I have a 100W MV lamp, and I have run it on a 100W MH ballast knowing that it will be slightly overdriven. I hear some people say that 100W MH ballasts are good for 100W MV lamps, and I hear other say that 70W MH ballasts are good for 100W MV lamps, but I would like a consistent answer. I did some calculations, but I know I am not seeing everything. Here we go:

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100W MH Ballast:
- 100W MV runs at .85A
- 100W MH runs at 1.1A
This means that 100W MH lamps use 29% more current than 100W MV lamps. Stay with me here.

70W MH Ballast:
- 100W MV runs at .85A
- 70W MH runs at .9A
This means that 70W MH lamps use 6% more current than 100W MV lamps. But wait.

I used to think from that quick calculation that a 70W MH ballast would be a much better fit to a 100W MV lamp. But we are not seeing the full picture. Magnetic ballast ARE NOT constant current sources, (especially not HX ballasts, which are the most common for 70/100W). Even CWA ballasts aren't truly constant current. If the arc voltage is higher (like with MV), then the current will drop slightly from where it was at with MH. Lets look at what I think is a more sensible approach to determining ballast compatibility:

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100W MH Ballast:
- 100W MV HX ballast acts like 169 ohms in series with 220V supply
- 100W MH HX ballast acts like 157 ohms in series with 220V supply
This means that 100W MH ballasts provide 8% less impedance than 100W MV ballasts.

70W MV Ballast:
- 100W MV HX ballast acts like 169 ohms in series with 220V supply
- 70W MH HX ballast acts like 188 ohms in series with 220V supply
This means that 70W MH ballasts provide 11% more impedance than 100W MV ballasts.

So now it seems like a closer match for both of them. 100W MH ballasts seem to be closer, but they will still overdrive slightly as opposed to 70W MH ballasts which will underdrive slightly. I suppose it is the user's choice as to which one works best for their situation.

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Am I seeing this right? Am I on the right track? I just need a sanity check. I am not at home right now so I can't measure the current on my MV lamp. Once I get the chance to do so I definitely will, and I will see if it matches these results.

The ballast impedance is mostly inductive. So the approximate calculation would be :

Vballast = sqrt( Voc^2 - Varc^2 )
I = Vballast / Xballast

Not Vballast = Voc - Varc

Qualitatively the meaning is that the ballast current is a bit less sensitive to the lamp arc voltage than initially expected

In addition there are the ballast's resistive losses (mostly the winding resistance) and the lamp power factor (the lamp itself is a little lagging), but that does not affect the result much

The other important part is, that a Mercury lamp is not too sensitive to exact driving parameters. There are no halides to evaporate a the correct temperature etc. As long as it has enough power to evaporate the Mercury and achieve some pressure, and not enough to initiate failure mechanisms (by overheating the electrodes or the arctube wall) it'll be ok

Over here (230V, series chokes) i can confirm that 125W Mercury lamp (1.15A) works reasonably well on both 100W and 70W PulseMH/HPS ballasts (1.20 and 1.00A rated with their proper lamps respectively)

@Ash
Thanks so much for that equation! I thought that would be based on some super complicated concept that I would never understand, but I suppose not. I will play with this a little more later today and see what I can learn from it.

@Ash
Alright I did some more figuring.

This equation works very reliably, and I would like to use it, but I have some questions.

I was using this equation in conjunction with ohm's law to calculate desired ballast impedance when given lamp voltage, circuit voltage, and lamp current.

This consistently overshot the specified impedance necessary for the lamp based on datasheets, but very precisely. For MV, it was almost exactly 20% overshooting, for MH it was more or less 15% overshooting, and for HPS it was pretty consistently 10%. I took the averages of all of the overshots and then the inverse and got these constants to multiply with the results to get the right approximate answer:
MV:  0.831
MH:  0.873
HPS:0.913

This is okay, all I have to do is remember these numbers when calculating. But I want to know where they came from. Is this the power factor of the discharge itself? That is what I am thinking, but I don't know for sure. I can't think of any other reason it would be so consistent across different wattages but so different between different HID technologies. I have yet to try this for fluorescent and LPS lamps but I might do that later.

Thanks again.

Yep this is a lamp 'power factor' but not the power factor in the meaning of the school-level classic circuit theory (which is just a phase shift).

Lamp voltage is not near sinewave (see here for my real life captures https://www.lighting-gallery.net/gallery/thumbnails.php?album=7753) and this is what throws off the result up to 20%.

@RRK
Wow, I am very pleasantly surprised that I got that right. So I just accidentally calculated average power factors for different lighting technologies. This is all coming together. That means with a given technology with given specs, I can calculate the impedance necessary to ballast it. Very nice.

The lamp power factor consists of both Harmonic power factor and Displacement power factor :

The Harmonic power factor is result of the voltage waveform, approximately square. This accounts for most of the lamp power factor

The Displacement power factor is result of the lamp reignition behavior after zero crossing, where each half cycle begins with a high voltage overshoot before the flat area of the voltage clamped by the arc. Part of the voltage waveform is leading before the current peak, but in terms of the current that's lagging

The significance of the latter effect may vary based on lamp technology, on how much the specific lamp is pushing the stable Varc limits (higher power lamps are naturally more stable, but then they are also designed with higher Varc so push the limit as well), and how hot the lamp is



Then we have the ballast resistive losses, which sum up with the lamp Varc according to your old formula. If we account for them, the new formula will be :

Vballast_reactance = sqrt( Voc^2 - ( Varc + Vballast_losses )^2 )
I = Vballast_reactance / Xballast

Vballast_losses approx = ( 1 - BallastEfficiency ) * Voc

HID ballasts (series choke, and probably HX choke part bahaves the same) have typical efficiency around 0.90..0.92 for >100W lamps, 0.85..0.87 for <100W lamps