3 phase to single phase ampere calculation

[Jpflex]

We have a 3 phase delta 480 volt to 208Y/120
30KVA transformer supplying a single phase panel

To determine primary and secondary conductor sizes all terminating at 75 degrees celcius and using THHN:

When calculating delta 3 phase primary current I obviously get 30,000 VA x 480 V x 1.732 = 36.08 amperes

If I calculate the output secondary current for the 3 phase Y output I get 30,000 / 208 x 1.732 = 83.31 amperes

However, supplying a single phase panel with just 2 legs of the Y secondary becomes single phase and mathematically appears to produce more current then when using all 3 legs of the Y because 1.732 is factored into the equation.

Now when using the single phase formula to determine secondary current, the 2 legs of Y windings magically appears to increase beyond what the 3 legs of the 3 phase Y could produce. Which makes no sense

30,000 VA / 208 V = 144.23 amperes (single phase)

Vs

30,000 VA / 208 V x 1.732 = 83.21 amperes ( 3 phase all legs used in Y

If i calculate secondary conductor size for 3 phase at 1.25 % of amperes using 30,000 / 208 x 1.732 I’ll use a # 2 AWG THHN at 75 deg c. (110 amperes)

However if I calculate secondary conductor size as it is single phase at 1.25% (just A and B phases used) I use a 3/0 AWG THHN at 75 degree c (200 amperes)?

So do I size secondary conductors and OCPD to 110 amperes or 200 amperes? And would wire sizes plus OCPD be correct?

 

[wwhitney]

Now when using the single phase formula to determine secondary current, the 2 legs of Y windings magically appears to increase beyond what the 3 legs of the 3 phase Y could produce. Which makes no sense

30,000 VA / 208 V = 144.23 amperes (single phase)

Vs

30,000 VA / 208 V x 1.732 = 83.21 amperes ( 3 phase all legs used in Y

The top computation would only apply to a single phase transformer with a 2-wire 208V secondary that was rated at 30 kVA. With a 3 phase transformer, you must use the bottom computation to determine the maximum current per leg that the transformer can support. You can also think of your 3 phase transformer as (3) 10 kVA transformer, each with a 120V secondary, so the maximum current per leg is 30,000 VA / 120V = 83.3A (same answer other than rounding).

Then if you run only two legs and a neutral to a "single" phase panel, you are not using the full transformer capacity, because you are only using 2 of 3 secondary windings. So you'll have 20 kVA available from that panel, for 120V loads, if you can balance the 120V loads into two groups of at most 83.3A each. Furthermore if you supply 208V 2-wire loads from that panel, the total VA available will be below 20 kVA, as those loads do not use the two windings as efficiently.

Cheers, Wayne

 

[Jpflex]

The top computation would only apply to a single phase transformer with a 2-wire 208V secondary that was rated at 30 kVA. With a 3 phase transformer, you must use the bottom computation to determine the maximum current per leg that the transformer can support. You can also think of your 3 phase transformer as (3) 10 kVA transformer, each with a 120V secondary, so the maximum current per leg is 30,000 VA / 120V = 83.3A (same answer other than rounding).

Then if you run only two legs and a neutral to a "single" phase panel, you are not using the full transformer capacity, because you are only using 2 of 3 secondary windings. So you'll have 20 kVA available from that panel, for 120V loads, if you can balance the 120V loads into two groups of at most 83.3A each. Furthermore if you supply 208V 2-wire loads from that panel, the total VA available will be below 20 kVA, as those loads do not use the two windings as

You can also think of your 3 phase transformer as (3) 10 kVA transformer, each with a 120V secondary, so the maximum current per leg is 30,000 VA / 120V = 83.3A (same answer other than rounding).

Cheers, Wayne

When you say to think of the 3 phase transformer as 3 of 10KVA transformers each with a 120 volt secondary to get 83.3 Amperes you are calculating each winding in Y as a single phase

So by using the derived neutral, the amperes available are higher rather than if using higher voltage 1 leg to 1 leg

But why do you use 30KVA / 120 instead of 10KVA / 120 for 1 leg and the derived neutral to get 83.333 amperes available per 1 winding and neutral?

If I do 30KVA / 120v I get 250 amperes but not 83.33? Also when you say per leg do you mean one end winding and neutral or phase to phase leg to leg measurement? Thanks

 

[Jpflex]

Also what should I be setting the OCPD for the secondary to single phase panel at 20KVA / 208 x 1.732 (2 legs and a neutral supplying single phase panel for 20KVA)

secondary panel main breaker 20KVA / 208 x 1.732 = 55 amperes main breaker?

 

[ptonsparky]

IDK but...
20000/208*1.732=166
20000/(208*1.732)=55

 

[Jpflex]

IDK but...
20000/208*1.732=166
20000/(208*1.732)=55

Wait what?

 

[ptonsparky]

The transformer is capable of 83 amps each leg. You don't care that you are only using two, You will need to know what you have provided for the primary protection to determine what the secondary is allowed.

 

[xformer]

The top computation would only apply to a single phase transformer with a 2-wire 208V secondary that was rated at 30 kVA. With a 3 phase transformer, you must use the bottom computation to determine the maximum current per leg that the transformer can support. You can also think of your 3 phase transformer as (3) 10 kVA transformer, each with a 120V secondary, so the maximum current per leg is 30,000 VA / 120V = 83.3A (same answer other than rounding).

Then if you run only two legs and a neutral to a "single" phase panel, you are not using the full transformer capacity, because you are only using 2 of 3 secondary windings. So you'll have 20 kVA available from that panel, for 120V loads, if you can balance the 120V loads into two groups of at most 83.3A each. Furthermore if you supply 208V 2-wire loads from that panel, the total VA available will be below 20 kVA, as those loads do not use the two windings as efficiently.

Cheers, Wayne

Calc should be 10,000 VA / 120V = 83.3 volts

 

[ptonsparky]

Calc should be 10,000 VA / 120V = 83.3 Amps

IFIFY

 

[ptonsparky]

60 amp primary protection would amount to about 110 amps secondary.

eta for a 30 KVA

If it is only good for 20 KVA as Whitney stated, 70 A primary and 70 secondary

 

[xformer]

IFIFY

???

 

[ptonsparky]

I Fixed It For You. His result should have been amps, not volts. An oops.

 

[ptonsparky]

IDK but...
20000/208*1.732=166
20000/(208*1.732)=55

My school teacher wife corrected me.

 

[wwhitney]

But why do you use 30KVA / 120 instead of 10KVA / 120 for 1 leg and the derived neutral to get 83.333 amperes available per 1 winding and neutral?

That was an unfortunate typo, sorry about that. As others confirmed, when thinking of it as (3) single phase 10 kVA transformers, I meant to type 10 kVA / 120V = 83.3A.

Cheers, Wayne

 

[wwhitney]

Also what should I be setting the OCPD for the secondary to single phase panel at 20KVA / 208 x 1.732 (2 legs and a neutral supplying single phase panel for 20KVA)

secondary panel main breaker 20KVA / 208 x 1.732 = 55 amperes main breaker?

20 KVA / 208V * sqrt(3) isn't the correct computation or a useful computation. The allowable current on each leg will still be 83.3A, from either formula 30 kVA / 208V * sqrt(3) or 10 kVA / 120V.

So if you want to get the full available VA out of your panel (which will be 20 kVA if you have only 120V loads), you'll need to use a panel OCPD at least 83.3A; or if you have continuous loads and want to get the full available continuous VA out of the transformer (whose rating is continuous, so no further 125% factor is required for the transformer itself), you'll need a panel OCPD at least 83.3 * 125% = 104A.

There are of course other rules on primary and secondary OCPD for transformers and primary and secondary conductors, but I won't go into those, as my familiarity with them is less.

Cheers, Wayne

 

[Jpflex]

That was an unfortunate typo, sorry about that. As others confirmed, when thinking of it as (3) single phase 10 kVA transformers, I meant to type 10 kVA / 120V = 83.3A.

Cheers, Wayne

Thanks for clear up

 

[Jpflex]

20 KVA / 208V * sqrt(3) isn't the correct computation or a useful computation. The allowable current on each leg will still be 83.3A, from either formula 30 kVA / 208V * sqrt(3) or 10 kVA / 120V.

So if you want to get the full available VA out of your panel (which will be 20 kVA if you have only 120V loads), you'll need to use a panel OCPD at least 83.3A; or if you have continuous loads and want to get the full available continuous VA out of the transformer (whose rating is continuous, so no further 125% factor is required for the transformer itself), you'll need a panel OCPD at least 83.3 * 125% = 104A.

There are of course other rules on primary and secondary OCPD for transformers and primary and secondary conductors, but I won't go into those, as my familiarity with them is less.

Cheers, Wayne

If 104 isn’t a standard size breaker you can or can not go up to the next size up breaker for the single phase panel?

 

[Jpflex]

When you say to think of the 3 phase transformer as 3 of 10KVA transformers each with a 120 volt secondary to get 83.3 Amperes you are calculating each winding in Y as a single phase

So by using the derived neutral, the amperes available are higher rather than if using higher voltage 1 leg to 1 leg

But why do you use 30KVA / 120 instead of 10KVA / 120 for 1 leg and the derived neutral to get 83.333 amperes available per 1 winding and neutral?

If I do 30KVA / 120v I get 250 amperes but not 83.33? Also when you say per leg do you mean one end winding and neutral or phase to phase leg to leg measurement? Thanks

When you say 1 leg I think of one end of the winding and opposite end terminatingbto a common Y neutral

If you say 2 legs I think of two ends of separate windings A and B or A and C or C and A

 

[wwhitney]

If 104 isn’t a standard size breaker you can or can not go up to the next size up breaker for the single phase panel?

Here's a lengthy answer, that hopefully I got right, as I'm not super familiar with transformers. Starting at the primary supply side, going towards the transformer, you have (everything needs to be large enough for the load, so I won't keep repeating that):

Primary OCPD--needs to be large enough for the transformer inrush not to trip it but small enough to protect the transformer (450.3).
Primary Conductors--need to be large enough that they are protected by by the Primary OCPD, and 240.4(B) applies.
Transformer--needs to be large enough that the Primary OCPD protects it.
Secondary Conductors--need to be large enough to be protected by the Secondary OCPD per 240.21(C), and 240.4(B) does not apply.
Secondary OCPD--needs to be small enough to protect the Secondary Conductors, and possibly the transformer, and the panelboard bus
Secondary Panelboard

Cheers, Wayne

 

[Carultch]

Wait what?

Order of operations issues.

20000/208*1.732=166, because the division sign only puts the 208 value downstairs, and the 1.732 is upstairs by default. This implies (20000/208)*1.732.

20000/(208*1.732)=55, because it snares the (208*1.732) and puts them both downstairs.
20000/(208*1.732) is the calculation you want to do in this context, for calculating the corresponding Amps to 20 kVA at 120/208V 3-phase.