Optimal Control for Robust Dynamic Performance in Inverter-Dominated Power Systems. Part I: Modeling and Problem Formulation

Future power systems will rely heavily on Inverter-Based Resources (IBRs), introducing significant challenges for operational reliability and stability. Although grid-forming and grid-following control structures have been proposed for Inverter-Dominated Power Systems (IDPS), reliable methods for centralized control design optimization, capable of ensuring satisfactory performance under large disturbances while accounting for complex nonlinear dynamics such as current saturation, remain absent. To address this gap, we propose solving a robust optimal control problem that jointly determines the control structure and parameter tuning of IBRs in IDPS, ensuring reliable dynamic performance for large-signal disturbance events. To formulate this problem, we develop a general and unified modeling framework that integrates IDPS dynamics with flexible disturbance, dispatch, and control models. This framework explicitly captures post-disturbance and fault-recovery transients during largesignal events across a wide range of disturbances, dispatch, and control realizations. In Part I, we present the modeling framework and foundational principles of the robust optimal control problem, along with a discussion of its broader implications and practical limitations. By bridging the gap between power system and control research, this work provides a comprehensive resource for addressing modern IDPS challenges and establishes the theoretical foundation for the solution approach and results presented in Part II.