On Power Control of Grid-Forming Converters: Modeling, Controllability, and Full-State Feedback Design

The popular single-input single-output control structures and classic design methods (e.g., root locus analysis) for the power control of grid-forming converters have limitations in applying to different line characteristics and providing favorable performance. This paper studies the grid-forming converter power loops from the perspective of multi-input multi-output systems. First, the error dynamics associated with power control loops (error-based state-space model) are derived while taking into account the natural dynamical coupling terms of the power converter models. Thereafter, the controllability Gramian of the grid-forming converter power loops is studied. Last, a full-state feedback control design using only the local measurements is applied. By this way, the eigenvalues of the system can be arbitrarily placed in the timescale of power loops based on predefined time-domain specifications. A step-by-step construction and design procedure of the power control of grid-forming converters is also given. The analysis and proposed method are verified by experimental results and system-level simulation comparisons in Matlab/Simulink.