Michael Chertkov

Bio: Michael Chertkov is an academic researcher from University of Arizona. The author has contributed to research in topics: Belief propagation & AC power. The author has an hindex of 50, co-authored 394 publications receiving 10829 citations. Previous affiliations of Michael Chertkov include Tel Aviv University & Skolkovo Institute of Science and Technology.

Synchronization in complex oscillator networks and smart grids

Abstract: The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.

Options for Control of Reactive Power by Distributed Photovoltaic Generators

Abstract: High-penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit present several challenges and opportunities for distribution utilities. Rapidly varying irradiance conditions may cause voltage sags and swells that cannot be compensated by slowly responding utility equipment resulting in a degradation of power quality. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g., by minimizing thermal losses. We discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters. An important design decision that weighs on the speed and quality of communication required is whether the control should be centralized or distributed (i.e., local). In general, we find that local control schemes are able to maintain voltage within acceptable bounds. We consider the benefits of choosing different local variables on which to control and how the control system can be continuously tuned between robust voltage control, suitable for daytime operation when circuit conditions can change rapidly, and loss minimization better suited for nighttime operation.

Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty ∗

Abstract: When uncontrollable resources fluctuate, optimal power flow (OPF), routinely used by the electric power industry to redispatch hourly controllable generation (coal, gas, and hydro plants) over control areas of transmission networks, can result in grid instability and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by our simulations of real grids, is considered undesirable in power engineering practice. Possibly, it can lead to a risky outcome that compromises grid stability---line tripping. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our chance-constrained (CC) OPF co...

Options for Control of Reactive Power by Distributed Photovoltaic Generators

Abstract: High penetration levels of distributed photovoltaic(PV) generation on an electrical distribution circuit present several challenges and opportunities for distribution utilities. Rapidly varying irradiance conditions may cause voltage sags and swells that cannot be compensated by slowly responding utility equipment resulting in a degradation of power quality. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g. by minimizing thermal losses. We discuss and compare via simulation various design options for control systems to manage the reactive power generated by these inverters. An important design decision that weighs on the speed and quality of communication required is whether the control should be centralized or distributed (i.e. local). In general, we find that local control schemes are capable for maintaining voltage within acceptable bounds. We consider the benefits of choosing different local variables on which to control and how the control system can be continuously tuned between robust voltage control, suitable for daytime operation when circuit conditions can change rapidly, and loss minimization better suited for nighttime operation.

Optimal Distributed Control of Reactive Power Via the Alternating Direction Method of Multipliers

Abstract: We formulate the control of reactive power generation by photovoltaic inverters in a power distribution circuit as a constrained optimization that aims to minimize power losses subject to finite inverter capacity and upper and lower voltage limits at all nodes in the circuit. When voltage variations along the circuit are small and losses of both real and reactive powers are small compared with the respective flows, the resulting optimization problem is convex. Moreover, the cost function is separable enabling a distributed online implementation with node-local computations using only local measurements augmented with limited information from the neighboring nodes communicated over cyber channels. Such an approach lies between the fully centralized and local policy approaches previously considered. We explore protocols based on the dual-ascent method and on the alternating direction method of multipliers (ADMMs), and find that the ADMM protocol performs significantly better.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Graphical Models, Exponential Families, and Variational Inference

Abstract: The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

Stochastic Processes in Physics and Chemistry

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects