# Power factor for Synchronous Motor+Lagging Load



## tobeeepe (Apr 14, 2007)

Someone posted this question to the "the other board" website:

Three 2000 horsepower synchronous motors of 92% efficiency and 80 % power factor are to be added to an existing 10000 kva load with lagging 82% power factor. If the motors are operating fully loaded, what will be the new kva and power factor?

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For Single motor the appeerent power = (2000*746)/.92 = 1621739W

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My quick answer was this:

Both are lagging loads (motors are lagging), so you add the reactive parts, and real parts.

Total kW = 10,000*0.82+3x1621.7 =13065.22

Total kVar = 10,000*sin (cos-1 0.82)+3x1216.31 = 9372.57

Total kVA = sqrt(kW**2+kVAr**2) = 16079 kVA

pf = kW/kVA = 0.81

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But we could also argue that the motors would be overexcited, to make up for the reactive consuption of the lagging load connected with them. In that case, the answer would be:

Total kW = 10,000*0.82+3x1621.7 =13065.22

Total kVar = 10,000*sin (cos-1 0.82)-3x1216.31 = 2075

Total kVA = sqrt(kW**2+kVAr**2) = 13229 kVA

pf = kW/kVA = 0.99

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Any comment on these approaches and which is correct?

Thanks!


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## tobeeepe (Apr 14, 2007)

Explaining steps further:

Motor kW = (2000*746)/.92 = 1621.7 kW/motor

Total kW = 10,000*0.82+3x1621.7 =13065.22

Total kVar = 10,000*sin (cos-1 0.82)+3x1621.7*tan (cos-1 0.8) = 9372.57


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## grover (Apr 14, 2007)

Why would the motors be overexcited? That lagging current isn't flowing through the new motors- it sees just the voltage coming through the wires. The generator down the line has to put up with the PF, but it matters not to the other loads, so long as the generator is still putting out a clean sinusoidal voltage source.

The answer is .81 lagging, just as you calculated.

Actually, this is a good example of a typical PE questions and one you might not actually ever have to solve to get correct! If you "understand" it (and it looks like you do), a quick glance of the problem- adding two loads of .82 and .80 lagging PF tells you the final value is going to be somewhere between .80 and .82 lagging PF. The PE exam does not generally give multiple answers within the margin of error for rounding, so you could read the question, tick off the box for 0.81 lagging (if there were no options for .80 or .82 lagging) and move on to the next question with complete confidence in your abilities and correct answer with only 30 seconds elapsed


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## tobeeepe (Apr 14, 2007)

grover said:


> Why would the motors be overexcited?
> 
> We would like to keep the power factor at the load high, to reduce the apparent power (kVA) drawn by the load. This means the current on the line is low and the line (I**2*R) losses are low. (This is the basis for the pf correction problem- In some places, there is a penalty for keeping the pf low (for keeping the kVA high), so the industrial consumers are encouraged to keep pf high.)
> 
> In this problem, we can see that if we overexcite the synchronous motors, the overall pf is brought to 0.99 (almost 1!) and kVA is reduced. So, a sensible consumer might decide to take that approach by using the seemingly free 'power factor correction' from the motors he is already using. I mean, he doesn't have to spend extra money to install cap baks to improve pf.


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## Dark Knight (Apr 14, 2007)

tobeeepe,

I posted a very similar example previously here. I think I still have the problem so if you think you need it please PM me your e-mail and I will send it to you.


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## tobeeepe (Apr 14, 2007)

Luis said:


> tobeeepe,
> I posted a very similar example previously here. I think I still have the problem so if you think you need it please PM me your e-mail and I will send it to you.



I think I read that. Wasn't that on the principles of pf correction?

The question I ask here is: Do we assume OVEREXCITED mode whenever there a synchronous motor load?

Wasn't sure if this was addressed there...


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## tobeeepe (Apr 14, 2007)

tobeeepe said:


> I think I read that. Wasn't that on the principles of pf correction?The question I ask here is: Do we assume OVEREXCITED mode whenever there a synchronous motor load?
> 
> Wasn't sure if this was addressed there...



Luis,

Please send the article to:

[email protected]

Thanks.


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## Dark Knight (Apr 14, 2007)

tobeeepe said:


> I think I read that. Wasn't that on the principles of pf correction?The question I ask here is: Do we assume OVEREXCITED mode whenever there a synchronous motor load?
> 
> Wasn't sure if this was addressed there...


tobeeepe,

Sorry for not trying to answer your question on my first post.

Because it's characteristics Synch Motors, theorically, can work under or overexcited. Depends on the application. Now, in real life, the use of synch motors is power factor correction. In these cases the answer is yes: the motor has to be overexcited or operating with a leading pf.

As a rule of thumb, is the motor is operating with a leading power factor then is overexcited. Under that conditions the motor's maximun torque is increased and there is no chance to exceed the pullout torque.

Hope that helps

Good Luck this Friday


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## grover (Apr 14, 2007)

Oh! Syncronous... wasn't paying close enough attention, but that's a damned good question :/


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## tobeeepe (Apr 15, 2007)

Luis said:

"Because it's characteristics Synch Motors, theorically, can work under or overexcited. Depends on the application. Now, in real life, the use of synch motors is power factor correction. In these cases the answer is yes: the motor has to be overexcited or operating with a leading pf."

So we conclude that, we assume OVEREXCITED mode whenever there a synchronous motor load?

This particular question (that was posted originally) is either going by the above assumption or it is 'damn good' as Grover said or 'damn tricky' as I would say.

I found this in some texts: .... "(Over excitation)... is common practice for syncronous motor operation"

I haven't worked with sync motors in the field. What do we actually see in the field? Are they always over excited?


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## Dark Knight (Apr 15, 2007)

tobeeepe said:


> Luis said:"Because it's characteristics Synch Motors, theorically, can work under or overexcited. Depends on the application. Now, in real life, the use of synch motors is power factor correction. In these cases the answer is yes: the motor has to be overexcited or operating with a leading pf."
> 
> So we conclude that, we assume OVEREXCITED mode whenever there a synchronous motor load?
> 
> ...


If I have to say something based on my experience then the answer is yes. But the application I have seen the most is for power factor correction and then the Synch Motor has to be overexcited because in that way will provide a leading power factor.

Always is a dirty word. I was told that in Power the only always we have is that positive sequence is ABC with counter-clokwise rotation.

tobbeeepe, I took the darn test three times and there was always a power factor correction problem. Don't remember all the details but I am 100% sure you will find something like that. The worst you can expect is them to tell you that you have a synch motor as a load. In that case don't even think about it and assume leading power factor. If it is overexcited or not would be a key if they tell you something like " A xxhp synch motor is running overexcited and....etc. etc".

Again, assume a leading power factor and kill the sucker.

Synch motors are not supposed to run overexcited "always". But 90% of the time you will find them running like that becuase that is when then perform at their best. That is for what they are made for.


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## singlespeed (Apr 15, 2007)

Luis said:


> Now, in real life, the use of synch motors is power factor correction. In these cases the answer is yes: the motor has to be overexcited or operating with a leading pf.



I agree Luis, the purpose of synch motors is to provide leading pf - why spend all that additional money if you don't get something for it?


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## Dark Knight (Apr 15, 2007)

singlespeed said:


> I agree Luis, the purpose of synch motors is to provide leading pf - why spend all that additional money if you don't get something for it?


To be honest, I have never seen an application with synchies running for something else than provide leading pf. Have you seen any? I have not.


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## Platinum (Apr 16, 2007)

Luis said:


> tobeeepe,
> I posted a very similar example previously here. I think I still have the problem so if you think you need it please PM me your e-mail and I will send it to you.



I know what example you're talking about Luis. For that problem, the synchronous motor was running at pf 95% LEADING.

But that was specifically stated in the problem that it was leading.

I probably would have assumed leading too for sync motor problems anyways.

Good stuff!


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