## 8 Conclusions  
Power system inertia is decreasing due to decarbonisation efforts and the integration of grid inverter connected power generation sources such as wind turbine generators and solar PV systems. Inertia is an essential part of grid frequency stability and therefore, a minimum synchronous system inertia as well as an overall system inertia, consisting of either a synchronous or an emulated share, has to be maintained. However, this development is not represented appropriately in energy system modelling. If considered at all, power system models only depicted inertia provision by synchronously connected generators of fossil-fuel-fired power plants. This results in increased carbon dioxide emission, must-run capacities and increased system costs and of course is contradictory to the general objective of modelling power systems with high shares of non-synchronously connected generation and storage systems. The presented research closes the research gap of insufficient representation of power system inertia in energy system models. Therefore, an open-source unit commitment and economic inertia dispatch model of the future German power system is created and analysed. The power system dispatch model is created, applying the open-source modelling framework OpInMod. Dispatchable sources for synchronous inertia are synchronously connected generators and synchronously connected condensers. Dispatchables sources for SI are wind turbines as well as battery storage units. A 2040 power system model of the German power system is analysed based on data from the TYNDP as well as a 2050100% RES scenario of the e-Highway 2050 study of the ENTSO-E. Different parameter combinations of the maximum permitted ROCOF determining the required synchronous inertia as well as the maximum time until full activation of primary load frequency control determining the overall required power system inertia are analysed. Although the German power system is embedded in the Continental European power system in which power system inertia is shared transnationally, it is assumed that in future power systems, inertia has to be provided by each country in a principle of joint action likewise to primary frequency control. Results show that retaining a full activation time of primary frequency control of 30 s as applied today, system costs increase significantly. Highest system costs occure in the 100% RES scenarios of bn 31.924 EURO. System costs in the two 2040 scenarios are with bn 17.546 EURO and bn 9469 EURO lower in the NT and DE, respectively. High system costs in these scenarios are due to investments in additional synchronous condensers to meet inertia constraints. Decreasing primary load frequency control activation time to 2 s as for the case of fast frequency response, overall system costs can be reduced significantly to bn 6.6 EURO in the 100% RES scenario and even down to bn 3.9 EURO in the DE. Allocating additional system costs to the additionally provided inertia results in values ranging from 0.002 EURO/kg\(\cdot\)m\({}^{2}\) to 0.61 EURO/kg\(\cdot\)m\({}^{2}\). The results indicate that in some cases, it is less costly to dispatch fossil-fuel-fired power plants to provide an inertial response than to invest in non-CO\({}_{2}\)-emitting storage units. Hence, overall carbon dioxide emissions increase. Thus, a further analysis with increasing CO\({}_{2}\) emission prices to support a market-based solution to decarbonise energy system has been conducted. CO\({}_{2}\) emission prices of more than 225 EURO/t\({}_{\text{CO}_{2}}\) do not further decrease carbon dioxide emissions. In this case, fossil-fuel-fired power plants are dispatched independently from inertia constraints to meet power demand. A further sensitivity analysis shows that in power systems based on a high share of supply-dependent generation sources such as wind turbines, times with less wind potential or hydro inflow result in increased system costs.