Single Coordinate Bode Plots for Stability Evaluation of MIMO Power Electronics Systems via a Frequency Coupling Corrective Factor

When the stability assessment of a power electronic-dominated system is performed on a single coordinate, for example, through Bode plots in $dd-$ and $qq-$axis, accuracy is compromised in frequency ranges where the frequency coupling is strong. Thus, the stability of such systems is normally analyzed using a multi-input-multioutput (MIMO) framework, which involves employing generalized Nyquist plots. However, if the frequency coupling in these systems is quantified and used to correct the diagonal elements of the MIMO system, the stability evaluation could be greatly simplified using single coordinate Bode plots. To achieve that, this article introduces a corrective factor based on a quantified frequency coupling parameter, referred as coupling strength. This approach allows MIMO systems to be analyzed within a single-input-single-output framework. The corrective factor ensures simpler and precise analysis using single coordinate Bode plots. In addition, this method provides an accurate estimation of resonance frequencies and frequency coupling-based stability margins by direct inspection of the Bode plots. Simulation and experimental results are presented to validate the proposed stability assessment technique.