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   Home      Harmonics      K-Factor

K-factor

It is possible to determine the K-factor needed when measurements can be obtained from the load. To do this, measurements of the harmonic currents need to be taken. The harmonic current at each harmonic needs to be found, which can easily be done using a harmonic analyzer. If a current value is given for each harmonic, simply divide that value by the total current value. This will yield a per unit value for that given harmonic. If a percentage of the overall current is given, multiply that number by 100, which will also give a per unit value. Then take these values and plug them into the formula:
 
K = S [Ihn(pu)2(hn2)]
 
where Ihn(pu)2 is the value of the harmonic current squared (in the per unit form), hn2 is the order of the harmonic (3rd, 5th, 7th, etc.) squared.
 

Multiply these two numbers together for each harmonic order. The sum of these numbers gives the K-factor rating. This procedure may look difficult, but it is actually pretty simple. An example is demonstrated in Table 2. Column 1 shows the harmonic orders present, column 2 shows the harmonic current on a per unit basis, columns 3 and 4 show the square of the harmonic orders present and the harmonic order respectively, and column 5 shows the product of columns 3 and 4. The K-factor is found by summing all the numbers in column 5. A K-factor of 9.802 is formulated. This means that 9.802 times as much heat is produced by the non-linear current than would have been produced by the same value of linear current.

While K-factor shows how much more heat is produced from a non-linear load, it doesn’t portray anything about distortion of the sine wave.

K-Factor Calculation

hn

Ih(pu)

Hn²

Ih(pu)²

Ih(pu)² hn² I

1
3
5
7
9

0.897
0.568
0.376
0.189
0.091

1
9
25
49
81

0.7726
0.3226
0.1414
0.0392
0.0083

0.7726
0.2904
3.5344
1.9210
0.6708

S =9.082           


 
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