Model Hysteresis and Eddy Current Losses in an Iron Core Using BH Curve Data

Since R2024b

This example shows how to model hysteresis and eddy current losses of an iron core using the magnetic core block. This block represents a magnetic core with magnetic hysteresis and implements the Jiles-Atherton model. You can parameterize the block using BH curve data or Jiles-Atherton parameters.

Model Overview

Open the modelHysteresisEddyTransformerLosses model.

myModel = 'modelHysteresisEddyTransformerLosses';
open_system(myModel);

In this example, you model an electrical transformer with hysteresis and eddy current losses by using the Magnetic Core block only.

Plot the BH curve using a fixed frequency and variable amplitude magnetic field intensity input.

modelHysteresisEddyTransformerLossesPlotBHCurve(myModel, 'Amplitude', 'Variable', 'Frequency', 'Fixed', 'ModelEddyLosses', 'false', 'stopTime', 500/f);

The model simulates the inner and saturated hysteresis cycles. The curve is within bounds of the saturation values.

Model Hysteresis Losses

Set up the model to simulate without eddy losses and have a variable frequency and fixed amplitude magnetic field intensity input. Plot the BH curve.

modelHysteresisEddyTransformerLossesPlotBHCurve(myModel, 'Amplitude', 'Fixed', 'Frequency', 'Variable', 'ModelEddyLosses', 'false');

For a magnetic field intensity with a fixed amplitude, the BH curve is independent of frequency. You can see this because the curves for magnetization cycles at different frequencies overlap. The hysteresis losses are proportional to the area inside the BH curve and to the frequency of the input signal. The input signal is a chirp signal which has a frequency that increases linearly with simulation time so the hysteresis losses must also increase approximately linearly with simulation time. Plot the hysteresis losses over time to verify this.

modelHysteresisEddyTransformerLossesPlotLosses

The energy is zero until 5e-2 s, which is the averaging period for hysteresis losses. Once the block start averaging the losses, they increase linearly with the frequency.

Eddy Losses

Increase the Thickness of laminations parameter so the eddy losses are significant.

laminationThickness = 1.2; % mm

Set up the model to simulate both hysteresis and eddy current losses and have a variable frequency and fixed amplitude magnetic field intensity input. Plot the BH curve.

modelHysteresisEddyTransformerLossesPlotBHCurve(myModel, 'Amplitude', 'Fixed', 'Frequency', 'Variable', 'ModelEddyLosses', 'true');

For a fixed amplitude, the curve does not overlap when the frequency increases. The curve becomes wider with the frequency. Given the increase in frequency and the area inside the curve, the eddy losses must increase faster than linearly with the frequency of the magnetization cycle. Plot the hysteresis and eddy current losses to verify this.

modelHysteresisEddyTransformerLossesPlotLosses

Both the hysteresis and eddy current losses are counted after the first averaging period. The eddy losses are smaller than the hysteresis losses at low frequencies, but they increase faster with frequency.

Reduce Eddy Losses

You can avoid eddy current losses by laminating the transformer iron cores. Decrease the Thickness of laminations parameter and then plot the BH curve and the eddy losses over time.

laminationThickness = 0.3; % [mm]
modelHysteresisEddyTransformerLossesPlotBHCurve(myModel, 'Amplitude', 'Fixed', 'Frequency', 'Variable', 'ModelEddyLosses', 'true');

modelHysteresisEddyTransformerLossesPlotLosses

With thinner laminations, The BH curve is not as wide, and the eddy losses grow at a slower rate.