## 1 Introduction
An energy system dispatch model was created applying the modelling tool PLEXOS. Ireland's RES curtailment increased by 11% and the average interconnector congestion during 24% of the modelled time periods. Minimum inertia requirements on the other side are neglectable for Continental Europe, since sufficient inertia is shared amongst member countries. [PERSON] et al. 's objective is to close the gap of knowledge of insufficient inertia in unit commitment and dispatch models [19]. Therefore, a linear programming model of the ERCOT power system using PLEXOS software is created. When constraining inertia to meet minimum thresholds, fossil-fuel-fired generation plants are dispatched, resulting in increased system costs of $85 million. [PERSON] et al. also implemented a ROCOF threshold into a mixed linear integer programming model of the European power system, analysing effects on curtailment of variable RES, carbon dioxide emissions and production costs [20]. A ROCOF threshold of 1 Hz/s results in increased system costs by 53.1% and CO\({}_{2}\) emissions by 48.9%. In conclusion, the four publications showed that inertia constraints result in increased must-run-capacities, as well as higher system costs and carbon dioxide emissions. It has to be highlighted that none of the presented publications included sources for SI such as wind turbines of battery storage systems, although they acknowledged their beneficial support or synchronous storage units [19; 20]. The work at hand adds an evaluation of system costs because of the provision of inertia in the German power system to the literature. The German power system is already characterised by high shares of frequency inverter connected generation sources and ambitious goals in terms of RES integration [21]. Although 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 [22]. Thereby it is to some extent ensured that power provided by an inertial response is not restricted by transmission capacities between member states. To evaluate system costs in the German power system,a novel unit commitment and economic inertia dispatch model is designed, applying an open-source modelling tool. Minimum inertia constraints are defined and sources for synchronous and SI are provided. The model's innovative approach is to consider inertia not only by synchronously connected generators but also by synchronously connected storage units and the provision of SI from wind turbines and battery storage systems. Hence, sources for inertia are dispatched alongside variable RES and dispatchable units to supply power demand. Different energy system pathways are assessed, including the impact of fast frequency response and CO\({}_{2}\) emission prices. Scenarios are based on the 2020 Ten-Year Network Development Plan (TYNDP) [23] and a 100%-RES scenario based on the e-Highway 2050 study [24]. The work is structured as follows: Section 2 presents the methodology. The scenarios are introduced in Section 3 and data in Section 4. Section 5 presents results, and sensitivities are presented in Section 6. The results of this study are discussed in Section 7 and concluded in Section 8.