## 5 Experimental Data Analysis of the Isolated PVPS (Acquisition and Log)
Finally, Figure 9d shows successive intermittent operation during the fully cloudy day, which reinforces the need for the implemented safety strategy to prevent excessive cycling under conditions of low and fluctuating solar power availability. Figure 10 compares the measured and theoretical angular velocity of the induction motor, expressed as electrical frequency (Hz), to drive the centrifugal pump under rated conditions (flow and pressure). Comparing the measured with the theoretical induction motor during the clear-sky day from Figure 10a, it can be seen that both frequencies overlapped at rated operation. Similarly, as in Figure 9b, in Figure 10b, it can be seen that the system needed to start half an hour (30 min) earlier than the real system. The same as in Figure 9a, in Figure 10a, it can be seen that at the beginning of the day, the real system started its operation with two failed attempts. At sunrise and sunset, it can be seen that the electrical frequency of the motor varied in order to generate the power absorbed by the induction motor of the pump to track the power produced by the PV generator. Figure 9: Measured and theoretical power consumption by the pump motor during the 4 representative days: (**a**) clear-sky day, (**b**) day with a big cloud, (**c**) day with many small clouds and (**d**) fully cloudy day. The pump operating time \(T_{operating}\) [**s**] for one day was calculated based on the measured frequency according to Equation (5):  
\[T_{operating}=\int_{t=0\;\text{s}}^{t=24\;\text{h}\cdot\frac{3600\;\text{s}}{d \beta}}t(f(t+1)\geq f_{min})dt \tag{5}\]  
where \(f\) represents the electrical frequency of the induction motor expressed in Hz; it was considered that the PS was operating only when the induction motor frequency was above \(f_{min}\) as, below this frequency, the pump just span the water without actually pumping it, leading only to heating the electrical motor. Applying Equation (2) for the measured electrical frequency of the pump's induction motor during the clear-sky day (Figure 10a), it was found that the PS was operating for 9.2617 h, while, theoretically, the PS was supposed to operate for 9.4525 h.  
For calculating the theoretical operation time \(T_{operating\_theoretical}\) [**s**] of the PS, Equation (6) was applied:  
\[T_{operating\_theoretical}=\int_{t=0\;\text{s}}^{t=24\;\text{h}\cdot\frac{3600\; \text{s}}{d\beta}}dt\;\text{when}\;P_{PV}>P_{motor\_min} \tag{6}\]  
where \(P_{PV}\) represents the power produced by the PV generator and \(P_{motor\_min}\) represents the minimum power required by the induction motor of the pump to pump the minimum flow required for cooling the electrical motor in order to keep its temperature below the maximum allowed limit. Analyzing Figure 10a, it can be seen that during a clear-sky day, according to the theoretical electrical frequency of the induction motor, the PS should start at sunrise and operate continuously until sunset. However, the measured electrical frequency indicated  
Figure 5:0 Measured and theoretical induction motor frequency during the 4 representative days: (**a**) clear-sky day, (**b**) day with a big cloud, (**c**) day with many small clouds, and (**d**) fully cloudy day. that the PS started and stopped three times during the day: it started three times and stopped two times during sunrise and stopped at sunset without any starting attempt.