State Estimation for the Individual and the Population in Mean Field Control with Application to Demand Dispatch

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it has been shown that local control can be carefully designed so that the aggregate of loads behaves as a controllable resource with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements,Comment: To appear, IEEE Trans. Auto. Control. Preliminary version appeared in the 54rd IEEE Conference on Decision and Control, 201

Comparing Kalman Filters and Observers for Power System Dynamic State Estimation with Model Uncertainty and Malicious Cyber Attacks

Kalman filters and observers are two main classes of dynamic state estimation (DSE) routines. Power system DSE has been implemented by various Kalman filters, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). In this paper, we discuss two challenges for an effective power system DSE: (a) model uncertainty and (b) potential cyber attacks. To address this, the cubature Kalman filter (CKF) and a nonlinear observer are introduced and implemented. Various Kalman filters and the observer are then tested on the 16-machine, 68-bus system given realistic scenarios under model uncertainty and different types of cyber attacks against synchrophasor measurements. It is shown that CKF and the observer are more robust to model uncertainty and cyber attacks than their counterparts. Based on the tests, a thorough qualitative comparison is also performed for Kalman filter routines and observers.Comment: arXiv admin note: text overlap with arXiv:1508.0725

Inverse Problems and Data Assimilation

These notes are designed with the aim of providing a clear and concise introduction to the subjects of Inverse Problems and Data Assimilation, and their inter-relations, together with citations to some relevant literature in this area. The first half of the notes is dedicated to studying the Bayesian framework for inverse problems. Techniques such as importance sampling and Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the desirable property that in the limit of an infinite number of samples they reproduce the full posterior distribution. Since it is often computationally intensive to implement these methods, especially in high dimensional problems, approximate techniques such as approximating the posterior by a Dirac or a Gaussian distribution are discussed. The second half of the notes cover data assimilation. This refers to a particular class of inverse problems in which the unknown parameter is the initial condition of a dynamical system, and in the stochastic dynamics case the subsequent states of the system, and the data comprises partial and noisy observations of that (possibly stochastic) dynamical system. We will also demonstrate that methods developed in data assimilation may be employed to study generic inverse problems, by introducing an artificial time to generate a sequence of probability measures interpolating from the prior to the posterior

Graphical Convolution Network Based Semi-Supervised Methods for Detecting PMU Data Manipulation Attacks

With the integration of information and communications technologies (ICTs) into the power grid, electricity infrastructures are gradually transformed towards smart grid and power systems become more open to and accessible from outside networks. With ubiquitous sensors, computers and communication networks, modern power systems have become complicated cyber-physical systems. The cyber security issues and the impact of potential attacks on the smart grid have become an important issue. Among these attacks, false data injection attack (FDIA) becomes a growing concern because of its varied types and impacts. Several detection algorithms have been developed in the last few years, which were model-based, trajectory prediction-based or learning-based methods. Phasor measurement units (PMUs) and supervisory control and data acquisition (SCADA) system work together to monitor the power system operation. The unsecured devices could offer opportunities to adversaries to compromise the system. In the literature review part of this thesis, the main methods are compared considering computing accuracy and complexity. Most work about PMUs ignored the reality that the number of PMUs installed in a power system is limited to realize observability because of high installing cost. Therefore, based on observable truth of PMU and the topology structure of power system, the graph convolution network (GCN) is proposed in this thesis. The main idea is using selected features to define violated PMU, and GCN is used to classify susceptible violated nodes and normal nodes. The basic detection method is introduced at first. And then the calculation process of neural network and Fourier transform are described with more details about graph convolution network. Later, the proposed detection mechanism and algorithm are introduced. Finally, the simulation results are given and analyzed

Directional statistics and filtering using libDirectional

In this paper, we present libDirectional, a MATLAB library for directional statistics and directional estimation. It supports a variety of commonly used distributions on the unit circle, such as the von Mises, wrapped normal, and wrapped Cauchy distributions. Furthermore, various distributions on higher-dimensional manifolds such as the unit hypersphere and the hypertorus are available. Based on these distributions, several recursive filtering algorithms in libDirectional allow estimation on these manifolds. The functionality is implemented in a clear, well-documented, and object-oriented structure that is both easy to use and easy to extend