In another way, when a semiconductor is illuminated by sunlight, a free electron-hole bond circulates in the material. Under the effect of the electric field, the electron goes to the N side and the hole to the P side. The holes behave in different ways, like particles with a positive charge equal to that of the electron. The potential difference can be measured between the positive and negative terminals of the cell. The maximum cell voltage is approximately 0.6 V at zero current. This voltage is known as the open circuit voltage (VCO). The maximum current produced is called the short-circuit current (ICC) [18] .

Charge Controller MPPT prevents overcharging and excessive discharging of the battery. In the case of lead-acid batteries, overcharging is prevented by charging the batteries in three stages (bulk, absorption, or boost and float).

The microcontroller is a microprocessor-type information processing unit to which internal peripherals have been added to facilitate interfacing with the outside world without requiring the addition of external components. With the Arduino board, we can write programs, create interface circuits and develop algorithms to control switches, sensors, etc.

In this study, we will use relay. A relay is a pre-actuator consisting of at least an electromagnet, a moving leg supporting the moving contact, a fixed contact and a moving contact return spring. By energizing the coil from an electrical source, the moving contact is moved, thus closing the electrical contact.

The DHT11 sensor is a module for detecting the temperature and a microcontroller can process the humidity of an object that sends an analogue voltage output. Compared with other types of sensors, it is more responsive, quickly detects the temperature and humidity of objects, and does not easily disturb the data read.

A solar battery is a device designed to store the electrical energy produced by photovoltaic solar panels. The current entering or leaving the battery is necessarily direct current (DC) and not alternating current (AC) as in the domestic electricity network.

Lead-acid batteries are the most widely used storage element in photovoltaic systems. The main function of lead-acid batteries is to store and supply energy in a PV system. The stored chemical energy can be converted into electrical energy and vice versa. Electrochemical reactions are described by the following reactions [19] .

${\text{PbO}}_2+2{\text{H}}_{\text{2}}{\text{SO}}_4+\text{Pb}\underset{\text{charge}}{\overset{\text{discharge}}{\rightleftarrows }}2{\text{PbSO}}_4+2{\text{H}}_{\text{2}}\text{O}$ (1)

The expression that describes the behavior of battery voltage is:

$V=V_{oc}\pm IR$ [19] (2)

where, V_oc is the open circuit voltage, I is the battery current and R is the internal resistance of the battery.

The charge/discharge models of Lead-Acid battery are given by Equation (3) and Equation (4).

$V_{bat}=V_0-Ri-Rpo{l}_1\left(i+i^{*}\right)+Exp\left(t\right)$ [20] (3)

$V_{bat}=V_0-Ri-Rpo{l}_2\left(i^{*}\right)-Rpo{l}_1\cdot i+Exp\left(t\right)$ [20] (4)

Where: V_bat is battery voltage (V), V₀ is battery constant voltage (V), K is polarisation constant (V/Ah), C = battery capacity (Ah), it is actual battery charge (Ah), A is exponential zone amplitude (V), b is Exponential zone time constant inverse (Ah⁻¹), R is internal resistance (Ω), Rpol₁ is polarisation resistance when i > 0, Rpol₂ is polarisation resistance when i < 0, i is battery current and i* filtered current. The battery current i and the filtered current i* are equal [20] .

The polarisation resistance in discharge mode is given by Equation (5)

$Rpol=K\frac{C}{C-it}$ [20] (5)

The polarisation resistance in charge mode is given by Equation (6):

$Rpol=K\frac{C}{it-0.1C}$ [20] (6)

The exponential voltage of the Lead-Acid battery is given by Equation (7):

$Exp\left(t\right)=B\cdot \left|i\left(t\right)-(-Exp\left(t\right)+A\cdot u\left(t\right)\right|$ [20] (7)

where, Exp(t) is the exponential zone voltage (V), is the battery current (A), u(t) is the charge or discharge mode. The exponential voltage depends on the initial value of Exp(t₀) a u(t) = 1 in charge mode or u(t) = 0 in discharge mode. When the battery is fully charged, the battery’s real charge is equal to zero (it = 0). In this case, the battery voltage begins to drop. The charge continues to overcharge the battery (it < 0). The decrease in voltage is due to the decrease in polarisation resistance. When it = 0 (battery fully charged), the polarisation resistance is infinite [20] .

The discharge voltage equation is given by the following expression:

$V=\left(2.085-0.12\left(1-soc\right)\right)-\frac{1}{C_{10}}\left(\frac{4}{1+I^{13}}+\frac{0.27}{so{c}^{15}}+0.02\right)\cdot \left(1-0.007\Delta T\right)$ [19] (8)

The charge voltage equation is given by the following expression:

$V=\left(2-0.16soc\right)+\frac{1}{C_{10}}\left(\frac{6}{1+I^{0.86}}+\frac{0.48}{{\left(1-soc\right)}^{12}}+0.036\right)\cdot \left(1-0.025\Delta T\right)$ [19] (9)

The temperature variation is given by:

$\Delta T=T-25$ [19] (10)

We know that the expression that describes the thermal effect on resistance is:

$R_t=R_0\ast \left(1+0.004\ast \left(T-25\right)\right)$ (11)

The state of charge (SOC) is an indication of a battery’s charge level, expressed in percentage. Several techniques are used to estimate the state of charge of the battery (SOC). The techniques are [14] [21] :

Various mathematical methods of estimation are classified according to methodology in the various literature:

In this project, using the Coulomb-counting method, the state of charge is given by Equation (7) [9] :

$\text{SOC}\left(t\right)=\text{SOC}\left(t-\Delta t\right)+{\displaystyle {\int }_{t-\Delta t}^t\frac{i}{C}\text{d}t}$ (12)

i > 0 in charge, i < 0 in discharge

where, $\text{SOC}\left(t-\Delta t\right)$ is the previous state of charge and i is the battery current.

The voltage applicable to the microcontroller is approximately 5 V. In this case, a voltage rectifier bridge must be added to adapt the voltage of the battery bank to the input of the Arduino microcontroller. Figure 4 illustrates the voltage divider bridge.

We apply the voltage divider law, and the expression is:

$V_{out}=\frac{R_1}{R_1+R_2}\cdot V_{BAT}$ (13)

In our case, V_BAT = 14 V, R₁ = 33 KΩ and R₂ = 57 KΩ.

$V_{out}=\frac{33}{33+57}\cdot 14=5\text{V}$ (14)

When the battery is discharged to a SOC of 80% of its rated capacity, we have V_MIN = 11.2 V. Converting V_MIN into binary corresponds to 818.4.

The aging of a battery is directly linked to the conditions in which it is used. It depends essentially on the number of charge-discharge cycles. To achieve a service life of 10 to 15 years, the battery must be kept in a state of charge of more than 50%. In this research, the algorithm developed maintains the state of charge of the battery at a SOC of 80% to reduce the aging of the battery. The aging of lead-acid batteries is determined by the following three factors [22] :

High overloads cause corrosion, deformation, erosion of the plates, and overheating, and they can lead to the coalescence of the Pb particles with a consequent loss of porosity.

This type of architecture will allow great flexibility in the maintenance and management of the installation’s uptime by using only the number of inverters required. This management also ensures that the inverters are used at their optimum power depending on the amount of sunlight. Figure 5 illustrates the architecture of centrally managed multi-inverters.

In this section, we describe the design of the system studied and the results obtained by simulation using MATLAB software, Arduino IDE software and Proteus. Based on Equations (3)-(8), the block diagram for modelling the lead acid battery using MATLAB software is shown in Figure 6 . The SOC is calculated using the Coulomb counting method.

For K = 0.0058935; A = 1.0154; V₀ = 12; V = 2.0354; C = 30; R = 0.073 and SOC₀ = 100. Simulation results in discharge mode are shown in Figure 7 .

From the SOC and Vbat variation curves, we can see that the battery is discharged to a SOC of 90.32%, corresponding to a battery discharge voltage of 12.65 V. The discharge current is also negative, which shows that the battery is in discharge mode (ut = 0). For K = 0.0058935; A = 1.0154; V₀ = 12; V = 2.0354; C = 30; R = 0.073 and SOC₀ = 90.32. Simulation results in charge mode are shown in Figure 8 .

The simulation results show that the battery is in charge mode (ut = 1). We can see that the battery is fully charged (V_AB = 14 V) with a state of charge of 100% and that it = 0. The polarisation resistance is infinite, as the theory states. Figure 9 illustrates the Effect of temperature on resistance.

From the variation curve, we can see that when the temperature increases, internal resistance also increases. We also know that heating metal increases its electrical resistance. Figure 10 illustrates the Effect of temperature on battery voltage.

We found that the voltage decreased when the temperature fell below 25˚C. At temperatures above 25˚C, the voltage increases. So, if the voltage drops, this also affects the battery’s SOC. Figure 11 shows the influence of temperature on the battery’s capacity.

We note an increase in discharge capacity as the SOC decreases. If the discharge capacity increases, this indicates that the battery capacity is decreasing. When the battery is at a temperature below 0˚C, the resistance of the sulphuric acid solution will continue to increase, the polarization effect, reducing the capacity of the battery. Consequently, when the state of charge decreases, the depth of the battery increases, causing the battery to age. For K = 0.00004308; A = 1.889; V₀ = 12.16; B = 0.3053; C = 30; R = 0.0006, Figure 12 illustrates the influence of battery discharge current on the battery voltage.

Simulation results show that the voltage decreases rapidly as the current increases.

Figure 13 illustrates the design of the battery charging and discharging system algorithm with temperature control using MATLAB software.

We began to design the algorithm developed using MATLAB Simulink for a State of Charge (SOC) of 80% corresponding to a minimum voltage of discharge of 11.2 V. Figure 14 shows the simulation results of the algorithm developed using MATLAB software.

In the range [0, 3], SOC_BAT1 = SOC_BAT2 = 70%, Battery 1 is prioritized at the HIGH level indicating charging mode and Battery 2 at LOW level, indicating the discharging mode. Interval [3, 6] SOC_BAT1 = 100% and SOC_BAT2 = 70%, battery 1 is at LOW level indicating discharge mode and battery 2 is at HIGH level indicating charge mode. From interval [6, 8.5], SOC_BAT1 = SOC_BAT2 = 100%, batteries 1 and 2 are at the LOW level for discharging and the DC loads are at the HIGH level for charging mode. At the interval [8.5, 10], SOCBAT1 decreases below 80%, and SOC_BAT2 = 100%, so battery 1 is activated for charging mode. On the temperature control side, in interval [3, 6], the temperature is above 25˚C, a HIGH level is detected indicating a high temperature while for the interval [6, 10] the temperature is below 20˚C, and a low frequency is detected. Figure 15 illustrates the designed and simulated algorithm of the battery charging and discharging system with temperature control using Arduino IDE software and Proteus software. We have fitted LEDs to indicate the operating status of the battery charge or discharge system for each switch.

The simulation results show that if battery 2 is fully charged, the Arduino microcontroller receives an analogue signal at the voltage divider bridge from the first grouping of batteries. This analogue signal is converted into a digital signal by the Arduino microcontroller, which sends a command to switch relay 1 across pin 8 to charge the first battery ( Figure 15(a) ). Once the first group of batteries has been charged, the microcontroller opens the contact of relay 2 and sends a command to close relay 2 via pin 10 to charge the second group of batteries. Once all the batteries are charged and the sun is still shining, the Arduino microcontroller sends a command via pin 12 to close relay 3 to charge other DC electrical loads ( Figure 15(b) ). Also, if the local temperature exceeds the battery’s operating range, the microcontroller sends a signal to close relay 4 or relay 5 for air conditioning. We can see that the simulation results obtained using Proteus and MATLAB Simulink software match.

This part is devoted to the practical implementation of the battery charge/discharge management system combined with a temperature control system for the algorithm developed. We used an experimental set-up consisting of two batteries (6FM-7AH (12V7AH/20HR)), Rechargeable Sealed Lead-acid battery, Cycle; use: 14.5 - 14.9 V (25˚C); Initial current: less than 2.1 A; Standby use: 13.6 - 13.8 V (25˚C), an Arduino board, two potentiometers, four resistors, two voltage divider bridges, connection cables, four relays, four LEDs, a DHT11 temperature sensor and a test plate. In this study, the LEDs will be powered if the relay is activated for each test of the algorithm developed. Figure 16 and Figure 17 show the assembly of the developed algorithm using arduino IDE software.

From the experimental results, we can see that for a discharge of 80% of the rated capacity, relay 1 is activated to charge battery 1 (VBAT1) first. If the first group of batteries is charged, relay 2 is activated by the Arduino UNO microcontroller to charge battery 2. In addition, if all the batteries are 100% charged, relay 3 is activated by the Arduino UNO microcontroller to charge other DC electrical loads. For temperature control, if the temperature exceeds 25˚C, relay 4 is activated for fan conditioning.

Figure 18 shows the display of the experimental results of the algorithm studied using the serial monitor.

We transferred the experimental results to Excel using the Plx_DAQ application. Figure 19 shows the variation in temperature and humidity as a result of temperature and humidity saved in Excel.

From the temperature and humidity variation curve, we can see that if the temperature increases, the humidity decreases and vice versa. The measured values of temperature using DHT11 are between 23˚C to 27˚C. Based on the measured values on 7/11/2024, we can see that the temperature was high. According to the operating range of the lead-acid battery, we note that the battery requires air conditioning, because we see that the minimum temperature obtained by experimentation is over 25˚C.