Influence of Linear, Mixed-Integer Linear, Piecewise-Linear, and Nonlinear Thermal Power Flow Models on District Heating Network Design

The following files contain the datasets needed to reproduce the results of the publication "Influence of Linear, Mixed-Integer Linear, Piecewise-Linear, and Nonlinear Thermal Power Flow Models on District Heating Network Design", submitted to Applied Energy. The dataset consists of the following files:- matrices_mts_2_src: Folder containing the districts for multiple heat sources and multiple design periods.- matrices_sts_1_src: Folder containing the districts for a single heat source and a single design period.- config_multiple_sources.yaml: Boundary conditions (formatted for the usage in topotherm), forced expansion and multiple design periods.- config_multiple_sources_eco.yaml: Boundary conditions (formatted for the usage in topotherm), economic expansion and multiple design periods.- config_single_source.yaml: Boundary conditions (formatted for the usage in topotherm), forced expansion and single design periods.- config_single_source_eco.yaml: Boundary conditions (formatted for the usage in topotherm), economic expansion and single design period.- run_mts_base.py: Example Python file to run the district with multiple design periods and the base topotherm model.- run_sts_base.py: Example Python file to run the district with a single design period and the base topotherm model.Abstract of the submitted publication "Influence of Linear, Mixed-Integer Linear, Piecewise-Linear, and Nonlinear Thermal Power Flow Models on District Heating Network Design": Optimization is a valuable method to design cost-effective district heating networks, but remains limited by its scalability to large urban districts. This paper examines the impact of various regression-based thermal power flow models on optimal design outcomes and computational performance. Six regression approaches for pipe investment costs and heat losses are systematically compared, including constant, linear, and nonlinear models. Based on regression accuracy, piecewise-linear models perform best for pipe investment costs, while logarithmic models yield the highest accuracy for heat losses. Afterwards, linear, mixed-integer linear, and nonlinear programming models using the aforementioned regressions are formulated and benchmarked systematically on 53 real-world districts ranging from 50 to 10000 heat sinks, including forced expansion and economic objective functions, single and multiple design periods, and single and multiple heat sources. Results show that while purely linear models offer the shortest computation times, they often lead to inferior network designs. Piecewise-linear models consistently achieve the best objective values due to lower regression errors, but suffer from limited scalability. Affine and hybrid models provide near-optimal solutions with significantly improved scalability, whereas constant models trade limited optimality decreases for substantial gains in computational efficiency. For single-period designs, most models yield comparable network topologies. In multi-period and economic optimization settings, computational complexity increases sharply. In this case, only linear formulations achieve optimal designs within the allowed computational time for very large districts, while hybrid and constant models offer the best balance between solution quality and efficiency for medium-scale systems.