Linear or mixed integer programming in long-term energy systems modeling – A comparative analysis for a local expanding heating system

Most computer models used in energy systems optimization modeling studies are formulated using linear equations. However, since linear formulations do not always well reflect real-world conditions, they may not always be adequate as policy and support tools. This is particularly the case for local system studies attempting to represent technologies at the individual scale, as in the case for local heating system modeling. Thus, the aim of this paper is to investigate differences in the resulting heating solutions and model solution times for a local expanding heating system. Three different investment cost structures for individual and district heating solutions for the heating of new housing are investigated using linear and mixed integer linear programming. The results show that the use of district heating is higher for the cost structures that use mixed integer linear programming than it is for the linear cost structures. This result is attributed mainly to the fact that individual air-to-water heat pumps benefit from the linear equation formulation due to its high coefficient of performance during summertime. This finding is important to consider when modeling local energy systems. The solution time is, however, significantly shorter for the linear formulations than for the mixed integer linear formulations.