# Time Variable Efficiency¶

It is possible to manipulate the operation of a process by introducing a time series, which changes the output ratios and thus the efficiency of a given process in each given timestep. This introduces an additional set of constraints in the form:

$\begin{split}&\forall p \in P^{\text{TimeVarEff}},~c\in C \setminus C^{\text{env}} t\in T_m:\\ &\epsilon^{\text{out}}_{ypct}=r^{\text{out}}_{ypc}f^{\text{out}}_{ypt} \tau_{ypct} .\end{split}$

Here, $$f^{\text{out}}_{pt}$$ represents the normalized time series of the varying output ratio. This feature can be helpful when modeling, e.g., temperature dependent effects or maintenance intervals. Environmental commodities are intentionally excluded from the output manipulation. The reason for this is that they are typically directly linked to inputs as, e.g., CO2 emissions are linked to the fossil inputs. A manipulation of the output for environmental commodities would thus screw up the mass balance of carbon in this case.

When the process in question is a process with part load behavior the equation for the time variable efficiency case takes the form:

$\begin{split}&\forall p\in P^{\text{partload}}~\text{and}~ p \in P^{\text{TimeVarEff}}, ~c\in C,~t\in T_m:\\\\ &\epsilon^{\text{out}}_{ypct}=\Delta t\cdot f^{\text{out}}_{ypt}\cdot \left(\frac{\underline{r}^{\text{out}}_{ypc}-r^{\text{out}}_{ypc}} {1-\underline{P}_{yp}}\cdot \underline{P}_{yp}\cdot \kappa_{yp}+ \frac{r^{\text{out}}_{ypc}- \underline{P}_{yp}\underline{r}^{\text{out}}_{ypc}} {1-\underline{P}_{yp}}\cdot \tau_{ypt}\right).\end{split}$