# Design Optimization of a District Heating Network Expansion, a Case Study for the Town of Kiruna
## 1 Introduction  
The first generation of district heating (DH) systems appeared in Europe in the beginning of the 19 th century, and subsequently, there has been continuous development that has led to the current transition between the third and the fourth generation. A DH system is often set up by connecting the boilers of different buildings into small networks; the boilers in the buildings are then replaced by one or more common boilers concentrated in a heat production site, subsequently the different small networks are connected, and so on [1]. DH systems in eastern European countries have followed a different path. They are centrally planned and built with CHP plants as basic heat sources that also supply electricity to the local market, in order to increase overall energy efficiency [2]. The typical stages in the evolution of a Swedish DH network are shown in Figure 1. A similar process occurs with the urbanization of new areas beyond the existing perimeter of a town, when DH is still considered as the best alternative among the technologies providing room heating and hot tap water, and therefore the network is expanded to supply new user areas. In this case, the features that should be evaluated carefully to minimize both the investment and operation costs of the expanded network are: the layout of new piping loops and branches, the diameters of the new pipes, and the capacity of the new heat production site(s) that may be needed to meet the increase in the final user demand. However, rigorous design methodologies and guidelines to determine these features in an optimal way are not well established because of the progressive nature of network expansion, so that the configuration of a network is often the result of several different interventions performed at different times, and largely on the basis of the sole expertise of network designers and operators. In principle, a trade-off always exists when selecting the proper size for a DH pipe. Pipes with smaller diameters are cheaper than the larger ones, but, for a given mass flow rate through the pipe, a smaller pipe has a higher flow velocity that results in a larger pressure drop and therefore in a greater requirement for pumping power. One design criterion is to determine the pipe diameter by fixing the pressure drop per unit length (often in the range between 50 and 200 Pa/m), but selecting a constant value of this parameter for the whole network may result into overly large variations of flow velocity (in order to avoid this, the Swedish District Heating Association has recommended pressure drops per unit length that are a function of pipe diameter). A more reliable design procedure is to use optimization algorithms to determine the most suitable pipe diameters. Figure 2 shows a simplified representation of how pipe investment cost and pumping power cost vary with pipe diameter [1]. It is apparent from this that a trade-off can be found. However, thermal losses should be taken into account as well, since larger pipe diameters correspond to larger heat transfer surfaces and higher thermal losses, which in turn result in an increase of operational costs due to a higher fuel consumption to satisfy a fixed level of user demand. Figure 1: The typical stages of the development of a district heating (DH) network in Sweden: (**a**) separated islands; (**b**) tree structure; (**c**) ring structure; (**d**) meshed structure [1]. Figure 2: Pipe investment cost and pumping power cost as a function of pipe diameter [1] (thermal losses are not considered to find the trade-off). A literature review in the field of structure optimization for meshed DH networks shows that current knowledge is still insufficient. Previous studies are usually performed on networks with a small number of heat production sites and/or users, or the tools that are used for the numerical simulations are based on heavy simplifications in the physical description of network behaviour. For instance, [PERSON] et al.