I have been trying some lights powered by a MSW Inverter, Powered by a lead acid battery.
LEDs have a slight hum, And the GU10 LEDs have a hum so quiet, You have to put your ear up to it to hear a faint buzz.

Incandescent bulbs have no hum, Except for my big 300 Watt bulb.

CFLs have a more substantial hum, Enough to be annoying, Unless it's high up, You have bad hearing, Or like lots of hum.  

The inverter used for these tests is a Cobra CPI 475, And it works like new.
The other inverters I have are a small Enercell (Radioshack) 150 Watt Cigarette lighter plug inverter.
And my other inverter is a Powerdrive 1500 Watt, Supposedly made for trucking, But I got it to run a portable air conditioner.

The only reason I did not test my lighting with the other inverters is that the Enercell inverter has a Cigarette lighter plug, Which is hard to connect to outside of a car, And the Powerdrive inverter complains about a low voltage.

Have you used lighting on an inverter? There are lots of possibilities.

If an inverter has true sinewave output, there should be no problem with it.
But many of them, mainly the low power ones, use modified sinewave and then it strongly depends on what type of ballast is in the lamp.
The least problems I would expect with those starting with a rectifier and then using some electronic powered from the DC. That is the case for all CFL's and many LED's (all types rated for worldwide supply range such as "90-240V" or so).
But many LED's do use just a series capacitor as a ballast. Although it may not seem to complain, the damping series resistor inside will overheat (it is rated for just the low currents, limited by the capacitor; here, with the sharp edges, the capacitor won't limit anything). And it may end up in fire.
So unless you really know what is inside of the LED ballast, better to not use them on the modified sinewave.

If the application is primarily off-grid and only occasionally connected to the AC power (vehicle installation,...), I would consider to power the lighting circuits from the DC and put there an AC/DC converter (/charger) to provide the DC supply for the lighting when the AC is available.

For 12V systems work well the "12VAC" MRxx format - it contains a regulated SMPS working from the whole range of the 12V battery voltage, so from 8 (end of discharge) till 20V (more than 18V when the charger regulation fails and the voltage is limited by the water electrolysis). But it isn't suitable to operate inside of a running car - the transients coming from the main engine systems and the car electric auxiliaries (starter pulses, turning ON and OFF large loads,...) may damage some of them (it requires at least 40V rating to operate on a 12V system).
Note, the "12V" LED stripes are not suitable to operate directly on a battery, the LED current varies there way too much over the battery voltage and e.g. the 14V in a car makes the stripes overpowered by about factor of 2. So they need at least some low dropout 12V regulator to make sure no higher voltage will pass to the LED's. Fortunately these LED stripes are not sensitive to very short spikes (the problem is mainly with overheating, all the extra voltage will remain across resistors, so just long time exposure is what matters), so quite low loss, low Iq circuit may be build for that (power PMOS pass element and few components around, made so, when the voltage is below the regulated level, there are no currents even when the thing is permanently powered)

Good question!  I can answer this one, at least for 120v/60Hz land (AKA North America) from personal experience, as my current house is in a rural area not served by "grid" power. 

Everything fluorescent I've ever used (and I have just about every common type of fluorescent in my house) works fine for the most part.  Spiral CFLs work fine, albeit sometimes with a slightly annoying high-pitched buzz, which I can ignore.  (It might bother some people enough to be unacceptable, but I'm not one of those people).  And we're talking many different brands/wattages.  I'd say in general the 23ish watt (100w incandescent "equivalent") are a little more noisy than the 13-ish watt (60w "equivalent" ones.  I'd also go on the record as saying that Feit/Western Family brand ones are buzzier than GE or Satco units are.

Small preheat fluorescents like F15T8 "undercabinet" fixtures or the screw-in 22 watt circline adapters (Which I still prefer over the modern spirals):  They also work fine but are definitely louder.  When starting, they're noticeably more "blink-happy" and take longer to light than on "normal" power.  Case in point, stuff like the plastic Lights of America preheat F15T8 undercabinet fixtures, and the Lights of America or TCP-made, GE-branded "Circlite 75" 22w preheat circlines.  Starter "Misfires" that result in a rectifying lamp seem more common too.  Another thing:  With an inverter/charger unit (1997 Trace "Mariner" 2000w) running my house, switching between incoming AC power (Read: A generator) and inverter power, which is a split second, will make preheat fluorescents go out and restart.  Manual preheat, however "Push, Hold, Release" fluorescents don't seem affected by the switchover though.   They can also be noticeably dimmer and "flicker" erratically, with varying ballast sounds to match.  This might annoy some people but I ignore it.

F32T8 electronic:  Works fine, but some ballasts I had in use (two have since died; they were older Advance) were pretty buzzy and would sometimes light only "halfway" and flicker.  Their replacements and every other T8 ballast I've used have been just fine, like CFLs.

Cheap, residential-grade, low/normal-power-factor 2-lamp "rapid start" or "trigger-start" ballasts, of the type commonly found in 2-lamp F20T12 fixtures or the 2X34/40w ballasts like the aforementioned ones but for 4' lamps commonly found in residential-grade "Wraparound" or "Shoplight" fixtures from before the T8 craze of the last few years:  I'd say these don't perform as well, but they still work without any adverse effects.  They run noticeably dimmer, flicker at times, and buzz.  Startup can also be slower, but a lot of lighting enthusiasts like "Startup Flicker" on rapid/trigger start, anyway.  I'd say these perform the worse honestly out of any fluorescent.  Single-lamp 14/15/20w trigger-start ballasts, however, seem to work fine, with no noticeable effect than being noisier. 

High-power-factor, commercial-grade, and/or pre-cheapening-out-on-residential-fluorescent-light-fixtures-ballasts, including our favorites, the PCB-laden rapid-start ballasts: These are better than LPF without a doubt on MSW.  They are louder, but work fine otherwise with a lot less flicker and no noticeable reduction in light output (And I had one running all day long as a plant light, a '70s GE "Bonusline".  It was also the quietest ballast I've ever used on MSW, almost silent! 

While we're on the subject of HPF ballasts, I also was running a 2XF96T12 slimline fixture (Magnetic instant-start, high-power-factor ballast) without issue...louder but otherwise fine.  One interesting thing:  It was a replacement ballast, a modern GE/Universal 1.34-amp-line-current replacement unit, its predecessor which I removed because it was having trouble even on normal power, an '89 Advance full-power, 1.45a line current unit, had a degraded capacitor, common on Advance ballasts from that era, and it would act like rapid-start on modified-sine-wave!  Even odder, the 60 watt "energy saver" tubes I was using (Which suck anyway) didn't striate on MSW on the old ballast, but they did on the new/replacement one.  Something with the AC waveform? Both of those were loud ballasts anyway, even by Sound-rated-D slimline standards, and that was exacerbated further by modified-sine-wave.  (And it was installed in my bedroom, no less, the worst place for a loud ballast!).

HIDs:  My only experience here is with a 175w mercury-vapor "Yardblaster" fixture, which sounds like a hockey buzzer on modified sine wave, as if those things aren't already naturally loud anyway.  And a 400-watt CWA, HPF metal-halide ballast in an old highbay fixture like the ones which were common until the last few years in school gyms, big-box stores, etc. was arguably THE noisiest, as you might imagine. 

LEDs: Not much experience there, but the ones I've got in use (Philips A-line , 8.5w, 2700K) work fine but buzz slightly like a CFL will.  Some other, older, primitive by today's standards 6400K 3-watt PAR30 "Designer's Edge" floods seem unaffected. AND they're in a motion-sensor light, run on modified sine wave too without issues.

Incandescents:  I've even had 60-watt bulbs give a high-pitched, scream-like buzz like they will on a dimmer.  75w and 100w are definitely louder. 

Other lighting controls and accessories:  Standard "TRIAC" wall dimmers will burn up if used on MSW and will stop dimming lights, and will just be either "on" or "off".  That's the only thing I've ever fried on MSW that's lighting-related (MSW WILL fry other things though, just not lighting-related).  Photocells, motion sensors, etc. seem fine, from cheap little "button" photocells all the way up to a Fisher-Pierce twist-lock unit on a 175w mercury "Yardblaster" light; they turn lights on at dusk and off at dawn just like they should. 



In summary:  Everything I've really ever used has worked fine, albeit noisier.  Never burned anything up except dimmer switches. And I have many different types of lighting in use in an off-grid situation: Incandescent, CFL, preheat, rapid start, and instant-start fluorescents, T8 and T12, from F15T8 preheat lights all the way up to an 8' slimline, work fine.  Same for 175w mercury on a HX-NPF ballast and 400w probe-start metal halide on CWA ballasts.

On my experience :

Incandescents make some thin buzz sound. Not mains frequency hum

Fluorescent 36W and S10 starter, the lamp lights, but the starter remains glowing a bit all the time and is hot after a while. I would not leave it like that. Apparently there are bigger restriking overshoots after the long zero crossing, and the starter lights to them

Maybe would be less of a problem with 18W and S10 starter (Generally for 18W T8 it is sometimes recommended to use the S2 with low starting voltage, but here the S10 may be preferred exactly for its high starting voltage if it is above the overshoots that happen with 18W lamp). For 120V system, S10 (FS-4) is not expected to light at all on a choke ballast, but maybe it will light from some overshoots in the UPS output when there is no load. If not, maybe some tiny extra capacitor in parallel to the starter would make overshoots happen - But hopefully not when the lamp is working, or else the entire point of using S10 is missed. But i dont expect relying on overshoots for it to work to be reliable

CFLs appear to work fine

I expect basic Electronic ballasts (without power factor correction or anything else smart, ie CFL ballast equivalents) to work fine as well

HPS ligths up but is cycling. Not sure why

Makes me want to try HPS on 120v/60Hz modified sine wave here in North America.  Maybe the waveform isn't enough to maintain an arc?

The HPS suffers from the long gap and the consequent high reignition peaks.
Normally, with the sinewave, the HPS al;ready operate quite close to the border of being extinguished (MV's starting probe eases the reignition as well, so allows to work the lamp even on resistive ballast; HPS has no such aid). As the modified sinewave tends to make the reignition spike worse, it may easily exceed the available voltage.
And as the MV arc voltage strongly depends on the arctube temperature, it yields cycling: It ignites, with colder arctube the arc is stable, but as it warms up, it becomes unstable and extinguishes...

With the PIR detectors and LED lamps: They may seem to work fine, but overloading the internal resistor (typical 30mA feed for the common PIR sensors yields about 2W on 120V and 3.5W on 230V models, compare to about 0.3W with sinewave) makes it way more likely to fail too soon (the affected resistor uses to be rated 2W on free air and even normally there use to be traces of heat degradation around the resistor even on the sinewave; with LED's using the capacitive dropper it will be about 2W on MSW vs 0.1W on a sinewave for a 3W LED).

OK, I'm in the process of converting just about everything in my house with an E26 screw socket to LED.  They all buzz like CFLs (different brands/models).  But some seem more tolerant to the MSW than others, some "flicker" somewhat more, like the LPF fluorescents. 

Another one, some people claim you can't run refrigeration equipment on MSW.  I call BS to that, I run a refrigerator on modified sine wave and it works fine. 

Another odd one I never mentioned:  The Christmas lights with the little controller box to make them fade/flash/strobe/change color with each color as a different circuit, etc:  Those act erratic on MSW, but work.

OK, I'm in the process of converting just about everything in my house with an E26 screw socket to LED.  They all buzz like CFLs (different brands/models).  But some seem more tolerant to the MSW than others, some "flicker" somewhat more, like the LPF fluorescents. 

Another one, some people claim you can't run refrigeration equipment on MSW.  I call BS to that, I run a refrigerator on modified sine wave and it works fine. 

Depends, what motor is there, mainly the starting method and the eventual power factor compensation. And on the inverter design. If you are unsure about both being OK, there is high risk you blow up something. And that "something" may be neither the inverter, nor the fridge, but something else on the same AC line.
The simplest NPF (so not compensated) motors with a resistive phase shift (with an auxiliary starting high resistance winding controlled either by a relay or a PTC) for starting have no problems. But that applies for the device, but not for the inverter.
The inverter may suffer two major problems: First such motors have really high inrush current - a 60W 230V compressor tend to draw about 8A for about half seconds or so. So a 60W real load needs an inverter short term overload rated for more than 1kVA.
Second problem is with the reactive current component. Upstream the chopper stage, it forms rather high AC current, really with both polarities. And most inverter designs have the voltage step up converter able to transfer the power just in one direction. With that, the momentary reverse power (first 1..2 ms after the pulse start) may boost the intermediate voltage above what the inverter components survive (and all the rest connected to the AC side). The only way to suppress this is for the inverter to have large tank capacitor on the boosted DC bus. And because the high inrush current of the refrigerator compressor is mainly reactive, that capacitor has to be sized for the peak VA rating. So become quite an expensive component of the inverter.
Both the peak rating and the high capacitance make such inverter so expensive, if it would be the true sinewave type, it won't cost that much more.
So the main reason for the "better do not connect the refrigerator" is, most inverters are just lacking the capability to properly handle the high reactive inrush power.
Plus if the motor circuit does contain any form of a capacitor, it becomes a stric NO-GO for any MSW. The thing is, the leakage inductances together with the capacitor may easily form either a resonator, building up high voltage and currents on some of the harmonics, or just cause huge current spikes on the edges in case of just a PFC capacitor connected to the input.
So unless the refrigerator manual guarantee the device is designed for operation on an MSW, you never know which of the ill effects may kill either the refrigerator, or the inverter, or something else connected to the AC.

The true sinewave types are usually designed way more robust in that way (because their control is way more expensive than the simple MSW control), so usually are way easier able to handle such inrush currents (and their rating usually starts at 500W or so, so they have way greater reserve) and because the sinewave is smooth, the previous problems are either nonexistent or insignificant.

Another odd one I never mentioned:  The Christmas lights with the little controller box to make them fade/flash/strobe/change color with each color as a different circuit, etc:  Those act erratic on MSW, but work.

Again, the electronic most likely uses the capacitive dropper for supply and that does not work that well with the sharp edges. Plus if the timing runs off the mains frequency, all the ringing at the edges disturbs the master clock generation for the controller.

i had an annoying buzz from the torroidial chokes in my ge 22w circlines in some table lamps.
they were borderline annoying anyway on line voltage.
this on a trace sw series inverter here and the remote garage.
irrelevant anyway as lighting was changed to dc fluorecent ballasts and leds on mr16 drivers.
the circline adapters went into the collection box.the spiral cfl were ok till they died.not sure if their life was cut short by the inverter though.didnt care as they are all disposable trash anyway.cheap being the only desirable attribute.
most led bulbs are in the same class so i did conversions to fixtures that offered good heatsinking.since i dont tolerate modern cheap junk nearly all were modified.
the inverter is now only used for the "heavy lifting"loads.in search mode its standby losses were more than what i have running on the dc side most of the time.

One other interesting/odd thing I've observed:  Now that I've replaced most of my CFLs with LEDs, the Feit 9w 5000K 800 lumen ones I'm using take a full second or so to light on MSW once power is applied (switch flipped) but don't do this on "normal" power.  Any idea why?

One other interesting/odd thing I've observed:  Now that I've replaced most of my CFLs with LEDs, the Feit 9w 5000K 800 lumen ones I'm using take a full second or so to light on MSW once power is applied (switch flipped) but don't do this on "normal" power.  Any idea why?

I kind of see this with out kitchen lights, on the lowest dimming setting, they take a while to turn on. But they are reflector LEDs.

I'm trying out some lighting loads on my 400 Watt inverter, and I made it so it's more like 460 Watts, because I want to be able to use my electronic HID ballasts with it. I will try it out with the real load.

Update: I tried it out, and the inverter can barely handle it, then starts beeping and eventually might cut out.
Maybe I can try it on 250 Watt mode.

400W but how many VA ?

400W but how many VA ?

Didn't see, but I imagine it would be nearly the same as Watts because the ballast has a very high power factor.