  Aggregated flexibilities or PQ-capabilities (active and reactive power
capabilities) are termed in literature as Feasible Operating Regions (FORs).
The FORs from underlying active distribution grids can effectively contribute
to the operational management at the HV grid level. The HV buses are allocated
aggregated FORs from the underlying MV grids, which are inherently nonlinear
and non-convex. Therefore, two approaches are proposed in the paper to apply
the FOR constraints in the HV grid operational management. First, a mixed
integer linear programming (MILP) based optimization approach for alleviating
the HV grid constraint violations is proposed, which addresses the
non-convexity of the FOR using piecewise segmentation. Furthermore, the MILP
method is enhanced to consider the influence of the HV bus voltage on the
underlying MV grid flexibilities resulting in a three dimensional PQ(V)-FOR.
Second, a convexification approach is proposed, which uses a convex
approximation of the non-convex 3D PQ(V)-FOR shape for implementation in a
linear optimization method. Results reveal a robust utilization of the
distribution flexibilities to maintain grid security and reliability at the HV
grid level. Comparisons present increased computation times for the MILP method
which are significantly improved using the convexification based approach.
