This paper proposes a model order reduction (MOR) technique based on the proper orthogonal decomposition method, to speed up nonlinear magnetostatic analysis of inverter-driven electrical machines. In this method, a set of solutions of the original problem is obtained at relatively large intervals, covering the whole cycle. The solutions, known as snapshots, are then used for the linearization as well as the order reduction of the matrices at the intervals. The reduced linearized matrices are then interpolated for time instance within the strides, supplemented with initial guess obtained by interpolating the snapshots. The method enormously reduces the number of matrix projections. Furthermore, it limits the number of the Newton-Raphson iteration to one. The results of applying the method on the magnetostatic analysis of interior permanent magnet motor shows that the method is several time faster than the conventional MOR with almost the same accuracy.