Monday, 19 September 2016

Concept of GMD and GMR


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 Mena of n numbers a1,a2,a3,….,an is

(a1a2a3a4….an)1/n

The same concept is also used for the calculation of GMD and GMR. In GMD we take the Geometrical Mean if distances between the stands 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 compositeconductors 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 1st strand of Go and Return conductor

D12 = Distance between the 1st strand of Go and 2nd strand of Return conductor

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

Dmn = Distance between the mth strand of Go and nth 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 n2 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 = [92+62]1/2

                                                                = 10.81 m

Distance between strand c and d, Dcd = [92+122]1/2

                                                              = 15 m
Therefore,

GMD for the configuration,

= [9x10.81x10.81x9x15x10.81]1/6  


= 10.74 m    

5 comments:

Unknown said...

awesome explanation with numerical.. thnx.

Aditya Kumar said...

thank you!

Aakash Aggarwal said...

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

Aditya Kumar said...

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.

Aditya Kumar said...

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.