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\title{A Saturation Model Based on a Simplified Equivalent Magnetic Circuit for Permanent Magnet Machines}



\author[1]{Francesco Lelli}%
\author[2]{Marko Hinkkanen}%
\author[1]{Fabio Giulii Capponi}%
\affil[1]{Dept. of Astronautical, Electrical and Energy Engineering, Sapienza University of Rome Rome}%
\affil[2]{Dept. of Electrical Engineering and Automation, Aalto University}%


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  \date{June 13, 2024}


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\begin{abstract}
This paper proposes an explicit mathematical model to describe the nonlinear behavior of the permanent magnet synchronous reluctance machine. Although different models for the synchronous reluctance machines are available, extending them to the case of the permanent magnet machine is not trivial due to the effect of the permanent magnets on the rib saturation. This work uses a simplified equivalent magnetic circuit to derive the structure of the proposed model. A nonlinear reluctance is introduced to model the rib saturation. It can be added to the existing model for the synchronous reluctance machine to take into account the effect of the permanent magnets. A simple fitting procedure based on the steepest descent method is proposed to estimate the parameters of the model.%
\end{abstract}%



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