Synchronous Generator Homework: Finding Required Field Current and Input Torque

In summary, the conversation discusses calculating the required field current for a generator operating at its rated voltage of 13.8kV. The first part is deemed simple, with the required field current being just 225 amps. However, another participant suggests that the excitation may be higher due to the synchronous impedance and shares their approach to calculating the field current. The original poster then questions their approach and references a lecture problem where they are given load voltage and power to solve for current and find the generator voltage. The conversation concludes with confirmation that the generator voltage is the terminal voltage, which can be reduced due to armature reaction and must be brought back to the rated value by raising the field excitation.
  • #1
Brianrofl
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Homework Statement



t.PNG

The Attempt at a Solution



First up, part a.

The first one is really simple. The generator is working at its rated voltage of 13.8kV, right? So, would the required field current not be just 225 Amps?

Next, part b.
20160404_194024.jpg


To sort of explain what's going on, I first found the saturated reactance of the generator by using the data from the table (for 175 field amps). Then, I draw out a per-phase circuit using 13.8kV for the voltage source, the reactance Xs, and the load in Y-connection. I used 13.8kV because the instructions say the generator operates at rated voltage, correct? [Divide by sqrt 3 to convert to line-to-neutral voltage].

Using that, the current is found easily.

20160404_194045.jpg


Which then translates into finding the input torque rather easily.

I'd appreciate any input. I think I know how to solve this problem but it seemed too easy, and there are just so many things you can make mistakes on doing 3 phase systems that I just want to make sure.

Thanks.
 
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  • #2
Brianrofl said:
The first one is really simple. The generator is working at its rated voltage of 13.8kV, right? So, would the required field current not be just 225 Amps?
I believe the excitation will be higher. For 225A field current, "open circuit" voltage is 13.8kV. This voltage will sag once you connect the load, due to the synchronous impedance. From the OC and SC data given, you can calculate synchronous impedance Zs and use E=Vterminal+I*Zs.
You can calculate current I from the load. For the value of E(generated emf), you can find the field current required by interpolation-extrapolation technique using Voc vs field current table.
 
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  • #3
Ok, I'll work it out again and see what I get. Are there any issues with my part b?
 
  • #4
Brianrofl said:
Ok, I'll work it out again and see what I get. Are there any issues with my part b?
Your approach looks right to me. I haven't verified the calculations, but I'm sure they are correct.
 
  • #5
cnh1995 said:
Your approach looks right to me. I haven't verified the calculations, but I'm sure they are correct.

I'm really getting hung up on one thing. In the problem, he states: "while operating with the rated voltage." Wouldn't that just mean that the generator voltage is the 13.8kV line-to-line?

I'm referencing a lecture problem where when solving for the field current, you're given the voltage at the load and the power at the load. Using those two values, you can solve for the current, and then find the voltage dropped at the synchronous impedance. You then add the load voltage to this impedance voltage and find the voltage Ea supplied by the generator. In my homework problem's case, wouldn't my voltage Ea just be 13.8kV line-to-line?

I did try putting the voltage given (13.8kV) across the load, then calculated current, then found the generator voltage from there, which gave me a field current of ~300 amps.

So many nit picky things in this material, and I really hate turning in problems for credit. I'd so much rather just be given a solution and figure out how to do it.
 
  • #6
Brianrofl said:
Wouldn't that just mean that the generator voltage is the 13.8kV line-to-line?
It is terminal voltage of the generator. When you connect a load, this voltage reduces due to armature reaction. To bring it back to the rated value, field excitation is raised.
 
  • #7
cnh1995 said:
It is terminal voltage of the generator. When you connect a load, this voltage reduces due to armature reaction. To bring it back to the rated value, field excitation is raised.

Like this?

20160404_231946.jpg


Where I find my new value of Ea at which the voltage across the terminals is still 13.8kV?
 
  • #8
Brianrofl said:
Like this?

View attachment 98562

Where I find my new value of Ea at which the voltage across the terminals is still 13.8kV?
Yes.
 

1. What is a synchronous generator?

A synchronous generator is a device that converts mechanical energy into electrical energy by using the principle of electromagnetic induction. It consists of a rotor and a stator, with the rotor being the rotating part and the stator being the stationary part.

2. How does a synchronous generator work?

A synchronous generator works by using a magnetic field generated by the rotor, which rotates within the stator. This creates a changing magnetic field, which induces an alternating current in the stator windings. The frequency of the generated current is dependent on the speed of the rotor and the number of poles on the rotor and stator.

3. What are the main components of a synchronous generator?

The main components of a synchronous generator include a rotor, stator, excitation system, and a prime mover. The rotor is the rotating part of the generator that produces the magnetic field, while the stator is the stationary part that contains the windings. The excitation system supplies the direct current needed to create the magnetic field, and the prime mover provides the mechanical energy to rotate the rotor.

4. What are the applications of synchronous generators?

Synchronous generators have a wide range of applications, including power generation in electric power plants, hydroelectric dams, wind turbines, and diesel-electric trains. They are also used in industrial processes such as steel and chemical production, as well as in backup power systems for hospitals, data centers, and other critical facilities.

5. What are the advantages and disadvantages of synchronous generators?

The main advantage of synchronous generators is their ability to maintain a constant voltage and frequency, making them ideal for large-scale power generation. They also have a higher efficiency compared to other types of generators. However, synchronous generators can be more complex and expensive to maintain, and they require a direct current source for excitation, which can be a potential source of failure.

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