# Inductance in Three Phase Transmission Line

In the **three phase transmission line**, three conductors are parallel to each other. The direction of the current is same through each of the conductors.

Let us consider conductor A produces magnetic flux φ_{A},
Conductor B produces magnetic flux φ_{B},
And conductor C produces magnetic flux φ_{C}.
When they carry current of the same magnitude I, they are in flux linkage with each other.

Now, let us consider a point P near three conductors. So, flux linkage at point P due to current through conductor A is, Flux linkage at point P for conductor A due to current through conductor A =

Flux linkage at point P for conductor A due to current through conductor B = Flux linkage at point P for conductor A due to current through conductor C = Therefore, flux linkage at point P for conductor A, As, and in balanced system, then we can write that

If we arrange them in matrix form, then we get

Where, λ_{A}, λ_{B}, λ_{C} are the total flux linkages of conductor A, B and C.

L_{AA}, L_{BB} and L_{CC} are the self inductances of conductor A, B and C.

L_{AB}, L_{AC}, L_{BC}, L_{BA}, L_{CA}, L_{CB} are the mutual inductances of between conductors A, B and C.

Again balanced system
And
In balanced system, then we can write that
Similarly,