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.

中文翻译：

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电网区域供热系统灵活性的量化

产生/消耗电力的区域供热系统（DHS）越来越多地用于为电网提供灵活性。由于DHS具有复杂的热动力学和时滞效应，因此量化DHS的灵活性具有挑战性。本文提出了一种三阶段方法来量化DHS的最大灵活性。DHS首先被分解为具有更简单拓扑结构的多个并行子系统。然后，将每个子系统的最大灵活性公式化为带有状态变量时间延迟的最优控制问题。最后，通过汇总所有子系统的灵活性来估算原始DHS的可用灵活性。数值结果表明，具有更长管道的DHS具有更大的灵活性，但是使用这种灵活性可能会导致设备中的其他动作，例如调节阀门的打开位置，以便在提供灵活性之后将DHS恢复到正常状态。量化了供热器的供应温度，建筑物的热损失系数和环境温度对可用柔韧性的影响。