Selling and transporting electricity

Let’s imagine in a hypothetical world that Australia goes nuts and builds loads and loads of solar energy farms. So many that they only use a small percentage (say 5%) of the energy they produce. Is there a good means for transporting this energy for sale to other countries? Imagine USA wanted to buy all of the surplus to reduce their dependence on oil/coal/nuclear and the energy was being sold at a cost that made it wise to do so. How would Australia transport the energy to America?

For the sake of the hypothetical we can ignore the initial cost of setting up the solar farms but we want the method of transportation to be economically viable. Can you lay electricity lines across the ocean or would there be too much loss due to resistance? Are there any high capacity capacitors that could be shipped over in converted coal/oil tankers?

Hydrogen could be shipped in tanks and used in fuel cells at the destination.