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Purpose – 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 focusses 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 purpose of this paper is to present the performances of each formulation and compare the results of both formulations for the modeling of a single-phase diode rectifier. Design/methodology/approach – 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. Findings – 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. Research limitations/implications – The number of the conducting phase per half period is a priori, as the operating mode. Originality/value – 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. [ABSTRACT FROM AUTHOR]

Purpose – Multiphysical models are often useful for the design of electrical devices such as electrical machines. In this way, the modelling of thermal, magnetic and electrical phenomena by using an equivalent circuit approach is often used in sizing problems. The coupling of such models with other models is difficult to take into account, partly because it adds complexity to the process. The purpose of this paper is to propose an automatic modelling of thermal and magnetic aspects from an equivalent circuit approach, with its computation of gradients, using selectivity on the variables. Then, it discusses the coupling of various physical models, for the sizing by optimization algorithms. Sensibility analyses are discussed and the multiphysical approach is applied on a permanent magnet synchronous machine. Design/methodology/approach – The paper allows one to describe thermal and magnetic models by equivalent circuits. Magnetic aspects are represented by reluctance networks and thermal aspects by thermal equivalent circuits. From circuit modelling and analytical equations, models are generated, coupled and translated into computational codes (Java, C), including the computation of their Jacobians. To do so, model generators are used: CADES, Reluctool, Thermotool. The paper illustrates the modelling and automatic programming aspects with Thermotool. The generated codes are directly available for optimization algorithms. Then, the formulation of the coupling with other models is studied in the case of a multiphysical sizing by optimization of the Toyota PRIUS electrical motor. Findings – A main specificity of the approach is the ability to easily deal with the selectivity of the inputs and outputs of the generated model according to the problem specifications, thus reducing drastically the size of the Jacobian matrix and the computational complexity. Another specificity is the coupling of the models using analytical equations, possibly implicit equations. Research limitations/implications – At the present time, the multiphysical modelling is considered only for static phenomena. However, this limit is not important for numerous sizing applications. Originality/value – The analytical approach with the selectivity gives fast models, well adapted for optimization. The use of model generators allows robust programming of the models and their Jacobians. The automatic calculation of the gradients allows the use of determinist algorithms, such as sequential quadratic programming, well adapted to deal with numerous constraints. [ABSTRACT FROM AUTHOR]