3 PHASE XFMR IMBALANCE CALCULATION

[mjv29]

Hello,

I am in search for a calculation (formula) to determine the maximum imbalance of a 3 phase XFMR.

for example,

2000 KVA, 277/480

phase a = 480 amps
phase b = 490 amps
phase c = 470 amps

what is the "offical way" to determine the maximum imbalance.

Background. I have over 2000 3-phase XFMR's with a,b,c current readings. I want to develop a systematic approach to "solving or prioritizing" the worst imbalances.

My idea is the following.

(1) Sort the data from highest to lowest (from left to right as it is oprganized in excel)
(2) Subtract HIGH from LOW
(3) divide by average amps
(4) sort list descending for the worst imbalance to be at the top.

suggestions???

thanks
--mjv

 

[unclebob]

The official way is :

1- You calculate the mean current

2- You pick the current that is the most "far" from the mean
current

3- You calculate the difference between them

4- You divide the difference by the mean current and
multipli by 100.

Example: A: 350 A
B: 370 A
C: 352 A

Mean current is: 357.3 A
You pick 370 A
The difference is 12.7 A
Witch gives a % imbalance of (12.7/357.3)*100 = 3.55 %

I'm trying to find the IEEE reference.

By the way, can we use both unbalance and imbalance?

 

[dpc]

unclebob's method is consistent with NEMA MG-1 for determining motor voltage imbalance.

 

[buzzp]

I agree with the formula.
I also use the terms unbalance and imbalance interchangibly.

 

[cuky2000]

Keeping the phase-voltages balanced within reasonable close limits is one good indicator of the quality of the power source. However, I am not sure if current unbalance calculation has the same connotation or impact on the quality of the power system.

Voltage unbalance calculation is documented in the IEEE Standard 141 and other engineering guidelines. However, I did not have opportunity to see any similar calculation applied for current unbalance.

Even though is desirable to have balance current in a three phase system, It is not uncommon to have a healthy source with momentarily unbalanced single-phase load.

I suggest consider determine the purpose and meaning of this calculation and what benefit provides.

 

[buzzp]

I did not comment on 'the maximum imbalance".
The maximum imbalance is only determined by the current rating of the equipment being used (assuming all is sized properly for the loads). As long as no one leg exceeds the ratings then you should be fine. Of course, for motors and other three phase equipment, the current imbalance can have negative consequences (negative sequence currents increasing losses and heat).
I do not know of any standards which identify acceptable CURRENT unbalances for distribution, but then again, I don't work in the area of transmission and distribution.
You kind of need to work backwards on this depending on what your trying to accomplish. For motors anyway, the current unbalance is directly related to the voltage unbalance with current unbalances being up to ten times the voltage unbalance. If your just trying to equally distribute loads then using current unbalance is the way to go. If your trying to reduce the unbalance and you have motor loads, you can try to distribute the loads equally and rearrange the incoming phases (keeping the phase sequence the same). One of the three positive sequences will provide the least voltage unbalance (you have probably heard of rolling leads to determine if the unbalance is utility or load related, this is the same thing). Okay I will quit rattling on.

 

[waross]

The first rule of trouble shooting is:
Identify the problem.
Second rule of trouble shooting is;
Recheck rule 1.
The are are several more similar rules of trouble shooting.
It is quite frustrating and very counterproductive to try to correct symtoms when you don't know the cause.

In this case, the current imbalances are not the problem but a symtom of a possible problem.
Three possible causes;
1, Unbalanced loading.
Solution, redistribute single phase loads, check and repair three phase loads that are unbalanced. (Imbalanced??)
2, Unequal primary voltages, causing unequal secondary currents.
3, All of the above, that is, a secondary load unbalance causing a primary voltage unbalance.
Reread buzzp for comments on current unbalance caused by unequal voltages.
Solution, use any reasonable formula to locate the worst cases.
You may use the ratio of greatest current to least current.
Using the mean current as suggested by unclebob may be more correct, but we are not trying to pass final exams in transformer calculations.- We are trying to identify the worst cases, and any formula that does this is OK.
Pick a few of the worst cases and investigate.
Are the primary voltages equal?
Are there single phase loads, and if so, can they be rearranged to balance the load?
Check the three phase loads for balanced currents, and equal terminal voltages.
Be aware that unequal loading can cause unequal voltages, due to impedances in both the primary and secondary conductors and the %impedance voltage of the transformer.
I assume from the 480/277 that you have star connected secondaries.
What are the loads?
Are these one time current readings, or do you have a current history for the transformers?
And lastly, if I encountered the results that you gave in your example;
phase a = 480 amps
phase b = 490 amps
phase c = 470 amps
My reaction would be, no problem here.
In fact if there are single phase loads involved, such as a large amount of 277 volt lighting as in a large shopping mall, I would consider the currents you gave to be much better than expected.
If the loads were mainly three phase motors, I would suspect slightly unequal voltages, but I wouldn't worry about it.
Recheck buzzp re; If no lead to a motor exceeds the rated current of the motor and the motor is not overheating, then don't worry.
Hope this helps.