Understanding the Inefficiency of Security-Constrained Economic Dispatch

The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks

Learning the LMP-Load Coupling From Data: A Support Vector Machine Based Approach

This paper investigates the fundamental coupling between loads and locational marginal prices (LMPs) in security-constrained economic dispatch (SCED). Theoretical analysis based on multi-parametric programming theory points out the unique one-to-one mapping between load and LMP vectors. Such one-to-one mapping is depicted by the concept of system pattern region (SPR) and identifying SPRs is the key to understanding the LMP-load coupling. Built upon the characteristics of SPRs, the SPR identification problem is modeled as a classification problem from a market participant's viewpoint, and a Support Vector Machine based data-driven approach is proposed. It is shown that even without the knowledge of system topology and parameters, the SPRs can be estimated by learning from historical load and price data. Visualization and illustration of the proposed data-driven approach are performed on a 3-bus system as well as the IEEE 118-bus system

Single case experimental designs: Introduction to a special Issue of Neuropsychological Rehabilitation

This paper introduces the Special Issue of Neuropsychological Rehabilitation on Single Case Experimental Design (SCED) methodology. SCED studies have a long history of use in evaluating behavioural and psychological interventions, but in recent years there has been a resurgence of interest in SCED methodology, driven in part by the development of standards for conducting and reporting SCED studies. Although there is consensus on some aspects of SCED methodology, the question of how SCED data should be analysed remains unresolved. This Special Issues includes two papers discussing aspects of conducting SCED studies, five papers illustrating use of SCED methodology in clinical practice, and nine papers that present different methods of SCED data analysis. A final Discussion paper summarises points of agreement, highlights areas where further clarity is needed, and ends with a set of resources that will assist researchers conduct and analyse SCED studies

Single-case experimental designs: Reflections on conduct and analysis

In this editorial discussion we reflect on the issues addressed by, and arising from, the papers in this Special Issue on Single Case Experimental Design (SCED) study methodology. We identify areas of consensus and disagreement regarding the conduct and analysis of SCED studies. Despite the long history of application of SCEDs in studies of interventions in clinical and educational settings, the field is still developing. There is an emerging consensus on methodological quality criteria for many aspects of SCEDs, but disagreement on what are the most appropriate methods of SCED data analysis. Our aim is to stimulate this ongoing debate and highlight issues requiring further attention from applied researchers and methodologists. In addition we offer tentative criteria to support decision making in relation to selection of analytical techniques in SCED studies. Finally, we stress that large-scale interdisciplinary collaborations, such as the current Special Issue, are necessary if SCEDs are going to play a significant role in the development of the evidence base for clinical practice