  With the increasing amount of distributed energy resources (DERs)
integration, there is a significant need to model and analyze hosting capacity
(HC) for future electric distribution grids. Hosting capacity analysis (HCA)
examines the amount of DERs that can be safely integrated into the grid and is
a challenging task in full generality because there are many possible
integration of DERs in foresight. That is, there are numerous extreme points
between feasible and infeasible sets. Moreover, HC depends on multiple factors
such as (a) adoption patterns of DERs that depend on socio-economic behaviors
and (b) how DERs are controlled and managed. These two factors are intrinsic to
the problem space because not all integration of DERs may be centrally planned,
and could largely change our understanding about HC. This paper addresses the
research gap by capturing the two factors (a) and (b) in HCA and by identifying
a few most insightful HC scenarios at the cost of domain knowledge. We propose
a data-driven HCA framework and introduce active learning in HCA to effectively
explore scenarios. Active learning in HCA and characteristics of HC with
respect to the two factors (a) and (b) are illustrated in a 3-bus example.
Next, detailed large-scale studies are proposed to understand the significance
of (a) and (b). Our findings suggest that HC and its interpretations
significantly change subject to the two factors (a) and (b).
