  Solar hosting capacity analysis (HCA) assesses the ability of a distribution
network to host distributed solar generation without seriously violating
distribution network constraints. In this paper, we consider risk-sensitive HCA
that limits the risk of network constraint violations with a collection of
scenarios of solar irradiance and nodal power demands, where risk is modeled
via the conditional value at risk (CVaR) measure. First, we consider the
question of maximizing aggregate installed solar capacities, subject to risk
constraints and solve it as a second-order cone program (SOCP) with a standard
conic relaxation of the feasible set with power flow equations. Second, we
design an incremental algorithm to decide whether a configuration of solar
installations has acceptable risk of constraint violations, modeled via CVaR.
The algorithm circumvents explicit risk computation by incrementally
constructing inner and outer polyhedral approximations of the set of acceptable
solar installation configurations from prior such tests conducted. Our
numerical examples study the impact of risk parameters, the number of scenarios
and the scalability of our framework.
