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 \(Z_f\)

    image

  • The relations to be developed will apply only when the fault is on phase \(a\), but any phase can be designated as phase \(a\)

  • \[I_{fb} = I_{fc} = 0, ~~~ V_{ka} = Z_fI_{fa}\]
    are expressed by : The conditions at the fault bus
  • \[\begin{aligned} \left[\begin{array}{c} I_{fa}^{(0)}\\ I_{fa}^{(1)}\\ I_{fa}^{(2)} \end{array}\right] & = \dfrac{1}{3}\left[\begin{array}{ccc} 1 & 1 & 1\\ 1 & a & a^{2}\\ 1 & a^{2} & a \end{array}\right]\left[\begin{array}{c} I_{fa}\\ 0\\ 0 \end{array}\right]\\ &\Rightarrow I_{fa}^{(0)}=I_{fa}^{(1)}=I_{fa}^{(2)}=\dfrac{I_{fa}}{3} \end{aligned}\]
    : The symmetrical components of the current are, with

  • Implies three sequence currents are in series for the LG fault.

  • \[\begin{aligned} V_{ka}^{(0)} & =-Z_{kk}^{(0)}I_{fa}^{(0)} \\ V_{ka}^{(1)}&=V_{f}-Z_{kk}^{(1)}I_{fa}^{(1)}\\ V_{ka}^{(2)}&=-Z_{kk}^{(2)}I_{fa}^{(2)} \end{aligned}\]
    Recall

  • Therefore,

    \[\begin{aligned} V_{ka}^{(0)} & =-Z_{kk}^{(0)}I_{fa}^{(0)}\\ V_{ka}^{(1)}&=V_{f}-Z_{kk}^{(1)}I_{fa}^{(0)}\\ V_{ka}^{(2)}&=-Z_{kk}^{(2)}I_{fa}^{(0)} \end{aligned}\]
  • \[\begin{aligned} V_{ka} & =V_{ka}^{(0)}+V_{ka}^{(1)}+V_{ka}^{(2)}\\ & =V_{f}-\left(Z_{kk}^{(0)}+Z_{kk}^{(1)}+Z_{kk}^{(2)}\right)I_{fa}^{(0)}\\ & =3Z_{f}I_{fa}^{(0)} \end{aligned}\]
    Noting that
  • \[I_{fa}^{(0)}=I_{fa}^{(1)}=I_{fa}^{(2)}=\dfrac{V_{f}}{\left(Z_{kk}^{(0)}+Z_{kk}^{(1)}+Z_{kk}^{(2)}\right)+3Z_{f}}\]
    Solve for
image