University:
University of Cincinnati Blue Ash
Course:
EPD501 | Electric Power Distribution & Transmission
Academic year:

2024
Views:

363

Pages:

2
Author:

Michael K.

Michael Kurniawan 2018123456 University of Cincinnati Assignment 3 Electric Power Distribution & Transmission In Mathematics, Geometric Mean (GM) is an average or mean value that signifies the central tendency of a set of numbers by finding the product of their values. Basically, we multiply all the numbers and take the nth root of the multiplied numbers, where n is the total number of data values. For example: for a set of two numbers like 3 and 1, the geometric mean is equal to (3×1) = 3 = 1.732. In other words, the geometric mean is defined as the nth root of the product of n numbers. It should be noted that the geometric mean is different from the arithmetic mean. Because, in arithmetic mean, we add up the data values and then divide it by the total number of values. But in geometric mean, we multiply the given data values and then take the root with the radical index for the total number of data values. For example, if we have two data, take the square root, or if we have three data, then take the square root, or if we have four data values, then take the 4th root, and so on. The same concept is also used for GMD and GMR calculations. In GMD we take the Geometric Mean of the distance between strands of two Transmission Lines while in GMR, the Geometric Mean of the distance between stands of a single composite conductor is calculated. Let us assume two composite conductors are used in a Transmission Line as shown in the figure below. As shown in the figure above, one conductor is Go and the other is Return for current for a single-phase line. The current is assumed to be equally divided among all the strands of the conductor. Therefore,  Current carried by each strand in conductor Go = I/n  Current carried by each strand in the return conductor = -I/m  Here I is the total current carried by each conductor. Now, we will calculate the GMD and GMR for the conductor configuration shown in the figure above. To get the GMD, we first need to calculate the distance between the Go and Return conductor strands. Let,  D11 = Distance between the first strand of Go and Return conductors  D12 = Distance between 1st strand of Go and 2nd strand of Return conductor  D21 = Distance between 2nd strand of Go and 1st strand of Return conductor  Dmn = Distance between mth strand of Go and nth strand of Return conductor The Geometric Mean Radius of a solid conductor or strand of radius R is defined as the fractional radius R' which has no internal flux linkage but has the same inductance as the original conductor of radius R. R' = 0.7788R To calculate GMR, we first find the distance between the individual strands. So if there are n strands in a composite conductor then obviously there will be n2 distances between strands

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