In this paper, we study the optimal storage investment problem faced by an owner of renewable generator the purpose of which is to support a portion of a local demand. The goal is to minimize the long-term average cost of electric bills in the presence of dynamic pricing as well as investment in storage, if any. Examples of this setting include homeowners, industries, hospitals or utilities that own wind turbines or solar panels and have their own demand that they prefer to support with renewable generation. We formulate the optimal storage investment problem and propose a simple balancing control for operating storage. We show that this policy is optimal for constant prices and some special cases of price structures that restrict to at most two levels. Under this policy, we provide structural results that help in evaluating the optimal storage investment uniquely and efficiently. We then characterize how the cost and efficiency of storage, dynamic pricing and parameters that characterize the uncertainty in generation and demand impact the size of optimal storage and its gain. One surprising result we prove is that for storage to be profitable under the balancing policy the ratio amortized cost of storage to the peak price of energy should be less than 1 over 4