Harmonic Number is the sum of the reciprocals of the first n natural numbers. It represents the phenomenon when the inductive reactance and the capacitive reactance of the power system becomes equal.

Formula

H=WrWwhere Wr=1LC−−−√and W=2πfH=WrWwhere Wr=1LCand W=2πf

Where −

·        ff = Harmonic resonance frequency.

·        LL = inductance of the load.

·        CC = capacitanc of the load.

Example

Calculate the harmonic number of a power system with the capcitance 5F, Inductance 6H and frequency 200Hz.

Solution:

Here capacitance, C is 5F. Inductance, L is 6H. Frequency, f is 200Hz. Using harmonic number formula, let’s compute the number as:

H=1LC√2πf⟹H=16×5√2×3.14×200=0.182571256=0.0001H=1LC2πf⟹H=16×52×3.14×200=0.182571256=0.0001

Thus harmonic number is 0.0001.