Core Loss for Transient Solvers

Core loss allows the solver to find the total core loss on an object, or group of objects due to the distribution of the electric or magnetic field in the design.

For frequency domain applications:

At a given frequency, the core loss for electrical steel is based on the following expression:

where

• K_h is the hysteresis coefficient.

• K_c is the classical eddy coefficient.

• K_e is the excess or anomalous eddy current coefficient due to magnetic domains.

• B_max is the maximum amplitude of the flux density.

• f is the frequency.

Similarly, the power ferrite core loss is based on the following expression:

where

• C_m is a constant value determined by experiment.

• f is the frequency.

• B_max is the maximum amplitude of the flux density.

For transient (time domain) applications, the above expressions need to be modified in the following ways:

In the frequency domain, the core loss for power ferrites is given by the above formula, where C_m, x, and y are measured based on sinusoidal B(t) waveform. If x = 1, y = 2, and C_m= K_h, the formula for power ferrite is that for hysteresis loss. If x = y = 2, and C_m= K_c, it corresponds to classic eddy loss. If x = y = 1.5, and C_m= K_e, it becomes excess loss. Therefore, the formula of power loss for ferrite can be used to describe all individual components for core loss for both electric steel and power ferrite.

Based on the formula for ferrite core loss in the frequency domain, the following expression can be derived to compute core loss in the time domain:

where H_irr is the irreversible component of the magnetic field strength H_irr= H-H_rev, with H_rev being the reversible component of H, which can be obtained from the BH curve based on B. To obtain H_irr, an equivalent ellipse is used with the property that the area of the ellipse equals the are of the original hysteresis curve. This explains why, in the process of obtaining the hysteresis loss, the B(H) curve and K_h coefficient are used.

The equation of the equivalent ellipse is given by

where

and B_m is the amplitude of a minor B-H loop which is obtained based on continuously updated history information of the magnetic flux density, which allows the algorithm to account for the contribution of minor loops to the core loss.

With H_irr and dB/dt, the loss can be easily evaluated. For the other components of the core loss (that is, different combinations of x and y), unknown coefficients can be derived using the property that the formula for core loss in the time domain gives the same result as the formula for core loss applied for the frequency used in the experiment.