Robust design of large district heating networks through topology optimization

Large water distribution networks greatly benefit from topological changes brought by the construction of loops. In fact, besides the reduction of pumping power, adding loops can smooth the overall effects of random malfunctions, making existing networks intrinsically robust. In this paper, we use the tools of topology optimization to generate an optimized looping strategy that minimizes the effect of pipe breakage. The objective is an original robustness index that is formulated as a weighted sum of the minimum supply pressure sensitivities to an infinitesimal valve shutdown. Furthermore, a maximum cost constraint is added to limit investment cost. Predictably, robustness and cost are found to be antagonist objectives: the optimized designs, obtained by systematically relaxing the cost constraint, lay on a smooth Pareto curve that should serve as a reference to both practitioners in the field and decision makers. For the specific network analyzed in this paper, we found that topological modifications can raise the robustness of the system by 29.3 % with an investment limited 200 k€ and decrease the maximum pressure drop by 10.8 %. Above this threshold, we observed no topology modifications of the optimal designs: with a further 800 k€ investment, additional benefits are limited to 2.5 % and 2.3 % in terms of robustness and pressure drop respectively.