## 1 Introduction  
Energy systems are decarbonised to limit the consequences of climate change by integrating a Renewable Energy Source (RES). To a large extent, such state-of-the-art RES such as wind turbines and photovoltaic systems are connected to the power system via grid frequency converters [1]. Due to the fluctuating nature of feed-in from wind turbines and photovoltaic systems, the demand for energy storage systems increases [2]. Most short- and medium-term energy storage units are connected to the power system via grid frequency converters as well [3]. The integration of large shares of frequency converter-connected generation sources and energy storage units imposes considerable challenges on grid operators, power producers and authorities [4]. Grid frequency stability due to decreasing power system inertia is a challenge of increasing interest [1, 5]. Sufficient power system inertia is the basis for grid frequency controllability [1]. The speed with which the grid frequency changes, also known as the Rate of Change of Frequency (ROCOF), is minimised by system inertia. Further, system inertia supplies time to units providing ancillary services such as primary frequency control to adapt power output [1]. The grid frequency is the indicator for power balance in AC power systems and has to be maintained within limitations for the purpose of power system security, e.g., to prevent disconnection of generators, interconnectors or power consumers [6, 7]. The replacement of fossil-fuel-fired power plants and their synchronously connected generators by frequency converter connected RES reduces overall power system inertia [1]. Inertia can either be provided by synchronously connected rotating masses [1], e.g., synchronously connected generator or storage units, or emulated by frequency converter connected generation sources [8] and storage units [3]. An emulated inertial response is commonly referred to as Synthetic Inertia (SI) [1]. Hence, in future power systems, generation units and storage units also have to be dispatched intentionally with the purpose of securing sufficient system inertia. Grid operators already face times with low inertia systems. The Canadian transmission network operator Hydro-Quebec required wind turbines to provide an inertial response with the same performance as a synchronously connected generator in the case of a power imbalance [9; 10]. The Irish Transmission System Operator (TSO) defines a frequency-sensitive mode for wind turbines [11] and curtails wind feed-in in times of low power system inertia [12]. Further, thresholds for non-synchronous penetration, the ROCOF and an operational limit for system inertia are defined [13]. The European Network of Transmission System Operators for Electricity (ENTSO-E) addresses the importance of inertia for grid frequency stability [4] as well as defining ROCOF withstand capabilities [14]. Although some power systems are already characterised by decreasing power system inertia, the development of system inertia in future power systems due to the integration of large shares of RES is a topic which has barely been focused on in energy system modelling. In general, energy system modelling is a key approach for energy system analysis [15] and aids in designing, planning and implementing future energy systems [16]. Four publications stand out in modelling inertia in future energy systems. [PERSON] et al. analysed the 2030 Great Britain electricity network applying a unit commitment and economic dispatch model [17]. The ROCOF threshold is increased stepwise from 0.5 Hz/s up to 0.2 Hz/s to determine needed system inertia and assesses the impact on the system dispatch. In conclusion, a ROCOF threshold of 0.2 Hz/s will result in a 120% increase of operation costs as well as increased wind feed-in curtailment of 35%. [PERSON] et al. implemented a 0.75 Hz/s ROCOF threshold into the PRIMES-REF 2030 European Union (EU) scenario analysing wind and PV curtailment, levels of interconnector congestion and power prices [18].