GMD & GMR stands for
Geometrical Mean Distance and Geometrical Mean Radius. This concept is very
useful in Power System for the calculation of Inductance and Capacitance of Transmission
Line.

Basically, as we know that
Geometrical Mean of n numbers a

_{1},a_{2},a_{3},….,a_{n}is
(a

_{1}a_{2}a_{3}a_{4}….a_{n})^{1/n}^{}

The same concept is also
used for the calculation of GMD and GMR. In GMD we take the Geometrical Mean of
distances between the strands of two Transmission Lines while in GMR,
Geometrical Mean of distances between the stands of a single composite
conductor are calculated.

Let us assume two composite conductors used in Transmission Line as shown in figure below.

As shown in the figure
above, one conductor is Go and another is Return for current for single phase
line. The current is assumed to be equally divided among all the strands of a
conductor.

Therefore,

Current carried by each
strand in Go conductor = I/n

Current carried by each strand in Return
conductor = -I/m

Here I is the total current
carried by each conductor.

Now, we will calculate the
GMD and GMR for the configuration of the conductors shown in figure above.

For getting the GMD, first
we need to calculate the distance between the strands of Go and Return conductors.

Let,

D11 = Distance between the 1

^{st}strand of Go and Return conductor
D12 = Distance between the 1

^{st}strand of Go and 2^{nd}strand of Return conductor
D21 = Distance between the 2nd
strand of Go and 1st strand of Return conductor

Dmn = Distance between the m

^{th}strand of Go and n^{th}strand of Return conductor
Geometrical Mean Radius of a
solid conductor or a strand of radius R is defined as the factious radius R’
having no internal flux linkage but having the same inductance as the original
conductor of radius R.

R ‘ = 0.7788R

**Method for Calculating GMR of a Composite Conductor:**

For calculating GMR, first
we find the distance between the individual strands. Thus if there are n
strands in a composite conductor then obviously there will be n

^{2}distances between the strands.
Let us now consider an
example to make our concept clear. As shown in figure below, go conductor
contain three strands of radius 2.5 mm while the return conductor contains two
of radius 5mm.

GMR of individual strands in
Go conductor R’ = 0.7788xR

= 0.7788x2.5

= 1.947mm

GMR of Go Conductor

= [(1.947x6x12)(1.947x6x6)(1.947x6x12)]

^{1/9}
= 0.4809m

Similarly,

GMR of individual strands in
Return conductor R’ = 0.7788xR

= 0.7788x5 mm

= 0.003894 m

Hence, GMR of Return
Conductor

= [(0.003894x6)(0.003894x6)]

^{1/4}
= 0.1528 m

Now, distance between strand
a and e Dae = [9

^{2}+6^{2}]^{1/2}^{}

= 10.81 m

Distance between strand c
and d, Dcd = [9

^{2}+12^{2}]^{1/2}^{}

= 15 m

Therefore,

GMD for the configuration,

= [9x10.81x10.81x9x15x10.81]

^{1/6}
= 10.74 m

## 8 comments:

awesome explanation with numerical.. thnx.

thank you!

radius is in mm and distance is in m and u have solved it without unit conversion

This much unit conversion you can do dear. Once unit conversion has been done, carefully see. Thank you very much next time I will do this much of unit conversion.

This much unit conversion you can do dear. Once unit conversion has been done, carefully see. Thank you very much next time I will do this much of unit conversion.

Thank u so much good and easy exppanations

From where u got R'=0.778R?

Please read Geometrical Mean Radius (GMR) and Inductance to know why R'=0.7788R.

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