## 4 Results  
### Energy Storage System Requirements  
ESS energy and power capacity requirements are presented in Table 1. Energy capacity requirement \(E_{\text{ESS}}\) is the difference between the maximum and minimum state of charge during one year with respect to the PV plant nominal power. It describes how many hours the ESS needs to be able to deliver the nominal power. Accordingly, power capacity requirement \(P_{\text{ESS}}\) is the maximum absolute power ESS needs to be able to deliver or receive with respect to the PV plant nominal power. As is shown in Table 1, the energy capacity requirement for ESS is directly proportional to the PV plant size since the values are normalized to the PV plant nominal power. For 60 min ISP, the ESS needs to be able to deliver the PV plant nominal power for 0.36 h. This result is in line with earlier studies on the ESS energy capacity requirements to compensate PV power plant fluctuations with respect to different ramp rate limits. For example, the ESS energy capacity requirement for a 3%/min ramp rate limit of the PV plant nominal power was around 0.3 h decreasing with increasing ramp rate limit [15]. This is plausible since the grid feeding power varies very smoothly when a 3%/min ramp rate limit is applied, which is close to the approach of this study with a constant grid feeding power during each ISP. The ESS energy capacity requirement decreases almost linearly with decreasing length of the ISP time being just over 0.09 h when 15 min ISP is applied. This linear decrease of the required ESS energy \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PV Generator Size**} & \multicolumn{2}{c}{**ESS/P\({}_{\text{nom}}\) (h)**} & \multicolumn{2}{c}{**PESS/P\({}_{\text{nom}}\) (p.u.)**} \\ \cline{2-5}  & **60 min ISP** & **15 min ISP** & **60 min ISP** & **15 min ISP** \\ \hline
0.1 & 0.36 & 0.093 & 0.85 & 0.83 \\
1 & 0.36 & 0.093 & 0.78 & 0.78 \\
10 & 0.36 & 0.091 & 0.78 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ESS energy and power capacity requirements with respect to the PV plant nominal power for compensating the output powers of the studied PV generators for 15 and 60 min ISP on the electricity markets. Figure 3: On top is the PV generator output power and the power fed to the grid, i.e., reference power for SoC for one hour ISP, and below is the state of charge of ESS during three days from 11 April to 13 April in 2015.  
capacity with decreasing ISP time is caused primarily by the used method of analyses, i.e., use of an ideal production forecast and a constant grid feeding power for each ISP. The probability of having very different irradiation behavior within an ISP decreases with decreasing ISP time leading directly to decreasing capacity requirements. However, this apparently trivial result provides an important hint for the future. The ESS energy capacity requirement can be decreased considerably with decreasing ISP time and by improving the PV power production forecasting accuracy. Power capacity requirement for ESS is also directly proportional to the PV plant size being roughly 80% of the PV plant nominal power (Table 1). It decreases only slightly with increasing PV plant size due to increased smoothing of power fluctuations with increasing PV plant area. Power capacity requirements for ESS are nicely in line with irradiance fluctuations caused by cloud shading [2]. On rare occasions, shading strength of a moving cloud can be as high as 90% and, accordingly, duration of a shading transition can be of the order of one second. Thus, it is very rare that an irradiance transition will have both features at the same time leading to power capacity requirements close to the PV plant nominal power. Power capacity requirements are almost the same for both ISP times, since single fast power fluctuations having high shading strength define the maximum capacity requirements. Therefore, the length of the ISP does not affect to the power capacity requirements. Small differences in Table 1 are only of statistical origin.