Hi Kitestrings. My bedtime used to be when the bars closed. Now... not so much.
Good catch, I did use "phase" where I meant "line" but I hope my added emphasis through the rest of the post was enough to clear it up.
I've been looking for DIY turbines running heaters, too, and not finding many. I know I've seen plenty over the years, so really it's my fault not using the right search terms or something.
Big picture: don't worry too much about reactance and stuff, it's not a big thing and just adds confusion.
Windy,
I have to introduce a new piece of terminology - the technical term is "Electromotive Force". EMF. A generator that's producing electricity is creating an EMF, which is literally electrons motivated by magnetic force. It's what produces the voltage. Is EMF = Voltage? No, except for one case, but they are both measured in volts.
The only time when EMF = Voltage is when current = 0. This is known as open-circuit and when you measure the voltage across the lines with no current, you are also measuring the EMF. Once current starts to flow, though, the voltage you measure drops, even though the EMF is the same. Voltage drops are caused by resistance, as Ohm's law shows us. You could call this "back EMF" but I would rather not. That term is much more useful in motors. The same thing happens in our alternator but we really don't need special terms for it.
So, time for an experiment. We couple our alternator to a motor so that we can drive it, and measure the electricity that comes out. Let's say our motor is big and not bothered by the load the alternator might put on it, and the motor turns at a fixed speed. No matter what load the alternator applies, this motor won't slow down. So, we flip it on and leave the alternator's wires unconnected. The alt is running open-circuit now, so if we put our voltmeter on the leads we get a high voltage and we are also measuring at the same time the EMF. If we speed up the motor, the EMF goes up.
Next, for the sake of demonstration, we connect a very high-resistance load to the leads of the alternator. I could pick a number from the air... 1 kOhm. While picking numbers, let's say the resistance in the alternator is 10 ohms, and the EMF we measured was 300 Volts. Then the current that will flow in the alternator's wires is
(300V) / (1000 ohm + 10 ohm) = 0.30 Amps.
The voltage that we measure on the alternator's leads won't be 300V any more. Instead it will be (10 ohm) * (0.3Amp) = 3 Volts -> 300V-3V=297V.
Nothing dramatic is going to happen because this is a puny load on our alternator: I^2*R = (0.3A)^2*(1000ohm) = 90 Watts
Meanwhile, inside the alternator, only 0.9 Watts of heat will be shed off. The power input to drive the alternator is just 91W.
As an aside, since we are experimenting with a motor with a fixed speed, our drive motor didn't speed up because we made it drive a tiny load.
Wind does not behave this way. It behaves the opposite.
One more run of our theoretical alternator. This time, same alternator with its 300V of EMF, and 10 ohm stator. Now we hook up a 10 ohm resistance to its leads and see what happens. Same calculations:
(300V) / (10 ohm + 10 ohm) = 15 Amps.
Voltage measured across the leads: (10 ohm) * (15Amp) = 150 Volts -> 300V-150V=150V.
Note how the voltage across the leads is dropped exactly in half!
Now the power is much higher: I^2*R = (15A)^2*(10 ohm) = 2250 Watts
Since the resistance in the alternator is the same as the load resistance, then the heat shed by the alternator is ALSO 2250 Watts.
The sum of the two is the power input required: 2250+2250 = 4500 Watts. Lots of power (not enough for a 20-foot diameter turbine though. But you can scale up the numbers until they work for a 20' turbine.
I'll leave it to you to try the same calculations for different resistances - it always comes out with the highest power when the resistance of the load matches the generator's resistance. Notice that I haven't mentioned the connection in Star yet. That's because it hasn't mattered yet. If you connected a 3-phase alternator to a 3-phase load both in Star and did all the same measurements you'd get the same thing.
Another thing worth noting is that the voltage measured line-to-line was a step in our calculation, but not really the driving force in the machine. It's also dependent on the resistance load you hook up to it. It still matters if you're connecting standard water-heater elements as your load, since their ratings are for standard 240VAC, but most of the time the wind isn't blowing like mad, so your heating elements will only be exposed to dozens of volts to 100 V or so.
How does this help us design a wind turbine alternator? Because EMF is driven by the speed of the alternator. When doing open circuit tests like in our experiment above, we were measuring EMF at a specific speed. Let's say it was 100 RPM. Then we had 3V/RPM of EMF. If we have this much EMF on the leads of our alternator, then we can work out some facts about the coils inside it. This is still just an example. Play with the numbers until you find the size that's right.
Since you drew 5 coils per phase, then our line-to-line EMF is composed of 5 coils on one leg plus 5 coils on the other leg, out of phase, on those lines.
So our EMF can be broken down per coil:
3 V/RPM = 5*(E_coil) + 5 * cos(60deg)(E_coil) = 0.4 V/RPM/coil
And since we already worked out that our alt has 10 ohms per phase line-to-line, then each coil is 1.0 ohm.
This is enough information to roughly size the coils, choose the wire gauge (to handle the current), and the number of turns (to get the EMF). A few spin tests to confirm the calculations are right.
Since you've got 20' blades, there's no way this guesstimate is powerful enough to hold them. In my post yesterday, I showed that he wind power in the blades will be more than 16kW in a stiff wind, and having some margin of safety means the alt should actually take in about 20kW or more before getting too hot. Ultimately, heat often kills these things, and while strong winds are an excellent way of dissipating heat, there are a hundred details that can either improve or worsen this.
Well it's late again.
There's more to say about matching wind loads to electrical resistance loads, starting with "they don't, not easily".