Electrical Engineering

, Volume 100, Issue 2, pp 565–579

# A new approach for torque ripple reduction in a faulty surface permanent magnet synchronous motor by inverse current injection

• Elmehdi Bahri
• Rémus Pusca
• Raphael Romary
• Driss Belkhayat
Original Paper

## Abstract

The aim of this paper is to present a new method to generate stator currents supplying a surface permanent magnets synchronous motor (SPMSM) presenting an asymmetry of the stator windings. This asymmetry may be due to a lack of turns in one of the stator windings or to an inter-turns short circuit. An analytical model of the SPMSM is developed to calculate the current which allows minimizing the torque ripple generated by the asymmetry. This model is based on the combination of the space harmonics of the flux densities of stator and rotor for the generation of the torque. Our study leads to define a stator inverse current system able to compensate the harmonic torque component at the double of the supply frequency. In the experimental tests, several cases of supply were applied and the results confirmed those obtained by the analytical study essentially concerning the amplitude of the inverse current.

## Keywords

Permanent magnet synchronous motor Torque ripple Vibrations Winding asymmetry

## List of symbols

$${\alpha }^\mathrm{s}$$ (rad)

Angular abscissa of the point M, related to the stator reference axis

$${\alpha }^\mathrm{r}$$ (rad)

Angular abscissa of the point M, related to the rotor reference axis

$${\beta }_{j}^\mathrm{s}$$ (rad)

Angular position of the stator slot j

$$\varGamma _{h}$$

Coefficient linked to the linear evolution of the mmf along the slot width

$${\delta }$$ (m)

Half slot width $${\delta }=(1-{r}_\mathrm{d}^\mathrm{s} ){\pi }/{N}_\mathrm{t}^\mathrm{s}$$

$${\varepsilon }_{j}^\mathrm{s}$$ (A)

Magnetomotive force created by conductors contained in the slot j

$${\varepsilon }^\mathrm{s}$$ (A)

Total magnetomotive force generated by all slots

$${\theta }$$ (rad)

Rotor position related to the stator reference axis

$${\mu }_{0}$$ (H/m)

Vacuum permeability

$$\varphi _{j}$$ (rad)

Current phase angle in the slot j

$$\varphi _{n}^\mathrm{r}$$ (rad)

Phase of the rotor flux density space harmonic relating to the fundamental

$$\varphi _{h}^\mathrm{s}$$ (rad)

Phase of the stator flux density space harmonic relating to the fundamental

$${\omega }$$ (rad/s)

Supply angular frequency

$${b}^\mathrm{s}$$ (T)

Stator flux density

$${b}^\mathrm{r}$$ (T)

Rotor flux density

e (m)

Minimum air gap thickness

h

mmf space harmonic rank

$${i}_{j}^\mathrm{s}$$ (A)

Current flowing in the conductors of slot j

$${k}_\mathrm{s}$$

Permeance rank

K

Ratio of faulty turn in one slot

$${l}_{e}^\mathrm{s}$$ (m)

Stator slot width

$${l}_\mathrm{d}^\mathrm{s}$$ (m)

Stator tooth width

$${\hbox {mmf}}$$

Magnetomotive force

$${N}_\mathrm{t}^\mathrm{s}$$

Total stator slot number

$${n}_{e}$$

Number of conductors in stator slot

$${n}_{{j\mathrm{def}}}^{e}$$

Conductors number in faulty slot j

p

Pole pair number

P (H)

Air gap permeance

$${p}^\mathrm{s}$$ (m)

Stator fictive slot depth

$${R}_\mathrm{s}$$ (m)

$${r}_\mathrm{d}^\mathrm{s}$$

Stator toothing ratio $${r}_\mathrm{d}^\mathrm{s} =\frac{{l}_\mathrm{d}^\mathrm{s} }{{l}_\mathrm{d}^\mathrm{s} +{l}_{e}^\mathrm{s}}$$

$${V}\,({\hbox {m}}^{3})$$

Total volume of the air gap

$$W_\mathrm{mag}$$ (J)

Magnetic co-energy

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## Authors and Affiliations

• Elmehdi Bahri
• 1
• 2
• Rémus Pusca
• 1
• Raphael Romary
• 1
• Driss Belkhayat
• 2
1. 1.EA 4025, LSEEUniv. ArtoisBéthuneFrance