## 3 Results
### Analysis of the Marginal Emission Factor  
The average \(\mathrm{MEF_{fc}}\) in 2020 is over 770 \(\mathrm{g_{CO2 eq}/kWh_{el}}\) in both scenarios. These are the GHG emissions that an additional demand increase by one kilowatt-hour in 2020 causes on average. It is assumed that the demand change will only be met by domestic, conventional, dispatchable power plants. Figure 8 shows the hourly values of the change in load \(\Delta E_{d,t}^{NPP}\) and the corresponding change in emissions \(\Delta Em_{d,t}\). The gradient \(\beta\) of the linear regression line represents the average annual \(\mathrm{MEF_{fc}}\). The coefficient of determination \(R^{2}\) is above 0.93 in all milestone-years.  
In 2020, the \(\mathrm{MEF_{fc}}\) is still strongly influenced by coal-fired power plants, which play a significant role in load changes. The higher value in the lower-emissions scenario CAP is due to the fact that here, more gas-fired power plants also provide base load and coal-fired power plants react to load changes more often than in the BAU scenario and provide less base load. In other words, although the entire generation is lower-emission, the more emission-intensive power plants also react to changes in demand and peak load. The capacity factor (Cf) of the group of gas-fired power plants is 34.5% in the BAU scenario (\(\mathrm{Cf_{Coal,2020}}\): 77.2%; \(\mathrm{Cf_{Lignite,2020}}\): 49.6%) and 48.4% in the CAP scenario (\(\mathrm{Cf_{Coal,2020}}\): 69.0%; \(\mathrm{Cf_{Lignite,2020}}\): 33.1%).  
Furthermore, it can be seen that the data points spread out slightly from the zero crossing. The load changes are characterized by different emission-intensive power plants and the data cloud indicates a line of coal and a line of gas power plants comparable to [27].  
Figure 8: Change in GHG emissions from the domestic, conventional, dispatchable power plants \(\Delta Em_{d,t}\) over the change in domestic, conventional, dispatchable power production \(\Delta E_{d,t}^{NPP}\) from the BAU and CAP scenarios for three selected milestone years. The marginal emission factor according to the linear regression method is given as the gradient \(\beta\), with the associated coefficient of determination \(R^{2}\). Model results.  
The same effect of spreading out around the linear fit caused by the different shares in the change in demand of the different power plant classes can also be observed in 2030, especially in the BAU scenario. The higher \(\mathrm{MEF_{fc}}\) of the CAP scenario is also caused here by the gas-fired power plants running in more base load compared to the BAU scenario. The Cf of the gas-fired power plants in the BAU scenario is 32.3% (\(\mathrm{Cf_{Coal,2030}}\): 80.3%; \(\mathrm{Cf_{Liginite,2030}}\): 86.6%) and in the CAP scenario 35.8% (\(\mathrm{Cf_{Coal,2030}}\): 76.7%; \(\mathrm{Cf_{Liginite,2030}}\): 73.4%).  
In 2040, only natural gas and, in very small quantities, oil will be combusted for fossil, dispatchable power production. This means that, with a similar use and efficiency of the power plants, the \(\mathrm{MEF_{fc}}\) of the scenarios becomes more or less the same.  
Despite the fact that in both scenarios, almost exclusively gas-fired power plants act as marginal power plants, the \(\mathrm{MEF_{fc}}\) in the CAP scenario falls to 368 \(\mathrm{g_{CO2 eq}/kWh_{el}}\) by 2050 and is thus significantly lower than the \(\mathrm{MEF_{fc}}\) of 475 \(\mathrm{g_{CO2 eq}/kWh_{el}}\) in the BAU scenario. This discrepancy is due to the fact that in the CAP scenario, considerably less installed capacity and energy quantities of gas-fired power plants are used and thus relatively more combined-cycle gas turbine power plants with combined heat and power generation are used to react to changes in load than the more inefficient open cycle gas turbine power plants. The annual average net efficiency of the aggregated gas-fired power plants in 2050 is 45.4% for the BAU scenario and 54.7% for CAP.