arXiv:1708.03981v1 [cs.SY] 14 Aug 2017
PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches Vassilis Kekatos, Gang Wang, Hao Zhu, and Georgios B. Giannakis
∗
August 15, 2017
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Introduction
With the advent of digital computers, power system engineers in the 1960s tried computing the voltages at critical buses based on readings from current and potential transformers. Local personnel manually collected these readings and forwarded them by phone to a control center. Nevertheless, due to timing, modeling, and instrumentation inaccuracies, the power flow equations were always infeasible. In a seminal contribution [61], the statistical foundations were laid for a multitude of grid monitoring tasks, including topology detection, static state estimation, exact and linearized models, bad data analysis, centralized and decentralized implementations, as well as dynamic state tracking. Since then, different chapters, books, and review articles have nicely outlined the progress in the area; see for example [74, 55, 1]. The revolutionary monitoring capabilities enabled by synchrophasor units have been put forth in [58]. This chapter aspires to glean some of the recent advances in power system state estimation (PSSE), though our collection is not exhaustive by any means. The Cram´er-Rao bound, a lower bound on the (co)variance ∗
V. Kekatos is with the Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, USA. G. Wang is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA, and also with the State Key Lab of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology, Beijing 100081, P. R. China. H. Zhu is with the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801. G. B. Giannakis is with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA. E-mails:
[email protected]; {gangwang, georgios}@umn.edu;
[email protected].
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of any unbiased estimator, is first derived for the PSSE setup. After reviewing the classical Gauss-Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. A disciplined paradigm for distributed and decentralized schemes is subsequently exemplified under linear(ized) and exact grid models. Novel bad data processing models and fresh perspectives linking critical measurements to cyber-attacks on the state estimator are presented. Finally, spurred by advances in online convex optimization, model-free and model-based state trackers are reviewed. Notation: Lower- (upper-) case boldface letters denote column vectors (matrices), and calligraphic letters stand for sets. Vectors 0, 1, and en denote respectively the all-zero, all-one, and the n-th canonical vectors of suitable dimensions. The conjugate of a complex-valued object (scalar, vector or matrix) x is √ denoted by x∗ ;
