Investigation of $d$- and $q$-Axis Inductances Influenced by Slot-Pole Combinations Based on Axial Flux Permanent-Magnet Machines

Abstract

Flux-weakening capability of permanent-magnet synchronous machines (PMSMs) is fundamentally determined by <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> -axis inductances. Based on axial flux permanent-magnet machines (AFPMs), this paper extracts the intrinsic factors that influence the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $q$</tex></formula> -axis inductances of PMSMs, meanwhile revealing the fact that the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> -axis inductances of fractional slot concentrated winding machines are not inevitably larger than that of distributed ones. The proportion of each of the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex> </formula> -axis component inductances for multigap AFPMs is first studied. By analyzing armature inductance in conjunction with differential leakage inductance, this paper introduces a novel parameter to decouple the influence of slot-pole combinations and physical dimensions so that the “inductance ability” of different slot-pole combinations can be quantified. An improved method of calculating the slot leakage inductance of semiclosed slots is then put forward, which proves to be more accurate than the conventional method. The investigations and conclusion in this paper are not restricted to AFPMs but applicable to radial flux permanent-magnet machines as well. Validations of various slot-pole combinations are carried out with finite-element analysis and experiments.