On the Applicability of SISO and MIMO Impedance-Based Stability Assessment of DC-DC Interlinking Converters

This article presents a formal mathematical correlation between the standardly used port-level (terminated) single-input single-output (SISO), and the recently acknowledged device-level (unterminated) multiple-input multiple-output (MIMO) impedance-based method for the stability assessment of dc-dc interlinking converters. Based on this, the conditions that must be met to ensure the correct stability assessment by the SISO method applied to a single port-pair are derived. It is shown that without prior knowledge on whether these conditions are met, the SISO method must be applied to every port-pair to account for possible port-level hidden dynamics. Alternatively, the MIMO method can be used, which is revealed to inherently account for any port-level hidden dynamics. It is further analyzed which method is advantageous in terms of computational complexity, intuitiveness, and simplicity for applications featuring meshed grids or multiport interlinking converters, as well as in terms of interpreting the resulting stability margins. Finally, suitability of the MIMO method for termination-independent stability-oriented controller design and stability assessment based on measurements is highlighted. The presented methodology is illustrated for a simplified dc system with a current-controlled buck converter. Analytical stability predictions are validated using hardware-in-the-loop simulations and also experimentally, using a laboratory hardware prototype.