## 4 Data  
Data to model the DE and NT scenarios are extracted from the 2020 TYNDP of the ENTSO-E [23; 49]. The data set provides installed capacities for conventional generation units, RES capacities, transmission line capacities and installed capacities for storage units, such as hydro pump storage units or battery storage systems [49]. The data sets to model the RE100 scenario are extracted from the e-Highway 2050 study [24; 50]. Figure 4 provides an overview of the power generation mix per scenario and the respective installed capacities [49; 50]. Wind turbine and photovoltaic system feed-in time series in hourly resolution are provided by the Pan-European Climate Database. The data source provides a fixed power factor in a per unit quantity, per generation unit [61]. The power factor in per unit is applied to determine the provided SI with wind turbines as introduced in Section 2.2.4. Inflow of hydro units such as run-of-river plants is provided in a daily time resolution and for hydro reservoir and open pump storage units on a weekly basis [61]. The inflow profiles are converted into hourly inflow profiles. As introduced above, the instantaneous ROCOF after the power imbalance is primarily determined by the system synchronous inertia, \(J_{sys,sync}\) (see Equation (1)). The ROCOF has to be limited to avoid ROCOF relays from triggering [1]. Thus, grid components such as generators or interconnectors are not damaged by high ROCOF values [1]. According to the ENTSO-E, ROCOFs higher then 1 Hz/s are critical and might lead to chain reactions of negative events [26]. However, the ENTSO-E has also concluded that grid users in future power system shall be able to withstand a ROCOF of at least 2 Hz/s [26]. Therefore, the minimum system's synchronous inertia, \(J_{min,sys,sync}\), to build the constraint depicted in Inequation (7) is determined by rearranging Equation (1) for \(J_{sys,sync}\) assuming once a maximum ROCOF of 1 Hz/s and once considering a maximum ROCOF of 2 Hz/s. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Storage Type** & **Investment Cost** & **O\&M** & **Lifetime** \\  & **[EUR/kg\(\cdot\)m\({}^{2}\)]** & **[EUR/kg\(\cdot\)m\({}^{2}\)\(\cdot\) a]** & **[Years]** & **WACC** \\ \hline Synchronous condenser & 176.24 & 0.01 & 20 & 0.05 \\ Battery storage (Li-ion) & 222.27 & 0.02 & 20 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Overview of investment parameters. Synchronous condenser parameters are derived by data from [42; 43; 59]. Li-ion battery storage parameters are derived by data from [3; 60]. \begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Prime Energy** & **Generator Type** & **Var. Costs** & **Efficiency** & **Min. Stable** & **CO\({}_{2}\) Emissions** & **Inertia** \\  & & **[EUR/MWh]** & **[\%]** & **Op. [\%]** & **[\(\mathbf{t_{CO_{2}}}\)/MWh\({}_{\text{el}}\)]** & **Constant [s]** \\ \hline Nuclear & - & 9.00 & 33.0 & 50.0 & 0.0 & 5 \\ Hard coal & - & 28.68 & 40.0 & 43.0 & 0.8495 & 3.125 \\ Lignite & - & 30.57 & 40.0 & 43.0 & 0.9127 & 3.5 \\ Natural gas & Conventional old 1 & 16.49 & 36.0 & 35.0 & 0.5700 & 4.25 \\ Natural gas & Conventional old 2 & 16.49 & 41.0 & 35.0 & 0.5005 & 4.25 \\ Natural gas & CCGT \({}^{\text{a}}\) old 1 & 16.99 & 40.0 & 35.0 & 0.513 & 4 \\ Natural gas & CCGT old 2 & 16.99 & 48.0 & 35.0 & 0.4275 & 4 \\ Natural gas & CCGT present 1 & 16.99 & 56.0 & 30.0 & 0.3664 & 4 \\ Natural gas & CCGT present 2 & 16.99 & 58.0 & 30.0 & 0.3537 & 4 \\ Natural gas & CCGT new & 16.99 & 58.0 & 35.0 & 0.3537 & 4 \\ Natural gas & OCGT \({}^{\text{b}}\) old & 16.99 & 35.0 & 30.0 & 0.586 & 5.25 \\ Natural gas & OCGT new & 16.99 & 42.0 & 30.0 & 0.4885 & 5.25 \\ Light oil & - & 22.16 & 35.0 & 35.0 & 0.8022 & 3.25 \\ Heavy oil & - & 24.36 & 37.5 & 35.0 & 0.7524 & 3.25 \\ Shale oil & - & 30.30 & 29.0 & 40.0 & 1.0822 & 3.5 \\ Biomass & - & 10.00 & 40.0 & 43.0 & 0.0 & 3 \\ Other RES & - & 10.00 & 37.5 & 35.0 & 0.0 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Generator characteristics. Data from [20; 51; 52; 53; 54; 55; 56; 57; 58].