It is very likely that a single portable propane bottles like the kind you get to power a bbq will not feed a 15 KW genset very long before the boiling off of the liquid to gas gets the liquid too cold to provide enough pressure, and even if it did provide the pressure ( witch I think it will not) a BBQ size bottle will not run a 15 KW genset very long. I think you would need a set-up of quite a few of them to feed a 15 KW fast enough and also long enough to make it work.
The 200 gallon tank is a realistic approach to what would be required. You need to calculate how long a gallon of propane will run a 15 KW genset, and then figure out how long you need to run your system in the longest outage you will see. And calculate how big a tank you will need.
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Someone who sells and installs generators along with the propane tanks could give you exact data on what is required,
But here are some rough calculations of what is going on:
1 gallon of propane has 91,500 BTUs of heat energy when its vapors are burned
15 KW = 51,181 BTUs per hour
An realistic approximation of the efficiency of a small internal combustion engine is 20 %
So the engine will consume 5 times the 51,181 BTUs per hour if the genset is running at 100 % load
So lets be generous and say it is running at 2/3 of 100 % load, .66 X 5 X 51,181 = 168,897.3 BTUs per hour to power the engine
168,697.3 / 91,500 = 1.846 gallons of propane per hour to power a 15 KW genset running at 2/3 load capacity.
in 24 hours that would require 24 x 1.846 = 44.3 gallons of propane per day.
At that rate a 200 gallon tank will last 200 gallons / 44.3 gallons per day = 4.51 days
And a 200 gallon tank is the kind of size required to provide enough surface area to keep the liquid propane warm enough from the cooling effect of the liquid changing into gas to power your 15 KW genset at a rate of 1.85 gallons per hour continuously when the weather is cold.
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These are just some calculation using realistic numbers for the amount of BTU a gallon of propane has, and an approximation of how much an internal combustion engine powering a 15 KW generator running at 2/3 of maximum load will require. I do not work in the propane or generator industry. But I did get straight A in both my college physics courses. So these approximations are probably very close to what you will experience in real life.
BTW, a 20 Lb BBQ bottle has 4.7 gallons of propane. That would run your 15 KW genset for: 4.7 gallons / 1.846 gallons per hour = 2.546 hours ( that is almost exactly 2 and a half hours ) if it was running at 2/3 of full rated capacity.
But if it was cold out the bottle would get too cold and loose pressure from the cooling effect of the liquid propane boiling off and becoming gas, and it probably would not be able to supply enough pressure to run the genset for even one hour before the pressure of the gas coming off of the bottle was not enough to supply what the genset needed to keep running.
And often those 20 Lb bottles are not filled up all the way. Instead of 4.7 gallons, you can expect to get something like 4.4 gallons.
Which works out real nice to show that with the above calculation of 44.3 gallons per day, you would need 10 of the 20 LB bottles to run a 15 KW genset at 2/3 load for one day ( 24 hours ).
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So if you wanted to run that 15 KW genset at an average usage of 2/3 rated load for a one week outage without having a propane truck come out and refill the tank every 3 or 4 days ( which is what would be required if you only had one of the 200 gallon propane tanks ), you would need 2 of the 200 gallon propane tanks on your property. Two of the 200 gallon tanks would last 9 days at 2/3 average load on a 15 KW genset. But you would want to get them refilled every 7 or 8 days.