Rectifier Regulation

The regulation of a rectifier comprises three distinct components:

1.  The d-c resistance or IR drop.

2.  The commutation reactance or IX drop.

3.  The capacitor charging effect.

The first component can be reduced to a small value by the use of tubes, transformers, and inductors having low resistance. Mercury-vapor tubes are of noteworthy usefulness in this respect, as the internal voltage drop is low and almost independent of load current variations.

Commutation reactance can be kept to a low value by proper transformer design, particularly where the ratio of short-circuit current to normal load is high.

During part of each cycle, both tubes of a single-phase full-wave rectifier are conducting. During this interval one tube loses its current and the other one builds up to normal current. Because of the inevitable reactance in the transformer, this change does not take place immediately but during an angle θ as in Fig. 87.

Fig. 87. Commutation current effect on rectifier voltage.

Short-circuit current is initiated which would rise as shown by the dotted lines of Fig. 87, if it could pass through the rectifier tubes; it prevents the rectified voltage wave from retaining its normal shape, so that for a portion of each cycle the rectified output is zero.

Let the transformer winding resistance be temporarily neglected; if the current could rise to maximum, the short-circuit value would be 2E_pk/X, where X is the leakage reactance of the whole secondary, but it is limited by the rectifier to I_dc. The short-circuit current rises to (1 - cosθ) times maximum in the commutation period, or

The average voltage from zero to the re-ignition point V is

Combining these relations gives, for the average voltage cut out of the rectified voltage wave by commutation,

[50]

By similar reasoning, the commutation reactance drop for polyphase rectifiers is

[51]

where X' = the transformer leakage reactance from line to neutral on the secondary side, and p = the number of phases in Fig. 83.

In this formula, the leakage reactance per winding is associated with the voltage across that winding. This is accurate when each phase is supplied by a separate transformer. But it fails for p = 2 in the single-phase full-wave rectifier, using one plate transformer, where half of the secondary voltage is rectified each half-cycle. In such a rectifier, during commutation the whole secondary voltage is effective, and so is the leakage reactance of the whole secondary. This reactance has 4 times the leakage reactance of each secondary half-winding, but only twice the half-winding voltage acts across it. Hence equation 50 must be used for the single-phase rectifier; here X = the reactance of the entire secondary.

When high winding resistance limits short-circuit current, commutation has less effect than equation 50 would indicate. This condition prevails in small rectifiers; the IX drop is negligibly small because of the small transformer dimensions. For example, in the plate transformer designed in Fig. 58 the leakage inductance is 0.166 henry. The commutation reactance drop is, from equation 50,

or 0.1 per cent. This is negligible compared to the 3.7 per cent regulation calculated in Fig. 58. In this case the short-circuit current would be limited by winding resistance rather than by leakage inductance.

In large rectifiers, all rectifier components have low losses to prevent power wastage or overheating, and the IR drop is a very small percentage of the total. At the same time, a large transformer requires careful design in order to keep the IX drop reasonably small. Therefore, in large rectifiers the IX drop is the dominant cause of regulation. An example with 60 kva rating has 0.7 per cent IR drop and 6 per cent IX drop.

In medium-size rectifiers the IR and IX drops may be of equal, or at least comparable, value. In such rectifiers these two components of regulation do not add arithmetically. Commutation interval 8, Fig. 87, depends on the short-circuited reactance when resistance is negligible, but if resistance is appreciable θ is related to the ratio X/R exponentially.⁽¹⁾

Fig. 88. Increase in rectifier regulation due to transformer reactance.

The increase in regulation caused by commutation reactance may be found from Fig. 88, in terms of d-c output voltage E_dc. In this figure the regulation of three widely used rectifiers (single-phase full-wave, three-phase half-wave, and three-phase full-wave) is given in a manner which enables one to proceed directly from the IR component of regulation to total regulation.

X and R are ohms per phase except X/R ratio is for the whole secondary in single-phase full-wave rectifiers. R in X/R ratio includes primary R in all cases. R in I_dcR/E_dc is for two windings in three-phase full-wave rectifiers. To obtain total regulation, project I_dcR/E_dc vertically to one-phase or three-phase line. Project this point to the left to proper X/R line. Abscissa at left gives total regulation. An example is indicated by the dotted line. In this example, the rectifier is three-phase full-wave.

Total regulation = 1.68 · 3 = 5.04 per cent. If the IX regulation had been added directly to IR it would be 6 per cent + 3 per cent = 9 per cent, and the calculated regulation would be nearly 4 per cent higher than actual.

(1)	See Mercury-Arc Rectifiers and Their Circuits, by D. C. Prince and P. B. Vogdes, McGraw-Hill Book Co., New York, 1927, p. 216.