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.

The power generation and consumption of distributed energy resources (DERs) offer significant flexibility potential, which can be utilized to provide services such as peak and frequency regulation. DERs introduce a vast number of variables and constraints, making it complicated to directly integrate them into upper-level dispatch. To address this challenge, virtual power plants (VPPs) emerge, which treat diverse DERs as a collective entity and use aggregated flexibility envelopes to reduce the variable and constraint scale, facilitating upper-level optimization. In VPPs, unified DER modeling and efficient DER aggregation play a crucial role but are challenging. This paper first introduces a novel unified polytope model to represent heterogenous DERs' flexibility region. A coordination transformation is utilized to eliminate redundant variable dimensions and maintain DERs' interface characteristics. A sample-based projection method is then developed, further removing all state variables, resulting in a unified flexibility region. This method is then utilized to calculate the Minkowski sums of individual flexibility polytopes for aggregation. The results of numerical tests demonstrate a considerable reduction in computation time and maintain satisfactory accuracy when the proposed modeling and aggregation approach is adopted.