Anyway, EI transformers have air gaps so their iron losses are significant. I really wonder how your transformer has such a small idle consumption - it must be a masterpiece.
It's true that the air gap in EI transformers is somewhat larger than in a toroid, but it's not a major contributor to losses. Perhaps you're thinking of high frequency ferrite transformers where the fringing flux from an air gap in the center leg causes eddy current losses in the nearby copper windings. In an EI transformer the laminations are interleaved in opposite directions and flux at the butt joints does pass through the neighboring lamination, causing the flux density to be higher in the immediate neighborhood of the butt joint. This does cause the flux density there to be higher than nominal, and therefore losses are somewhat higher there, but the volume of iron so affected is very small compared to the total volume of iron in the transformer.
The major contributor to iron losses is the quality of the laminations. We always use M6 laminations, but when we have asked for sample transformers from a possible new vendor in the far east, they sometimes try to pass off M19 or worse in the sample.
Inverter transformers are designed differently than others in that no load losses are so important that iron loss is minimized at the cost of greater copper loss. The total losses in the transformer pictured in the image above are somewhat over 200 watts at full load (compared to 9 watts no load); those losses are essentially all copper loss (the iron loss remains essentially a constant 9 watts) and a fan is definitely required!
We are aware that customers want higher efficiency at the same time as lower no load losses. These requirements are contradictory! One way to achieve this, other than using toroids, is to use M4, or even M3 laminations, but the cost of the transformer is then significantly higher.
The leakage inductance in an EI transformer has no copper loss (beyond the unavoidable copper loss in the existing primary and secondary winding), whereas the additional external inductor that is required with a toroid is wound with real copper and has core losses too. Those losses negate some of the efficiency improvement due to the use of a toroid. The transformer in the image above gives a total efficiency of about 92% for the inverter. It might go up to 94% or 95% with a toroid, but then the additional inductor losses might bring it back down to 93% or so. Not much overall improvement.
As far as i read, EI transformers used in UPS/inverters have lousy windings (on purpose) to use their leakage inductance as a low pass filter (together with the output capacitor).
EI transformers are constructed with concentric windings; copper foil on first and then the secondary. This leads to a leakage inductance that is just right for use with the filter action. Leakage inductance could be made much less with interleaved windings like they do in audio output transformers used with tube power amps; (secondary split into two halves with primary in between the two primary halves), but then the leakage inductance would be too low. An external inductor would then be required with its additional losses; not a good trade off! I actually had our transformer shop (when we had one) make a transformer in the split bobbin mode, with the primary and secondary side by side rather than concentric. The leakage inductance was much too high. The ordinary concentric winding method works out just right.
Another issue raised in this thread is power factor correction on the primary side. The "bad" power factor is due to the fact there is some lagging primary current due to the less than infinite primary inductance. The primary inductance in a typical inverter transformer is in the 10s or millihenries; the transformer shown in the image has 100 mH. The additional losses due to the small magnetizing current being out of phase is negligible. You don't want to have any additional capacitance across the primary winding because there are fast rising voltages applied there. The high dv/dt edges would cause large spikes of current in an added capacitance, with attendant losses and EMI production. The filtering to get rid of the high frequency components of the SPWM waveform should be on the secondary side. A suitable inductor on the primary side would have be wound with large wire or foil to carry the high primary current with its attendant proximity losses in addition to the ordinary I²R losses.
My current toroidal transformer costs me almost 450 EUR (btw, I live in Europe) so I hope it's really worth the money. Being used by Xantrex in their high-end design it's a good news.
I'm unaware of transformers suitable for inverter use being available as a standard item from transformer vendors. Usually the transformers have to be custom designed for proper turns ratio and other important parameters. Is the toroid you bought designed specifically for inverter use? Can you provide a link to the manufacturers web site? I'd like to have a look at their product line.
A commercial inverter is expected to provide a surge of at least 2 times the continuous rating for a few minutes. To do this, plus to provide high efficiency, the H bridge is composed of a number of paralleled FETs in each leg of the bridge. Modern FETs used in this application are typically capable of 100 amps continuous each. If there are, say, 5 such FETs in each leg then 500 amps continuous (more for a few tens of milliseconds) won't hurt anything.
The internal resistance of a bank of L16 batteries, for example, plus the resistance of the cabling, the FETs, the DC resistance of the transformer, etc., will limit the start up surge to several hundred amps max. We don't do anything special to deal with a start up surge; just let it happen.
Your toroid will only see inrush current like this: "(reading from the datasheet: 30 kA peak / 10 kA RMS!!)." when connected to something capable of supplying 10 kA--something like the grid.