*5.1. Simulation Conditions*

In this section, the MPPT simulation results are obtained through the PSIM simulation software. Indeed, the efficiency of MPPT by optimization techniques is evaluated under irradiation conditions similar to the real conditions. Moreover, a variable irradiance profile (from 200 to 1250 W·m−2) is chosen to test the system performance. This profile includes fast, slow, strong, and stable fluctuations, as shown in Figure 11.

**Figure 11.** Irradiance profile used for simulation.

The graph in Figure 11 shows the different levels of irradiance fluctuations as a function of time *ti*, which are modeled by:


This irradiation profile is very unstable in terms of meteorology, which is a good test to evaluate the behavior of the solar pumping system.

#### *5.2. Simulation Results of the Direct Coupling*

Figure 12 shows the simulation results of the SWPS in the direct coupled case. It should be noted that the irradiance variation leads to a significant power fluctuation. In addition, the power transmitted to the pump is considerably less than that generated by the GPV, as shown in Table 2. Under standard conditions where the irradiance has a value of 1000 W·m<sup>−</sup>2, the motor pump receives a power of 961 W, which presents 58% of the peak power (1650 W) produced by the GPV. Moreover, a significant variation of the motor pump voltage is undesirable for the safety of this type of system. Moreover, this configuration has as a problem the dependence between the power supplied by the GPV and the load characteristic. Indeed, the optimization of the energy requires another configuration in which an adaptation unit is introduced downstream of the GPV.

**Figure 12.** Simulation results for direct coupling. (**a**) Instantaneous power extracted from the GPV, (**b**) terminal voltage at the pump motor, (**c**) rotation speed of the pump motor.

## *5.3. Simulation Results Using the P&O Optimization Algorithm*

Figure 13 shows the evolution of the variables in the indirect coupling between the GPV and the motor pump using the SEPIC converter in the case of optimization by the P&O technique. Figure 13a–c shows, respectively, the variation of the instantaneous electrical power, voltage, and rotational speed of the motor pump as a function of time. Under the standard irradiation conditions applied to the pumping system, the extracted power remains much higher and presents an increase of 47% compared with the direct coupling. In this regard, it is important to note that a clear improvement of the system from the power point of view with the developed controller is observed. Indeed, the power is perfectly improved compared with the direct coupling. However, this technique presents oscillations of about ±2 W, while with the decrease in the duty cycle, it is possible to decrease these oscillations, but the tracking will be much slower. To test the behavior of the MPPT–P&O technique under a fast variation of the irradiance, the instant t3 presents an instantaneous drop of this one. Under these climatic conditions, the extracted power undergoes a decrease proportional to the irradiance. Compared with the direct coupling, the extracted power remains much higher. Finally, the P&O technique allows a good optimization of the pumping system. However, the decrease in the increment step of the duty cycle leads to a decrease in the power fluctuation, while the tracking speed does not adapt quickly to the irradiance changes. From Figure 13b, compared with direct coupling, the terminal voltage of the pump motor is significantly improved, especially during abrupt changes in irradiance (*t*3, *t*4, and *t*5). Moreover, under steady-state conditions, the voltage has fluctuations of the order of 0.05 V, which is quite acceptable for pump systems. From Figure 13c, the speed of the motor pump is significantly improved and is almost generated for the entire range of weather variations. Compared with the direct coupling, this speed is significantly increased. In fact, it shows a significant improvement in that it has become 667 rpm instead of 310 rpm, a gain of 46%.

**Figure 13.** *Cont*.

**Figure 13.** Simulation results associated with the P&O technique. (**a**) Instantaneous power extracted from the GPV, (**b**) terminal voltage at the pump motor, (**c**) rotation speed of the pump motor.
