IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 42, NO. 6, NOVEMBER/DECEMBER 2006 1429 Effect of Paralleling the Stator Coils in a Permanent-Magnet Machine Mohammad S. Islam, Senior Member, IEEE, Sayeed Mir, Senior Member, IEEE, and Tomy Sebastian, Fellow, IEEE Abstract—As low-voltage machines require smaller number of turns per phase compared to higher voltage machines, it is normal to connect the various stator phase coils in parallel to form the phase winding. The placement of various coil sides in the slot and the difference in the field produced by different poles of the rotor magnet can influence the induced voltage in various coils and the impedance of the coils. The difference in the induced volt- ages in the various parallel paths results in a circulating current in the winding and will cause increased losses in the machine. The unequal induced voltage and impedance will cause unequal distribution of stator current in the various parallel paths and will impact the torque-ripple contents. This paper will discuss the effects of these unbalanced parallel paths on the machine performance. Index Terms—Circulating current, harmonics, inductance, parallel paths, permanent-magnet (PM) machines, torque ripple, winding. I. I NTRODUCTION L OW-VOLTAGE machines require smaller number of turns per phase compared to high-voltage machines. It is very common to connect the various coils in parallel to form the phase winding. The placement of various coil sides in the different layers of the stator slot and the difference in the field produced by different poles of the rotor magnet can influence the induced voltage and the impedance in the various coils. If the induced voltages in the various parallel paths for such machines are different, it will result in a circulating current in the winding and will cause increased losses as well as the increased risk of the health of the machine. Also, the unequal induced voltage and impedance of various coils will cause unequal distribution of stator current in the various parallel paths. This imbalance in the parallel paths will cause torque ripple in the developed electromagnetic torque. This paper addresses the effect of unbalanced parallel paths in a permanent-magnet (PM) brushless machine due to the winding asymmetries. The machine performance is quantified as the ripple contents in the developed torque. Similar influence may result from stator and rotor misalignments, magnet dimen- sional variations, etc., which are not the focus of this paper. Paper IPCSD-06-062, presented at the 2005 IEEE International Electric Machines and Drives Conference, San Antonio, TX, May 15–18, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. Manuscript submitted for review July 30, 2005 and released for publication July 27, 2006. The authors are with Delphi Corporation, Saginaw, MI 48601 USA (e-mail: mohammad.islam@delphi.com; sayeed.mir@delphi.com; tomy.sebastian@ delphi.com). Color versions of Figs. 1–6 and 8–24 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2006.882687 Fig. 1. Cross-sectional view of the balanced winding for 27-slot six-pole motor. II. WINDING CONFIGURATIONS IN PM BLDC MOTOR For a three-phase motor, a variety of winding approaches does exist, depending on the slot/pole combination. The indi- vidual coils constituting each phases may be connected in series or parallel. The parallel connection may not be possible for some slot/pole combinations. The phase imbalance issue does exist for both series and parallel connections of the individual coils. For series connection of the coils, the impedance and induced voltage imbalance of the coils do not create any cir- culating currents. The imbalance among the phases is still an issue for torque-ripple performance. With parallel connection of the coils, unbalanced induced voltage and impedance among various parallel paths will cause a circulating current and an unequal sharing of the current among the paths. The severity on the machine performance depends on the degree of imbalance. The phase imbalance in PM machines mainly arises from the following factors: 1) conductor location inside the stator slot; 2) magnet pole-to-pole variation; 3) eccentricity between stator and rotor magnets; and 4) drive- and controller-circuit-induced imbalance [1]. The motor for discussion in this paper has been selected such that it offers parallel connection of the coils. Fig. 1 shows the winding diagram of a 27-slot six-pole motor, where the identical paths are connected in parallel. The phases are denoted as A, B, and C. The subscripts represent the path number and 0093-9994/$20.00 © 2006 IEEE