## 5 Results
Battery storage units to provide a synthetic inertial response are not included by the model's investment module. In the DE scenario and parameter combination 1 Hz/s, 30 s, synchronous condensers provided an overall additional moment of inertia of 6 \(\times\) 10\({}^{9}\) kg\(\cdot\)m\({}^{2}\). This investment optimisation result is reflected by higher system costs of bn 17.5 EURO for the NT scenario and bn 9.5 EURO for the DE scenario. The RE100 scenario and the parameter combination 1 Hz/s, 30 s, is also characterised by increased system costs of bn 31.9 EURO. Reducing the demand for overall inertia due to faster response of primary frequency control (from 30 s response time to 2 s time until full activation) results in decreasing system costs for the NT and DE scenario. However, CO2 emissions increase with respect to the base scenario. For these parameter combinations, it is overall less costly to dispatch fossil-fuel-fired power plants compared to investing in additional storage units providing synchronous inertia or SI. The last column of Table 7 depicts additional cost per provided additional inertia. Obviously, with decreasing demand for inertia, the cost per provided inertia decrease significantly. For the parameter combination 1 Hz/s, 30 s, to 1 Hz/s, 2 s, of the NT scenario, costs decrease from 0.44 EURO/kg\(\cdot\)m\({}^{2}\) to 0.04 EURO/kg\(\cdot\)m\({}^{2}\). For the parameter combination 1 Hz/s, 30 s, to 1 Hz/s, 2 s, of the DE scenario, costs decrease from 0.21 EURO/kg\(\cdot\)m\({}^{2}\) to 0.03 EURO/kg\(\cdot\)m\({}^{2}\) and for the RE100 scenario from 0.61 EURO/kg\(\cdot\)m\({}^{2}\) to 0.003 EURO/kg\(\cdot\)m\({}^{2}\). Figure 6: Visualisation of a 24 h time period considering inertia constraints of the NT scenario and the parameter combination 1 Hz/s, 2 s. The top subplot illustrates results of the power output flows, and the bottom subplot shows the supplied moment of inertia inertia inertia. Figure 7 depicts the overall system costs of each scenario and parameter combination in bn EURO. The overall system costs for all of the RE100 scenarios are higher, because investments in additional storage units providing inertia have to be conducted to meet the inertia constraints. The overall system costs of the DE scenarios are lowest for all parameter combinations. Figure 8 shows the additional system costs with respect to the additionally provided inertia due to the inertia constraints depicted as bar plots. Costs for inertia for the parameter combination of 1 Hz/s, 30 s, are highest in all scenarios due to the high investments. Decreasing the activation time of primary frequency control, resulting in less overall inertia needed, decreases the costs for additional inertia significantly. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Parameter** & **CO\({}_{\mathbf{2}}\) Emissions** & **No. of Sync.** & **System Costs** & **Costs per Inertia** \\  & **Combination** & **[10\({}^{9}\) t\({}_{\mathbf{CO_{2}}}\)]** & **Condensers [-]** & **[bn EURO]** & **[EURO/kg\(\cdot\)m\({}^{2}\)]** \\ \hline \multirow{4}{*}{**NT**} & **Base Scenario** & 70,305 & 0 & 4.513 & 0.00 \\  & **1 Hz/s**, 30 s & 70,325 & 13 & 17.546 & 0.44 \\  & **1 Hz/s**, 2 s & 70,353 & 3 & 5.518 & 0.04 \\  & **2 Hz/s**, 2 s & 70,306 & 2 & 4.655 & 0.01 \\ \hline \multirow{4}{*}{**DE**} & **Base Scenario** & 43,729 & 0 & 3.260 & 0.00 \\  & **1 Hz/s**, 30 s & 43,737 & 11 & 9.469 & 0.21 \\  & **1 Hz/s**, 2 s & 43,731 & 3 & 3.971 & 0.03 \\  & **2 Hz/s**, 2 s & 43,726 & 2 & 3.558 & 0.01 \\ \hline \multirow{4}{*}{**RE100**} & **Base Scenario** & 0 & 6.589 & 0.00 \\  & **1 Hz/s**, 30 s & & 18 & 31.925 & 0.61 \\ \cline{1-1}  & **1 Hz/s**, 2 s & & 2 & 6.640 & 0.003 \\ \cline{1-1}  & **2 Hz/s**, 2 s & & 1 & 6.610 & 0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Overview of the optimisation results per scenario and parameter combination. Figure 7: Illustration of the overall system costs in bn EURO of the analysed scenarios and parameter combinations.