Multi-lag stochastic differential dynamic programming algorithm for multi-reservoir hydropower systems

Dynamic programming (DP) is an optimization technique especially suited for reservoir operation because of its sequential decision abilities. However, one problem is always present whenever DP is used. This problem is the "curse of dimensionality" or the excessive memory and computational time requirements to solve multi-dimensional problems. One of the most promising techniques to solve the dimensionality problem is the differential dynamic programming (DDP).; In this research, the DDP technique is applied in a stochastic environment. A general stochastic DDP algorithm is developed for that purpose and tested on a multi-reservoir hydropower system. The algorithm is developed by extending and improving earlier stochastic DDP approaches by Trezos and Yeh (1987) and Ouarda (1991). The algorithm solves a quadratic programming (QP) problem at every time stage in a backward solution process to yield a linear feedback control law, which is a function of the state, for every stage. The forward run of the process solves another QP problem at each stage to yield an open loop optimal release policy for the system.; The algorithm in its original form considers the system inflows to be independent. The original algorithm is modified to be able to handle the cases where the forecasted stochastic inflows are serially correlated. Two different cases are considered. In the first case, the system inflows are considered to have a lag-one markovian structure. In the second case, the serial correlation of these inflows is considered to have a lag-two structure. Single and multiple time lags are directly included in the inflow expressions in the objective function and the linear feedback release laws of the modified versions of the algorithm.; The original version of the algorithm is tested on a hypothetical four-reservoir hydropower system. Its capabilities as an efficient approach to solve multi-dimensional stochastic problems are shown. The two modified versions are tested on a single reservoir hydropower system. The performances of the two versions are compared through a real time simulation model developed for that purpose. The linear feedback release rules of the two versions are compared for their average annual energy production and their associated system failure risk. (Abstract shortened by UMI.)...