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I understand that it would be catastrophic for the two phases shorted together. Say the line to neutral voltage is 2 volts and line to line voltage is √3×2 volts.

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  • \$\begingroup\$ Well, to find "middle between two phases", you could use two like resistors as a voltage divider or a 1:1 transformer. Or use a 1:1 isolation transformer "to put them in series". Draw vectors. \$\endgroup\$
    – greybeard
    Commented Mar 19, 2023 at 7:14

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This all depends on the propertys of the source in question.

If you assume:

  • R1..3 to be the source impedances (50Hz also has complex components)
  • R4 is infinite
  • The phase-difference is 120 degrees exactly:
  • And V1..V3 to be equal

Then VM4 will show your normal "line potential delta ", e.g. sqrt(3)*V1

If you assume:

  • R4 is 0 (Short)

Then, due to R1 and R2 there will still be a potential different from GND/PE on the Points L1/L2. This potential also has a phase different from L1/L2/L3. Therefore, L3-L2 voltage will not be "normal line potential delta".

In conclusion:

  • In an academic world i suggest deriving the equations from the circuit shown below.
  • In an real world AC-Mains scenario: Some fuse will blow.

schematic

simulate this circuit – Schematic created using CircuitLab

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