Portfolio optimization in district heating: Merit order or mixed integer linear programming?

Long-term portfolio optimization is commonly used to find the most cost-effective design and operation of a district heating system, subject to technical, financial, and environmental restrictions. Optimizing a district heating system is not trivial and demands high accuracy and high computational speed. However, existing methods addressing this problem offer one or the other but not both at the same time. The state-of-the-art method for portfolio optimization is mixed integer linear programming (MILP), which is extensively used in industry and academia but can be computing and resource-intensive for large portfolio models. This limitation has motivated the development of various options to reduce the computation time while maintaining the ac-curacy to a large extent. An alternative method to MILP is the merit order (MO) method, which has been used especially for power generation applications due to its simplicity and faster computation but somewhat reduced accuracy. The aim of this paper is to investigate the potential advantages and disadvantages of MO models compared to MILP models in the context of optimizing the portfolio of assets supplying a district heating network. As a study case, we analyze a large portion of the district heating network in Berlin. Four MO model variants with different levels of complexity are proposed and compared to a reference MILP model. Results suggest that MO models variants including heat storage and describing CHP plants with significant detail have the potential to reduce calculation time by nearly three orders of magnitude compared to the reference MILP model, without significantly sacrificing accuracy. In fact, differences in heat generation and net present value (NPV) between the most accurate MO model and the reference MILP model account for +/- 4% and-6%, respectively. Moreover, results show that combining MO and MILP models is advantageous and offers high computational speed and at the same time high accuracy, especially when a large number of runs might be necessary. MO models could thus be used prior to MILP models to perform a pre-evaluation, an exploration of sensitivities, or for downsizing the initial optimization problem. Combining MO and MILP models could result in faster and more robust decision-making, which could otherwise not be attained with any of the two options individually.

Automated summary

Long-term portfolio optimization for district heating systems is challenging due to the need for high accuracy and computational speed. This paper investigates the advantages and disadvantages of using merit order (MO) models compared to mixed integer linear programming (MILP) models. Results suggest that MO models, especially those incorporating heat storage and detailed description of CHP plants, can significantly reduce computation time without sacrificing accuracy. Combining MO and MILP models offers a faster and more robust decision-making process.