Analysis of STATCOM Small-Signal Impedance in the Synchronous d-q Frame

Small-signal model impedances of grid-tied converters have recently attracted researchers' attention and have shown great importance in stability analysis. This article proposes an impedance model in d-q frame for static synchronous compensators (STATCOMs), including dynamics from synchronization, current, voltage loops, and QV droop and reveals the significant features compared to other types of grid-tied converters that: 1) impedance matrix strongly coupled in d and q channel due to nearly zero power factor; 2) different behaviors of impedances at low frequency due to inversed direction of reactive power; and 3) coupled small-signal propagation paths on the voltage at point of common coupling (PCC) from synchronization and ac voltage regulation. All these characteristics render difficulty in identifying instability patterns using existing knowledge and pinpointing the main contributor to instability among control loops, which was discussed and solved in this article. To better understand the frequency coupling effects of STATCOMs, the d-q frame impedance model was further transformed in its complex matrix form. An example of possible instability with STATCOMs was presented and analyzed using the proposed model. The impedance model was verified experimentally with a scaled-down STATCOM prototype.