I think it would take somebody knowing more details about your AC load to answer that. If it might help, here's a quick description of how the cheap MSW inverters work. They first upconvert the DC input to about 140 volts DC (for a 120 volt RMS output). The minus side of this 140 volts is tied (hardwired) to the negative battery input. Then at the output frequency, the inverter reverses the polarity of the 140 volt DC on the AC output terminals, creating a 280 volt peak-to-peak waveform. The AC outputs are at zero volts for the mid-step of the MSW waveform. This, each of the two AC output lines is sometimes connected to the DC negative input, and sometimes connected to the positive output of the 140 volt supply. If the DC input is connected to a common or ground wire, connecting either AC output line to common or ground results in the 140 volt DC supply being short-circuited, and the transistors that perform the polarity switching go up in smoke. (I did learn this the hard way). That 140 volt value of the DC supply is nominal. It's unregulated and proportional to the voltage of the inverter's DC input. The RMS output voltage is regulated by changing the pulse width of the PSW waveform. As the battery voltage goes down, the AC peak voltage goes down, and the width of the active part of the waveform increases. If you have something really, really weird going on, maybe the differing peak output voltage and/or pulse width could be related. A longshot I realize. You might not appreciate my opinion, which is to get a decent quality PSW invcerter.