Single Line-to-Ground (LG) Faults in Power Systems
Demonstrative Video
Single-Line-to-Ground Fault
The LG fault, the most common type, is caused by lightning or by conductors making contact with grounded structures
A LG fault occurred at node \(k\) on phase \(a\) through impedance \(Z_f\)
The relations to be developed will apply only when the fault is on phase \(a\), but any phase can be designated as phase \(a\)
The conditions at the fault bus \(k\) are expressed by : \[I_{fb} = I_{fc} = 0, ~~~ V_{ka} = Z_fI_{fa}\]
The symmetrical components of the current are, with \(I_{fb} = I_{fc} = 0\): \[\begin{aligned} \left[\begin{array}{c} I_{fa}^{(0)}\\ I_{fa}^{(1)}\\ I_{fa}^{(2)} \end{array}\right] & = \dfrac{1}{3}\left[\begin{array}{ccc} 1 & 1 & 1\\ 1 & a & a^{2}\\ 1 & a^{2} & a \end{array}\right]\left[\begin{array}{c} I_{fa}\\ 0\\ 0 \end{array}\right]\\ &\Rightarrow I_{fa}^{(0)}=I_{fa}^{(1)}=I_{fa}^{(2)}=\dfrac{I_{fa}}{3} \end{aligned}\]
Implies three sequence currents are in series for the LG fault.
Recall \[\begin{aligned} V_{ka}^{(0)} & =-Z_{kk}^{(0)}I_{fa}^{(0)} \\ V_{ka}^{(1)}&=V_{f}-Z_{kk}^{(1)}I_{fa}^{(1)}\\ V_{ka}^{(2)}&=-Z_{kk}^{(2)}I_{fa}^{(2)} \end{aligned}\]
Therefore,
\[\begin{aligned} V_{ka}^{(0)} & =-Z_{kk}^{(0)}I_{fa}^{(0)}\\ V_{ka}^{(1)}&=V_{f}-Z_{kk}^{(1)}I_{fa}^{(0)}\\ V_{ka}^{(2)}&=-Z_{kk}^{(2)}I_{fa}^{(0)} \end{aligned}\]
Noting that \(V_{ka}=3Z_{f}I_{fa}^{(0)}\) \[\begin{aligned} V_{ka} & =V_{ka}^{(0)}+V_{ka}^{(1)}+V_{ka}^{(2)}\\ & =V_{f}-\left(Z_{kk}^{(0)}+Z_{kk}^{(1)}+Z_{kk}^{(2)}\right)I_{fa}^{(0)}\\ & =3Z_{f}I_{fa}^{(0)} \end{aligned}\]
Solve for \(I_{fa}^{(0)}\) \[I_{fa}^{(0)}=I_{fa}^{(1)}=I_{fa}^{(2)}=\dfrac{V_{f}}{\left(Z_{kk}^{(0)}+Z_{kk}^{(1)}+Z_{kk}^{(2)}\right)+3Z_{f}}\]
