Microgrids can be distinguished from traditional power systems based on their ability to perform the islanded operation. This study explores the problem of optimizing the microgrid operation in the context of uncertain islanding events. This occurs when the microgrid is isolated from the main grid and it operates as an independent system. A multistage stochastic optimization model that considers multi-occurrence and multi-period islanding events is proposed to optimize the proactive policy. This is achieved by creating parameters for the maximum number of time periods of the islanded operation in the planning horizon. To solve the resulting large-scale mixed-integer program, an efficient algorithm based on the two-stage Benders’ decomposition method is proposed. Numerical experiments show that the proposed policy significantly reduces the expected operation costs of a microgrid. This is more cost-effective in comparison to the other reactive policies that prepare a certain reserve level and reschedule the resources after an islanding event occurs. This study demonstrates that the proposed decomposition algorithm can efficiently solve large-scale problems that have longer planning horizons or a larger number of time periods for the islanded operation.

The large-scale integration of electric vehicles (EVs) into power systems is expected to lead to challenges in the operation of the charging infrastructure. In this paper, we deal with the problem of an aggregator coordinating charging schedules of EVs with the objective of minimizing the total charging cost. In particular, unlike most previous studies, which assumed constant maximum charging power, we assume that the maximum charging power can vary according to the current state of charge (SOC). Under this assumption, we propose two charging schemes, namely non-preemptive and preemptive charging. The difference between these two is whether interruptions during the charging process are allowed or not. We formulate the EV charging-scheduling problem for each scheme and propose a formulation that can prevent frequent interruptions. Our numerical simulations compare different charging schemes and demonstrate that preemptive charging with limited interruptions is an attractive alternative in terms of both cost and practicality. We also show that the proposed formulations can be applied in practice to solve large-scale charging-scheduling problems.

Principal component analysis (PCA) has been a widely used technique for dimension reduction while retaining essential information. However, the ordinary PCA lacks interpretability, especially when dealing with large scale data. To address this limitation, sparse PCA (SPCA) has emerged as an interpretable variant of ordinary PCA. However, the ordinary SPCA relies on solving a challenging non-convex discrete optimization problem, which maximizes explained variance while constraining the number of non-zero elements in each principal component. In this paper, we propose an innovative least angle SPCA technique to address the computational complexity associated with SPCA, particularly in ultrahigh dimensional data, by sequentially identifying sparse principal components with minimal angles to their corresponding components extracted through ordinary PCA. This sequential identification enables solving the optimization problem in polynomial time, significantly reducing computational challenges. Despite its efficiency gains, our proposed method also preserves the main attributes of SPCA. Through comprehensive experimental results, we demonstrate advantages of our approach as a viable alternative for dealing with the computational difficulties inherent in ordinary SPCA. Notably, our method emerges as an efficient and effective solution for conducting ultrahigh dimensional data analysis, enabling researchers to extract meaningful insights and streamline data interpretation.