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

This article is dedicated to the general presentation of the electromagnetic Permeance MagnetoMotive Force (PMMF) model available in MANATEE. For the user-guide articles related to this method, see the howtos section.

### 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

In MANATEE, the PMMF is available for the 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, including uneven rotor slot spacing

### An accurate and fast method

In linear conditions, PMMF model can be as accurate as Finite Element Method (FEM) as shown in MANATEE electromagnetic validation cases on the following topologies:

• Surface Permanent Magnet Synchronous Machines at full load

The advantage of the PMMF model is that magnetic and geometrical asymmetries can easily be included (demagnetization, eccentricities, uneven airgap).

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, otherwise a comparison with FEA (using FEMM from MANATEE) is advised.

### Available post processing

Standard MANATEE post-processings can be directly done after the simulation, for example: