## 4 Results
### Energy Cycling Analysis  
Cycled energy is the energy charged to ESS from the PV generator and then discharged from ESS to the grid. If PV generator output power and the PV system reference power match exactly, energy cycling does not happen. The worst-case scenario is when the PV generator output power and the PV system grid feeding reference power during some period do not match at all. Then all the energy fed to the grid pass through the ESS.  
The amount of cycled energy through ESS \(E_{\text{cyc}}\) with respect to the annual production of the PV plant \(E_{\text{tot}}\) is presented in Table 2. The amount of cycled energy is around 11% of the total energy productions for the 60 min ISP, which is 60-75% more compared to the 15 min ISP. The cycled energy is directly proportional to the PV generator nominal power decreasing only slightly with increasing system size due to increased spatial smoothing of irradiance fluctuations.  
Daily energy cycled through ESS in 2015 for the 0.1 MW PV power plant with 60 min ISP time is shown in Figure 7a as an example. The amount of cycled energy follows closely the seasonal variation of irradiation and peak PV generator power available in early summertime. All the studied PV generators and ISP times have quite similar use of ESS capacity and most of the energy cycling through ESS takes place just within a few summertime months, i.e., roughly within 10% of the time of the year (see Figure 7b). However, a considerable portion of the produced energy pass through the ESS all through the year (see Figure 7c).  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**PV Generator Size (MW)**} & \multicolumn{2}{c}{\(E_{\text{cyc}}\)/\(E_{\text{tot}}\) (p.u.)} \\ \cline{2-3}  & **60 min ISP** & **15 min ISP** \\ \hline
0.1 & 0.12 & 0.071 \\
1 & 0.11 & 0.068 \\
10 & 0.11 & 0.060 \\ \hline \end{tabular}
\end{table}
Table 2: Cycled energy through ESS in 2015 for the studied PV generators and ISP times.  
Figure 6: (**a**) Probability density distributions of ESS power requirements for the studied PV generators and ISP times; (**b**) ESS power requirement, PV generator power and grid feeding power probability density distributions for the 10 MW PV generator using 60 min ISP time and observation period.  
From a cycled energy point of view, most cycling occurs when small and thick clouds are constantly passing over the PV generator. The amount of cycled energy through ESS in 2015 was highest on 17 th of June and on the 4 th of June, when using 60 and 15 min ISP, respectively. As can be seen in Figures 8 and 9, a huge number of power fluctuations has taken place on those days between 20 and 100% of the nominal power. These fluctuations cause a lot of ESS charging and discharging throughout the days as well as fluctuations in the state of charge of ESS. One should also note that the used ESS power capacities are almost equal for the two days and ISP times, but the used energy capacity is much smaller in case of 15 min ISP than in the case of 60 min ISP.  
Figure 8: **(a)** 10 MW PV generator power and the grid feeding reference power; **(b)** the corresponding power taken from the ESS and **(c)** the energy stored in ESS (state of charge) with 60 min ISP on 17 th of June 2015.  
Figure 7: **(a)** Daily energy cycled through ESS in 2015 for the 0.1 MW PV power plant with 60 min ISP. Probability density distributions of the cycled energy; **(b)** with respect to the PV generator nominal power and **(c)** with respect to the PV generator electricity production for the studied generators and ISP times.