## 1 Introduction
From the linear regression of the difference in emissions over the difference in conventional power generation, the gradient of the fitted regression line is calculated, which can be assumed to be a reasonable approximation of the average MEF [30]. This approach works on the assumption that the marginal power generators are always conventional fossil-fueled power plants, because renewable energies are usually fluctuating, except bioenergy and some hydropower plants, and are subject to feed-in priority [36; 39]. The average MEF can be further specified by time- or load-dependent classification (binning) [30; 36]. In addition, the MEF can be divided into a direct (short-term) and indirect (long-term) MEF. The latter describes the effects of changes in demand on the composition of the future power plant park. In this paper, a direct MEF is formed which does not consider changes in the composition of the power plant park in the long term. This is due to the fact that the development of the generated scenarios is predetermined on the basis of national expansion plans, such as the German nuclear and coal phase-out, and the promotion of renewable energies and their regulated expansion volumes (tendering mechanism). There are significant discrepancies in the choice of system boundaries, depth of investigation and the distinction between the average electricity mix (AEF) and a marginal emission factor (MEF) when determining the \"appropriate\" emission factor. Furthermore, different methods of allocation (for cogeneration) and different fuel-based emission factors can be used to calculate the emissions of the combusted energy source, depending on the composition and the consideration of the upstream processes of the fuels. An overview of the different methods and the application of the factors for the evaluation of electrical appliances is further described in [8; 22; 23]. In an empirical context and with lower temporal resolution, the AEF and MEF are rather easy to determine. The need for at least hourly resolved emission factors of electricity supply (AEF) combined with analyses based on historical market data have already been shown by [13; 17; 40]. Historical hourly emission factors to evaluate emission saving measures have been used in the areas of load shifting [20; 41], energy efficiency measures in buildings [16], emission reduction in households [13], smart-home solutions [42], electromobility [39; 43; 44; 45], and emission reduction through the use of RES in power production [46; 15; 47]. The analysis and application of hourly emission factors for Germany was carried out by [12; 18; 39; 48] from the respective current structure of power production derived from empirical data. The authors of [49] determined an AEF and an indicator-based MEF for Germany derived from the merit order of the power plants from an electricity market model, as well as an annual and an hourly MEF using the linear regression method according to [30]. These emission factors from historical data are used for the ecological assessment and dispatch of battery storage systems. The authors of [19] showed that it is essential for the development of low-emission local energy systems in Germany to use dynamic, rather than constant, emission factors of power production. This is the only way to achieve the emission reduction intended by sector coupling, by correctly planning the use of flexible and hybrid technologies. In addition to the current hourly emission factor, which is important for an accurate ecological assessment, the emission factor of future electricity supply is also required for the calculation of emissions over the entire lifetime of an electricity-using technology. Prospective emission factors with high temporal resolution are calculated, for example, by [32] for England and by [45] for California. A future consideration of the emission factors for Germany was calculated by [50] using capacity factors and the planned installed capacity from two different scenarios up to the year 2030 with annual averages.