Calculating 208V load, purpose of sqrt(3) and power factor?

[JJinNR]

Hi all, a pretty simple question. I want to be able to calculate the load on a 100amp 3 phase service. As an example if I have 9 lighting fixtures that are rated @ 11 amps 208v each (auto ranging 200-240v actually but service will be 3 phase so 208v ish)
Putting evenly across each leg x,y,z I get 66 amps per leg. At this point you would multiply by 1.732 or divide by 1.732 each leg total to get a more accurate load? Or am I missing a step? Or just totally off...
What is the purpose of the sqrt of 3?
Where does power factor come in? How is power factor determined?
Also, if you metered a 208v system that let's say has 8 units instead of 9, would that voltage difference be seen on the neutral and nothing on the ground? The neutral should be able to carry up to the rating of the cable rating? A service from the power company can handle unbalanced loads as opposed to a smaller generator which one would want to balance with more care?

Thanks for your expertise.

 

[jim hardy]

if I have 9 lighting fixtures that are rated @ 11 amps 208v each

How is power factor determined?

Should be written on the lamp fixture's dataplate.

Also, if you metered a 208v system that let's say has 8 units instead of 9, would that voltage difference be seen on the neutral and nothing on the ground?

It will be a current difference.

The neutral should be able to carry up to the rating of the cable rating?

In US that's so. Check your local code.

 

[JJinNR]

Thank you for your response. Just a follow up. You list 33amp *sqrt3 = 57amps per leg. why 33amp to start? Power Distro wiring would distribute power as:

Leg X...leg Y...leg Z
11a...11a
...11a...11a
11a.....11a

It wouldn't be 22a * sqrt 3 = 33amp per leg
Where did the additional 11amps come from?

 

[jim hardy]

if I have 9 lighting fixtures that are rated @ 11 amps 208v each

so i drew three fixtures across each phase, as shown, and 11 X 3 = 33 .

Leg X...leg Y...leg Z
11a...11a
...11a...11a
11a.....11a

It wouldn't be 22a * sqrt 3 = 33amp per leg <<<<My calaculator says 22 * sqrt(3) = 38.1

Where did the additional 11amps come from?

That's only six fixtures not nine.
Did i miss something ?

 

[sophiecentaur]

@jim hardy . I notice you chose a delta connection for your example. I don't know much about standard practice but isn't WYE connection more common?

 

[JJinNR]

Thank you for your response. Just a follow up. You list 33amp *sqrt3 = 57amps per leg. why 33amp to start? Power Distro wiring would distribute power as:

Leg X...leg Y...leg Z
11a...11a
...11a...11a
11a.....11a

It wouldn't be 22a * sqrt 3 = 33amp per leg
Where did the additional 11amps come from?

Sorry, you missed I'm an idiot and on very little sleep. Thanks for your patience.

 

[JJinNR]

Sorry, you missed I'm an idiot and on very little sleep. Thanks for your patience.

But it does bring to light what seems to be the crux of my confusion. My little chart showed 3 lights and the legs that it would be using to get 208v. Horizontally is a unit and the columns show the amp draw for that leg.

......leg X.....leg Y.....leg Z

Unit 1...11amp...&...11amps

Unit 2......11 amps ..&...11amps

Unit 3 ...11amps....&.....11amps

Etc.

So why consider the units across all 3 phase so you can say divide 9 units down to 3 units on each leg (3*11=33amps) why don't you add up each column (leg) & multiply by 1.732? ( so 66 amps * 1.732 = 114.312amps)

I've been told to take ( #of units * rated amps /3 ) *1.732 = load.on leg.balanced.

JJ

 

[jim hardy]

why don't you add up each column (leg) & multiply by 1.732? ( so 66 amps * 1.732 = 114.312amps)

Ahhhh back to your original question, where does the √3 come from...
Take a snip from my sketch:

(sorry- the brown print didn't stand out as bold as i wanted..)

 

[jim hardy]

@jim hardy . I notice you chose a delta connection for your example. I don't know much about standard practice but isn't WYE connection more common?

Ahhh here in US for medium size facilities like a motel or something
they bring in four wire wye three phase 208 volt phase to phase
because phase to neutral for that arrangement 208/√3 = 120.
Big loads they connect phase to phase, hence his 208 volt lighting fixtures ,
observe he's hooking up 208V X 11A X 9 = 20.6 kva of them. ( Imagine the resistance heat load for such an installation. )
Ordinary 120 volt receptacles are connected line to neutral.
We call it informally 'a 208/120 feed'..

That's why i drew his 208 volt lamps phase to phase. I just divided them equally among the phases.
I didn't show the neutral because the drawing was cluttered enough , and he didn't mention any 120 volt loads.

Surely you guys have something similar over there ? The equivalent would be 416/240 ? 400/230?
I found this at https://www.schneider-electric.co.uk/en/faqs/FA163890/

What are the differences between 380VAC, 400VAC and 415VAC Mains Supplies and what voltage equipment should I use?
For many years, mainland Western Europe has used a mains, 3 phase, electricity supply rated at nominally 380VAC 50Hz. The UK used 415VAC 50Hz.

Currently, ALL Western European 3 phase supplies are classified 400VAC. In reality there is no 400VAC supply unless you create one locally. 400VAC was a “standard” created during European "harmonisation" to give a single voltage standard across Western Europe, including UK and Irish Republic.

Although the ideal would have been to have a single voltage there were too many political, financial and technical obstacles to reduce UK voltage to European levels or to increase European voltage to UK levels, so a new standard was created to cover both. This was achieved by changing the tolerances of previously existing supply standards. UK voltage to 415VAC + 6% and - 10% and European to 380VAC +10% and -6% (thereby creating a manageable overlap) and we would call these two combined 400VAC, despite the fact that nobody was intentionally generating at 400VAC!

but I'm 4000 miles away... do you indeed have 415 volt commercial appliances ?
My favorite metal recycle / scrapyard gets a lot of 208 volt airconditioners.

old jim

 

[sophiecentaur]

but I'm 4000 miles away.

You have good long distance vision, nonetheless. I only know about 415V 3 Phase equipment and 240 V single Phase in UK. But I have never been in a Factory Environment so I cannot be sure.
This is a typical Trans Atlantic thing where there are more differences than a chap could ever imagine. Thing is, 240V single phase is quite enough for equipment powers where 110V would need thick cables for the same power. We perhaps have a slight safety issue but I have to say, it's not in the News that people are dropping like flies from 240V shocks.

 

[jim hardy]

I only know about 415V 3 Phase equipment and 240 V single Phase in UK.

Thanks Sophie ! 415 / √3 = 239.6 . Same music different octave.

 

[sophiecentaur]

Thanks Sophie ! 415 / √3 = 239.6 . Same music different octave.

Showee offee with your trigonometree!
We have rules about mixing two phases in one dwelling. You guys can have much more fun than us.