## Friday, August 26, 2011

The primary effect of harmonics on power cables is the additional heating due to increase in the I2R losses. This can be attributed to the two phenomena known as skin effect and proximity effect, both of which vary as a function of frequency as well as conductor size and spacing. Also, cables involved in system resonance, may be subjected to voltage stress and corona, which can lead to dielectric (insulation) failure.

I2R Losses

These losses are dependent on two electrical parameters: the current that flows through the cable and its resistance.

RMS Current

I2R losses vary as the square of the RMS current, thus, harmonics should be minimized since it will lead to higher conductor losses, which in turn result to increased temperature and in the worst case a significant reduction in conductor life.

The equation below illustrates how harmonic currents contribute to the increase in the total RMS current:

Irms = √[(I1)2 + (I2)2 + (I3)2 +…..+ (In)2]

where:
I1 = fundamental current
I2 = 2nd harmonic current
I3 = 3rd harmonic current
In = nth harmonic current

It is quite easy to notice that nonsinusoidal components can considerably increase the net RMS current, since their squares are added directly to the square of the fundamental component prior to taking the square root.

Cable Effective Resistance

As mentioned, the cables resistance may increase due to skin effect and proximity effect. The former is a case where unequal flux linkages across the cross section of the cable causes the AC current to flow on the outer periphery of the conductor. On the other hand, conductors that are spaced close to one another and carrying alternating current will have the current distribution in each conductor changed by mutual reactance. This results in increased cable effective resistance known as proximity effect. Even so, if conductor spacing exceeds 10 times the conductor diameter, proximity effect will be less than 1% and can be neglected.

Both phenomena, which tend to be greater when the frequency of the AC current is higher, could cause the effective AC resistance (R) to increase above the DC resistance (RDC). Consequently, when a current waveform that is rich in high-frequency harmonics will flow in the cable, the equivalent R for the cable is raised even higher, thus, magnifying the I2R loss.

Cable Derating

The effect of harmonic heating in cables is normally not a matter of great concern. However, in designing and sizing, one should consider derating the conductor in order to account such unwanted effects.

Moreover, the usual capacity derating curves have been plotted for a number of cable sizes for a six-pulse harmonic distribution. Please refer to the table below as published by IEEE.
 Power Cable Derating with Harmonics
References:
IEEE 519-1992. Recommended Practice and Requirements for Harmonic Control in Electrical Power Systems
Sankaran, C. (1999). Effects of Harmonics on Power Systems 1