Development of a Mathematical Model of a Two-stage DC-DC Converter

The article considers an aggregated power supply system containing two stages of DC-DC conversion. Each stage is a completely autonomous converter with an individual control system serving to stabilize the output voltage. Such systems belong to the class of nonlinear dynamic systems; therefore, nonlinear dynamic models need to be used for analyzing their dynamics. Currently, such systems are studied using small-signal modeling, which implies linearization of the system in a small vicinity of the operating point; however, such approach limits the capabilities of such models. The mathematical model proposed in the article is piecewise linear in nature. In this model, the movements in the system in the linearity section are described in analytical form. Each linearity section of the mathematical model corresponds to a certain combination of open (conducting) switches in the circuit. The transition from section to section is carried out using the fitting method. The valve switching moments in the circuit are found either analytically or using numerical methods, so that the proposed model can be called a combined numerical-and-analytical one. To check how correct the proposed mathematical model is, a comparison was made between the results obtained using the verified MatLab Simulink software package and the results obtained using the proposed mathematical model. It has been demonstrated that the proposed model yields acceptable accuracy and features higher computation speed in comparison with the model implemented in the MatLab Simulink environment, which is important when studying the nonlinear dynamics of such devices. The proposed mathematical model is versatile in nature and after certain adaptation can be used to model aggregated two-stage power supply systems based on other types of DC-DC converters.