now there is something else that's interesting about the solid state relay. it only turns on and off at the zero cross point of the sine wave, to avoid surge, rfi/efi. could this be a solution to the charging problem?
It's exactly this that I'm referring to.
I've seen some of these relays refuse to turn off at all, depending on the nature of their "zero-crossing" detector.
For a giggle, lets hypothetically ask a couple of questions?
Is the zero-crossing based on volts, or current?
If you have a reactive load, current will lead or lag volts, so when volts=0, current will be non-zero.
One would assume that in order to minimise RFI/EMI, it would be switching at 0 *CURRENT*, but most of the ZCD circuits I've seen are zero *VOLTS*.
Depending on the technology in the SSR (and I've seen it happen) - with certain scenarios of load, they simply won't turn off.