Power Calculations for Home made generator

[keith03]

Hello all,

This is my first forum post and any problems with the post are openly accepted.

I would like a sanity check on my approach to this problem. I have built a permanent magnet three phase AC generator. I need help in properly calculating power values for this. This is for practice, as well as a learning experience. Regardless, it is my first time doing this, and my power knowledge is mostly all related to single phase component apps. Please keep in mind that some of these specs were selected by budget, not optimization.

Specs of gen.

number of poles=12
number of coils=18 (four per phase) air core
wired in Delta
number of turns per coil= 78t of 20AWG enameld wire.
estimated Tesla at coil= .25[T]
Estimated output voltage at 240 rpm =34.128VAC[p] at 134[HZ]

Here is my thought process for the Power:

Voltage is known from Faradays Law(Vm=N*(2pi(p/2))A*Bm): v(t)=34.128sin(841.95t+90)

To find Current: i(t)= 1/L * the integral of v(t).
I am assuming that L would be total inductance of that phase

Real Power:[W] P=I^2*R ([R] will be internal resistance of wire and will be RMS current of one phase.)

Complex Power [VA] S=VI* (polar form) S=(P+jQ) Q=Ssin(theta) P=Scos(theta)
Assuming that V and I are of a single phase.

Reactive Power [VAR] =jQ

Power Factor cos(theta)

This is my thought process, but I know that things get a little different with the sqrt(3) in three phase Delta systems. Cant I just use the single phase calculations and apply them to the three phase system keeping in mind that:

sqrt(3)*coil current=Line current

R (y) = 3*R(delta)

 

[judemartins]

Helloooooo,

This is my first post in this forum but i have an ideal on how it works.

Specs of gen.

number of poles=12
number of coils=18 (four per phase) air core
wired in Delta
number of turns per coil= 78t of 20AWG enameld wire.
estimated Tesla at coil= .25[T]
Estimated output voltage at 240 rpm =34.128VAC[p] at 134[HZ]

Here is my thought process for the Power:

Voltage is known from Faradays Law(Vm=N*(2pi(p/2))A*Bm): v(t)=34.128sin(841.95t+90)

To find Current: i(t)= 1/L * the integral of v(t).
I am assuming that L would be total inductance of that phase

Real Power:[W] P=I^2*R ([R] will be internal resistance of wire and will be RMS current of one phase.)

Complex Power [VA] S=VI* (polar form) S=(P+jQ) Q=Ssin(theta) P=Scos(theta)
Assuming that V and I are of a single phase.

Reactive Power [VAR] =jQ

Power Factor cos(theta)

This is my thought process, but I know that things get a little different with the sqrt(3) in three phase Delta systems. Cant I just use the single phase calculations and apply them to the three phase system keeping in mind that:

*******************************************************
the answer to your question is YES, i mean you can use the single phase calculation for the three phase system but it depends on the angle you apply it from. it just have to do with notifying the basic line current and connecting it appropriately.
wish you all the best.

 

[keith03]

Awesome. Sanity checks are great sometimes. I had a last minute thought on my way home last night. I know that the magnets will be placed in 30 [deg] intervals and the coils will be placed at 22.5 [deg]. But how long should the radius of the disk be to allow for the most acurate sin wave? I started to look into air gap calculations, and got pretty confused. I don't have the means to even come up with half of what I found. What I would really like to see is a relation of the distance between the magnets relative to the coil size. Too far apart, and I have 0V at cos (0) and cos(180). To close and I would be opposing my own EMF. [CSA]. Oh, yeah, CSA is the cross is the sectional area of the entire coil? Or just the wire? Seems to be some contraversy here.

 

[famousken]

What is the resistance of the coils? If you can find out what the resistance is of the coils, you can plot a chart of different amperages vs. what the voltage is in the coils. By calculating watts out , you will be able to find your peak efficiency. If you think about it, you will really only be limited by heat buildup in the stator. With 20 AWG coils, just a guess, I would say you could probably pull about 2-3 amps from each phase before you have heating problems. That would equate to approx. 200ish watts for your alternator, but you have to factor in winding resistance for 20AWG it is 10.15 ohms per 1000 feet, if that helps you

 

[keith03]

Good info. I was going to apply that principle, but the graph is definitely worth making. My main problem at the moment is attempting to estimate the best size of the coils per air gap between magnets. All magnets will be 30 degrees apart. All coils will be 22.5 degrees apart. All good an dandy, but depending on the size diameter, (yes, a design change from above) the distance between the magnets will change as well. Where is my sweet spot? I understand the consequences of too far apart or too close together, but there has to be a theoretical starting point. The further out they are placed, the greater the distance, but the higher the velocity. and vice versa. Will it equal out? The magnets are my fixed variable. They are circular at 1" in diameter. Let the debate begin!.


By the way, my main job for the last couple of years has been flight instrumentation for boeings 787 dreamliner. Let's hope all goes well! Good day for me!