To capture the stochastic characteristics of renewable energy generation output, the chance-constrained unit commitment (CCUC) model is widely used. Conventionally, analytical solution for CCUC is usually based on simplified probability assumption or neglecting some operational constraints, otherwise scenar-io-based methods are used to approximate probability with heavy computation burden. In this paper, Gaussian mixture model (GMM) is employed to characterize the correlation between wind farms and probability distribution of their forecast errors. In our model, chance constraints including reserve sufficiency and branch power flow bounds are ensured to be satisfied with predetermined probability. To solve this CCUC problem, we propose a Newton method based procedure to acquire the quan-tiles and transform chance constraints into deterministic con-straints. Therefore, the CCUC model is efficiently solved as a mixed-integer quadratic programming problem. Numerical tests are performed on several systems to illustrate efficiency and scalability of the proposed method.

The integration of large-scale renewable distributed generation (DG) units in distribution networks brings new challenges for real-time power dispatch, including active power & reactive power (P-Q) coupling and operational uncertainties. To reduce the conservativeness of robust optimization (RO) solutions, this paper proposes a distributionally robust real-time power dispatch model, which characterizes the uncertainty of DG output with the information of first-order and second-order moments. Furthermore, a two-stage scheme, which includes economic dispatch (ED) and corrective control (CC), is incorporated in the model, in which ED optimizes the active power schedule and corrective control strategies of P-Q are generated to eliminate overvoltage problems. The proposed model can be transformed into an equivalent semidefinite programming (SDP) problem and solved via the delayed constraint generation algorithm. Numerical test results show that the proposed model reduces operational costs and mitigates overvoltage problems significantly compared with the conventional one-stage model. The proposed model also outperforms the conventional RO model by exploiting probability information to achieve statistically optimal dispatch.

Chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality solution.

Background: Epilepsy and Alzheimer's disease are common neuropathies with a complex pathogenesis. Both of them have some correlations in etiology, pathogenesis, pathological changes, clinical manifestations and treatment. Objective: This study investigated the key genes and molecular genetic mechanism in epilepsy and Alzheimer’s disease by bioinformatics analysis. Method: Two gene expression profiles were used to screen differentially expressed genes by GEO2R tool. The Gene Ontology (GO) and Kyoto Encyclopedia of Gene and Genome (KEGG) pathway enrichment analysis was performed using the Database for Annotation, Visualization and Integrated Discovery (DAVID). Then the protein-protein interaction (PPI) network was constructed by Search Tool for the Retrieval of Interacting Genes (STRING) and Cytoscape software which can be used to analyze modules with MCODE. Results: A total of 199 differentially expressed genes (DEGs) in the two groups. According to GO_BP analysis and KEGG pathway enrichment by DAVID, we found DEGs referring to several pathways significantly down-regulated in endocytosis, such as endocytosis, synaptic vesicle cycle, lysosome, cAMP signaling pathway, circadian entrainment, LTP, glutamatergic synapse and GABAergic synapse pathway. The regulator genes of the upstream pathway of circadian rhythms were obviously downgraded. Conclusion: Our research demonstrated that the regulatory genes of the upstream pathway of circadian rhythms were obviously downgraded. These biological pathways and DEGs or hub genes may contribute to revealing the molecular relationship between Alzheimer's disease and epilepsy.

The increasing penetration of distributed energy resources into active distribution networks (ADNs) has made effective ADN dispatch imperative. However, the numerous newly-integrated ADN operators, such as distribution system aggregators, virtual power plant managers, and end prosumers, often lack specialized expertise in power system operation, modeling, optimization, and programming. This knowledge gap renders reliance on human experts both costly and time-intensive. To address this challenge and enable intelligent, flexible ADN dispatch, this paper proposes a large language model (LLM) powered automated modeling and optimization approach. First, the ADN dispatch problems are decomposed into sequential stages, and a multi-LLM coordination architecture is designed. This framework comprises an Information Extractor, a Problem Formulator, and a Code Programmer, tasked with information retrieval, optimization problem formulation, and code implementation, respectively. Afterwards, tailored refinement techniques are developed for each LLM agent, greatly improving the accuracy and reliability of generated content. The proposed approach features a user-centric interface that enables ADN operators to derive dispatch strategies via simple natural language queries, eliminating technical barriers and increasing efficiency. Comprehensive comparisons and end-to-end demonstrations on various test cases validate the effectiveness of the proposed architecture and methods.

With numerous distributed energy resources (DERs) integrated into the distribution networks (DNs), the coordinated economic dispatch (C-ED) is essential for the integrated transmission and distribution grids. For large scale power grids, the centralized C-ED meets high computational burden and information privacy issues. To tackle these issues, this paper proposes a spatio-temporal decomposition algorithm to solve the C-ED in a distributed and parallel manner. In the temporal dimension, the multi-period economic dispatch (ED) of transmission grid (TG) is decomposed to several subproblems by introducing auxiliary variables and overlapping time intervals to deal with the temporal coupling constraints. Besides, an accelerated alternative direction method of multipliers (A-ADMM) based temporal decomposition algorithm with a good initialization strategy, is developed to solve the ED subproblems of TG in parallel. In the spatial dimension, a multi-parametric programming projection based spatial decomposition algorithm is developed to coordinate the ED problems of TG and DNs in a distributed manner. To further improve the convergence performance of the spatial decomposition algorithm, the aggregate equivalence approach is used for determining the feasible range of boundary variables of TG and DNs. Moreover, we prove that the proposed spatio-temporal decomposition method can obtain the optimal solution for bilevel convex optimization problems with continuously differentiable objectives and constraints. Numerical tests are conducted on three systems with different scales, demonstrating the high computational efficiency and scalability of the proposed spatio-temporal decomposition method.