Efficient implementation of sampling stochastic dynamic programming algorithm for multireservoir management in the hydropower sector

Despite decades of operational use, stochastic dynamic programming (SDP) is still a popular method for solving hydropower management optimization problems. From an operational perspective, there are many advantages to using this type of method: it provides a feedback operating policy that can be used for simulation purposes, marginal values of water stored in reservoirs are easy to compute, and it is relatively simple and easy to understand. However, for systems with more than two or three reservoirs, some issues arise that must be resolved in order to create efficient and fast operational software. This paper presents a case study which solved a problem of four reservoirs by sampling SDP (SSDP). Several improvements were proposed, such as using parallelization techniques, efficient discretization of the state space, and piecewise linear approximation of the water value function utilizing a strategy similar to Benders cuts as in stochastic dual dynamic programming, to build fast, efficient, and robust SSDP operational software. Program implementation details and numerical results were presented for a real hydropower system owned by Rio Tinto in Canada.