The averaging bias ‐ A standard miscalculation, which extensively underestimates real $C{O}_2$ emissions

The substitution of energy based on fossil fuels in different sectors like household or traffic by electric energy saves $C{O}_2$ of this specific sector due to decreased fossil fuel consumption. An important quantity is the additional $C{O}_2$ emission $\Delta 𝐹(\overline{𝐷},\Delta 𝐷)$ due to an increased electric power demand $\Delta 𝐷$ for the average electricity power demand $\overline{𝐷}$. Commonly, the formula $\Delta 𝐹(\overline{𝐷},\Delta 𝐷)\approx 𝑀(\overline{𝐷})\Delta 𝐷$ is used (called simplified formula), where $𝑀(\overline{𝐷})$ represents mean average $C{O}_2$ footprint. It is shown in the present manuscript, that the simplified formula may underestimate the $C{O}_2$ footprint significantly if the average $C{O}_2$ footprint depends on the average electricity power demand, which is the case for most of mixed partly renewable and partly non-renewable electric energy systems. Therefore, the real $C{O}_2$ emissions would outmatch those according to simplified easily by factor 2 in reality depending on the status of the electricity system. In order to establish a more precise calculation of the $C{O}_2$ footprint, the general formula $\Delta 𝐹(\overline{𝐷},\Delta 𝐷)=\overline{𝐷}\Delta 𝑀(\overline{𝐷},\Delta 𝐷)+\Delta 𝐷𝑀(\overline{𝐷}+\Delta 𝐷)$ which is exact and contains the simplified formula as a special case, is derived in this article. ... mehrThe simplified formula requires an additional term that takes into account the change of the mean average $C{O}_2$ footprint $\Delta 𝑀$ depending on the electricity power demand.