
214 Shipboard Electrical Power Systems
The particular solution to Equation (9.8) with the initial condition (9.9) is the fol-
lowing transient fault current,
i t I t e
z z
R
X
t
( ) sin( ) sin( )= + − − −
−
2
rms
ω θ θ θ θ
ω
(9.10)
where R = total resistance in the fault circuit, X = ωL = total reactance, θ
Z
= tan
−1
(X/R)
= impedance angle, and I
rms
= rms value of the ac component superimposed on the
exponentially decaying transient term. The fault current, therefore, is a complex
function of the switch closing (fault inception) angle θ and the fault circuit time
constant τ = L / R = X / (ωR).
The fault current given by Equation (9.