This paper presents a comparison between two optimization models used to simultaneously select the optimal configuration and the design of a district heating network (DHN). In the meanwhile, this work explains how to link the heat demand at the building scale and the supply at an urban scale. In the first model, a mixed integer non linear programming (MINLP) in steady state is considered.

The second model is a multi-period formulation of DHN, a logical perspective of the first one in steady state. In those models, the non linearities are due to the detailed physics taken into account (heat losses and pressure drops) and that linked variables are considered (such as temperature, diameter and velocity). Moreover as the configuration (existence and location of the technology of production and the network layout) is studied, a combinatory optimization problem has to be solved. The optimization objective is to minimize the global cost of the DHN. It includes both operative cost (fuels and pumping cost, maintenance) and investment cost (line, trench, heating plant, heat exchanger). The main originalities of this work are the simultaneous optimization of the configuration (including combinatory) and the design of DHN (including non linearities) and the method of resolution (with GAMS, solver DICOPT which use determinist methods OA/ER).

The first main difference between the two models is the consideration of time dependency for most of the parameters and variables, otherwise all the equations (logical, physical, economics) remain the same. The second difference concerns the input data (nominal heat demand required and capacity factor). This time dependency input will be described and finally the DHN optimal results from those two models will be compared.