Faults involving abnormal conduction from one phase to another without involving ground may be represented using the interconnection of Figure below.
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Sequence interconnections for a phase-to-phase fault not involving ground
The zero-sequence network is not involved and may be ignored. As for the three-phase condition, Zf would normally be the fault impedance, but it could also be a phase-to-phase load impedance if the problem of interest is the response of the system to a phase-to-phase-connected single-phase load.
An interesting and often useful relationship develops from Figure.
In the special case of a zero-impedance phase-to-phase fault, if the negative-sequence impedance of nearby synchronous machines is approximately equal to the positive-sequence impedances of such machines or if no synchronous generators are nearby at all, then the phase-to-phase fault current will be 0.87 times the corresponding three-phase fault current.
This relationship can be proven by calculating sequence currents in Figure for the specified condition and then converting them to phase currents using symmetrical components equation.
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