Real-time Optimization of a Hydropower Cascade Using a Linear Modeling Approach

For the sub-hourly real-time optimization of a hydropower cascade, it is important to model in detail the three factors which most heavily influence hydropower generation: reservoir elevation, tailrace elevation, and turbine-generator efficiency. The method proposed in this paper uses three-dimensional piecewise linearization to accurately approximate the nonlinear and non-convex hydropower production function as a function of hydraulic head and turbine discharge. We show how this piecewise linear approximation can be implemented in a model predictive control framework with promising results. We present a case study of this model applied to seven dams along the Columbia River in the United States, with a particular focus on simulating the integration of variable wind generation. The primary contribution of this paper is to introduce a new method to model power generation from hydropower facilities and to simulate and demonstrate its efficacy on a real-world system.