With regard to your edit: take a look at the note at the end of the article you are quoting, where the author acknowledges being sloppy with respect to units. Here, he says anthropogenic climate change is heating up the Earth by 300 terawatt-hours per hour (which is, of course - and more simply stated as - a rate of 300 TW or 0.3 PW). Therefore, while it would be correct to say that this results in an extra 0.3 petawatt-hours every hour, this is not the same as nor justifies the statement "...0.3 petawatts of extra energy circulating in the atmosphere as a result of anthropogenic changes...", which is incoherent.

As for "1 order of magnitude (out of 16!)", the "out of 16" is meaningless - the number 16 is merely a consequence of the arbitrary choice of unit size. Your original figure was simply off by a factor of ten, in any units.