Vdc from Vac 3 phase

[Mike Grzesiek]

Hi, I'm new here (although I have pestered Rob Beckers personally more than he deserves). I am building a dump load for a wind system, and am planning on where to set the voltage to transfer the load to dump. My intention was to set the 3 phase voltage to ~320Vac thinking this would keep the Vdc to about 450 (320*1.414).

However, I was digging around the net and came across an article that mentioned rectifing 3 phase power to DC. They used the square root of 3 (1.732) as their conversion from 3 phase Vac to Vdc. I have always been using the square root of 2 (1.414) for this calculation.

Is this article incorrect? or should I be considering a lower setting for the dump load.

TIA.

(and thanks for all your help Rob!!! I also wish I would have followed your link to this forum sooner)

[Rob Beckers]

Hi Mike, good to see you here!

The actual value is less than 1.4. It's not related to the square root of 2 either. That sqrt(2) value comes from a single-phase sine wave, where the top is 1.414 times the RMS value. In 3-phase and a full-wave rectifier the DC value is very close to the top of the phase-to-phase wave form, hence the factor of 1.4.

The actual value is a rather nasty equation that works out to something close to 1.4 (and that I don't recall the details, so I would have to look it up). Maybe 1.35, maybe 1.37, or thereabouts for a 3-phase sine wave. The crux is in that "sine wave" part; most wind turbines under load produce something that is a far cry from a sinusoidal waveform. The good part is that the ugly wave shapes tend to be closer towards a square wave, and if you are measuring RMS voltage of the AC part, the DC rectified voltage will be less than 1.4x that.

Since 3-phase power electrical engineering is not exactly my forte (it's been 25 years since I was in University, and while we had some of it, EE focused more on electronics), I ran a simulation in Spice a little while ago to verify I wasn't sprouting nonsense. So, with a 3-phase generator and full bridge rectifier plus load, it worked out that DC was very close to 1.4x AC phase-to-phase voltage. Short of building things, Spice is as close as one can get to real life in electrical components.

-RoB-

[Rob Beckers]

For the fun of it, just re-run the Spice scenario with voltages and power levels closer to what you're looking at. It's a 3-phase alternator, phase-to-phase sine wave with RMS value of 315 Volt AC.

After rectifying and some smoothing by capacitors this turns into 420 Volt DC. So, the factor between phase-to-phase AC and DC is 420/315 = 1.33x

I put a load on of 15 Ohm, drawing 11.8 kW from the alternator. The currents from the alternator get really ugly. Because of the rectifier there's only current being drawn during the peaks of the AC voltages, for a very short time. In other words; the power factor is piss-poor (that's normal for this type of setup)! That makes for very large current spikes, measuring in at 66A, and the RMS current value of the AC wave is 30.0A per phase. On the DC side, the current is 28.0A.

So, for current the factor between RMS AC per-phase, and DC is 28/30 = 0.93x

While voltages and currents will of course be different for different alternators and loads, the factors should remain pretty much the same. That should give some guidance.

-RoB-

[Mike Grzesiek]

Rob,

Thanks for your input. You have made this a bit more clear (I'm looking at it through a cup of Tim Horton now instead of a Espresso). Now I know very little, however I'm a far cry more knowlageable than when I started this project (at least now I can say I know very little). Most of which has come from your input and advice. Your passion is impressive!

Thanks again,
Mike