Sensitivity-Based Impedance Modeling of AC Voltage-Controlled Converters

Loads affect the stability of grid-forming (GFM) converters, both in stand-alone and grid-connected modes. This has motivated the development of methods that study the stability of GFM converters using an impedance-based analysis. AC impedance-based stability analyses usually study the stability of GFM converters by applying the Nyquist criterion to an impedance ratio denoted as minor loop gain. A limitation of the previous approach when applied to GFM converters, which is not always clearly stated, is that the output impedance of a GFM converter depends on the impedance seen by the converter. This loading effect is not accurately modeled in the literature. This article proposes an impedance model that accounts for this loading effect on the GFM converter output impedance, without introducing approximations. As a direct consequence of the presented impedance model, the stability of the GFM converter when connected to different loads can be determined by checking the stability of a single transfer function, the sensitivity function. Using the sensitivity function, the impedance model presented also reveals a clear link between the voltage controller characteristics and the converter output impedance, which has been reported as a limitation of prior impedance-based analysis methods.