Impedance-Based Stability Boundary for Two-Stage Solid-State-Transformer EV Fast Chargers

Two-stage SST fast charger is appealing for high power EV charger since it provides regulated front-end converter followed by another DAB isolated stage, however, the common dc link can cause instability even if both front-end converter and DAB are individually stable. This paper will delve into the interaction through impedance-based analysis and present the closed-form expressions for the DAB input and PFC output impedances by cascading their PI-controlled dynamics. The minor-loop gain obtained is utilized to determine a realistic stability limit of a 10~kW 800/400~V charger. The nominal design has been validated to have a 10.4~dB interaction margin and $|T|_{\max}=0.301$. The minimum capacitance of the dc-link depends on the converter: $C_{dc,pfc}>12.55~\mu\mathrm{F/kW}\times P_0$; for the nominal $C=414.5~\mu$F, the converter is operated at $3.32\times$ above the minimum capacitance. A sweep of the PFC equivalent controller reveals that the critical bandwidth of the PFC voltage-loop is around 6~Hz, which indicates that the cascaded bandwidth must not be reduced too much or the cascade will be unstable. The accuracy of the predicted boundary is verified by an independent 13-state nonlinear model , whose deviations in critical capacitance and boundary frequency are 0.01\,\% and 2.9\,\% respectively . Furthermore, the boundary is validated through nonlinear free-response and switching-level impedance verifications.As shown, the results indicate that after crossing the instability boundary, the value of $\min_{\omega}|1+T|$ may be misleading whereas the value of $|T|_{\max}$ and the Nyquist plot encirclement remain reliable indicators of interaction.