## 6 Results and Discussions  
Table 3 summarizes the comparative analysis between measured and theoretical parameters, including daily pumped volume, operating time and total start/stop cycles across four representative day types: a clear-sky day, a day partially obstructed by a single large cloud, a day characterized by frequent small clouds and a fully cloudy day. Based on these data, performance indicators detailed in Tables 4 and 5 were calculated. To quantitatively and qualitatively evaluate the photovoltaic pumping system (PVPS) under scenarios with different solar irradiation and temperature conditions, two performance indicators were proposed: pumped volume performance (PVP) and equivalent operating time performance (EOTP). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Day Type** & **Pumped Volume** & **Equivalent Operating Time Performance (EOTP)** \\ \hline Clear sky & 99.96\% & 99.60\% \\ One big cloud & 88.33\% & 87.96\% \\ Many small clouds & 77.51\% & 77.77\% \\ Fully cloudy & 42.99\% & 42.99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PVPS performance indicators during the four representative days. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Day Time** & \multicolumn{3}{c}{**Measured No. of Stank/Sleep Each Heart/Day**} & \multicolumn{3}{c}{**Transcritical No. of Stank/Sleep Each Heart/Day**} \\ \cline{2-7}
**Cover Sky** & **One Big Cloud** & **Many Small Clouds** & **Fully Greedy** & **Cover Sky** & **One Big Cloud** & **Many Small Clouds** & **Fully Greedy** \\ \hline
000-100 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
200-100 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
200-400 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
400-500 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
600-700 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
3500-800 & OFF & OFF & OFF & OFF & OFF & OFF & OFF \\
3500-800 & 350K/S & 150K/S & 150K/S & 150K/S & 25K/S & 25K/S & 25K/S \\
700-800 & 25K/S & 150K/S & 150K/S & 150K/S & 850K/S & 150K/S & 150K/S \\
800-900 & ON & 15K/S & 35K/S & 35K/S & 25K/S & 25K/S \\
900-1000 & ON & ON & 15K/S & 35K/S & 25K/S &The pumped volume performance (PVP), expressed as a percentage, was calculated as shown in Equation (14):  
\[PVP=\frac{V}{V_{theoretical}} \tag{14}\]  
where \(V\) [m\({}^{3}\)] represents the total volume that was actually pumped (measured), obtained using Equation (11), and \(V_{theoretical}\) [m\({}^{3}\)] represents the total volume that was expected to be pumped (theoretical), calculated using Equation (12). Similarly, the equivalent operating time performance (EOTP), also expressed as a percentage, was defined by Equation (15):  
\[EOTP=\frac{TE_{operating}}{T_{operating.theoretical}} \tag{15}\]  
where \(TE_{operating}\) is the equivalent operating time, determined by Equation (13), and \(T_{operating.theoretical}\) is the theoretical operating time, obtained using Equation (6). Table 4 summarizes two performance indicators (PVP and EOTP) of the PVPS across four representative days, the PVP representing the ratio between the measured and theoretical daily pumped volume (%), and the EOTP representing the ratio of measured to theoretical operating time (%). On a clear-sky day, the PVPS achieved 99.96% of the theoretical pumped volume while operating for 99.6% of the theoretical time. The slightly lower EOTP was attributed to partial-load operation below the pressure setpoint, a condition not accounted for in the theoretical model. Under a single large, slow-moving cloud, EOTP was 87.96%, with a corresponding PVP of 88.33%. The difference again reflects sub-nominal operation facilitated by the controller, which adjusted motor load to match PV power output. During intermittent shading caused by numerous small, fast-moving clouds, EOTP was 77.77%, while PVP dropped slightly to 77.51%. Here, frequent start-stop cycles prevented the system from reaching nominal operating conditions, inflating operating time without a proportional increase in pumped volume.