# Design Optimization of a District Heating Network Expansion, a Case Study for the Town of Kiruna
## 4 Results and Discussion  
The multi-objective design optimization minimizing the investment and operating costs for the expansion of DH network in Kiruna was performed considering not the peak thermal load, but a frequent demand level that registered in about 40% of the days in the three coldest months of the winter period. This was the demand level that has already been considered for half of the operation  
Figure 5: Flowchart of the multi-objective evolutionary algorithm used to solve the design optimization problem about the expansion of the DH network in Kiruna..MILP: mixed integer linear programming. TVAB: Tekniska Verken i Kiruna AB company. scenarios optimized in [12], and amounted to 39 MW for the existing user areas (including room heating and hot tap water). The planned new user areas will require an additional 11.4 MW in the same outdoor conditions (see the demand for each area in Figure 3). Table 1 shows the values for the heat output and the supply temperature at the heat production sites that were taken from the optimal results of the \"39 MW no LKAB\" case in [12]. The new bio-oil boiler is supposed to run at full load at the capacity set by the optimization algorithm, whereas the heat output of the TVAB site is the result from the overall balance of the heat loads in the network (it must be equal to the difference between the overall user demand and the output of the other sites, plus the thermal losses along the network). Figure 6 shows the Pareto front of the design solutions representing the optimal compromises between the operating costs (expressed in SEK/s on the ordinates of the diagram) and the investment costs (expressed in MSEK on the abscissae). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Site** & **Heat Output (MW)** & **Tsupply (\({}^{\circ}\)C)** \\ \hline TVAB & balancing heat loads & 103.2 \\ LKAB & inactive & \\ Bath & 8.9 & 75.7 \\ Ferrum & inactive & \\ Glacier & 0.8 & 82.4 \\ School & inactive & \\ New Boiler & to be optimized & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Setup of the heat production sites in the model of the expanded network in Kiruna (see also the results of the “39 MW no LKAB” optimized case in [12]). Figure 6: Pareto front of the optimal design solutions that represent the best compromises between investment and operating costs for the expansion of the DH network in Kiruna. The markers are colored according to the configuration of the piping layout in the design solution (which are shown in Figure 8). It was immediately apparent that the front was far from continuous, it rather appeared quite scattered. This was a direct consequence of the discrete nature of the decision variables of the optimization problem. For the same reason, the shape of the front was not perfectly convex. In particular, it showed a major concave region close the lowest investment costs, just before the operating costs started to grow significantly. The design solutions belonging to the Pareto front were able to be sorted into different groups according to the capacity of the new bio-oil boiler. Each group occupied a well-defined portion of the front (see Figure 6), as it is logical to expect. In fact, a higher capacity of the new bio-oil boiler resulted in higher investment costs, obviously, and in lower operating costs, since the pumping power required to deliver the hot water to the new user areas is reduced when more and more hot water is produced close to the new town center, and for the same reason the thermal losses are also reduced. Surprisingly, not all of the considered bio-boiler capacities had a corresponding group of optimal design solutions along the Pareto front. For example, the group of solutions with a 10 MW bio-oil boiler was immediately adjacent to the group with a 13 MW boiler, while there was no optimal design solution having a bio-oil boiler with a capacity of 11 or 12 MW.