# Synchronous Machines - Motors and Generators



## Kovz (Mar 4, 2015)

Hey guys, I'm having difficulty understanding the basic expressions for calculating Terminal voltage, phase generated voltage, Internal Voltage and output phase voltage for generators and motors. Is it different equations for motors and generators?

I can't figure out what the correct equation should be. I thought to solve for terminal voltage, the equation would be Vt = Ei + XsIs

where Vt is terminal voltage

Ei is internal voltage

Xs is sych. reactance

Is is current.

But trying to solve Problem 54 on Volume 2 of Complex Imaginary has my brain racked.

Also see problem 135 and 522 on NCEES.

Any help is appreciated.


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## dayrongarcia (Mar 4, 2015)

You have the correct formula, just remember that the phase angle between the voltage and current is given by the inverse cosine of the power factor. Then just take into consideration if its lagging or leading. Then solve for Vt.

Can you take a snapshot of 135 and 522?


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## kduff70 (Mar 4, 2015)

Hi Koz I don’t have the problem in front of me but what I tried do is look at the phasor diagram for a generator remember Ei voltage for a synchronous generator is Ei=Vt+jXI but you have look at the phasor diagram but it also depends on the leading or lagging power factor of jXaIa. Sorry I hope that give some insight if you have Grainger power analysis book the section on synchronous machine will have phasor diagram witch help me understand how to use the equation properly


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## Kovz (Mar 4, 2015)

kduff70 said:


> Hi Koz I don’t have the problem in front of me but what I tried do is look at the phasor diagram for a generator remember Ei voltage for a synchronous generator is Ei=Vt+jXI but you have look at the phasor diagram but it also depends on the leading or lagging power factor of jXaIa. Sorry I hope that give some insight if you have Grainger power analysis book the section on synchronous machine will have phasor diagram witch help me understand how to use the equation properly




See that's why I am confused. Why is Ei=Vt + jXI if Vt=Ei+jXl.

Shouldn't Ei=Vt - jXI??? Look at the solution to problem 522 in NCEES.

But this problem is operating as a motor not a generator. Does it make a difference?


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## Kovz (Mar 4, 2015)

I've attached pictures of the NCEES 135 and 522.









*I've also attached pictures from Complex Imaginary Volume 2, Problem 54. This one has me really confused. The subtraction instead of addition. And why you have subtract 14* from -34.9**


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## dayrongarcia (Mar 4, 2015)

https://drive.google.com/file/d/0B5uJgUyE_qjfdFR5RUZiX2Y0Vmc/view?usp=sharing


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## dayrongarcia (Mar 4, 2015)

You add them for generators and subtract for motor operations, see the link I provided.


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## MyBeardAndMe (Mar 4, 2015)

dayrongarcia said:


> You add them for generators and subtract for motor operations, see the link I provided.


This.

"Them" is j*Ia*Xs. So E=V+j*Ia*Xs is generators, and E=V-j*Ia*Xs is motors.

I had the same problem a couple days ago, Kovz. If you have Camara look at pg. 42-8 and 42-9.


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## MyBeardAndMe (Mar 4, 2015)

Kovz said:


> *I've also attached pictures from Complex Imaginary Volume 2, Problem 54. This one has me really confused. The subtraction instead of addition. And why you have subtract 14* from -34.9**




You subtract because the problem provided the angle of the voltage. If no voltage angle was provided, the angles would be relative and you could use -34.9 in the solution (assume voltage angle is 0). But because the voltage angle was provided, the angles are absolute and the current angle lags the voltage angle by -34.9, so the current angle is -20.9.


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## Kovz (Mar 5, 2015)

Very good explanation. Thank you guys, that helps a lot!


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## achang135 (Aug 29, 2016)

In the answer for 522, i understand that they derive that Is = 1.05&lt;-18.19. 

However in the final solution for the current used in the E = V - jXs * Is; the power angle then becomes (90-18.19)

E = 1 - 0.9*1.05&lt;(90deg-18.19deg) to be exact. 

Where did that 90-18.19 angle come from, and why don't we just use -18.9?

thanks for reading


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## creeg2 (Sep 9, 2016)

That "90deg" comes from the "j" of -jXs.  The imaginary impedance has an angle of 90 degrees.


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## Zach Stone P.E. (Dec 8, 2016)

Kovz said:


> Hey guys, I'm having difficulty understanding the basic expressions for calculating Terminal voltage, phase generated voltage, Internal Voltage and output phase voltage for generators and motors. Is it different equations for motors and generators?
> 
> I can't figure out what the correct equation should be. I thought to solve for terminal voltage, the equation would be Vt = Ei + XsIs
> 
> ...




You are on the right track. 

Remember that synchronous generators and motors have the same equivalent circuit, except backwards. 

Comparing these equivalent circuits is the easiest way to remember how to add the voltages in the loop. 

Even though this question was asked in 2015, here is an excerpt from our online course in case anyone else reading this is also struggling with the same concept:

*Synchronous Generator Equivalent Circuit:*




Synchronous Generator Voltage loop:




Synchronous Generator Current:




*Where:*

*Ix *- Rotor DC Excitation Current

*Φ* - Flux induced from rotor field to stator windings

*Eo* - Induced stator line to neutral generated voltage.

*Ex *- Voltage drop across synchronous the reactance.

*E* - Terminal load voltage.

*Xs* - Stator winding synchronous reactance per phase
*I *- Stator load current

*Z *- Load impedance

So your Terminal Load Voltage for a *Synchronous Generator *would be:

E = Eo - Ex


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## Zach Stone P.E. (Dec 8, 2016)

Let's look at and compare to Synchronous Motors:

*Synchronous Motor Equivalent Circuit:*




Synchronous Motor Voltages Loop:




Synchronous Motor Current:




*Where:*

*E* - Terminal stator winding applied voltage line to neutral

*Ex* - Voltage drop across the synchronous reactance.

Eo - Induced stator winding voltage line to neutral

*Xs* - Stator winding synchronous reactance per phase

*I *- Stator supply current

*Φ* - Flux induced from rotor field to stator windings

*Ix* - Rotor DC Excitation Current

Now your Terminal voltage is actually the supplied voltage (instead of the Load Voltage) and you can solve for it by:

E = Ex + Eo

Notice how the polarity of the voltage loop changes between the synchronous generator and motor equivalent circuit, and how that also changes the polarity and direction of the current.


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## Zach Stone P.E. (Dec 8, 2016)

Here is a video from taken directly from our course available on youtube that does a quick introduction on Synchronous Machines and covers the differences between Synchronous Generators and Synchronous Motors:

&lt;iframe width="560" height="315" src="https://www.youtube.com/embed/vYFl0FQyUBc" frameborder="0" allowfullscreen&gt;&lt;/iframe&gt;

More video's from our online Electrical Power PE Exam review course are on our YouTube channel:

Electrical PE Review on YouTube

Good luck studying.


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## Zach Stone P.E. (Dec 8, 2016)

Electrical PE Review said:


> Here is a video from taken directly from our course available on youtube that does a quick introduction on Synchronous Machines and covers the differences between Synchronous Generators and Synchronous Motors:
> 
> &lt;iframe width="560" height="315" src="https://www.youtube.com/embed/vYFl0FQyUBc" frameborder="0" allowfullscreen&gt;&lt;/iframe&gt;
> 
> ...




I can't seem to embed youtube videos or edit posts (please send me a message if you can point me in the right direction)

Here is a direct link to the Synchronous Machine youtube video explaining the differences:

Electrical PE Review.com YouTube - Synchronous Machines Introduction and the Differences between Motors and Generators


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