When two generators are operated in parallel at generated voltage as in Figure below, there is the possibility of circulating harmonic currents.
This is true whether the neutrals are interconnected or not. The two conditions necessary for the flow of harmonic current are: the presence of a resultant harmonic voltage, and a path for the flow of current. It is important to note the term “resultant.”
If the two machines are duplicates and are being operated under identical conditions, they will probably generate the same harmonics of about the same magnitude and phase position. If the harmonics are thus equal and opposite, there will be no resultant voltage available to circulate harmonic current. If, however, the machines are dissimilar, one may generate harmonic voltages that the other does not. There will then be a circulating harmonic current between them whose magnitude is equal to the resultant harmonic voltage divided by the impedance at the harmonic frequency. For line-to-line harmonics the latter is approximately equal to the negative sequence reactance in ohms at rated frequency times the order of the harmonic. For two machines as illustrated, the resultant reactance would be the sum of the harmonic reactance of the two machines, as they are in series for harmonic-current flow. If more than two machines are in parallel, but only one generating a high-harmonic voltage, the harmonic reactance of the one machine is added in series with the paralleled reactance of the remaining generators. If all machines are generating considerable harmonic voltage, an analysis is almost impossible because slight shifts in fundamental frequency phase position with load will greatly alter the resultant harmonic voltages.
The situation with respect to neutral harmonics is much similar to that for line harmonics except that only triple series harmonics, 3rd, 9th, 15th, 21st, etc., can flow in the neutral. This is because the 120 degrees relationship of phases causes all other harmonics to be balanced and thus total to zero in the three phases. Also the zero sequence impedances apply rather than the negative sequence. Referring again to above Figure, it is apparent that neutral circulating harmonic currents cannot flow unless both neutral circuit breakers are closed.
Then, if there is a resultant zero-sequence harmonic voltage, a current will flow equal to the voltage divided by the zero-sequence reactance at the harmonic frequency.
The harmonic currents circulating in the neutral are likely to be somewhat higher in magnitude than the line to line harmonic currents. This is because the third harmonic voltage is usually higher than any other and because the zero-sequence reactance is usually lower than the negative-sequence reactance. In the case of two- thirds pitch machines, the triple series (neutral) harmonics will be practically zero, so that it will not create harmonic currents. On the other hand, the zero-sequence reactance of a two-thirds pitch machine is quite low so that it is a likely pitch for the flow of triple harmonics generated by other machines.
Circulating harmonic currents between apparatus in a station arc not particularly objectionable unless unusually large. A circulating neutral harmonic current of %30 would offhand appear to be of an order to be injurious to a machine. However, this means only 10 percent harmonic current per phase. The rms value in combination with full-load current would be √(1002
) = 100.5 percent. The heating effect will be somewhat greater than this, but probably not more than another 1/2 percent so that the loss of load-carrying capacity is inappreciable.