Momentary overloading of a mains transformer at low duty cycle operation - what could go wrong?

I'm planning on using a 120 VA Hammond 1182P12 toroidal transformer to deliver 24 VAC to a 2.5 Ω resistive load (a JBC C245 soldering iron cartridge), implying 9.6 A RMS, 230 W if continously applied. A microcontroller-driven solid state AC switch in series with the load would open or close at zero crossings, modulating the delivered power. A slow fuse would protect the device at the primary side.

simulate this circuit – Schematic created using CircuitLab

The transformer is rated for 5 A continous (at 24 V), and I suspect this limitation to be determined almost exclusively by the heating of the transformer due to losses. Mains transformer losses can be split into two components - core losses (hysteresis and eddy currents), which are mostly load invariant (determined by primary frequency and voltage) and copper losses, which are only proportional to the square of the load current (neglecting the small primary current present due to core losses).
Assuming a worst case scenario where all transformer losses are due to copper losses, half a cycle (50 ms) of operation at 9.6 A produces the same losses as 50 ms * (9.6 A)2 / (5 A)2 = 184 ms at the rated 5 A.

My control algorithm would make sure that:

• DC balance is maintained to prevent core saturation (the number of positive half cycles delivered to the load always matches the number of negative ones, +/- one)

• The average power delivered on a timescale of 10 minutes or more is always 85 W or less (with the above assumptions, 85 W average in the form of 9.6 A pulses generates the same copper losses as 5 A continous)

• The average power delivered on a timescale of 5 s or more is always 140 W or less

Can I avoid a bulkier, heavier and more expensive transformer and larger case?

• Why would you assume that long-term transformer heating is the only limitation? What if there are conductors or connections that will melt in less than 5 seconds if you try to pass nearly twice their rated current? Dec 9, 2019 at 1:29
• @ElliotAlderson Were I assuming that, I wouldn't have asked the question in the first place. I'd just have started ordering parts. I'd like to know what else could go wrong besides heating.
– jms
Dec 9, 2019 at 1:30
• Saturation is dependent on instantaneous current. It can happen even if DC balance is maintained. DC isn't inherently associated with saturation. It doesn't mean you can't saturate the transformer as long as there is no DC. Dec 9, 2019 at 2:19
• @DKNguyen I thought core saturation is only induced if the magnetizing current (which depends on input frequency and voltage) gets too high. I double checked, and answers seem to agree (electronics.stackexchange.com/a/256828/46582 electronics.stackexchange.com/a/440741/46582) It's true that any DC imbalance in the secondary would have to be balanced by saturation, which is why I emphasized that the load will be balanced.
– jms
Dec 9, 2019 at 2:26