Quantification of flexibility of a district heating system for the power grid

District heating systems (DHS) that generate/consume electricity are increasingly used to provide flexibility to power grids. The quantification of flexibility from a DHS is challenging due to its complex thermal dynamics and time-delay effects. This article proposes a three-stage methodology to quantify the maximum flexibility of a DHS. The DHS is firstly decomposed into multiple parallel subsystems with simpler topological structures. The maximum flexibility of each subsystem is then formulated as an optimal control problem with time delays in state variables. Finally, the available flexibility from the original DHS is estimated by aggregating the flexibility of all subsystems. Numerical results reveal that a DHS with longer pipelines has more flexibility but using this flexibility may lead to extra actions in equipment such as the opening position adjustment of valves, in order to restore the DHS to normal states after providing flexibility. Impacts of the supply temperature of the heat producer, the heat loss coefficient of buildings and the ambient temperature on the available flexibility were quantified.