Modeling medium frequency transformers for solid state transformer designs

Key Takeaways

• Leakage inductance, core behaviour and winding capacitance set the limits of an isolated stage, so they belong in the model from the first study.
• Model detail should match the design question, with saturation, capacitance and loss maps added only where a result depends on them.
• Testing the controller against a realistic transformer model before ordering magnetics turns the transformer specification into a set of tested limits.

A medium frequency transformer model earns its place when it predicts leakage, core loss and saturation limits before you commit to winding a core.

Solid state transformers replace a heavy line frequency core with power electronics and a much smaller transformer that runs at kilohertz frequencies. Interest keeps rising because conventional units are hard to source, and NREL estimates that United States distribution transformer capacity may need to increase 160% to 260% by 2050 compared with 2021 levels. Every one of those designs depends on a magnetic part nobody can buy from a catalogue.

The schematic draws that part as two coupled coils and a turns ratio. The limits you’ll hit in the lab sit somewhere else, in leakage inductance, core behaviour and the capacitance between windings. Treat those three as first-class model parameters, test them against your controller in closed loop, and the isolated stage stops being the riskiest item in the design. Leave them out and the first prototype becomes your model.

What a medium frequency transformer does inside a solid state transformer

A medium frequency transformer provides galvanic isolation and voltage scaling inside a solid state transformer while operating from roughly 1 kHz to a few tens of kilohertz. Core area falls as frequency rises for the same voltage, which is why the part is so much smaller than a 60 Hz unit of equal rating.

Picture a stage fed with an 800 V square wave. With 20 turns and a core cross-section of 10 cm², peak flux density at 20 kHz works out to about 0.5 T. Run the same winding at 60 Hz and the core would need hundreds of times more area to stay out of saturation.

The saving isn’t free. Higher frequency raises core loss per kilogram, pushes current to the surface of each conductor and shrinks the surface available for cooling. Medium voltage insulation also has to fit inside a far smaller window. Your model has to carry all of these effects, because each one moves when you adjust frequency.

Why leakage inductance sets the power limit of an isolated stage

Leakage inductance sets the power limit because it is the element that actually carries energy between the two bridges. Too much of it caps the power you can deliver and steals duty cycle. Too little leaves no stored energy for soft switching and lets current slew faster than the control loop can manage.

“Leakage inductance sets the power limit because it is the element that actually carries energy between the two bridges.”

Take a phase shifted full bridge at 800 V and 20 kHz with 20 µH of leakage and 50 A of reflected load current. Each polarity reversal needs the primary current to swing by 100 A, which takes 2.5 µs. A half period lasts 25 µs, so 10% of every half cycle delivers nothing to the output.

An ideal transformer model reports full duty and full output voltage for that operating point. The hardware will regulate 10% lower at full load, and your turns ratio will be wrong on the first build.

Leakage also trades against insulation. Thicker barriers between windings raise the isolation rating and raise leakage with it, so the mechanical layout and the electrical limit are one decision. Tie the modelled value to winding geometry early.

How a phase shifted full bridge behaves with a practical transformer

A phase shifted full bridge with a practical transformer loses soft switching at light load, rings at the rectifier and is prone to flux walking. All three come from the transformer’s parasitics, and none appear when the transformer is ideal.

Soft switching on the lagging leg relies on energy stored in the leakage. With 20 µH and 5 A, that energy is 250 µJ. Two 300 pF device capacitances swinging through 800 V need roughly 190 µJ, so the margin is thin, and at 4 A the stored energy falls to 160 µJ and the leg hard switches. Small differences in on-time between the two diagonals also leave a net direct voltage on the primary. Magnetizing current then drifts toward saturation over many cycles, which only a model with a saturating core will show.

Core material choice decides loss at medium frequency

Core material decides how much flux swing you can use and what each watt of throughput costs in heat. Ferrite has low loss but saturates near 0.4 T. Nanocrystalline alloys tolerate roughly 1.2 T, which allows a smaller core, at the price of a tape-wound shape that is harder to cool and assemble.

Measured results show how close the two options can land. A Chalmers University of Technology thesis built two 50 kW, 5 kHz prototypes and measured 99.66% for the nanocrystalline unit against 99.58% for the ferrite one. The gap looks trivial until you convert it to heat, since those figures mean about 170 W and 210 W of loss inside a compact, heavily insulated package.

Loss data from a supplier sheet assumes sinusoidal flux. Your converter applies square voltages with dwell intervals, so a loss model that accounts for waveform shape will give a different answer, and that answer sets hot spot temperature.

Which model detail each design question needs

Each design question needs a specific level of transformer detail, and using the most detailed model everywhere wastes simulation time. An ideal ratio with series leakage answers power flow questions. Saturation, winding capacitance and loss maps only pay off for the questions that depend on them, as the summary shows.

Inter-winding capacitance deserves a closer look. A 100 pF barrier capacitance exposed to a 50 kV/µs switching edge passes 5 A of common mode current into your grounding and measurement circuits.

Mistakes that make a transformer model look better than the hardware

Transformer models flatter the hardware when they use small-signal measurements, ignore temperature and run at a time step too coarse for the switching edges. Each shortcut removes a loss or a limit. The simulated stage then meets targets that the built stage misses by a margin you can’t recover with control tuning.

Time step is the easiest of these to quantify. A 20 kHz bridge has a 50 µs period, so a 500 ns step gives 100 points per cycle and a phase shift resolution of 1%. Run the same model at 10 µs and you can’t represent the 2.5 µs current reversal at all.

The common shortcuts are easy to list.

• Using leakage measured at low current for a full load study.
• Treating magnetizing inductance as linear up to rated flux.
• Taking core loss from sinusoidal data without waveform correction.
• Leaving out winding capacitance because the frequency seems low.
• Assuming resistance stays at its room temperature value.

Engineers who run these stages on OPAL-RT simulators execute the transformer and bridge models in real time against the physical controller. Dead time, sampling delay and protection thresholds then meet the same leakage and saturation behaviour the hardware will present.

Validating the isolated stage before a core is wound

“The discipline of modelling the awkward parts early is what keeps the first wound core close to the last one.”

Validating before winding means your controller has already seen duty loss, light load hard switching and a saturating core by the time the magnetics order is placed. The transformer specification then comes out of tested limits. It doesn’t come from a turns ratio and a hopeful efficiency number.

That order of work matters because a custom medium frequency transformer is slow and costly to revise. A second iteration means new tooling, new insulation tests and weeks of waiting, all to correct a leakage value you could have swept in an afternoon. Teams that sweep first tend to specify a leakage range and a saturation margin, and they hand the winder a tolerance they know the control loop will accept.

Good judgment here is mostly restraint. You don’t need every parasitic in every study, but you do need the right ones present when a decision depends on them. OPAL-RT models medium frequency transformer behaviour in real time for this reason, so the isolated stage inside a solid state transformer gets tested against its controller while the core is still a drawing. The discipline of modelling the awkward parts early is what keeps the first wound core close to the last one.