Mutual GMD – Power Transmission Lines

Mutual GMD an abbreviation for mutual geometrical mean distance is the geometrical mean of the distances form one conductor to the other. As evident there must be between the largest and smallest such distance.

Mutual-GMD simply indicates the equivalent geometrical spacing.

There are three important causes of interests in reference to mutual GMD that are worth noting here.

Mutual-GMD

The mutual GMD between two conductors equals the distance between their conductors

D_m = Spacing between conductors = d

Mutual-GMD for single circuit 3 Phase Power Line

In such case the mutual GMD equals equivalent equilateral spacing

D_m = (d₁ d₂ d₃)^1/3

3 Phase Double Line Circuit

Consider six conductors of double circuit 3 phase line arranged as below:

A             c

B             b

C             a

Suppose radius of each conductor is r

Now Self-GMD of conductor = 0.7788r

Self GMD of combination Aa is

D_s1 = (D_AA * D_Aa * D_aa * D_aA)^1/4

Self GMD of combination Aa is

D_s2 = (D_BB * D_Bb * D_bb * D_bB)^1/4

In case of Cc it is:

D_s3 = (D_CC * D_Cc * D_cc * D_cC)^1/4

The equivalent self-GMD of one phase is expressed as follows:

D_s = (D_s1 * D_s2 * D_s3)^1/3

The mutual GMD between phase A and B expressed mathematically will be:

D_AB = (D_AB * D_Ab * D_aB * D_ab)^1/4

Mutual GMD between B and C is

D_BC = (D_BC * D_Bc * D_bC * D_bc)^1/4

Mutual GMD between C and A is

D_CA = (D_CA * D_Ca * D_cA * D_ca)^1/4

Equivalent mutual GMD D_m = (D_AB *D_BC* D_CA)^1/3

The mutual GMD depends on the spacing and is independent of exact size, shape and orientation of the conductor.