## 1 Introduction
[23] presents a very complete model applied to the control of three-phase push-pull converters. This model is also formulated as a transfer function, and integrates the non-idealities associated with the magnetizing inductance of the HF transformer, the internal resistance of certain passive components and electronic switches, and the rectifier diodes. The improvements brought by these models are noticeable, as they consider some non-idealities of the classical model of the real transformer (Figure 2), as well as the parasitic output capacitor of the transistors (Figure 3). However, the complete modelling of the converter, with particular attention to all the practical non-idealities associated with the HF transformer, remains to be addressed. From the analysis of the scientific literature review, it is concluded that, despite the large number of applications and published works, no analytical mathematical model has been found that integrates all the practical non-idealities of the push-pull converter. The main problem of the analyzed models, including the few T3M models found, lies in the deviations between theoretical and experimental behavior outside specific operating conditions, since the push-pull converter is a strongly non-ideal system [25]. This implies that the models presented in the literature are not completely general, regardless of the converter power and operating conditions. Figure 3: (**a**) Equivalent circuit reduced to the secondary for case 1; (**b**) for 2; and (**c**) for 3. Figure 2: Non-ideal (actual) circuit reduced to the secondary of the push–pull converter in Figure 1.  
This analysis leads to the conclusion that there is a clear need for a general, accurate, fully interpretable, and practical model of push-pull converters to serve as a tool for the design and testing of high-performance model-based controllers for power system management, advanced analysis, precision simulations and digital twins. This is precisely the objective of this work and its main novelty. Although the procedure used to o build the developed model is well known, since it is based on [PERSON]'s laws and a standard averaging method, the main contribution of this work, in the authors' opinion, is the development of the most general and complete model published to date (at least to the authors' knowledge). To summarize the contributions of this research, the novelties of the proposed model are listed below:  
* A control-oriented linear parameter-variable state space (LPV) model is presented. * The model is general, simple, and accurate. To achieve this, it considers, in a very intuitive way, the main non-idealities of the converter associated with the HF transformer, electronic switches, diodes, and passive components. * The model is fully discrete and linear each time, at each sampling period, which implies that a different transfer function can be generated at each sampling period. However, perhaps more important is that, if the sampling period is small enough, the model perfectly captures the nonlinear dynamics of the converter over time. * Its direct formulation in a state space from a first-order differential equation in each energy storage element allows for the development of a very high-order model (a transfer function model that was mathematically developed in the usual way would require a differential equation of order 13), which is necessary to consider the high number of non-idealities of the converter. In any case, using the developed state model, it is very easy to obtain an impedance or transfer function model for each sampling period; this is sufficient to solve the linear state equation each time. Regarding the latter, although the procedure used to obtain transfer functions from linear state models is straightforward, there is no guarantee that an output-input relationship can always be found, especially in complex and very high-order models such as this one.