GMD

What is GMD and GMR in Transmission Lines

Two key terms, GMR (self GMD) and mutual GMD, are used to simplify the inductance and capacitance calculations of an overhead transmission line. The process of solving inductance and capacitance is made easier by GMR and GMD, especially when there is a multiconductor arrangement.

GMR (self GMD) :

GMR stands for Geometrical Mean Radius. It is also called the self GMD (Geometrical Mean Distance) It is represented by Ds. We know that the expression for the inductance per conductor per meter is given by,

The term (0.5 x 10-7) in the above equation represents the inductance due to the flux which is present inside the conductor. Hence, the above equation can be simplified by introducing GMR that eliminates the term (0.5 x 10-7). This can be done as follows.

The solid conductor can be replaced by an equivalent hollow conductor whose surface is extremely thin. As the ac current flows through the surface, the internal conductor flux linkage becomes zero. This eventually reduces the internal flux to zero and the term (0.5x 10-7) gets eliminated.

The radius of the equivalent hollow conductor is chosen to be smaller than the physical radius of the solid conductor in order to accommodate more flux to make up for the absence of the internal flux linkages. Mathematically, it is demonstrated that GMR is equal to 0.7788 x r if ‘r’ is the radius of the solid conductor. The result of the above equation is,

Ds equals self-Geometrical Mean Distance in the equation above, or GMR equals 0.7788r. The size and shape of the conductor have an impact on the GMR. The conductor spacing has no effect on GMR.

Mutual GMD :

Geometrical Mean Distance, or GMD, is indicated by the symbol Dm. The calculation of mutual inductance between the spaced conductors is made simpler by the use of the term mutual GMD. The mutual Geometrical Mean Distance actually represents the geometric mean distance between the two conductors. It also shows the corresponding geometrical spacing. GMD has different values depending on how the conductors are arranged.

GMD of Two Adjacent Conductors :

When two conductors are placed next to one another and their distance from one another is much greater than their combined diameter, the mutual Geometrical Mean Distance is equal to the distance between their centres. As a result, mutual GMD, Dm = D conductor spacing.

3-Phase Single Circuit Line :

For a 3-phase single circuit line, the mutual GMD is equal to the equivalent equilateral spacing. Therefore, mutual GMD is given as,

3-Phase Double Circuit Line :

Consider a 3-phase double circuit line with the arrangement of conductors as shown in the figure.

In the figure above, the conductors a,b, and c belong to the first circuit, and a’, b’, and c’ belong to the other circuit. Now, GMR (self GMD) of each conductor = 0.7788 x r, the self GMD of the combination of aa’, bb’, and cc’ is,

Where, Daa = Da’a’ = Dbb = Db’b’ = Dcc = Dc’c’ = Self Geometrical Mean Distance of conductor Daa’ = Da’a = Distance between a and a’Dbb’ = Db’b = Distance between b and b’Dcc’ = Dc’c = Distance between c and c’. Therefore, the equivalent self Geometrical Mean Distance per phase is given by, Now mutual-Geometrical Mean Distance between the phases AB, BC, and CA is, Therefore, the equivalent mutual Geometrical Mean Distance is given by,

So The distance between the conductors affects Geometrical Mean Distance. It doesn’t matter what the conductor looks like, how big it is, or which way it is oriented.