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

Journal article, 2023

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.