Fault Calculations

Formulas

The different types of short-circuit fault which occur on a power system are:

• single phase to earth,
• double phase,
• double phase to earth,
• three phase,
• three phase to earth.

For each type of short-circuit fault occurring on an unloaded system:

• the first column states the phase voltage and line current conditions at the fault,
• the second column states the phase ‘a’ sequence current and voltage conditions at the fault,
• the third column provides formulae for the phase ‘a’ sequence currents at the fault,
• the fourth column provides formulae for the fault current and the resulting line currents.

By convention, the faulted phases are selected for fault symmetry with respect to reference phase ‘a’.

I _f = fault current

I_e = earth fault current

E_a = normal phase voltage at the fault location

Z₁ = positive phase sequence network impedance to the fault

Z₂ = negative phase sequence network impedance to the fault

Z₀ = zero phase sequence network impedance to the fault

Single phase to earth – fault from phase ‘a’ to earth:

Double phase – fault from phase ‘b’ to phase ‘c’:

Double phase to earth – fault from phase ‘b’ to phase ‘c’ to earth:

Z_net = Z₁ + Z₂Z₀ / (Z₂ + Z₀) and S_zz = Z₁Z₂ + Z₂Z₀ + Z₀Z₁ = (Z₂ + Z₀)Z_net

Three phase (and three phase to earth) – fault from phase ‘a’ to phase ‘b’ to phase ‘c’ (to earth):

The values of Z₁, Z₂ and Z₀ are each determined from the respective positive, negative and zero sequence impedance networks by network reduction to a single impedance.

Note that the single phase fault current is greater than the three phase fault current if Z₀ is less than (2Z₁ – Z₂).

Note also that if the system is earthed through an impedance Z_n (carrying current 3I₀) then an impedance 3Z_n (carrying current I₀) must be included in the zero sequence impedance network.