A Weak-Consistency–Oriented Collaborative Strategy for Large-Scale Distributed Demand Response

Large-scale distributed demand response is a hotspot in the development of power systems, which is of much significance in accelerating the consumption of new energy power generation and the process of clean energy substitution. However, the rigorous distributed algorithms utilized in current research studies are mostly very complicated for the large-scale demand response, requiring high quality of information systems. Considering the electrical features of power systems, a weak-consistency–oriented collaborative strategy is proposed for the practical implementation of the large-scale distributed demand response in this study. First, the basic conditions and objectives of demand response are explored from the view of system operators, and the challenges of large-scale demand response are discussed and furthermore modelled with a simplification based on the power system characteristics, including uncertainties and fluctuations. Then, a weakly consistent distributed strategy for demand response is proposed based on the Paxos distributed algorithm, where the information transmission is redesigned based on the electrical features to achieve better error tolerance. Using case studies with different information transmission error rates and other conditions, the proposed strategy is demonstrated to be an effective solution for the large-scale distributed demand response implementation, with a robust response capability under even remarkable transmission errors. By integrating the proposed strategy, the requirement for the large-scale distributed systems, especially the information systems, is highly eased, leading to the acceleration of the practical demand response implementation.

Higher-Order Spectral Clustering for Geometric Graphs

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated with a higher-order eigenvalue. We establish the weak consistency of this algorithm for a wide class of geometric graphs which we call Soft Geometric Block Model. A small adjustment of the algorithm provides strong consistency. We also show that our method is effective in numerical experiments even for graphs of modest size.

On Variable Precision Generalized Rough Sets and Incomplete Decision Tables

We present variable precision generalized rough set approach to characterize incomplete decision tables. We show how to determine the discernibility threshold for a reflexive relational decision system in the variable precision generalized rough set model. We also point out some properties of positive regions and prove a statement of the necessary condition for weak consistency of an incomplete decision table. We present two examples to illustrate the results obtained in this paper.