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Running up and pulling into step of PM line-start motors with surface-mounted magnets

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Abstract

Permanent magnet (PM) synchronous motors with starting cage, already developed in the 1960s for variable-speed textile drives, become increasingly important as energy-efficient PM line-start motors. Differing from the standard design with integrated magnets, a rotor design with surface-mounted magnets is presented. In the planning and design phase of drives with PM line-start motors, the simulation of switching on, running up, and pulling into step is essential. An analytical model is presented leading to voltage and mechanical differential equations that have to be solved simultaneously. Based on a prototype, the suitability of the presented model is demonstrated by direct comparison of simulated to measured data. Besides, the mean influence factors of the pulling-into-step behavior are identified and discussed.

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Abbreviations

p :

Number of fundamental pole pairs

\(\tau _{\mathrm{p}}\) :

Pole pitch

\({\delta }_{\mathrm{g}}\) :

Air-gap between stator and rotor core

\({\delta }_{0}\) :

Clearance between banding and stator core

\({\delta }''\) :

Effective air-gap

\({k}_{\mathrm{C}1, 2}\) :

Carter’s coefficient stator/rotor

\({k}_{\mathrm{S}}\) :

Saturation coefficient

\({\alpha }_{\mathrm{p}}\) :

Pole-pitch factor of PM

\({h}_{\mathrm{banding}}\) :

Banding thickness

\({h}_{\mathrm{M}}\) :

Magnet thickness

\({\mu }_{0}\) :

Permeability of vacuum

\({\mu }_{\mathrm{SE}}\) :

Permeability of rare earth magnets

\({\mu }_{\mathrm{FE}}\) :

Permeability of laminated core

\({m}_{1, 2}\) :

Number of stator/rotor phases

\({N}_{1, 2}\) :

Number of stator/rotor slots

\({x}_{1, 2 }\) :

Coordinate of stator/rotor

\({w}_{1}\) :

Number of turns per phase

\({\xi }_{1}\) :

Fundamental winding factor

\({\xi }_{\mathrm{Schr}}\) :

Skew factor

l:

Laminated core dimension

\({\gamma }_{\mathrm{stag}}\) :

Stagger angle

\({\omega }_{1}\) :

System angular frequency

\({R}_{1,2}\) :

Resistance of stator/rotor

\({L}_{1,2}\) :

Cyclic inductance of stator/rotor

M :

Mutual inductance

\({R}_{\mathrm{bar}}\) :

DC resistance of cage bar

\({L}_{\sigma \mathrm{bar} }\) :

DC leakage inductance of cage bar

\({R}_{\mathrm{S1},\ldots ,\mathrm{S4} }\) :

Resistance elements of R-L network

\({L}_{\mathrm{S1},\ldots ,\mathrm{S4}}\) :

Inductance elements of R-L network

\(\underline{{i}}_{{m21},\ldots ,24}\) :

Positive-sequence rotor current component of R-L network

\({U}_{\mathrm{P}}\) :

Synchronous generated voltage

\(\Psi _{\mathrm{P}}\) :

Fundamental flux linkage

\(\gamma \) :

Mechanical angle between stator and rotor

\(\underline{{u}}_{1{m}}\) :

Positive-sequence stator voltage component

\(\underline{{i}}_{1{m}}\) :

Positive-sequence stator current component

\(\underline{{i}}_{2{m}}\) :

Positive-sequence rotor current component

\({m}_{{i}}\) :

Intrinsic torque

W :

Load torque

J :

Rotating mass

c :

Spring constant

d :

Damping torque coefficient

\(\phi \) :

Mechanical angle

\(\Omega \) :

Mechanical angular velocity

\(\sigma \) :

Heyland factor

\({M}_{\mathrm{b}}\) :

Breaking torque

\(\underline{{i}}^*\) :

Complex conjugate of i

References

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Huth, G., Fischer, R. Running up and pulling into step of PM line-start motors with surface-mounted magnets. Electr Eng 97, 13–24 (2015). https://doi.org/10.1007/s00202-014-0308-z

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  • DOI: https://doi.org/10.1007/s00202-014-0308-z

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