|> I suggest that you check it out by drawing a phasor diagram - then make a |> comment- with backup reasoning. |> Open delta is 3 phase but capacity limited to 57% of what would be there |> with a 3rd transformer. |> -- |>
|> Don Kelly @shawcross.ca |> remove the X to answer |> ---------------------------- |>
| OK agreed, but show me the neutral in a open delta. | only time i ever found "neutral" imbalances like this | involved harmonics
The neutral, or common, wire will have a current equal to the vector sum of the currents of the loads attached to it. If these currents are equal in amperage, and 180 degrees of opposite phase, the vector sum is zero and the neutral will have no current flowing. That is the typical single phase setup in most places in North America.
If the currents are unequal, there will be some neutral current. We say it is the difference current because the opposing 180 degree phase angles really give the current components their opposite polarities. But the correct way to think about how this happens is the summation of currents at their respective phase angles ... the vector sum.
If the currents are equal, but the phase angle is less than 180 degrees, then there will be some current flowing due to the fact that at any instant, these currents do not cancel out. Just how much current there will be depends on the actual phase angle of these two equal amperage currents.
Here is a list of the common/neutral currents given a 100 amp load on each of two phases. If wires A B C have B grounded, then 100 amps on A-B and 100 amps on B-C would give these currents on wire B for these phase angles.
0 degrees -> 200.000000 common amps 15 degrees -> 198.288972 common amps 30 degrees -> 193.185165 common amps 45 degrees -> 184.775907 common amps 60 degrees -> 173.205081 common amps 75 degrees -> 158.670668 common amps 90 degrees -> 141.421356 common amps
105 degrees -> 121.752286 common amps
120 degrees -> 100.000000 common amps
135 degrees -> 76.536686 common amps
150 degrees -> 51.763809 common amps
165 degrees -> 26.105238 common amps
180 degrees -> 0.000000 common amps
Notice that with a phase angle of 0, the current is the exact sum of both loads. This would the the equivalent of wiring both sides of a two pole single phase (as found in the USA) on the same phase instead opposite phases. The neutral bus would have to carry the sum of the loads (instead of the difference), and thus be overloaded.
In some places in USA and Canada, and in many places in Mexico and Central America, it is common to wire a "single phase service" using 2 out of 3 phases from a three phase transformer (bank). The voltage combination is typically 208/120 or 220/127. In these cases the phase angle is 120 degrees. The neutral current will be equal to the 2 phase currents when they are both drawing the same current. This is why there is a rule in the National Electrical Code (NEC) that requires the neutral wire be counted when figuring wiring deratings for cable assemblies and conduits when wired to this kind of service. Otherwise with true single phase at
180 degrees, a 3-wire (2 poles plus neutral) circuit can be counted as 2 wires for conduit fill ratings since the actual dissipation will never be greater than what 2 wires would dissipate. But any angle smaller than 120 degrees poses a danger because the neutral current will be greater than either of the poles/phases, all the way up to twice the value for the extreme case of 0 degrees.
With a corner grounded delta you will have a 60 degree angle, and thus the common neutral wire will have about 1.732 times the current of balanced loads from 2 phases. Only loads connected directly between the 2 phases (and not connected to the neutral at all) will avoid drawing current on the neutral. But that's not the usual practice when supplying ordinary single phase loads. Supplying circuits intended for single phase with corner grounded delta is therefore a serieous hazard (mitigated only be very uncommon and expensive wiring practice).
FYI, the 1.732 value is the square root of 3, which is closer to:
1.7320508075688772935274463415058723669428052538103806280558069794519330169 or if you prefer a rational number, is fairly close to:
539095242162880600113350770354161026 / 311246783181585603728705429114242815