### Description

The electrical module EL.PMSM for permanent magnet synchronous machines calculates the following quantities:

stator currents

Id and Iq current

average electromagnetic torque, active and reactive power

power factor and efficiency

These calculation are done using an **equivalent electrical circuit** extended to all harmonics (PWM time harmonics and back emf space harmonics):

Without harmonics and without iron loss the fundamental equivalent circuit that is used is:

The elements of the equivalent circuit include

stator resistance including skin effect

stator leakage inductance including skin effects

magnet flux linkage

magnetization inductance

iron loss resistance

The stator resistance is calculated using analytical geometrical model of the stator conductors, handling both random and formed windings, and any winding type. Some analytical skin effect factors are used depending on the conductor shape and arrangement.

The stator leakage inductance can be calculated analytically or numerically using FEMM.

The inductances along d-axis and q-axis can be calculated analytically without saturation, or numerically using non linear magnetostatic simulation under FEMM.

The fundamental back electromotive force (emf) can be calculated using semi analytical models or FEMM. For more details please refer to the back emf calculation article.

The saturated B(H) curve can be defined using numerical values in a .txt file, or using an analytical model. The analytical model can be fit to a given B(H) curve using a GUI interface. For more details please refer to the B(H) curve setup article.

All the parameters of the fundamental equivalent circuit can also be enforced by the user if necessary.

### Application to e-NVH

The electrical circuit is useful when the noise and vibrations due to PWM has to be quickly estimated.

### Validations

Several validations can be found in the electrical part of validation cases, such as:

### Plot commands

To plot the equivalent circuit parameters the following plot commands are available: