230VAC? Should be 240 VAC. 15,000W divided by 240VAC = a max current draw of 62.5A
You have also hit on the reason why most gensets this large are usually hard wired into the panel.
That 50A plug is usually used in RV service installations where regular hook/unhook are required. Common use, commonly available at a reasonable price. There are larger ones out there, but I sure wouldn't want to try and carry a wallet with enough cash to pay for one

Look to the marine/shore tie suppliers. Over 50A is not so common use I think, so not so avaialble, and not at a very reasonable price...
Another good reason to ask "Do you really need 15KW?"
Options:
1. Hardwire the generator.
2. Drop the coin for a 75-100A shore-tie plug and receptical.
3. Evaluate your EXACT maximum power needs and see if you can get by with less. If you can get your needs under that 50A plug limit, use it with a 50A circuit breaker on the generator output and limit yor capacity to that.
There are a couple of ways to calculate your eact needs:
1. Get a Kill-A-Watt, you should have it anyway if you are making your own power. It will tell you peak and overall average over time power use of individual appliances, as well as if their start and run capacitors are maintaining a proper power factor.
2. Do you have a mechanical power meter on your comercial power service? If so, you can see the watt/hour load of your home at any given time using a stopwatch. Here is how, courtesy of Wikipedia:
The amount of energy represented by one revolution of the disc is denoted by the symbol Kh which is given in units of watt-hours per revolution. The value for Kh should be printed on the face of the meter. The value 7.2 is commonly seen. Using the value of Kh, one can determine the power consumption at any given time by timing the disc with a stopwatch. If the time in seconds taken by the disc to complete one revolution is "t", then the power in watts(P)= 3600 X KH Divided by "t".
For example, if Kh = 7.2, and one revolution took place in 14.4 seconds, the power is 1800 watts. This method can be used to determine the power consumption of household devices by switching them on one by one.
I tried this and it seems to work pretty well. 3600 represents the number of seconds in an hour. This is similar to the formula I use for checking a speedometer. 3600 divided by the number of seconds required to cover a measured mile = speed in MPH. The value for Kh should be on the face of The meter somewhere. Mine was 7.2. Just time the wheel thru one complete revolution. and use this number to divide 3600 X Kh...