@Ash
I am aware that CWA is pretty much a fixed impedance when running at a fixed voltage load, and yes impedance this is easy to calculate. But I want to be able to know all of it's possible range of impedances at all of the voltages that could be on it. I want to make it into an equation. Preferably this would not be through load testing, but if that is what must happen then I have no choice.

I was thinking of load testing my two CWA ballasts to see their specs, just as I have done for my HX ballast. When I did it with my HX ballasts, I used the output terminals of an old Variac as a load (variable inductive load). This worked fine, starting at a short circuit and making my way up the windings of the variac. Unsurprisingly when I tried this with CWA, working my way up from a dead short on the Variac actually increased the measured current, because of the capacitor acting as the primary impedance.

Do you have any other suggestions to be able to load test a CWA ballast and get it's characteristics, or ways to calculate instead of load testing? Could I use various different value capacitors as a load (I have countless)? I don't really want to shell out a bunch of money for a Variac-sized wirewound pot just to do this. I only have a lamp for one of my two CWA ballasts, and I really don't want to have to use it because it is very temperamental.

I was not aware that CWA OCV wasn't sinusoidal, that is news to me. I can't even begin to imagine why that is the case.

If I do get these current/voltage points somehow, I will likely plot it on a graph in Desmos so I can have it make the equation of best fit for it. Then I can actually use the data.

Any light bulb that have a bright arc is HID. Fluorescent and LPS lamps, don't have a bright arc, so they aren't HID lamps.

@Ash
Yes absolutely, we have deer, rabbits, and birds everywhere. I would use my screened-in porch if I were to ever do this (which I probably won't).

All calculations we have done so far using those (and related) formulas refer to a steady state condition, or at least an assumed steady state condition. (i.e. they will hold for a warming up lamp too, as long as you use voltage and current measurements made at the same moment)

All processes which are slow (ie. temperature related, as well as any feedback loops going through temperature) are not covered by those calculations, but the opposite is also true : The calculations do hold for any momentary condition, regardless of the long term trends



In steady state, the characteristics of any electrical circuit, which only passes sinewave voltages and currents, can be calculated by linear equations (e.g. Ohms law, vector sum of voltages, etc). When our voltage is not a sinewave, the first thing we can do is disregard this and keep assuming it is sinewave, which is often close enough (and the differences can be packed into empirical factors, such as the lamp power factor)

CWA is not that much different, but there are 2 caveats :

The magnetic saturation mechanism changes the ballast impedance. I.e. we can calculate the impedance from measurements in the running circuit and it will be correct, but not useful because the impedance will be different if the same ballast is powered in another circuit / at different warm up state / etc

With an array of measurements, we can plot a dependence graph which will be correct and useful, even if we don't have the formula for it

CWA Voc is sometimes not sinewave, but sort of a sinewave with warped peaks. However, it is sinewave enough for many purposes, and is clamped to far different waveforms when a lamp is running anyway, and even with them we still use the same calculations....



Go test a bunch of lamps....



If you do accumulate such data, put it in a spreadsheet (e.g. Libreoffice Calc) and you will be able to make useful reference plots with it, interpolate it and more

@AngryHorse
That is what I would think, but one of the definitions I came across specifically said that the light output shouldn't be by the incandescence of the electrodes (which CA is). I don't know why they made this distinction (or if it is even accurate). I always considered it HID but of course I don't know for sure.

@Ash
Of course for things like that there are many arbitrary personal definitions of high and low voltage. I was hoping there was a more concrete definition applying to discharge intensities.

Go ask a linesman, commercial electrician, home electrician, and various electronics people in specific fields, what counts as "high" and "low" voltage

ED is an evolution of E, and those single letter lamp designations can only encode so much information about the actual shape of the lamp. Besides, are there any luminaires where the dimple makes any difference for the use of the lamp ?

Any water left outside in the open becomes drinking water for wildlife

Inverters often have very limited overcurrent headroom

Typical C-curve (back in the day when those highbays were made, G-curve) breakers may let through up to 10x their nominal rating for a cycle or two, 6x for few cycles, and 3x for several seconds. gL/gG fuses are about same. This often covers the charging current of capacitors in expected conditions (current limited by runs of wiring)

Inverters often can put out only as much as 2x..3x nominal at all (even for the shortest time), and their protection may not have any significant time delays either (as this puts big stress on any switching components, especially at the output, in case of a real short circuit)



Then, what about hot restrike times ?

400W highbay (drawing 440W at PF0.9) = 2.1A
40uF capacitor alone across the line (same highbay during a hot restrike event) = 2.9A
Same highbay working without the capacitor = 3.5A

Assume the circuit was sized initially with 1.25x design margin (ie. circuit loaded to 80%, which is a common recommendation) :

During a hot restrike it will be overloaded at 1.1x nominal. Not going to trip anything ever or be noticed

During normal operation with multiple failed capacitors (very common condition) it will be overloaded at 1.3x nominal. May trip breakers after an hour or more, but if the circuit is just a little less loaded, then it won't trip anything either



Also, many inverters put out quite dirty wave on the output (harmonics, HF switching noise, ...) which will make capacitors draw more current than in a line voltage powered system. Even "pure sine wave" ones may momentarily glitch in case of load steps (such as switching in a high capacitance)

Failing photocells, ignitors, and users switching on breakers which function they don't know, explain a lot of things. (i mean, users in a commercial setting tripped some circuit. Then they go to a DB and reset something else, that might have been tripped or manually off for years)

Another option, if it is controlled via some timers etc, those often default to "ON" after a power outage until somebody sets the time again, even if there ar no switching hours configured