JOINT DEVELOPMENT AND NOISE FREQUENCY INDUCTION 191 



A limited amount of iheoretical work has been carried on having to 

 do with the effects of load on the harmonics observed in the open- 

 circuit voltage of rotating machines. This work which was based on 

 Blondel's two-reaction theory was supplemented by laboratory tests 

 on several small machines. It was found that the reactions which 

 take place within the rotating machines, particularly when two or more 

 are operating in parallel, are so complicated as to practically preclude 

 accurate computations of the effects. However, the data obtained 

 from this investigation have been valuable in connection with later 

 studies. 



Balance. — A balanced power circuit is one in which the voltages 

 between the various phase conductors and ground are equal in magni- 

 tude and sum up vectorially to zero and in which the phase currents are 

 also equal in magnitude and sum up vectorially to zero. In a three- 

 phase system where the currents or voltages are not equal but do sum 

 up to zero, the currents or voltages can be resolved into two balanced 

 three-phase systems, one of positive phase sequence and one of negative 

 phase sequence. In cases where the currents or voltages do not sum 

 up to zero they contain a single-phase component which is usually 

 termed residual or zero-phase sequence component. Any three-phase 

 system can be resolved into its balanced and residual components and 

 each treated separately. The coupling for the residual components 

 is usually much larger than for the balanced components and is there- 

 fore frequently of major importance in coordination problems. Differ- 

 ences in the magnitudes or departures from phase symmetry of the 

 three impressed phase-to-neutral voltages, load or line unbalances, 

 give rise to residual currents or voltages. 



Experience has indicated that the outstanding factor in the unbal- 

 ance of power systems is the existence of triple-harmonic voltages and 

 currents which may arise either in rotating machinery or in trans- 

 formers which are connected in star with grounded neutral. Since the 

 triple-harmonic voltages in the three phase-to-neutral legs are in phase, 

 they act in a path consisting of the phase conductors and an external 

 return as, for instance, a metallic neutral or ground. 



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- 



