The spoke-array PMVM desirably introduces higher torque density compared to other PM arrangements with the disadvantage of higher cogging torque. The cogging torque can be decreased using a V-shaped PMVM structure. This paper proposed a special K-shaped VPM machine aiming to combine the advantages of different PM arrangements by achieving high torque density, low cogging torque, enhanced efficiency and power factor, and achieving wide constant torque-speed region. The FEA revealed a torque-density of 36.7 kN·m/m3, a cogging torque of almost 5%, and an efficiency of 91.2%. In addition, the power factor was 0.87, which is comparable with conventional PM synchronous machines. These promising features make the proposed machine a good choice for EV applications. Considering the complex behavior of magnetic flux lines in the rotor core and air-gap region, a conformal mapping-based nonlinear harmonic model was established for predicting the operating features analytically, providing further theoretical basis and validation. The contribution of the modeling method includes a special mapping function to simplify the shape of PM housing, deriving harmonic distributions of magnetic fields in different regions, and an accurate flowchart with a high convergence rate. A K-shaped PMVM with 12 slots/8 pole pairs on the stator and 16 pole pairs on the rotor was prototyped, and its performance was measured. The accuracy of the proposed harmonic model was verified by comparing the results with the FEA and experimental results. The calculated error was below 5% for all studied waveforms, which proved the effectiveness of the analytical model.