A somewhat new inverter transfer relay on the market is offered by Xantrex. This relay is suitable for switching a single 15 amp circuit and is designed specifically for inverter applications as described here, and comes in a smaller and easier to install form factor than the traditional 30 amp transfer relays. From the Xantrex description: An easy to mount 15A Inline Transfer Relay provides switching between camp-ground and inverter AC source. It comes with a power plug for convenient connection to the inverter GFCI and a hardwire cord for the AC input and output interface.
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A 115 vac inverter can be permanently installed in an RV, and connected through an automatic change-over relay. The relay is wired in such a way that the normally closed contacts are used for the inverter output, and the normally open contacts are used when external (camp ground or generator) power is available. By connecting this way, inverter power is not used to energize the relay coil, saving battery power. You will most likely need to do some 120 VDC re-wiring in the RV to isolate the wall receptacles that will be powered by the inverter from built-in appliances that require external power. This discussion assumes an RV with 30 amp electrical service. An inverter installation as described here can be done on an RV with 50 amp service, but a simple inverter as described here should only be connected to a single 120 VAC outlet circuit from the 50 Amp circuit breaker panel.
Xantrex XS(RS)-400 True Sine Wave Inverter (Example)