基于图论的供热管网水力计算研究
Research on hydraulic calculation of heating pipe network based on graph theory
摘要：
集中供热管网为多连通网络且拓扑结构相对复杂,而图论可以将复杂管网简化为图形和数据的形式表达,使用节点及管段的拓扑结构反映热网模型。通过建立矩阵方程,对管网节点压力、管段流量实施计算和分析。本文以管网实际参数为基础,基于图论基本原理和基尔霍夫压流定理,建立了供热管网数学模型。根据已知管网结构、流体参数和运行条件,计算出供热管网中各个节点的压力、流量分布;并以太原市供热管网为算例验证数学模型及求解方法,其计算结果相对误差小于8%。该研究结果可为供热管网的运行状态分析、优化设计、调度控制和故障诊断提供依据。
Abstract：
The centralized heating pipe network is a multi-connected network with a relatively complex topological structure. Graph theory can simplify the complex pipe network and express it in the form of graphics and data, using the topological structure of nodes and pipe segments to reflect the heating pipe network model. By establishing matrix equations, the pressure at pipe network nodes and the flow rate of pipe segments can be calculated and analysed. Based on the actual parameters of the pipe network, this paper establishes a mathematical model of the heating pipe network according to the basic principles of graph theory and Kirchhoff’s voltage-current law. According to the known pipe network structure, fluid parameters and operation conditions, the pressure and flow distribution at each node in the heating pipe network are calculated. Taking the heating pipe network in Taiyuan as an example, the mathematical model and the solution method are verified, and the relative error of the calculation results is less than 8%. The research results can provide a basis for the operation state analysis, optimal design, scheduling control and fault diagnosis of the heating pipe network.
Keywords:graph theory; heating pipe network; hydraulic calculation; mathematical model; matrix equation; Kirchhoff’s voltage-current law