Running the generator on gas and running as a combined heat and power it can be very cost effective. Running on gas gets rid of a lot of the duties applied to fuel including red diesel which is now hard to come by. Engine efficiencies at best are only 25 to 30% so gas at 11p kWh would cost around 40p per kWh of electricity. Using the heat however, the 70% waste heat then starts to become more cost effective. By charging batteries, heating hot water and heating the house while the genny is running that will give some real energy cost savings.
Earlier in my working life I did a similar project on a much bigger scale (350 kWa Volvo Generator) it fed 12 factory units, had an Allen Bradley PLC controlling it all and was fully automatic. It collected the price of red diesel on a daily basis, had the outdoor temperature and could assess the demand of each factory unit. It then made the decision whether to run off genny or grid. There were times that it had to be a generator supply because our grid feed was too small for some of the equipment we had, if that equipment was switched on the genny started and all units switched over to generated power. Likewise, if the grid supply failed, the genny started up within 3 seconds and powered all of the units.
I really enjoyed this project and it's still in operation to this day (20 years old).