Targeting at demagnetization fault, this paper establishes a new analytical model (AM) and carries out comprehensive analysis for the maximum torque per ampere (MTPA)-driven permanent magnet motors (PMM) with distributed lap windings. First, the back electromotive force (B-EMF) and dynamics of the PMM are modeled based on the working properties of the motor and the Faraday's law of electromagnetic induction. In this process, the advantages include that the PMM is regarded as a motor, all conductors are taken into consideration, the magnetic field generated by the permanent magnets is trapezoid, and the control strategy is integrated. Second, the amplitudes and harmonics of the B-EMF and currents are analyzed theoretically based on the proposed model, revealing the system performance before and after uniform and partial demagnetization faults. Finally, the proposed motor model and the motor analysis results are validated by finite element simulation which is conducted on a PMM prototype with 24 slots and 4 poles.