Inductance of Two Wire Single Phase Transmission Line
Suppose conductor A of radius rA carries a current of IA in opposite direction of current IB through the conductor B of radius rB. Conductor A is at a distance D from conductor B and both are of length l. They are in close vicinity with each other so that flux linkage takes place in both of the conductors due to their electromagnetic effects.
Let us consider the magnitude of current in both conductors are same and hence IA = - IB, Now, total flux linkage in conductor A = flux linkage by self-current of conductor A + flux linkage on conductor A due to current in the conductor B. Similarly, flux linkage in conductor B = flux linkage by self-current of conductor B + flux linkage on conductor B due to current through conductor A. Now if we consider a point P in close vicinity both conductor A and B, the flux linkage at point P would be, flux linkage at point P for current carrying conductor A + flux linkage at point P for current carrying conductor B i.e.
Now, ……… shown in the figure below in figure (a) and (b).
- λAAP is the flux linkage at point P for conductor A due to current through conductor A itself.
- λABP is the flux linkage at point P for conductor A due to current through conductor B.
- λBAP is the flux linkage at point P for conductor B due to current through conductor A.
- λBBP is the flux linkage at point P for conductor B due to current through conductor B itself.
λABP and λBAP are negative in value because the directions current are opposite with respect to each other.
If we consider that both conductor are with same radius, i.e. rA = rB = r and point P is shifted to infinite distance then we can write that If conductor A becomes bundled conductor, then its geometrical mean radius (GMR) will be calculated for n number of conductors per bundle. Where, d is the distance between the central axis of conductors within the bundle.