Reactors with Large A-C Flux

With the increasing use of higher voltages, it often happens that the a-c flux is no longer small compared to the d-c flux. This occurs in high-impedance circuits where the direct current has a low value and the alternating voltage has a high value. The inductance increases by an amount depending on the values of a-c and d-c fluxes. Typical increase of inductance is shown in Fig. 68 for a reactor working near the saturation point. Increasing a-c flux soon adds to the saturation, which prevents further inductance increase and accounts for the flattening off in Fig. 68.

Fig. 68. Increase of inductance with a-c induction.

Saturation of this sort may be avoided by limiting the value of the d-c flux.

To illustrate the effect of these latter conditions, suppose that a reactor has already been designed for negligibly small alternating flux and operates as shown by the minor loop with center at G, Fig. 69.

Fig. 69. Change of permeability with a-c induction.

Without changing anything else, suppose that the alternating voltage across the reactor is greatly increased, so that the total a-c flux change is from zero to B_m. (Assume that the reactor still operates about point G.) The hysteresis loop, however, becomes the unsymmetrical figure OB_mD'O. The average permeability during the positive flux swing is represented by the line GB_m, and during the negative flux swing by OG. The slope of GB_m is greater than that of the minor loop; hence, the first effect exhibited by the reactor is an increase of inductance.

The increase of inductance is non-linear, and this has a decided effect upon the performance of the apparatus. An inductance bridge measuring such a reactor at the higher a-c voltage would show an inductance corresponding to the average slope of lines OG and GB_m. That is, the average permeability during a whole cycle is the average of the permeabilities which obtain during the positive and negative increments of induction, and it is represented by the average of the slopes of lines OG and GB_m. But if the reactor were put in the filter of a rectifier, the measured ripple would be higher than a calculated value based upon the bridge value of inductance. This occurs because the positive peaks of ripple have less impedance presented to them than do the negative peaks, and hence they create a greater ripple at the load. Suppose, for example, that the ripple output of the rectifier is 500 volts and that this would be attenuated to 10 volts across the load by a linear reactor having a value of inductance corresponding to the average slope of lines OG and GB_m. With the reactor working between zero and B_m, suppose that the slope of OG is 5 times that of GB_m. The expected average ripple attenuation of 50:1 becomes 16.7:1 for positive flux swings, and 83.3:1 for negative, and the load ripple is

or an increase of nearly 2 : 1 over what would be anticipated from the measured value of inductance.

This non-linearity could be reduced by increasing the air gap somewhat, thereby reducing H_dc. Moreover, the average permeability increases, and so docs the inductance. It will be apparent that decreasing H_dc further means approaching in value the normal permeability. This can be done only if the maximum flux density is kept low enough to avoid saturation. Conversely, it follows that, if saturation is present in a reactor, it is manifested by a decrease in inductance as the direct current through the winding is increased from zero to full-load value.

In a reactor having high a-c permeability the equivalent length of core l_c/μ is likely to be small compared to the air gap l_g. Hence, it is vitally important to keep the air gap close to its proper value. This is, of course, in marked contrast to reactors not subject to high a-c induction.

If a choke is to be checked to sec that no saturation effects are present, access must be had to an inductance bridge. With the proper values of alternating voltage across the reactor, measurements of inductance can be made with various values of direct current through it.

If the inductance remains nearly constant up to normal direct current, no saturation is present, and the reactor is suitable for the purpose. If, on the other hand, the inductance drops considerably from zero direct current to normal direct current, the reactor very probably is non-linear. Increasing the air gap may improve it; otherwise, it should be discarded in favor of a reactor which has been correctly designed for the purpose.

Filter reactors subject to the most alternating voltage for a given direct voltage are those used in choke-input filters of single-phase rectifiers. The inductance of this type of reactor influences the following:

Value of ripple in rectified output.

No-load to full-load regulation.

Transient voltage dip when load is suddenly applied, as in keyed loads.

Peak current through tubes during each cycle.

Transient current through rectifier tubes when voltage is first applied to rectifier.

It is important that the inductance be the right value. Several of these effects can be improved by the use of swinging or tuned reactors. In a swinging reactor, saturation is present at full load; therefore the inductance is lower at full load than at no load. The higher inductance at no load is available for the purpose of decreasing voltage regulation. The same result is obtained by shunt-tuning the reactor, but here the inductance should be constant from no load to full load to preserve the tuned condition.

In swinging reactors, all or part of the core is purposely allowed to saturate at the higher values of direct current to obtain high inductance at low values of direct current. They are characterized by smaller gaps, more turns, and larger size than reactors with constant inductance ratings. Sometimes two parallel gaps are used, the smaller of which saturates at full direct current. When the function of the reactor is to control current by means of large inductance changes, no air gap is used. Design of such reactors is discussed in Magnetic Amplifiers.

The insulation of a reactor depends on the type of rectifier and how it is used in the circuit. Three-phase rectifiers, with their low ripple voltage, do not require the turn and layer insulation that single-phase rectifiers do. If the reactor is placed in the ground side of the circuit one terminal requires little or no insulation to ground, but the other terminal may operate at a high voltage to ground. In single-phase rectifiers the peak voltage across the reactor is E_dc, so the equivalent rms voltage on the insulation is 0.707E_dc. But for figuring B_max the rms voltage is 0.707 · 0.67E_dc. Reactor voltages are discussed in Rectifier Performance.