Risk-Aware Hosting Capacity Analysis for Flexible Load Interconnection in Distribution Networks

The increasing penetration of flexible loads, such as electric vehicles and AI data-centers necessitates new methodologies for quantifying electrical load hosting capacity under operational constraints and flexible connection agreements. We propose a risk-aware hosting capacity framework that explicitly accounts for both flexibility, in the form of load curtailment, and system reliability. The proposed method incorporates a Conditional Value-at-Risk (CVaR) constraint to control the tail risk of excessive curtailment, ensuring that extreme interventions remain limited. Additionally, a weighted $\ell_1$ approach is introduced to limit the number of utility-controlled interventions, enabling control over the frequency of curtailment actions. A regularization parameter is used to tune the intervention count to a desired intervention budget. The resulting optimization formulation is convex and efficiently solvable, allowing scalable implementation. Numerical results demonstrate that the proposed method significantly increases hosting capacity while maintaining strict risk guarantees and limiting intervention frequency, providing a practical balance between flexibility and reliability in distribution systems.