Frequency response feasible region of DER cluster based on tightened convex relaxation in transformed power flow space

Aggregating distributed energy resource (DER) clusters for participation in primary frequency regulation (PFR) services can significantly enhance power system frequency stability. To ensure power flow (PF) security, it is crucial to evaluate the maximum frequency regulation capability (FRC) of DER clusters before initiating the PFR process. However, the PF model of DER clusters is inherently nonlinear and non-convex, with the droop characteristics of DERs further complicating analytical solutions, especially in medium- and low-voltage clusters without accurate parameters. This paper proposes an FRC assessment method for cluster, which integrates a physics-informed data-driven PF approach with a convex relaxation algorithm. By applying incomplete state-space dimension-lifting based on the Koopman operator, the complex nonlinear PF is substantially simplified in the transformed high-dimensional space. Additionally, an adaptive McCormick method is developed, combining piecewise relaxation with boundary contraction to efficiently handle bilinear terms in the optimization problem. To address the co-expansion characteristics of the bulk grid and clusters, an alternating iteration method is introduced. The simulation results indicate that the proposed method can achieve fast and accurate FRC assessment without relying on physical parameters.