Multi-scale Modeling And Analysis Of DC-DC Converter Based On Device Mechanism Model

The DC-DC converter is a complex system with multi-scale characteristics.Generally,the macro-scale describes the overall working principle of the circuit,while the micro-scale mainly involves the mechanism model of circuit components.Modeling on the macro scale alone cannot reflect the influence of the internal effects of the device on the overall circuit,while modeling on the micro scale cannot show the operating characteristics of the circuit.Therefore,a comprehensive analysis of the interaction between different scales and the establishment of a multi-scale unified model are of great significance to the analysis of DC-DC converters.In order to obtain the analytical solution of the state variables of the DC-DC converter at the circuit level and the device level,this paper proposes a multi-scale modeling method for the DC-DC converter based on the mechanism model of the power semiconductor device.This method combines the device mechanism at the micro-scale with the circuit model at the macro-scale,replaces the traditional piecewise switching function with a continuous switching function,and establishes a multi-scale unified mathematical model of the DC-DC converter described by a non-linear continuous function.Compared with the single-scale circuit model widely used at present,this model contains the characteristics of the device-level scale in the circuit,so it can more accurately describe the actual working condition of the circuit.Moreover,by using the equivalent small parameter method to solve the established nonlinear mathematical model,we can quickly obtain an approximate analytical solution for the steady state of the converter system’s state variables.The main works of this paper are as follows.1.The mechanism model of power electronic devices is analyzed,and the concept of multiscale is introduced into the modeling process of DC-DC converters,and a multi-scale model combining the macro-scale and micro-scale of the switching converter is established.In view of the continuous voltage change characteristics of switching devices during the turn-on process,a modeling method that replaces the traditional piecewise linear switching function with a continuous smooth switching fitting function is proposed to better describe the turn-on and turnoff process of the switching device.2.Taking the Boost converter working in CCM as an example,the nonlinear multi-scale models of its open-loop and closed-loop operating states are established respectively.Then,the equivalent small parameter method is used to derive and solve,and the expression of the steadystate approximate analytical solution of the converter state variables is obtained.The approximate analytical solution obtained by the method in this paper is consistent with the MATLAB numerical simulation and experimental test results,indicating that the proposed multi-scale modeling method can accurately and effectively analyze the steady-state characteristics of the converter in CCM operation.3.The above modeling method is further extended to the analysis of Boost converter working in DCM mode.According to the working modal analysis of the converter during DCM mode,the relationship between the duty cycles of the switches in the multi-scale model is rederived,and a modeling method of the converter in multi-mode operation is proposed.This method uses a smooth fitting function that considers both the rising and falling edges of the switch to characterize the operating characteristics of the converter,thereby establishing a multiscale nonlinear mathematical model for the DCM operation of the Boost converter.Similarly,the equivalent small parameter method can be used to solve the model,and the expression of the steady-state approximate analytical solution of the state variable can be obtained.Furthermore,the analytical results obtained by the method in this paper are compared and analyzed with the simulation and experimental results.The results obtained by the three methods are very close,indicating that the proposed multi-scale modeling method can also be used accurately and effectively for the steady-state analysis of converters operating in DCM.The above analysis examples of Boost converters working in CCM and DCM modes show that the modeling method based on the mechanism model of power semiconductor devices and the nonlinear continuous function proposed in this paper is accurate and effective.And the expression of the approximate analytical solution to the state variables of the DC-DC converter in steady-state operation can be quickly obtained.Therefore,the method in this paper can be further extended to the modeling and analysis of high-order DC-DC converters.