## 1 Introduction  
The main driver of the continuous rise in the Earth's temperature is the increase in the concentration of greenhouse gases in the atmosphere, of which carbon dioxide is the most significant [1]. The German government has developed a climate action plan that stipulates a reduction in GHG emissions of 80 to 95% by 2050, compared with 1990 levels [2]. The electric power industry is one of the largest emitters of GHG worldwide [3]. In 2018, 269 million tons of carbon dioxide (CO\({}_{2}\)) emissions were released in Germany as a result of the combustion of energy sources to generate electricity. As the share of renewable energy sources (RES) in net power production (NPP) has increased to \(41\%\) in 2018, absolute and specific CO\({}_{2}\) emissions have decreased [4]. The specific emission factor of electricity supply is \(31\%\) lower in 2018 at \(468\ \mathrm{g_{CO2}/kWh_{el}}\) than in 1990 at \(764\ \mathrm{g_{CO2}/kWh_{el}}\)[5]. Preliminary data show a further decrease of the emission factor to about \(401\ \mathrm{g_{CO2}/kWh_{el}}\) in 2019 and a continuing increase of the share of RES in NPP to approximately \(51\%\) in 2020 [5, 6]. The environmental impact or carbon footprint of power supply is often analyzed through a life cycle assessment using GHG emission factors. In the scope definition, the functional unit, geographical and temporal boundaries, and the attributive or consequential perspective are defined. The following inventory analysis collects information about the physical flows in terms of input of resources and, for example, the output of the emissions [7]. Often, as in the case of electromobility, the use phase of a product is the sub-process with the most significant impact on GHG [8; 9]. Therefore, in this paper we want to analyze the direct GHG emissions resulting from the electricity supply. Because of the production of electricity with a mixed power plant park in Germany, the emission factor of power production fluctuates continuously. This is due to the growing share of fluctuating RES, such as photovoltaic and wind power plants, in power production and the German coal phase-out by 2038 [10]. The future energy supply system must therefore be flexible, both on the supply side and on the demand side [11]. This development will increase seasonal and diurnal fluctuations and cause an overall decrease in emission factors [12]. For the assessment, GHG emissions of consumers with fluctuating energy demand emission factors that vary over time must be used. The effects of demand-side management, efficiency measures, or the expansion of RES on the emissions can only be examined in detail with dynamic emission factors [13; 14; 15]. This necessity of varying emission factors is clearly shown in previous studies by [8; 16; 17; 18; 12; 19]. A significant error is made when the yearly average emission factor is used for the ecological assessment as long as the demand for electricity is not constant for every hour of a year [20; 21]. In this paper we develop prospective hourly emission factors for the German power supply. First, we identify the various methodologies and interpretations of power supply emission factors. Then we look at the publications of emission factors for the German electricity supply and where their shortcomings lie. A fundamental decision in defining the emission factor for power production is the one between the electricity mix and the marginal emission factor [22]. The system-average emission factor method takes into account all emissions from the power-generating plants that produce to meet demand in the area under consideration with or without exchanged power [23]. In scenario-based emission models, the AEF is often calculated using the average emission factors of the generating power plant types, weighted according to the share of demand met by each power plant type, for each time interval [22]. The AEF is most commonly used in studies where the emission savings are a side effect of energy savings from any kind of technoeconomic measures [24].