An improved grid impedance estimator for grid-forming converters in consideration of controller dynamics

•The relationship between active power and power angle is expressed by the grid impedance, and the elements affecting the grid impedance estimation are revealed.•The influence of phase error caused by controller dynamics on the equivalent grid impedance model is revealed. It manifests that this error limits the accuracy and speed of the conventional PQ variations technique.•By compensating for the phase error, an improved grid impedance estimator with only the active power disturbance is proposed. It brings about more accurate estimation and a higher power factor for grid-forming converters.