## 3 Scenario Design  
The system costs evaluation in the work at hand is based on a unit commitment and economic inertia dispatch model of the German power system. Although the German power system is part of the Continental European power system and inertia is shared transnationally, it is assumed that in future systems, similar to primary load frequency control, inertia has to be provided by each member of the Regional Group of Continental Europe in a principle of joint action [22]. Figure 3: Visualised methodology to calculate \(H_{var}/H_{dem}\). First, the NREL 5 MW wind turbines’ normalised power vs. normalised rotational speed specifications are applied to calculate the normalised rotational speed [46]. Second, the normalised specifications of the variable H controller are applied to determine the variable inertia output [8]. Figure is based on data from [8; 46]. Each TSO has to contribute to primary load frequency control with respect to its contribution coefficient, which is the proportional expression of the generated electricity in the respective control block with respect to the overall generated electricity of all participants [22]. In a future power system when inertia is not a secondary product of power generation units and has to be provided intentionally to maintain controllability of the grid frequency, a similar regulation has to be established. Hence, a principle of joint action to share synchronous inertia and SI between the participants of the Continental European power system has to be introduced. It is calculated as depicted in Equation (13). Since such a regulation has to be implemented into national law by each member country, the analysis of this work is conducted for the future German power system, aggregating its current four control blocks, i.e., the four German TSOs. \[C_{i}^{inertia}=\frac{E_{i}}{E_{u}} \tag{13}\]  
As Germany is still embedded in the European power system and to account for cross-border flows, the neighbouring countries of Germany are modelled as well. However, only power generation is modelled, and provision of inertia for these countries is neglected. To reduce model complexity, smaller power systems are aggregated and grouped into single nodes: the Netherlands, Belgium and Luxemburg are grouped into one node; Switzerland and Austria are grouped into another node; and Poland and the Czech Republic are grouped into one node as well. France, Denmark, Sweden and Norway are each represented by a single node. Three scenarios are designed, of which two are based on the 2020 TYNDP of the ENTSO-E [23], and one scenario is based on the e-Highway 2050 study [24]. A detailed description including all assumptions and limitations of the 2020 TYNDP scenarios is provided by the ENTSO-E [23; 48] and of the scenarios of the e-Highway 2050 study [24]. Basic assumptions of the three scenarios are summarised in the following paragraphs:  
* **National Trends (NT):** The NT scenario from the 2020 TYNDP sums up the individual commitments and climate policies of the EU member states fixed in the National Energy and Climate Plans CO\({}_{2}\) emission reduction target lines, with the requirement to meet European 2030 energy strategy targets. The power sector in particular experiences a high increase in installed capacity of photovoltaic systems and wind turbine generators. Solutions for large-scale battery units are limited. Generators driven by natural gas or nuclear power replace fossil coal generation plants. * **Distributed Energy (DE):** The DE scenario from the 2020 TYNDP is designed with a decentralised approach to meet the Paris Agreement Objective of an average global temperature increase of 1.5 \({}^{\circ}\)C or at least well below 2 \({}^{\circ}\)C by the end of the century. Especially small-scale photovoltaic system solutions such as rooftop photovoltaic systems of power consumers actively participating in the transformation process and regional use of biomass are applied as well as high generation from onshore wind capacities.