Integrated System Models for Networks with Generators & Inverters

Synchronous generators and inverter-based resources are complex systems with dynamics that cut across multiple intertwined physical domains and control loops. Modeling individual generators and inverters is, in itself, a very involved activity and has attracted dedicated attention from power engineers and control theorists over the years. Control and stability challenges associated with increasing penetration of grid-following inverters have generated tremendous interest in grid-forming inverter technology. The envisioned coexistence of inverter technologies alongside rotating machines call for modeling frameworks that can accurately describe networked dynamics of interconnected generators and inverters across timescales. We put forth a comprehensive integrated system model for such a setting by: i) adopting a combination of circuit- and system-theoretic constructs, ii) unifying representations of three-phase signals across reference-frame transformations and phasor types, and iii) leveraging domain-level knowledge, engineering insights, and reasonable approximations. A running theme through our effort is to offer a clear distinction between physics-based models and the task of modeling. Among several insights spanning the spectrum from analytical to practical, we highlight how differential-algebraic-equation models and algebraic power-flow phasor models fall out of the detailed originating electromagnetic transient models.