Dynamic Harmonic Domain Modeling and Stability Augmented Design of Inverter Interface to Weak and Unbalanced Grid

Unbalanced distribution network/loads and asymmetrical faults are frequent in power systems. Distributed energy resources employing inverter interfaces need to ride through them to abide by emerging grid codes. The balanced grid operation has been a well-researched topic. However, literature lacks a unified framework to model, analyze, and design controllers for unbalanced interfaces. This work develops a nonlinear time-domain state-space model of inverter interfaced to an unbalanced grid. It includes details of frame transformation, synchronization, inner current controller, and filter dynamics. Its linearization around the steady-state trajectory results in a linear time-periodic (LTP) system. The model is then transformed to the dynamic harmonic domain for ease of analysis, consideration of multiple frequency couplings, and controller design. Precise stability boundaries in parameter space are obtained to understand margins for safe operation intuitively. A stability augmentation using output feedback is presented for increasing these margins. Feedback gain is designed using the generalized Nyquist criterion. Proposed augmentation is shown equivalent to the adaptive active damping of unstable periodic trajectories. Simulation test cases confirm the validity of the proposed design.