  In order to prevent conflicting or counteracting use of flexibility options,
the coordination between distribution system operator and transmission system
operator has to be strengthened. For this purpose, methods for the standardized
description and identification of the aggregated flexibility potential of
distribution grids are developed. Approaches for identifying the feasible
operation region (FOR) of distribution grids can be categorized into two main
classes: Random sampling/stochastic approaches and optimization-based
approaches. While the latter have the advantage of working in real-world
scenarios where no full grid models exist, when relying on naive sampling
strategies, they suffer from poor coverage of the edges of the FOR due to
convoluted distributions. In this paper, we tackle the problem from two
different angles. First, we present a random sampling approach which mitigates
the convolution problem by drawing sample values from a multivariate Dirichlet
distribution. Second, we come up with a hybrid approach which solves the
underlying optimal power flow problems of the optimization-based approach by
means of a stochastic evolutionary optimization algorithm codenamed REvol. By
means of synthetic feeders, we compare the two proposed FOR identification
methods with regard to how well the FOR is covered and number of power flow
calculations required.
