## 1 Introduction  
DC-DC power converters, in their isolated and non-isolated variants, are a fundamental part of the design of switch-mode power supplies (SMPS) [1]. Among all possible converter configurations, the push-pull topology is one of the most widely used architectures in power electronics design (SMPS and power inverters) [2]. There are many advantages of this architecture compared to other converter topologies: with respect to non-isolated topologies, its high input-output ratio and galvanic isolation [2]; with respect to isolated topologies in general, the reduced number of switching devices and, consequently, the associated lower losses; with respect to half-bridge and full-bridge topologies in particular, the lower complexity for their control (the sink of the power transistors is referenced to the circuit ground); and, finally, with respect to single-switch topologies, its high efficiency and the excellent utilisation of the high-frequency transformer [3]. Moreover, these particular characteristics confer a wide range of operating powers, varying from a few watts to tens of kW, with typical switching frequencies between 20 kHz and 500 kHz, depending on size, cost and performance constraints [4]. Thanks to all of the above advantages, the range of applications of this topology is becoming more and more diverse. Some of the most significant and recent examples of the use of push-pull topology are electric propulsion systems in electric vehicles [5], the integration of renewable energy sources in microgrids [6] and the integration of energy storage systems based on supercapacitors [7], batteries [8] or hydrogen technologies [9]. This is the reason for the special interest in the study of this topology. For their implementation and the design of model-based controllers in real applications, it is essential to have analytical models as representative as possible of the real behaviour of the converter [10]. For this purpose, it is crucial that the push-pull converter model considers its intrinsic non-idealities, or at least those representatives in real applications, which may vary depending on the converter topology and the rated power and operating frequency [10]. Determining the correct model must be a trade-off between accuracy and simplicity, which is not always an easy task. To this end, the search for trade-off solutions must consider that an overly complex model increases its computational burden for the implementation of real-time controllers. However, a high simplification may generate a large deviation between the proposed model and the real converter, which will have a negative impact on the performance and behaviour of the converter-controller duo [10]. Therefore, it is necessary to analyse on a case-by-case basis the possible influence that certain non-idealities may have on the dynamic and steady-state response of the converter depending on the application and operating conditions. Many papers in the scientific literature propose and validate push-pull converter models for different uses and applications. Although all of them start from the ideal model of the converter (Figure 1), the main difference between the different variants lies in the non-idealities considered for their definition. First, the most widespread solutions are based on the complete ideal model of the converter (Figure 1). This model is based on the analysis of the second-order buck equivalent model of the transformer secondary circuit and has been successfully applied in the scientific literature in different applications and scales, among others, for the management and power supply to LED lighting systems [11]; the control and management of renewable energy sources, wind and photovoltaic, in microgrids [12,13]; the integration of energy storage systems based on hydrogen technologies in HVDC buses [9] and the design of charge balancing circuits in battery management systems [14], as well as in the design of battery chargers for electric vehicles applications [15,16].