Stochastic Dual Dynamic Programming to schedule energy storage units providing multiple services

When energy storage units, such as batteries, are installed to support photovoltaics and defer power system upgrades they are inactive or only partially used most of time. Their unused capacities could be used to provide frequency control, allowing them to generate additional revenues. However, the challenge is to decide how much of their energy and power capacities to allocate to either service. Photovoltaic generation profiles are difficult to forecast accurately, and frequency deviation is a highly stochastic process. This paper develops a Stochastic Dual Dynamic Programming (SDDP) approach to generate decision rules for determining how much capacity to assign to each service at each time step, depending on the time of day and the storage energy level. Unlike Stochastic Dynamic Programming (SDP), our approach does not require us to discretize the state and decision spaces. We show that, when storage efficiency is high, SDDP outperforms SDP, but when short computation times are required, SDP may be preferred. We also discuss challenges associated with using SDDP when storage efficiency is lower than unity. Finally, we show that the number of tuning parameters is lower for SDDP than for SDP, and that the relation between tuning parameters and policy quality is more intuitive for SDDP than for SDP.