Torque Optimization of Six-Phase Arcuate Sine + Third Harmonic Shaping Surface Permanent Magnet Synchronous Motor

To increase the torque density of direct-drive surface permanent-magnet synchronous motors (SPSMs), the model of arcuate sine + third harmonic (3rd) shaping SPSM with parallel magnetization and the optimal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{3rd}$</tex> current when the machine loaded with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> current are derived. The finite-element (FE) models of six-phase arcuate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> shaping and sine shaping SPSMs are established based on the principle of the same maximum permanent-magnet (PM) thickness, and their air-gap flux densities under no-load are compared. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> current and sine current are applied to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> shaping and sine shaping motors, respectively, based on the principle of equal current amplitude. The results show that the amplitude of air-gap flux density fundamental wave under no load condition of the Sine shaping SPSM is significantly lower than that of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> shaping SPSM, and the amplitude of other higher harmonics is unchanged except for the third harmonic. When a rated load is applied, the average torque of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> shaping SPSM loaded with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> current is increased by 17.5<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup> compared with the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Sine}+3\text{rd}$</tex> shaping SPSM which is only loaded with the sine current mentioned above, and is increased by 26.5% compared with the sine shaping motor. The result is consistent with the theoretical calculation and provides theoretical guidance for torque optimization of direct-drive SPSMs.