Yes driven as the transformer and the primary current determines how much current flows through the lamp as apposed to the lamp determining how much current it will take from the supply.
I cannot be 100% certain but logic would suggest that with with a ring current of for example 1 Amp then a ratio ( primary : secondary ) of 100 : 30 in the transformers would result in an LED current of 300 mA.
I must confess that I have always had difficulties getting my head around the concept of 'current transformers' and 'current transformation', so perhaps you can help to educate me.
I have always thought of wirewound transformers transforming voltage (according to the turns ratio) with the current flowing in the secondary (hence also primary) determined by the impedance of the load connected to the secondary (with its secondary voltage). Using some very simple numbers for convenience ...
If one has just one transformer, with a 100:30 turns ratio, with its primary connected to a 240V supply, the 'secondary voltage will be 72 volts. If one connects a 10Ω load to the secondary, then the secondary current will be 7.2A and the primary current will (ignoring losses etc.) be roughly 2.16A. If one changes the load to, say, 100Ω, then the currents will be 0.72A and roughly 0.216A respectively - i.e. the impedance of the load determines what current will flow in both secondary and primary.
On the face of it, I don't see why this concept changes if one has the primaries of several transformers in series. Say there are 10 such transformers in series across the 240V sup[ply, each with a 10Ω load connected to its secondary. The primary voltage of each transformer will then be 24V, hence the secondary voltage 7.2V ... hence secondary current at each transformer of 0.72A, with about 0.216A flowing through the primaries of all the transformers.
If one increases the impedance of the load on the secondary of one
of the transformers, from 10Ω to 100Ω, then the maths then gets a little more complicated, since the 240V supply will presumably no longer be equally shared between all of the primaries (and I haven't yet tried to analyse the situation precisely), but there is surely no doubt that current through that one (much higher impedance) load will be much lower than it was when it was the same impedance as all the others, and that the current through (all of) the primaries will be a little lower..
To my simple mind, it therefore seems that, even with the transformers in series, the current flowing through each (secondary) load will be determined by the impedance of that load. If, as you are suggesting, the setup attempted to maintain the same current through the secondary when its impedance increased 10-fold, that would require a 10-fold increase in the secondary voltage - which, as well as being impractical/impossible, would violate my conception of the primary : secondary voltage ratio being equal to the turns ratio.
Can you help me?
Kind Regards, John