Power-System Harmonics

Slot harmonics have been the source of much of the trouble caused by rotating machinery. They are produced because the armature has slots cut in its surface into which the conductors are placed. These harmonics have been reduced by improved design. Harmonics are also caused if the flux distribution in the air gaps is non-sinusoidal. The type of armature winding influences the wave shape also.

Interference may be caused by generators with grounded neutrals,^10,26 This can be controlled¹⁰ by (1) isolating the generator neutral, and supplying the system ground through properly designed transformer banks; (2) grounding the neutrals of only those generators that have no detrimental triple harmonics in their phase-to-neutral voltage; and (3) grounding the neutrals through devices such as reactors and parallel-resonant circuits (wave traps), which suppress the undesired harmonics,

The harmonics caused by transformers are due to the magnetizing requirements of the transformer core. When the primary of a transformer is connected to a source of voltage, the back or counter-electromotive force induced in the transformer windings must at each instant (approximately) equal the instantaneous value of the impressed voltage. If the impressed voltage is a sine wave, the back voltage must also be a sine wave. The flux in the transformer determines the back electromotive force, and thus, under the conditions just assumed, the flux must also follow sine-wave variations. These relations are shown in Fig. 16.

Figure 16. Current distortion caused by hysteresis in iron-cored coils.

Suppose that the voltage is at zero as indicated at point (1). The flux must be maximum at this point, since the induced voltage is given by the relation e = -Ndφ/10⁸dt. But, from the hysteresis curve, when the flux φ is maximum the current I is maximum, and thus a point on the current curve is obtained. Ninety electrical degrees later at point (2) the voltage will be maximum, and the flux must accordingly be passing through zero; but, to produce zero flux, the current must be negative as indicated on the hysteresis curve. Similarly, the values at points (3), (4), and (5) are found to be as shown, and also, the intermediate values can be determined. The current wave is therefore considerably distorted, the amount depending on the degree of saturation of the core. For this reason, transformers should not be operated at above rated voltage. In much the same manner it can be shown that, if a sine-wave current is passed through a transformer, then a distorted voltage results. These current and voltage waves therefore contain harmonics and are a source of inductive disturbance, as has been discussed.

Transformers are usually connected to three-phase lines in banks of three and may be connected either delta or wye (also called star). If they are wye connected, the triple harmonic components add directly. If the neutral of the transformers is not connected to the system neutral (either ground or a fourth wire), then a large triple-harmonic (or residual) voltage will appear between the neutral of the transformer bank and system neutral. If the neutral is grounded, then a residual current composed of these triple-harmonics flows through the neutral ground and ground to line capacitance, and the residual voltage is decreased. If the transformers are delta connected, the triple harmonics flow around the closed delta and do not appear as residuals on the line.

The effects of the various possible connections are well summarized as follows.¹⁰

A large measure of control may be exercised on the magnitudes of the triple-harmonic residual voltages and currents by the use of certain transformer connections and by not operating the transformers at high flux densities.

The magnitudes of triple-harmonic residual currents in grounded-neutral systems may be minimized by the use of star-delta connected transformers, in which case nearly all the required triple-harmonic current circulates in the delta. The opposite extreme occurs with star-star connections in which case the full triple-harmonic magnetizing current flows in the two systems which the transformer interconnects, the relative magnitudes in each depending on their relative impedances. Where a star-star bank is connected at one terminal of a line, with a star-delta at the other, the neutrals at each end being grounded, practically the entire third harmonic required by the star-star bank may be expected to circulate in the line connecting the two.

An effective method of control for cases in which star-star connections are required due to phase relations is the provision of a third set of windings or tertiaries in the transformers, the impedance of the tertiaries with respect to the other windings being sufficiently low to furnish an adequate path for the triple-harmonic magnetizing current. An alternate method of control, which also provides like phasing on the two sides of the bank, is the use of zig-zag connected transformers.⁽¹⁾

In addition to the sources of harmonics that have been considered here, many others exist. One that is particularly bad is mercury-arc rectifiers²⁸ used to convert from alternating to direct current. Electric railways using alternating-current trolley systems have been a source of trouble.

(1)	Reprinted by permission, courtesy H. L. Wills, O. B. Blackwell, and the American Institute of Electrical Engineers.