District heating systems (DHSs) have the potential to play a big part in the energy transition. The efficient operation of DHSs is therefore also an important subject of study. The operation of DHSs where combined heat and power (CHP) plants are used are particularly interesting, because CHPs can operate with high efficiency.

In this work, the operational optimization of DHSs with CHP plants is considered. Determining the optimal heat and electricity production for CHPs for multiple time steps into the future is a complex problem. Because of the heat storage capabilities in the network many solutions are feasible, but determining which solutions are infeasible because of constraint violations in the DHS involves computing time delays that depend on complex network dynamics.

In this work, the possibility of using an input convex neural network (ICNN) to learn the network dynamics of a DHS is explored. ICNNs have limitations on their learning capabilities, but theoretically allow for easier optimization. Experiments on the learning capabilities of ICNNs reveal that caution should be used when they are used to learn non-convex constraints, as the accuracy of the ICNN highly depends on how non-convex the function is. Experiments on the feasible space of supply temperatures to a small district heating network (DHN) reveal that although the network does not provide the same flexibility as heat storage tanks, still some flexibility in the operation can be found. This is due to the fact that water with a higher supply temperature is consumed by consumers at a slower pace and this increases the time delay between production and consumption. Supply temperatures that follow can then be lowered if the increased time delay causes this water to arrive when the heat demands are lower.

In the experiments it was found that this flexibility in operation translates to non-convex areas in the feasible space. When this space would be learned by an ICNN, this space would be made convex. How much of the flexibility would be removed by doing this is yet unknown and could be researched in future work. Other future work can be done on safely learning non-convex constraints with an ICNN.

District heating systems (DHS) are considered the best alternative to individual heat boilers as they have higher efficiency and enable the use of sustainable heat sources, like geothermal heat sources or waste heat from industry. Currently, most DHSs are operated by choosing a temperature once every day depending on the weather. This setting is chosen such that peak demand can be satisfied. However, when demand is lower, the supply temperature will be higher than necessary and heat will be wasted. In addition to this, heat production costs can be dynamic over time, which allows more cost-efficient heat production scheduling. By choosing a dynamic temperature over the day losses and operating costs can be reduced. However, determining these dynamic temperatures is not easy, as there are several factors that need to be taken into account to ensure that demand can always be fulfilled. In this research, the use of metaheuristics is explored for finding supply temperatures. Optimisation of DHS operations results in up to 5% savings with respect to typical heating curve operations. The second contribution is a method to determine a theoretical lower bound on the operating costs of a DHS, as this was not yet found in literature.