Finely dispersed energy storage systems contain storages at thousands of distribution network sites which will often make use of the spare morning and evening capacity of photovoltaic inverters. Second use batteries, those retired from electric vehicle fleets, will typically retain 80% of their initial amp-hour capacity at the end of life and provide a large scale source of low cost storage. The lithium-ion vehicle battery market is forecast to grow to tens of thousands of megawatt hours and exceed $30 billion annually in 2020. This paper presents an efficient algorithm for optimizing the sizing and cyclic operation of battery storages. The periodic daily or weekly battery state of charge profile is compactly represented by a vector of Fourier coefficients. A key optimization constraint, that the solution is periodic, is inherently embedded allowing a number of optimization algorithms to be efficiently applied.