Optimal sizing of a solar water pumping system for Koyli Alpha Village, Senegal

Received Aug 21, 2021 Revised Feb 19, 2022 Accepted Mar 3, 2022 Our objective is to solve problems of water supply in the village of Koyli Alpha, in Senegal. Theirs boreholes are supplied by diesel fuels causing environmental drawbacks and the populations don’t satisfy their water demand. In order to bring a positive response, we used solar energy to give back the borehole’s autonomous and proposed intuitive and numerical methods applying on solar water pumping for finding the best method. A previous study used intuitive methods for determining the size of various components. In order to optimize the energy production, we propose two numerical sizing approaches in order to have an optimal operation. Then, we developed two solar cell temperature models in the numerical sizing method and did a simulation of system operating in MATLAB software. The first model of solar cell temperature depends only on the ambient temperature and the second one combines wind speed and ambient temperature. The results of simulation showed that among these numerical sizing methods, we choose the second solar cell temperature expression, which gives the best performance. The numerical sizing method which uses the second solar cell temperature model yields to the reduction of battery’s size and the total life cycle cost found in the intuitive method, by 54% and 32%, respectively.


METHOD
In the literature, we have found several methods for the sizing a water pumping photovoltaic solar system: the intuitive, the numerical, the analytical [14], and the artificial intelligence techniques [15]. In this part, we present at first two models of solar cell temperature using the hourly data such as the temperature and the solar radiation of the village of Koyli Alpha. We begin with the intuitive sizing methods that allow to delimit the workspace i.e. the size of the components, then after, we are looking to optimize the system. Thereby, we applied those meteorological data to the numerical sizing method. Therefore, two models of cell temperature have presented in this study and used the meteorological data in 2016 and in 2017. Secondly, we use an algorithm for the numerical sizing method and utilized as inputs the instantaneous meteorological data. The objective of this method is to choose the best numerical sizing method from these two models of solar cell temperature. For the choice of the best model, we first simulated the operating of the water pumping solar photovoltaic system in order to find the lowest power supply probability (LPSP). According to the chosen and fixed LPSP, we are looked for the optimal torque (panels-batteries) with a view to a future sizing.

Solar cell temperature modelling
Two models are used to calculate the cell temperature for the years 2016 and 2017. The first model of the cell temperature is given by (1) [16], [17]: Where:

( ))
: instantaneous cell temperature of the first model : is the time expressed in hours : nominal operating cell temperature ( ) : instantaneous ambient temperature : reference irradiance The second model of the cell temperature is expressed in (2) [12], [18]: : empirical coefficients of the second model of cell temperature ( ) is the instantaneous wind speed. After using the regression model, we found the empirical coefficients. Hence 1 = 0.32, 2 = 8.91and 3 = 2. This leads to a new expression of solar cell's temperature located in the ferlo zone. This expression is described by the first expression's model of the solar cell temperature, which becomes:

Solar cell's temperature evolution
The first model of solar cell temperature depends only on the ambient temperature while the second model of solar cell temperature takes into account both the ambient temperature and the wind speed. We presented in Figures 1 and 2 the evolution of the solar cell temperatures obtained from these two models in 2016 and 2017, respectively.
The variation of the solar cell temperature in these two models is taken over a range of 24 months between 2016 and 2017. In the literature, some authors utilized the model n°1 based on the ambient temperature and the solar radiation to estimate the values of the solar cell temperature [13], [14]. Our study showed that the model n°1 of solar cell temperature almost reaches its maximum value, 67. 2

Intuitive sizing methods
Intuitive sizing methods give the size of solar photovoltaic system components. The application of the intuitive sizing method allows to find the total power capacity of the PV field required to satisfy the demand of Koyli Alpha site and the requisite battery capacity for two days without sunshine and during night. There are two different approaches of sizing on the intuitive methods. The first approach is based on the choice of the worst month corresponding to use the month having the lowest irradiations in the year. Leye et al. considered december as the worst month in their study done in Ndem, Senegal [19]. Sadio et al. [7] opted for the second approach, ie, the use of mean values such as the annual average monthly data in the sizing process, to ultimately find out an optimal photovoltaic solar systems.
According to the monthly mean data taken between august 2015 and august 2018, the month of december 2017 recorded the lowest value of solar radiation, therefore we adopt the approach of worst month. The intuitive methods use inherent formulas for each component. The sizes of photovoltaic field and batteries storage are given by (4) and (5), respectively [20].
is the daily energy, estimated to 133640 Wh; is the peak power and is equal to 530044 WP; is the reference irradiance that is evaluated to 1000W/m²; is the monthly average of daily solar irradiation estimated to 3.877 kWh/m²/day, recorded in December 2017 from the meteorological station of Widou, k is the loss factor = 0.65. It takes into account all the losses of system, namely the different efficiencies of components, the resistive and the PV cell temperature losses. N is the number of the autonomous days, V b corresponds to the voltage of the system and is equal to 48 V, deep of discharge (DOD) is estimated to 0.80 for acid batteries, η b is the efficiency of the storage battery, evaluated to 80%. It is important to estimate the cost of solar PV system installation. Hence, the technical parameter for evaluating the price of the components and the maintenance is named total life cycle cost (TLCC). It is the best indicator to evaluate the total cost of the solar PV system in order to predict an optimal system. Thus, the TLCC used five components: the PV panels, the pump, the motor AC, the storage battery, and the inverter. Moreover, the TLCC is defined as the sum of initial investment cost, the replacement cost and the maintenance cost. It is given by (6) [21]: The initial total cost is the sum of all components of our PV system and takes into account to the price of the installation, and the civil works. The initial total cost is given by (7) [21]. and , are the total capacity and the unit cost of the motor, respectively. C 0 represents the total constant cost which includes both the civil work and the installation cost. All these components required to be replaced during the system lifetime which depends on the storage battery, the pump, the motor AC and inverter. Thus, the replacement cost CR is given by (8) [21].
The values of the inflation rate (FR) and interest rate (IR) of the components of the system are considered in this work. C unit represents the unit component cost of the storage battery, the pump, the motor AC, and the inverter; C,nom means the nominal capacity of the replacement system components; and NR refers to the number of replacement of each component over the system life period (LP). The operation and maintenance cost are defined by (9) and (10) [21]: & 0 is the operation and maintenance cost in the first year.

Numerical sizing method using instantaneous meteorological data
Before elaborating the sizing algorithm to find the best combination of components, we deal with the parameters. The adopted model to describe the PV generation gives the instantaneous photovoltaic energy after taking into account the solar cell temperature expressed here in two different models as presented above. Hourly data of the ambient temperature, the solar radiation, and the wind speed are obtained from weather station of Koyli Alpha. Our objective is to determine which of these two models of solar cell temperature is the most appropriate for the numerical sizing method. Hence, the instantaneous energy production of the PV array for the two models is given in (11) and (12), respectively: and : the instantaneous photovoltaic energy field for first model;

EPV, 2 (t)
: the instantaneous photovoltaic energy field for the second model; APV : the area photovoltaic field; ηinv and η W are the inverter and wire yields, respectively; ηref : the reference yield; β: the temperature coefficient.
Replacing the expressions of ;1 ( ) (1) and ;2 ( ) (3), in (11) and (12), we end up with (13) and (14), respectively: and The instantaneous energy difference between energy produced by the modules and the daily energy load expressed from (15) and (16), respectively, for the two models allows to know the batteries behavior. The instantaneous energy difference is calculated using (15) and (16), respectively [20]: and E 1 (t) and E 2 (t) correspond to the instantaneous energies difference given by the expression of the models n°1 and n°2 of the solar cell temperature, respectively, Ed is the daily load energy. If the values E,1 (t) and E2 (t) are less than zero, and the batteries are discharged, then, the instantaneous energy stored is calculated for the first and second models from (17) and (18), respectively [18]- [20]: and If the values of E1 (t) and E2 (t) are greater than zero, respectively, then, the batteries are charged, and the instantaneous energies stored, in the batteries, are calculated using (19) and (20) [20], for model 1 and model 2, respectively: and In order to protect the batteries against overcharge, discharge, and drastic reduction of its life cycle, instantaneous energy stored in the battery is subject to the given restriction [22]: and are the maximum and minimum energies of the batteries. The instantaneous loss of power supply which represents the missing energy quantity to satisfy the load demand during 24 hours is computed for the two models by (23) and (24) The instantaneous loss of power supply probability (LPS) represents the percentage of power supply that is not able to satisfy load demand and is obtained by the summation of all instantaneous loss power supply at specific time over the load energy, in accordance with (25) and (26) for the two models, respectively: and Loss of power supply probability (LPSP) indicates the reliability of power supply to load. If LPSP (t) is equal to 0, it means that the system satisfies totally the load demand while on the other hand, if LPSP is equal to 1, it means that the load demand is not satisfied by the PV system. An LPSP (t), which is between 0 and 1 means that the supplied power cannot fully cover the load demand because there are an insufficient energy production from the PV array and not enough energy stored in the batteries [22]. The objective is to calculate the storage capacity corresponding to each PV capacity value, considering all these operating conditions of the PV system. The PV capacity varies from a minimal value equal to the unitary PV module capacity, up to a maximal value corresponding to the PV power found by applying the intuitive method. The Figure 3 shows the sizing algorithm of numerical method.

Results
In the intuitive sizing method, we found a total PV array capacity and a storage system capacity, equal to 53,044 Wp and 6,960 Ah, respectively. If we increase this storage capacity about 20% to take into account the depth of allowed discharge, it grows to 8,352 Ah. The TLCC of the pumping photovoltaic solar system then turns around 920,304.8998EUR. After modeling the system operating, the sizing algorithm using two models of solar cell temperature is running on Python software. The results are shown in Figures 4-7. Figure 4 shows the different combinations of PV array capacity and the storage system capacity at different reliability levels, called isoreliability curves, when the first expression's model of the solar cell temperature is utilized. The goal of this work is to look for a good combination panel/battery in order to have a good reliability and a reduction cost. In this optimization, we worked with the probabilistic approach using hourly data in the energetic photovoltaic model. We remarked that the batteries capacity increases inversely proportional with photovoltaic capacity. It means that, during the sunnies days, the photovoltaic field ensures the energetic production, therefore, the batteries supply the load during the night and the days without sunrise. This study is done between 10 am and 3 pm and we observed that the best reliability corresponding to the best production in capacity (photovoltaic/batteries). Among the is reliability curves, we chose the one which corresponds to the lowest loss of power supply probability to find the best PV/battery combination. It depends on high power produced by panels and batteries in the PV system. The values of LPSP vary between 0.026 and 0.11. The best PV/battery combination which satisfies a reliability level of 97.4% is given in Figure 5.
From Figure 5, it is noted that a value of total PV array capacity of 49,250 Wp necessitates a storage system capacity of 2,700 Ah. If we increase this storage capacity about 20 % to take into account of the depth of allowed discharge, it grows up to 3,240 Ah. The TLCC of this combination is 143,477.268 EUR. The proposed sizing method enabled to reduce the number of batteries needed by the PV system to 68 % and the TLCC to 40 %, with only 0.026 of LPSP, when compared to intuitive method. Figure 6 presents different combinations of PV/battery at different reliability levels using the second expression's model of the solar cell temperature.
The values of LPSP, from Figure 6, vary between 0.62 and 0.0197. When the value of LPSP is 0.62, we record many losses energy, which lead to a poor reliability. For a constant value of LPSP, the batteries capacity vary conversely proportional and increase corresponding to the decreasing of the panel's capacity. For example, for a LPSP equal to 0.0197, the best combination is found with the lowest TLCC. The results of our study are compared to a work done in Sohar region, in Oman. In this study, H. A. Kazem et al utilized geographic, climatic and sunshine coordinates as inputs of photovoltaic/battery system [23]. Theirs results generated a good reliability of 98.7%, i.e a LPSP equal to 0.013 while our study applied in Koyli Alpha site has given a reliability of 98.03% corresponding to a LPSP equal to 0.0197 when, the second expression's model of the solar cell temperature is used. The best PV/battery combinations that satisfies a reliability level of 0.0197 are shown in Figure 7.
From Figure 7, it is noted that the best PV/battery combination corresponds to a value of total PV array capacity equal of 51,080 WP and at a storage system capacity estimated to 3,847 Ah. If we increase this storage capacity about 20% to take into account of the depth of allowed discharge, it grows to 4,680 Ah. The results of our study are summarized in Table 1. Here, a comparative study of the intuitive method is made compared to numerical methods using respectively models 1 and 2 of cell temperature. The use of numerical methods allows an optimization of the photovoltaic solar water pumping system applied to the boreholes of the village of Koyli Alpha. These methods reduce the cost of batteries and TLCC. The goal is to choose the best cell temperature model applied to the numerical sizing method. The choice is based on the lowest LPSP justifying good energy production at an acceptable cost.

Discussions
The TLCC of this combination is 163,917 EUR. The proposed sizing method based on the second expression's model of cell temperature and when the LPSP equal to 0.019 enables to reduce the number of battery needed by the PV system by 54 % and the TLCC by 32%. Sadio et al. [24], in their researches, compared the intuitive and numerical methods and the results showed that the storage capacity decreases by 25% and permitted to reduce the TLCC by 49% with numerical method. Bilal et al. [25] adopted a sizing methodology of a hybrid solar/wind/battery systems using a multi-objective genetic algorithm to minimize cost and increase reliability. They worked with hourly solar irradiation, temperature and wind speed annual data from Potou located in the northwest coast of Senegal. Compared to the case study applied in one region of Malaysia using data of the year 1999, Shen [26] kept the load demand constant and fixed the LPSP at 1%. Therefore, W.X. Shen simulated a solar photovoltaic system on MATLAB, and the results generated a ratio battery/panel equal to 0.18 Ah/Wp while in our study, the first expression's model generated a ratio battery/panel equal to 0.095 Ah/WP. The obtained results showed that the cost of the optimal configuration decreases by 25% when the probability of loss of power supply (LPSP) goes from 0% to 1%. The reliability of our solar photovoltaic water pumping systems system can be justified by the use of hourly weather data of Koyli Alpha site. To show the importance of taking into account the parameters, which can influence the PV system performance, two expression's models cell solar temperature are considered. In terms of reliability, the second model of cell solar temperature, which integrates wind speed, is better than the first model of cell solar temperature, which doesn't consider the wind speed influence. Indeed they provided LPSP values, equal to 0.0197 and 0.026, respectively. The convection of wind speed is a cooling factor for the solar cell, confirming the effectiveness of numerical method using expression's second model of solar cell temperature.

CONCLUSION
In this study, we presented a technique for optimizing the size of panels and batteries in a solar PV water pumping system for hourly weather data from Koyli Alpha village. The objective is to find an optimal response to energy demand for good reliability at minimum cost. This numerical sizing method using hourly data revealed two solar cell temperature models applied to the energy model. The first model depends only on ambient temperature, and the second is expressed as a function of ambient temperature and wind speed. The comparative study showed that the numerical sizing method which uses the second model is more accurate because it recorded at the lowest LPSP which is equal to 0.0197 versus 0.026 for the numerical sizing method based on the first model of of the solar cell temperature. This study concluded the positive yield of wind speed in energy production. Finally, the lowest LPSP which equals 0.0197 and gives the best reliability is chosen and several PV capacity/battery capacity combinations are found. The best panel / battery combination is the one with the lowest cost. The comparison between the numerical sizing method using the second expression model of solar cell temperature and the intuitive method revealed a reduction of 54% for storage batteries and of 32% on the TLCC.

Badara Mbow
is a PhD student at Alioune Diop university of Bambey, Senegal. At university, he integrated the Interuniversity Master of Renewable Energies. He has been starting to study the different sources of renewable energies and focused a big part of his study in solar energy. For finishing his master, he worked on the following subject: Empowerment in solar energy of village of Baol: NDEM. In this study, he did the design of an autonomous photovoltaic power station to ensure the supply of electricity from the village of NDEM. In 2018, he began his PhD study at Alioune Diop university of Bambey. The objectives of his thesis are to size a photovoltaic solar water pumping system for empowerment of the drilling in the great green wall. He then studies two types of water pumping system, namely the autonomous solar systems (with batteries or/and with supercapacitors) and solar systems without storage energies or/and with supercapacitors). At the end a comparison of these two systems for the most profitable one is going to be made and the solar PV pumping systems and the diesel pumping systems will be compared. He can be contacted at email: badara.mbow@uadb.edu.sn.

Int J Pow Elec & Dri Syst
ISSN: 2088-8694  Amy Sadio is a postdoc scholar & teaching assistant in the department of physics, at the Alioune Diop University. She holds a BSc and a MSc in Physical Science from Alioune Diop University, in Senegal. In 2018, she received her PhD in physics from the Cheich Anta Diop University, Senegal. She is specialized in renewable energies, and solar energy in particular. She worked on the design and simulation of a standalone photovoltaic systems using numerical methods and genetic algorithm (GA). She published several papers in indexed journal. The first paper analyses meteorological data for photovoltaic applications, and in the second one, a new numerical sizing approach of a standalone photovoltaic power is investigated. The third paper regards a comparative study based on GA for the optimal sizing of standalone photovoltaic systems. The fourth paper is focused on the sizing of a standalone photovoltaic water pumping systems. Her current and future works are centred on the research for a solution to make more reliable and economically viable the renewable energy systems and meet the challenges of climate change by using the artificial intelligence techniques. She can be contacted at email: amysadio12@gmail.com.

Bertrand Tchanche Fankam
is holding a position of assistant professor in the Dept. of Physics at the Alioune Diop University of Bambey, Senegal. He held previous positions at University of Lorraine and ESIEE-Amiens (France). His main research is in the field of Energy and Environmental Engineering. He works on a wide range of topics: organic Rankine cycles for power generation, analysis of energy systems, transportation systems, classical and quantum thermodynamic systems, energy and atmospheric pollution, energy governance and the anthropology of electricity. He has edited three books and published several papers in international journals as well as in many conference proceedings. He took part in several international projects and is member of many organizations. He acts as external expert for many international organizations, is member of the editorial board and reviewer for several international journals. He can be contacted at email: bertrand.tchanche@uadb.edu.sn.

Senghane Mbodji
is a professor at Alioune Diop University, Bambey, Senegal. He is a specialist of Semiconductor Physics applied to Solar Energy. He holds two PhDs. He is an author or co-author of more than sixty publications in his field. To this end, his works are based to the concept of junction recombination velocity which permits to determine all operating points of the solar cell: from the open circuit operating point to the short-circuit one. He used the steady state operating conditions, the transient state defined on two steady state conditions or the frequency dynamics state in 1D and 3D modeling studies. These studies helped him to calculate, based on the concept of "junction recombination velocity", the solar cell power, the open circuit photo-voltage, the effective diffusion length of carriers, the intrinsic junction recombination velocity which is related to carriers lost to the junction of the solar cell, the back surface recombination velocity of the solar cell, the shunt and series resistance, to make simulations and validate the electric circuit types equivalent to the solar cell. A study on the effect of grain size and grain boundary recombination velocity on Shunt and series resistance has been made via the junction recombination velocity at the junction (Sf). All these techniques have been used and published in journals and conferences. He can be contacted at email: senghane.mbodji@uadb.edu.sn.