Global Optimization of Flexible District Heating Networks
District heating networks are a central tool to achieve low-carbon heat supplies. In this realm, they face the challenge of dealing with increasingly heterogeneous, partially time-varying renewable sources, thermal storage, and meshed topologies. This paper examines global optimization of the operation of such district heating networks over multiple time steps, based on a stationary, yet realistical nonlinear network model. To accelerate the solution performance of a spatial branch-and-bound algorithm for one time step, the following new methodological ingredients are introduced: exclusion of cyclic flow, symmetry exploitation between supply and return networks, reduction of temperature mixing constraints, novel primal heuristics and branching rules. The proposed methods are evaluated on a set of generated and real-world benchmark network instances with cycles and several suppliers. On the generated benchmark instances, using these methods more than doubles the number of solved instances and more than halves the runtime. For the real-world benchmark instances, the resulting algorithm produces solutions with guaranteed quality in reasonable run time. For multiple time steps that are coupled by a storage, a time decomposition approach is investigated. Under assumptions that are reasonable in practice, this approach is shown to yield an optimal solution. On a small example network, this decomposition is able to compute optimal solutions in less than a second, while solving the complete time-coupled problem is not possible within one hour.