  The enormous technological potential accumulated over the past two decades
would make it possible to change the operating principles of power systems
entirely. The consequent technological evolution is not only affecting the
structure of the electricity markets, but also the interactions between
Transmission System Operators (TSOs) and Distribution System Operators (DSOs).
New practical solutions are needed to improve the coordination between the grid
operators at the national, TSOs, and local level, DSOs. In this paper, we
define the flexibility range of coordination between TSOs and DSOs. By doing
so, we propose an algorithm based on epsilon-constrained methods by means of
mathematical programming and power systems principles. We evaluate and compare
different classical optimal power flow formulations (AC-OPF, DistFlow,
DistFlow-SOCP, and LinDistFlow) for building the flexible TSO-DSO flexible
domain. The presented approaches in this paper are analyzed in an IEEE 33-bus
test radial distribution system. We show that for this particular problem, the
DistFlow-SOCP has the worst accuracy, despite the popularity among the academic
community of convex relaxation approaches.
