Perhaps we are both missing something. I agree with you that it is not the instantaneous maximum. But it is not the average either (or rather, not quite the average). Looking at the wording again (i.e., applying Charlies’s Rule), I now see that it says to use the “highest average kilowatts reached and maintained (my emphasis) for a 15-minute interval.” Putting the word “highest” next to the word “average” tends to muddy the waters. Here is one way to interpret that phrase:
Suppose the load for a given 15-minute interval was as follows: 3 KW for 3 minutes, 4 KW for 3 minutes, 5 KW for 3 minutes, 6 KW for 3 minutes, and 7 KW for the last 3 minutes. That is an average of 5 KW. But the load was not sitting at 5 KW for the entire 15-minute period. Nor was it sitting at 4 KW, 6 KW, or 7 KW. The only load value that was (now quoting from the exception) “maintained for a 15-minute interval” was 3 KW. What I mean is that the load was 3KW or more for the entire 15 minutes, and it was not 4, 5, 6, or 7 KW for the entire 15 minutes.
This reasoning brings to my mind the ancient riddle that asks how many months have 28 days. The correct answer is all of them. Some don’t stop at 28, but they all make it to 28 days before the next month begins.
What, then, should be assigned as the load for the 15-minute loading cycle I describe above? Using a strictly literal interpretation of the words, my answer would be 3 KW. But I don’t think that is the intent. As a design engineer, I would be inclined to go with 7 KW in the interests of conservatism. However, if I were reviewing someone’s calculation and noticed that they used 5KW, I don’t think I would cite that as a design error.