Long‐term management of a hydroelectric multireservoir system under uncertainty using the progressive hedging algorithm

[1] Among the numerous methods proposed over the past decades for solving reservoir management problems, only a few are applicable on high-dimensional reservoir systems (HDRSs). The progressive hedging algorithm (PHA) was rarely used for managing reservoir systems, but this method is a promising alternative to conventionally used methods for managing HDRSs (e.g., the stochastic dual dynamic programming). The PHA is especially well suited when a new stochastic optimization model must be built upon an existing deterministic optimization model (DOM). In such case, scenario subproblems can be resolved using an existing DOM with minor modifications. In previous studies, the PHA was rarely used and only tested on problems covering short-range planning horizons (2 months with six time periods) where a small number of nonanticipativity constraints (NACs) must be satisfied. Large reservoirs often need to be managed over a much longer planning horizon (1–5 years) containing many tens of time periods. In such case, convergence becomes much more difficult to achieve because of the larger number of NACs to be satisfied. Finding a nonanticipative solution becomes particularly difficult when the input scenarios differ drastically. In this study, we demonstrate the applicability of the PHA for managing HDRSs over long-term (more than a year) horizons in highly uncertain decision environments. We apply the PHA on Hydro-Quebec's reservoir system over a 92 week (period) horizon. We analyze the performance of the PHA for different penalty parameter values. Deterministic solutions are compared to stochastic solutions.