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A smart building energy system usually contains multiple energy sources such as power grids, autonomous generators, renewable resources, storage devices, and schedulable loads. Storage devices such as batteries, ice/heat storage units, and water tanks play an important role in reducing energy cost in building energy systems since they can help sufficiently utilize renewable energy resources and time-of-use electricity prices. It is important to plan, schedule, and coordinate all the storage devices together with schedulable loads in a building facilitated by microgrid technology. To consider the above problem with uncertainties in solar radiation and demand profiles, a stochastic optimization problem is formulated and solved by the scenario tree method. The best combination and the optimal capacities of storage devices for specific building energy systems are then determined. Furthermore, the optimal operating strategy of building energy systems can be obtained. The performance analysis on the storage devices is conducted and the numerical results show that thermal storage devices (e.g., ice storage units, water tanks) are good for saving energy costs but batteries may not be economical due to their high investment cost and short lifetime. It is also observed that the aforementioned uncertainties have an impact on selecting which type and capacity of storage device should be used.