Transformer Ka Calculation

[Sourabh Doherty]

Wye-connected transformers have one lead from each of three windings connected to a common point. The other leads from each of the windings connect to the line conductors. A wye-configured secondary is often represented with a Y-shaped arrangement of the windings (Fig. 2)

When the fault current is lowered to 300 amps, the line to neutral voltage will be 1,800 volts. We can see that when resistance is constant, the voltage will decrease as the current decreases and vice versa.

For instance, if the total connected motor load is rated for 60 amps continuous in a circuit, the actual demand that circuit puts on the transformer could be something like 72 amps when you factor in the additional power that is wasted in keeping the motor running (60 amps to perform the actual work the motor needs to do, and 12 amps just to operate so to speak).

This additional demand should be taken into account as well when you calculate the peak load the transformer will see. If a motor has an efficiency rating of 80% (like the example above), then, an additional 20% will need to be factored into the initial load calculation to ensure the transformer is not undersized.

We refer to this ratio between the power used to perform the actual work the load is designed for (measured in watts) and the total power consumed by the circuit (measured in volt amperes or VA) as Power Factor. The value for power factor will always be below 1 (unity), since there is always some power loss in an electrical system. A good power factor would be as close to 1 as possible (0.9 through 0.99). Systems that waste more energy will have a lower power factor (0.8 and lower for example).

We are doing calculations on a design that should have 650-900Vin and 68V 0.6A output. I have never seen transformers with inductance in 10mH range. Is our calculation correct here? What happens if the inductance is too high, will it still work?

Yes, 10mH is an unusual value for magnetizing inductance, but it comes from the combination of high minimum input voltage and the specified high maximum duty cycle of 65%.
This calculates to a peak current of about 0.2A, so 1/2*10mH*0.2A^2*200kHz = 40W (for rough estimate).
Furthermore, the recommended turns ratio (as a consequence of the Dmax = 65% requirement) of 17.57:1 results in a reflected voltage of 1195V, on top of a max input of 900V requires a switch rating in excess of 2100V.

I suggest that a lower maximum duty cycle will allow a higher peak current and lower reflected voltage. I'm not sure why that parameter is an input rather than a result.
The problem with specifying a much smaller Dmax (such as 10%, for example) is that Dmax applies at full load lowest Vin and D will be even lower at the highest Vin, and even lower at light load at high Vin. At some point, the leading-edge-blanking time (which essentially defines a minimum on-time) may result in a forced peak current that could require a fairly high minimum load to absorb to avoid output overvoltage.

If your output load range is fairly constant near max power, then tLEB should not be a problem and you can experiment to find a small enough Dmax to obtain a reasonable Lm and turns ratio. If your load does go to zero, then it is likely to require a minimum preload to keep in regulation.

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Objective. To present a transformer-based UNet model (TransDose) for fast and accurate dose calculation for magnetic resonance-linear accelerators (MR-LINACs).Approach. A 2D fluence map from each beam was first projected into a 3D fluence volume and then fed into the TransDose model together with patient density volume and output predicted beam dose. The proposed TransDose model combined a 3D residual UNet with a transformer encoder, where convolutional layers extracted the volumetric spatial features, and the transformer encoder processed the long-range dependencies in a global space. Ninety-eight cases with four tumor sites (brain, nasopharynx, lung, and rectum) treated with fixed-beam intensity-modulated radiotherapy were included in the dataset; 78 cases were used for model training and validation; and 20 cases were used for testing. The ground-truth beam doses were calculated with Monte Carlo (MC) simulations within 1% statistical uncertainty and magnetic field strengthB = 1.5 T in the superior and inferior direction. Beam angles from the training and validation datasets were rotated 2-5 times, and doses were recalculated to augment the datasets.Results. The dose-volume histograms and indices between the predicted and MC doses showed good consistency. The average 3Dγ-passing rates (3%/2 mm, for dose regions above 10% of maximum dose) were 99.13 0.89% (brain), 98.31 1.92% (nasopharynx), 98.74 0.70% (lung), and 99.28 0.25% (rectum). The average dose calculation time, which included the fluence projection and model prediction, was less than 310 ms for each beam.Significance. We successfully developed a transformer-based UNet dose calculation model-TransDose in magnetic fields. Its accuracy and efficiency indicated its potential for use in online adaptive plan optimization for MR-LINACs.

In many industries, including health care, manufacturing, electrical contracting, higher education and corrections, reliable, high-quality transformers are essential for keeping operations running efficiently. Large facilities and industrial processes require substantial amounts of power, and they need dependable transformers to convert the energy coming from the power plant into a form they can use for their equipment and building utilities.

The kVA unit represents kilovolt-amperes, or 1,000 volt-amperes. A transformer with a 1.0 kVA rating is the same as a transformer with a 1,000 VA rating and can handle 100 volts at 10 amps of current.

Standard transformer sizes refer to predefined and commonly available ratings of transformers that are on the market. These sizes are established by industry standards and provide a range of options to choose from. As a result, you can find a transformer that meets your specific needs without requiring custom manufacturing. Standard transformer sizes also facilitate compatibility and interchangeability, and allow for easy replacement of or adding to transformers in electrical systems without significant modifications.

Standard sizes cover a variety of transformer kVAs, from smaller systems used in residential applications to larger ones for industrial settings. Especially for commercial buildings, the most common sizes for transformers are the following:

When selecting a transformer, these standard sizes provide reliable and readily available solutions that have been tested and proven in various applications. For example, if you need a transformer size of 52.5 kVA to convert a system, you would select a 75 kVA transformer out of the available standard ratings since it has a better capacity than a 45 kVA transformer.

Sometimes transformers are rated in megavolt-amperes, or MVA, to indicate the bigger size and capacity of the system. In other words, it is typically used when the ratings of electrical systems and equipment exceed the kVA range.

Like kVA, MVA is a unit used to measure the power capacity of large electrical systems and equipment. Since MVA represents the product of voltage and current on a very large scale, it is commonly used when dealing with high-power systems, such as:

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An output of 265 volts at 5 mA is a power of 1.325 watts and this means that the energy that needs to be transfered each switching cycle is 1.325 W divided by the switching frequency. Hence, the energy released by the flyback transformer is 2.65 J. Accounting for losses, you should probably bump that up to around 3.3 J.

So, immediately I'm not all that confident that your choice of 56 H is good. It's a little close to not working at the lower voltage supply using my assumptions. Yes, we might believe that a slightly lower energy per cycle (say more like 3 J) would be fine and, that would require a primary current of 327 mA. But, the minimum supply rail would still be be 12.2 volts. Or, we could also make the maximum duty cycle closer to 90% (1.8 s) and that would allow a supply voltage as low as 10.2 volts.

But personally, I'd go for lowering the inductance because I also know that winding many hundreds of turns for the secondary is a pain and if you can get away with fewer turns, all the better. So, I'm going to go for 26 H instead of 56 H. We can now say: -

You should avoid peak flux densities much over 200 mT so I don't think you need one. However, if you have got your current output wrong and meant to say 50 mA then you will likely need one but, the same data sheet gives options: -

In a flyback transformer, a gap is mandatory for energy-storing reasons but also for stabilizing the inductance in production. We can show that the magnetizing inductance of an iron-core inductor featuring an air gap is expressed by:

In the below picture, you can see two cores made of N48 material as an example. We want to build a 600-H inductor. In the first gapped case, the inductance factor is low and you would need 49 turns to realize the inductor. With this gapped version, you can see a very precise inductance factor. In the second case, with an ungapped core (which for a flyback converter it is not an advisable option), you would require less turns (better dc resistance) but the spread in the value would be wide.

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