Brigadoon - An Occasional Corner on the Internet
Houseboat Hot Water System
Designed by Mark Little
Hot Water System Relay Selection
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To select a relay to control the DC Power to the Inverter, it is necessary to know the power that the Hot Water System (HWS) will consume. From there, the power that needs to be supplied to the Inverter can be calculated, taking into account the Inverter inefficiencies.

The HWS unit being used is a Bosch C16 and it is expected that if there is a failure, it will be replaced by the same model. I have not been able to determine the power (watts) required to run the HWS, but I'm using 80W when selecting the relay that needs to be used to control the 12V DC connected to the Inverter. Based on the use of the hot water system on the houseboat, I believe this is conservative.

The inverter documentation claims that the inverter is >90% efficient, so 90% will be used for the purposes of calculation. This means to provide the 80W, the battery will need to supply the Inverter with 88W.
When a lead-acid 12V battery reaches a terminal voltage of 10.5A, the inverter will shut down to protect the battery. When the battery is fully charged, it will have a terminal voltage of 12.7V (unless being charged which may result in a higher voltage).

Since Power is the product of the Volts and Amps, as the voltage falls, the current must rise to supply the same amount of power. As a result, the maximum current that will be switched will be when the battery voltage is low (10.5V). This means to supply 88 Watts at 10.5V, the Inverter will draw just less than 8.5A, so a  relay module capable of switching 10A  should be adequate for this project.