Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables

Abstract

This paper addresses the real-time energy dispatch of a hybrid system comprising cascaded run-of-the-river hydropower plants, wind, and solar photovoltaic units, operated under uncertainty in water inflows and renewable power generation. Traditional scenario-based stochastic model predictive control (MPC) schemes suffer from severe computational limitations due to the high dimensionality induced by both the temporal and scenario dimensions of the dispatch problem, as well as the inherent nonconvexities associated with cascaded hydropower dynamics. To overcome these challenges, we propose a novel control scheme that seamlessly integrates time series aggregation (TSA), distributed optimization, and stochastic MPC. The resulting temporally aggregated distributed stochastic MPC scheme simultaneously reduces the temporal dimension of the dispatch problem via TSA and decomposes it across scenarios through distributed optimization. Our main theoretical result establishes a formal performance guarantee for the proposed controller, enabling a rigorous quantification of its solution accuracy at every MPC iteration. Numerical results based on a real-world case study show the effectiveness of the proposed controller, achieving up to 74% reduction in computational effort relative to the full-scale centralized counterpart when the required solution accuracy is at least 99%, and up to 85% when the accuracy requirement is relaxed to 95%. Notably, the proposed controller not only significantly enhances computational efficiency relative to the traditional full-scale centralized counterpart, but more importantly restores computational tractability, whereas the traditional controller fails to solve the dispatch problem within the prescribed time limit for computing control actions.