how do transistors convert our 220v supply to 2000-3000v?

Transformers are used to do that. Thistechnique uses one or two transductors (for full wave operation) i.e. a square loop magnetic core current transformers with secondaries connected in series. AC current bias is passed through the secondary windings. The DC current in the single turn bar primary progressively biases the cores into saturation. This reduces the impedance of the inductors allowing proportionately more ac current to pass in the secondary circuit. The current waveforms become very similar to thyristor ac control.
This ac current is rectified, and the ripple smoothed and passed through a load resistance. The response is inherently slow but normally this is not an issue. Very high permeability tape wound toroidal cores are used for this application with an ac bias current of around 1kHz to 5kHz depending on acceptable core loss.