Cross-Current Predeterminations from Crank-Effort Diagrams
Authors: Illmer Louis 
Published: December 2023

Abstract
This paper is a research study into the cause of excessive cross-current flow between paralleled alternators when driven by reciprocating engines. Cross-currents determined by ammeter measurement show a flow far greater than can be traced directly to the unevenness of the primary crank-effort forces.
The uneven crank effort of the reciprocating engines does, however, superimpose small oscillatory displacement movements upon the rotating paralleled armatures, which in turn cause a correspondingly small cross-current flow, the pull of which is still sufficient to set up independent armature oscillations. The time period imposed by the cross-current pull differs from that imposed by the primary crank-effort forces, and the reactive effect is a periodic variation in the engine load against which the uneven crank effort must work.
This condition is shown to be conducive to cumulative armature-displacement movements, since at times these two distinct periodic forces, i.e., excess effort and cross-current pull, act in unison, while subsequently they act in opposition. The combined action of these two forces subjects the rotating wheel parts to a cumulative oscillatory movement, the amplitude of which may readily build sufficiently to account for the relatively heavy cross-current flow found by actual measurement.
The theory underlying cumulative motions of this kind is developed, and formulæ are derived for predetermining the maximum armature-displacement shift and accompanying cross-current flow that may be expected for any given set of conditions.
The character of motion and the maximum amplitude of such cumulative oscillations are found to depend largely upon the relation which the time period of the excess crank effort bears to that of the cross-current pull. The crank-effort period is fixed by the cylinder arrangement and engine speed, while the cross-current-pull period is found to be most readily controlled by the selection of a suitable wheel weight.
The wheel-weight constants prescribed for paralleled reciprocating-engine units provide a guide for confining the cumulative armature oscillations within satisfactory limits. When a relatively light wheel is used for such engines, the resulting oscillatory movement is likely to have a comparatively rapid period and its maximum cumulative amplitude may be expected to be approximately twice that which occurs when using a heavy wheel oscillating with a relatively slow period.
The author advocates a reasonably heavy wheel as most likely to obviate excessive cross-current flow, mainly because of its beneficial secondary effects. The greater maximum amplitude of oscillation in the case of the relatively light wheel may lead to serious electrical disturbances, and under adverse conditions the detrimental secondary effects of the more rapid cumulative oscillations may become so aggravated as completely to upset the regulating functions of the engine governor.
The characteristic behavior of paralleled alternators is briefly set forth in the Appendix by means of vector diagrams. Therein is also discussed the manner in which periodic displacement movements of the paralleled armatures affect a momentary change in engine load.
The paper further treats of the principles underlying harmonic motion as applied to the effect which uneven crank-effort forces exert upon the rotating wheel mass. Wheel-displacement increments, graphically determined, are compared with those approximated by the more direct method of calculation.
In discussing the subject of harmonic armature oscillations and their application to paralleled alternators, the author points out reasons for considering untenable some of the basic assumptions made in the German literature relating to this subject. Cross-current determinations made by the author upon a set of paralleled 500-hp. gas engines are analyzed with the view of substantiating the contention as to the defect in the Rosenberg theory, and Bonte’s deductions based thereon.