Robust Optimization for Hydroelectric System Operation Under Uncertainty

In this paper,  we propose an optimal dispatch scheme for a cascade hydroelectric power system that maximizes the head levels of each dam, and minimizes the spillage effects taking into account uncertainty in the net load variations, i.e., the difference between the load and the renewable resources, and inflows to the cascade. By maximizing the head levels of each dam the volume of water stored, which is a metric of system resiliency, is maximized. In this regard, the operation of the cascade hydroelectric power system is robust to the variability and intermittency of renewable resources and increases system resilience to variations in climatic conditions. Thus, we demonstrate the benefits of coupling hydroelectric and photovoltaic resources. To this end, we introduce an approximate model for a cascade hydroelectric power system. We then develop correlated probabilistic forecasts for the uncertain output of renewable resources, e.g., solar generation, using historical data based on clustering and Markov chain techniques. We incorporate the generated forecast scenarios in the optimal dispatch of the cascade hydroelectric power system, and define a robust variant of the developed system. However, the robust variant is intractable due to the infinite number of constraints. Using tools from robust optimization, we reformulate the resulting problem in a tractable form that is amenable to existing numerical tools and show that the computed dispatch is immunized against uncertainty. The efficacy of the proposed approach is demonstrated by means of an actual case study involving the Seven Forks system located in Kenya, which consists of five cascaded hydroelectric power systems. With the case study, we demonstrate that the Seven Forks system may be coupled with solar generation since the “price of robustness” is small; thus, demonstrating the benefits of coupling hydroelectric systems with solar generation.