three phase voltage calculation question

[Electric-Light]

Suppose a building receives power at 208Y/120v

If everything was perfectly symmetric, then you'd have 120v L to N, and 207.8v L to L, but lets say it isn't.

A dorm room receives a neutral, A and B.

Currently, there is a microwave running from an outlet fed from A. There is nothing connected to an outlet fed from B.

N to A is 118v
N to B is 123v

I know I can measure A to B, but if I wanted to can I calculate voltage between A and B from the above and the fact they're shifted 120deg from eachother?

Also, would a load between N and C in the room next door affect my calculation?

Something that gave me a pretty close answer is average of the above, (118+123)/2 = 120.5*sqrt(3) = 208.7v. The value looks reasonable, but I'm not certain if I'm using the right formula.

 

[charlie b]

When the load is imbalanced, the phase angles are no longer 120 degrees. Your approximation is probably close. But to calculate an "exact value" of the voltage from A to B, given the magnitude of the voltages of A and B, you would also need to know the actual phase angle between them. I suspect there are ways to measure that angle, but I can't tell you what those ways might be. Once you have the angle , the formula for calculating the "third side of the triangle" is as follows:

• Let "A" and "B" be two sides of a triangel.
• Let "w" be the angle between then.
• Let "Y" be the third side of the triangle.
• Then Y = square root of (A*2 + B*2 - 2ABcosine (w))

If this looks a bit like the Pythagorean Theorem, it would be exactly that, if the angle "w" is 90 degrees, since the cosine of 90 degrees is zero. The more general equation, as shown above, is called "The Law of Cosines," and the Pythagorean formula is really a special case of that law.

 

[busman]

When the load is imbalanced, the phase angles are no longer 120 degrees.

Charlie,

Are you saying that the voltages are no longer 120 degrees apart? The only way I can see this happening would be a long run where there is significant capacitance or inductance between the source and the load, or are you talking about harmonic voltages?

Mark

 

[charlie b]

If the three phases are not balanced, and if the loads are not purely resistive, then there is no reason to expect the angles between the phases to remain at 120 degrees. You don't need long runs with impedance in the cables; you can get there with short runs to inductive or capacitive loads.

 

[busman]

I agree that non-resistive loads will result in phase angles on the currents that are not at 120 degrees. I don't agree that it will have much effect on the voltage phasor angles (unless there is REALLY excessive voltage drop).

Mark

 

[jghrist]

Even with a resistive load, there will be a phase difference between sending end and receiving end voltages if there is inductance in the line (and there always is). For low voltage drops, there is not much of a phase shift, but it is there.

 

[BJ Conner]

Phase Angle won't change.

Phase Angle won't change.

You have to go back to the generator(s) and rewind them all to get the voltage phase angle to change. Current phasne angles will change but not voltage.

 

[Electric-Light]

You have to go back to the generator(s) and rewind them all to get the voltage phase angle to change. Current phasne angles will change but not voltage.

So, that would mean rewiding the generators at the Bonneville dam
Ain't gonna happen

 

[wirenut1980]

For all the monitoring data I have seen on a wye system, the line to neutral voltage phase angles may vary by 1-2 degrees from 120 degrees apart, but not more than that, even with unbalanced voltages around 2%.

Edited to change unbalanced currents to unbalanced voltages in teh past few words...

 

[nollij]

You have to go back to the generator(s) and rewind them all to get the voltage phase angle to change. Current phasne angles will change but not voltage.

Think of two different 2-port parallel systems (transmission line) with the same voltage regulation. Now say one of those systems has 10x the current flowing through it. What is the voltage/angle at the secondary? The voltage and angle will be changed greater than the other. Now, just apply this to this particular case where one phase is being loaded up higher than the others. The transmission losses will create a change in voltage and phase that the other phases do not experience.

 

[BJ Conner]

How does the phase angle of one relative to the other change?
In diagraming send-recieve diagrams for power lines I have never considered phase angles changing. In line to line and line to ground faults the resultant voltages may change but the ones back at the power plant are still A-B-C at 0 ,120 and240

 

[busman]

If you're familiar with phasor diagrams, draw a long phasor for the 120V at the source and a short one for the voltage drop on the line. If the line is purely inductive (not reality), the voltage drop phasor is at 90 degrees to the source one. It makes a very small change in the voltage at the load (as long as the voltage drop is kept to a reasonable level.

Hope this helps.

Mark

 

[dkarst]

How does the phase angle of one relative to the other change?
In diagraming send-recieve diagrams for power lines I have never considered phase angles changing. In line to line and line to ground faults the resultant voltages may change but the ones back at the power plant are still A-B-C at 0 ,120 and240

Using the assumption that through power line transposition, balancing of loads, diveristy and maybe a bit of luck, the voltages at the supply panel are a perfect 120 volts and 120 phase angles. Then, getting back to OP question, assumed a 50' line of #12 feeding a load of 15A with a lagging power factor of 0.95.

Those assumptions (I did this quickly with a sandwich in one hand so may have to double check) give me an angle difference of ~ 0.2 degrees from source to load. When comparing at the load end from this loaded circuit to an unloaded circuit, the the angle would be the same 0.2 degrees (+/- the 120 of course).

 

[SOG38]

Poly Phase Calculations

Poly Phase Calculations

After reading all this I was confused so I went back to the text book
What I found was as follows.
In a three phase 4 wire systems
Single-phase loads are served by any of the three line wires and the common neutral wire the neutral carries the vector sum of the currents in the single phase loads.
The single phase loads are completely independent of one another.
The line to line voltages are kept equal by the source. This would the three phase loads would not be effected by single phase loads.
This was written by professor of electrical engineering Charles Suskind at Perdue University.
Of course this assumes the transformers are within their load limits and regulating.
I think where this got twisted in my mind was Phase angles vs. Vector diagrams.

 

[mityeltu]

ooops. Never mind.

 

[mull982]

I agree the 120deg angle between two voltage phases can change at the load if there is a large unbalanced complex impedance differnece between the source and load on each phase. The voltage angle can shift if there is alot of reactive impedance.