3 Phase Minus 1 Phase Calculation

The other 2 should be unaffected if the 3rd phase is open...

If the neutral is absent, each of the two remaining phases will get 207.5 V.

Thank you , May I ask, how is that calculated?

415/2.

That would be true if the phases were 180 degrees apart, i.e. single phase. However, they are 120 degrees apart, so the voltage across the elements is unchanged, determined by the ratio of the transformer windings, unchanged.

The transformer's output voltages are unchanged, as I understand you to have said. In the presence of 3 heaters connected in a wye/star method they are 120 degrees apart with 240 volts across each heater. However, when one heater is disconnected, this central wye/star connection point shifts to be in the middle between the two remaining phases, so the remaining heaters are now effectively connected 180 degrees apart. The voltage across each one is now 415/2=208 volts (rounding up the decimal part). This is true because the original poster's question assumed that there was no other connection between this wye/star point between the three heaters and any other wires in the circuit or transformer secondary. Incidentally, the voltage between the shifted mid-point between the two remaining heaters and the disconnected output has increased to 360 volts from its former 240 volts. You can confirm my math with the trigonometry of a 30/60/90 degree right triangle, the sides being in ratio of hypotenuse = 2x adjacent side and the opposite side being 1.732x the adjacent side.

--JMM

The phase relation does not shift, it follows the supply windings, 120 deg displacement. It is still a 3 phase supply, and unless you use a phase shifting transformer, the phases will be displaced 120 deg per cycle or Hertz, as supplied by the upstream transformer or generator. The load current still flows between the two active phases, no neutral is needed to make it work, similar to a star connected motor winding. Except of course the motor will not tolerate being single phased.

I had not understood before. Thanks.

And increased amperage draw on those 2 lines...

SE,

I think you missed this one. These are heating elements, which are essentially resistive loads. Standard Ohm's law: I = E/R. Since R is constant, I will decrease because E was dropped from 240 down to 207.5 V. I realize there may be some non-linearity in R, but that is a second order effect.

JMM

Yes you are correct, I believe the current declines slightly....good catch

In real life applications R is not really a constant. Most resistive elements have a resistance value that changes as a function of temperature. The change may be small enough to not make a practical difference.

Thank you, but there is no neutral in the design that I mentioned.

The point where the three phases come together is a neutral point, you can connect it to ground or not, it's still neutral...you have two ways to hook it up, line to line or line to neutral...

..."Once we have three line terminals and a neutral terminal, we can have two kinds of voltages:

A higher voltage (say 400V) between any two lines L₁↔L₂ (red & green) , L₂↔L₃ (green & blue) or L₃↔L₁ (blue & red).

This is called ‘Line Voltage’ or Line to Line Voltage.

A lower voltage (say 230V) between any one line and the neutral ( L₁↔N (red & neutral), L₂↔N (green & neutral) or L₃↔N (blue and neutral) .

This is called ‘Phase Voltage’ or Line to Neutral Voltage."...

If you're using the lower voltage hookup, like you said, then you are line to neutral...

https://www.quora.com/What-is-difference-between-line-to-line-voltage-and-line-to-neutral-voltage

In that case, the voltage across two of the elements will drop to half the supply voltage (=415/2) and the voltage across the third will be unchanged.

Correction: if they are connected in star, then the voltage across two of them in the absence of a neutral will be 415/2, assuming identical resistances, and across the third, zero.

( see #26)

there is always a neutral of the 3 phases, maybe no wire, but on ac circuits, it is established capacitively. If there is some disturbance, like a ground fault, then the line to ground voltage will change. The line to line voltage will remain according to the transformer ratio, not arithmetically to half of the line to line voltage, regardless of other posts.

If there is no neutral, then it must be a Delta connection.

If there is no neutral, then how can you have heating ? If you omit a neutral line, then you just have an element.

Er, um, one can have two elements in series across 2 phases.

The neutral point is virtually grounded even not physically connected to ground when the loads are distributed equally in the system..

That's abstruse.

Sorry PWSlack, what I meant was, the neutral point in a balanced star configured 3-phase system is virtually sitting at a ground potential..

The neutral wire being at zero potential can be considered grounded, as long as the loads are balanced, Even when not physically connected to the grounding point of the circuit..

Vsar,

In the electrical trade, the word "grounded" has a very specific definition and intent when used. Even if the neutral wire is at zero potential, it is NOT GROUNDED unless there is a physical connection between this wire and ground at the source of supply such as the service disconnect enclosure or at the source of supply if a separately derived system. Because the neutral wire must be treated as a current carrying conductor, it is only bonded to ground at the service disconnect... Everywhere else in a structure the unbalanced current it carries (due to the resistance of the wire and the current flowing through it) will cause its voltage to be different than the ground voltage.

The original poster of the question was talking about a 3-phase circuit with three equal loads connected together in a star (wye) configuration. The midpoint of this star/wye can act like a neutral, but is not connected to any neutral conductor in the building. In the original post, the question was what would happen to this midpoint of the star/wye when one of the three connections through a heater was lost. At that point, its voltage will shift from a fairly low voltage (close to ground, but not necessarily exactly so) to approximately 120 volts from ground! That definitely is NOT a voltage you would want to see on a neutral. --JMM

Jmueller-

I am 100% in agreement with what you stated..

for that very same reason why (in my very first comment), I described that neutral point to appear as a virtually grounded point...Which would be true only As long as the loads are balanced..

Thank you..

It all depends what you mean by "lose one phase." If the one heating element becomes disconnected from its phase voltage source, it is just hanging there off the star point. It has no voltage across it because its circuit is open. The other two elements will still have the same 240V across each one because the phase relationship of their sources remains the same.

If the "lost" element instead becomes shorted, then you are applying its phase voltage to the star point. Then each of the other two elements will have 415V across them.

It all depends on how you lost that phase.

Some people are so clumsy...

It seems that nobody grasped my comment that it all depends on how one loses a phase.

• If the phase is lost by a break in the wiring between a sound working delta transformer and the resistive star connected heater load then you get the scenario most have discussed.
• If the phase is lost upstream of the delta transformer then a different scenario happens.
• If the phase is lost due to an earth fault of one of the transformer output phases a different scenario will occur. Hopefully, circuitry protection will automatically respond to this condition eventually but it is good to understand what the condition is before breakers trip.
• If an unbalanced load on the failing phase is causing the loss in the core due to saturation.

Each of these scenarios will produce a "phase lost" condition with different voltage results.

I believe that the statement that when the heaters are connected in star then the above hold true that the heaters will only have 240V RMS across them if the neutral point of the heaters is connected to the neutral point of the supply transformer which would be a star delta connected transformer where the HV of the transformer is connected in delta and the secondary is connected in start where the output of the phase windings on the LV side has a relationship of 240V RMS to the neutral point.

If star point of your star connected heaters are not connected to the star point of the transformer then the star point of the heaters may not be at the same voltage as the star point of the transformer.

When one phase is lost what was the star connection of the heaters becomes the center point of a resistor divider network connected to 415V RMS. To work out the voltage at any instant of the waveform add the peak values of the two remaining phases and multiply by 0.707 to obtain the RMS value. Peak value = 1.414 times the RMS value.

So the common point of the two heaters floats around when referenced to the transformer neutral subject to the individual heater resistances. Nominally the heaters would have 207.5V RMS across them which means that the heater center point could be 40V RMS when measured against a transformer neutral.