Definition of safe operating limits for dq control-based Voltage Source Converters under unbalanced grid voltages

The most conventional control structure for Voltage Source Converters (VSC) is based on the stationary reference frame dq theory, which may result in varying levels of harmonic content in the AC currents and DC voltage oscillations under unbalanced voltage conditions. In the last two decades, numerous papers have proposed controllers with diverse levels of complexity to address these issues. However, a scientific gap exists in the current state of the art regarding the operational limits of conventional dq control in the face of these undesirable operational conditions. The primary contribution of this paper is a mathematical model capable of calculating the phase and magnitude of non-characteristic elements of AC currents, such as negative sequence and third harmonic components, present during unbalanced conditions. These components depend on the power handled by the VSC, the level of voltage unbalance and the bandwidths of the control loops, where the selection of the latter can either enhance the system performance or lead it towards instability. Thus, based on this model, it is now possible to quantitatively define the safe operating limits of a VSC driven by dq control under unbalanced voltages. The validation and effectiveness of the model are confirmed through real-time simulations and prototype experiments. Finally, the proposed novel framework holds potential utility for both industrial and academic applications.