Unified equivalent-circuit models for voltage-source inverters that capture averaged dynamics and power-flow solutions in distribution networks

This paper demonstrates how three-phase distribution networks composed of voltage-source inverters can be modeled as a single unified equivalent-circuit network realized with familiar circuit elements. Such a model is derived by representing all physical- and control-subsystem dynamics as equivalent circuits. Two versions are put forth: the first captures averaged dynamics; while the second is a steady-state version of the first and it captures the power-flow solution in sinusoidal steady state. The main challenge in undertaking such an effort is presented by the fact that inverters are composed of subsystems (filters, pulse width modulators, phase-locked loops, controllers, direct-quadrature reference-frame transformations) that belong to multiple domains (physical and control). We demonstrate how all these constituent subsystems can be transcribed as equivalent circuits which then promote a single and unified circuit model that captures network physical- and control-layer dynamics. Numerical simulations for a representative distribution network compare results from the averaged model and the steady-state model with high-fidelity switch-level simulations. The results establish the validity of the circuit-based models and the computational benefits of the proposed approach.