Inverter Control with Time-Varying and Nonconvex State and Input Constraints

The growing integration of inverter-based resources (IBRs) into modern power systems poses significant challenges for maintaining reliable operation under dynamic and constrained conditions. This paper focuses on the power tracking problem for grid-connected IBRs, addressing the complexities introduced by voltage and power factor constraints. Voltage constraints, being time-varying and nonlinear input constraints, often conflict with power factor constraints, which are state constraints. These conflicts, coupled with stability requirements, add substantial complexity to control design. To overcome these challenges, we propose a computationally efficient static state-feedback controller that guarantees stability and satisfies operational constraints. The concept of achievability is introduced to evaluate whether power setpoints can be accurately tracked while adhering to all constraints. Using a parameterization framework and the S-lemma, we develop criteria to assess and maximize the continuous achievable region for IBR operation. This framework allows system operators to ensure safety and stability by precomputing a finite set of control gains, significantly reducing online computational requirements. The proposed approach is validated through simulations, demonstrating its effectiveness in handling time-varying grid disturbances and achieving reliable control performance.