Simultaneous optimization of temperature and energy in linear energy system models

Linear programming is used as a standard tool for optimizing unit commitment or power flows in energy supply systems. For heat supply systems, however, it faces a relevant limitation: For them, energy yield depends on the output temperature, thus, both quantities would have to be optimized simultaneously and the resulting problem is quadratic. As a solution, we describe a method working with discrete temperature levels. This paper presents mathematical models of various technologies and displays their potential in a case study focused on integrated residential heat and electricity supply. It is shown that the technique yields reasonable results including the choice of operational temperatures. Finally, MTRESS, an open source implementation of the method is introduced briefly.