District Heating Networks - Dynamic Simulation and Optimal Operation

District heating networks will play a prominent role in sector coupling. On the one hand, they can help compensating for fluctuations in renewable power generation. On the other hand, they allow to use waste heat from industrial processes instead of natural gas. However, this new role of district heating will also require new operating modes, deeper insight into the network and, consequently, more sophisticated simulation and optimization tools. Here, we deal with an optimal control problem which is dominated by time-varying delays between heat source and consumers: optimal preheating. The goal is to satisfy a periodic demand with a constant heat supply. This problem is still simple, as no devices like turbines are involved. But it contains already all challenges of simulating dynamic networks and, therefore, represents an ideal benchmark. We present a suitable mathematical model, some illustrative analytic examples, an efficient numerical scheme, and a solution to optimal preheating for a real municipal network. The model is both, accurate enough to predict pressure drop or cooling, but also simple enough to allow for fast numerical solution by a method of characteristics. Automatic differentiation is used for both, computing exact Jacobians within Newton’s method and providing an optimizer with sensitivities.