## 1 Introduction
Thus, [10] and [17] show, respectively, state-space models that are oriented to the control of fuel cell systems in DC microgrids and auxiliary starting systems for electric vehicles. Similar models, formulated as impedance models, are used for the control and design of converters in DC power systems for the integration of electrolyzers in renewable grids [17], and the design of modular multilevel converters for high-voltage applications [10]. Finally, a more complete converter model for photovoltaic microinverter control is described in [7]. This model is based on the small-signal model of the converter, formulated as a transfer function, and integrates the non-idealities associated with the output filter. The use of T1M may be a good starting point for the preliminary design of the converter and its control loops, but often leads to considerable discrepancies with actual behavior. Figure 1: Ideal circuit of the push–pull converter. This is mainly due to the strong influence of the converter's non-idealities with respect to its operating conditions, power and switching frequency [18]. Secondly, type 2 models (T2M) are those that consider some non-idealities in the HF transformer (leakage resistances and inductances of the primary and secondary windings) and, depending on the work, they also consider some non-idealities in the switching devices and in the filter inductance and capacitor. An example of such models is developed in [19]. Specifically, this model is formulated in state-space representation, and is a control-oriented average model of bi-directional dual active bridge converters for use in solid-state transformers, smart grids, and electric/hybrid vehicle applications. It is a simplified model that integrates the effect of the resistance and inductances of the HF transformer windings, and the series resistance of the output filter components. Refs. [20; 21] present a model formulated as a transfer function for the analysis and control of push-pull converters. In particular, Ref. [20] models a bidirectional pulse-width modulation (PWM) plus phase-shift-modulated push-pull converter, while [21] models a classical topology converter for use in isolated high-voltage applications. Again, these models are highly simplified, as they only integrate the non-idealities associated with the HF transformer windings. Finally, a more complete model for the sizing and control of bidirectional converters is developed in [22]. This model is formulated as an average and small-signal state-space model, and integrates non-idealities of the HF transformer, such as winding inductance and magnetization losses. Despite the improvement in T2M compared to T1M, none of the reviewed works presents a complete solution that models all the non-idealities (at least all the practical ones) of the converter. In particular, as far as the HF transformer is concerned, the parasitic capacitances of its windings, which can have a considerable effect on the dynamic response of the model depending on the switching frequency and the winding technique used, are ignored [23]. Furthermore, the non-idealities associated with the switching devices are also not considered. Finally, type 3 models (T3M) encompass the most complex and complete models found in the literature. These models consider an important part of the non-idealities of both the HF transformer and the rest of the fundamental components of the converter. Such models are scarce in the literature; however, some recent examples can be found. Thus, Ref. [24] presents the analysis and modeling of a voltage-compensated push-pull converter. In this case, the model includes non-idealities associated with the HF transformer, specifically its magnetization inductance, as well as non-idealities of the electronic switches, namely its output capacitances. It is a control-oriented model represented in the form of a transfer function, where simplicity is paramount, and whose formulation is based on the small-signal model of the converter. On the other hand, Ref.