Low-speed Permanent-magnet Machines Research Articles

Effects of Loading and Slot Harmonic on Radial Magnetic Forces in Low-Speed Permanent Magnet Machine With Concentrated Windings

This paper investigates the effects of loading and slot harmonic on radial magnetic forces in a low-speed permanent magnet (PM) machine with non-overlapping concentrated windings. Vibration level of the PM machines with concentrated windings can be potentially higher compared with that of the traditional machines with distributed windings. It is mainly due to the presence of low-order spatial harmonics in radial force density distribution. In this paper, magnetic flux density distribution in the air-gap of a 120-slot/116-pole machine is computed using finite-element method. Maxwell’s stress tensor method is then employed to calculate radial and tangential forces in the air-gap. Flux density and radial and tangential force distributions are studied in different loading conditions and the effect of ${d}$ - and ${q}$ -axis currents are investigated. It is shown how the lowest mode of vibration is produced by different harmonic pairs in the flux density. It is found that ${d}$ -axis current significantly changes the amplitude of the lowest spatial harmonic of the radial force distribution and consequently the vibration behavior. The main reason is found to be the changes in the amplitude of the slot harmonic, which is heavily affected by loading. Experimental tests are carried out to compare the vibration level of a PM generator supplying resistive, inductive, and capacitive loads. There is a good agreement between simulations and experimental results.

Slot Harmonic Effect on Magnetic Forces and Vibration in Low-Speed Permanent-Magnet Machine With Concentrated Windings

In this paper, the influence of slot harmonics on magnetic forces and vibration is studied in a 120-slot/116-pole low-speed PM machine at no-load. It is shown how the lowest mode of vibration is produced at no-load due to slotting. Comparing the cases of open slots, semi-closed slots and magnetic wedges, the effect of slot closure on radial forces and torque production capability is discussed. Magnetic flux distribution in the airgap is computed using finite element analysis. Spatial harmonics due to slotting are investigated in different cases. Maxwell's stress tensor is employed to calculate radial and tangential components of the force density in the airgap. Spatial distribution of the total forces on the teeth and also time-dependent force waveform on one tooth are analyzed and discussed for different cases. It is shown how the magnitude of the lowest mode of vibration is reduced in the case of using semi-closed slots and magnetic wedges. Tangential force density distribution and torque production capability are also discussed. Structural analysis is presented to compute the maximum amplitude of the stator deformations due to the radial forces. Experimental results of the prototype generator are presented verifying the existence of the lowest mode of vibration at no-load because of the slot harmonics.

Selection of Main Design Variables for Low-Speed Permanent Magnet Machines Devoted to Renewable Energy Conversion

Permanent magnet machines are great candidates to be chosen as the preferred option in many low-speed applications. The improvement in the magnetic material's characteristics and the reduction in their cost are the key factors for this trend. The level of irreversibility achieved by a permanent magnet machine, i.e., the losses for a given power output, may be reduced to almost half of that got by an electrically excited synchronous machine, being the stator copper loss virtually the only source. The efficiency is, therefore, directly related with the ratio between the stator copper loss and the torque developed through the machine's air gap, being the minimization of this ratio the way to get a better machine design, once some other design constraints are fixed. In this paper, the authors provide a methodology devoted to the selection of the main dimensions of a permanent magnet machine in order to achieve an optimal machine's performance in low-speed applications, reaching a set of conclusions that may be applied to any machine of this kind.

Force Density Limits in Low-Speed Permanent-Magnet Machines Due to Saturation

This work discusses the practical limits imposed by magnetic saturation for the force density in low-speed permanent-magnet electric machines. The force density dependence on current density and slot depth is investigated with the aid of finite-element modeling. For saturation reasons, shallow slots are more favorable for achieving high force densities. However, for thermal reasons, deeper slots become favorable. Therefore, an optimum slot depth that maximizes the force density for each current density level exists. The maximum allowable slot depth range for four low-speed applications has been identified for a given maximum motor diameter.

Force Density Limits in Low-Speed PM Machines Due to Temperature and Reactance

This paper discusses two of the mechanisms that limit the attainable force density in slotted low-speed permanent-magnet (PM) electric machines. Most of the interest is focused on the force density limits imposed by heating of the windings and by stator reactance. The study is based on analytical models for the force and reactance calculations and a lumped parameter thermal model. It is found that in a machine with an indirectly cooled stator, it is difficult to achieve a force density greater than 100 kN/m/sup 2/ due to temperature limits. A high force density is achieved by using deep slots, which lead to high reactance. The high reactance severely increases the converter kilovolt-ampere requirement and total system cost. It is also shown that the cost caused by the high reactance will also limit the force density reached. In machines with one slot per pole per phase, the reactance limited the useful slot depth to approximately 200 mm. However, in machines having a greater number of slots per pole per phase the reactance becomes no longer an important limiting factor for the slot depth and force density.