Open circuit test on rated voltage

By definition, an OC test of a transformer is an Open Circuit test. Why would you connect the HV windings? The open circuit test primarily is used to determine the core (magnetic) losses of the transformer, as with no load, you don't have to worry about copper (winding) losses.

For an SC test, the low voltage side is shorted in order to measure the impedance of the transformer. The high voltage winding is connected to a variable voltage supply, and the supply is increased until the high voltage leg reads it's maximum current. You don't need full rated voltage to achieve full current this way, and it makes it a simple matter to measure the transformers impedance, as well as the actual copper (winding) loss at full load since the magnetic structure of the transformer isn't driven into saturation (or anywhere near it, the magnetic losses are extremely low when a transformer is excited in this manner).

I think I understand your question so first here's a representation of the equivalent circuit of a transformer: -

Under no load conditions the only current flowing into the primary is the current taken by the "parallel components" Xm and Rc. For a normal power transformer that current will be small compared to the current normally taken by the primary when the secondary is driving a load. For that reason you can ignore (short circuit) Xp and Rp and of course the secondary is only producing an open circuit voltage so Rs and Xs are of no consequence.

The "thing" in the middle that looks like a transformer is a perfect power transformer and because no current is being delivered to the secondary that perfect transformer takes no current.

So, it boils down to Rc and Xm being connected to the incoming power and no further components need to be analysed.

I was wondering why exactly you have to use the nominal voltage of the transformer for the open-circuit or no-load test.

There is one very important reason for this and that is core saturation - if you don't use the normal applied voltage you'll either have too much saturation or too little and you won't have a representive measurement. Saturation of the core is non-linear with voltage so it's important to use the right applied voltage. Look at the BH curve to see why: -

You can see that it is very non-linear once you start approaching saturation and, most transformers will be designed to run at a magnetic field strength (H) in the early to mid areas of saturation. This of course means a smaller transformer size and less iron. Commercial reasons prevail.

So, to do the test justice you need to run at nominal levels.

If you were doing a test to find out the values of the series components then you'd run the primary from a variac and short circuit the output. The sort of voltage that is now applied is a fraction of the nominal voltage so core losses are low (very linear BH curve) and eddy current losses (Rc) are also quite small.