An improved winding function theory (IWFT) is presented in this paper, which can be also used to calculate the self and mutual inductances of large air-gap electric machines, while accurately considers the air-gap length function and the magnetic saturation in iron parts, simultaneously. In IWFT, the radial length of flux path in different points inside air-gap is calculated using the conformal mappings (CMs). The total air-gap length is the resultant of air-gap length at differential elements in radial direction. A modified inverse air-gap function is then presented for a typical cage rotor induction motor (CRIM) and a typical surface permanent magnet synchronous motor (SPMSM), which considers the real paths of flux lines in slotted air-gap. The high accuracy of these modified inverse air-gap functions are verified through comparing with the corresponding results obtained through finite element method (FEM). To consider the magnetic saturation, a virtual winding function as a 2-D function is introduced in this paper, which can consider the magneto-motive force (MMF) drops in iron parts of stator and rotor obtained through magnetic equivalent circuit (MEC) model. By using IWFT, dependent on the structure of relevant motor, a 2-D or 3-D lookup table is pre-calculated and stored for self/mutual inductances and their derivatives, and they are then used to model the running condition of CRIM and SPMSM under different loading conditions. Finally, the accuracy of IWFT results are verified by comparing with the corresponding results obtained through FEM.
