An academic answer?

??
In physics, the letter P is perhaps the most frequently symbol used for power. But I am sure others have also been used.
In electronics the same letter is used in equations, but perhaps you are really referring to symbols used in drawings. That brings up the type of drawing you want. And exactly what you mean by "power". In electronics there are schematic drawings, wiring diagrams, pictorials, and then styles like "fritzing" and each of them can use different symbols.
A pictorial type drawing will often try to make the symbol for something look a lot like the actual item. So a battery would be drawn looking like a physical battery and different types of batteries would have different appearances. A plug for the power cord would be drawn to look like the plug found on a living room lamp of kitchen toaster. Etc. This is the type of drawing that is often used for beginners so they can relate to the item.
Wiring diagrams are more abstract. Often AC or DC power is brought into the diagram with simple rectangles or open arrow heads with text in them to show the type of power. They can even have just a line, which represents a wire, starting next to such text. The text may be very descriptive (230 VAC, three phase, 100 Amps) or very abbreviated (phase 1, phase 2, L1, L2, etc.)
Schematic diagrams are highly abstract but also highly organized (at least they should be) to allow the function of the circuit to be shown by that structure of the drawing. An important element of this is signal flow from left to right and top to bottom. So Power should be introduced into a schematic drawing at the left and/or top with standard symbols in those locations. Additional symbols can then be used to distribute those power sources around the drawing as needed. Different types of power will have different symbols. A circle with either plus and minus signs or a sine wave inside can be used for DC and AC power. A connector symbol - there are many types - can also be used. Like the wiring diagrams; boxes, open arrow heads, and even the end of a line with text can be used. And again, that text can be very descriptive or very abbreviated.
In schematics and wiring diagrams I have seen a large amount of different ways of showing almost every element that is included, including power symbols. My examples are by no means intended to be all inclusive.
"Fritzing" is a very stylized version of the pictorial style of drawing. It uses actual photos or very accurate drawings of the actual items. In this it is, perhaps, the easiest of all to define. Take a photo, reproduce it close to actual size and you have your symbol. I hate "fritzing" because it does nothing to make the circuit understandable. It only shows what it looks like and it only does that for one set of parts: if your part looks different, TOUGH.
You ask for standards. I am afraid there are many and there are none. Virtually any country, industry, company, group, or even individual is free to use whatever standard they wish. Pseudo standards have jelled around loosely defined groups for loosely defined time frames. Companies have published their own standards. Different industries may use different styles. Etc. So, NO there is no real, universal standard for power or any other of the symbols we use. I am afraid that is not very academic. Or, perhaps it is.
And I will give you one very big reason why there are no universal standards: $$$$ and exclusivity. The people who usually develop and try to propagate standards first, do not include the potential users in the considerations. And second, they always want large amounts of money for copies of those standards. None of them ever seems to understand that if they want people to adopt their standards, then those PEOPLE need to be a part of the development process and then actually know what the standards are. But they exclude most users and then assume that all users can afford their arbitrarily high prices. This is a double formulae for failure and it seems to be practiced by, guess who (hint, hint: a c a d e m i c s).
If you want "academic" standards, then, INCLUDE ALL users in their development and maintenance. And make them completely FREE to all who want them. Oh, and no copywrite: anyone can reproduce them. Then, and only then, will you ever have real and universal standards. But you and I both know that is not the academic way because it does not force the "superior" knowledge of the few on the masses.
Personally, I like it the way it is. And if the academics don't like it, then #### them if they can't take a joke.