Optimization of district heating networks considering pressure losses in pipe fittings

The design of modern district heating networks requires tools that can simultaneously minimize economic costs and maximize operational efficiency. The goal of this study is to develop a computationally efficient optimization framework that minimizes the total cost of the district heating network, defined as the sum of the initial pipe investment and the operational pumping energy cost, while ensuring reliable thermal delivery to all consumers. To achieve this, a comprehensive gradient-based optimization framework is presented. The model integrates nonisothermal pipe flow and optimization to simultaneously determine the optimal supply and return pipeline diameters, radiator diameters, pump pressure, and radiator valve settings for a district heating network comprising 72 buildings. A constraint aggregation function ensures adequate heat delivery to prevent freezing, while the objective function minimizes total cost, balancing initial capital expenditure against long-term pumping energy expenses. The novelty of this work lies in the inclusion of 90° elbows and T-junctions within the one-dimensional hydraulic model to account for localized pressure drops caused by turbulent flow separation—a significant source of energy loss in real networks that is typically neglected in simplified optimization models. The obtained numerical results demonstrate that the optimized design reduces pipe costs by 10.66%, while increasing network efficiency from 93.8% to 95.3% and guaranteeing thermal performance. The total cost savings after optimization amounted to 10.45%. This model provides a robust, scalable, and accurate methodology for the pre-design and optimization of district heating systems.