# Predictive Optimization of the Heat Demand in Buildings at the City Level
## 4 Results
### Optimization of the Heat Demand
#### 4.2.2 Cutting of Peak Loads  
To examine the full peak load cut capacity, days eight and nine from the 480-h optimization period were chosen for further study as they contain the highest consumption peak. The peak load cutting for this 48-h period was performed as discussed in Section 3.3.2 and presented in Figure 2. Six different sets of parameters for the indoor temperature model (Equation (1)) were estimated for each of the buildings as this affects to their heat storage capability. The results of 1000 randomly chosen combinations of optimization results including the largest and lowest peak cuts are presented in Figure 6. Each combination contains results using one of six estimated indoor temperature models for each of the buildings. As large as 33% peak load cuts in total heat demand of 201 buildings were achieved between 8 and 12 a.m. At 10 a.m. on the second day, this cut corresponded to 30 MW reduction in heating power. That amount of reduction in heat load will have a significant effect on city level. However, most of the time the peak load cut was 16-22% meaning 17-21 MW reduction in heat load. The minimum peak load cut was 9% corresponding to 9 MW reduction. Furthermore, it can be seen how the heat demand is shifted from morning to night. In the indoor temperature of buildings, this means that the indoor temperature is increased during the night and then let to drop during the peak load cutting. It is important to notice that there are no additional peaks in the heat demand after the peak load cutting period, rather the heat demand returns to the original level. This means that the indoor temperature will slowly rise to the set point always staying between the defined limits.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**r**} & \multicolumn{6}{c}{**MAPE**} \\ \cline{2-7}  & **<30\%** & **<25\%** & **<20\%** & **<15\%** & **<10\%** & **<5\%** \\ \hline \multirow{2}{*}{\(>\)0.5} & 181 & 177 & 170 & 161 & 128 & \multirow{2}{*}{47 (23.4)} \\  & (90.0) & (88.1) & (84.6) & (80.1) & (63.7) & \\ \multirow{2}{*}{\(>\)0.6} & 173 & 170 & 163 & 154 & 126 & \multirow{2}{*}{47 (23.4)} \\  & (86.1) & (84.6) & (81.1) & (76.6) & (62.7) & \\ \multirow{2}{*}{\(>\)0.7} & 163 & 160 & 155 & 148 & 122 & \multirow{2}{*}{47 (23.4)} \\  & (81.1) & (79.6) & (77.1) & (73.6) & (60.7) & \\ \multirow{2}{*}{\(>\)0.8} & 117 & 115 & 112 & 108 & \multirow{2}{*}{87 (43.3)} & \multirow{2}{*}{38 (18.9)} \\  & (58.2) & (57.2) & (55.7) & (53.7) & \\ \multirow{2}{*}{\(>\)0.9} & 47 (23.4) & 47 (23.4) & 45 (22.4) & 43 (21.4) & 31 (15.4) & 11 (5.5) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The number and percentage of individual buildings with mean absolute percentage error (MAPE) lower than 30% and Pearson correlation coefficient (r) greater than 0.5 for the 48-h heat demand forecast.  
Table 3 presents the peak load cuts achieved among the different building groups. In individual buildings, 70% cuts in peak loads were possible which was the defined upper limit for the peak load cut. However, the median peak load cut over all the 201 buildings was 15%, and in some buildings the peak loads could not be cut at all. These results are comparable to the earlier study [28] where 70% peak load cut was achieved in an apartment building while in another apartment building 30% cut was too much to maintain the desired indoor temperature.