Third harmonic

Sipe J E, Moss D J and van Driel H M 1987 Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals Phys. Rev. B 35 1129-41... 

Question. Show that the third term in Equation (9.11) results in the generation of radiation of frequency 3v when radiation of frequency v is incident on a crystal capable of third harmonic generation. 

Because the second term in the brackets contains 3v in the sine function, radiation at a frequency which is three times that of the incident radiation is generated. This is referred to as third harmonic generation. The first term in brackets indicates that some radiation of unchanged frequency also results. 

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. 

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. 

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. 

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. 

Another remedial measure is the use of blocking circuits by providing a high-impedance path in the ground circuit when a phase-to-ground circuit is used for the com-munication network, to block the entry of the third harmonic quantities into the system from other systems. 

Isolated neutral In i symmetrical ihree-phtise three-wire star-connected system the summation of all phase quantities, voltage or cunent will be zero, as illustrated in Figure 21.7. When a few harmonics exist in such a system, this balance is disturbed and the sum of these quantities is not zero. The third harmonic quantities can find their outlet only through t neulral of the system. Since there is no neutral available in this system, no third harmonic quantities will tlow into or out of the supply system and affect the equipment associated with it or a communication network if existing in the vicinity (Figure 23.12(a)). 

Grounded neutral When the neutral is grounded, the third harmonic quantities will be able to find their w ay through it. This system can thus be considered to contain the third harmonic quantities and will affect operation of the equipment connected on it and communication networks if existina in the vicinitv (Figure 23.12(c)),... 

Inductive equipment generates moderate amounts of harmonic disorders, except the third harmonics on an LT system. 

The odd harmonics (non-multiples of 3), generated by hexaphase rectifiers, are more severe than any other harmonic disorders present in the system, except LT systems, where third harmonics too are pronounced. An LT system and the devices connected on it must take cognisance of these effects and suitable measures be taken, either to diminish such effects or to select higher ratings of the devices to operate on such systems without overloading. HT systems must take particular cognizance of odd harmonics. 

In an HT system, either the star is not grounded or it is a delta-connected system and hence the third harmonic is mostly absent, while the content of the. second harmonic nuiy be too small to be of any significance. For this purpose, where harmonic analysis is not possible, or for a new installation where the content of harmonies is not known, it is common practice to use a series reactor of 6% of the reactive value of the capacitors installed. This will suppress most of the harmonics by making the circuit inductive, up to almost the fourth harmonic, as derived subsequently. Where, however, second harmonics are significant, the circuit may be tuned for just below the second harmonic. To arrive at a more accurate choice of filters, it is better to conduct a harmonic analysis of the system through a harmonic analyser and ascertain the actual harmonic quantities and their magnitudes present in the system, and provide a correct series or parallel filter-circuits for each harmonic. 

Similarly, the third harmonic may also be suppressed by grounding the generator or the transformer neutral through a suitable impedance (LC circuit), as discussed in Section 23.5.2(e) and equation (23.6). 

The third harmonic was almost absent, hence it was not considered. The second and other even harmonics were also insignificant. Similarly, higher harmonics (above the thirleenth) were also insignificant, hence were not considered for ease of illustration. 

This can be used for the pipe between the surge drum and the pipe header. The length of pipe should be such that the fundamental and third harmonic are avoided, and these should differ by at least five cycles from the base and harmonics produced by the compressor. 

Almost every unique frequency contained in the vibration signature of a machine-train can be directly attributed to a corresponding mechanical motion within the machine. For example, the constant endplay or axial movement of the rotating element in a motor-generator set generates elevated amplitude at the fundamental (lx), second harmonic (2x), and third harmonic (3x) of the shaft s true running speed. In addition, this movement increases the axial amplitude of the fundamental (lx) frequency. 

Axial movement and the resulting presence of a third harmonic of running speed is another indication of instability or imbalance within the motor. The third harmonic is present whenever there is axial thrusting of a rotating element. 

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. 

The third (3x) harmonic of running speed is a critical monitoring parameter. Most, if not all, generators tend to move in the axial plane as part of their normal dynamics. Increases in axial movement, which appear in the third harmonic, are early indicators of problems. 

---