# Predictive Optimization of the Heat Demand in Buildings at the City Level
## 5 Discussion  
The presented optimization results are comparable to the results found in the literature that validates the achieved results and the applicability of the modelling approach. [PERSON] et al. [22] optimized heat consumption in a system of multiple buildings and reported peak load cuts from 2-5.7%. Figure 6: Peak load cutting in 201 buildings during the morning hours from 8–12 a.m. Upper figure: Black line is the predicted total heat demand in 201 buildings, the grey lines are the 1000 different optimized heat demands when peak load cutting is performed and the black lines with upward and downward triangles are the optimized heat demands with maximum and minimum peak loads, respectively. Middle figure: Grey lines are the load cuts in percentages with 1000 different optimized heat demands and the black lines with upward and downward triangles are the maximum and minimum load cuts in percentages respectively. A negative number corresponds to the reduction in heat demand and a positive number to the increase in heat demand. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Building Group**} & \multicolumn{4}{c}{**Peak Cut [\%]**} \\ \cline{2-5}  & **Median** & **Minimum** & **Maximum** & **Median Maximum** \\ \hline All & 15.0 & 0 & 70.0 & 30.0 \\ Apartment buildings & 17.5 & 5.0 & 70.0 & 32.5 \\ Schools & 12.5 & 5.0 & 70.0 & 25.0 \\ Commercial, public and office buildings & 20.0 & 0 & 70.0 & 35.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak load cut in different building groups. [PERSON] et al. [25] reported peak load cuts between 6-8% in January for residential, office and education buildings. These are similar to the results in Section 4.2.1 where simulated peak load cuts were between 8-11%. In his review, [PERSON] [8] reported peak load cuts ranging from 0-50% in individual buildings achieved in simulation studies. In this work, peak load cuts between 0-70% were achieved median being 15%. In this work, the optimization was done in individual buildings. Considering how the cost functions were defined, this leads to global optimum among all the individual buildings. There would not have been any benefit from coupling the optimization of individual buildings. For example, in electrical scenarios, there is typically a number of different electrical appliances in buildings and time varying pricing [33]. Then the optimization of multiple buildings together can lead to better results [34]. On the other hand, if in the current work the cost function for peak load cutting had been defined so that only a certain amount of peak load cut would have been desired among all the buildings instead of maximum that is achievable, then the optimization should have been considered between all the buildings as the allocation of the cut among the buildings would had to be determined. It should be noted that in the presented optimizations the indoor temperature of the buildings was simulated utilizing the developed indoor temperature model as no actual indoor temperature measurements were available from the investigated buildings. The applicability and validity of the applied parameter estimation method was investigated using data from five buildings with indoor temperature measurements. It was shown that the model with the applied parameter estimation method overestimates the changes in the indoor temperature. Therefore, more significant peak cut results could possibly be achieved if actual indoor temperature measurements were available. Furthermore, the parameter estimation method for the indoor temperature model applied in the simulations can yield different indoor temperature profiles for the same building depending on the estimated model parameters. Therefore, the results have been reported applying indoor temperature models with different sets of parameters. The applied indoor temperature modelling method also assumes that the actual indoor temperature is always at the set point, meaning that the controller is working perfectly.