This paper addresses photovoltaics (PV) power prediction and energy storage problem which are known to be a key technology in energy management systems (EMS). Extending results of the point prediction of PV power, we first describe a prediction interval (PI) method using a copula, which can express the relation between a multivariable joint distribution and each marginal distribution. Then, resorting to the PI method, the energy storage optimization problem in a building is developed. A scenario robust (SR) optimization theorem, which calculates the robustness of the optimal solution, is applied to the proposed PI method, and hence we obtain an optimal energy storage solution taking the robustness of the solution into account. Additionally, we propose a method which combines a model predictive control (MPC) technique and SR to reduce the total electricity costs. The simulation results finally illustrate the cost reduction and robustness of the proposed method.