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Single-switch quasi-resonant DC inverters are preferred in low-power induction-heating applications for their cheapness. However, they pose difficulties in enforcing soft-switching and show limited controllability. A good design of these converters must proceed in parallel with the characterization of the load and the operating conditions. The control of the switching frequency has a critical relationship to the non-linear behavior of the load due to electro-thermal coupling and geometrical anisotropies. Finite element methods enable the analysis of this kind of multiphysics coupled systems, but the simulation of transient dynamics is computationally expensive. The goal of this article is to propose a time-domain simulation strategy to analyze the behavior of induction heating systems with a quasi-resonant single-ended DC inverter using pulse frequency modulation and variable load. The load behavior is estimated through frequency stationary analysis and integrated into the time-domain simulations as a non-linear equivalent impedance parametrized by look-up tables. The model considers variations in temperature dynamics, the presence of work-piece anisotropies, and current harmonic waveforms. The power regulation strategy based on the control of the switch turn-on time is tested in a case study with varying load and it is shown that it is able to maintain the converter in the safe operation region, handling variations up to of 22% in the equivalent load resistance.

The design and management of thermoforming systems based on radiation heat transfer require the development of a mathematical model that can be used at all stages of the system's life cycle. For this reason, in this paper, we present a digital twin based on a hybrid ElectroThermal model that can integrate mathematical equations and data acquired in the field. The model's validity is verified with experiments performed on a test bench. The presented model is modular and can be easily used to represent new configurations of the heating elements for simulation and design. Thanks to the low computational complexity of the proposed Digital Twin, it enables the development of advanced control strategies and the analysis and optimization of the main geometric parameters of the system. In addition, it can support the identification of the best configuration and choice of measurement points.