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An analytical technique for predicting the instantaneous magnetic field distribution in the airgap region of radial-field topologies of brushless permanent magnet dc motors, under any specified load condition and accounting implicitly for the stator winding current waveform and the effect of stator slot-openings, has been developed. It is based on the superposition of the component fields due to the permanent magnet and the stator excitation. In this paper, which is one of a series of four, a 2-d analytical method for predicting the opencircuit airgap field distribution in both internal and external rotor radial-field motor topologies is presented. It involves the solution of the governing field equations in polar coordinates in the annular airgaplmagnet region of a multi-pole slotless motor in which the magnets are assumed to have uniform radial magnetization and a constant relative recoil permeability. Results for various radial-field motors are compared with predictions from corresponding finite element analyses.

Abstract-A general analytical technique predicts the magnetic field distribution in brushless permanent magnet machines equipped with surface-mounted magnets. It accounts for the effects of both the magnets and the stator windings. The technique is based on two-dimensional models in polar coordinates and solves the governing Laplacian/quasi-Poissonian field equations in the airgap/magnet regions without any assumption regarding the relative recoil permeability of the magnets. The analysis works for both internal and external rotor motor topologies, and either radial or parallel magnetized magnets, as well as for overlapping and nonoverlapping stator windings. The paper validates results of the analytical models by finite-element analyses, for both slotless and slotted motors.

This paper presents a new direct active and reactive power control (DPC) of grid-connected doubly fed induction generator (DFIG)-based wind turbine systems. The proposed DPC strategy employs a nonlinear sliding-mode control scheme to directly calculate the required rotor control voltage so as to eliminate the instantaneous errors of active and reactive powers without involving any synchronous coordinate transformations. Thus, no extra current control loops are required, thereby simplifying the system design and enhancing the transient performance. Constant converter switching frequency is achieved by using space vector modulation, which eases the designs of the power converter and the ac harmonic filter. Simulation results on a 2-MW grid-connected DFIG system are provided and compared with those of classic voltage-oriented vector control (VC) and conventional lookup table (LUT) DPC. The proposed DPC provides enhanced transient performance similar to the LUT DPC and keeps the steady-state harmonic spectra at the same level as the VC strategy. Index Terms-Constant switching frequency, direct power control (DPC), doubly fed induction generators (DFIGs), sliding-mode control (SMC), wind power. NOMENCLATURE I s , I r Stator, rotor current vectors. L m Mutual inductance. L s , L rStator, rotor self-inductances. L σ s , L σ r Stator, rotor leakage inductances. P s , Q s Stator output active and reactive powers. R s , R r Stator, rotor resistances. U s , U r Stator, rotor voltage vectors. θ r Rotor angle. ψ s , ψ r Stator, rotor flux linkage vectors. ω 1 , ω r , ω slip Stator, rotor, and slip angular frequencies. Subscripts α s , β sStationary α s β s axis. α r , β r Rotor α r β r axis.

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