# Power formula for 3-phase motor

1. Jun 6, 2013

### Ahmedzica

What is the power formula for 3-phase Y connected motor. I've read that

P = sqrt(3) Vt*Ia*Cos(theta)
and P = sqrt(3) Vt*E*sin(sigma)/Xs

Where sigma is the the angel between Vt and E
Is that 2 formulas hold true for both delta and star connected 3 phase motor? and if so, Where the sqrt(3) came from?

2. Jun 6, 2013

### psparky

If you are referring to the amps actually coming thru the lines (what would be read by an ampmeter) you would use the formula P=V*I*1.73. This is the total power needed from power company to make the motor run. This is what is refered to as VA.

The actual power from the shaft is going to be somewhat less. Like you say above P=V*I*1.73*PF (power factor)....or you could say Cos(theta) instead of PF..same thing. This number is expressed in watts or horsepower (HP)

So to deliver 10 HP (10*745=7450 watts) to the shaft of a motor, it may take 14 HP (14*745=10,430 VA) worth of electricity to make this happen. Some say the extra power is "used" in the magnetic field of motor. You can alter PF with capacitors, but that is another story.

Where does 1.73 come from? Take the vector form and set 3 vectors 120 degrees apart from eachother. If want line to line, you must subtract phase B from phase A for example.....voltage is always the DIFFERENCE between to points. So knowing this you must flip the vector B a complete 180 degrees (the opposite or DIFFERENCE). This will now give you 60 degrees between the two vectors, which you now add. Using simple trigonometry or geometry, you will see the resultant vector (line to line voltage) is now 1.73, or the square root of three multipled by your line to neutral voltage. (original length of vectors). Also, the resultant vector just shifted 30 degrees.

To answer the question of different formulas for star or delta motors....the power formula (VA) will be the same if the current is measured outside of the motor, P=V*I*1.73

If you measure the current inside the motor in the delta to be exact, that is the only time you will need to alter the power formula.

Last edited: Jun 6, 2013
3. Jun 6, 2013

### psparky

Last edited: Jun 6, 2013
4. Jun 7, 2013

### Ahmedzica

Thanks psparky!!