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Join Date: Jan 2017
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# Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/26/2017 3:19 PM

Is there a fairly simple formula to solve current per Leg in an unbalanced 3ph delta if only the L-L current is known? PF is not a consideration. Voltage is 460V if it's relevant.

I'm building a control panel using resistive loads.

Need to know the current per leg so I can determine fusing, wire awg, ect...

Ex.

L1:L2 - 91amps

L2:L3 - 78amps

L3:L1 - 91amps

How do I determine the line current of each leg?

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Guru

Join Date: Jun 2009
Location: South of Minot North Dakota
Posts: 7745
#1

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/26/2017 3:49 PM

Standard US code would have you size your fuse/breakers so that whatever upper continuous load is no grater than 80% of the breakers capacity but if that ends up giving a odd or uncommon breaker size just round that value up to the next common size available.

Also if its a three phase source feeding three heater banks that are all activated or turn off at the same time by one single contactor then all three phases need to be on one three phase breaker and not the separately sized and mechanically isolated ones.

If that doesn't make sense then I suggest, at minimum, you have your system design reviewed by a qualified electrician or electrical inspector who knows the code details of your area.

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#2

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/26/2017 3:52 PM

Guru

Join Date: Jun 2009
Location: South of Minot North Dakota
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#4

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/26/2017 6:53 PM

"I'm building a control panel using resistive loads.

Need to know the current per leg so I can determine fusing, wire awg, ect..."

so I answered the bold print part of your question or did you forget you asked for that or do you feel that what aspects of the design that you would need to meet regarding general design codes with your fusing, cabling and whatnot is irrelevant somehow?

As in this is this some home based/backdoor business transaction 'off the records project' where you could care less about it being built or controlled properly because you plan to go as cheap and undersized with every cable and component as you can get away with and still have it somewhat functional in the end?

Guru

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Location: Richland, WA, USA
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#5

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/26/2017 9:11 PM

Maybe that will be explained after "ect" is explained.

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#7

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/27/2017 9:10 AM

The "ect." is irrelevant. The "ect.", as far as coding and sizing requirements are not in question. That is the known part of the equation.

The unknown is how to determine the current per leg in an unbalanced delta circuit.

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Posts: 7
#6

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/27/2017 9:05 AM

The bold part of the question is actually Need to know the current per leg.

I don't need you to regurgitate well known standards without actually answering the question of how to determine the current. Conductors and switching devices need to be sized 125% of the current per leg. Without knowing the actual current per leg, it would be built improperly.

If you don't know the answer to the question asked, you are merely trying to provide some type of answer in order to feel relevant.

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Guru

Join Date: Jun 2009
Location: South of Minot North Dakota
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#8

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/27/2017 1:04 PM

Good luck with that theory and you should hope that no one here is having a day where they want to kick someone around over the semantics of the questions they asked.

There are a good number of members here who actually consider that a rather fun sport.

Don't tell a group of experienced engineers and like what you think is relevant to your problem you clearly couldn't answer yourself. You may not like the responses you will get.

(The fox is loose. Will the hounds chase it? let's wait and see. )

Score 1 for Off Topic
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Guru

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Posts: 4837
#3

### Re: Finding the individual Line current in an unbalanced 3Ph Delta

01/26/2017 5:02 PM

Figure out the equivalent delta resistances of the load using the line-to-line voltages and line-to-line currents. Convert delta resistances to wye resistances using delta-wye transformation formulas. Now each phase current equals phase voltage divided by the wye resistance.

Guru

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#9

### Re: Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/27/2017 4:08 PM

I am sorry as I am not to agree with Mr.Rixter but these formulae are for d.c. current only.

For a.c. the transformer impedances are parallel or series with the load so it is not possible to calculated it so.

The simplest way is to use complex number and an excel workbook.

L1-L2 will be 91 A and 0 argument if power factor is 1 or -acos(pf) for another pf.

L2-L3 will be 78 A and the argument -120-acos(pf) and L3-L1 91 and -240-acos(pf) argument.

If we use A,B and C instead of 1,2,3 then

IA=IAB-ICA

IB=IBC-IAB

IC=ICA-IBC

I the above case if the power factor is the same in all L_L phases and if the L1_L2 phase voltage argument will be 0 and all phases power factor is 0.8 then the line currents will be:

IA =157.6A<-66.87; IB= 146.5A<170.59 ;IC= 146.5A<55.67

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Julius
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#10

### Re: Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/27/2017 4:31 PM

Thank you to the two individuals that actually tackled the question that was asked. I truly appreciate it.

@ 7anoter4: Those value are within 2/10A from what I came up with using a simplistic method. I simply took the average of 2 legs, then multiplied by 1.73. The answers were within mA of each other. Do you see a problem using this method?

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#11

### Re: Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/27/2017 6:34 PM

There are simple and proper ways of finding out everything in a 3-Ф circuit.

The first thing would be to explain what you have - and then what you wish to know. There is no such thing as a L-L Current, there can be only a L-L Voltage.

Are you referring to the current within the delta load? And then wish to determine the line current? What accuracy do you desire?

If this is only for building a "control panel", . . then just multiply the current withing the delta by 1.7321. Close enough for your application,

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#13

### Re: Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/30/2017 9:12 AM

"Are you referring to the current within the delta load? And then wish to determine the line current? What accuracy do you desire?"

You're exactly right.

I have (20), 1Ph, 13A heater arrays. By "line to line" current, I'm referring to the expected load. Since the number of arrays is not divisible by 3, I am going to have to wire them in an unbalanced fashion. Accuracy is not crucial, but this application raised a larger question about what to do in the future if the difference between line currents is more substantial.

Guru

Join Date: Oct 2012
Location: 100 miles North from the World Center
Posts: 699
#12

### Re: Finding the Individual Line Current in an Unbalanced 3Ph Delta

01/27/2017 11:50 PM

If the current differences [values and power factors] are small then any way is close enough and

for your application you don’t need more accuracy,indeed.

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Julius
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