Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with   Battery Storage using Approximate Dynamic Programming
  There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations in electricity spot prices, is becoming an important way of paying for expensive investments into grid-level storage. Independent system operators such as the NYISO (New York Independent System Operator) require that battery storage operators place bids into an hour-ahead market (although settlements may occur in increments as small as 5 minutes, which is considered near "real-time"). The operator has to place these bids without knowing the energy level in the battery at the beginning of the hour, while simultaneously accounting for the value of leftover energy at the end of the hour. The problem is formulated as a dynamic program. We describe and employ a convergent approximate dynamic programming (ADP) algorithm that exploits monotonicity of the value function to find a revenue-generating bidding policy; using optimal benchmarks, we empirically show the computational benefits of the algorithm. Furthermore, we propose a distribution-free variant of the ADP algorithm that does not require any knowledge of the distribution of the price process (and makes no assumptions regarding a specific real-time price model). We demonstrate that a policy trained on historical real-time price data from the NYISO using this distribution-free approach is indeed effective. 
Daniel R. Jiang and Warren B. Powell
math.OC