Winding Losses
The calculation of winding losses is done using an algorithm that takes in the current waveform and spits out the total losses.
The first step is to detect and define the conduction modes inside one period: for example, in a flyback we will have two conduction modes: when only the primary is conducting, where we will have skin and proximity losses on the primary, but only proximity losses on the secondaries; and when only the secondaries are conducting, where we will have skin and proximity losses on the secondaries, but only proximity losses on the primary.
As the existing models and equations are developed for sinusoidal waveforms, we must break down the corresponding waveform and extract its harmonics using a Discrete Fourier Transform. With these harmonics we are now able to apply the models to calculate the losses for each harmonic, adding them in the end to have the total losses.
Depending on the magnetic configuration we use different models to calculate the harmonic losses, including DC, skin, external and internal proximity losses:
Wojda’s model [1] in the case winding windows with only one winding on them (e.g., inductors or top-down transformers) made of solid sound, foil or Litz wires, as it is derived from Dowell’s and Ferreira’s work and has good accuracy with non-interleaved windings.
Albach’s model [2] in the case of winding windows with more than one winding on them (e.g,, interleaved transformer). Albach’s model is able to calculate the H field distribution along the radial component for any combination of layers, even with different windings and currents, making it ideal for interleaved designs.
Alternatively to Wojda’s model, we use Payne’s model [3] for edge-wound inductors, as he has empirically investigated the losses mechanisms in this kind of windings.
Once the losses of each harmonic and conducting mode has been calculated, we add them up together to obtain the ditribution of total losses.
Finally, once we have the total losses, the AC resistance is obtained by calculating the equivalent resistance that, for our primary RMS current, would give us the total losses obtained before.
[1] R. P. Wojda and M. K. Kazimierczuk, "Winding Resistance and Power Loss of Inductors With Litz and Solid-Round Wires," in IEEE Transactions on Industry Applications, vol. 54, no. 4, pp. 3548- 3557, July-Aug. 2018, doi: 10.1109/TIA.2018.2821647.
[2] M. Albach, "Two-dimensional calculation of winding losses in transformers," 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018), 2000, pp. 1639-1644 vol.3, doi: 10.1109/PESC.2000.880550. It presents a calculation of the winding losses based on the field distribution in the winding area, with which the skin and proximity losses in each turn are analytically calculated.
[3] Payne, Alan 2021/05/04 - THE AC RESISTANCE OF RECTANGULAR CONDUCTORS