Electromagnetic interference (EMI) rectification of grid-tied inverters is crucial for their practical application, and the variable frequency modulation (VFM) technique is a low-cost and simple way for EMI reduction. However, changes in loss and harmonic behaviors make it hard for parameter determination of VFM. In this paper, the parameters required for switching frequency (SF) function are determined for loss optimization of MOSFETs and inductors, while total harmonic distortion (THD) and temperature rise in MOSFETs and inductor core are constrained to guarantee the feasibility of the calculated parameters. Current transient is derived through multidimensional Fourier decomposition (MFD) and characteristics of Bessel function for loss estimation of MOSFET and inductor. Modified Steinmetz equation (MSE) is applied for core loss estimation and AC resistance is considered for copper loss estimation. With the constraints of THD and temperature, the loss optimization problem is solved by the augmented Lagrangian (AL) method. With the assistance of the proposed method, total loss optimization can be realized in feasible regions while the temperature rise in essential components can be restricted to the preset values.
Cheng et al. (2026) studied this question.