At the time of the fault, assuming fault is between line b and c, the fault current flowing into the fault is;
Ifa+Ifb+Ifc = 0
Since line a is not involved, Ifa = 0, therefore; Ifb= - Ifc
and Vb = Vc
Then the solution to determine the various values becomes an exercise in symmetrical components whereby:
Va1 = Va2 and
Ia1 = Vf/(Z1 + Z2)
indicating that the positive and negative sequence networks should be connected in parallel at the fault point in order to simulate/calculate a line-line fault.
As far as seeing the "explosion" 3 times, could have been the conductors touching, then the arc caused them to separate, but the momentum then caused them to touch again, etc., and the level of fault current did not meet the threshold on the relaying so it did not trip, or more likely there was a fault (first explosion) the line relaying tripped to clear the fault, and tried to automatic reclose, but fault was still present (2nd explosion) and tripped again, the line relaying tried a 2nd automatic reclose, but fault was still there (3rd explosion) and tripped again and stayed tripped, i.e. 3 explosions.
This type of event/with two reclosure attempts is very common for utilities.