Electrical Calculations

Electrical Calculations and Iron Losses

Electrical Design

The electrical design of standard machines based on magnetically equivalent circuits, know-how and measured values is fast and easy. After an initial 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 programs mostly written in Fortran or programmed with Simulink; these have been calibrated with measurement results. Developers of small and medium standard motors prefer to use commercial tools.
The magnetic field of new electrical machines should be calculated with Finite Element Analysis (FEA). It allows precise localization of the distribution of the iron losses. For the concept of a long motor, 2D calculations are usually sufficient. For large machines, it might be necessary to perform these calculations for several sections. For more complex and detailed analysis, the calculations should be performed in 3D using commercial software.

Magnetic field of an asynchronous motor
Magnetic field of an asynchronous motor (© Institute for Energy and Automation, Technical University of Berlin)

Localization of the Losses

The allocation of the electrical losses to the locations of generation 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. However, good knowledge of the locations of heat generation is required for temperature calculations.

Losses in electrical machines are divided into ohmic losses (copper losses), magnetic core losses (iron losses), mechanical losses (ventilation losses, bearing losses), and stray load losses. The copper losses are the dominant losses for most machines; they can be determined directly from resistance and current, taking the skin effect into account. The losses in the stator and rotor windings as well as the losses in the stator yoke and in stator teeth caused by the fundamental field can be homogeneously localized in the associated volumes. With the help of existing FEA magnetic field calculations, the iron losses for larger machines can be assigned even more precisely according to the source.

Iron Losses and Supplementary Losses

The iron losses can be calculated analytically using the equations of Steinmetz, Howe or Bertotti. The iron losses are calculated as the specific losses of the steel [W / kg] multiplied by the weight and an empirical coefficient. The specific loss is given in the steel data sheet for 1.5 T and 50 Hz; this value must be corrected to the design flux density and frequency. The empirical coefficient for determining the actual iron loss relates to manufacturing defects, strength and type of lamination, and harmonic waves. It is usually between 1.3 and 2.0.

It is much more difficult to calculate and localize the stray load losses. Electrical engineers still struggle with this topic and are usually unable to provide satisfactory input for the thermal calculation. Load-dependent stray load losses are caused by the converter supply. Load-independent stray load losses of the magnetic circuit occur in the air gap. Determining the stray load losses during measurements proves to be difficult, especially for fast-rotating machines. A typical method for determining stray load losses is to subtract the measured iron losses from the calculated hysteresis and eddy current losses. Unfortunately, with this method, all measurement and calculation errors are included in the stray load losses. In addition, items related to hysteresis and eddy current losses that the traditional equations do not cover, such as minor hysteresis loops, also fall into the stray load losses category.

Distribution of the flux density for a machine with salient poles
Distribution of the flux density for a machine with salient poles

Multiphysics: Coupling of Electromagnetic and Flow Calculations

Commercial tools usually advertise multiphysics; do we really need the coupled calculation of electromagnetism, flow and heat transfer? The iron losses are practically independent of temperature. Only the copper losses increase with temperature, due to the increase in resistance. If measurement results of the winding temperature are available, the losses should be determined using this value. Otherwise a formula can easily be written in the CFD tool to estimate the winding losses based on the calculated winding temperature. A coupling between the FEA electromagnetism tool and the thermal calculation tool is not strictly necessary.