# Renewables and Advanced Storage in Power Systems: The Iberian Case
## 4 Study Case: The Iberian System in 2030 According to the National Energy and Climate Plans (NECPs)
### Sensitivity to Uncertainty of Storage Costs. Application of the Power Estimate Method  
The standard deviation of investment costs of the installed power of Li-ion batteries in 2030 is estimated as 59% of the mean value, while for capacity, it is 61% of the mean value [6]. In our study, 60% was taken for both parameters. Both random variables have been assumed to be Gaussian, so their skewness is zero. Under these conditions, the parameters defined in Section 3.2 take the following values:  
\[p_{1}=p_{2}=\frac{1}{2}\hskip 28.452756 pt\xi_{1}=\xi_{2}=1 \tag{12}\]  
\[x_{1}=\eta_{x}+\sigma\hskip 28.452756 ptx_{2}=\eta_{x}-\sigma \tag{13}\]  
Then, the first- and second-order moments can be obtained as:  
\[E[z]=\eta_{z}=\frac{1}{2}h(x_{1})+\frac{1}{2}h(x_{2})\ E\Big{[}z^{2}\Big{]}=m_ {z,2}=\frac{1}{2}h^{2}(x_{1})+\frac{1}{2}h^{2}(x_{2}) \tag{14}\]  
The standard deviation of the output variable is found as \(\sigma_{z}=\sqrt{m_{z,2}-\eta_{z}^{2}}\), where \(x\) is the cost of storage, and the output variables are the installed power and capacity factors of the optimized variables. In summary, simulations are run for the following cases:  
1. The base case, with the cost parameters shown in Table 3.
2. A second case, where the costs of storage have been increased by a standard deviation. 3. A third case, where the costs of storage have been decreased by a standard deviation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Technology**} & \multirow{2}{*}{**Fixed Costs (\(\upepsilon\)/MW y)**} & \multicolumn{2}{c}{**Variable Costs**} & \multirow{2}{*}{**Lifetime (Years)**} \\  & & **(\(\upepsilon\)/MWh)** & & \\ \hline Combined cycle & 84,464 & 57.22 & 30 \\ \hline Open cycle & 47,234 & 86.90 & 30 \\ \hline Onshore wind & 136,428 & 0.010 & 25 \\ \hline Photovoltaics & 76,486 & 0.010 & 25 \\ \hline CSP & 215,913 & 0.010 & 30 \\ \hline Biomass & 278,015 & 28.42 & 30 \\ \hline Batt. storage (*) & 24,720 & 17,438 (*) & 20 \\ \hline \hline \end{tabular} (*) Annuitized fixed costs for MWh capacity in battery storage.  
\end{table} 
Table 3: Cost hypothesis. Carbon price equal to 35 \(\upepsilon\)/tCO\({}_{2}\). Data from References [6, 11, 39, 40]. Compared with the generation mix of the Iberian countries in Table 1, the installed power of the combined cycle plants is much lower in the simulation because the national plants maintain the existing capacity. The capacity factors of wind and PVs are higher in the national plans than in actual past years, and nuclear plants are still present (the phaseout in Spain will end in 2035). In addition, batteries should be already installed in 2030, so costs before that date should have been used in the simulation. This inconsistency is considered in the sensitivity study, where higher storage costs have been considered. In any case, the constraint of keeping the study as close as possible to the present power system moves the generation mix of the national plans away from that obtained from scratch. Comparisons to \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**Base Case**} & \multicolumn{2}{c}{\(x_{1}\) = \(\eta\) + \(\sigma\)} & \multicolumn{2}{c}{\(x_{2}\) = \(\eta\) - \(\sigma\)} \\ \hline  & **P (GW)** & **CapF (\%)** & **P (GW)** & **CapF (\%)** & **P (GW)** & **CapF (\%)** \\ \hline Comb. cycle & 12.86 & 63.39 & 12.96 & 62.17 & 12.78 & 64.41 \\ \hline Open cycle & 8.25 & 2.73 & 11.01 & 2.94 & 6.73 & 2.15 \\ \hline Wind & 72.34 & 21.69 & 86.08 & 20.68 & 47.74 & 23.26 \\ \hline PVs & 84.58 & 17.62 & 73.71 & 17.13 & 107.76 & 18.37 \\ \hline Storage (batteries) & 12.95 & - & 6.25 & - & 31.18 & - \\ \hline Storage hours & 6.74 & - & 4.99 & - & 7.14 & - \\ \hline Storage capacity (GWh) & 87.28 & - & 31.19 & - & 222.63 & - \\ \hline Storage as \% of demand & 0.0502 & & 0.0359 & & 0.0848 & \\ \hline Spillage VRE (\%) & 10.7 & & 14.69 & & 4.07 \\ \hline \end{tabular}
\end{table} 
Table 4: Optimization results. Total generation: 367.01 TWh. Figure 3: Optimization results. Capacity factors and VRE spillage.