Fault‐tolerant permanent magnet synchronous machine – phase, pole and slot number selection criterion based on inductance calculation

Abstract

Interest in permanent magnet synchronous machines for safety-critical applications has been increasing over the years. One of the most common methods for providing fault tolerance to a permanent magnet machine is the active control from the drive side. This method requires designing machines with the lowest possible mutual coupling between phases and a selfinductance that is high enough to limit the fault currents. Fractional-slot concentrated windings have been proposed as the most advantageous solution to meet these requirements. When comparing the numerous combinations of phases, poles and slots that give rise to a fractional-slot concentrated winding, the usual criteria only focus on obtaining a single-layer winding and do not actually consider the relationship between the self-inductance and the mutual inductance between phases. Moreover, they give no recommendations regarding the optimal number of phases from a magnetic point of view. The present work aims to cover this gap by obtaining analytical expressions for the calculation of the inductances in a permanent magnet machine. The derived expressions are investigated regardless of the geometry of the machine, and the criteria for selecting the most promising combinations in terms of the machine's fault tolerance are extracted. Nomenclature List of acronymsFEA finite-element analysis FEM finite-element method FSCW fractional-slot concentrated winding GCD greatest common divisor (mathematical function) ISA integrated starter alternator MMF magneto motive force PMSM permanent magnet synchronous machine List of symbols A magnetic vector potential [T·m] B magnetic flux density [T] H magnetic field intensity [A/m] L b base inductance [H] L ii phase self-inductance [H] L ij mutual inductance between phases [H] N s number of turns wound in series per phase Q number of stator slots R r rotor outer radius [m] R s stator inner radius [m] W magnetic energy [J] B slot width [m] b 0 slot opening width [m] g air-gap length [m] h slot height [m] h 0 slot opening height [m] i slot slot current [A] j slot slot current density [A/m 2 ] k w, s1 fundamental winding factor l ef effective length of the machine [m] m number of phases p number of pole pairs q number of slots per pole and phase t electric periodicity of the machine, GCD( p, Q) w magnetic energy density [J/m 3 ] α 0 slot opening angle [rad] α slot slot angle [rad] β slot leakage-related dimensionless parameter γ slot leakage-related dimensionless parameter δ air-gap inductance-related dimensionless parameter l permeance coefficient μ 0 permeability of free space [H/m] j relationship between air-gap inductance coefficients ς relationship between slot inductance coefficients f figure of merit

Modularity techniques in high performance permanent magnet machines and applications

“…It clearly shows that each phase of this modular machine is also electrically, thermally and magnetically isolated from other phases. Since the alternate teeth wound winding was proposed, this kind of winding has been investigated for quite a long time [11], [52][53][54][55][56][57][58][59]. Besides 6 phases, it can also be applied to PM machines with other phase numbers [60], [61], as shown in Fig.…”

Decoupling of the Secondary Saliencies in Sensorless PMSM Drives using Repetitive Control in the Angle Domain

“…Papers [20], [24] pointed out that the mutual inductances of a concentrated-winding PMSM account for approximately one-tenth of the self-inductance or even less. The major difference between the distributed windings and the concentrated windings is the mutual-inductance.…”

“…The major difference between the distributed windings and the concentrated windings is the mutual-inductance. In the design of the concentrated windings, the low mutual-inductance between the phases is required [24]. Therefore, the mutual-inductance is ignored in this analysis.…”

Fault‐tolerant structure for cascaded H‐bridge multilevel inverter and reliability evaluation

“…Therefore, fault-tolerant systems have attracted lots of interests in recent years [2][3][4][5]. Reliability calculations in power electronic systems are considered [6] and many solutions have been proposed to make power electronic converters and drive systems more reliable and fault tolerant [7][8][9][10][11][12][13].…”