Power Sample Question 517

[roadrunner]

Can anyone walk me through this question?

3phase induction motor and a 3 phase synchronous motor are connected to a 480V system. the synchronous motor, operating at 8kVA, 480V, 60 Hz is overexcited producing a leading pf of 0.7. the induction motor draws current of 14.43 A and has a lagging pf of 0.6. the system load pf is most nearly? answer is 0.96 but I can't follow the solution guide as they skip way to many steps.

 

[Flyer_PE]

Here's my stab at it:

SSM = 8 KVA with 0.7 leading pf = 8 kVA at -45.6 deg

SIM = Sqrt(3)*0.48*14.43 = 12.0 kVA with 0.6 lagging pf = 12.0 KVA at +53.1 deg

STotal=SSM+SIM= 13.38 kVA at +16.9 deg.

Cos 16.9 = 0.96

 

[roadrunner]

Wow I really way over thought that one. Thanks for the speedy response and the great reminder to take a step back and look at the problem first before grabbing equations! Thanks again

 

[Flyer_PE]

One thing I kept in mind while studying for the exam is that there isn't a single problem on the exam that doesn't have a simple and quick solution. What this meant for me is that if I was about to fill a page with math, I was probably going down the wrong road.

 

[kwatson18]

Here's my stab at it:
SSM = 8 KVA with 0.7 leading pf = 8 kVA at -45.6 deg

SIM = Sqrt(3)*0.48*14.43 = 12.0 kVA with 0.6 lagging pf = 12.0 KVA at +53.1 deg

STotal=SSM+SIM= 13.38 kVA at +16.9 deg.

Cos 16.9 = 0.96

dumb question here (and yes there are dumb questions)...

in these PF correction problems (NCEES 502, 503, 517) when they list the loads as lagging or leading, i'm noticing that when they convert the PF's to Theta that they're not using the (-) before the arcsin (theta) for lagging like we do in other problems.

THEN on this problem, NCEES 517, I'm wondering maybe because of the wording "synch motor is OVEREXCITED, PRODUCING a leading power factor..." is why we the angle is a negative 45.6 degrees?

S synch motor = 8 KVA < -45.6

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has been bugging me for a while and figure i'd ask, thanks for the help!!!

 

[Flyer_PE]

A lagging power factor equates to a positive value of theta for apparent power. The angle of current in relation to voltage is negative.

Conversely, a leading power factor equates to a negative value of theta for apparent power and the angle of current in relation to voltage is positive.

In problems 502 and 503, all of the loads have lagging power factors so the angles for power will be positive.