Combining Temperature and Mass Flow as Variables in Linear Optimisation Models

Linear programming is a powerful tool for optimizing unit commitment or power flows in energy supply systems. However, it faces a significant limitation when applied to certain systems. Power in heat supply systems, for example depends on the velocity of the medium as well as temperature. Thus, both quantities must be optimized simultaneously, resulting in a bilinear problem. To address this issue, either of the quantities can be discretized. This paper presents a method that combines the two options and describes mathematical models for heat pumps, solar thermal collectors, and heat storages following that approach.