Electric power systems are increasingly turning to energy storage systems to balance supply and demand. But how much storage is required? What is the optimal volume of storage in a power system and on what does it depend? In addition, what form of hedge contracts do storage facilities require? We answer these questions in the special case in which the uncertainty in the power system involves successive draws of an independent, identically-distributed random variable. We characterise the conditions for the optimal operation of, and investment in, storage and show how these conditions can be understood graphically using price-duration curves. We also characterise the optimal hedge contracts for storage units.