  Hosting capacity (HC) and dynamic operating envelopes (DOEs), defined as
dynamic, time-varying HC, are calculated using three-phase optimal power flow
(OPF) formulations. Due to the computational complexity of such optimisation
problems, HC and DOE are often calculated by introducing certain assumptions
and approximations, including the linearised OPF formulation, which we
implement in the Python-based tool ppOPF. Furthermore, we investigate how
assumptions of the distributed energy resource (DER) connection phase impact
the objective function value and computational time in calculating HC and DOE
in distribution networks of different sizes. The results are not unambiguous
and show that it is not possible to determine the optimal connection phase
without introducing binary variables since, no matter the case study, the
highest objective function values are calculated with mixed integer OPF
formulations. The difference is especially visible in a real-world low-voltage
network in which the difference between different scenarios is up to 14 MW in a
single day. However, binary variables make the problem computationally complex
and increase computational time to several hours in the DOE calculation, even
when the optimality gap different from zero is set.
