# What is Permeance / MagnetoMotive Force (PMMF) or Winding Function Model (WFM)?

### Introduction to the Permance MagnetoMotiveForce Model

The Permance MagnetoMotiveForce is an analytical method which has been initially developped to compute the radial air gap flux density in electrical machines. Other machine characteristics can be deduced from the air gap flux density such as electromagnetic torque, electromotive force, magnetic losses, Maxwell forces for noise and vibrations analysis.

The principle of the method is to decompose the airgap flux as the product of airgap permeance (the inverse of airgap reluctance, the magnetic equivalent of an electric resistance) and magnetomotive forces (MMF). Magnetomotive forces represent the ampere turns of the excitation winding or magnets.

Different version of the PMMF exists. In particular it can be hybridized in the following ways:

• calculation of permeance using FEA (e.g. FEMM in MANATEE)
• calculation of magnetomotive forces using FEA (e.g. FEMM in MANATEE), subdomain model or magnetic reluctance networks
• calculation to a complex relative permeance using FEA (e.g. FEMM in MANATEE) or subdomain model in order to extend the PMMF model to tangential airgap flux density

The PMMF model can be applied on following topologies:

• Surface PMSM
• Interior PMSM
• Squirrel Cage Induction Machine (SCIM)
• Double Fed Induction Machine (DFIM)
• Wound Rotor Synchronous Machine (WRSM), salient pole or smooth pole

### An accurate and fast method

In linear conditions, PMMF model can be as accurate as Finite Element Method (FEM). The advantage of the PMMF model is that magnetic and geometrical asymmetries can easily be included (demagnetization, eccentricities, uneven airgap, uneven pole or slot position) to perform qualitative studies.

More examples of PMMF validations are given in our ISEF 2019 article.

### Method and Assumptions

In its basic version PMMF model cannot account for the tangential flux density component, which is very important when calculating surface permanent magnet synchronous machine noise and vibrations. However the notion of complex relative permeance can be used to account for tangential field effect. It is recommended to use PMMF model mainly for induction machines.