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Leakage Inductance of Medium-Frequency Transformers Compared with Measurements

TRAFOLO computes the leakage inductance of two 50 kW medium-frequency transformers within 5 to 7 % of the measured value, at every frequency from 1 to 10 kHz.

  • Result: ferrite core 42.4 µH against 40.4 µH measured (+4.9 %), nanocrystalline core 32.3 µH against 30.2 µH (+6.7 %).
  • Source: M. Eslamian, M. Kharezy, T. Thiringer, "An Accurate Analytical Method for Leakage Inductance Calculation of Shell-Type Transformers With Rectangular Windings", IEEE Access 9 (2021), pp. 72647–72660, doi:10.1109/ACCESS.2021.3080242 (open access).
The ferrite transformer in TRAFOLO as a half model with the HV winding shorted, flux density per element in the core and the windings
The ferrite transformer in TRAFOLO, half model at 1 kHz, HV shorted: B per element in the core and the windings.

Case

Both prototypes as modelled, to scale: top view (left) and the symmetry plane z = 0 (right). Grey core, blue LV, orange HV.
Part Material in the model Ferrite prototype [mm] Nanocrystalline prototype [mm]
Core, one block ESL core mur1000: μr = 1000, σ = 0, no core loss 182 × 148 × 158; windows 34 × 92; centre leg 58 230 × 192 × 64; windows 41 × 120; centre leg 76
LV winding, primary Copper, Stranded & Litz 18 turns in 3 layers 16 turns in 2 layers
HV winding, secondary Copper, Stranded & Litz 54 turns in 3 layers 48 turns in 2 layers
  • Windings: litz of 181 strands × 0.2 mm in rectangular layers, placed as in the paper's Table 6.
  • Excitation: LV at 54 A rms, the rated current, with the HV shorted; 11 frequencies from 1 to 10 kHz, as measured.
  • Measured: with an LCR meter (Agilent E4980A) from the LV side, HV shorted.
  • Air box: automatic, 3 × the part.

Results

Leakage inductance against frequency from 1 to 10 kHz for both prototypes, measured and TRAFOLO
Leakage inductance referred to LV, measured and TRAFOLO, from 1 to 10 kHz.
Prototype Measured, mean 1–10 kHz [µH] TRAFOLO [µH] Difference [%]
Ferrite 40.44 42.42 +4.9
Nanocrystalline 30.24 32.26 +6.7

Like the measurement, TRAFOLO's leakage inductance does not change with frequency.

Flux density per element on the symmetry plane of both transformers at 1 kHz with the HV winding shorted
B per element on the symmetry plane at 1 kHz, HV shorted: ferrite core (left), nanocrystalline core (right).

With the HV shorted, the flux runs between the two windings and closes through the core. Most of the energy is stored in the space between LV and HV, so their distance sets the leakage inductance.

TRAFOLO model

Built from STEP files of the paper's geometry (attached), in TRAFOLO 1.66.1beta.

ESL_ferrite.stepESL_nano.step

Tab Setting
Setup DOMAIN TYPE Symmetric: a half model, cut at the mid-depth plane. ELECTROMAGNETICS Inductance.
Geometry CAD import of the core and the two windings, scale mm.
Materials Core: ESL core mur1000 (μr = 1000, σ = 0). Windings: Copper.
Coil Stranded & Litz; Turns per solid LV 18, HV 54 (nanocrystalline: 16, 48).
ElMag Secondary Winding on: LV on the primary with current excitation, HV on the secondary with Urms [V] 0, a short circuit.
Waveform Inductance Sweep, SWEEP BY Frequency: 11 frequencies from 1 to 10 kHz; primary 54 A rms.
Mesh Max Element Edge Size: windings 1.5 mm, core 4 mm, air 20 mm; 670 000 to 770 000 elements.
Solve Linear Solver MUMPS on 16 cores: the 11 frequencies in 15 to 16 minutes.

Checks

  • Mesh: a mesh with a third of the elements solves the 11 frequencies in 3 to 4 minutes and gives the same inductance within 0.6 %.
  • Air box: doubling the automatic air box changes the inductance by 0.2 % (ferrite) and 0.7 % (nanocrystalline).
All runs
Run Prototype Mesh: windings / core / air [mm] Air box, x and y [mm] Elements Mesh / solve time [s] L [µH] vs measured [%] Note
R0 Ferrite 2.5 / 6 / 30 ±326.7 237 988 52 / 223 42.25 +4.5 First run
R0 Nanocrystalline 2.5 / 6 / 30 ±345 223 298 47 / 183 32.06 +6.0 First run
R1 Ferrite 1.5 / 4 / 20 ±326.7 668 771 174 / 965 42.42 +4.9 Reference run
R1 Nanocrystalline 1.5 / 4 / 20 ±345 765 415 182 / 882 32.26 +6.7 Reference run
R2 Ferrite 2.5 / 6 / 30 ±653.4 316 099 82 / 250 42.33 +4.7 Air box doubled
R2 Nanocrystalline 2.5 / 6 / 30 ±690 368 715 92 / 276 32.30 +6.8 Air box doubled

Each run solves the 11 frequencies on 16 cores; the half model reaches in z from 0 to the x value of the air box.

Limits

  • Windings as blocks: each winding is one stepped block with uniform current density, as in the paper's own FEM model.
  • Core as one block: the 2 mm (ferrite) and 4 mm (nanocrystalline) gaps between the core pieces are left out; the core grades are not stated, so μr = 1000.
  • Surroundings: bobbins, heatsinks and mounting plates are not modelled.
  • Low frequency: no eddy currents in the core or the litz, so the model gives the flat low-frequency leakage inductance.