Node impedance matrix is an important analysis tool in power network fault
calculation. There are mutual inductance or partial mutual inductance between parallel
double circuit lines on the same tower in power network, which brings challenges to
the formation and correction of node impedance matrix. In this paper, theoretical
analysis and method derivation are carried out for mutual inductance transmission
line, partial mutual inductance line and fault situation on mutual inductance line.
The network node numbering strategy and specific numbering method are given. The
relationship matrix between node voltage, node current, branch voltage and branch
current is enriched and perfected. The corresponding formula derivation also verifies
the formation method in theory It provides a new analysis tool for fault analysis and
calculation in smart grid.