The amount of copper you would need to constantly convey electricity from the sunny side of the earth to the dark side would be absolutely massive. It is not an issue of common grids, as long distance high power transmission is done at many different voltages depending on the specific route, and has nothing to do with your mains voltage and frequency.

Current long distance power transmission is most often used as a way of 'balancing' production and demand between different types of plants; it is not intended or capable of transmitting the full power needs of the recieving area.