## 5 Results  
To analyse system costs in future German power systems due to the provision of inertia, the scenarios are compared to the base scenarios. The base scenarios are optmised for each scenario (NT, DE and RE100) without consideration of provided inertia and system inertia constraints. Thus, the influence of of the inertia constraints on the dispatch and resulting system costs as well as carbon dioxide emissions can be isolated. As introduced in Section 3, two parameters which determine the required minimum system synchronous inertia as well as the minimum system inertia are varied. An overview of the parameter combinations and required system inertia parameters is provided via Table 6. Each possible scenario and parameter combination is optimised. Figure 5 depicts a 24 h time series of the results of the NT base scenario without the consideration of inertia in the optimisation problem. To depict the influence of inertia constraints in the optimisation results, Figure 6 illustrates the exact same scenario and point in time as shown in the previous figure. However, Figure 6 shows results of the 1 Hz, 2 s parameter combination. The time series is selected randomly to illustrate the model's functionality, hence the impact of the introduced inertia constraints on the flow and inertia output of dispatchable units. Thus, the presented results within the two figures are a qualitative validation of the model functionality and outcome. The top subplots of Figures 5 and 6 each illustrate the electric power flow in GW. In positive direction of the y-axis, feed-in to the power system is depicted, i.e., generated power by RES or fossil-fuel-driven generation units and power output from storage units and imports from transmission cross-border units. In negative direction of the x-axis, cross-border outputs and energy inflow of energy storage units are shown. The bottom subplot shows the supplied moment of inertia in kg\(\cdot\)m\({}^{2}\). In the previouly published literature, the supplied inertia is expressed via the system-wide stored kinetic energy or the system inertia constant of all connected synchronously generators [19; 20; 54]. As the wind turbine inertia provision concept introduced by [PERSON] et al. [8] is applied, the stored kinetic energy in the wind turbine's rotor or wind turbine's inertia constant is not an appropriate expression of the actual emulated inertia introduced by [PERSON] et al. [8]. Further, the moment of inertia in future systems should be introduced as a tradeable commodity [3]. The top subplot in Figure 5 shows the electric power flow results. Until 15:00 of the day, power demand could potentially satisfied by feed-in from onshore and offshore wind turbines as well as photovoltaic system feed-in. However, electric energy is still imported and at the same time exported. Hence, during this time, the German power system is a transit country for electrical energy. Electrical energy is also to a large extent stored in energy storage units such as batteries and pump storage units. By the end of the day, natural-gas-driven generators are dispatched to complement decreasing feed-in from onshore and offshore wind turbines and meet the power demand. During the first three hours of the day, hydro power plants and pump storage units are dispatched with minimum power output. Thereafter, with decreasing wind power feed-in, their output increases, thus resulting in the provided inertia as depicted by the bottom subplot during