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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 φA, Conductor B produces magnetic flux φB, And conductor C produces magnetic flux φC. When they carry current of the same magnitude I, they are in flux linkage with each other.

three phase transmission line 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, λA, λB, λC are the total flux linkages of conductor A, B and C.
LAA, LBB and LCC are the self inductances of conductor A, B and C.
LAB, LAC, LBC, LBA, LCA, LCB are the mutual inductances of between conductors A, B and C.
Again balanced system And In balanced system, then we can write that Similarly,



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