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The enormous technological potential accumulated over the past two decades would make 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.

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