Performance of Implicit Stochastic Approaches to the Synthesis of Multireservoir Operating Rules

With increasing pressure on water resources availability and dependability and constraints due to environmental concerns, the traditional approaches for defining reservoir management rules are often inadequate. In particular, in multireservoir systems, when multiple input variables (e.g., the storage of other reservoirs in the system, water demand in different districts) must be taken into account, it is almost impossible to figure out which shape the operating rule(s) could have. For these reasons, neural network (NN) based rules have been increasingly adopted in the last decade. NN-based rules are well known as universal approximators that can help determine the most interesting input variables, their mutual relations, and how they contribute to the definition of the optimal releases. Two approaches to the identification of neural management rules are discussed in the paper. The first solves a deterministic open-loop (i.e., with known inflows) problem and then identifies neural closed-loop policies using the classical regression method, so that the rules approximate as much as possible the solution found in the first step. The second approach, direct policy search, assumes that the operating rule is represented by an NN, the parameters of which are optimized directly by solving the optimal closed-loop problem. This work applies the two approaches to the case of the downstream portion of the Nile River basin system, which contains some large reservoirs, and for which several years of synthetic streamflows are available. The comparison of the two approaches highlights intrinsic differences, showing the benefits and disadvantages of each. In the specific case of the Nile, the first approach performs better in terms of global agricultural deficit and hydropower production.