The Variable Resistance on the Calculation of the Hydraulic Regime of a District Heating System

District heating systems (DHS) comprise complex hydraulic networks that include multiple consumers, distribution pipe networks, and power sources. By analyzing key parameters such as pressure, flow rate, and resistance within a hydraulic system, it is possible to predict system performance and optimize adjustments. Calculating the hydraulic regime of a heat supply system means solving a system of large-scale quadratic equations. Unlike electrical systems, typically modeled by linear equations, hydraulic systems require nonlinear equations, making analysis more challenging and often necessitating iterative methods. In defining the scope of our study, we focused on stabilizing the network's hydraulic regime by adjusting the supply water temperature at the source. We observed that changes in a user’s automatic valve resistance altered the total resistance, causing the entire system to operate in a variable mode. Conversely, we analyzed how variations in source pressure influenced user resistance. Our study aimed to characterize constant and variable resistances in hydraulic systems and to determine the system’s equivalent total resistance. Kirchhoff's laws are applied to determine resistance, head loss, and flow distribution. Yet, many nonlinear equations call for transforming the problem into a linear system under hydraulic stability assumptions. This paper proposes a methodology to simplify computations by distinguishing between variable and constant hydraulic resistances, representing them as equivalent resistances for enhanced modeling accuracy. When performing hydraulic calculations of heat supply systems, we mainly relied on software from countries such as Russia and Denmark. As a result, engineers often neglected the theoretical development of hydraulic calculation methods. To address this issue, we began investigating these methods and developed a hydraulic calculation model, which we aim to improve through ongoing research. Based on this foundation, we present this study.