Reduced-Order Decomposition and Coordination Approach for Markov-Based Stochastic Unit Commitment With Distributed Wind Farms

States in the US increasingly integrate renewable energies to facilitate the transition to carbon neutrality. However, there are still many operational challenges to their efficient integration. This paper presents an innovative approach to solve the day-ahead Markov-based stochastic unit commitment (MSUC) problem with distributed wind generation. The MSUC utilizes a Markovian uncertainty set to represent the uncertainties in wind and other distributed intermittent renewable energies. While the Markovian uncertainty set intricately captures the stochasticity via states and state transitions, the set grows exponentially under the multi-dimensional uncertainties of distributed intermittent resources, thus rendering the MSUC intractable for systems with five or more such resources. In order to reduce the MSUC’s complexity, the problem is decomposed into approximate area problems (AAP), where each AAP utilizes a reduced, area-centric uncertainty set created using principal component analysis. Furthermore, the AAPs consider the binary commitment variables of only the local units, thus rendering much reduced complexity than the original MSUC. The AAPs are iteratively solved, and their solutions are coordinated in a novel Surrogate Absolute-Value Lagrangian Relaxation-based framework. Numerical testing is performed on test cases based on the IEEE 118-bus system with up to ten distributed wind farms, and solutions are validated via Monte Carlo simulations with typical and extreme wind generation scenarios. The simulation results demonstrate the ability of our method to obtain robust and cost-effective solutions to the MSUC in a constrained time frame.