Multistage Decision-Making Under Uncertainty with Applications in Operations of Hybrid Power Systems

Abstract

Multistage optimization is a powerful technique that is employed to address sequential decision-making problems under uncertainty. It allows decision-makers to progressive observe the historical uncertain parameters and adaptively make decisions. In this dissertation, we study the theories and applications of multistage optimizations on hybrid power systems operations. The major objective is to develop novel multistage optimization approaches to address the uncertainties of renewable energy in the short, mid and long-term operations of the power systems with large-scale penetration of wind, solar, and hydro power. First, we adopt multistage stochastic optimization to study the mid-term integrated generation and maintenance scheduling of hybrid power systems. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of cascaded hydroelectric systems. We also develop a tailored Benders decomposition algorithm equipped with several algorithmic enhancement strategies to address large-scale cases. Second, we adopt multistage robust optimization to study the day-ahead operations of hybrid power systems with renewable energy uncertainty. We explore how the operational flexibility of hydroelectricity and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under the sequential decision-making framework modeled by multistage robust optimization. A novel solution approach combing mixed decision rules and enhanced column-and-constraint generation algorithm is developed to solve the multi-level multistage robust optimization model. Third, a data-driven hybrid stochastic-robust optimization approach is developed for multistage decision-making with temporally correlated uncertainty. Discrete-time autoregressive stochastic process is employed to model the random vectors over the planning horizon, which enables us to make inference on the future uncertain parameters based on the historical data. A hybrid stochastic-robust optimization model is proposed, which requires that the solution must be feasible under any realization of random vectors in the confidence region. We propose a novel sequential decision-making framework based on this hybrid stochastic-robust optimization model. We also develop efficient constraint generation algorithm to explicitly derive the robust feasible region of the proposed model. The data-driven hybrid stochastic-robust optimization approach is tested in the economic dispatch problems of power systems to demonstrate its capability and characteristics.