  The increase of generation capacity in the area of responsibility of the
distribution system operator (DSO) requires strengthening of coordination
between transmission system operator (TSO) and DSO in order to prevent
conflicting or counteracting use of flexibility options. For this purpose,
methods for the standardized description and identification of the aggregated
flexibility potential of distribution grids (DGs) are developed. Approaches for
identifying the feasible operation region (FOR) of DGs can be categorized into
two main classes: Data-driven/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. To underpin
the need for improved sampling strategies for data-driven approaches, in this
paper we point out and analyse the shortcomings of naive sampling strategies
with focus on the problem of leptocurtic distribution of resulting
interconnection power flows (IPFs). We refer to this problem as convolution
problem, as it can be traced back to the fact that the probability density
function (PDF) of the sum of two or more independent random variables is the
convolution of their respective PDFs. To demonstrate the convolution problem,
we construct a series of synthetic 0.4 kV feeders, which are characterized by
an increasing number of nodes and apply a sampling strategy to them that draws
set-values for the controllable distributed energy resources (DERs) from
independent uniform distributions. By calculating the power flow for each
sample in each feeder, we end up with a collapsing IPF point cloud clearly
indicating the convolution problem.
