# Electrical calculations

## Electrical design

Losses in electric machines are ohmic losses (winding copper losses), re-magnetization (iron losses), mechanical losses (ventilation losses and bearing losses) and supplementary losses. The copper losses are usually the largest. The copper losses of the stator winding and pole winding can be directly calculated based on the current and the voltage waveforms including skin effect. The magnetic field and iron losses can be analytically calculated based on the equations of Steinmetz, Howe or Bertotti.

The electrical design of standard machines based on magnetically equivalent circuits, know-how and measured values is fast and easy to perform. After a rough first dimensioning, the optimization can be carried out with the calculation of different geometry variants and operation points. Developers of large generators prefer to use their in-house program mostly written in Fortran or programmed with Simulink; these have been tuned with measurement results. Developers of small and medium standard motors prefer to use commercial tools.

Magnetic field of an asynchronous motor
(© Institute for energy and automation, technical university in Berlin)

The magnetic field of new electrical machines should be calculated with the Finite-Elements Analysis. It allows to precisely localize the distribution of the iron loss. For the concept of a long motor, 2D calculations are usually good enough. For large machines, it might be necessary to perform these calculations for several sections. For more complex and detailed analysis, the calculations should be made in 3D using commercial software.

## Localization of the losses

The allocation of the electrical losses to the places of production is not a subject of focus during the concept phase; the project members are mostly interested in the values of the total losses and the corresponding efficiency. Good knowledge of the locations of production is however required for temperature calculation.

It is much more difficult to calculate and to localize the supplementary losses. Load-dependent supplementary losses are due to the frequency converter. Load-independent supplementary losses of the magnetic field occur on the rotor and stator side of the air gap. The supplementary losses can be calculated and localized using formulas from freely-available literature.

Distribution of the flux density for a machine with salient poles

Coupling of Electromagnetic and Flow Calculations
Commercial tools usually advertise for Multiphysics, do we really need it? The iron losses hardly depend on the temperature, only the copper losses increase with the temperature as the resistance increases. The losses should be calculated with measured values of the temperature, if available; otherwise, an initial temperature must be guessed. If the calculated temperature differs then one can simply recalculate the resistance and the copper losses with the calculator. The thermal calculation should be then restarted.