The study of multilevel dual-active-bridge (DAB) converters has garnered significant attention in recent years thanks to their advantages with respect to the conventional two-level (2L) DAB; namely, its greater performance and its capability to operate at higher voltage. The analysis of the converter high-frequency inductor current (iL) is crucial, for instance, to compute its root mean square (RMS) value, required to estimate the conduction losses in the converter. The mathematical expression of iL is piecewise and multiple variations, i.e., modes, exist depending on the modulation parameter values. This increases the complexity of converter performance analytical study. Thus, a more practical and generalizable expression of iL current is desirable. This paper proposes novel compact analytic expressions for the instantaneous and RMS inductor current in the 2L-NL DAB converter, leveraging binary functions to define the piecewise intervals and to identify the mode as a function of the modulation parameter values. The proposed method paves the way for more simple and computationally efficient DAB performance optimization software tools that allow exploring any given converter structures and modulation strategies.
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