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

Rigidity of fiber-preserving quasisymmetric maps

We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that quasisymmetric maps on Carnot groups with reducible first stratum are biLipschitz

False Analog Data Injection Attack Towards Topology Errors: Formulation and Feasibility Analysis

In this paper, we propose a class of false analog data injection attack that can misguide the system as if topology errors had occurred. By utilizing the measurement redundancy with respect to the state variables, the adversary who knows the system configuration is shown to be capable of computing the corresponding measurement value with the intentionally misguided topology. The attack is designed such that the state as well as residue distribution after state estimation will converge to those in the system with a topology error. It is shown that the attack can be launched even if the attacker is constrained to some specific meters. The attack is detrimental to the system since manipulation of analog data will lead to a forged digital topology status, and the state after the error is identified and modified will be significantly biased with the intended wrong topology. The feasibility of the proposed attack is demonstrated with an IEEE 14-bus system.Comment: 5 pages, 7 figures, Proc. of 2018 IEEE Power and Energy Society General Meetin

Nonparametric Estimation of Multi-View Latent Variable Models

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to mixtures of discrete or Gaussian distributions. In this paper, we propose a kernel method for learning multi-view latent variable models, allowing each mixture component to be nonparametric. The key idea of the method is to embed the joint distribution of a multi-view latent variable into a reproducing kernel Hilbert space, and then the latent parameters are recovered using a robust tensor power method. We establish that the sample complexity for the proposed method is quadratic in the number of latent components and is a low order polynomial in the other relevant parameters. Thus, our non-parametric tensor approach to learning latent variable models enjoys good sample and computational efficiencies. Moreover, the non-parametric tensor power method compares favorably to EM algorithm and other existing spectral algorithms in our experiments