In the electromagnetic field simulation of modern servo drives, the computation of higher time and space harmonics is essential to predict torque pulsations, radial forces, ripple torques and cogging torque. Field computation by conformal map ping (CM) techniques is a time-effective method to compute the radial and tangential field components. In the standard CM approach, computational results of cogging torque simulations as well as overload operations observe deviations to nonlinear finite element (FE) simulations due to the neglection of slot leakage and saturation effects. This paper presents an extension of the classical CM. Additional CM parameters are computed from single finite element computations so as to consider both effects listed above in the model over a wide operation range of the electrical drive. The proposed approach is applied to a surface permanent magnet synchronous machine (SM-PMSM), and compared to numerical results obtained by finite element analysis (FEA). An accuracy similar to that of FE simulations is obtained with however the low computation time that is characteristic for analytical models.