Our expiremental setup is located in a village with a rural community in Kadiogo Province, Burkina Faso’s central region. The Hybrid plant is made up of three diesel generators: two of 16 kW generators (DG2 and DG3) and one of 24 kW generator (DG1). The total installed apparent power is 70 kVA. The diesel generators are displayed in Figure 1 . In terms of renewable energy, the plant consists of five photovoltaic arrays: two 7.5 kWp and three 5 kWp arrays, bringing the total installed photovoltaic power to 30 kWp, the photovoltaic arrays are presented in Figure 2 . The load bank used in this paper is depicted in Figure 3 and has a total power capacity of 82.5 kVA. It is composed of six identical channels, each channel consisting of:

For this task, the following equipment was employed:

In “generator only” mode, each diesel generator operates under predetermined load profiles, with power factors of 0.8, 0.9, and 1. These load profiles are applied using the 82.5 kVa load bank presented in Figure 3 . Critical metrics, such as hourly fuel consumption, efficiency, and electrical output quality, are carefully tracked using the scale, the network analysers and the generators controllers. The load profiles are set up to ensure that generators operate at specific load levels: 13.75%, 27.5%, 41.25%, 55%, 68.75%, and 100% of their rated power. Equation (1) shows how the load rate is determined, considering both the active and reactive power of the electrical loads. Before the experiment began, the fuel consumption of each generator was measured during no-load tests. These tests consisted of ten 3-minutes periods of operation under no-load conditions, with at least 15 minutes between each run. For each of the three generators, this procedure was repeated.

In these experiments, tests are conducted with one generator at a time. Therefore, all other generators in the plant are disconnected during the tests. The test Protocol includes the following sequences:

This process is repeated for each load level. For each one, the hourly and specific fuel consumption, as well as the efficiency, are determined.

For each one, you will need to determine the

$\text{Load}\text{rate}\left(\%\right)=\frac{\text{Load}\text{apparent}\text{power}\left(\text{kVA}\right)}{\text{Diesel}\text{generator}\text{apparent}\text{power}\left(\text{kVA}\right)}\times 100$(1)

$$Equation (2) is used to calculate the mass flow rate.

$d_m\left(Charge\right)=\frac{\left(\left(m_i-m_f\right)-\left(t_{v1}+t_{v2}\right)\times d_{mv}\right)}{t_{charge}}$(2)

where:

$d_m\left(Charge\right)$ = mass flow rate(g/s) for a given load rate;

$d_{mv}$ = mass flow rate (g/s) for no load;

$\left(m_i\right)$ = initial mass (g), which is the total weight of the external tank, fuel, suction and return lines;

$\left(m_f\right)$ = final mass (g), which is the total weight of the external tank, remaining fuel at the end of an experiment, suction and return lines;

$\left(t_{v1}\right)$ = time (s) of no-load operation of the diesel generator at the start of the test;

$\left(t_{v2}\right)$ = no-load operating time (s) of the diesel generator at the end of the test.

Equation (3) $$ is used to obtain the specific consumption.

$C_S=\frac{\left(\left(m_i-m_f\right)-\left(\left(t_{v1}+t_{v2}\right)\times d_{mv}\right)\right)}{E}$ (3)

where:

$C_S$ = Specific consumption (kg/kWh);

$E$ = Energy produce (kWh).

$$Equation (4) is used to calculate the global efficiency.

${\eta }_{GD}=\frac{E_{electrical}}{PCI\times C_S}$(4)

$E_{electrical}$ = Electrical energy equivalent to 1 kWh or 3600 kJ;

$PCI$ = Lower calorific value of diesel (43.8 MJ/kg ≈ 12.17 kWh/kg);

$C_S$ = Specific consumption (kg/kWh).

The Equation (5) to Equation (8) were used to determine the uncertainty of type B in the mass flow rate and the specific consumption of the Diesel generators. When a value is derived from measured values of $Y$ and $Z$ with uncertainty, the resulting value for $X$ is also subject to uncertainty. To determine this uncertainty $u\left(X\right)$ , the uncertainty $u\left(Y\right)$ and $u\left(Z\right)$ must be considered.

If $X=Y-Z$ or $X=Y+Z$ then $u\left(X\right)=\sqrt{u{\left(Y\right)}^2+u{\left(Z\right)}^2}$(5)

If $X=Y\times Z$ or $X=Y/Z$ then $\frac{u\left(X\right)}{X}=\sqrt{{\left(\frac{u\left(Y\right)}{Y}\right)}^2+{\left(\frac{u\left(Z\right)}{Z}\right)}^2}$(6)

If $X=Y^n$ then $\frac{u\left(X\right)}{X}=n\frac{u\left(Y\right)}{Y}$(7)

Finaly $X=x\pm U\left(X\right)$(8)

$U\left(X\right)$ is the uncertainty expanded to 95% confidence. With $U\left(X\right)=2\times u\left(X\right)$.

This phase examines the performance of parallel diesel generators. Two or more generators are required to meet electrical demands. The experiment focuses on load distribution and current quality. To facilitate this phase, a set of load profiles with power factors of 0.8, 0.9 and 1 were established. Generator 2’s voltage regulator malfunctioned, stopping it from being paralleled with other generators. Consequently, all tests were conducted with generators 1 and 3 only. This failure to parallel generator 2 highlights the crucial importance of ensuring the hybrid plant’s performance during commissioning.

These trials employed only generators 1 and 3. The testing procedure consisted in the following phases:

Hybrid tests involved studying the distribution of electrical loads among different system sources, as well as evaluating the quality of the generated current. Load profiles were developed using power factors of 0.8, 0.9, and 1. The performance of the PV arrays was assessed by calculating their global efficiency with Equation (9). The actual output power of the PV arrays was determined by the network analysers.

$\eta =\frac{P{V}_{peakinstalled}\times \frac{G}{G_{STC}}}{P{V}_{measured}}$(9)

$P{V}_{measured}$ = Measured power of the PV array (W);

$P{V}_{peakinstalled}$ = Peak power of the PV array (Wpeak);

$G$ = Measured irradiance on site (W/m²);

$G_{STC}$ = Irradiance under standard test conditions (1000 W/m²);

$\eta$ = Global efficiency of the PV array.

The tests conducted on hybrid mode as part of this work involved a generator coupled with one or more photovoltaic arrays. The following procedure is used:

Figures 4-6 show the fuel consumption of diesel generators 1, 2, and 3, respectively, as a function of their load factor. The consumption pattern is similar to the hourly fuel flow rate depicted in the graphs, with a “k” factor applied to the consumption values.

The data from Figures 4-6 suggest that the indicated load rate experimented do not exceed 80%. During testing, we noticed that the generators stopped operating before their maximum output power specified by the constructer. Although each alternator met the expected power range, the actual output of the generators fell short of the expected values. These findings suggest that the performance of the generators does not align with expectations. Several possible reasons [27] - [31] can explain these underperformance of the generators:

Overload protection, fuel issues, incomplete combustion, cooling system faults, speed governor malfunction, voltage regulator deficiency and undersize of the engine driving the alternators. These findings will guide us in identifying specific solutions.

Figure 4 and Figure 5 depict an increase in fuel consumption as the power factor decreases. However, Figure 6 reveals a surprising finding: the maximum consumption occurs at a power factor of 0.8. This is followed by consumption rates for power factors of 1.0 and 0.9. Interestingly, all three figures exhibit a high correlation coefficient of 0.99, with relative uncertainty levels of around 7%. Although the effect is visible in the figures, due to the uncertainty level we were not able to assess the impact of the power factor on the consumption of Diesel generators in the range from 0.8 to 1. Figures 4-6 are similar to the findings of [32] , who exclusively used active power to derive his results.

Figures 7-9 illustrate the specific fuel consumption of Diesel Generators 1, 2 and 3. These values were derived using Equation (3) and are remarkably similar to the mass flow rate curves ( Figures 4-6 ).

The correlation coefficients are all around 0.99 with a relative error rate of approximately 7%. The results obtained were not sufficient to evaluate the effect of the electrical equipment’s power factor on generator fuel consumption, as it ranges from 0.8 to 1.0. The specific fuel consumption curves obtained are all similar to those in [33] [34] .

Figure 10 shows the Diesel generators efficiencies and was obtained using Equation (4).

Figure 10 shows that generator 1 is the most efficient. Furthermore, the analysis shows that Diesel generators 2 and 3 have very similar efficiencies. This can be explained by the fact that they have the same nominal power. However, we note that during the tests, generator 3 was able to meet electrical loads up to 80% of its nominal power. Generator 2, on the other hand, could not meet loads exceeding 65% of its nominal power. The efficiency curves are consistent with the usual efficiency curve of a diesel engine, as shown in [35] [36] .

This section presents the results obtained when diesel generators 1 and 3 are running in parallel. Figures 11-13 show the distribution of active loads (a), the distribution of reactive loads (b), and the load profile for power factors of 0.8, 0.9, and 1. Figures 14-16 focused on the quality of the generated.

Analysis of Figures 11-13 shows that the sharing of active loads takes place in a proportionate and stable manner throughout the duration of the tests under power factors 0.8, 0.9 and 1. Indeed, the higher the generator’s nominal power, the more it will contribute to satisfying the load profile. Reactive loads, for their part, are distributed in a proportionate and relatively stable manner for power factors of 0.8 and 0.9. Interestingly, when the power factor is 1 (as shown in Figure 13 ), generators 1 and 3 exhibit alternating positive and negative contributions to

reactive power. This behaviour suggests that the generators alternately absorb and supply reactive power. Despite the system loads being purely resistive, significant reactive power flows are recorded. This apparent contradiction highlights the effect of excitation system dynamics and control limitations, which may lead to oscillatory or imprecise regulation when the reactive power demand is very low [37] [38] . An analysis of the quality of electricity produced in cases of parallel operation of generator sets was also carried out in this section. Figures 14-16 present in detail the elements for assessing the quality of electricity in the above-mentioned cases. It appears that the voltage variations during experiments under power factors 0.8; 0.9 and 1 remain within the ranges recommended by the EN 50 160 standard (±10%). In addition, the harmonic distortion rate remains below 8%, as recommended by the BT EN 50 160 standard. The failure of the voltage regulator on DG2 introduces a limitation on the findings of the multi-generator performance assessment. Indeed, although the load-sharing dynamics were quite informative with DG1 and 3, DG2’s non-participation may have affected the load-sharing dynamics. Therefore, the generalisation of the results obtained for parallel diesel operations is limited.

In this section, we present the results obtained with two hybrid configurations:

The outcomes were found to be extremely consistent across various power factors. As a result, the data discus sed in this section comes from a power factor of 0.8. Figure 17 and Figure 18 show the results of the two different configuration experiments. Each figure displays the load profile satisfaction using various energy sources. The left y-axis represents the load profile, generator power and solar array power. The right y-axis shows the irradiance profile during the test. In both

cases ( Figure 17 and Figure 18 ), the irradiance was declining while the load profile was increasing as to the contribution of the diesel generators. When calculating the global efficiency of the arrays using Equation (9), it was shown that they were always above 80%, which could be considered satisfactory.

At the beginning of the trials, solar energy penetration was extremely high, leading to reverse power flow in some instances.

During the experiments, we observed that the output of the PV arrays slightly followed the irradiance shapes. However, the generators’ output followed the load profile. This result can be explained by the MPPT (Maximum Power Point Tracking) function of the inverters. The inverters inject the maximum available power at each instant. This configuration gives PV arrays precedence over diesel generators, which only provide supplementary energy to match load requirements. The identical conclusions emerge from [39] [40] .

Regarding the power quality parameters during the tests on hybrid modes, they all conduct to the same findings. Therefore, only Figure 19 , which provides a comprehensive analysis of electricity quality for the hybrid configuration consisting of Diesel Generator 1 and PV1, will be discussed. This figure represents: (a) voltage fluctuations, (b) harmonic distortion, (c) the active power share, (d) the reactive power share, and (e) the total apparent power.

The voltage fluctuations remained within 10% of the recommended limit throughout the test, as outlined by the EN 50 160 standard. The harmonic level, initially at 4.5%, gradually decreased to below 1% over a period of 36 minutes. This trend can be attributed to the fact that at the beginning of the test, solar energy penetration was almost 100%, with occasional returns of power to the diesel generator. The harmonic rate gradually fell during the experiment with the increase in electrical load and the contribution of the Diesel generator, somehow it always stayed in the admissible range recommended by standard EN 50160. Although no damage occurred during the returned power cases, it is crucial to include reverse power relays in such plants to protect the generators.

Regarding reactive energy, we see that the PV array neither consumes nor produces reactive power.