Aggregating DER Uncertainty: Minkowski Sum Under Joint Chance Constraints

Addressing uncertainty is essential in power systems with high levels of renewable energy penetration. Distributed energy resources (DERs), due to their partially controllable nature, are a major source of uncertainty. However, due to their large numbers and complex correlations, their aggregated uncertainty is highly complex. This paper aims to track how the uncertainty is modeled from individual DER prediction errors to the aggregated-level. By enforcing a specified confidence level, the aggregated-level probabilistic flexibility boundary is formulated as a Minkowski sum under joint chance constraints (JCCs). Despite the inherent intractability of this problem, we establish an equivalent representation that allows for an effective approximation using the proposed quantile cube approximation method. An iterative algorithm is also developed to enhance computational efficiency in implementing the method. Numerical tests demonstrate that the proposed method effectively reduces the conservativeness of the aggregated confidence boundary and the computation time at the same time.