Dynamic operation of a reservoir system with discontinuous and short-term data

Abstract

The objective of this study is to develop a practical mathematical model to determine optimal operating rules for the reservoir system of the West Branch Penobscot River in the State of Maine of the US. This system is composed of five major lakes and it has three objectives. The hydrological data are not available in winter in the upstream four lakes due to freeze and the length of flow data is less than 25 years. Dynamic programming (DP) has been used extensively for solving reservoir operation problems. One major drawback of DP for multiple reservoir operation is the "curse of dimensionality". Many variations of the original DP have been proposed to ease this problem, for example, incremental DP, discrete differential DP, differential DP, gradient DP, and spline DP. Instead of a DP approach, this study proposes using a nonlinear programming (NLP) approach to solve the multi-reservoir system. NLP has been developed extensively in the field of operations research but not yet widely used in reservoir operations. A distinct advantage of using an NLP model is that it can avoid the dimensionality problem because it solves directly the problem without discretizing the decision variables. To use the NLP approach, a real time operation model is specified at first. Then, a multivariate first-order autoregressive model is used to generate a large number of future inflow sequences. The MINOS software package is then used to optimize the problem with each inflow sequence. MINOS can be implemented seemly in the simulation process and can solve the problems without starting values of variables. The number of runs in a simulation is determined by a statistical model, which shows that 500 runs are sufficient. Finally, the expected values and standard deviations of decision variables are tabulated and the distributions of decision variables are plotted. The proposed real time operation model runs once every month. An information-updating scheme is embedded into the simulation and optimization models. For each month, the synthetic streamflows are updated to reflect the most recent hydrological conditions. Besides, the objective function and constraints can be modified if the situation of the system changes.