RELAYS 101

Phase-Neutral to Phase-Phase Conversion

Enter your phase-to-neutral values for any two phases of a 3-phase system and the output is the phase-phase value. 
To calculate Phase-To-Phase Voltage on your own: -
Note that everything learned to calculate phase-to-phase voltages also applies to calculating phase-to-phase current values.

Too often we are tempted to declare that the voltage phase-to-phase is equal to the phase-to-neutral voltage times the square root of three.

This is only true if both voltages are equal and if they are 120 degrees apart. This usually happens only during non-fault conditions. (Or relay testing.)

There is no great secret to calculating the phase-to-phase voltage.
For systems with a phase sequence of 1-2-3:
VAB ("Vee-Ay-Bee") is Va minus Vb.
VBC ("Vee-Bee-See") is Vb minus Vc.
VCA ("Vee-See-Ay") is Vc minus Va. 
(This is also the case for currents, IAB is Ia minus Ib. Etc.)

And likewise for those systems with a reverse phase sequence of 2-1-3:
VBA ("Vee-Bee-Ay") is Vb minus Va.
VCB ("Vee-See-Bee") is Vc minus Vb.
VAC ("Vee-Ay-See") is Va minus Vc. 
(This is also the case for currents, IBA is Ib minus Ia. Etc.)

To subtract one phasor from another you must first convert them both to their rectangular components.

Then you subtract the second set of rectangular coordinates from the first  (such as Vb from Va).

Then you convert the new resultant rectangular coordinates back to polar form.

Open Delta Voltage Conversion

Sometimes in relay testing, you might have to use two voltage channels to produce three voltages. This is done with an open delta configuration.

The process to convert a 3-phase Wye configuration to an open delta configuration is only two phase-to-phase voltage conversions.

The first would be Va minus Vb to yield VAB. The second would be Vc minus Vb to yield VCB.

This works with fault voltages as well as normal system voltages.

So, really the only trick to converting to open delta is that you use Vb BOTH times as the subtractor.

Phase 1 magnitude : Phase 1 angle (deg) :

Phase 2 magnitude : Phase 2 angle (deg) :

Phase-Phase magnitude : Phase-Phase angle (deg) :