Calculating Line-Line from Line-Neutral with voltage imbalance

Status
Not open for further replies.
W

WillyB

Member
Location
United States
All,

In college, I thought I'd never really use power systems analysis, so I avoided the advanced power classes my senior year. However, now I'm working on power plants so I'm regretting my decision...

I'm wanting to calculate the Line-Line voltages on the low side of a pad-mounted transformer when given the Line-Neutral voltages. I've tried googling it to no avail and I'm on a construction site so I don't have my textbooks with me.

I have line-line and line-neutral readings on a couple of transformers, but want to be able to calculate the Line-Neutral for the rest without having to shut down everything on the load side. Here are the readings for one of the transformers where we do have both readings:

L1 - 175
L2 - 187
L3 - 191

L12 - 319
L13 - 321
L23 - 320

I tried using c^2 = a^2 + b^2 - 2*a*b*cos(120), and was getting 317, 314, and 324 for L12, L13, and L23 respectively. Can anyone help with this?
 
augie47

augie47

Moderator
Staff member
Location
Tennessee
Occupation
State Electrical Inspector (Retired)
Welcome to the Forum.
(most unusual L-L numbers. I will leave the answer to more educated members)
 
G

GoldDigger

Moderator
Staff member
Location
Placerville, CA, USA
Occupation
Retired PV System Designer
Your analysis assumes that the phase relationship is exactly 120 degrees.
If the transformer is heavily loaded, causing a significant voltage drop and the loads are low power factor and unbalanced this assumption will not be valid.
Not sure whether this is enough to explain your results.
Also harmonics in the output voltage can invalidate your formula.

Tapatalk...
 
Rick Christopherson

Rick Christopherson

Senior Member
In a 3-phase system, converting between line and phase voltages is just a matter of multiplying or dividing by ?3. Even though your voltages are unusual, the ?3 factor is still the difference in the numbers.

As for your unusual voltages, is there any chance you are reading peak voltages instead of RMS? They would still be a little high, but a ?2 factor does bring them fairly close to a 120/208 system.
 
P

Phil Corso

Senior Member
Location
Boca Raton, Fl, USA
WillyB...

1st Step
Use the longest Line-neutral measurement as the horizontal (0-deg) reference.

2nd Step
Form a closed triangle with the other two Line-neutral measurements as sides, using same sequence 1-2-3

3rd Step
Use Law-of-Cosines to calculate interior angles.

4th Step
Arrange the three line-neutral measuremets and their repective angles in a Wye arrangement.

5th Step
Calculate Line-Line vectors by adding ajacent sides, vectorially!

Regards, Phil Corso
 
G

GoldDigger

Moderator
Staff member
Location
Placerville, CA, USA
Occupation
Retired PV System Designer
But the OP also said he wanted to calculate the Line-Line voltages given the Line-Neutral.

Since measuring either set seems just as easy as the other given access to the terminals, I suspect that there may be fixed Line-Neutral metering in place as part of the equipment.
If so, we can also ask how accurate those measurements are. (Unless all three readings come from switching one meter.)

Tapatalk...
 
G

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
131130-1325 EDT

WillyB:

Using the measurements you provided there is waveform distortion, or something changed in loading as you went from one measurement to another.

I did a graphical analysis using 3 circles centered at 0,0 and of radii 175, 187, 191. Then from 0,175 I created two circles of radii 319 and 321. From the intersections I measure vector 2 to 3 to be 316 instead of 320.

If you assume each phase angle to be exactly 120 and use the three vectors 175, 187, and 191, then V12 = 313 V, V13 = 317 V, and V23 = 327 V. Instead of your values 319, 321, and 320.


If you only know line to line voltages, then there is a wide variety of voltages that can exist for line to neutral. Thus, you have to pick some reasonable assumption with which to work.

Check my numbers and see if you get the same results.

.
 
W

WillyB

Member
Location
United States
All measurements were made with a calibrated fluke 289 by a journeyman electrician and are the RMS values. Phase angles were verified to be 0, 120, and -120 by a SEL 751A. This is for a solar plant so the 320V seems weird, but it's to match the inverter output voltages.

I misspoke about calculation L-N. I have all the L-N readings and I'm only interested in calculating the L-L given the L-N.

I'm doing commissioning for a solar project on 2 difference sites. Some of these transformers have high legs and some don't. Most of these transformers feed 2 inverters, which means it has 2 sets of bushings on the low side. Even between those 6 bushings, sometimes X1 might be high and all the others will be normal. There is no load on these transformers other than a small PLC for our SCADA. I've worked on other solar sites and talked to others who have noticed that there is a high leg on their transformers as well, so it's fairly common occurrence.

The transformer is a 1600KVA 13.2kv-324 delta-wye and the taps are set to +2.5%.

I also used the vectors earlier and got 314, 317, and 327.

I'm thinking this boils down to a good ole' "field vs office" battle. Where on paper, it should be a certain number but in real life it's different. I need accurate measurements for my paperwork to turnover to the client and 8 of the transformers are currently in operation. I'd rather not shut down the inverters if I don't have to but it seems as if that's going to be the best option. Taking readings while in operation isn't an option due to the 1,300 amps/phase the inverters put out.
 
G

GoldDigger

Moderator
Staff member
Location
Placerville, CA, USA
Occupation
Retired PV System Designer
My biggest concern would be whether the POCO side voltages are balanced.
A grid tie inverter will follow whatever voltage is required to push the necessary current back into POCO.
Without that measurement you cannot be sure that the difference has anything to do with either the inverter or the transformer.

Are the inverter outputs connected wye or delta?
Presumably the POCO side is delta with no neutral connection?
Is it possible that all of the xformer high reading legs are linked to the same primary leg?

Do you have access to the inverter current or power output readings at the same time that you measure the voltages?

Tapatalk...
 
P

Phil Corso

Senior Member
Location
Boca Raton, Fl, USA
WillyB...

Is this a Sub-Grid-connected PV system, where each of the transformer's LV wye-legs is supplied by the output of a single-phase inverter?

If true, then a problem could arise within the transformer!

Phil
 
W

WillyB

Member
Location
United States
The inverters are SMA 720's which are 3-phase and they are not powered up yet. The AC backfeed comes in to an ABB 3-phase breaker which is open, so there is no current draw from the inverters; only the SCADA system is drawing current, which is right around 1A at 120VAC. The inverter outputs are wye connected.

I talked some more with my field hands and we actually measured all the voltages with reference to ground, not neutral. In this particular system, we have a floating netural. Since readings were actually line-to-ground and we have a floating neutral, this may be why my calculations are off.

Also, excuse my ignorance, but what is POCO? I've searched on the forums/google but haven't found anything...
 
J

John120/240

Senior Member
Location
Olathe, Kansas
WillyB said:
The inverters are SMA 720's which are 3-phase and they are not powered up yet. The AC backfeed comes in to an ABB 3-phase breaker which is open, so there is no current draw from the inverters; only the SCADA system is drawing current, which is right around 1A at 120VAC. The inverter outputs are wye connected.

I talked some more with my field hands and we actually measured all the voltages with reference to ground, not neutral. In this particular system, we have a floating netural. Since readings were actually line-to-ground and we have a floating neutral, this may be why my calculations are off.

Also, excuse my ignorance, but what is POCO? I've searched on the forums/google but haven't found anything...
Click to expand...

POCO is short hand for Power Company
 
G

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
131201-0823 EST

WillyB:

You need to provide a more accurate description of the transformer and inverter wiring.

RMS measurements are an averaging type of measurement with the purpose to relate a steady state signal to its heating effect in a purely resistive load. For oddball waveforms you can not necessarily expect RMS measurements to simply add. Many simplified equations assume the the signals to be sinusoidal and correlated.

Are your transformer windings that connect to the inverters wired as a wye or delta? I believe you mentioned the inverter outputs are wired wye? Are there three inverters? I thought I had read above two inverters. Also if I remember correctly you referred to some wild leg connections?

If you have either a delta or wye secondary with no grounding and no load, then line to ground will be a function of distributed capacitance, leakage resistance, and other voltage sources. Adding an ungrounded load will most likely change the distribution of the readings. Further there could be some very unusual readings, like 1000 V where you might not expect more than 240 V. Your original post line-to-line voltage are relatively close. Thus, your problem originated from your expectation that earth (ground) was the neutral of a wye connection. Also it is not clear if you are dealing with wye circuits for the transformer windings that connect to the inverters. If these are delta, then what is your definition of neutral? Is it a synthetic point based on an assumption of three equally (angle) spaced vectors?

.
 
G

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
131201-2223 EST

WillyB:

One synthetic neutral that you can create is as follows:

Make a triangle of the three line-to-line vectors (219, 321, and 320). Let 219 be vertical or 90 deg., 321 is at -30.00097, and 320 is at 29.68959 .
-
Next inscribe a circle thru the three intersecting points. Determine each of the radial vectors. These are all of length 184.75389, with angles of 120.30965, 0.311580, and -120.30965 .

Another approach is to assume that each vector to neutral is spaced by 120 deg. At this point I do not see a geometric approach to find this point other than by trial and error.

In the real world I do not believe each of your phase angles are precisely 120 apart at the terminals of the transformer on the side that connects to the inverter, nor on the other side of the transformer. I am avoiding using the words primary and secondary.

.
 
Besoeker

Besoeker

Senior Member
Location
UK
gar said:
131201-2223 EST

WillyB:

One synthetic neutral that you can create is as follows:

Make a triangle of the three line-to-line vectors (219, 321, and 320). Let 219 be vertical or 90 deg., 321 is at -30.00097, and 320 is at 29.68959 .
Click to expand...
From the OP, 319, 321, and 320.
Balanced to all intents and purposes.
 
Status
Not open for further replies.
Top