# Exploring Phase Potential Difference in 3-Phase Power

• oscarrod5
In summary, the potential difference between two phases in 3 phase power is:0 when the phases are in -phase.
oscarrod5
I understand phase voltage (phase to neutral) well, but I'm still confused by what exactly the potential difference is between any 2 phases in 3 phase power. If you were to try to find the potential difference where 2 sine wave phases cross, then at that instantaneous point, the potential difference looks to be 0.
https://en.wikipedia.org/wiki/Mathe...ric_power#/media/File:3_phase_AC_waveform.svg

I think it is easiest to visualize using a vector diagram. Does the following help?
Line-to-neutral voltages are in blue and line-to-line voltages in red. Note that the magnitude of the line-to-line is ##\sqrt{3}## times larger, and ±30 degrees different in phase compared to line-to-neutral.

Klystron, DaveE, jim mcnamara and 2 others
oscarrod5 said:
at that instantaneous point, the potential difference looks to be 0.

Yes. Have you taken into account it actually is not different from the case of a single phase and neutral: you can also find the instantaneous point at which potential difference is zero?

Interested_observer
oscarrod5 said:
what exactly the potential difference is between any 2 phases in 3 phase power.
Here in the U.S. the 3-phase to residential areas is often 16kV between phases (DELTA connected). One phase of this is then stepped down to the usual 240V centertapped for residential use.

For larger apartment buildings with an elevator and air conditioning (and for larger restaurants) the 16kV 3-phase is stepped down to 120/208 3-phase/4-wire (WYE connected). This causes some complaints about electric stoves not heating as fast as they 'should.' Of course this is because of the 208V feeding a 240V stove. Try explaining that to an upset housewife!

Medium size industrial plants are often fed with 416/240 3-phase/4-wire with a 240/120V transformer on the customer site. This has its own quirk in that the transformer often has a fuse mounted right on the transformer, which is behind a blank panel on the circuit breaker box. If the maintenance guy hasn't run across this before, the lights may be out for quite a while during troubleshooting. There is/was a nominal 440V feed and a 480V feed, but I have no details on those.

Cheers,
Tom

Single phase, 230 Vrms, is now the international standard domestic voltage.
The peak single phase voltage is 230 * √2 = 325 Vpk.
See the plot of the 'Y', single phase voltagess a, b, and c, relative to the neutral.

The Δ difference voltages between phases are also shown. V(a)-V(b), V(b)-V(c), V(c)-V(a).
The difference voltages are 400 Vrms. The peak difference voltage is 400 * √2 = 563 Vpk.

The three phase voltage is root 3 times the single phase voltage.
230 Vrms * √3 = 400 Vrms.
325 Vpk * √3 = 563 Vpk.

Klystron
Tom.G said:
There is/was a nominal 440V feed and a 480V feed, but I have no details on those.
277/480 Wye is quite common in US industrial settings. My last company sold Lasers that used this feed and it was seldom a problem in any sort of place that would want a big laser. Everyone overseas had to buy an autotransformer though. The cooling water, OTOH, was always a PITA for everyone.

480/277 is the US Industrial Standard - I only remember seeing 440 in OLD scott connected arrangements in Philly.

While the vector diagram are helpful - I think they are best as the second or final step to looking at this. The 3 Phase waveform is the good first step - a vertical line on this diagram shoes the REAL TIME potential difference for each connection.

oscarrod5 said:
I understand phase voltage (phase to neutral) well, but I'm still confused by what exactly the potential difference is between any 2 phases in 3 phase power. If you were to try to find the potential difference where 2 sine wave phases cross, then at that instantaneous point, the potential difference looks to be 0.
https://en.wikipedia.org/wiki/Mathe...ric_power#/media/File:3_phase_AC_waveform.svg
You can use the standard Mathematics expression to find the Potential Difference. notably, the difference between the two Sine functions. Sin A - Sin B = 2 x Cos [(A+B)/2] x Sin [(A-B)/2]
We used to recite that as " sine minus sine equals two cos a half sum, sine a half difference." (With similar expressions for sin plus sin, cos plus cos and cos minus cos)*

The phases in -phase electricity are 120 degrees difference, so you are looking at two expressions like Sin(A) and Sin(A+120). (if I could type pi I could do that in radians rather than degrees)
"a half sum" equals (A +60), but cos(A+60) is just a phase shifted Sin(A)
"a half difference" equals 120, but sin(120) = √3 / 2

so 2 x {cos half sum) x (sin half difference) effectively means √3 sin(A), so the 3-phase PD is √3 times the single phase PD.

*
sin plus sin equals two sine a half sum, cos a half difference
sin(A) + sin(B) = 2 . sin[(A+B)/2] . cos[(A-B)]/2
cos plus cos equals two cos a half sum cos a half difference
cos(A) + cos(B) = 2 . cos[(A+B)/2] , cos[(A-B)/2]
cos minus cos equals two sine a half sum sine a half difference reversed.
cos(A) - cos(B) = 2 . sin[(A+B)/2] . sin[(B-A)/2]

## 1. What is a phase potential difference in 3-phase power?

A phase potential difference in 3-phase power refers to the difference in voltage between two phases in a 3-phase power system. In a 3-phase power system, there are three separate voltage sources that are out of phase with each other by 120 degrees. This results in a more efficient and balanced distribution of power compared to single-phase power systems.

## 2. How is phase potential difference measured in 3-phase power?

Phase potential difference in 3-phase power is typically measured using a voltmeter. The voltmeter is connected between two phases and the voltage reading is taken. This reading represents the potential difference between those two phases.

## 3. What is the importance of exploring phase potential difference in 3-phase power?

Exploring phase potential difference in 3-phase power is important because it helps ensure a balanced distribution of power and prevents overloading of any one phase. It also allows for more efficient use of power and can help identify any potential issues or imbalances in the system.

## 4. How does phase potential difference affect the performance of electrical equipment?

Uneven or unbalanced phase potential difference can lead to uneven distribution of power and can cause electrical equipment to malfunction or fail. This can result in downtime, increased maintenance costs, and potential safety hazards.

## 5. What are some common methods for maintaining balanced phase potential difference in 3-phase power?

Some common methods for maintaining balanced phase potential difference in 3-phase power include using balanced loads, regularly monitoring and adjusting phase voltages, and implementing phase balancing techniques such as swapping loads between phases. It is also important to properly size and install equipment to handle the expected phase potential difference.

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