  Citation: Fiaz, M.F.; Calligaro, S.; Iurich, M.; Petrella, R. Analytical Modeling and Control of Dual Active Bridge Converter Considering All Phase-Shifts. Energies 2022, 15, 2720. https://doi.org/10.3390/en15082720 Academic Editors: Miguel Castilla, Alberto Reatti and Salvatore Musumeci Received: 5 January 2022 Accepted: 22 March 2022 Published: 7 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Analytical Modeling and Control of Dual Active Bridge Converter Considering All Phase-Shifts † Muhammad Faisal Fiaz 1 , Sandro Calligaro 1, * , Mattia Iurich 2 and Roberto Petrella 2 1 Faculty of Science and Technology, Free University of Bozen-Bolzano, Piazza Università 5, 39100 Bolzano, Italy; muhammadfaisal.fiaz@natec.unibz.it 2 Polytechnic Department of Engineering and Architecture, University of Udine, Via delle Scienze 206, 33100 Udine, UD, Italy; iurich.mattia@spes.uniud.it (M.I.); roberto.petrella@uniud.it (R.P.) * Correspondence: sandro.calligaro@unibz.it † This paper is an extended version of our paper published in 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 11–15 October 2020; Analytical Modelling and Control of Dual Active Bridge Converter Considering all Phase-Shifts. Abstract: In the field of power electronics-based electrical power conversion, the Dual Active Bridge (DAB) topology has become very popular in recent years due to its characteristics (e.g., bidirectional operation and galvanic isolation), which are particularly suitable to applications such as interface to renewable energy sources, battery storage systems and in smart grids. Although this converter type has been extensively investigated, its analysis and control still pose many challenges, due to the multiple control variables that affect the complex behavior of the converter. This paper presents a theoretical model of the single-phase DAB converter. The proposed model is very general, i.e., it can consider any modulation technique and operating condition. In particular, the converter is seen as composed by four legs, each capable of generating voltage on the inductor, and by the two output legs, which can steer the resulting inductor current to the load. Three variables are considered as the control inputs, i.e., the phase-shifts with respect to one leg. This approach results in a very simple yet accurate closed-form algorithm for obtaining the inductor current waveform. Moreover, a novel analytical model is proposed for calculating the average output current, based on the phase-shift values, independently of the output voltage. It is also shown that average output current can be varied cycle-by-cycle, with no further dynamics. In fact, average output current is not affected by the initial value of inductor current or by DC offset (which may arise during transients). The proposed models can be exploited at several stages of development of a DAB: during the design stage, for fast iteration, when selecting its operating points and when designing the control. In fact, based on the analytical results, a novel control loop is proposed, which adopts a “fictitious” (i.e., open-loop) inner current regulation loop, which can be applied to any modulation scheme (e.g., Single Phase-Shift, Triple Phase-Shift, etc.). The main advantage of this control scheme is that the simple dynamics of the output voltage versus the average output current can be decoupled from the complicated relationship between the phase-shifts and the output current. Moreover, a Finite Control Set (FCS) method is proposed, which selects the optimal operating points for each operating condition and control request, ensuring full Zero-Voltage Switching (ZVS) in all cases. The analytical results obtained and control methods proposed are verified through simulations and extensive experimental tests. Keywords: dual active bridge; zero voltage switching; phase-shift; average output current; inductor current 1. Introduction Due to several factors, including the increasing utilization of renewable energy and the trend towards electrification of mobility, there is a strong demand for electrical power conversion solutions for the interfacing between different systems, such as energy storage devices, renewable sources, local and wide grids and specific loads [1,2]. In this scenario, Energies 2022, 15, 2720. https://doi.org/10.3390/en15082720 https://www.mdpi.com/journal/energies