This is getting way outside what I am familiar with.
I guess that you are looking at a transformer around 1000 W to 2000 W, in which case I would expect the voltage to change by less than 10% under load.
However, I have no experience with such high voltage transformers, and the voltage measured depends on the load type. I guess you are rectifying, and that will only load the peaks of the output waveform, so the loaded voltage will be far from sinusoidal, and the voltage you measure depends on how your voltmeter interprets odd waveforms.