Analytical frequency modeling of a diode rectifier: formulation for SQP solving versus formulation for Newton-Raphson solving

Static converters generate current harmonics in grids. Numerous studies on analytical frequency models of converters are often required to carry out their harmonic modeling in the context of sizing by optimization. Some formulations are proposed to solve such models. Each formulation has its own advantages and drawbacks. The paper mainly focuses on two formulations: the first to be solved by Sequential Quadratic Programming (SQP) and the second to be solved by Newton-Raphson (NR). In this way, the paper presents the performances of each formulation and compares the results of both formulations for the modeling of a single-phase diode rectifier.

The paper aims to compare SQP formulation and NR formulation, and to propose the ways to improve their convergence. In the modeling, by using an explicit formulation of the state variables combined to a numerical method, equations are defined to reduce, as far as possible, the number of unknowns.

The difficulty is to find the good operating mode of the static converter. So, outside the equations and the constraints, the paper proposes to use the eigenvalues of the state space matrixes to initialize the duration of every configuration and to consider the operating symmetries of the static converter that allow to reduce the research area and also the variables calculated.

The number of the conducting phase per half period is a priori, as the operating mode.

The modeling is based on the use of linear components, ideal switches and the static converter operates in steady-state. The main difficulties are to formulate the equations representing the non-controlled switching of semiconductors, and to solve them.