### Effects of Harmonics on Power Cables

The power cables are used to carry power from supply source to the load point. The cable has DC resistance which depends on the size of the cable. When current flows through the cable the heat loss I2R takes place in the cable. The heat loss in the cable is proportional to the square of the current flowing through the cable and proportional to the cable resistance. The harmonic current cause additional heating in the power cable due to increased I2R losses.
The DC resistance of the cable does not change if the cable carries the DC power, however in the case of AC power transmission the resistance gets increased with increase in the frequency and also increase in the current. The AC resistance of the cable is higher than the DC resistance of the cable. Thus the power loss caused by the heating of the cable gets increased if the cable carries high frequency AC current.
Increased I2R Losses due to Harmonics

The RMS value of the current increases when the magnitude of the harmonics current increase. In the harmonic rich supply system, the cable losses increase due to two reasons.

• Increase of the cable resistance with harmonics
• Increase of RMS current due to Harmonics
How the RMS current increase with Harmonics?
The harmonic current waveform is not sinusoidal. According to Fourier series, the non sinusoidal waveform can be resolved into sinusoidal and the integral multiples of the sinusoidal waveform. The integral multiples of fundamental frequency is known as harmonics. For example, take a non sinusoidal current waveform as given below.
This sort of current waveform contains harmonics. If we synthesize this waveform let the magnitude of the harmonics are as follows.

The harmonic spectrum of the current waveform is as given below.

The RMS value of the non-sinusoidal current waveform cab be calculated by taking the harmonic current into account.

Where,
I= fundamental current
I= 5th harmonic current
I= 7th harmonic current
I11= 11th harmonic current
The RMS value of the current increase by 5 % of the fundamental RMS current. If the fundamental current is 100 amperes and the load draws harmonic current from the supply source then the total current flowing will be 105 amperes.The increase of  current due to harmonic current cause 10% additional power loss in the cable.The power cable needs to be de-rated according to the harmonic current flowing through the cable.
While selecting cable for a particular load the harmonic current must be taken into consideration.
The other factor that also contribute to the increase of power loss is the AC resistance of the cable. The harmonic current has higher frequency -250 Hz, 350Hz,550 Hz etc.At higher frequency the current tends to flow on the outer surface of the conductor.The phenomenon is called the SKIN EFFECT. The effective resistance gets increased when the power cable carry the high frequency current. The AC resistance of the power cable is always more than the DC resistance because of the skin effect and the proximity effect. The skin effect is proportional to the frequency and the proximity effect is proportional to the square of the frequency. Thus the effective resistance of the conductor carrying harmonics current gets increased.
Over Voltage due to Harmonics
If the capacitor banks installed for power factor correction resonate with the inductance of the transformer, the resonance phenomenon can boost the system voltage. In this condition the power cables experience voltage stress and the cable insulation may get failed.
Cable Derating
The effect of heating due to harmonic current must be taken into consideration while sizing the cable. The usual derating curves as per IEEE519 have been plotted for a number of cable sizes for 6 pulse harmonic distribution.