The Measurement of Power in Polyphase Circuits

Abstract

The object of this paper is to point out that the existing methods of measuring power when applied to unbalanced three-phase systems are not equitable for symmetrical polyphase machinery. On the other hand, unsymmetrical loads on polyphase systems are not sufficiently penalized for the trouble which they create in the system. It is first of all shown that a symmetrical generator cannot deliver power except through the balanced components of current. The unbalanced currents are capable of resolution into two balanced systems of currents, one of which is of the same phase sequence as the generator e. m. f., and the other component is of reversed or negative phase sequence. The generator cannot deliver power through the medium of this latter component of the currents, because the instantaneous product of the generated voltage and these currents in the three phases is always zero. However, the volt-ampere product per phase is of great significance, because it is a measure of the effect of the current unbalance on the system. The generator therefore delivers power only through the medium of the positive phase sequence currents. Any power that appears in the system through the negative phase sequence currents is positive phase sequence power which has been supplied by the generator and degraded through unbalanced loads and fed back to the system in the form of negative phase sequence power. This power is always additional loss in all rotating machines on the system, and with the present method of charging, the consumer having symmetrical machines is charged with this additional power, which serves him no useful purpose but reduces the output of his machine and decreases his load power factor. In the paper it is proposed that the positive phase sequence power output only be measured, and the power charges be made on the basis of this measurement. It is further proposed that the unbalanced k-va., which is the product of the positive sequence voltage and the negative sequence current be measured either by means of a negative sequence ammeter, indicating or recording, or a k-va. meter, and a charge made for the amount of unbalance. The user of symmetrical polyphase rotating machinery should then be given a lower rate, based on the estimated cost of unbalance, and the consumer having unbalanced loads should be charged directly for the amount of unbalance he creates, or else should have his positive phase sequence power rate increased, based upon the estimated cost of unbalance. It is pointed out that the unbalanced kv-a. is a factor of the same order of importance as reactive kv-a. and in any system subject to unbalanced conditions this factor should be considered and the unbalanced factor, as well as the power factor, should be measured. The unbalanced factor is the ratio of the negative phase sequence kv-a. and the positive phase sequence kv-a., the former being obtained by taking the product of the positive phase sequence voltage and the negative phase sequence current. Devices for measuring these quantities are being developed and the outfit for making these measurements will be no more complicated than the present existing measurement devices. In fact the tendency is towards greater simplicity. In presenting this subject the author has no intention of suggesting how rates should be made, but merely wishes to point out what factors enter into the question of equitable rates when the polyphase system is subject to unbalance.