## 5 Conclusions  
This paper presents a general, complete, and very accurate state-space dynamic model of a push-pull converter. In contrast to the works reviewed in the scientific literature, which present simplified models designed around certain operating conditions, the proposed model considers all the practical non-idealities present in any push-pull converter due to the transformer, the switching devices (electronic switches and diodes) and the other passive elements.  
The state-space formulation that was developed confers modularity, versatility, and computability to the model and, despite its high order, it is essentially simple, orderly, intuitive and, above all, very practical. In addition, the model is adaptive, so it can follow the intrinsically nonlinear behavior of the converter, depending on the operating conditions (voltage, current and temperature) for each sampling time. This means that there can be a different model at every sampling time, which is possible in practice because its formulation does not require a very high computational burden. Therefore, the developed model opens the door to the design of model-based adaptive controllers for the more efficient real-time control of power systems. In addition, the developed model allows for the construction of accurate push-pull converter simulators that, being adaptive and capable of running in real-time, allow, with the appropriate sensing, for the implementation of digital twins.  
The performance of the developed model was evaluated and validated against a real 2 kW push-pull converter. Steady-state and dynamic response tests were carried out for variations in both the converter input signal and duty cycle, respectively. The performance of the developed model was also compared with reference models that are widely used in the scientific literature. The developed model had an excellent performance, with mean absolute percentage errors below 2.7% in all cases, considerably lower than the error of the reference models, and with a dynamic response (including fast transients) that is very similar to that of the real converter.  
Based on the above, it is concluded that the developed model is a powerful tool to predict the transient and steady-state response of the converter, obtain information on the effect of non-idealities on the dynamic response of the converter and evaluate the performance of different model-based control architectures.  
Future work will focus on two different lines. First, the development of sensitivity analyses for characterization and isolation, considering that they are present as coordinates of the state vector, and the influence of non-idealities according to the sizing and use of the converter (mainly power and operating frequency). Second, the design of more complete models that allow for the ripple in the output magnitudes of the converter to be modeled. Third, the design of optimal controllers to obtain the best possible converter performance.  
F.J.V.: writing--original draft, methodology, conceptualization, software, investigation, formal analysis, writing--review and editing. F.S.: writing--review and editing, conceptualization, methodology, funding acquisition. J.M.A.: writing--review and editing, conceptualization, supervision, project administration, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This work is a contribution of the two following projects: \"H2 Integration&Control. Integration and Control of a hydrogen-based pilot plant in residential applications for energy supply\", Ref. PID2020-116616 RB-C31 supported by the Spanish State Program of R+D+I Oriented to the Challenges of Society, and \"SALTES: Smartgrid with reconfigurable Architecture for testing control. Techniques and Energy Storage priority contaminant waste\", Ref. P20-00730 supported by Andalusian Regional Program of R+D+I.  
Not applicable.  
The authors declare no conflict of interest.