## 4 Data
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Scenario** & **NT** & **DE** & **RE100** \\ \hline Price of CO\({}_{2}\) [EUR/t] & 75.00 & 100.00 & - \\ Demand per year [TWh] & 625.1 & 644.0 & 665.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Carbon dioxide prices and annual power demand per scenario. Data from [23; 24]. The power imbalance, \(\Delta P\), needed to determine \(J_{sys,sync}\) is assumed to be the loss of the largest transmission line in the respective scenario. Currently, the power imbalance is the ENTSO-E reference incident, i.e., 3 GW [22]. However, the ENTSO-E concludes that the Continental European power system must be able to resist split scenarios, i.e., the loss of transmission lines or interconnectors [26]. The transmission line with the largest capacity, which in the case of its disconnection marks the worst-case scenario in terms of the power imbalance, is 6 GW for DE and NT scenario (a transmission line between France and Spain) and 10.4 GW for the RE100 scenario (a transmission line between Germany and Norway). Additionally, the nominal grid frequency, \(f_{grid}\), of 50 Hz is assumed to calculate \(J_{sys,sync}\). In future power systems, the combination of both synchronous inertia and SI is needed to limit the grid frequency nadir. To dimension the minimum needed system inertia and to build the constraint depicted in Inequation (8), a simplified grid frequency model which is also used in [3] is applied in this work as well. The model depicts the grid frequency development in the event of a power imbalance and calculates the grid frequency nadir considering the balancing effect of power system inertia and primary load frequency control with characteristics specified by the ENTSO-E [22]. A self regulation effect of loads of 1%/% is assumed [22]. The objective is to limit the grid frequency nadir to a lower bound of 49 Hz, since this is the lower threshold before load is shedded [22]. The needed system inertia is once determined assuming load frequency characteristics as currently specified [22], e.g., a deployment time of 30 s, and once considering the application of a fast frequency control service with a deployment time of 2 s as applied by the Irish grid operator [11]. Thereof, three parameter combinations of the ROCOF threshold and deployment time of primary load frequency control to limit the grid frequency nadir are combined to determine the required system synchronous inertia as well as the overall system inertia:  
1. A minimum ROCOF of 1 Hz/s and a deployment time of 30 s representing the current system specifications. This parameter combination is hereafter referred to as **1 Hz/s**, **30 s**;
2. A minimum ROCOF of 1 Hz/s and a deployment time of 2 s. The parameter combination is hereafter referred to as **1 Hz/s**, **2 s**;
3. A minimum ROCOF of 2 Hz/s and a deployment time of 2 s, which is hereafter referred as **2 Hz/s**, **2 s**. It is introduced in Section 3 that in the future Continental European power system, participants have to provide inertia in a principle of joint action likewise to current standards of primary frequency control [22]. Table 5 depicts the total energy generation in Germany and Continental Europe per scenario [49, 50], as well as the resulting inertia contribution coefficient, \(C_{i}^{inertia}\), in percent as calculated when applying Equation (13). Table 6 provides an overview of the required system synchronous inertia and system inertia for Germany per scenario and parameter combination. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Generation** & **Generation** & **Inertia Contribution** \\  & **Germany** & **Total [TWh]** & **Coefficient (C\({}_{1}^{inertia}\)) [\%]** \\ \hline NT scenario & 699 & 3184 & 21.95 \\ DE scenario & 855 & 4503 & 18.98 \\ RE100 scenario & 503 & 3215 & 15.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Overall power generation in Continental Europe and Germany as well as the calculated inertia contribution coefficient. Data from [24, 49].