Intro to 3-Phase AC Motors: Understanding Wattmeter Measurements | Help Needed

[ohadbx]

Homework Statement

hello everyone
I'm a little confused with the whole 3- phase system.
for example:

An AC motor is connected to a 3-phase R-S-T system with 400 volts.
The motor is in Delta configuration and every load is Z=1+2.5j .
A wattmeter is connected between the RS lines.
W=|V_RS|*|I_R|*cos(∠I_R-∠V_RS)=?

I tried solving using differenet methods we were taught, but every way i try i get a different result.

For example: 1) I thought that the wattmeter will measure the Real Power of a single load, which should be a third of the total Real Power of the motor. so:

on the other hand:

I'm starting to feel lost in this, so any help would be appreciated.

P.S. Maybe I should have done a Y-DELTA transformation? Although I'm not sure what good would that do...

Thank you and have a great weekend

 

[NascentOxygen]

A wattmeter connected as described will sense the voltage of each phase of the motor, but it will sense more than the current of a single phase of the motor, it will sense the phase current x √3.

With this correction, does that confirm your analysis?

 

[ohadbx]

Thank you for your reply

when I chekced the reading of the wattmeter (the second solution) I did multply the phase current by sqrt(3).
Or am I not getting your point?

 

[NascentOxygen]

What you calculated in the first step is the power in one phase of the motor. You will want to multiply this by √3 to compare it with your second calculation.

Where you write V_RS / Z I think there is a missing √3.

and a warm greeting ... http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

 

[ohadbx]

Thanks for the nice greeting

Sadly, I am still unsure of what I am doing wrong.
This is my understaing of the setup:

To my understanding, in a delta configuration (such as shown),
V_LINE=V_PHASE , so wouldn't that mean that I_PHASE=$\frac{V}{Z}$? where does the √3 come from (if I want to use the power formula I mentioned in the first solution)?

BTW it has come to my attention that this question was originally a multiple-choise question.
The possible answers were: A. (-44.03) B. 22.07 C. (-14.68) D. 66.21 (all in [kW])
bit I have no Idea which is the correct one.

 

[NascentOxygen]

A wattmeter has 2 pairs of sensing coils, one for voltage and another for current. I think it is unreasonable to believe you can routinely break open a delta motor and connect something in series with one of its phases to sense phase current!

You performed 2 calculations. Basically, the first is for 1/3 of the motor's power. The second is for 1/3 of (√3 of the motor's power).

My contention is that the best you can do is to have the wattmeter measuring the latter (whether you like it or not), sensing V_RS and I_R. You can't sense the motor's phase current, even if you wish you could. Well, that's my thinking.

 

[NascentOxygen]

A wattmeter is connected between the RS lines.

Is that the wording of the original question? It sounds a sloppy way of expressing the arrangement.

It seems motor phase power is 22kW and total power is 66kW. So they must want the answer of 22kW.

 

[ohadbx]

Is that the wording of the original question? It sounds a sloppy way of expressing the arrangement.

Yes, that is the original statement, and in addition there is a drawing like the one I have posted.

I agree with you, I also think the right answer is 22. That means I shouldn't have multiplied by √3 in second solution, but the reason escapes me.

Thank you for your help

 

[NascentOxygen]

Yes, that is the original statement, and in addition there is a drawing like the one I have posted.

I'd like to see the original drawing. Can you attach it here?

 

[ohadbx]

here you go, though its not very informative.
The switches are for a different, unrelated, part of the question- the setup is changed to Wye.

 

[NascentOxygen]

So it looks like the construction brings out the ends of each motor phase so that you can connect a meter in series with a single phase of the motor to meter the phase current! (Or at least it is intended to represent that.)

Thanks.