Aggregate Feasible Region of DERs: Exact Formulation and Approximate Models

The aggregation of distributed energy resources (DERs) draws much attention since their penetration increases continuously. We derive the mathematical formulation of the exact aggregate feasible region (AFR) of multiple DERs. The derivation is based on analyzing the redundancy of all possible constraints in the Fourier-Motzkin Elimination (FME) process. In the exact AFR model, the number of constraints is regardless of the number of DERs but exponential with the number of time intervals. Although the computational complexity of the exact AFR is dramatically simplified compared with the original FME, there are still too many constraints for the exact AFR model to be applied in practice. Hence, we propose the $k$ th-order approximate models and two types of multi-timescale approximate models. Illustrative cases show the necessity of each constraint in the proposed models compared with the aggregated power and energy boundary model. Numerical simulations verify the accuracy of the exact AFR model. Besides, the second-order approximate model performs best considering the balance between accuracy, economics, and computational complexity.