Most applications of stochastic dynamic programming have derived stationary policies which use the previous period's inflow as a hydrologic state variable. This paper develops a stochastic dynamic programming model which employs the best forecast of the current period's inflow to define a reservoir release policy and to calculate the expected benefits from future operations. Use of the best inflow forecast as a hydrologic state variable, instead of the preceding period's inflow, resulted in substantial improvements in simulated reservoir operations with derived stationary reservoir operating policies. While these results are for a dam at Aswan in the Nile River Basin, operators of other reservoir systems also have available to them information other than the preceding period's inflow which can be used to develop improved inflow forecasts.

Stochastic dynamic programming models for reservoir operation optimization

Reservoir operating policies can be derived using stochastic dynamic programming (SDP) with different hydrologic state variables. This paper considers several choices for such hydrologic state variables for SDP models of the Shasta-Trinity system in northern California, for three different benefit functions. We compare how well SDP models predict their policies will perform, as well as how well these policies performed when simulated. For a benefit function stressing energy maximization, all policies did nearly as well, and the choice of the hydrologic state variable mattered very little. For a benefit function with larger water and firm power targets and severe penalties on corresponding shortages, predicted performance significantly overestimated simulated performance, and policies that employed more complete hydrologic information performed significantly better.

The Value of Hydrologic Information in Stochastic Dynamic Programming Models of a Multireservoir System

A model for the optimal operating policy of a reservoir for irrigation under a multiple crops scenario using stochastic dynamic programming (SDP) is developed. Tntraseasonal periods smaller than the crop growth durations form the decision intervals of the model to facilitate irrigation decisions in real situations. Reservoir storage, inflow to the reservoir, and the soil moisture in the irrigated area are treated as state variables. An optimal allocation process is incorporated in the model to determine the allocation of individual crops when a competition for water exists among them. The model also serves as an irrigation scheduling model in that at any given intraseason period it specifies whether irrigation is neede and if it is, the amount of irrigation to be applied to each crop. The impact on crop yield due to water deficit and the effect of soil moisture dynamics on crop water requirements are taken into account. A linear root growth of the crop is assumed until the end of the vegetative stage, beyond which the root depth is assumed to be constant. The applicability of the model is demonstrated through a case study of an existing reservoir in India.

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Optimal Reservoir Operation for Irrigation of Multiple Crops

Two dynamic programming models — one deterministic and one stochastic — that may be used to generate reservoir operating rules are compared. The deterministic model (DPR) consists of an algorithm that cycles through three components: a dynamic program, a regression analysis, and a simulation. In this model, the correlation between the general operating rules, defined by the regression analysis and evaluated in the simulation, and the optimal deterministic operation defined by the dynamic program is increased through an iterative process. The stochastic dynamic program (SDP) describes streamflows with a discrete lag-one Markov process. To test the usefulness of both models in generating reservoir operating rules, real-time reservoir operation simulation models are constructed for three hydrologically different sites. The rules generated by DPR and SDP are then applied in the operation simulation model and their performance is evaluated. For the test cases, the DPR generated rules are more effective in the operation of medium to very large reservoirs and the SDP generated rules are more effective for the operation of small reservoirs.

Comparison of Stochastic and Deterministic Dynamic Programming for Reservoir Operating Rule Generation

Building more realistic reservoir optimization models using data mining – A case study of Shelbyville Reservoir

A stochastic dynamic programming is used to develop optimal policies for operating the multipurpose pool of the Elk City Lake in Kansas with serially correlated inflows. The model determines a long‐term operating policy to minimize the expected average annual loss. Using the developed optimal policy to operate the lake from 1967 through 1977 shows a marked reduction in the expected annual losses as compared with the historical operation. The sensitivity of the optimal policy and computation effort to the number of discrete states used is also investigated.

Siavash Esmaeil‐Beik

Papers

Optimal Operation of Multipurpose Pool of Elk City Lake