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# Calculating KVA

04/07/2017 5:23 AM

When calculating KVA of a 3-phase balanced system I use the following equation:

KVA = (Volts x Ampere x √3) ÷ 1000

or

KVA = (V x I x 1,732) ÷ 1000

My question: In the case of I (ampere) in this equation, will I be the value of ONE single phase or the value of all THREE phases added together?

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#1

### Re: Calculating KVA

04/07/2017 6:51 AM
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#8

### Re: Calculating KVA

04/08/2017 11:47 AM

I was disappointed in the contents of your link! Too many details left out, poor separation of items, everything dealing with generators, and who says the power factor is usually 0.8?. Ours changes all over the place, commonly under 0.5 (saturated reactors at low power output).

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#10

### Re: Calculating KVA

04/08/2017 11:59 AM

Well, that's what I get for posting before the morning's first cuppa.

4
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#2

### Re: Calculating KVA

04/07/2017 10:03 AM

It's best to understand the theory, if possible, to avoid confusion on the formulas.

First, in 3-phase you have to specify if the voltage is phase-to-neutral or phase-to-phase. Phase-to-phase voltage is sqrt(3) = (1.732) times phase-to-neutral voltage.

A three-phase circuit can be considered as 3 single-phase circuits. In a single-phase circuit, KVA = KV x Amps. (To get power, multiply by power factor.) So total KVA for a 3-phase circuit is 3 x KV x A, where KV is the phase-to-neutral voltage

So where does the sqrt(3) factor come from in your formula? It's because the voltage (in the formula is phase-to-phase voltage or sqrt(3) times phase-to-neutral voltage, and 3 (phases) / sqrt(3) = sqrt(3).

So your answer is: I is one line current in amps, V is phase-to-phase voltage in KV.

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#12

### Re: Calculating KVA

04/08/2017 12:25 PM

I've been struggling with this for years!

In your third paragraph, you say: "A three-phase circuit can be considered as 3 single-phase circuits. In a single-phase circuit, KVA = KV x Amps. (To get power, multiply by power factor.) So total KVA for a 3-phase circuit is 3 x KV x A, where KV is the phase-to-neutral voltage"

That sure looks to me like total kVA=kV x 3 x A, which is equivalent to kV x (A1 + A2 +A3), and that is totally logical, except that it says nothing about the phase angles between the three phases. This looks like adding the three currents...

I know the OP asked about a balanced system, but in our plant, some large circuits have very significant unbalanced currents, so I need to understand the differences. For determining wire sizes, it's pretty clear that one should use the largest current plus a safety factor, but for determining energy used, how does a 3-phase kWh meter handle unbalanced currents?

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#3

### Re: Calculating KVA

04/07/2017 6:23 PM

o come on now! none of you guys are going to jump on this post and bash the hell out of the op for asking a simple question?

I mean why not? you do it to me every day for asking things far more complex then this.

And the answer to the question is, it depends on if the source is wye or delta which people left out and when given the voltage, is it line to line or line to phase.

Generally its line to line but with homework questions you never know

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#5

### Re: Calculating KVA

04/08/2017 9:09 AM

This is the newer, kinder CR4. Get used to it and don't ask such a stupid question.

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Commentator

Join Date: Jan 2017
Posts: 57
#9

### Re: Calculating KVA

04/08/2017 11:57 AM

O yes I know calculating relay current and discussing Laplace transforms is sooooo easy I mean why would any one ask those questions.

Asking something as simple as 3 phase power calculation that can be found on the first page of any power book makes much more sense to this forum

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#11

### Re: Calculating KVA

04/08/2017 12:08 PM

Oh gawd, Laplace transforms are soooo old-skool when discussing relays and other electromechanical devices. Why bother when you've got Hilbert transforms and algebraic topology? I mean, c'mon! Quitcherwhinging and get to work, slacker.

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#7

### Re: Calculating KVA

04/08/2017 11:40 AM

To me, this is NOT a simple question. After working on single phase and split-phase electric systems for 40 years, I got pushed into 3-phase systems about 20 years ago. After all that time, I still don't really feel that I fully understand it!

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Active Contributor

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#4

### Re: Calculating KVA

04/08/2017 5:51 AM

V = 400VAC/50HZ (phase-to-phase of a 3-phase supply from a generator with a star-point. Neutral becomes irrelevant in this calculation)

I = 595Ampere measured from the red phase (phase with highest load)

√3 = 1.732

Therefore: KVA = (400 X 595 X 1.732) ÷ 1000

KVA = 412.22

Thank you for confirming my calculation method. In am aware that this is a kindergarten question but it needed to be asked here in order to get a confirmation in black and white from a reputable source to prove that I am correct. There are semi-political dynamics at play here in Nigeria that go far beyond engineering, dynamics that you knowledgeable folks will not even begin to understand.

I thank you.

John Meyer, Chevron, Niger Delta

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#6

### Re: Calculating KVA

04/08/2017 11:39 AM

"it needed to be asked here in order to get a confirmation in black and white from a reputable source"

We're a disreputable source. You have no idea. The dark, shadowy corner of the engineering world, one full of grumpy old geezers. It's a wonder we haven't all been arrested.

Guru

Join Date: May 2008
Posts: 1796
#13

### Re: Calculating KVA

04/08/2017 12:49 PM

Dear Mr.John365,

You have asked " in this equation, KVA = (V x I x 1,732) ÷ 1000 will the I be the value of ONE single phase or the value of all THREE phases added together?"

It is the current in single phase. Here the relation between Line Current and Phase Current is the key which will clear your doubt.

The equation for Line Current and Phase Current is, Line Current = Root3 (or 1.732) x Phase Current.

Now the Power in KVA of 3 phase circuit is 3 x V x (I/Root3)/1000. Here, 3/Root3 = (Root3 x Root3)/Root3 Therefore this results in Root3 as dividend - as Root3 in the Numerator and Denominator gets cancelled, and one Root3 remains.

Therefore Power in the equation KVA = (V x I x 1,732) ÷ 1000 is the current in phase.

I think now your doubt is cleared.

DHAYANANDHAN.S

Commentator

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Posts: 57
#14

### Re: Calculating KVA

04/08/2017 10:23 PM

amazing to me how so many people are assuming a certain connection delta or wye

it makes a difference people!! and not a single person has asked the OP what the source and load configuration is?

Is a delta delta? is it a wye wye how about a delta wye or a wye delta

it matters!

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#15

### Re: Calculating KVA

04/08/2017 10:38 PM

[unsubscribe]

Commentator

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Posts: 57
#16

### Re: Calculating KVA

04/08/2017 10:53 PM

you have a partially valid point but that is how jaded this forum has made me

I can't ask a question around here without getting rediculed I can only imagine if I answered one. Everyone would be totally up my ass with a microscope if it wasn't 110% correct with every detailed filled in

o wait, that was me bitching again!

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#17

### Re: Calculating KVA

04/09/2017 12:13 AM

Dear Mr.Rscott9399,

The formula for the power in 3 phase circuit - is the same Root3 x v x I x Power Factor - whether it is delta delta or a wye wye how about a delta wye or a wye delta.

In the case of Y connection, the Line Voltage = Root3 x Phase Voltage and the Line Current and Phase Current is the same.

In Delta Connection the Line Current = Root3 x Phase Current. and the Line Voltage and Phase Voltage is the same.

I think your doubt is cleared.

DHAYANANDHAN.S

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#18

### Re: Calculating KVA

04/09/2017 9:11 AM

I'm glad you corrected your #13, as I was about to . You said "The equation for Line Current and Phase Current is, Line Current = Root3 (or 1.732) x Phase Current"

That's only true for Δ connection, as you now say.

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