The method is based on the use of monthly meteorological data available up to the year 2020, together with geographical coordinate information obtained using PVGIS5.2 software by entering the name of each site studied in Burundi. The choice of study site depends on which commune in the province has the minimum or maximum latitude. In first, the optimum yearly tilt angle of a fixed solar panel is determined using pvsyst 7.4 software, based on optimization with respect to the yearly irradiation yield and yearly meteorological yield as follows:

The performance ratio (PR) or performance index (PI) is expressed as a percentage and designates the ratio between the actual yield and the theoretical yield of the photovoltaic system. It is generally between 70% and 80% [21] . Figure 3 illustrates the configuration technique for finding the solar panel’s angle of inclination using pvsyst software.

The R method in SPSS software based on a linear regression model, is used to develop a model for calculating the optimum yearly tilt angle of inclination of the solar panel for calculating the energy available for a solar panel at any site of Burundi. Analysis of the results to test our hypotheses is carried out using the analysis of variance test by simple or multiple linear regressions, which consist in using SPSS software to analyze quantitative variables by determining two coefficients R and $R^2$ belonging to [−1, 1] and a P-value of less than 0.05 [22] . Thus, the European Union’s PVGIS (Photovoltaic Geographic Information System Data Base) software, which includes European and African countries on solar radiation data prepared by the Joint Research Center (ECJRC), enables us to obtain meteorological data and geographic coordinate information [23] . We will use also data from the Ministry of Energy and Mines’ report for 2023 in Burundi. Pvsyst is a design, sizing and simulation software package suitable for stand-alone and grid-connected photovoltaic and hybrid PV/Diesel systems, as well as DC-grid systems [24] . We will use also MATLAB software [25] .

The photovoltaic system under study is simulated using the following components:

In the experimental step, we will use a solar panel with the following characteristics:

Figure 4 shows the orientation of the solar panel in the northern hemisphere using Archicad software in all sites of Burundi.

This orientation of the solar panel in the northern hemisphere is due to the fact that Burundi is located in the Southern Hemisphere between meridians 29˚00' -30˚25' East and parallels 2˚20' - 4˚25' South, elevation 1614 m with a surface area of 27,834 km² [26] .

Table 1 shows daily meteorological data and geographical coordinates for each site studied. Monthly data obtained using PVGIS v5.2 software, which were converted to daily data using PVSYST software.

We continue to show our contribution to the optimization of photovoltaic efficiency by introducing MPPT technology. We will show the importance of an MPPT controller compared to a non-MPPT controller. It should be noted that most of the controllers used in Burundi are PWM controllers. An MPPT control algorithm is needed to achieve higher efficiency and continuously extract the maximum available power from the PV module under static, variable and partially shaded weather conditions.

The DC-DC converter using the MPPT algorithm plays a crucial role in the PV system to ensure maximum power transfer between the source and the load, while improving system efficiency. Author [18] [27] discusses the details of DC-DC converters. To simulate the algorithm, we are going to develop, we need a boost chopper described by equations:

$i_1=i-c_1\frac{dV}{dt}$ (1) [27]

$i_b=\left(1-D\right)i_1-c_2\frac{d{V}_b}{dt}$ (2) [27]

$V=\left(1-D\right)V_b+L\frac{d{i}_1}{dt}$ (3) [27]

where D indicates the duty cycle of the boost converter, which is the time the switch is closed over period of time. The literature on MPPT techniques proposes several MPPT algorithms that can be divided into two main categories, conventional and non-conventional algorithms [18] . Among the conventional algorithms are the P&O MPPT algorithm and the incremental conductance MPPT algorithm.

The Incremental Conductance MPPT (Inc) is calculated using the derivative of the PV system’s power, respecting its voltage, which must be equal to zero at the MPPT; however, it would be positive to the left of the MPPT and negative to the right of MPPT. The P&O method is an iterative technique for MPPT; it measures the photovoltaic characteristics and then perturbs the respective operating point of the PV system to respond to the direction of change [18] . Thus, for the MPPT technique based on the incremental conductance algorithm, the cost of its application is very high and its efficiency is high; but for the P&O MPPT technique, the cost of its application is medium, while its efficiency is very high. Taking into account the average cost of its application and the fact that Burundi is a developing country, in this project we have chosen the MPPT P&O algorithm. The P&O algorithm, exhibit oscillations around the maximum power point due to its disturbance nature. This can lead to system instability and reduced MPPT efficiency as well as overshoot of the optimal maximum point in the event of rapidly changing atmospheric conditions. To overcome these drawbacks, we will combine the MPPT P&O algorithm technique with the artificial intelligence technique based on fuzzy logic.

Figure 5 illustrates the block diagram of the MPPT P&O algorithm.

In recent years, a number of studies have been carried out into more robust control techniques, such as fuzzy logic, neural networks and neuro-fuzzy systems [28] . Lofti A. Zadeh created fuzzy logic in 1965 based on his theory of fuzzy subsets [29] . The FL (fuzzy logic) approach is based on decomposing a range of variation of a real variable into linguistic variables and assigning a membership function to each variable. The rules developed from the human operator’s expertise are expressed in linguistic form.

The proposed FL controller consists of four basic elements:

In this project, the fuzzy logic technique was combined with the MPPT P&O technique to control the different variations in solar irradiation due to climate change in order to improve tracking performance in terms of dynamic response and robustness.

Each input/output variable in the fuzzy logic controller is required to define the control surface which can be expressed in fuzzy set notations using linguistic levels. Variables are expressed as (PB: big positive, PM: medium positive, PS: small positive, ZE: zero, NS: small negative, NM: medium negative, NB: big negative). Defuzzification uses the centroid method to calculate the output duty cycle. Our contribution to the MPPT technique consists of combining the MPPT P&O algorithm with fuzzy logic. With fuzzy logic, the method consists of controlling the variation in solar irradiation, in relation to the variation in solar panel voltage in proportion to the variation in solar panel current according to the following equations.

$dIrr=Irr-\frac{dIrr}{dt}$ (4)

$dE=\frac{V}{I}-\frac{dV}{dI}$ (5)

where Irr is solar irradiation, V is the voltage and I is the current of the output of solar panel. The values were found after a simulation of the solar system. We recorded the output values of the voltage and current in the solar panel, which enabled us to determine the operating ranges of the variations dE. Figure 6 shows the system configuration of the MPPT P&O algorithm combined with fuzzy logic.

We have parameterized the fuzzy logic controller according the three conditions of climate change:

Table 2 illustrates the rules for membership.

With the rapid climate change in recent years, the power generation efficiency of fixed-angle solar systems with optimal angle will be affected. That is why we introduce Maximum Power Point Tracking (MPPT) technology to dynamically improve power generation efficiency in this party.

Figure 7 shows the design of a fixed solar panel system of 610 Wp controlled with the MPPT P&O algorithm combined with fuzzy logic controller in MATLAB.

Figure 8 illustrates the 3D curve of relationships between the inputs and the fuzzy output constructed as a function of the tree conditions.

Figure 9 illustrates the power output of a fixed solar panel for the P&O MPPT algorithm associated with fuzzy logic controller compared with a solar panel without MPPT. Figure 10 shows Curve of variation of the irradiance, Current and voltage using MPPT algorithm.

Simulation results show variations in current, voltage and power in response to changes in irradiance. This technique, based on the algorithm developed, enables the MPPT to be reached in 0 second and provides good reference power tracking. We can evaluate the effectiveness of the MPPT tracking and the speed with which the system responds to changes in irradiance. A small delay in MPPT tracking is also noticeable.

In this section, the yearly optimal tilt angle was calculated using PVSYST 7.4 software. Three parameters were evaluated to determine the yearly optimum angle of inclination of the fixed solar panel: the yearly Transposition Factor (FT), the yearly losses with respect to optimum (Lopt) expressed in %, the Global on collector plane (GlobHor_opt) expressed in kWh/m². Table 3 shows the optimal solar panel tilt angle for different sites in Burundi. We will evaluate the simulation results of the above-mentioned parameters for an average angle of 30˚ in relation to the optimal yearly tilt β_opt in degrees and their effect on the available energy (E_Avail).

The simulation results show that the optimum yearly tilt angle for fixed solar panels in the provinces of Burundi range from 12˚ to 15.7˚. The results show losses for the 30˚ tilt angle, while for the optimal yearly tilt the transposition factor is 1 and losses relative to the yearly optimum are zero and remain constant, while the global on collector plane varies as a function of tilt angle in all the sites studied. We note a performance index (PR) for all sites ranging from 73.5% to 79.3%. Figure 11 shows the variation in overall horizontal irradiation (data obtained using PVGIS) for the optimum angle for the sites studied.

Based on the results obtained using MATLAB software, the curves show that all the provinces of Burundi have a high solar energy yield all year round. We notice that only Mpanda, Marangara, Bukemba and Nyanza-Lac have a high solar energy yield from May to September.

In this section, we have also evaluated the effect of the solar panel’s tilt angle on the energy captured for one of the sites studied. Table 4 shows the results obtained on the effect of solar panel tilt angles on the energy produced at the Marangara site.

We see that the energy produced for the optimum tilt angle of the solar panel is significant compared with the other angles.

Table 5 and Table 6 illustrate the main balances and results for solar panel tilt at an angle of 30˚ and an optimum angle of 13˚ at the Marangara site.

Where E_Load is Energy for Load, GEff is Effective Global, SolFrac is Solar Fraction, Eunused is Unused Energy, E_User is Energy Supplied to the use, E_Miss is Missing Energy and GlobHor Global Horizontal irradiation.

The results obtained show that the energy required (load) is 892.06 kWh/year. For the optimum yearly tilt angle of inclination of 13˚, the energy available is 964.61 kWh/year and we have the energy demanded (load) of 892.06 kWh/year which corresponds to the energy given to users. For the angle of inclination of 30˚, the energy produced is 900.33 kWh/year with the energy given to users of 845.14 kWh, which is less than the load energy (892.06 kWh/year).

Figure 12 shows the monthly and yearly values of the performance ratio obtained for the Marangara site.

We obtained a PR ranging from 73.5% to 79.3% in our study (see Table 2 ), which shows that Burundi has a significant yield on the photovoltaic system. Figure 8 shows a PR of 79.3%, which means that around 21.7% of the energy radiated during the observation period could not be used, due to losses such as 2.98% unused battery energy, 10.35% solar panel collection loss and 7.37% system loss, as detailed by a loss diagram.

In this section, we will show the novelty of the project. Using the R method in SPSS software based on the linear regression model, we will develop a model for calculating the optimum yearly tilt of inclination of the solar panel and a model for calculating the energy available for a solar panel at any site with a latitude of less than 10. We will analyse whether the input parameters to the models allow us to obtain an output value applicable to each site studied based on the linear regression model.

Analyzing the results in Table 3 using SPSS software to verify that the solar panel tilt angle varies with latitude. The input parameters are the latitude of the site and the angle. The angle is a dependent variable. Table 7 shows a summary of the model of the coefficients for determining R.

a. Predictors: (Constant), latitude.

In the regression model, we have a Correlation Coefficient R equal to 0.825 and a Coefficient of determination R² equal to 0.681 indicating a relationship between solar panel tilt angle and latitude with an average percentage of 68.1%. Table 8 illustrates the non-standardized and standardized coefficients and the P-value (sig).

a. Dependent variable: Angle.

From this table, we note a P-value of less than 0.05, showing that there is a statistically significant relationship between solar panel tilt angle and latitude. The mathematical model developed that expresses the solar panel’s optimum yearly tilt of inclination for any site studied is:

$\beta =0,939.\lambda +11,079$ (6)

where $\beta$ is optimum yearly tilt of inclination (in ˚); where $\lambda$ is latitude of the site (in ˚S). By entering the latitude coordinates of the site under study, we can easily obtain the optimum yearly tilt angle of inclination of the solar panel at each site from this mathematical model.

Analyzing the results in Table 3 using SPSS software to test the effect of optimum tilt angle of the solar panel on the energy available. The input parameters are the optimum yearly angle, the global horizontal irradiation and the available energy. The available energy is a dependent variable. Table 9 shows a summary of the model of the coefficients for determining R.

a. Predictors: (Constant), Angle, GlobHr.

In the linear regression model, we have a Correlation Coefficient R equal to 1 and a Coefficient of Determination R² equal to 1, validating the influence of solar panel tilt angle and overall horizontal irradiance on available energy in the high percentage of 100%. Table 10 shows the non-standardized and standardized coefficients and the P-value (sig).

a. Dependent variable: E_avail.

We note P-values of less than 0.05 for GlobHor and Angle, showing that there is a statistically significant relationship between the variables (tilt angle and global horizontal irradiance) and available energy. From the values of B and Beta, we see a strong positive significant implication for horizontal global irradiation and a weak negative significant implication for solar panel tilt angle on available energy. The mathematical model representing available energy for any site studied is given by the following expression where $\beta$ is the angle, P_C power of solar panel in Watt:

$EAvail=\left(-\mathrm{0.913.}\beta +\mathrm{178.893.}GlobHr+64.583\right).\frac{P_C}{610}$ (7)

By entering the values of the yearly tilt angle of inclination of the solar panel and the value of the global horizontal irradiation of the site studied, we can easily obtain the energy available per year for any power of solar panel in each site. Table 11 shows the verifications of the models developed using the geographical coordinates and meteorological data used in Table 3 .

In this Table 11 , we have shown the verification for a few sites, but the models developed verify all the sites studied. We note that the results obtained by the models developed are close the simulation results obtained with pvsyst software.

In this section, we will evaluate the experimental results of two solar panels of 10Wp with two regulators victron BlueSolar charge controller MPPT 75/10A-12V tilted one at 30˚ and the other at optimum tilt of 14˚ at the Nyakabiga site in the locality of Kinama ( Table 3 ) as shown in Figure 13 and Figure 14 . Victron MPPT controller is ultra-fast rapid MPPT controller improves solar production compared with PWM charge controller.

Figure 15 and Figure 16 illustrate the curves of the experimental results obtained for the dates 12/21/2023 and 12/28/2023.

From 9:00 a.m. to 11:00 a.m. and from 2:00 p.m. to 5:00 p.m. for the date 21/12/2023, we notice an increase of around 2W for a solar panel tilted at an angle of 14˚ compared with the 30˚ tilt. This increase is also observed for the date 28/12/2023 from 10:00 a.m. to 5:00 p.m, that is a gain of 20%. Under cloudy skies, we observe a significant decrease for all mounts, with a difference of around 0.7 W, the one at 1:00 pm and the second at 2:00 pm. It is mean that there is a lowering of solar irradiation when there is a cloudy sky.