Harmonics current magnitude

It can be seen that it was again difficult to obtain results from specimens where no stable rest potential could be measured. The harmonic currents in all cases were low and for certain specimens were of the same order as the distortion resulting from the input sine wave. The Tafel slopes obtained were in general anomalously high and the corrosion rates varied over several orders of magnitude. 

The examples illustrate that even though the magnitudes of the harmonic currents are the same, the distortion percentages are different because of a change in the definition. It should be pointed out that it really does not matter what convention is used as long as the same one is maintained throughout the harmonic analysis. In this book, the 1F.F.E convention will be followed, and all harmonic distortion calculations will be based on the fundamental. 

Active filters use active conditioning to compensate for harmonic currents in a power system. Figure 4.23 shows an active filter applied in a harmonic environment. The filter samples the distorted current and, using power electronic switching devices, draws a current from the source of such magnitude, frequency composition, and phase shift to cancel the harmonics in the load. The result is that the current drawn from the source is free of harmonics. An advantage of active filters over passive filters is that the active filters can respond to changing load and harmonic conditions, whereas passive filters are fixed in their harmonic response. As we saw earlier, application of passive filters requires careful analysis. Active filters have no serious ill effects associated with them. However, active filters are expensive and not suited for application in small facilities. 

Non-linear loads have a distorted periodic wave form. Any periodic wave shape can be broken into or analyzed as a fundamental wave and a set of harmonics. Fundamental wave, 60 Hz, and harmonics currents exist within the branch circuits and feeders that serve non-linear equipment. The highest magnitudes of currents exist at the 3rd, 5th, 7th, 9th, 11th, and 13th harmonics. 

The current magnitude of each harmonic component of an AC voltammogram increases with an increase in AP (to a limiting value defined by frequency,/(Hz)), while the presence of // -drop suppresses the current. Nevertheless, the accuracy in the determination of Ip available with FT AC voltammetry is vastly superior to that possible in the DC mode. A careful selection of frequency of the periodic component in FT AC voltammetry provides a straightforward possibility to tune the sensitivity of the method to the kinetics of interest, analogous to varying the scan rate in DC voltammetry. The upper limit of frequency in an experiment is usually determined by the f a-CjjL time constant of the electrochemical cell, and by instrumental limitations. 

One of the most important theoretical contributions of the 1970s was the work of Rudnick and Stern [26] which considered the microscopic sources of second harmonic production at metal surfaces and predicted sensitivity to surface effects. This work was a significant departure from previous theories which only considered quadrupole-type contributions from the rapid variation of the normal component of the electric field at the surface. Rudnick and Stern found that currents produced from the breaking of the inversion symmetry at the cubic metal surface were of equal magnitude and must be considered. Using a free electron model, they calculated the surface and bulk currents for second harmonic generation and introduced two phenomenological parameters, a and b , to describe the effects of the surface details on the perpendicular and parallel surface nonlinear currents. In related theoretical work, Bower [27] extended the early quantum mechanical calculation of Jha [23] to include interband transitions near their resonances as well as the effects of surface states. 

The magnitude of the two parts is divided by 3 to obtain the primary line current of the delta-star transformer. The result is then added to the hue current of the star-star transformer. The total magnitude of the supply line harmonic coefficient nsum is given by. 

Figure 15.7 Primary line currents in the transformers feeding a 12-pulse thyristor bridge, with the commutation angle u = 5°. The waveforms are composed of 25 harmonics, some of which are zero in magnitude.

If the harmonic content of the applied voltage is known in terms of magnitudes and phase shifts of the components, then the circuit can be solved for each frequency. The result for each branch current or voltage will be the sum of all their harmonic components plus their fundamentals. 

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