## 2 Materials and Methods
### Calculation of the Developed Emission Factors
#### 2.3.2 Average Emission Factor  
The fuel input of fossil \(E_{ec,t,y}\) and renewable sources \(E_{re,t,y}\) resulting from the generating units and their efficiency of power production is multiplied by the respective specific emission factor of the fuel \(E_{fc}\) (Equation (1)). Specific emission factors related to the power generated from RES and nuclear energy \(E_{fr}\) are used to calculate the emissions of RES. This results in the total hourly GHG emissions of gross power production \(Em_{tot,t,y}^{GPP}\) in one milestone-year \(y\). \[Em_{tot,t,y}^{GPP}=\left(\sum_{ec=1}^{n}E_{fc}\cdot E_{ec,t,y}\right)+\left( \sum_{re=1}^{m}E_{fr}\cdot E_{re,t,y}\right) \tag{1}\]  
In the case of exports, the trading balance \(E_{ex,t,y}\) is assessed with the hourly emission factor of net power production \(E_{t,y}^{NPP}\) shown in Equation (2), and the resulting GHG emissions are deducted from total GHG emissions (Equation (4)), with \(E_{t,y}^{NPP}\) as the net power production in hour \(t\) and milestone-year \(y\). \[E_{t,y}^{NPP}=\frac{Em_{tot,t,y}^{GPP}}{E_{t,y}^{NPP}} \tag{2}\]  
Following [16], which calculates an electricity mix factor from data of the European Network of Transmission System Operators for Electricity (ENTSO-E, Brussels, Belgium), the European emission factor \(E_{FLU,t,y}\) is used for the assessment of electricity imports \(E_{im,t,y}\) (Equation (4)). The IEA provides daily load profiles of electricity demand and average \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{\(\mathbf{g}_{\text{CO2 gs}}\)/\(\mathbf{k}\)\(\mathbf{W}\)\(\mathbf{h}\)\(\mathbf{e}\)\(\mathbf{f}_{ec}\))} & \multicolumn{3}{c}{\(\mathbf{g}_{\text{CO2 gs}}\)/\(\mathbf{k}\)\(\mathbf{W}\)\(\mathbf{h}\)\(\mathbf{e}\)\(\mathbf{f}_{w}\))} \\ \hline \multirow{2}{*}{**Type of Energy Source 3**} & \multirow{2}{*}{**Fuel**} & \multirow{2}{*}{**Upstream 1**} & \multirow{2}{*}{**LCA-Ef**} & \multirow{2}{*}{**LCA-Ef**} \\  & & & & \\ \hline Natural Gas & 2014. & 33.1 & 237.5 & - \\ Hardcoal & 338.2 & 50.5 & 388.7 & - \\ Lignite & 404.4 & 9.3 & 413.7 & - \\ Miscellaneous 4  & 270.3 & 20.2 & 290.5 & - \\ Oil & 282.6 & 12.3 & 294.9 & - \\ Nuclear & & & & 13 \\ Bioenergy & - & - & - & 41 \\ Photovoltaic & & & & 46.8 \\ Runoff River & & & & 6.6 \\ Offshore & & & & 11.4 \\ Wind & Onshore & & & 11.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Emission factors used for the different energy sources. emission factors of the European Union in hourly resolution. In a \"Stated Policies\" and a \"Sustainable Development Scenario\", possible future developments up to the year 2040 are modeled and continued on a linear basis until 2050 [65]. The grid losses associated with hourly net power consumption are calculated on the basis of the current German grid losses for 2018 at 4% of gross power production, comparable with [36; 66]. For an emission factor of power consumption, the energy for electricity storage is first not assigned to final energy consumption. The energy from discharging pumped storage and battery storage facilities is already burdened with GHG emissions when the storage facilities are charged. The energy from the discharging process is therefore compulsorily regarded as emission-free and reduces the emission factor in the hour concerned. At the time of charging, the electricity required for this purpose is consequently not made available in the power grid, the emission factor will therefore become higher at this time and a temporal distortion will occur when emission factors are considered on an hourly basis [35; 67]. Traceability of emissions is impossible due to intermittent charging and discharging processes, as well as variations in storage duration and the non-traceability of charge carriers (electrons). In order to minimize these distortions and to better reflect the emission factor of net power consumption, a specific emission factor for electricity storage, based on [67], is calculated endogenously.