K-factor

It is possible todetermine the K-factor needed when measurements can be obtained from the load.To do this, measurements of the harmonic currents need to be taken. Theharmonic current at each harmonic needs to be found, which can easily be doneusing 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 unitvalue 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 takethese values and plug them into the formula:
K = S [Ihn(pu)2(hn2)]
where Ihn(pu)2is the value of the harmonic current squared (in the per unit form), hn2is the order of the harmonic (3rd, 5th, 7th,etc.) squared.

Multiply these twonumbers together for each harmonic order. The sum of these numbers gives theK-factor rating. This procedure may look difficult, but it is actually prettysimple. An example is demonstrated in Table 2. Column 1 shows the harmonicorders 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 harmonicorder respectively, and column 5 shows the product of columns 3 and 4. TheK-factor is found by summing all the numbers in column 5. A K-factor of 9.802is formulated. This means that 9.802 times as much heat is produced by thenon-linear current than would have been produced by the same value of linearcurrent.

While K-factor shows how much moreheat is produced from a non-linear load, it doesn’t portray anything aboutdistortion 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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