Calculating a three phase feeder with single and three phase motor loads

[Knox]

I am in the process of sizing a 3 phase 208/120v 4-W service for an existing site currently fed single phase. We will be back feeding existing feeders that are feeding the single phase motors and additional non-motor continuous load of 165A. I have the following loads:
Motor Loads:
(1) 3ph, 208v, 20hp = FLA 59.4a
(1) 1ph, 208v, 10hp = FLA 55a
(5) 1ph, 208v, 7.5hp = FLA 44a
(1) 1ph, 208v, 3hp = FLA 18.7a
(2) 1ph, 120v, 1 hp = FLA 8.8a

59.4 x 1.25 = 74.25 + 55 + (44x5) + 18.7 + (8.8x2) = 385.55A

Other continuous load of 165A

Total Connected Load: 550.55A (551A)

Minimum service size 600A?

Please look over my calculations and confirm they are correct or feel free to comment as to what is incorrect.

Thank you in advance.

 

[wwhitney]

Please look over my calculations and confirm they are correct or feel free to comment as to what is incorrect.

I'm going to ignore the "other continuous load" portion, as you haven't specified whether it is 120V, 208V single phase, or 208V three phase, or some combination of the above.

Then what you have calculated with the motors at 386A is the worst case unbalanced loading on a single line conductor, say A, if you always use A for every load (so the 208V 1ph loads are A-B or A-C, and the 120V loads are A-N), and if the phase shifts of the component loads are ignored, so the currents add without cancellation. That's definitely an overestimate.

The typical approach is to assign a VA to each load and split that VA among 1, 2, or 3 lines according to whether the load is L-N, L-L, or 3 phase, in the most balanced way possible. Then add up the VA on each line, take the largest VA, and convert that back into amps.

So for example, taking your loads and splitting the VA as an ordered triple (A, B, C) for the 3 lines, you get try this balancing:

(1) 3ph, 208v, 20hp = FLA 59.4a gives 208 * 59.4 * sqrt(3) = 21,400 VA
divide as (7133, 7133, 7133)
(1) 1ph, 208v, 10hp = FLA 55a gives 208 * 55 = 11,440 VA
divide as (5720, 5720, 0)
(5) 1ph, 208v, 7.5hp = FLA 44a gives 208 * 44 = 9,152 VA
divide as a balanced triple of (9152, 9152, 9152)
plus 2 more as (4576, 4576, 9152)
(1) 1ph, 208v, 3hp = FLA 18.7a gives 208 * 18.7 = 3890 VA
divide as (0, 1945, 1945)
(2) 1ph, 120v, 1 hp = FLA 8.8a gives 120 * 8.8 = 1056 VA
divide as (1056, 0, 1056).

Then if we sum up the triples, with a factor of 1.25 on the first one as the largest motor, we get (29420, 30309, 30221). I think that is the most balanced we can do. So the worst case line VA is 30309, which we convert to amps by dividing the L-N voltage of 120V, or 30309/120 = 253A.

Which is quite a bit less than the 386A maximally unbalanced load you calculated. But you had best check my arithmetic in all the above.

Cheers, Wayne

 

[Knox]

Thanks for the reply Wayne. I do not see any error in your math or your method. In this case and maybe I should have expanded some in my original post, the single phase loads are currently being fed from a series of underground feeders that feed 100a and 200a single phase load centers which in turn each feed a combination of the above single phase motors. It is an old grain bin and grain dryer site that is getting some upgrades that will require 3 phase power. I figured worst case as I haven’t determined how the load centers would be balanced across the system at this point and also would need to determine what motors are on what phases on the single phase system. The other unbalanced load is single phase as well.

My hope is that I can show the farmer that it may be beneficial to changeout some of the larger motors that are aged to 3 phase in order to provide greater efficiency and reduce the load on the service or we oversize the service as it is currently calculated which will allow for future growth as time progresses. And with growth will eventually phase out the single phase motors. I just want to make sure my calculations are in line (worst case).

I do agree that if I were to run new power to all motors you’d be spot on with your calculation.

Thanks

 

[wwhitney]

Well, if you have existing 120/208V 3-wire feeders that you want to refeed, you can do the load calcs for those each of those feeders individually, and then try to balance those feeders as best you can. In which case if you have at least 3 such feeders you'll get a result somewhere between your initial answer and my answer.

Cheers, Wayne