# Question - rough estimate of the reduction of a power transformer's size with Freq

## Main Question or Discussion Point

I have a customer looking for a 100KW isolated DC/DC converter. What is a realistic transformer core weight reduction if we get 1000Hz fundamental.

Assume a 60Hz core is 300 Lbs, how much smaller could a 1kHz Core be?

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The most crude rule of thumb is that volume and weight are inversely proportional to frequency.

Linear dependence holds good only for small f2/f1 ratios.
The power loss in the core increases as the frequency increases, and transformer gets heated up more.
The efficiency drops...
For high power application the issue becomes how to get rid of more heat→the surface area has to be increased and/or air/oil flow intensified.
Allowed flux density in the core also drop down with frequency increase since saturation occurs earlier...
All this requires larger Xfrmr size than expected for big f2/60 ratios and high power applications

Baluncore
2019 Award
For higher frequencies you may need to change the transformer core material. Iron powder or thinner laminations will be needed at 1000 Hz due to the skin effect. Energy is wasted if the laminations are too thick, and the core weighs more. Also the windings are longer than needed if the core contains unreachable iron beyond the skin depth at that frequency.

berkeman
Mentor
I have a customer looking for a 100KW isolated DC/DC converter. What is a realistic transformer core weight reduction if we get 1000Hz fundamental.

Assume a 60Hz core is 300 Lbs, how much smaller could a 1kHz Core be?
Sorry, I'm not following the question. No DC/DC converter uses 60Hz, or even 1kHz for that matter. It sounds like you are asking about a straight line frequency isolation transformer (a big one), but if it's associated with a DC/DC function, why bother using line frequency for the isolation. Why not just use an isolated DC/DC converter topology?

berkeman
Mentor
a 100KW isolated DC/DC converter
BTW, you mention the power output required, but not the other specifications. What are the input/output voltages for this design? Thanks.

Assume a 60Hz core is 300 Lbs, how much smaller could a 1kHz Core be?
The mass (!) of the core could be reduced to ~ 1/8 or 1/16 of the original depending on the type of the converter, if the material is ~ similar to 60Hz transformers (laminated sheets).

Mind you, 1kHz DCDC converters are/were rare. There was some very old designs, based on thin (!) laminated core transformers, but these days it is about higher frequencies and even smaller cores.

anorlunda
Mentor
I have a customer looking for a 100KW isolated DC/DC converter. What is a realistic transformer core weight reduction if we get 1000Hz fundamental.
I have a different question. How is it in your customer's interest to design a converter rather than buy a commercial design?

Complicated -- but it is a 100KW - vehicle based design. We have a vehicle rated (qualified) inverter that will max out at about 1Khz fundamental. 500 to 800VDC in and out.

This does not exist in the market - well that we have found.

I know this would be a custom unit, but a custom transformer cost a lot less than a new inverter due to tooling development and qualification. It is still a lot of copper, so reducing the core, will probably not be enough.

AND I was just spitballing an idea.

We received a spec and are stumped how to even get close, but after some discussion we may get them to give up on the isolation requirement - then it is almost trivial from a concept standpoint.

The mass (!) of the core could be reduced to ~ 1/8 or 1/16 of the original depending on the type of the converter, if the material is ~ similar to 60Hz transformers (laminated sheets).
Core weight reduction factor 1/16 is mission impossible with frequency jump 60 Hz to 1000 Hz (assuming similar geometry and identical materials and modus operandi). Even 1/8 would be challenging. To illustrate this, I'll give one manufacturer's data of total weight of two transformers.
• 6kVA, 480/240V,1PH,60Hz
• 6kVA,480/240V,1PH,400Hz
First one weights ~ 90 LBS, second one ~33 LBS.
Both Xfrms have primary and secondary winding on the same leg, core windows of similar geometries with laminated sheets. However, the reduction factor 33/90=0.366 is nowhere near expected 60/400=0.15.
OK, one may argue that Xfrmr weight is not just a core. Nevertheless, the cores in these examples contribute at least 50% to total weights.

Thanks for the reality check- that is about all I needed.

Windings would be about the same, actually may need more copper due to skin effect, and HF insulation will increase flux leakage.

anorlunda
Mentor
Complicated -- but it is a 100KW - vehicle based design.
Ah you didn't say that before. Why not a power-takeoff or belt driven DC generator?

If you work at an engineering forum, the risk is that the customer's budget will be quickly eaten by engineering costs. A DC generator is old technology, not expensive to engineer.

It's an electric vehicle - I have 2 DC systems and needed bidirectional isolated conversion.

I realize everyone was curious - but basically I just wanted and idea of the potential weight (savings) of a transformer based design, so I was trying ask a simple question about core size relative to frequency, but no one seemed OK with a rough estimate answer.

Baluncore
2019 Award
I realize everyone was curious - but basically I just wanted and idea of the potential weight (savings) of a transformer based design, so I was trying ask a simple question about core size relative to frequency, but no one seemed OK with a rough estimate answer.
I am still curious why anyone would run a DC-DC converter at 60 Hz, or even at 1 kHz. That suggests early transistor technology from the 1960s. For DC-DC conversion today I would consider a minimum 100 kHz resonant sinewave converter, that would employ both a choke and an isolation transformer.

You cannot frequency scale a transformer if core material spec's do not cross the frequency boundary. That involves knowing the unspecified waveform, sinewave or square-wave.

If you ask the right question, you will get the right answer. If you knew upfront what question to ask, you could have answered it yourself. The question needed to be refined. You should not blame us for not answering a confused and insufficiently specified question.

I realize everyone was curious - but basically I just wanted and idea of the potential weight (savings) of a transformer based design, so I was trying ask a simple question about core size relative to frequency, but no one seemed OK with a rough estimate answer
Based on the limited information you provided, I try to roughly estimate that the core weight can only be reduced by up to 75%.

By the way, why not try a higher switching frequency?

Thank you again for your input. It did not seem a stretch since 400Hz was used specifically for the purpose of reducing magnetics in aircraft and shipboard applications. As I stated 1khz is the max that that the inverter is capable of, changing the inverter is 18-24 months of work, and the volumes for this part of the vehicle just do not justify the effort - and we do not have the bandwidth - resources. A complete purpose built solution with a more optimized architecture like 50 to 100 Khz ( we would probably need SiC - at least hybrid) with tooling and full qualification, probably $500K+ effort. A transformer we can have custom built in three or four months. eq1 Gold Member 100KW isolated DC/DC converter... how much smaller could a 1kHz Core be? At that power level the size is likely constrained by safety and isolation requirements. You should check those first. It might not be able to get any smaller, and be compliant, even if it is more efficient. Thank you again for your input. It did not seem a stretch since 400Hz was used specifically for the purpose of reducing magnetics in aircraft and shipboard applications. As I stated 1khz is the max that that the inverter is capable of, changing the inverter is 18-24 months of work, and the volumes for this part of the vehicle just do not justify the effort - and we do not have the bandwidth - resources. A complete purpose built solution with a more optimized architecture like 50 to 100 Khz ( we would probably need SiC - at least hybrid) with tooling and full qualification, probably$500K+ effort.

A transformer we can have custom built in three or four months.
I think you are confusing things, if an inverter is capable of 1kHz max output, this is most likely the highest fundamental machine frequency it can recreate, ie its likely switching at 8-10kHz. Also inverter maximum frequency has nothing to do with your DC-DC unless your plan is to use two inverters driving each side of a transformer, one pushing the other synchrectifying, but this would be a crazy way of doing it!

For a DC-DC converter, you do not recreate a low frequency sine wave with a higher freqency PWM like you do in an inverter (inverters are basically class D amplifiers), your switching frequency is the transformer fundamental.

1kHz would be absolutely obnoxious as a DC-DC, could you imagine driving around with this 1kHz squealing thing?!

10kHz minimum, >20kHz if you can, if doing DC-DC converter, you'd chose some semi resonant or ZVS switched topology, then you can get IGBT upt to 100kHz. If you have too much money SiC is awesomely fast, but poor design of the interconnects can shoot you in the foot here.

If this was me I'd look at interleaving to reduce ripple current requirement on your DC filter caps.

Baluncore
2019 Award
A bidirectional DC to DC converter has the following structure.

People who are talking about switching frequencies like 20, 50 or even 100 kHz , and 100 kW DC/DC converter toplogies involving xfrmr link, are living in clouds. It's not a 100 W table top toy with negligible leakage inductances & parasitics you can lift with two fingers up. It is quite a challenging engineering task to reach 20 kHz at 100 kW as shows the following read: https://hal.archives-ouvertes.fr/hal-01747437/document

Baluncore
2019 Award
Doubling the frequency utilises the core twice as often, so it can be half the mass, but the heating due to magnetic losses doubles. A smaller transformer runs hotter because the heat exchange surface area is reduced.

The wire is shorter because it surrounds less core, so the windings weigh less, have lower resistance, and so can have less cross-section area. At a higher frequency, skin effect indicates thinner but wider copper strap windings, or a finer litz wire.

The core material may need to change to reduce magnetic losses at higher frequencies, but higher frequency magnetic materials have a lower μr and lower saturation threshold. All is not lost because the inductance of the transformer must be reduced proportional to the rise in frequency.

The problem with estimating the change in size is knowing and juggling the balance between magnetic losses and copper losses. The operating temperature of the windings should be similar to the core. If that is not the case the design could be optimised further.

From 60 Hz to 1 kHz the factor is 16, which is not small, so more change will be required and prediction ratios will not hold. Skin depth will change by a factor of 1/√f = 0.25 There is no advantage having unreachable copper conductor, nor deep magnetic core material.

There is no question that a new 100 kW design would be a challenge, but it has been done several times in the last 5 years. Those products are out there.

There is a possibility of running 2 or more, smaller, faster converters in parallel. That would give some modular redundancy, distribute the heat better, and make the converter less of a lump.

Procedures for optimizing performance's efficiency given Xfrmr's size and operating frequencies are known.
Results of such optimizations are frequently not in agreement with constrains dictated by specific application. Hence some compromise must be made. Fortunatelly, in a correctly designed converter these two demands are not in significant confrontation regarding obtained parameters. Splitting one unit into 2 or more smaller identical converters for parallel operation is not a good alternative. Overall efficiency would decrease, space, weight and money expenditures would increase.

Baluncore