## 5 Experimental Data Analysis of the Isolated PVPS (Acquisition and Log)
The total number of starts/stops during one day \(N_{starts/stops}\) was calculated based on the measured electrical frequency (\(f\)) of the induction motor according to Equation (7):  
Figure 5:1  
The total number of theoretical starts/stops \(N_{starts/stops.theoretical}\) was calculated based on the theoretical electrical frequency (\(f_{T}\)) of the induction motor according to Equation (8):  
Figure 5:2  
For the day partially obscured by a large, slow-moving cloud (Figure 10b), the measured and theoretical frequencies overlapped again during steady-state operation due to the higher actual start thresholds (although the practical start occurred about 30 min later than predicted). The measured data indicated a total operational duration of approximately 6.4959 h versus the theoretical expectation of 7.5367 h. In particular, the theoretical model implied frequent cycling (63 start-stop events), which significantly exceeded the manufacturer's recommended maximum of eight cycles per hour. In practice, the system implemented a safety control mechanism whereby after two unsuccessful attempts to start, the pumping system executes a delay of 10 min until the next attempt and, if, after 10 min, there is another unsuccessful attempt, it executes another delay of 20 min simultaneously with resetting the attempts counter. Due to this reason, the total number of starts per hour \(N_{starts/stops\ H}\) was calculated according to Equation (9):  
Figure 5:3  
The total number of theoretical starts per hour \(N_{starts/stops.H.theoretical}\) was calculated according to Equation (10):  
Figure 5:4  
During the day characterized by multiple rapid cloud passages (Figure 10c), the measured operational duration was 6.7556 h compared to a theoretical expectation of 8.687 h. The system experienced 21 start-stop events versus 43 predicted theoretically, again highlighting the importance of implemented safety delays. Finally, on a fully cloudy day (Figure 10d), the operational duration was only 0.8103 h, substantially below the theoretical duration of 2.326 h, accompanied by 16 actual versus 87 theoretical start-stop events. These differences underscore the critical importance of considering real-world operational constraints in system design and control strategies. The purpose of this analysis was solely to detect and characterize pressure shocks, rather than evaluate their impact on the lifespan of the equipment, which will be investigated in future work. Figure 11 compares the measured and theoretical pump head (pressure) on the left \(y\)-axis and the corresponding pressure shocks (the time derivative of the measured pump pressure) on the right \(y\)-axis for the four representative days. Due to the submersible configuration of the centrifugal pump considered here, only water hammer effects (overpressure) that occurred when the pump abruptly stopped could be detected; cavitations [38; 39; 40] could not be identified without additional sensors (e.g., vacuum or suction-side pressure transducers). On the clear-sky day (Figure 11a), the measured and theoretical pressures aligned closely under nominal operating conditions. Minor oscillations and associated small-amplitude pressure shocks observed at sunrise correlated with two unsuccessful startup attempts and subsequent control strategy adjustments designed to match pump power consumption with available PV power [41]. These shocks remained within permissible limits and were considered negligible. During the day, partially obstructed by a large cloud (Figure 11b), the pressure variations increased in amplitude, coinciding with rapid decreases in PV power output. The day characterized by frequent, rapidly passing small clouds (Figure 11c) produced the largest pressure oscillations and notable shocks, including events exceeding amplitudes of 2.2 bar/s, which could potentially shorten the useful life of the equipment if they occurred [42]. Finally, on the fully cloudy day (Figure 11d), intermittent and insufficient PV power resulted in pump pressures consistently below the reference value.