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Graph partitioning, Linear programming, Quadratic programming, Bipartite graph partitioning,

A growing number of companies install wind and solar generators in their energy‐intensive facilities to attain low‐carbon manufacturing operations. However, there is a lack of methodological studies on operating large manufacturing facilities with intermittent power. This study presents a multi‐period, production‐inventory planning model in a multi‐plant manufacturing system powered with onsite and grid renewable energy. Our goal is to determine the production quantity, the stock level, and the renewable energy supply in each period such that the aggregate production cost (including energy) is minimized. We tackle this complex decision problem in three steps. First, we present a deterministic planning model to attain the desired green energy penetration level. Next, the deterministic model is extended to a multistage stochastic optimization model taking into account the uncertainties of renewables. Finally, we develop an efficient modified Benders decomposition algorithm to search for the optimal production schedule using a scenario tree. Numerical experiments are carried out to verify and validate the model integrity, and the potential of realizing high‐level renewables penetration in large manufacturing system is discussed and justified.

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We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-ε reliability criterion. This reliability criterion is a generalization of the wellknown N-k criterion, and dictates that at least (1 − ε j ) fraction of the total system demand must be met following the failures of k or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.