Electrical Engineering

, Volume 100, Issue 2, pp 565–579 | Cite as

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


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.


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


mmf space harmonic rank

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

Current flowing in the conductors of slot j


Permeance rank


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


Total stator slot number


Number of conductors in stator slot


Conductors number in faulty slot j


Pole pair number

P (H)

Air gap permeance

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

Stator fictive slot depth

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

Stator inner radius


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.EA 4025, LSEEUniv. ArtoisBéthuneFrance
  2. 2.LSETCadi Ayyad UniversityMarrakechMorocco

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