A inverter/charger has EN-IEC 60335-1, EN-IEC 60335-2-29, IEC 62109-1 but is not certified by UL standard.
So isn't the UL mandatory?
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Generaly speaking, UL is not mandatory (as isn't TÜV for instance) but it may be requested by certain markets specificaly if there are national deviations in some states that were not specifically covered by the mentioned standards. You may consider the CB scheme for your product(s) as an additional peace of mind. UL may be seen however as an advantage if your big clients demanded it as some will refuse products if there is no UL or CSA certificate on request.