Two-Stage Stochastic Linear Programming Model for Coordinated Multi-Reservoir Operation

Abstract

Operation planning for multiple reservoir systems is a complex and challenging problem because of inherent uncertainties in inflow forecasts. Long-term inflow predictions are required for mid-term planning. However the practice of using several inflow predictions does not fully reflect the various characteristics of the decision in uncertainty analysis, such as non-anticipating decisions or the serial correlations imbedded in the inflow. We therefore applied the stochastic linear programming (SLP) approach to tackle the uncertainties that are inherent in reservoir operation planning due to the inflow uncertainty. A SLP model is developed for coordinating the multi-reservoir operation to determine the efficient monthly target reservoir storage. The model is formulated as a multi-period, two-stage SLP based on the form of fan of individual scenarios. The inflow scenarios are generated by the multivariate periodic AR(1) model considering the serial and spatial correlations. The model becomes a large-scale, linear programming model (comprising over 120,000 columns and 80,000 rows), which was solved very quickly (in 5 minutes) using the linear programming solver CPLEX. The expected benefit of the stochastic model was analyzed quantitatively based on value of information measure. The results indicated that the solutions of the stochastic model are much more effective than those of the deterministic model with average inflows, and that this effectiveness is also maintained in real-time operation in the presence of uncertainty. The benefit of applying this stochastic model to the Nakdong River basin in Korea was presented. It implies that the use of the stochastic model in real-time operation is more effective in the presence of uncertainty.