We consider a system where inelastic demand for electric power is met from three sources: 1) the grid; 2) in-house renewables such as solar panels; and 3) an in-house energy storage device. In our setting, energy demand, renewable power supply, and cost for grid power are all time-varying and stochastic. Furthermore, there are limits and inefficiency associated with charging and discharging the energy storage device. We formulate the storage operation problem as a dynamic program with parameters estimated from real-world demand, supply, and cost data. As the dynamic program is computationally intensive for large-scale problems, we explore algorithms based on approximate dynamic programming (ADP) and apply them to a test data set. Using the real-world test data, we numerically compare the performance of two ADP-based algorithms against Lyapunov optimization-based algorithms that require no statistical knowledge. Our results ascertain the value of storage and the value of installing a renewable source.
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Kwon et al. (2015) studied this question.