How much money can an electrical engineering professor earn from grants in the US?
Professors typically do not supplement their salary with grants with one very large exception. The grant money can allow them to trade some number of required courses for research time. 

The big exception to this is that the typical appointment for a university professor in the US is for 9 months. If the professor wants to teach some summer courses, they can earn 3 more months of their salary for doing that, or they can get grants to fill in that time. The National Science Foundation limits US researchers who are professors to 2 months of summer time funding, though, so to get 12 full months of compensation, a professor will need income from some other source (summer teaching, another agency's grants, industrial grants, consulting, etc). 

So, that being said, typically professors cannot increase their salary rate. They can only use it to fill in the months that the university does not usually pay them for. Finally, most universities give the option for their professors to take the 9 months of salary over 12 months of payments, so filling in those 3 months may look like a monthly raise from the perspective of their bank statements.