Aggregation of Heterogeneous DERs by the Subgradient Vertex Search Method

The exploitation of distributed energy resources (DERs) is essential for the advancement of smart grids. However, the heterogeneity and scale of DERs pose major challenges to their aggregation, which is necessary to maximize their potential. This study adopts a linearized model that integrates a diverse array of DERs including power generation, energy storage, and flexible loads with varying dissipation rates. We used the model to analyze the compact form and mathematical implications of aggregation, for which we propose the subgradient vertex search method to solve. This method efficiently identifies vertices of the aggregate feasible region, which are used to construct its convex hull. Unlike traditional hyperplane-based methods, this method not only provides an inner approximation efficiently but also can converge to the exact solution. Numerical simulations validated its accuracy and efficiency. Additionally, we introduce an energy flowchart to visualize high-dimensional space of energy change processes and provide a case study involving two vehicle-to-grid (V2G) charging piles to explain the mechanism of feasible region scaling, demonstrating the practical significance of precise aggregation.