This paper describes a fast approach for synchronous reluctance machine flux linkage mapping considering the cross-saturation effects. The rapid prediction of the flux maps <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ<i><sub>d</sub></i></b> ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>i</i><i><sub>d</sub></i>,<i>i</i><i><sub>q</sub></i></b> ) and <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ<i><sub>q</sub></i></b> ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>i</i><i><sub>d</sub></i>,<i>i</i><i><sub>q</sub></i></b> ) only requires the data (from finite element analysis or measurements) along the boundaries of the range to be mapped. To this purpose, two proper functions are defined to predict the effect of cross saturation based on the coenergy variation. The two analytical functions can be computed directly from the data acquired on the boundaries of the ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>i</i><i><sub>d</sub></i>,<i>i</i><i><sub>q</sub></i></b> ) current plane depending respectively on <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>i</i><i><sub>d</sub></i></b> and on <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>i</i><i><sub>q</sub></i></b> values. The method is applied to predict the flux linkage maps of a synchronous reluctance machine. The results from the semi-analytical method are compared to the full finite element analysis approach and with measurements. In the last part of the paper, different saturation models, based on a limited set of simulations, are compared, showing the new proposed method's potential, against other simplified approaches for a fast mapping.
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