arXiv subjects

Xingyu Lei

Publications and source records attributed to Xingyu Lei.

4 recordsLinked to original sources

arXiv2024

Spectral extremal results on the $A_α$-spectral radius of graphs without $K_{a,b}$-minor

An important theorem about the spectral Turán problem of $K_{a,b}$ was largely developed in separate papers. Recently it was completely resolved by Zhai and Lin [J. Comb. Theory, Ser. B 157 (2022) 184-215], which also confirms a conjecture proposed by Tait [J. Comb. Theory, Ser. A 166 (2019) 42-58]. Here, the prior work is fully stated, and then generalized with a self-contained proof. The more complete result is then used to better understand the relationship between the $A_α$-spectral radius and the structure of the corresponding extremal $K_{a,b}$-minor free graph.

math.CO↗

arXiv2021

On graphs with exactly one anti-adjacency eigenvalue and beyond

The anti-adjacency matrix of a graph is constructed from the distance matrix of a graph by keeping each row and each column only the largest distances. This matrix can be interpreted as the opposite of the adjacency matrix, which is instead constructed from the distance matrix of a graph by keeping in each row and each column only the distances equal to 1. The (anti-)adjacency eigenvalues of a graph are those of its (anti-)adjacency matrix. Employing a novel technique introduced by Haemers [Spectral characterization of mixed extensions of small graphs, Discrete Math. 342 (2019) 2760--2764], we characterize all connected graphs with exactly one positive anti-adjacency eigenvalue, which is an analog of Smith's classical result that a connected graph with exactly one positive adjacency eigenvalue iff it is a complete multipartite graph. On this basis, we identify the connected graphs with all but at most two anti-adjacency eigenvalues equal to $-2$ and $0$. Moreover, for the anti-adjacency matrix we determine the HL-index of graphs with exactly one positive anti-adjacency eigenvalue, where the HL-index measures how large in absolute value may be the median eigenvalues of a graph. We finally propose some problems for further study.

math.CO↗

arXiv2020

Data-Driven Assisted Chance-Constrained Energy and Reserve Scheduling with Wind Curtailment

Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes possible to consider the wind curtailment as a dispatch variable in CCO. However, the wind curtailment will cause impulse for the uncertainty distribution, yielding challenges for the chance constraints modeling. To deal with that, a data-driven framework is developed. By modeling the wind curtailment as a cap enforced on the wind power output, the proposed framework constructs a Gaussian process (GP) surrogate to describe the relationship between wind curtailment and the chance constraints. This allows us to reformulate the CCO with wind curtailment as a mixed-integer second-order cone programming (MI-SOCP) problem. An error correction strategy is developed by solving a convex linear programming (LP) to improve the modeling accuracy. Case studies performed on the PJM 5-bus and IEEE 118-bus systems demonstrate that the proposed method is capable of accurately accounting the influence of wind curtailment dispatch in CCO.

eess.SY↗

arXiv2020

Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach

This paper proposes a data-driven approach for optimal power flow (OPF) based on the stacked extreme learning machine (SELM) framework. SELM has a fast training speed and does not require the time-consuming parameter tuning process compared with the deep learning algorithms. However, the direct application of SELM for OPF is not tractable due to the complicated relationship between the system operating status and the OPF solutions. To this end, a data-driven OPF regression framework is developed that decomposes the OPF model features into three stages. This not only reduces the learning complexity but also helps correct the learning bias. A sample pre-classification strategy based on active constraint identification is also developed to achieve enhanced feature attractions. Numerical results carried out on IEEE and Polish benchmark systems demonstrate that the proposed method outperforms other alternatives. It is also shown that the proposed method can be easily extended to address different test systems by adjusting only a few hyperparameters.

eess.SY↗