A contribution to the simplified determination of heat distribution costs in linear and radial district heating networks
District heating networks offer a great opportunity to make a significant contribution to the success of the energy transition, assuming that low-carbon heat supply is achieved. District heating networks have advantages over individual building heat supply systems, such as lower heat generation costs due to economies of scale, higher efficiencies in heat production, and the ability to integrate heat from various sources. However, district heating networks are not unconditionally advantageous, as they require an investment in network infrastructure, unlike individual building heat supply systems. Whether this investment outweighs the economic benefits on the heat supply side depends on a variety of factors and cannot be answered in general. In the literature, two methods are described for assessing the suitability of an area for district heating supply. The use of detailed network simulations allows for an accurate determination of heat distribution costs but requires significant expertise and effort in application. On the other hand, territorial assessment approaches rely on easily identifiable indicators from urban planning, but their accuracy is limited. Furthermore, the later methods often rely on data from existing district heating networks, raising doubts about their applicability to future generations of district heating networks. Therefore, the aim of this thesis is to develop a methodology for estimating heat distribution costs that does not rely on design parameters from existing district heating networks. This methodology aims to combine the advantages of territorial assessment approaches (ease of use) and detailed network simulations (accuracy). To achieve this, the main influencing factors will be identified to derive multiple methods for determining the costs of future heating networks. Additionally, the accuracy and limitations of these methods is analyzed. This thesis primarily focuses on analyzing the heat distribution costs of linear networks. Additionally, an approach is presented for determining the costs of radial networks. Overall, the heat distribution costs are divided into capital, heat loss, pressure loss, as well as operation and maintenance costs, and are examined in the form of levelized costs of heat. Two different configurations of consumer distributions are considered, representing the upper and lower limits of costs in a line network. One configuration assumes that all consumers are located at the end of a network, resulting in a constant diameter of the heat network at all locations. Another configuration assumes a constant distribution of consumers along the linear heat network. This leads to a successive reduction in pipe diameter with increasing network expansion. To address the research questions, a detailed network model was developed. Investigations show that capital and pressure loss costs increase with network expansion, while heat losses, as well as operation and maintenance costs, are largely independent of the network expansion. To determine the main influential factors, a one-factor-at-a-time (OFAT) and a Monte Carlo parameter study were conducted using the detailed model. In total, twenty-four parameters were investigated. Based on the OFAT parameter study, two significant groups of input parameters were identified. One group influences the heat distribution costs dependent on the network expansion, while the other group influences the heat distribution costs independent of the network expansion. Based on the results of the Monte Carlo study, correlations between the heat distribution costs and the input parameters were derived. The identified correlation coefficients range from correlation coefficients 0.0 to 0.58. The linear heat density, network expansion, and annuity factor exhibit the strongest correlations with respect to the heat distribution costs. Additionally, seven other influencing factors with moderate correlation coefficients were identified significantly challenging the determination of heat distribution costs based on only a few influencing factors. As only input parameter, the linear heat density exhibits a non-linear relationship with respect to the heat distribution costs. The results of the Monte Carlo study were used to derive one-dimensional and multi-dimensional regression models. These models can be easily applied by inserting the available design parameters of the district heating network into the derived correlation equations. However, the normalized relative error is relatively high. For the best one-dimensional model, a normalized relative error of NRMSE= 43.9 % was determined. This reduces to NRMSE = 25.9 % for the best multi-dimensional regression model. Unlike existing territorial estimation methods, the multi-dimensional regression model can consider a variety of different input parameters, enabling cost estimation for future heat network generations. However, to achieve a reliable prediction accuracy that goes beyond rough estimation, the achieved accuracies are not sufficient. To improve the prediction accuracy, an analytical approach has been developed based on the detailed model, but it eliminates iterative and interpolating calculation steps. This analytical approach leads to results that are very close to the achievable results of the detailed simulation model. On average, the normalized relative error could be reduced to NRMSE = 1.3 %. The application of the analytical method is slightly more complex than the application of the regression models, but this complexity is not comparable to the computational effort required for the detailed network simulation. The present doctoral thesis thus fills an existing gap in the literature and provides several easy-to-use methods for simplified determination of the heat distribution costs of future district heating network generations. Ultimately, the results support the transition towards sustainable and efficient heat supply systems.
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