Abstract
Heating networks are a crucial part of modern urban infrastructure, delivering heat to residential, commercial, and industrial consumers efficiently and reliably. Ensuring their safe and continuous operation is essential for maintaining comfort and supporting daily urban life. The integration of digital twins has become increasingly important, as they allow operators to monitor network behavior in real time, predict potential failures, and implement corrective actions promptly. By reducing response times and minimizing the frequency of accidents, digital twins help ensure a stable and uninterrupted heat supply. For a digital twin to be effective, it must be based on accurate numerical models that capture fluid flow, heat transfer, and pressure distribution throughout the network. Proper design and modeling enable efficient use of resources, including pumping power and pipe sizing, while reducing energy waste and operational costs. This study presents a comprehensive approach to optimizing heating networks. Control variables such as pipe diameters, pump pressure, and the settings of bypass and radiator valves for each consumer are defined. A constraint aggregation function ensures that no consumer experiences freezing, while the objective is to minimize both the initial installation costs and long-term operational expenses. Advanced numerical solvers were used to perform the calculations, enabling efficient optimization of large and nonlinear networks. This approach demonstrates how careful modeling and control can improve the efficiency, reliability, and cost-effectiveness of heating networks.