixed architecture configuration (annual gain range from 2.0 to 3.3% for Lr=Lpv/2). GPOA gain doubles from Lr=Lpv/2 to Lr=Lpv for monthly and seasonal varied architectures and triples for the fixed one. It's not the same behavior between Lr=Lpv and Lr=2Lpv where the gain increasing ratio is lower. In fact, the larger we extend the length of the mirrors beyond Lr=Lpv, the shading effect increases.

Figures 5 and6 compare the average gain according to the reflector's length in the different geographical locations studied through this work. Lr=2*Lpv and the monthly variation were taken as references in Fig. 5 and Fig. 6 respectively, thus all other scenarios were normalized and represented according to these references. From the previous results (Fig. 4 and Table II), we can notice the effect of the reflector's length as well as the angular variation on the computed gain. Almost the same behavior is observed for all regions (Fig. 5); increasing the length of the mirrors will increase the gain. Nevertheless, the gain sensibility in reflector's length increases for fixed architectures. Fig. 6 shows that limiting Lr to Lpv/2 in a fixed architecture will significantly decrease the plane of array irradiance reaching the PV panel. In the latter case, going from Lr=Lpv/2 to Lr=Lpv will triple the gain. On the other hand, going from Lr=Lpv to Lr=2*Lpv will double the gain for the fixed architecture because of the shading effect described previously. Fig. 6 shows that limiting ϴtilt and ϴR to a fixed architecture will significantly decrease GPOA especially for Lr=Lpv/2. Nevertheless, in the latter case Athens and Chicago are the most affected where we can clearly notice the drop of the gain by 80% going from monthly variation to a fixed architecture. However, for high reflector's length (Lr=2*Lpv) we have a drop ratio between 10 and 25% going from monthly to seasonal varied architectures for all regions. Therefore, the more Lr is high the more a monthly varied architecture is less advantageous compared to the seasonal varied one. The results for Ouarzazat and New Delhi cities were quite similar since they have close latitudes, the same observation can be noticed for Athens and Chicago having close latitudes as well. evertheless, according to the results presented in Table II, the GPOA gain in Ouarzazat and Athens exceeds that of New Delhi and Chicago respectively and that can be explained by the diffuse ratio around 0.28 in Ouarzazat compared to 0.42 in New Delhi and 0.26 in Athens compared to 0.39 in Chicago. Thus, the average direct irradiance is higher in Ouarzazat and Athens highlighted by slightly higher gains than the regions of their same latitudes. Finally, an interesting observation can be noticed for Oslo with the highest gain ratios for fixed architecture. In this location with high latitude, the sun reaches the lowest levels which introduces the advantage of lowering the mirrors in all optimization processes in order to avoid shading effects. Fig. 7. Gain comparison between PV-Reflector architectures according to angular variation frequency Figure 7 describes the gain ratios obtained comparing the GPOA between PV-reflector architectures: a seasonal varied architecture to a fixed one, a monthly varied to a seasonal varied and finally a monthly varied to a fixed architecture. We can observe that for all locations, the gain in GPOA comparing monthly varied to fixed is the highest and it increases by increasing the reflector's length. Gain seasonal vs fixed shows that the highest is Lr, the more significant is to choose the seasonal varied architecture.

IV. CONCLUSION

A GPOA estimation modelling for a photovoltaic installation equipped with planar reflectors was presented through this work. The architectural optimization study of such system was conducted for six different regions with different latitudes and meteorological conditions over a period of five years from 2012 to 2016. The optimization results showed that each region requires specific considerations.

GPOA gain doubles or triples from Lr=Lpv/2 to Lr=Lpv in monthly and seasonal variations. The gain does not increase similarly going from Lr=Lpv to Lr=2Lpv where the increasing ratio is lower. In fact, the larger we extend the length of the mirrors beyond Lr=Lpv, the mirrors shading effect increases. Regions with close latitudes like Ouarzazat and New Delhi showed quite similar results in terms of geometrical optimization and gain in GPOA the same fact was observed between Athens and Chicago having close latitudes as well. The highest gain was achieved was 35% considering a monthly varied architecture with Lr=2*Lpv in Athens where Oslo presented the highest gains in fixed architectures because of its geographical location. A fixed architecture with small reflectors (Lr<=Lpv) show low interest as the gain is 8.2% at the most (in Oslo). The described optimization process with smaller time step is under development and will be published in a future work. Finally, a power production average gain assessment will be conducted using the GPOA results obtained as well a MPPT model developed in a previous work [START_REF] Nour | Photovoltaic system equipped with flat reflectors: new MPPT model in case of non-uniform illumination on PV modules[END_REF].

Fig. 1 .

 1 Fig. 1. PV-Reflector system architecture

Fig. 2 .

 2 Fig. 2. Optimum ϴtilt for Athens according to the reflector's length for monthly varied (a) seasonal varied (b) and fixed architectures (c)

Fig. 4 .

 4 Fig. 4. Gain in GPOA for Athens according to the reflector's length for monthly varied (a) seasonal varied (b) and fixed architectures (c)

Fig. 6 .

 6 Fig. 6. Gain comparison according to the angular variation

TABLE I

 I

	II. METHODOLOGY
		DIFFERENT LOCATIONS STUDIED
	Country	Location	Latitude Longitude	Diffuse ratio
	Norway	Oslo	59.9	10.73	0.49
	France	Palaiseau	48.71	2.24	0.53
	USA	Chicago	41.87	-87.62	0.39
	Greece	Athens	37.98	23.72	0.26
	Morocco Ouarzazat	30.92	-6.91	0.28
	India	New Delhi	28.61	77.2	0.42

TABLE II GAIN

 II FOR THE OPTIMIZED ARCHITECTURES OBTAINED FOR THE ENTIRE STUDIES PERIOD (2012-2016)

			Monthly	Seasonal	Fixed
			variation	variation	architecture
	Location	Reflector's Length		Gain (%)
		Lr=Lpv/2	7.7	5.1	3.3
	Oslo	Lr=Lpv	17.6	12.2	8.2
		Lr=2 * Lpv	32.0	24.3	16.1
		Lr=Lpv/2	7.9	5.3	2.6
	Palaiseau	Lr=Lpv	17.1	12.0	6.9
		Lr=2 * Lpv	28.1	21.7	12.6
		Lr=Lpv/2	9.9	6.1	2.0
	Chicago	Lr=Lpv	20.1	13.7	6.5
		Lr=2 * Lpv	31.7	25.1	12.4
		Lr=Lpv/2	11.8	7.9	2.5
	Athens	Lr=Lpv	23.2	16.7	6.9
		Lr=2 * Lpv	35.4	29.2	12.7
		Lr=Lpv/2	10.8	6.6	2.7
	Ouarzazat	Lr=Lpv	20.6	15.0	6.7
		Lr=2 * Lpv	30.5	26.3	13.9
	New Delhi	Lr=Lpv/2 Lr=Lpv Lr=2 * Lpv	9.1 17.5 26.7	6.0 13.1 23.2	2.8 6.9 14.9

V. ACKNOWLEDGEMENTS This work was supported by the TREND-X research program of Ecole Polytechnique.


Mohammed Benzaouia

Anne Migan Dubois

Energy management strategy for an optimum control of a standalone photovoltaic-batteries water pumping system for agriculture applications

Keywords: Energy management strategy, PV generators, MPPT, Modified P&O, DC-DC converter, Batteries, Brushless DC motor, Centrifugal pump

Pumping water using multiple energy sources is the ideal solution for supplying of potable water in isolated or arid areas. In this paper, an effective control and energy management strategy for a stand-alone photovoltaic-batteries water pumping system for agriculture applications is presented. The system is composed of photovoltaic solar panels as primary energy sources, and Lead-Acid batteries as seconder energy sources to supply the brushless DC motor and the centrifugal pump. The energy management strategy uses an intelligent algorithm to satisfy the energy demanded by the motor, also to maintain the state-of-charge of the battery between safe margins in order to eliminate the full discharge and the destruction of the batteries. Drift is a major problem in photovoltaic systems; this phenomenon occurs when the solar irradiation changes rapidly. Classical MPPT algorithms do not solve this problem, for this reason a modified P&O has been implemented, the obtained results shown the efficiency of the algorithm compared to the conventional P&O. Computer simulation results confirm the effectiveness of the proposed energy management algorithm under random meteorological conditions.

Introduction

Water pumping is usually depends on conventional resources or a diesel generator . The use of these fossil energy resources (diesel generator, propane...) not only requires expensive fuels, but also creates noise and air pollution and high maintenance costs [START_REF] Aliyu | A review of solar-powered water pumping systems[END_REF].

Combining several renewable energy sources such photovoltaic panels, and wind turbine with batteries and supercapacitors has received considerable attention recently, especially for pumping water in isolated areas where there is no grid power [START_REF] Chandel | Review of solar photovoltaic water pumping system technology for irrigation and community drinking water supplies[END_REF] and [START_REF] Khiareddine | Power management of a photovoltaic/battery pumping system in agricultural experiment station[END_REF].

These systems are environment friendly, require low maintenance with no fuel cost, and provide a continuous energy whatever the variation of the load or the weather condition [START_REF] Yin | Energy management of DC microgrid based on photovoltaic combined with diesel generator and supercapacitor[END_REF]. These hybrid systems required a management strategy in order to satisfy the load demand and to manage the power flow while ensuring efficient operation of the different energy systems. Various configurations and power management algorithms have been proposed in scientific research, in [START_REF] Zaouche | Supervision and control strategy for photovoltaic generators with battery storage[END_REF] the system consist of photovoltaic (PV) source, batteries storage, and an algorithm of power management, the system is used for electrification and water pumping. In [START_REF] Roumila | Energy management based fuzzy logic controller of hybrid system wind/photovoltaic/diesel with storage battery[END_REF] the authors propose an algorithm based on fuzzy logic controller to manage a hybrid system composed wind/photovoltaic/diesel with storage battery.

In the present work, photovoltaic panels and batteries with an intelligent power management control is applied to pump a constant flow of water under different conditions (Solar irradiation and state of charge). In order to ensure maximum extraction of power from the photovoltaic panels a Modified Perturb and Observe (MP&O) have been used. The brushless DC motor is controlled by electronic commutation.

Presentation & Modeling of studied system

The structure of the studied system is shown in Fig. 1; it contains a photovoltaic generator connected to a DC-DC converter, which is controlled by the Modified P&O algorithm in order to extract the maximum power from the PV generators. The system also contains batteries connected to a bidirectional converter to allow the current to flow in both directions, so the batteries are charged and discharged according to the user's energy demand and the methodological conditions. An inverter is used as an intermediary between the two preceding components and the motor-pump. The control of the motor is done through the electronic commutation that allows to operate the motor in the nominal capacities. The system is managed with an intelligent algorithm, which depends on the state of the three switches (𝐾 1 , 𝐾 2 and 𝐾 3 ). The design of studied system is elaborated in following sections.

Photovoltaic panels modeling

Several mathematical models of photovoltaic generators were developed to describe their nonlinear behavior and their operation. In this work, the following model (Fig. 2) is chosen [START_REF] Kumar | Solar photovoltaic modeling and simulation: As a renewable energy solution[END_REF] [8] and [START_REF] Bellia | A detailed modeling of photovoltaic module using MATLAB[END_REF]. The PV module parameters used in this work are shown in Table 1. The output current (𝐼 𝑝𝑣 ) of the photovoltaic cell under standard operating conditions (1000 𝑤 𝑚 2 ⁄ , 25°𝐶) is given by the following Eq. 1. and Eq. 2.

𝐼 𝑃𝑉 = 𝐼 𝑝ℎ -𝐼 d -𝐼 𝑠ℎ (1)
𝐼 𝑃𝑉 = 𝐼 𝑝ℎ -𝐼 s 𝑒 ( 𝑞(𝑉 𝑃𝑉 + 𝐼.𝑅 𝑠 ) 𝑛𝑘𝑇

)-1 - (𝑉 𝑃𝑉 + 𝐼. 𝑅 𝑠 ) 𝑅 𝑠ℎ (2)
Where: 𝐼 𝑠 is the saturation current, 𝑞 is the electron charge (1,6.10 -19 (C)), 𝑘 is Boltzmann constant (1,38.10 -23 (J.K -1 )), 𝑛 is the diode ideality factor, 𝑇 is the PV cell temperature (K).

In this simulation, twenty four (24) panels has been used. The simulated I-V and P-V characteristics (Fig. 3. and Fig. 4.) present the effect of irradiation and temperature of the behavior of the adopted PV generators.

Storage modeling

The purpose of using the batteries is to store the excess power and satisfy the load demand in bad weather conditions or in night periods. Many varieties model of batteries exist in the literature. In this work, the proposed model is shown in Fig. 5. It contains two electrical element: a voltage source (𝐸 𝐵 ) and an internal resistance (𝑅 𝑖 ) [START_REF] Monem | Lithium iron phosphate based battery -Assessment of the aging parameters and development of cycle life model[END_REF], [START_REF] Saw | Electro-thermal analysis of Lithium Iron Phosphate battery for electric vehicles[END_REF], [START_REF] Tremblay | Experimental Validation of a Battery Dynamic Model for EV Applications[END_REF], and [START_REF] Zhu | Development of a theoretically based thermal model for lithium ion battery pack[END_REF]. The adopted model of battery is defined by the following equations: 𝑉 𝐵𝑎𝑡𝑡 = 𝐸 𝐵 ± 𝐼 𝐵𝑎𝑡𝑡 𝑅 𝑖 (3) Where: 𝐸 𝐵 is the voltage source, 𝑅 𝑖 the internal resistance and 𝐼 𝐵𝑎𝑡𝑡 is the current of the battery. The battery capacity 𝐶 𝐵𝑎𝑡𝑡 is given by [START_REF] Shakeri | Implementation of a novel home energy management system (HEMS) architecture with solar photovoltaic system as supplementary source[END_REF]:

𝐶 𝐵𝑎𝑡𝑡 = 𝐸 𝑑 . 𝑁 𝑑 𝑉 𝐵𝑎𝑡𝑡 . 𝐷𝑂𝐷. 𝜂 𝐵𝑎𝑡𝑡 (4)
Where: 𝐸 𝑑 is the daily electrical energy required by the load (Motor-pump), 𝑁 𝑑 number of autonomy days, 𝑉 𝐵𝑎𝑡𝑡 is the battery voltage, 𝐷𝑂𝐷 is the depth of discharge and 𝜂 𝐵𝑎𝑡𝑡 is the battery performance. The state of charge 𝑆𝑂𝐶 depends on the current of the battery (𝐼 𝐵𝑎𝑡𝑡 ). If it is positive (battery discharge) then the state will decrease and discharge if negative (battery charging) then the charge will increase [START_REF] Rabhi | Energy management for an autonomous renewable energy system[END_REF]. This is given by the following equation:

𝑆𝑂𝐶 (𝑡) = 𝑆𝑂𝐶(𝑡 -1) -∫ 𝐼 𝐵𝑎𝑡𝑡 𝐶 𝐵𝑎𝑡𝑡 𝑑𝑡 𝑡 𝑡-1 (5)
Where: 𝐶 𝐵𝑎𝑡𝑡 is the capacity of battery and 𝐼 𝐵𝑎𝑡𝑡 represents the current that flow to or from the battery. After sizing calculations, ten (10) batteries of 12 Volts, with a capacity unit 𝐶 𝐵𝑎𝑡𝑡 =50Ah, have been considered.

Maximum power point tracking (MPPT)

Various algorithm were developed in order to extract the maximum power from photovoltaic panels. Perturb & Observe (P&O), Incremental conductance (Inc.) and Fuzzy logic (FL) are the most algorithm used in research [START_REF] Zahab | Design and control of a standalone PV water pumping system[END_REF] and [START_REF] Killi | Modified perturb and observe MPPT algorithm for drift avoidance in photovoltaic systems[END_REF]. In this work, a Modified Perturb & Observe (MP&O) is implemented to avoid the failure of P&O algorithm under fast changes of solar irradiation (Drift phenomenon) [START_REF] Jana | Development and implementation of modified MPPT algorithm for boost converter-based PV system under input and load deviation[END_REF].

Perturb & Observe (P&O)

The P&O algorithm is widely used to extract the maximum power from PV panels. The simple structure and small measured parameters are among the reasons why this algorithm is chosen [START_REF] Waghmare | A drift free perturb & observe MPPT in PV system[END_REF] and [START_REF] Eltawil | MPPT techniques for photovoltaic applications[END_REF]. The entire P&O algorithm is given in Fig. 6.

Modified Perturb & Observe (P&O)

The P&O technique algorithm fails under rapidly changing of solar irradiation [START_REF] Abouadane | Performance of a new MPPT method for Photovoltaic systems under dynamic solar irradiation profiles[END_REF], the P&O algorithm confused or taken improper decision at changing primary step of dutycycle [START_REF] Logeswaran | A review of maximum power point tracking algorithms for photovoltaic systems under uniform and non-uniform irradiances[END_REF]. A modified P&O technique is proposed to avoid the drift problem by incorporating the information of change in current (𝑑𝐼) in the decision process in addition to change in power (𝑑𝑃) and change in voltage (𝑑𝑉). The steps of the algorithm are presented in Fig. 7 [START_REF] Ramos-Hernanz | Novel control algorithm for MPPT with Boost converters in photovoltaic systems[END_REF]. The obtained results (Fig. 8) show clearly the efficiency of the Modified Perturb & Observe (MP&O) algorithm compared to conventional P&O.

Energy management strategy

The power management for 48h is illustrated in the flowchart of Fig. 9. The strategy is based on the evaluation of daily demand of water (𝑃 𝑑𝑒𝑚𝑎𝑛𝑑 ) by the user and on the availability of the power of solar (𝑃 𝑃𝑉 ). The algorithm consists in generating three control signals 𝐾 1 , 𝐾 2 and 𝐾 3 starting from four inputs: power of PV generators (𝑃 𝑃𝑉 ), the 𝐺 = 600 𝑤 𝑚 2 ⁄ 𝐺 = 1000 𝑤 𝑚 2 ⁄ power demand (𝑃 𝑑𝑒𝑚𝑎𝑛𝑑 ) which is given by user, the measured power (𝑃 𝐿𝑜𝑎𝑑 ) and the battery state of charge (𝑆𝑂𝐶). For the beginning, it is necessary to set the maximum and minimum limits of the batteries 𝑆𝑂𝐶. In this work, the minimum 𝑆𝑂𝐶 𝑚𝑖𝑛 is fixed to 20% and the maximum 𝑆𝑂𝐶 𝑚𝑎𝑥 to 80%. The energy management strategy is described below:

 If 𝑷 𝒅𝒆𝒎𝒂𝒏𝒅 = 𝑷 𝑳𝒐𝒂𝒅 :
Mode 1 : This mode of operation occurus during the following case : if the power generated by PV panels is greater than the power required by the load and the state of charge is less than 𝑆𝑂𝐶 𝑚𝑎𝑥 , the excess power is stored by the batteries. Mode 2 : This mode of operation occurus during the following case : if the power generated by PV panels eqaul to the power demande and the 𝑆𝑂𝐶 = 𝑆𝑂𝐶 𝑚𝑎𝑥 , so the disconnection of the batteries is necessary in order to protect them. Mode 3 : This mode of operation occurus during the following case : if the power generated by PV panels equal zero and the 𝑆𝑂𝐶 > 𝑆𝑂𝐶 𝑚𝑖𝑛 ,this mode may accur during the night and the begining and end of the day, the batteries cover the power demanded by the load until the intervention of the PV generators. Mode 4 : This mode of operation occurus during the following case : if the power generated by PV panels is less than the power demanded by the load, The batteries are used to add the necessair power as long as the state of charge is not less than the 𝑆𝑂𝐶 𝑚𝑖𝑛 . Mode 5 : This mode of operation occurus during the following case : if the power generated by PV panels equal zero and the 𝑆𝑂𝐶 is less than 𝑆𝑂𝐶 𝑚𝑖𝑛 , The load is disconnected.

 If 𝑷 𝒅𝒆𝒎𝒂𝒏𝒅 = 𝟎 :

Mode 6 : This mode of operation occurus during the following case : the power of PV generators is 𝑃 𝑃𝑉 > 0, in this case this power is stored in batteries, as long as the state of charge of the batteries does not reach maximum (𝑆𝑂𝐶 < 𝑆𝑂𝐶 𝑚𝑎𝑥 ).

Mode 7 : This mode of operation occurus during the following case : the PV generators produce power, and the state of charge of the batteries is max in this case the batteries are diconnected. Mode 8 : This mode of operation occurus during the following case : there is no load demand and the PV generators do not produce power so the system is disconnected.

Simulation & Results

In the studied system, the renewable PV power is taken as primary source, while the batteries are used as a backup and storage system. The priority is given to the PV generators, not only to exploit the entire renewable energy but also to increase the life cycle of the battery.

To test and verify the effectiveness of the energy management strategy applied to the studied system (Fig. 1). The simulation under MATLAB/Simulink over a period of two different days has been performed. Fig. 10 and Fig. 11 present the solar irradiation and temperature profiles, in the 1st day (00h-24h) the maximum irradiation value reaches 1000 𝑤 𝑚 2 ⁄ , while in the 2nd day (24h-48h) it reaches 600 𝑤 𝑚 2 ⁄ . Depending on the variations in irradiation and temperature, the power profile produced by the PV generators is given by Fig. 12. Fig. 13 shows the different powers supplied by the sources (PV generators and batteries), in addition to the load profile desired by the user, this profile (𝑃 𝑙𝑜𝑎𝑑 ) has been chosen in different periods (night, day, sunrise and sunset). Based on these results, we can differentiate four cases, which are given as follows:

Case 1: During the intervals [0h, 3h] and [23h, 26h], the load power demand (Motorpump) is 1320W, the deficient power is only supplied by the batteries because 𝑃 𝑃𝑉 = 0 and the state of charge (𝑆𝑂𝐶) of batteries is not at the minimal value.

Case 2:

In intervals [5h, 6h], [10h, 12h], [14h, 20h], [30h ,33h] and [41h, 44h] , the photovoltaic generators produce Power (𝑃 𝑃𝑉 > 0) so the batteries are in charge mode since there is no demand of power (𝑃 𝐿𝑜𝑎𝑑 = 0), and the 𝑆𝑂𝐶 𝑚𝑖𝑛 < 𝑆𝑂𝐶 < 𝑆𝑂𝐶 𝑚𝑎𝑥 . Case 3: In intervals [6h, 10h] and [33h ,41h], The load requires a power of 1320W but the photovoltaic generators do not produce sufficient power, the compensation of power is done by the batteries taking in consideration that the 𝑆𝑂𝐶 is not under 𝑆𝑂𝐶 𝑚𝑖𝑛 , (𝑆𝑂𝐶 < 𝑆𝑂𝐶 𝑚𝑖𝑛 ). Case 4: In interval [12h, 14h], there is a surplus of power produced by PV generators, and the load requires a power of 1320W, so the excess of power is stored in the batteries as long the 𝑆𝑂𝐶 < 𝑆𝑂𝐶 𝑚𝑎𝑥 . The evolution of the state of charge (𝑆𝑂𝐶) is given in Fig. 14, the (𝑆𝑂𝐶) varies between the minimum (𝑆𝑂𝐶 𝑚𝑖𝑛 = 20%) and the maximum(𝑆𝑂𝐶 𝑚𝑎𝑥 = 80%), therefore the batteries are protected against complete discharge and overcharging.

The objective was to pump a fixed water flow over two successive days and in different periods. Fig. 15 shows clearly that the pumped flow is fixed at 30 𝑚 3 ℎ ⁄ .

Conclusion

In this paper, the control and management of a photovoltaic system with storage batteries for agricultural applications has been presented. The system configuration, the MPPT algorithm and the proposed management strategy were simulated in MATLAB/Simulink environment. The obtained results show the effectiveness and the reliability of the system during two successive days under different weather conditions. The proposed management strategy allow to ensure optimal operation of the system without human intervention, which makes the system more intelligent.

Fig. 1 .

 1 Fig. 1. Stand-alone water pumping system description.

Fig. 2 .

 2 Fig. 2. PV cell equivalent circuit.

Fig. 3 .

 3 Fig. 3. P-V and I-V characteristics for different values of solar irradiation.

Fig. 4 .

 4 Fig. 4. P-V and I-V characteristics for different values of temperture.

Fig. 5 .

 5 Fig. 5. Electrical model of the battery.

Fig. 6 .

 6 Fig. 6. Flowchart of the conventional P&O MPPT algorithm.

Fig. 7 .

 7 Fig. 7. Flowchart of the drift-free modified P&O MPPT algorithm.

Fig. 8 .

 8 Fig. 8. Comparison between conventional & modification of P&O algorithm for one panel.

Fig. 9 .

 9 Fig. 9. Flowchart of energy management strategy.

Fig. 10 .

 10 Fig. 10. Profile of the solar irradiation.

Fig. 11 .

 11 Fig. 11. Profile of ambient temperature.

Fig. 12 .

 12 Fig. 12. Power of PV generator.

Fig. 13 .

 13 Fig. 13. Power profiles (𝑃 𝐵𝑎𝑡𝑡 , 𝑃 𝑃𝑉 and 𝑃 𝐿𝑜𝑎𝑑 ).

Fig. 14 .

 14 Fig. 14. State of charge of batteries.

Fig. 15 .

 15 Fig. 15. Water flow.

Table 1 .

 1 The PV module parameters.

Parameters Values Numbers of cells in a module, 𝑁 𝑐 36 Open circuit voltage , 𝑉 𝑂𝐶 21.8 V Short circuit current, 𝐼 𝑆𝐶 7.24 A Maximum voltage at MPP, 𝑉 𝑀𝑃𝑃 17.2 V Maximum current at MPP, 𝐼 𝑀𝑃𝑃 6.69 A Maximum Power at MPP, 𝑃 𝑀𝑃𝑃 115 W


Khadim Ullah
email: khadim.jan@geeps.centralesupelec.fr

Waqar Uddin

Anne Migan

Mashood Nasir

Demba Diallo
email: demba.diallo@centralesupelec.fr

Imran Khan
email: imran.khan@u-psud.fr

Reuse Legacy to Repower the Microgrids-An Affordable Solution for Test and Restoration of Repurposed Lead Acid Batteries

Keywords: cost reduction, microgrids, battery testing, second life, lead acid batteries, battery restoration, legacy

Initial cost is an important consideration as many problems raised by the insufficient battery capacity had eventually resulted in microgrid failure. The trending use of expensive, but more efficient and maintenance free lithium-ion batteries in millions of light vehicles such as golf carts will decommission a large amount of existing lead acid batteries to be used for electrification purposes at much lower cost. These used batteries in their second life can significantly reduce the storage cost of electrification in off-grid systems or in the most demanding business activities such as powering vendor hand-carts and community shops. Though, the used batteries are sold at cheaper price, they still require costly equipment and time consuming tests to evaluate if and for how long they can be repurposed. This paper is prepared to propose a rapid, low cost, and bulk test procedure for lead acid battery characterization, capacity measurements, and restoration without any of their known history or datasheet using deep cycling process. Parameters are suggested to help in remaining life identification and to qualify these batteries for grouping in power packs based on their health and capacity. Finally, a process to review test results and make appropriate decisions regarding the battery reuse or recycling is provided.

I. INTRODUCTION

The market of the off-grid renewable or hybrid renewable electrification system is composed of very low income households [1], [START_REF] Habib | Design Optimization and Model Predictive Control of a Standalone Hybrid Renewable Energy System: A Case Study on a Small Residential Load in Pakistan[END_REF]. Initial cost of the battery bank had remained a major issue in achieving the ambitious target of sustainable energy for all and 24/7 energy access by every citizen and in particular by the poor in the remote locations [3]. This indeed put pressure on lowering the cost of any electrification system proposed for such applications [START_REF] Nasir | Solar PV-Based Scalable DC Microgrid for Rural Electrification in Developing Regions[END_REF]- [START_REF] Kumar | A Novel Methodological Framework for the Design of Sustainable Rural Microgrid for Developing Nations[END_REF].

It is a known field practice that a lot of common issues with the Photovoltaic (PV) or hybrid PV/diesel grid collapse [7] is the undersized battery storage system [START_REF]IEEE Approved Draft Recommended Practice for Sizing Lead-Acid Batteries for Stand-Alone Photovoltaic (PV) Systems[END_REF] to reduce high initial cost. In areas with increased power cut, the shop owners and the poor with vendor carts to sell fruits and vegetables are losing revenues and unable to fulfill their basic needs. In order to reduce the high initial cost on storage for households and electrification services on hand-carts, second life lead acid batteries are considered as a potential solution [START_REF] Mohsin | Lead-acid battery modelling in perspective of ageing: a review[END_REF], [START_REF] Dulout | Working towards greener golf carts -A study on the second life of lead-acid batteries[END_REF].

In light of the reports from Technavio [11], the global market of all light vehicles such as golf carts is dominated by the lead acid batteries about 99% a decade ago to about 86% in 2018 and is forecasted to reach up to $65billion by 2022. However, the golf carts market has seen a surge in using the lithium-ion batteries. Since, the lithium-ion batteries are more efficient, maintenance free, and having better life cycle enabling them attractive for future use in automobiles. In this context, the dominance of the lead acid batteries in light vehicles is forecasted to sink further and available for basic electrification as more and more lithium-ion batteries are deployed for traction purposes of light vehicles [START_REF] Ceraolo | Lithium-ion startinglighting-ignition batteries: Examining the feasibility[END_REF].

The chemical energy stored in a lead acid battery can be translated into reversible electrical energy [START_REF] Morse | Storage Batteries[END_REF]. This enables this simple battery-rechargeable, as indicated by (1). (1) whereas, the rate of chemical reaction changes with: (i) battery storage capacity, stage of charge, temperature, and ageing.

The simple inner chemistry had enabled this technology to be assembled even at local level. Simple refurbish techniques [START_REF] Krandikar | Review on desulfation of lead-acid battery for HEV[END_REF] had enabled the technology more attractive to the poor. However, due to the increased demand, the characterization of used lead acid batteries in bulk is still time consuming, laborintensive, and unreliable [START_REF]IEEE Guide for Selecting, Charging, Testing, and Evaluating Lead-Acid Batteries Used in Stand-Alone Photovoltaic (PV) Systems[END_REF]. All of these, and until now, as compared to other storage options, lead acid technology is mature enough to dominate the transportation and basic electrification needs at much affordable cost [START_REF] Nasir | Optimal Planning and Design of Low-Voltage Low-Power Solar DC Microgrids[END_REF].

The huge growth of battery markets [START_REF] Shah | Automotive Battery Market Outlook, Share, Size Growth, Business Report and Future Prospects[END_REF] in the 20 th century (eventually consuming about 75% of the world's lead production) largely paralleled the rise of the automobile, in which batteries found application for starting, lighting, and ignition (SLI) (the SLI battery), and uninterruptible power supplies in homes, shops, clinics, markets, and public places.

In parallel, the operation of PV or hybrid PV based micro/nanogrids using lead acid batteries for rural electrification is trending at least until the availability of the affordable second life lithium-ion batteries by 2025. The goal of electrifying the last billion will significantly demand an increased amount of the second life lead acid batteries for offgrid electrification purposes. Interestingly, the lead acid batteries are the mature and cheapest storage option, that will continue to have a hold on their use for the basic electrification. Lead acid batteries for their second life service are readily available at much cheaper cost by decommissioning them from millions of light vehicles such as forklifts or golf carts. The main goal of this paper is to present highly reliable, less labor intensive method for bulk test and restoration of second life lead acid batteries using readily available tools. The proposed method is effective in qualification of the legacy for re-deploying in off-grid electrification, or vendor hand-carts.

The rest of the paper is organized as follows: Section II explains the role of legacy and low cost storage batteries for electrification in more detail. Section III details the innermechanism of lead acid battery and highlights the basic action inside an electrolyte. In Section IV, the bulk characterization and test techniques are presented. Finally, Section V contributes to the main large scale experimental test setup and methods of restoration of lead acid batteries. Also, based on the obtained results, a concluding statement and possible future work is given in Section VI.

II. ROLE OF LEGACY BATTERIES FOR LOW COST OFF-GRID ELECTRIFICATION

World over the economic growth is driven by energy; either in the form of finite resources such as coal, oil, and gas or in renewable forms such as hydropower, wind, solar, and biomass, or their converted form; the electric power. This energy generation and consumption powers a nation's industries, vehicles, homes, and offices. It also has a significant impact on quality of the country's air, water, land, and forest resources. For growth to be sustainable, it must be both resource efficient and environmentally-safe. In most of the developing countries, like in Asia and Africa, the demand for electricity has always been more than the supply. This is the reason that most of the people living in rural areas and even the far flung cities face significant power cut.

People with unemployment due to limited energy access is a potential threat to global security. To start even a local small scale business need access to reliable energy to power-up at least an LED bulb for lighting purposes. The significant demand for household electrification and vendor hand-carts have find its way in use of legacy lead acid batteries using minimum cost on restoration. As, most of the local business activities and market visits starts by the evening, thus, keeping in view so, thousands of used car batteries up to capacities of 60Ah have been deployed in the city circle of district Mardan for electrification of vendor hand-carts as shown in Fig. 1. 2, that uses lead acid batteries remain an active practice, but in parallel a bit challenging one. The standalone microgrids are being frequently deployed not only for households, but for commercial facilities like market shops, rural banks, municipal hospitals, and gas stations where power supply is unreliable, limited, or of poor quality. Batteries plays an important role to back-up the load in all of the above mentioned cases.

The legacy batteries can be regrouped in power packs based upon their state of health and capacity. The power packs may be average, below or above average, and the best one. It is always desirable to avoid batteries from extreme operational environment that can quickly exhaust the batteries and result in system collapse. As an example, during the low load demand the weak battery power pack can be engaged to handle it. The fresh batteries are to be engaged in case of peak demand. This enable the battery packs life cycles longer and ensure the system safe from voltage collapse.

The use of legacy batteries in power packs is of particular interest as it also eliminates the circulating current caused by connecting batteries with different health and capacities together. Power packs are individually isolated from the DC bus using dedicated DC/DC convertors as reflected in Fig. 2 .

III. INNER CHEMISTRY OF THE LEAD ACID BATTERY

Lead acid batteries consist of several cells, also called accumulators. The nominal voltage of a cell is 2V. These cells are connected in series configuration to obtain the expected voltage for a variety of applications. The 2 volt cell is the basic unit of a lead acid battery. It consists of an alternately gathered group of positive plates whose active material is (PbO2) and negative plates (Pb). The number of plates of each polarity and their dimensions are the main parameters that define the cell capacity. In order to avoid short circuits between the different polarity plates, an insulating micro-porous separator is placed between these plates during assembling process. Positive plates are put together in pack as well as negative plates. These are illustrated in Fig. 3. Further, an assembled cross-sectional detail is as depicted in Fig. 4. No matter, what the function is planned for, commonly, the lead acid battery consists the essential components as depicted in Fig. 4. The positive and negative packs are then grouped together and finally put in a container filled with an electrolyte.

All of these, i.e. packs of negative and positive plates, electrolyte, and container, form a cell. The electrolyte is a solution of sulfuric acid and distilled water. The container is generally made of polystyrene. The container has to keep the acid within the cell and at the same time provides mechanical support to the battery. It is designed in a variety of ways to prevent leakage and dry-out while allowing accumulated gases to escape easily through vent plugs. The two terminals made of lead metal connected with the pack of each polarity allow the connection to an external circuit. IV. BULK CHARACTERIZATION AND TEST PROCEDURE Some of the most widely known battery parameters are: battery and cell voltages, environment and cell temperatures, battery cell current, and (for flooded cells) cell fluid level, and specific gravity. Less well-known are: cell internal resistances, cell connection resistances, ripple current, cell maintenance current, cell voltage oscillation, and cell selfdischarge that is also strongly dependent on temperature.

Resistive current-path segment is a condition in which some portion of the current path through the battery becomes overly resistive. In such event, i.e. discharge coincidentally, the flow of bank float current will cause excessive voltage drop across the impairment, and in some cases, the resulting 'I 2 R' heating power loss at the defect will initiate thermal runaway leading to melting, arcing (from 𝐿𝑑𝑣/𝑑𝑡 effects), and (potentially) explosion. Adverse environment is a condition in which the battery is frequently subjected to thermochemical stresses that will inexorably diminish its capacity, reliability, and life. Improper charger voltage is a condition in which the battery is being either over or undercharged because the charger voltage has not been set equal to the manufacturer's prescribed cell voltage multiplied by the number of cells in the bank. Specific gravity test is important as if the temperature corrected specific gravity is more than 15 points below the manufacturer's specified value, then the battery may not be receiving adequate charge or an individual cell may be damaged or not functioning properly.

In summary, if the measured capacity is more than 80% of the manufacturer's specification and there are no low cell voltages and/or specific gravities, then the battery and the charging parameters are probably acceptable. If measured capacity is significantly below specifications, then a re-test should be considered to determine if the battery replacement is necessary, and/or if the battery charging/discharging scheme needs to be modified.

A. Capacity rating and C (Charge/Discharge) Rate:

Stationary batteries are rated for a particular capacity in terms of Ampere-hour (Ah) normally at C10 (10-hour rate of discharge), that is a battery rated at 100Ah will provide 10A for 10 hours or 100% of its capacity at 10-hr rate of discharge. Further, at any higher rate of discharge, the output will be less than the rated output in Ah. Conversely, at the lower discharge rates, the output will be higher than the rated output at C10.

B. Self-Discharge Loss / Retention of Charge (ROC):

All types of batteries when unused and off-shelf, discharge slowly, but continuously by a phenomenon called selfdischarge [START_REF] Al-Jabarti | Data Center Flooded Lead Acid Battery Early Degradation Causes, Analysis, and Mitigation[END_REF]. This energy loss is due to local action inside the battery that depends on level of minute impurities in battery elements and accuracy of manufacturing process control. Also, a substantial rise in the operating temperature is an external factor which increases the self-discharge loss. The self-discharge loss is measured by ROC test which determines the amount of charge retained by a battery after free standing for 28 days at a standard temperature of 20C o .

The ROC test as per IS:15549 for VRLA batteries and IS:13369 for flooded tubular mono-block new batteries [START_REF]IS:15549 Stationary valve regulated lead acid batteries" Standards for Stationery Batteries[END_REF] accepts self-discharge loss within 10% and 5%, respectively. Customer can safely ascertain that the quality of material used and the manufacturing process control are good, simply by ensuring that the batteries meet the ROC limits. A battery with poor ROC can have multiple deficiencies (by way of raw material input or manufacturing defects) inside and the selfdischarge loss can grow by 3 or 4 times over the period of the battery useful lifetime.

V. METHODOLOGY OF RESTORING THE USEFUL CAPACITY OF SECOND LIFE BATTERIES AND EXPERIMENTAL SETUP

Once the used batteries in bulk are received at the workshop, some less labor intensive and quick procedure is used to regroup the batteries for later decision on their suitability to be reused or recycled. In Step 1, the collected or decommissioned batteries are sorted and passed through physical inspection. If the physical inspection is passed, then in Step 2, the batteries are passed through another test to determine the sulfated or shorted cells. Finally, in Step 3, the batteries are qualified to regroup in battery power packs based on their remaining useful capacity and health. It is to note that battery power pack is an assembled pack to reach a certain voltage, current handling capability, and power rating.

The battery power packs may be of very good, above average, average, or weak back-up capabilities that rely on their state of health and capacity. The battery packs serve an important role to the light and heavy loads in the form of individual groups or they could be charged discharged independently from the common bus to eliminate the internal discharge or circulating currents due to mismatch in the innerresistance of the battery plates. This is of particular interest especially in the microgrid scenario where the load is normally fed in tiers i.e. from low load such as general lighting, phone charging, air circulation, laptops, or television (~50W) to the average and high loads including community lighting and electric fans (~200W), all in the residual capacity of the repurposed used batteries.

A. Physical Inspection and Initial Tests: 1) Sorting

These tests are the easiest, less labor intensive, and much quicker one i.e. the (i) Open Circuit Voltage (OCV) test (ii) terminal condition (iii) color of plates (iv) color of vent plugs and (v) the specific gravity of electrolyte. This is the best way to start for physical inspection. Due to electrolyte stratification most of the lead acid batteries do not accept charge from low current sources such as solar. In this test, if any of the battery voltage is below 6V it is considered as completely dead and scrapped for lead recycling. It also indicates that if three or more cells are completely dead, then their refurbishment cost will be high. The battery terminal condition will quickly indicate the usage of battery. The plates color indicates the wear and tear and its chances of recovery. The color of vent plugs is a quick way of indication of the battery health. If it is black, the cells are in extreme wear and tear condition. The electrolyte had to be spilled-out and washed completely to remove the contaminations. After a satisfactory visual inspection, if everything appeared to be normal, the additional tests are carried out as follows.

2) Specific Gravity Test

Hydrometer, that is available in the market for nearly $1~2 can rapidly identify the battery condition. If the gravity of all the cells is uniform and low it means that battery is completely recoverable, only it is low on charge or was deeply discharged.

3) Individual Cell Test

It is possible that a battery passes all of the above tests, however, one test is necessary to identify the individual cell voltage. This can be done using multimeter probes dipped in the electrolyte one by one. The fully discharged cell indicates ~1.75V while the dead cell will show much less than that. The equation that best characterizes a cell is given as [START_REF] Habib | Design Optimization and Model Predictive Control of a Standalone Hybrid Renewable Energy System: A Case Study on a Small Residential Load in Pakistan[END_REF].

{ 𝐼 = 𝑃 𝑐𝑒𝑙𝑙 /𝑉 𝐶 𝑏 (𝑂𝐶𝑉). 𝑑 (𝑂𝐶𝑉) 𝑑𝑡 𝑂𝐶𝑉 (𝑆𝑂𝐶) + 𝑅 𝑖𝑛𝑡 (𝑆𝑂𝐶). 𝐼 (2)
Where, 𝐼 , 𝑃 𝑐𝑒𝑙𝑙 , 𝑉 , 𝑅 𝑖𝑛𝑡 , and 𝑆𝑂𝐶 are the individual cell's current, power, voltage, internal resistance, and state of charge, respectively. Also, 𝐶 𝑏 represents the battery capacity in RC equivalent model capacitance in series with 𝑅 𝑖𝑛𝑡 .

4) Light Load Test

This test is necessary before qualifying the battery for power packs. This load test can be done with a 100W bulb connected through a cheap invertor. If the voltage drops by more than 1V, every cell may be tested for their cell voltage.

5) Sulfated, Open, or Shorted Cells Tests

This is one of the easiest and fastest method of identifying the faulty cells using a short circuit between battery terminals for 10 seconds. Cell with no bubbles or few bubbles is hard sulfated; with reasonable bubbles are normal; and with boiling and gasification, is shorted. The hard sulfated cells can be recovered, however, shorted cells are to be refurbished as any of the recovery techniques with a shorted cell is waste of time.

The sulfation test is basically a high load test to obtain the information the way a battery gets fully discharged or accept charge. Use a conventional charger/invertor with lower cutoff voltage set at 10.8V. Note down the time and compare the voltage on load with the open circuit voltage. The fair good indication of a sulfation that causing much higher internal resistance is that the battery will have much lower amperage capacity at a high load test. When the load is removed the battery OCV suddenly bumps up to roughly above 12V.

6) Battery Charging Response Test

This test is carried out for batteries having no shorted cells as could be identified from the Test 5. The battery voltage with hard sulfation will quickly rise and the charger will shut down. If the battery is fine, the battery sulfation dissolves into electrolyte and the battery voltage will keep fall under charge condition that indicates that the battery is accepting charge. These are illustrated in Fig. 5 and Fig. 6, respectively.

B. Battery Reconditioning and Recovery:

After the batteries have qualified for reconditioning and recovery process, the following method has been proposed.

1) Heavy Cycling Method of Restoration

The thrown away or decommissioned batteries can be put to toxic lead recycling to get a new battery, but it won't be a favor to the environment. It has been observed that majority of the discarded batteries for whatever reasons, do not accept charge even for a very long time or the charging system refuse to charge these old batteries due to thick sulfation on the lead plates. These lead sulfate crystals resist to the flow of current and it is the number one cause of the failure of lead acid batteries. Such batteries have no amperage capacity and they exhaust within an unexpected short time. It is because the battery remained un-charged for indefinite time and hence heavily sulfated due to electrolyte stratification. Interestingly, these batteries are recoverable using heavy cycling method.

The proposed heavy cycling method relies on overcharging using an archaic cheap dumb charger and to deep discharge using a heavy load of amperage of at least twice the battery C10 discharge capacity in controlled manner. In this case, 20A (240W/12V) load is a good number that is twice that of the 100Ah discharge capacity of the battery. This way the plates breath and the crystals break down turning back into proper kind of lead raising the acid concentration in the battery. This allows to pass current through these plates from chemical reaction. The battery electrolyte will get boiled and outgassing, but that's normal and also it's an indication of the job going pretty well. Though, there are other techniques that sound good to non-technical people who like to believe them, but there's nothing behind such market snake-oil techniques like putting Aspirin, Baking soda, or Epsom salt in each cell. If these would have worked, the battery manufacturers could benefit by adding Epsom salt, they would do so, but they don't.

Since, the microcontroller based or standard smart charger won't desulfate batteries, as it simply won't go up for a while due to low voltage of the used battery. In this case a standard dumb old charger consists of a transformer and rectifier best fit for the cycling to break majority of the irreversible sulfates from the battery plates. These crystals will get settled down as a result of breathing by the battery plates during heavy cycling. However, due to overcharge a standard automotive light should be used in series to avoid boiling of the electrolyte for sealed Absorbed Glass Mat (AGM) batteries or to pop the vents up for flooded lead acid batteries. It is recommended to use a variable auto-transformer to crank the voltage of the charger a little bit down during the overcharge condition.

In this process, it is observed that during the first cycling, the battery didn't last very long, but that's normal. The dumb charger was hooked up again for the next heavy charge cycle and the readings in Table-II were observed. This indicates that the battery is recovering and the useable capacity is increasing as indicated by increase in charge acceptance. Further, an increased overcharge may easily break sulfation, however, gasses exhausted pretty aggressively causing the acid splattering around. It is observed that during the heavy cycling process more capacity out of these dead batteries has been achieved. It is also observed that at some point after four cycles the capacity recovery stops or increases negligibly. That's done. The battery was put out of the setup and was put back to service with a reasonable life, as in Fig. 7.

Finally, there are of course few market snake-oil such as: to break the sulfation by powerful machines in five minutes, or the battery-desulfators, but what they clean out is a person's wallet and not the resistive acid crystals. Epsom salts for the battery recovery is right on the money as well. In a pinch it works, but it's no long term magical fix. These are just debunked methods with no clear scientific validations in white papers and academic research. Though, Epsom salts can give a few more months of battery life for very little effort, but accelerated self-discharge, plate corrosion prevents using these in the technical context for long lasting second life service. This concludes our work that the lead acid batteries are mostly recoverable with simple test and restoration techniques. The highly sulfated battery in this case had initially refused to accept charge due to intact acid crystals on lead plates. They were cracked-down using slight overcharging by the dump charger and discharged through heavy load for few cycles. The standard charger can't be used in this application as it will turn-off as the voltage bumps up in the initial stage.

VI. CONCLUSION

Discussion on lowering the storage cost of the off-grid electrification for rural communities is pretty much spot on. Every year, millions of batteries are thrown away or junked due to a condition called-sulfation, that is recoverable. This paper had covered giving the second life of service to dead lead acid batteries using simple, quick, and low budget methods of restoring the capacity using the heavy cycling process. The second life service of batteries had proven to be better on the path of green theme than being thrown away for recycling. In the context of the off-grid electrification, the repurposed batteries had been trialed on many vendor handcarts and microgrid electrification purposes and an overall satisfactory response has been observed. Results have shown that thousands of vendor hand-carts, shops, and remote houses can be powered easily using such batteries. In doing so, they can delay the recycling process and extend the useful lifetime up to 3-4 years with reasonable capacity, thereby, obtaining new revenues and contribute to the green environment. Future work will particularly encompass more quick and reliable measurement methods in bulk for different installations and different used battery models. In order to extend the second life, a super capacitor based hybrid storage will be modeled and analyzed for an efficient and extended performance in off-grid electrification systems.

  P b + P b O 2 + 2H 2 SO 4 P b ⟷ 2P b SO 4 + 2H 2 O

Fig. 1 .

 1 Fig. 1. Electrification of the thousands of vendor hand-carts and local shops using repurposed batteries in Mardan district, Pakistan

Fig. 2 .

 2 Fig. 2. Illustration showing the topology of the hybridized diesel renewable based clustered microgrid with decentralized control scheme using local measurements; second life lead acid batteries in nanogrid clusters and in back-up microgrid Increasing attention to the global climate change and the sustainable development open new applications for off-grid renewable or hybrid renewable systems. Off-grid hybrid power systems (PV and diesel generator sets) such as the one shown in Fig.2, that uses lead acid batteries remain an active practice, but in parallel a bit challenging one. The standalone microgrids are being frequently deployed not only for households, but for commercial facilities like market shops, rural banks, municipal hospitals, and gas stations where power supply is unreliable, limited, or of poor quality. Batteries plays an important role to back-up the load in all of the above mentioned cases.

Fig. 3 .

 3 Fig. 3. Schematic representation of a flooded lead acid battery [18]

Fig. 5 .

 5 Fig. 5. Charge acceptance response of a completely sulfated battery

Table - I

 - indicates the approx. output as a '%' of C10 capacity.

TABLE I .

 I BATTERY OUTPUT CAPACITY AS A PERCENTAGE OF C10

		Lead acid battery
	Positive plate in pocket separator
	Positive plate
	Positive grid
		Negative plate
	Battery cell	group
	Negative plate
	Negative grid
	Positive terminal	Negative terminal
	Plugs
	Connectors Sulfuric acid solution		Cap Element separators	Max. Discharge Duration in Hours for Flooded Tubular Batteries	Max. Discharge Duration in Hours for Valve Regulated Lead Acid Batteries (VRLA)	Percentage Output	Current (Amperes)
				hours	hours	%	A
	Plate separators		Negative plates	10 hours (C10)	10	100	10.0
				08 hours (C8)	8	95.0	11.9
	Box		plates Positive	05 hours (C5)	5	83.3	16.7
				04 hours (C4)	4	78.2	19.5
				03 hours (C3)	3	71.7	24.0
	Battery element			02 hours (C2)	2	63.3	31.5
				01 hours (C1)	1	50.0	50.0

TABLE II .

 II HEAVY CYCLING FOR DESULFATION AND RECOVERY

	100Ah Lead Acid Battery	Connected Dumb Charger	Connected Load Through a Cheap Invertor	Initial Current Acceptance (A)	Charging Time (hrs.)	Discharge Time@ 20A (mins)	Percentage Capacity Recovery (%)
	Cycle 1	16V/6A	200W	0.1	24	10	3.30
	Cycle 2	16V/6A	200W	1.2	24	30	10.0
	Cycle 3	16V/6A	200W	2.5	24	50	16.7
	Cycle 4	16V/6A	200W	3.3	24	90	30.0

ACKNOWLEDGMENT

Special thanks to Dr. Imran Khan, the AIT Thailand alumnus and Professor in the Department of Electrical Engineering, University of Engineering & Technology Mardan, Pakistan for his valuable comments and feedback. Also, discussions with several colleagues were valuable in clarifying some of the thoughts given here, for which we are grateful.

This research is sponsored by the Islamic Development Bank (IsDB) under the Agreement No. 600036563 Sustainable Energy & Power. *As a faculty member of the Department of Electrical Engineering, full support is received from the


Dr Lu Liu

Dr Ning Guo

Dr Julie Champion

Dr Jérôme Graton

Dr Gilles Montavon

Dr Nicolas Galland
email: nicolas.galland@univ-nantes.fr

Rémi Maurice
email: remi.maurice@subatech.in2p3.fr

R Maurice Subatech

Towards a stronger halogen bond involving astatine: unexpected adduct with Bu 3 PO stabilized by hydrogen bonding

The halogen bond is a powerful tool for the molecular design, and pushing the limits of its strength is of major interest. Bearing the most potent halogen-bond donor atom, astatine monoiodide (AtI) was recently successfully probed [Nature Chemistry 2018, 10, 428-434]. In this work, we continue the exploration of adducts between AtI and Lewis bases with the tributylphosphine oxide (Bu3PO) ligand, revealing the unexpected experimental occurrence of two distinct chemical species with 1:1 and 1:2 stoichiometries. The 1:1 Bu3PO!AtI complex is found to exhibit the strongest astatinemediated halogen bond so far (with a formation constant of 10 4.24±0.35 ). Quantum chemical calculations unveil the intriguing nature of the 1:2 2Bu3PO!AtI adduct, involving a halogen bond between AtI and one Bu3PO molecular unit plus CH!O hydrogen bonds chelating the second Bu3PO unit.

With the ultimate aim of controlling the stability and properties of molecules and materials, it is of fundamental interest for chemists to improve the understanding of intermolecular interactions and to explore their strength limits. Among the non-covalent interactions available in the chemist's toolkit, the halogen bond (XB) has been recognized to be strongly impactful in various fields such as organocatalysis, drug design in biochemistry and medicinal chemistry, crystal engineering and production of liquid crystals. [1- 5] In short, XBs are attractive and highly directional interactions between an electrophilic region (called σ-hole) of a halogenated R-X compound (called XB donor) and a Lewis base (called XB acceptor). [6] To establish the propensity of XB acceptors to engage in XBs, Laurence et al. introduced in 2011 the diiodine basicity scale (pKBI2), [7] based on complexation constants measured in organic solution between a reference XB donor (I2) and a large set of Lewis bases. Among the halogen elements, astatine (At, Z = 85) is the heaviest naturally occurring one, and it has been predicted to be the strongest XB donor atom, [8][9][10] despite the persistent lack of experimental data. However, we have recently evidenced the very first XBs involving At via the formation of adducts between astatine monoiodide (AtI) and several Lewis bases. [11] The comparison between the measured equilibrium constants (log KBAtI) and the available pKBI2 values for the same Lewis bases, disclosed a quasi-proportional relationship:

log

KBAtI ≈ 1.56(22) × pKBI2 (1)
Hence, AtI indeed appears as a stronger XB donor than I2, even though a limited set of Lewis bases has been investigated so far.

It is of prime importance to reach the strongest possible XBs involving the astatine element.

To this end, both the XB donors and acceptors may be varied, although the relevant options are severely limited by experimental constraints. On the one hand, even though other halides such as AtBr and AtCl are expected to lead to even stronger donor abilities than AtI, [12] the experimental limitations coming from their narrow predominance domains [13] cause a great challenge to evidence further XB interactions. On the other hand, the selection of Lewis bases is also quite limited. First, the ligands must be stable enough in the acidic and oxidizing conditions which allow the appearance of the AtI species. Accordingly, nitrogen Lewis bases, such as amines, pyridines, anilines, guanidines or imines, should be avoided due to the protonation of the acceptor site under the applied conditions. Second, the ligands must be soluble in an organic solvent. Third, the ligands should have a good affinity for I2, which eventually leads to a large KBAtI value. For this purpose, tributylphosphine oxide (Bu3PO) has been selected as a potential candidate, actually displaying a pKBI2 value of 2.75. [7] According to the equation (1), a larger KBAtI constant than what has been reported so far (4.01 ± 0.31 for Et2S [11] ) is anticipated. Although this may not be the ultimate ligand for maximizing the XB bond strength, we focus on this sole ligand that has led to a very unexpected behavior: the occurrence of two adducts (vide infra). Actually, astatine is the rarest natural element on Earth and, as a radioelement, all of its isotopes are short-lived (t1/2 ≤ 8.1 h). [14] It can be artificially produced via nuclear reactions, but in minute quantities, limiting experimental investigations to the ultra-trace scale (concentrations below 10 -10 mol L -1 ). Consequently, conventional spectroscopic tools are unsuited to get experimental information at the molecular level, which can fortunately be obtained by molecular modeling tools. In fact, at ultra-trace concentration, only "indirect" experimental method, based for instance on electromobility, chromatography, or competition, can be used. [15][16][17][18][19] In this work, the liquid/liquid competition method has been applied. The underlying principle is to track the radioactivity distribution between two immiscible phases as a function of the experimental conditions. A variation of the distribution reveals an astatine speciation change in at least one of the two phases. [11,20] Here, a cyclohexane solution of Bu3PO was mixed with an aqueous solution containing 0.05 mol L -1 HClO4 and NaI, doped with 211 At. For a series of experiments, the NaI concentration was kept fixed while the Bu3PO concentration in the organic phase was increased. These two phases were well mixed by shaking for 2 hours to reach the reaction equilibrium, and were separated afterwards. An aliquot of each phase was then taken to measure the radioactivity by a liquid scintillation counter.

The distribution coefficient of astatine (D) is defined as the ratio between the volumetric radioactivity in the organic and aqueous phases. Considering the pKa value of HI (-9.5), dissolved NaI salt releases 100% of the ionic species I -. Under the experimental conditions (see SI), At + is the predominant astatine species and it readily reacts with I -. [20,21] The selected I -concentration range (from 0.01 to 0.2 mol L -1 ) ensures that AtI and AtI2 -initially predominate in the aqueous phase. In contrast to AtI2 -, AtI can be significantly extracted towards the organic phase, hence being the only species able to interact with Bu3PO in the organic phase. Thermodynamic models, based on the key equilibria at play in this biphasic system, are tested to reproduce the experimental D values. Three experimental cases with [I -] = 0.01, 0.1, and 0.2 mol L -1 are displayed in Figure 1 to illustrate our procedure to establish the best fitting model. In all the cases, D is practically constant below 10 -4 mol L -1 of Bu3PO. From 10 -4 to 10 -2 mol L -1 , D increases sharply with a maximal slope depending on the added I - concentration. The increase in D is finally slowing down at higher Bu3PO concentrations. For all the considered cases, AtI2 -is the initial predominant astatine species in the aqueous phase. [21] Its formation from AtI is ruled by reaction (2), with a previously determined equilibrium constant K (10 2.7±0.3 at zero ionic strength). [21] The partitions of Bu3PO and AtI in the two phases are taken into account via equilibria (3) and ( 4), overlined species relating to the organic phase. D1 (10 0.02±0.02 ) has been determined from total organic carbon (TOC) measurements in the absence of astatine, while D2 is a parameter adjusted during the fitting process. In the organic phase, all the models consider the formation of the expected 1:1 complex via reaction (5).

AtI+I -K ⇌ AtI 2 - K= [AtI 2 -] [AtI]×[I -] (2)
Bu 3 PO D 1 ⇌ Bu 3 PO $$$$$$$$$$ D 1 = %Bu 3 PO $$$$$$$$$$ & [Bu 3 PO] (3) AtI D 2 ⇌ AtI $$$$ D 2 = %AtI $$$$ & [AtI] (4)
Bu 3 PO $$$$$$$$$$ +AtI $$$$ K BAtI ⇌ Bu 3 PO⋯AtI $$$$$$$$$$$$$$$ K BAtI = 'Bu 3 PO⋯AtI $$$$$$$$$$$$$$$ ( %Bu 3 PO $$$$$$$$$$ &×%AtI $$$$ & (5)
With these equations, an analytical expression of D can be derived (model 1, see SI). The experimental data was then fitted with D2 and KBAtI as adjustable parameters, in a way that is similar to the previous seminal study. [11] However, this model fails to properly describe the experimental behavior (Figure 1 a,b,c). The unexplained D increase, corresponding to a stronger astatine transfer towards the organic phase, suggests the presence of another extractable astatine species. Under the experimental conditions, the most probable hypothesis is that AtI and Bu3PO can form a complex of different stoichiometry. Owing to the extremely low astatine concentration, we assume that a 1:2 adduct with 2 Bu3PO equivalents occurs in the organic phase via reaction (6):

2Bu 3 PO $$$$$$$$$$ +AtI $$$$ K B2AtI ⇌ 2Bu 3 PO⋯AtI $$$$$$$$$$$$$$$$ K B2AtI = '2Bu 3 PO⋯AtI $$$$$$$$$$$$$$$$ ( %Bu 3 PO $$$$$$$$$$ & 2 ×%AtI $$$$ & (6)
Based on equations ( 2)-( 6), model 2 leads to significantly improved fitted results (Figure 1 d, e, f), despite some imperfections observed at the highest ligand concentrations. The slight D overestimation may imply that some of the formed species, such as Bu3PO!AtI or 2Bu3PO!AtI, could be backextracted towards the aqueous phase. Visual adjustments suggest that with the additional hypothesis of the partial solubility of 2Bu3PO!AtI (equation ( 7)), the most refined model 3 best fits all the experimental results (Figure 1 g, h, i).

2Bu 3 PO⋯AtI D 3 ⇌ 2Bu 3 PO⋯AtI $$$$$$$$$$$$$$$$ D 3 = '2Bu 3 PO⋯AtI $$$$$$$$$$$$$$$$ ( %2Bu 3 PO⋯AtI& (7)
Table 1. Formation constants of AtI and Bu3PO adducts, obtained from the distribution coefficients fitting with model 3.

[I -] (mol L -1 ) log KBAtI [a] log KB2AtI [a] 0.01 4.41 ± 0.12 7.47 ± 0.12 0.1 4.19 ± 0.14 8.03 ± 0.06 0.2 -28.83 [b] 8.44 ± 0.34

[a] Uncertainties correspond to 95% confidence intervals.

[b] Unreliable.

The formation constants of the 1:1 and 1:2 adducts can now be derived from model 3, gathering the values extracted from all the measurements (Table 1 andS2). Note that for [I -] = 0.2 mol L -1 , the formation of the 1:1 complex does not play a significant role in the adjustment: the quality of the fit is maintained in a large interval of KBAtI value that we imposed (including the average value obtained from other I -concentrations), so does the adjusted value of KB2AtI. Therefore, the formation constants for the 1:1 Since the experimental approach can only give information at the macroscopic scale, quantum chemistry methods represent an appealing alternative to establish the nature of the formed species. Indeed, the molecular structure(s) can readily be determined from the (experimental) stoichiometry of a compound, as well as many other spectroscopic signatures at a desired level of accuracy. In this work, the two-component relativistic density functional theory (DFT) approach is used, as in previous successful works. [11,22] According to the former benchmark study focused on astatine species, the B3LYP hybrid functional appears as a safe costeffective choice, [23] which is also true for describing astatinemediated halogen bonds. [11] The calculated value of log KBAtI is 4.37 at the B3LYP/AVDZ level of theory, in excellent agreement with the experimental one. Furthermore, a very close value (4.50) was obtained using an alternative exchange-correlation functional of hybrid meta-GGA quality, namely PW6B95, which confirms the reliability of our cost-effective computational approach and the identification of the formed species as an At-mediated XB complex. Indeed, the most stable structure for the 1:1 adduct is displayed in Figure 2. The two molecular units, AtI and Bu3PO, interact via the astatine atom and the oxygen of Bu3PO, with dAt !O = 2.606 Å. The interaction distance, shorter than the sum of the corresponding van der Waals radii, together with the qO !At-I angle value close to 180°, constitute typical features of halogen bonding. We can therefore safely conclude that the 1:1 adduct is an XB complex and, interestingly, that it is stabilized by the strongest XB involving astatine ever characterized experimentally. Since it is the first time that a 1:2 adduct formed by AtI is observed, several hypotheses about its nature can be formulated. With two halogens in the AtI molecule, the hot question that firstly emerges is whether this adduct exhibits two different XBs. As mentioned at the beginning, the σ-hole concept can help to rationalize and to anticipate the formation of XB interactions. [24] The σ-hole can be characterized by computing the molecular electrostatic potential (MEP), as shown in Figure 3 for the AtI and Bu3PO AtI species.

In addition to the expected σ-hole at the astatine atom, [12,25] a σhole can be observed, for AtI monomer, at the iodine site with a local maximum value (VS,max) of +85 kJ mol -1 (Figure 3 a). However, the MEP of the AtI unit at the I site is drastically altered after formation of the 1:1 adduct (Figure 3 b). The VS,max at the iodine atom even becomes negative, meaning that the σ-hole is essentially disabled. Hence, the electrophilic site of the iodine atom in AtI is deactivated by the formation of a first XB in the 1:1 complex. It is therefore very unlikely that Bu3PO AtI forms a second XB with another Bu3PO molecule. Conversely, at the Bu3PO AtI molecular surface, the geminal methylene groups appear much more acidic (a marked blue color indicating more electrophilic sites). Thus, the second Bu3PO molecule would preferentially interact through hydrogen bonds involving polarized CH2 groups of the first Bu3PO molecule, rather than through halogen bonding. This hypothesis was thoroughly assessed by starting a search for possible structures of the 1:2 adduct. A slightly less sophisticated computational methodology, B3LYP/SVPD, was used due to the number and the size of considered chemical systems, at the expense of a moderate lessening of accuracy. Actually, the log KBAtI value for the 1:1 complex is 4.54 at this lower level of theory, which remains (i) close to the previous B3LYP/AVDZ value of 4.37, and (ii) in fair agreement with the measured one (4.24 ± 0.35). Hence, a reasonable accuracy is achieved at the B3LYP/SVPD level of theory. The most stable 1:2 adduct structure from the B3LYP/SVPD calculations (Figure 4) discloses (i) a halogen bond as described above, and (ii) two chelating hydrogen bonds involving the oxygen atom of the second Bu3PO unit and two geminal C-H bonds of the first Bu3PO unit. The interaction distances associated with the two hydrogen bonds, 2.232 and 2.487 Å, are significantly shorter than the sum of O and H van der Waals radii, while the XB appears slightly strengthened. Another strong support for this structure comes from the energy criterion: this structure is stabilized by about 25 kJ mol -1 while the formation of a second XB with the I atom would yield about 1 kJ mol -1 of stabilization. This firmly supports the occurrence of the 2Bu3PO AtI structure, rather than the Bu3PO!AtI!OPBu3 adduct. Moreover, it is worth noting that a binding energy of 25 kJ mol -1 , corresponding to a value of 4.38 in log units at 298 K, is consistent with the experimental stepwise constant (3.71 ± 1.07) for the formation of the 1:2 adduct from the 1:1 one.

In the present work, two adducts of AtI and Bu3PO have been evidenced by a coupled experimental and computational approach. The 1:1 adduct, Bu3PO!AtI, reveals the strongest XB involving astatine ever characterized, with a formation constant of 10 4.24±0.35 . The 1:2 adduct, 2Bu3PO!AtI, with a global formation constant of 10 7.95±0.72 , is the first adduct of its kind identified to date. The nature of these adducts has been established by means of relativistic DFT calculations, showing that the 1:1 complex is indeed a halogen bonded one while the 1:2 adduct is stabilized by one halogen bond plus two hydrogen bonds sticking together the two Lewis bases. Therefore, we confirm the unique power of quantum chemistry methods, as virtual spectroscopes, to scrutinize astatine species. Our experience indicates that, in view of attempting to form a 1:2 adduct ruled by two halogen bonds, a first strong XB with a Lewis base deactivates the iodine XB donor site of AtI. Nevertheless, it will be extremely difficult with moderate XB acceptors to experimentally distinguish the 1:1 complex from the 1:2 one. Such a study will naturally require strong input from computational modeling.

Figure 1 .

 1 Figure 1. Astatine distribution coefficient between the organic and aqueous phases as a function of Bu3PO and I -concentrations. The hollow symbols indicate data without Bu3PO. Data fitted with (a, b, c) model 1, considering the formation of the 1:1 Bu3PO!AtI adduct in the organic phase, (d, e, f) model 2, also allowing the formation of the 1:2 2Bu3PO!AtI adduct, (g, h, i) model 3, considering in addition the partial solubility of the 1:2 adduct in the aqueous phase.

1 [Bu 3 PO] / mol L - 1 D

 131 complex at the highest I -concentration are excluded. Finally, the average equilibrium constant values are log KBAtI = 4.24 ± 0.35 and log KB2AtI = 7.95 ± 0.72.

Figure 2 .

 2 Figure 2. Structure of the most stable 1:1 complex between AtI and Bu3PO calculated at the B3LYP/AVDZ level of theory.

Figure 3 .

 3 Figure 3. Molecular electrostatic potential calculated at the B3LYP/AVDZ level of theory for (a) AtI and (b) Bu3PO⋯AtI. The molecular surfaces were defined by isovalue of the electron density of 0.001 e bohr -3 . Color code: from red (most negative values) to blue (most positive values).

Figure 4 .

 4 Figure 4. Structure of the most stable 1:2 adduct between AtI and Bu3PO calculated at the B3LYP/SVPD level of theory.

Acknowledgements

This work has been supported in part by grants from the French National Agency for Research called "Investissements d'Avenir" (ANR-11-EQPX-0004, ANR-11-LABX-0018). It was carried out using HPC resources from CCIPL ("Centre de Calcul Intensif des Pays de la Loire").

Keywords: astatine • halogen bond • hydrogen bond • competition experiments • relativistic quantum chemical calculations

Entry for the Table of Contents

Liu et al. report on two distinct adducts between AtI and Bu3PO in their Communication on page xxx ft. These adducts are experimentally and theoretically characterized in terms of equilibrium constants and molecular structures. While the first adduct, Bu3PO⋯AtI, is bound by the strongest halogen-bond so far with AtI, the second adduct 2Bu3PO⋯AtI displays one halogen bond plus two hydrogen bonds between the Bu3PO units.