Multistage adaptive robust optimization for the hydrothermal scheduling problem

The current water scarcity faced by many countries increases the need to consider an appropriate representation of future hydro inflows in power system operation and planning models. Hydrothermal scheduling is the problem that seeks to use the water stored in reservoirs throughout time in order to find an optimal dispatch policy between hydro and thermal power plants. Due to both the inherent randomness of water inflows and the intertemporal decision process, this problem has been typically approached through multistage stochastic optimization, minimizing the total expected operational cost over the entire planning horizon. However, this approach has some practical disadvantages. Among the main ones we highlight (i) the complexity of balancing the statistical representativeness of the stochastic processes and the computational efficiency of the optimization model; (ii) the need to employ computationally intensive decomposition methods for its solvability; and (iii) the need to carry out network simplifications to tackle tractability issues arising in large networks. As an alternative, we propose a multistage adaptive robust optimization model for the hydrothermal scheduling problem. Robust optimization is useful to prevent the previous disadvantages because it does not make any distributional assumption and it works with the so-called uncertainty sets instead of carrying out sampling processes. In particular, we propose an efficient formulation based on linear decision rules and vector autoregressive models to represent the uncertainty in hydro inflows. Our experiments, based on the Chilean electric power system with hundreds of hydro nodes and connections, show the proposed model's efficiency for large-scale systems and provide insights into the adequate balance between cost-effectiveness and reliability that robust optimization models guarantee.