Input Impedance Modeling of Single-Phase Voltage Source Rectifier With Consideration of FrequencyCoupling Effect

Time-periodicity and non-linearity pose a challenge to the precise input impedance modeling of single-phase power converters. In this study, a precise input impedance model with measurability of the single-phase voltage source rectifier (VSR), which considers the frequency-coupling effect (FCE), is established. Meanwhile, it is revealed that the rectifier input impedance is dependent of the grid impedance. In the proposed modeling approach, only Laplace transform and frequencyshifting operation are required, which avoids the complicated convolution calculation in the frequency domain. In addition, the influence of grid impedance on the input impedance is studied. Simulations are conducted to verify the effectiveness of the proposed method. <br>

Input Impedance Modeling of Single-Phase Voltage Source Rectifier With Consideration of FrequencyCoupling Effect

Time-periodicity and non-linearity pose a challenge to the precise input impedance modeling of single-phase power converters. In this study, a precise input impedance model with measurability of the single-phase voltage source rectifier (VSR), which considers the frequency-coupling effect (FCE), is established. Meanwhile, it is revealed that the rectifier input impedance is dependent of the grid impedance. In the proposed modeling approach, only Laplace transform and frequencyshifting operation are required, which avoids the complicated convolution calculation in the frequency domain. In addition, the influence of grid impedance on the input impedance is studied. Simulations are conducted to verify the effectiveness of the proposed method. <br>

Mathematical analysis of a spatially distributed soil carbon dynamics model

The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction–diffusion–advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system.