Flexible Decision Variables in Short-term Operation of Reservoirs Using Dimension Reduction Approach

Abstract:

This paper presents a multi-objective optimization model to find flexible decision variables (e.g., turbine flows) in reservoir operation. Flexible decision variables could give the decision maker a range of options instead of single deterministic optimal solutions. In our formulation, each decision variable is modeled by a random variable, and the eventual decision will be but one realization. The optimal probability distribution is found by maximizing the expected value of the objective. Finding flexible decision variables can be computationally intensive especially for multi-reservoir systems. To increase the computational speed of the optimization, a dimension reduction method is used, namely the Karhunen Loe`ve (KL) expansion. KL expansion is closely related to Principal Component Analysis (PCA) and can be used to efficiently represent the random processes by only a few random variables. When using this method, deterministic optimal Pareto solutions are used as the initial population for the optimization. The Grand Coulee reservoir, located in the Columbia River, is used as the test case. The results show that the decision space can be represented with very few random variables and the computational time can therefore be drastically reduced.