## Materials and Methods
### Solar Energy and \"Solar Days\"  
Solar irradiance data with 1-s resolution were collected via an irradiance sensor (metecontrol; SI-12-TC, Germany) at the KIT Solar Park--a 1-MW PV system located on the KIT campus in Karlsruhe, Germany (latitude: 40\({}^{\circ}\)00\({}^{\circ}\)33.73\", longitude: 82\({}^{\circ}\)4\({}^{\prime}\)15.98\" E)--and used as the input for the SAS. The SI data were converted into a current-voltage (I-V) curve via the built-in Sandia formula [60], while the module temperature was provided via an external temperature sensor. There were two different settings for the SAS for the experiments conducted using i) batteries and ii) SCs (as well as the battery-less reference directly coupled with the pump). Both configurations rely on simulated PV panels with a 500-W maximum point power (P\({}_{\rm mp}\)) under standard solar radiation conditions (SI = 1000 W/m\({}^{2}\)) and a module temperature of 25 \({}^{\circ}\)C. The SAS parameters used for battery configurations were set as follows: V\({}_{\rm mp}\) = 75.2 V (voltage at maximum power) and I\({}_{\rm mp}\) = 6.6 A (current at maximum power), with a fill factor (FF) of 75% and a relative temperature coefficient of the maximum power (P\({}_{\rm mp}\)) \(-\)0.41%/\({}^{\circ}\)C. For the SC configurations, the SAS was used to simulate the output of an array of five 100-W silicon PV modules (Sunmodule SW100 Poly [61]) connected in a series. These PV modules resulted in a high system voltage at the maximum power point (V\({}_{\rm mp}\) = 188 V\({}_{\rm dc}\)) that could be used to charge the SCs. The PV module specifications--P\({}_{\rm mp}\), FF and temperature coefficient--were kept the same as mentioned above, along with the SI used as inputs for the SAS. The FF is defined as the ratio of the P\({}_{\rm mp}\) of the solar cell to the product of the open-circuit voltage (V\({}_{\rm OC}\)) and short-circuit current (I\({}_{\rm SC}\)) and is essentially a measure of the efficiency of PV modules. The temperature coefficient affects the output power of the PV panels, such that, as the temperature of the PV panel increases, the output power decreases. Note that the PV settings for the batteries were based on those used for previous SC experiments [40]; however, here, the PV area was scaled up by 25% in order to get a higher current and maintain the same voltage; hence, four PV panels were connected in a series to obtain a PV power of 500 W. The SAS combines all of these inputs to determine the PV power output at all times of the day. The SI data were chosen to represent very different levels of fluctuations that occurred within one year of data (2016) --namely, (i) a \"sunny day\" (5 May), (ii) a \"partly cloudy day\" (26 May) and (iii) a \"very cloudy day\" (13 October), as illustrated in Figure 2A. To demonstrate the impacts of SI on the performance of the system without Li-ion batteries, the PV output power on the three \"solar days\" is plotted in Figure 2B. The module temperature data is presented in Figure 2C for further comparisons. Note that the measurements can be slightly different from real weather conditions due to the occurrence of dust or shadows on the PV panels. On the \"partly cloudy day\", several sharp drops in the SI occurred in the periods around 8:30, 11:00-13:00 and 14:30. The timeframe of these fluctuations in the SI was typically seconds to minutes. The SI on a \"very cloudy day\" exhibited periods of large fluctuations as thick clouds passed overhead from 7:30 to 14:30, and subsequently, the already low SI dropped steadily from 14:30 to 15:30. The \"sunny day\" illustrated a typical SI in the range of 100-900 W/m\({}^{2}\). The SI does not reach 1000 W/m\({}^{2}\) due to the season in this latitude (beginning of May in Germany) and the temperature exceeding 25 \({}^{\circ}\)C (see Figure 2C). It can be seen from Figure 2B that the maximum PV power output maintains \(\sim\)400 W when it reaches the maximum SI, and the power saturation occurs at SI \(>\) 800 W/m\({}^{2}\).