The two conductor problem of Section 2.1 can be generalized
to a group of n conductors with a common ground return. If currents
i_{1}, i_{2}, …, i_{n}
are flowing through the conductors, the voltage drop along conductor i is

$\mathbf{V_{i}}=i_{1}Z_{i1-g}+\cdots+i_{i}Z_{ii-g}+\cdots+i_{n}Z_{in}$ | (16) |

Similar equations can be constructed for all conductors in the group. Expressing the complete set of n voltage drop equations in matrix notation yields

$\mathbf{V={Z}_{series}I}$ | (17) |

where

V is the voltage vector.

I is the current vector.

Z_{series} is the series impedance matrix.

The elements of the impedance matrix Z_{series} are computed using Carson’s
equations:

$\mathbf{z_{ij}}=\begin{cases}R_{ii-g}+jX_{ii-g}&\operatorname{if}i=j\\ R_{ij-g}+jX_{ij-g}&\operatorname{if}i\neq j\end{cases}$ | (18) |

where R_{ii–g}, R_{ij–g},
X_{ii–g}, and X_{ij–g} are defined by Equation
5
through Equation
8.

The series admittance of the n conductor configuration can be determined by inverting its impedance matrix, i.e.

$\mathbf{Y_{series}=Z_{series}^{-1}}$ | (19) |