root 3, how it comes 3 phase power calculations

RGA! (Really Good Answer) About the only way to improve that answer would be to include a diagram or two.

I've had this explained to me several times before, but your explanation is the first one EVER to make sense without a diagram! Well done!

I agree with dk -- a RGA!

1. end of discussion

Maybe you can help me. I see in some power calculations in three phase I see 400 volts multiplied by the square root of three ie 1.732* 400*pf*amps. When three phase is single phase * 1.732. Confused

Go back and read all of post #1 two or three times. Notice that 11 people (including myself) gave wareagle a GA rating for that post. VERY few posts ever get close to that!

Let's try for simplicity:

In an Isosceles triangle with 120⁰, 30⁰, 30⁰, you will note that the base = either leg X sq rt of 3.

Look here for detail. If you have 2 legs = 120, the base is 120 X sq rt 3 = 207.9

This applies directly to the electrical phasor diagrams. Does this help?

CJM

power= v x i x xos * where v=voltage, i= amp and * is phase angle between voltage and curent.

for 3 phases it would be = 3 x v x i x cos *. where all represent phase voltages.

In general we represent line voltages only and line voltage = root 3 x phase voltage.

shivaram

So we don't confuse the questioner, a few clarifications to your comment:

"and * is phase angle between voltage and Ephase."

That should be the cosine of the phase angle....

Please note that only in a Wye circuit can both Iphase and Ephase be measured directly. This is the only case where multiply X 3 works in practical application, and then only if the phases are balanced.

All other field measurements will include either Line to Line Voltage or Line to Line current which in all cases will then require the square root of 3 in the formula.

Also a small correction to "line voltage = root 3 x phase voltage." This is true for Wye but not true for Delta. In a Delta circuit it is the Line Current that must be multiplied by square root of 3 since the Line to Line Voltage is the Phase Voltage.

Regards, CJ

as far as summing up the three currents, it is OK.

but if we are calculating the total 3 phase power demand of the machine, why we have selected 230V in the formula? why not 415?

I just reread all of the posts twice to be sure: no one specifies a specific voltage anywhere in posts previous to yours. All the numbers given were related to geometry (angles and triangle side lengths), although the 120 and 207.9 values in post 2 could be correctly interpreted as voltages.

In the United States, virtually all portable (movable with one hand) electric devices use either batteries or 120 VAC. By using 208V 3 phase power for most medium powered machines (like mills, lathes, welders, etc.), we can get the 120V for lights, fans, and our portable tools by connecting them between one 208V line and neutral. Thus there is no need to run a separate cable for the low power devices.

Although the 120V devices do require more current and therefore larger wire than higher voltages, those larger wires are more robust and can withstand more shock and vibration. This is especially true in incandescent light bulbs; a low power (say 40W) 240V lamp has to have a really fine filament - bump it with your screwdriver while its hot, and it's gone. A similar 120V lamp is significantly stronger, and a 12V lamp better still. Back in the day when cars used 6V, you hardly ever had to replace headlights, because the filaments were so thick and strong.

Many industrial bulidings here are only supplied only with 208V 3Ø. A few years back, it cost us around $100,000 to bring in 480V to one of our buildings.

It is as simple as understanding where on the earth you are located.

In your location, you obviously are familiar with 415v as a normal voltage. You will see comments using voltages common to other locations, but don't let that cause confusion. Look at the application of the logic in the explanations and formulae, and insert your local values. Do the math using your local values, and you will get the same relative results.

At some point in the past, (see info on Tesla) it was determined that it was possible and practical for 3 phases to be created using the same generator or alternator. This is the origin of the 120⁰ phase relationship. 360⁰ divided into 3 equal segment results in a 120⁰ separation. Isosceles had already pointed out the √3 relationship centuries earlier working with triangles, which apply to the methods of measuring and calculating electrical values.

You may be familiar with pi (∏), when dealing with circles. It is not a nice rounded even number, but is widely accepted as the factor that explains certain relationships about circles. And so also you will get familiar with the proper uses of the constant √3 when dealing with 1/3 of a circle.

When a line intersects 2 radii separated by 120⁰ at a point where the radii each have a value of 1, the line is equal to √3.

You will find this relational value factored into every 3 phase equation using Line current and/or Line voltage.

When equations are given that use only phase voltage and phase current, the √3 factor has been applied to either the current or voltage Line value, and so is still present.

In actual measurements taken physically, it is not usually possible to measure both current and voltage in phase values, except in a Wye circuit, which is why multiplying by 3 then works (if circuits are balanced). Even then, one of the values (voltage) includes the √3 relationship to the Line to Line voltage.

Regards, CJM

The sqrt3 comes from using the Law of Cosine (c)2 = (a)2 + (b)2 - 2ab*cosC where a=1, b=1, c=unknown A=30, B=30, C=120 degrees. When you plug in the numbers and do the math you get sqrt3. When you draw the triange let a and b be the 2 short legs with the 30 degree angles and c be the longest leg with the angle C=120degrees. Sqrt3 is just a ratio of the triangle.

(c)2 = 1+1-(2*cos120)

(c)2 = 2-(-1)

(c)2 = 3

c=sqrt3

I think we lost the OP at "phasor", he probably started thinking about weapons in Star Trek at that point and drifted off...

There is a good article in Wikipedia on this topic.