In the current Energy market context, District Heating (DH) has an important role, especially in counties with cold climate, as it often leverages on Combined Heat and Power (CHP) units, capable to reduce the consumption of primary energy to fulfill a given electric and thermal request, as well as on existing significant sources of heat generated by industrial processes or waste-to-energy heat generation. On the top of that heating networks will need to increase its flexibility in operation due to an increasing mix of renewable sources, both heat sources or green electricity utilized by heat pumps, distributed generation and smart consumers as well as DH operational temperature reduction and heat storage integration [1, 2].
From a management standpoint, the design of the district heating network is a strategic business issue, since it requires large investments, due to the cost of materials and civil works for the realization of the network. Proper strategic design of network (i.e. definition of the most convenient backbone pipelines to lay down) and tactical targeting of most promising potential customers both aims at maximizing the Net Present Value (NPV) of the investment.
Finding the extension plan for an existing (or eventually empty) district heating network that maximizes the NPV at a given time horizon is a challenging optimization problem that can be stated as follows.
I. The subset of potential new customers that should be reached;
II. Which new pipelines should be installed;
III. The diameter of the new pipes
that maximize the NPV.
Research on modelling approaches for representing the behavior of the thermo-hydraulic network through sets of non-linear equations can be found in the literature (see for example  and ). Solving systems of non-linear equations is difficult and computationally expensive. For this reason, aggregation techniques of the network elements are often used to model large district heating networks, at the expense of some accuracy      .
In , an integer-programming model is proposed for the optimal selection of the type of heat exchangers to be installed at the users’ premises in order to optimize the return temperature at the plant. The authors achieve good system efficiency at a reasonable cost.
 present a mathematical model to support district heating system planning by identifying the most advantageous subset of new users that should be connected to an existing network, while satisfying steady state conditions of the thermo-hydraulic system.  extend the model proposed by  with the selection of the diameter for the new pipes and a richer economic model that takes into account
Moreover, while the investment on the backbone pipelines is done on the first year, new customers are not connected immediately, but following an estimated acquisition curve (e.g., 25% the first year, 15%, the second year,…). Hence, the corresponding costs and revenues have to be scaled accordingly.
The thermos-hydraulic model must ensure the proper operation of the extended network. The following constraints are to be imposed:
Continuous variables model pressures at nodes and flow rate on the links and binary variables model decisions on the connection of new customers, on the installation of new links, on the diameter choice and on ow direction on the links. The last ones are necessary since district-heating networks contains cycles: the potential network usually corresponds to the street network. Thus, it is not possible to know a priori the flow direction on the links (at least not for all of them) and such decision must be included into the model. The pressure drop along a pipe is a non-linear function that depends on ow rate, and on the diameter of the pipe. This can be approximated using a piecewise linear function, that translates into a set of linear constraints. The higher the number of segments in the piecewise linear function, the smaller will be the approximation error. At the same time, the number of constraints grows (there is one piecewise-linear function for each combination of pipe and diameter) and the solving time increases. To keep the number of segments small, while obtaining a good accuracy, breakpoints of the piecewise linear function can be concentrated in the most probable range of flow rate.
District heating networks can be quite large (hundreds of existing and potential users, thousands of links) making it difficult to solve the full MILP directly. Solution methods developed in  approach the problem in three steps.
Optit S.r.l. has developed a decision support system, in collaboration with the University of Bologna, based on the modelling mentioned above, that has been successfully used in two of largest multi-utility companies operating in the Italian District Heating market. The application leverages on open source Geographical Information System (GIS) to allow a simple user interface and a number of plug-in tools to manage the specific optimization issue.
Optit srl has developed a decision support system, in collaboration with the University of Bologna, based on the modelling mentioned above, that has been successfully used in two of largest multi-utility companies operating in the Italian District Heating market. The application leverages on open source Geographical Information System (GIS) to allow a simple user interface and a number of plug-in tools to manage the specific optimization issue.
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Dr. Robert Schwarz, ZIB
Dr Andrea Bettinelli,Optit
Prof Daniele Vigo, University of Bologna / Optit