A remote property has an ac load profile that can be approximated by the following graph:

What is the average daily load for this application $($in kWh$/$day$)?$

A switched diesel hybrid system is to be used to meet this load, and it will use a $4\mathrm{.}5$ kW diesel generator. The fuel consumption for this diesel genset is given by the following equation:

F $=0\mathrm{.}37+1\mathrm{.}2*$ X

where F is the fuel consumption in litres per hour

X is the load expressed as a fraction of the rated diesel output

When the diesel operates, it operates at $90\%$ of its rated output. For how long would the diesel need to operate to ensure that sufficient energy was stored in the battery to cover the rest of the twenty four hour period when the diesel is not operating? Assume that a time clock starts the diesel at $4$pm each day. Also assume that the battery efficiency is $80\%,$ the average inverter efficiency is $84\%$ and the battery charger efficiency is $88\%.$ Describe the method that you have used to calculate the operating hours of the diesel generator. Provide sufficient information to allow the marker to see how you arrived at your answer.

What is the average daily fuel consumption for the genset in this switched hybrid situation?