Abstract-Analytical calculation methods for all the major components of the synchronous inductance of tooth-coil permanentmagnet synchronous machines are reevaluated in this paper. The inductance estimation is different in the tooth-coil machine compared with the one in the traditional rotating field winding machine. The accuracy of the analytical torque calculation highly depends on the estimated synchronous inductance. Despite powerful finite element method (FEM) tools, an accurate and fast analytical method is required at an early design stage to find an initial machine design structure with the desired performance. The results of the analytical inductance calculation are verified and assessed in terms of accuracy with the FEM simulation results and with the prototype measurement results.Index Terms-Fractional slot winding, inductance calculation, leakage inductance, permanent-magnet synchronous machine (PMSM), tooth coil.

Permanent magnet synchronous machines with fractional-slot non-overlapping windings (FSPMSM), also known as tooth-coil winding permanent magnet synchronous machines (TCW PMSM), have been under intensive research during the latest decade. There are many optimization routines explained and implemented in the literature in order to improve the characteristics of this machine type.This paper introduces a new technique for torque ripple minimization in TCW PMSM. The source of torque harmonics is also described. The low order torque harmonics can be harmful for a variety of applications, such as direct drive wind generators, direct drive light vehicle electrical motors, and for some high precision servo applications.The reduction of the torque ripple harmonics with the lowest orders (6 th and 12 th ) is realized by machine geometry optimization technique using finite element analysis (FEA). The presented optimization technique includes the stator geometry adjustment in TCW PMSMs with rotor surface permanent magnets and with rotor embedded permanent magnets. Influence of the permanent magnet skewing on the torque ripple reduction and cogging torque elimination was also investigated. It was implemented separately and together with the stator optimization technique. As a result, the reduction of some torque ripple harmonics was attained.

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Wind is one of the most compelling forms of indirect solar energy. Available now, the conversion of wind power into electricity is and will continue to be an important element of energy self-sufficiency planning. This paper is one in a series intended to report on the development of a new type of generator for wind energy; a compact, high-power, direct-drive permanent magnet synchronous generator (DD-PMSG) that uses direct liquid cooling (LC) of the stator windings to manage Joule heating losses. The main param-eters of the subject LC DD-PMSG are 8 MW, 3.3 kV, and 11 Hz. The stator winding is cooled directly by deionized water, which flows through the continuous hollow conductor of each stator tooth-coil winding. The design of the machine is to a large degree subordinate to the use of these solid-copper tooth-coils. Both steady-state and timedependent temperature distributions for LC DD-PMSG were examined with calculations based on a lumpedparameter thermal model, which makes it possible to account for uneven heat loss distribution in the stator conductors and the conductor cooling system. Transient calculations reveal the copper winding temperature distribution for an example duty cycle during variable-speed wind turbine operation. The cooling performance of the liquid cooled tooth-coil design was predicted via finite element analysis. An instrumented cooling loop featuring a pair of LC tooth-coils embedded in a lamination stack was built and laboratory tested to verify the analytical model. Predicted and measured results were in agreement, confirming the predicted satisfactory operation of the LC DD-PMSG cooling technology approach as a whole.

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