The averaging bias ‐ A standard miscalculation, which extensively underestimates real $CO_{2}$ emissions

The substitution of energy based on fossil fuels in different sectors like household or traffic by electric energy saves $CO_{2}$ of this specific sector due to decreased fossil fuel consumption. An important quantity is the additional $CO_{2}$ emission $Δ𝐹(\overline{𝐷},Δ𝐷)$ due to an increased electric power demand $Δ𝐷$ for the average electricity power demand $\overline{𝐷}$. Commonly, the formula $Δ𝐹(\overline{𝐷},Δ𝐷)≈𝑀(\overline{𝐷})Δ𝐷$ is used (called simplified formula), where $𝑀(\overline{𝐷})$ represents mean average $CO_{2}$ footprint. It is shown in the present manuscript, that the simplified formula may underestimate the $CO_{2}$ footprint significantly if the average $CO_{2}$ 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 $CO_{2}$ 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 $CO_{2}$ footprint, the general formula $Δ𝐹(\overline{𝐷},Δ𝐷)=\overline{𝐷}Δ𝑀(\overline{𝐷},Δ𝐷)+Δ𝐷𝑀(\overline{𝐷}+Δ𝐷)$ 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 $CO_{2}$ footprint $Δ𝑀$ depending on the electricity power demand.