Electromagnetic Oscillation Stabilizer for Large-Scale Power Electronics-Dominated Power Systems in LTP Framework - Part I: Functional Derivative-Based Measures of Modal Controllability and Observability

Power electronics-dominated power systems (PEPSs) are highly susceptible to electromagnetic oscillations across a broad frequency range, posing significant challenges to system stability and security. Addressing these oscillations necessitates the development of electromagnetic oscillation stabilizers (EOSs). However, the time-periodic nature of PEPSs, characterized by multiple frequency components, complicates the design of effective EOSs. To tackle this complexity, this paper proposes stabilization analysis and control theories within the linear time-periodic (LTP) framework. The design of EOSs is approached in two key steps: 1) determining the optimal installation locations and 2) designing their structures and parameters. These aspects are addressed in a two-part series, with this Part I paper focusing on the first step. Leveraging functional derivatives and Hilbert space norms, this paper develops measures of modal controllability (MOC) and modal observability (MOO) for LTP systems, providing quantitative extensions to existing qualitative LTP controllability and observability theories. The proposed LTP-based MOC and MOO facilitate the optimal selection of control locations and feedback signals for EOSs. Case studies conducted on a real-world large-scale PEPS demonstrate that the LTP-based MOC and MOO achieve higher analytical accuracy and lower computational complexity compared to their linear time-invariant (LTI) counterparts, underscoring their suitability for large-scale time-periodic PEPSs.