How do I convert an inductor into the dq0 reference frame?
Formula U=jwL * I, where j=the imaginary unit, w=2 * Pi * frequency and L = the inductance gives the complex phasor of inductor voltage when the complex phasor of the inductor current is I.

This is true for stationary sinusoidal current and voltage that has been and will stay connected forever without a start or stop.  

It's derived from your general equation U = L * dI/dt which is the general induction law for separate inductors. This law is valid for all current vs. time functions, not only the sinusoidals. It holds as well the switching on/off as stationary cases.

The complex phasor algebra for sinusoidal currents and voltages was developed at late 1800's. It was a revolution, because the general formula was too difficult for practical AC circuit analysis.

So: Learn the complex phasor method from elementary AC electrical engineering books. For this you must have a good idea of complex numbers. Your general equation needs some understanding and skill in first year university level differential and integral calculus.