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I have an APC UPS that puts out modified squarewave (the marketing people calls it modified sinewave) when on battery. I connected a fluorescent fixture with an electronic ballast containing passive L-C power factor correction. The UPS crashed and shut down as soon as it switched over to battery. The UPS doesn't have issues with residential electronic ballast such as CFLs which doesn't have a PFC circuit. It must not be getting along with the PFC. UPS is rated at 600VA. Light only takes 100VA.
Electronic ballasts have the identical rectififier+capacitor front end as switchmode power supplies used in computers. Like electronic ballasts, computer power supplies are available with PFC. They're rare in the US, but EU legislations mandated power factor corrected power supplies on new computers.
An example of power factor corrected PSU:
My UPS shares the transformer between inverter operation and charging. It's a steel core transformer with center tapped secondary. When operating on battery, the center tap on secondary is tied to one of the battery terminals and the MOSFETs switch the other terminals back and forth between the two taps on the sides. A relatively common design.