Third harmonic current

Overloading of neutral conductors due to third harmonic currents flowing through the neutral. The size of the neutral must be increased by 150-200% of the normal size in such cases, depending upon the severity of the harmonics. 

It is common practice to leave the star-connected capacitor banks ungrounded when used in the system or use delta-connected banks to prevent the flow of third harmonic currents into the power system through the grounded neutral. 

For example, assume that the RMS value of the third harmonic current in a nonlinear load is 20 A, the RMS value of the fifth harmonic current is 15 A, and the RMS value of the fundamental is 60 A. Then, the individual third harmonic distortion is ... 

Level of continuous third harmonic current that will flow in the impedance. 

Such relays are normally instantaneous, highly sensitive and operate at low spill cuiTents. Since they detect the residual current of the system, the current may contain third-harmonic components (Section 23.6) and operate the highly sensitive relay in a healthy condition. To avoid operation of the relay under such conditions, it is a normal practice to supply the relay coil with a tuned filter, i.e. a series L-C circuit to filter out the third-harmonic components. The capacitance of the filter circuit may also tame a steep rising TRV (Section 17.10.3) during a momentary transient condition and protect the relay. 

The greatest effect of ageing is reflected by the variation in its resistive current, which is rich in the third harmonic. Variation in is used in assessing the condition of an arrester. By conducting laboratory tests to determine the characteristics of an arrester, we can establish a ratio between the total leakage current, IZnO and the content of If, to assess the condition of the arrester. If we can monitor this current, we can monitor the condition of the arrester. Below we discuss briefly one such method by which this component can be separated out. 

Leakage current monitor - this can be connected perma-nently for continuous reading or periodic monitoring. The normal practice is to measure only periodically for a short period to take average measurements on an hourly, daily, monthly or yearly basis. When not connected permanently, the instrument can also be used as a portable kit to monitor the condition of other arresters installed in the vicinity. Field probe - to compensate the third harmonic of the system voltage to make the IZnO free from the third harmonic of the system voltage. This method of /r measurement therefore provides more accurate and closer monitoring of the arrester. 

Current probe - to measure the third harmonic component of/p It is then converted to actual I, from the ZnO characteristic data provided by the arrester manufacturer, /r versus /jr, corrected to the site operating temperature and voltage. The value of is then used to assess the condition of the arrester. 

Many electrical problems, or problems associated with the quality of the incoming power and internal to the motor, can be isolated by monitoring the line frequency. Line frequency refers to the frequency of the alternating current being supplied to the motor. In the case of 60-cycle power, monitoring of the fundamental or first harmonic (60 Hertz), second harmonic (120 Hz), and third harmonic (180 Hz) should be performed. 

A small sinusoidal perturbation is applied potentiostatically to the system under investigation and the resulting current sine wave is analysed in terms of its second and third harmonics ( 2 and 13), i being the fundamental. The corrosion current is calculated... 

Most commercial multistory installations contain busways that serve as the primary source of electrical power to various floors. Busways that incorporate sandwiched busbars are susceptible to nonlinear loading, especially if the neutral bus carries large levels of triplen harmonic currents (third, ninth, etc.). Under the worst possible conditions, the neutral bus may be forced to carry a current equal to 173% of the phase currents. In cases where substantial neutral currents are expected, the busways must be suitably derated. Table 4.10 indicates the amount of nonlinear loads that may be allowed to flow in the phase busbars for different neutral currents. The data are shown for busways with neutral busbars that are 100 and 200% in size. 

A more complex analysis of the effect of laser phase diffusion has been appli fS the case of one-photon vs. three-photon absoiption (i.e., simultaneous absorption 3a)j and third-harmonic generation frqnt>t coi laser. As discussed in Section 3.3.2, current experiments vary the relative ph of two laser beams by passing co3 and co, through a gas. If the laser frequcnc somewhat unstable, then the relative phase of the two beams will acquire a fhtct y ing phase that is a source of phase loss in the system. The phase fluctuations q ... 

The voltage is thus a sum of two parts one with the same frequency as that of the applied current and the other with a frequency three times the original frequency - the so called third harmonic. The third harmonic coefficient B is defined as B = Vs//(7o). ... 

We suppose now that our sample is a random lattice resistor network with 1 — p fraction of missing resistors, where p > Pc such that the lattice is still conducting. We shall now show that there is a relation between the failure current 7f of such a network and its third harmonic coefficient B (Yagil et al 1993). 

Fig. 2.11. Failure current If versus the third harmonic coefficient B showing that the exponent x 0.48 If B ). The inset shows that B with ty 1.2 (from Yagil et al 1992).

If we include them, we find that the current response is not purely sinusoidal, but instead comprises a whole series of sinusoidal signals at m, 2m, 3m,. . ., which are summed together. The current component at 2m is the second harmonic response, while that at 3m is the third harmonic, etc. These higher harmonics arise from curvature in the i-E relation. 

The choice of current or voltage setting for the relay will depend upon the design value of earth fault current that will pass in the NER during the specihed time e.g. 20 amps for 10 seconds. If the setting is too low the relay may respond to stray and harmonic currents in the neutral circuit. The maximum expected third plus triplen currents should be determined and the relay set at say double their combined level, or higher. 

L. 1. Powell, Influence of third harmonic circulating currents in selecting neutral grounding devices. IEEE Transactions on Industrial Applications. Vol. IA-9, Paper No. 6, 1973. 

Third-order intermodulation performance for Class AB or B is generally worse than Class A, and harmonic distortion is better in the sense that even harmonics are canceled to a large degree in the primary of the output transformer. These currents flow in opposite directions at the same time and net to zero, whereas odd order harmonic currents do not. An amplifier model for a Class AB or B amphfier is shown in Fig. 7.54. Its topology is the same as that for the Class A in Fig. 7.51 except that listandardLoad(sL) inside the amplifier is replaced by liintemai or Ri t- For a maximum power efficiency, //niax = 78.5%,... 

An enhancement to the efficiency of the Class B amplifier makes use of the addition of a third harmonic component of the right amount to the collector-emitter voltage waveform to cause near square-wave flattening when it is near zero (where the collector current is greatest). This modification alters the amplifier enough so that it enjoys a different classification called Class F. Flattening enhances efficiency by as much as one-eighth so that... 

If a delta/wye connected power transformer is installed between the power source and the load, the power factor at the transformer input generally will reflect the average PF of the loads on the secondary. This conclusion works on the assumption that the low PF is caused by inductive and capacitive reactances in the loads. However, if the load current is rich in harmonics from rectifiers and switching regulators, some of the harmonic currents will flow no farther toward the power source than the transformer delta winding. The third harmonic and multiples of three will flow in the delta winding and will be significantly reduced in amplitude. By this means, the transformer will provide some improvement in the PF of the total load. 

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