Beyond Monotonic Droop: Expanding Feasible Control Regions for Optimal Frequency Regulation

With the growing integration of Inverter-Based Resources (IBRs) for renewable energy, power grids are shifting towards hybrid generations. As the system becomes more complex, it is challenging to ensure optimal and safe control. Recent work shows how to achieve a conditional optimal control with stability ensured by pre-selecting one subclass of activation functions for control. However, we demonstrate that the subclass leads to a sub-optimal control policy for IBRs. To address this issue, we propose a method to enlarge the feasibility space for true optimality while preserving the Lyapunov stability. The key idea is to implement a conditional control strategy based on the damping. When IBRs observe that synchronous generators are on the way to stabilize the grid sufficiently, IBRs do not necessarily need to conduct droop control with monotonic function. In some cases, IBRs can conduct actions that more closely align with non-monotonic control to encourage renewable generations. This extends from monotonic to non-monotonic functional space. Moreover, based on Pontryagin's maximum principle, we prove that the extended region is sufficiently large to contain a globally optimal solution. By leveraging our activation function, which can be both monotonic and non-monotonic, our numerical results on various test cases show significant improvement compared to existing solutions.