# Difference between Harmonics and Sub-Harmonics

Harmonics is generated when the equipment draws current which is non linear to the applied voltage. The elctronic devices are the non linear devices which draw non linear current when sinusoidal voltage is applied. The transformer at the time of charging also draws non-sinusoidal current.  This non- linearity in the current cause harmonics in the system. The non-sinusoidal current can be resolved into sinusoidal component and integral multiples of the sinusoidal component using Fourier series.

The sinusoidal component whose frequency is equal to the fundamental frequency is called the fundamental component, and the integral multiples of the fundamental frequency is called harmonics. This means, if the frequency of fundamental component is 50 Hz, then the frequency of harmonics will be 2×50 (=100 Hz), 3×50 (=150 Hz) and so on.

The harmonic frequency which is even multiples of the fundamental is called even harmonicsTherefore, signals with frequency 100 Hz, 200 Hz, 300 Hz are the even harmonics of fundamental component with frequency 50 Hz. The harmonic frequency which is odd multiples of the fundamental is called odd harmonics. Therefore, signals with frequency 150 Hz, 250 Hz, 350 Hz are the odd harmonics of fundamental component with frequency 50 Hz.

Thus, the harmonic frequency is always more than the fundamental freeqency. The harmonic frequency is equal to nxf, where n is the order of harmonics and f is the frequency of the fundamental component. The harmonic frequency for harmonic order 2,3,4,5,6,7,and 8 is 100Hz , 150 Hz , 200 Hz, 250 Hz, 300 Hz, 350 Hz respectively. Thus, the frequency of even and odd harmonic order is always more than the fundamental frequency.

Sub-harmonic frequencies are frequencies below the fundamental frequency  in a ratio of 1/n th of the fundamental frequency where,  n is a positive integer number.In other words, the subharmonics are the fractional frequency component. For example, if the fundamental frequency 50 Hz, sub-harmonics frequency is 1/n(f) = 1/2(50)=25 Hz, 1/3(50) = 16.66 Hz, 1/4(50)=12.5 Hz etc. . Thus, a frequency of 25 Hz, 16.66 Hz, 12.5 Hz etc. are sub-harmonics.

Thus, the  harmonics have frequency more than the fundamental frequency and the sub-harmonics have frequency less than the fundamental frequency. sub-harmonics is  having frequency of nf  and harmonics is having frequency of  (1/n)f ,where f is fundamental frequency.If the harmonics is a non-integer multiple of the fundamental frequency then then it is called interharmonics.

The series reactors are used to limit the amount of fault current since inductor limits the fault current. The series line capacitors are used to increase the amount of real power by improving the power factor of the electrical network. However, it creates a sub-harmonic current with frequency below the fundamental frequency.Another major source of subharmonics is PWM inverter run with asynchronous PWM (carrier wave frequency is not an integer multiple of the modulation signal) and cycloconverters.

How sub-harmonics affect the power system?

The major problems offered by Sub– harmonics are induction generator effects, torsional interactions, torque amplification, sub– synchronous resonance, and transformer saturation. Also, Subharmonics generated from capacitors may  introduce errors in phasor estimation. This may cause mal-operation of distance relays. Impedance over-reach and under-reach are two commonly reported conditions. Apart from that, significantly high amount of subharmonics can also affect directionality of the relay.The effect of interharmonics is similar to any other harmonics i.e. they are harmful and needs to be eliminated from the system.

The  most of the loads are inductive in nature.  The impedance of inductive load depends on the frequency. The sub-harmonic frequency offers lower reactance(XL = 2 πfL) as compared to the reactance offered at interharmonic frequencies. As a result, sub-harmonic current will be much higher than the inter-harmonic current. This makes the sub-harmonics more severe than the interharmonics.

In other words, the lower the order of the harmonics the more severe it can become as the reactance offered also gets lowered.