## 3 Simulation Results and Discussion
On the other hand, since the effluent quality index is included as an optimization objective in the [PERSON] and [PERSON] and [PERSON] (2016) formulation, the improvement in this index is notorious, while the advantages of the EMPC formulation proposed in this paper are associated with the economic performance. In the current work, it has been preferred to not work directly with the overall effluent quality index as part of the cost function, because it involves several concentrations not available for measurement. Instead, here, it has been preferred to keep the two main variables of interest (oxygen and nitrate) around desired values, while attempting to keep effluent ammonia under the established limits. Regarding this reduction in energy consumption, as the work conducted here is based on the BSM1 benchmark scenario, no specific WWTP was used. However, the BSM1 protocols define influent \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Controller**} & \multicolumn{2}{c}{**Average S\({}_{\text{NH}}\) in**} & \multirow{2}{*}{**EQ**} & \multirow{2}{*}{**AE**} & \multirow{2}{*}{**PE**} & \multirow{2}{*}{**PE + AE**} & \multirow{2}{*}{**S\({}_{\text{NH}}\) Violations**} \\  & & & & & & \\ \hline Default PI & 2.79 & 17.2 & 2747.0 & 18,031 & 0.84 & 0.98 \\ NMPC & 3.00 & 16.7 & 2747.3 & 18,055 & 0.96 & 0.73 \\ HEMPC-OCI & 3.21 & 17.4 & 2746.6 & 18,021 & 1.00 & 0.94 \\ HEMPC-OCI + NH & 2.74 & 17.3 & 2747.0 & 18,052 & 0.88 & 0.87 \\ HEMPC-NH & 2.55 & 18.2 & 2748.0 & 18,064 & 0.73 & 1.47 \\ EMPC-OCI & 6.05 & 19.5 & 2741.9 & 17,466 & 3.34 & 3.60 \\ EMPC-OCI + NH & 3.47 & 21.2 & 2748.0 & 17,988 & 1.15 & 3.80 \\ EMPC-NH & 2.37 & 21.8 & 2750.0 & 18,434 & 0.74 & 3.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance indices associated with variables of the plant optimized in the economic oriented model predictive controllers cost function (computed for a four-day operation period under dry weather disturbances). NMPC: non-linear model predictive controller; HEMPC: economic-oriented tracking controller; OCI: overall cost index penalization; NH: off-specification ammonium load in the effluent penalization; EMPC: economic-oriented model predictive controller. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Controller**} & \multicolumn{2}{c}{**Average S\({}_{\text{NH}}\) in**} & \multirow{2}{*}{**TN**} & \multirow{2}{*}{**Sludge Produced**} & \multirow{2}{*}{**OCI**} & \multirow{2}{*}{**S\({}_{\text{NH}}\) Violations**} & \multirow{2}{*}{**TN Violations**} \\  & & & & & & \\ \hline Default PI & 2.79 & 17.2 & 2747.0 & 18,031 & 0.84 & 0.98 \\ NMPC & 3.00 & 16.7 & 2747.3 & 18,055 & 0.96 & 0.73 \\ HEMPC-OCI & 3.21 & 17.4 & 2746.6 & 18,021 & 1.00 & 0.94 \\ HEMPC-OCI + NH & 2.74 & 17.3 & 2747.0 & 18,052 & 0.88 & 0.87 \\ HEMPC-NH & 2.55 & 18.2 & 2748.0 & 18,064 & 0.73 & 1.47 \\ EMPC-OCI & 6.05 & 19.5 & 2741.9 & 17,466 & 3.34 & 3.60 \\ EMPC-OCI + NH & 3.47 & 21.2 & 2748.0 & 17,988 & 1.15 & 3.80 \\ EMPC-NH & 2.37 & 21.8 & 2750.0 & 18,434 & 0.74 & 3.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance indices of the mean operating variables of the plant that are different from the variables included in the optimization problem (computed for a four-day operation period under dry weather disturbances). characteristics featuring a load of around 100,000 person equivalents (PE) (80,000 from households, and 20,000 from industrial origin). This helps to provide an idea of the repercussion of the mentioned energy savings. Of course, in order to get concrete monetary figures of actual order, there will be the need to link the cost indexes to actual energy costs. This may be highly dependent on the WWTP location.