# Design Optimization of a District Heating Network Expansion, a Case Study for the Town of Kiruna
## 1 Introduction
[3] found the optimal structure for a very simple DH network connecting four consumers and two heat production sites (it should be noted that the piping layout of the supply network piping may not be mirrored by that of the return network, so the number of potential configurations was much larger than usual). The network was modeled in the GAMS environment and mixed integer non-linear programming was used to find optimal solutions by minimizing the overall sum of the operating costs (pumping power and fuel consumption) and the investment costs (trench excavation and piping, heat production sites, and heat exchangers). The authors pointed out the importance of optimizing the network configuration together with some key design parameters, such as the capacity of the heat production sites. [PERSON] et al. [4] used MATLAB and mixed-integer linear programming in CPLEX to optimize the structure and the operation of a DH network in southern Finland. The terms of the total cost to be minimized were the investment costs related to the construction of new network components and the operation costs at each heat production site. The network was comprised of six heat production sites (plus two potential sites) and 26 potential user areas that were connected by a piping superstructure having a tree layout. In spite of that, the network model required about 600 binary and 6300 continuous variables. Heat storage and heat pump options were included in the model, so the optimal solution also indicated which sites/user areas were economically viable to connect to the DH network. [PERSON] et al. [5] obtained the Pareto front of the design solutions that minimized total costs (the sum of investment and operation costs) and CO\({}_{2}\) emissions over a 20-year period for a network with 12 users. A detailed time description of user demand and boiler operation was considered, so the mixed-integer linear model of the network consisted of more than 84,000 constraints and 70,000 variables (out of which about 3500 were integers). Some non-linear aspects of network behavior (e.g., thermal losses) were simplified to retain a linear formulation. The multi-objective optimization problem was solved by CPLEX using the \(\varepsilon\)-constraint method, and more than four days were required to solve the problem on a common personal computer. Different network layouts were found for different limits on CO\({}_{2}\) emissions, and the number of buildings connected to the DH network increased as the limit on CO\({}_{2}\) emissions was lowered. [PERSON] et al. [6] compared three different scenarios for a district energy network supplying the thermal and electric demand of five buildings (a store, a hotel, an apartment, an office and a hospital). In the first scenario each building used a conventional heating system where heat demand was satisfied by a gas boiler, while the electricity demand was satisfied by the grid. In the second scenario CHP units were installed in the buildings and a network was used to transport heat among the buildings. Finally, in the third scenario a thermal storage tank was also added in each building. Mixed integer linear programing was used for the optimization of each scenario, and the results from the second scenario indicated an optimal piping layout. However, this layout only showed how the heat surplus from some buildings should be distributed to other buildings, since the considered model of the network did not take into account a detailed description of pressure drops and thermal losses in the pipes. [PERSON] et al. [7] develop a methodology named the District Heating Network Design Problem, which was based on a mixed-integer linear description of the network and used CPLEX to solve the optimization problem. A town in Emilia-Romagna (northern Italy) was considered as a case study, with a tree-shaped network superstructure consisting of 20 existing and 12 potential users, and 4.3 and 1.9 kilometers of pipes for existing and potential users, respectively.