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Novel insights into lossless AC and DC power flow

Novel insights into lossless AC and DC power flow

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IEEE General Meeting Power& Energy Society

作者： Florian Dörfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA

A central question in the analysis and operation of power networks is feasibility of the power flow equations subject to security constraints. For large-scale networks the solution of the nonlinear AC power flow equations can be constructed only numerically or approximated through the linear DC power flow. The latter serves as well-used approximation to obtain the phase angle differences near an acceptable operating point, but the accuracy of the DC approximation drops in a stressed grid. Here, we propose a modified DC approximation that applies to lossless networks with parametric uncertainties and with voltage magnitudes bounded within security constraints. We show that the phase angle differences can be well approximated by the solution to a set of linear and interval-valued equations reminiscent of the DC power flow equations. Our proposed approximation improves upon the standard DC approximation, is computationally attractive and provably exact for a broad range of network topologies and parameters. We validate the accuracy of our approximation through standard power network test cases with randomized power demand at the loads.

关键词： Approximation methods Equations Mathematical model Accuracy Standards Power system stability Reactive power

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Direct Numerical Solution of Algebraic Lyapunov Equations For Large-Scale systems Using Quantized Tensor Trains

Direct Numerical Solution of Algebraic Lyapunov Equations Fo...

引用

IEEE Annual Conference on Decision and control

作者： Michael Nip Joao P. Hespanha Mustafa Khammash Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Center for Control Dynamical Systems and Computation University of California Santa Barbara California USA 93106 Department of Biosystems Science and Engineering ETH-Zurich 4058 Basel Switzerland

ISBN: (纸本)9781467357159

We present a novel method for solving high-dimensional algebraic Lyapunov equations exploiting the recently proposed Quantized Tensor Train (QTT) numerical linear algebra. A key feature of the approach is that given a prescribed error tolerance, it automatically calculates the optimal lowest rank approximation of the solution in the Frobenius norm. The low rank nature of the approximation potentially enables a sublinear scaling of the computational complexity with the number of states of the dynamical system. The resulting solutions appear in a new matrix tensor format which we call the Vectorized-QTT-Matrix format. We show the effectiveness of our method by calculating the controllability Gramians for discretized reaction-diffusion equations. We introduce an algorithm for the new tensor format of the solution for calculating the matrix-by-vector product and combine it with the celebrated Lanczos algorithm to compute the dominant eigenvalues/eigenvectors of the matrix.

关键词： large-scale systems Tensor TRAIN Algebra NUMERICAL SOLUTION

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On the Dynamics of Influence Networks via Reflected Appraisal

On the Dynamics of Influence Networks via Reflected Appraisa...

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American control Conference

作者： Peng Jia Anahita Mirtabatabaei Noah E. Friedkin Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Department of Sociology University of California at Santa Barbara

ISBN: (纸本)9781479901777

In any modern society, individuals interact to form opinions on various topics, including economic, political, and social aspects. Opinions evolve as the result of the continuous exchange of information among individuals where interpersonal influences play the key role. The study of influence network evolution has wide applications in the field of social organization and social psychology. A compelling model is Friedkin's reflected appraisal model where each individual's self-appraisal is set equal to the relative control and power that the agent exerted over prior issue outcomes. Motivated by this empirical framework, we (i) present a rigorous mathematical formulation of the reflected appraisal influence network dynamics, (ii) study the equilibria and the convergence properties of the dynamical influence systems, and (iii) construct the social conditions leading to the emergence of single opinion leaders, clusters of leaders, or diffuse and democratic power structures. In particular, an appropriately-defined eigenvector centrality of the influence network is proved to determine each individual's social power and self-appraisal evolution, and then determine the opinion formulation of the whole network.

关键词： Dynamics continuous emergence

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Voltage Stabilization in Microgrids via Quadratic Droop control

Voltage Stabilization in Microgrids via Quadratic Droop Cont...

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IEEE Annual Conference on Decision and control

作者： John W. Simpson-Porco Florian Dorfler Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Department of Electrical Engineering University of California Los Angeles

ISBN: (纸本)9781467357159

Motivated by the growing interest in energy technology and smart grid architectures, we consider the problem of voltage stability and reactive power balancing in low-voltage electrical networks equipped with DC/AC inverters ("microgrids"). It is generally believed that high-voltage equilibria of such networks are stable, but the locations of these equilibria are unknown, as is the critical network load where stability is lost. Inspired by the "control by interconnection" paradigm developed for port-Hamiltonian systems, we propose a novel droop-like inverter controller which is quadratic in the local voltage magnitude. Remarkably, under this controller the closed-loop network is again a well-posed electrical circuit. We find that the equilibria of the quadratic droop-controlled network are in exact correspondence with the solutions of a reduced power flow equation. For general network topologies, we study some simple yet insightful solutions of this equation, and for the frequently-encountered case of a parallel microgrid, we present a concise and closed-form condition for the existence of an exponentially stable high-voltage network equilibrium. Our condition establishes the existence of a critical inductive load for the network, which depends only on the network topology, admittances, and controller gains. We compare and contrast our design with the conventional droop controller, investigate the relationship between the two, and validate the robustness of our design through simulation.

关键词： Inverters Microgrids Equations Voltage control Mathematical model Vectors Reactive power

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Randomized sampling for large zero-sum games

Randomized sampling for large zero-sum games

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作者： Bopardikar, Shaunak D. Borri, Alessandro Hespanha, João P. Prandini, Maria Di Benedetto, Maria D. United Technologies Research Center Inc. Berkeley CA United States Rome Italy Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106 United States Dipartimento di Elettronica Informazione e Bioingegneria Politecnico di Milano Italy Department of Electrical and Information Engineering University of l'Aquila Italy

This paper addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure, termed as the sampled security policy (SSP) algorithm, by which a player can compute policies that, with a high confidence, are security policies against an adversary using randomized methods to explore the possible outcomes of the game. The SSP algorithm essentially consists of solving a stochastically sampled subgame that is much smaller than the original game. We also propose a randomized algorithm, termed as the sampled security value (SSV) algorithm, which computes a high-confidence security-level (i.e., worst-case outcome) for a given policy, which may or may not have been obtained using the SSP algorithm. For both the SSP and the SSV algorithms we provide results to determine how many samples are needed to guarantee a desired level of confidence. We start by providing results when the two players sample policies with the same distribution and subsequently extend these results to the case of mismatched distributions. We demonstrate the usefulness of these results in a hide-and-seek game that exhibits exponential complexity. © 2013 Elsevier Ltd. All rights reserved.

关键词： Game theory

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Stability, power sharing, & distributed secondary control in droop-controlled microgrids

Stability, power sharing, & distributed secondary control in...

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IEEE International Conference on Smart Grid Communications (SmartGridComm)

作者： John W. Simpson-Porco Florian Dörfler Francesco Bullo Qobad Shafiee Josep M. Guerrero Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara California Institute of Energy Technology Aalborg University Aalborg East Denmark

Motivated by the recent and growing interest in microgrids, we study the operation of droop-controlled DC/AC inverters in an islanded inductive microgrid. We present a necessary and sufficient condition for the existence of a synchronized steady state that is unique and locally exponentially stable. We discuss a selection of controller gains which leads to a sharing of power among the generators, and show that this proportional selection enforces actuation constraints for the inverters. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Finally, we present experimental results validating our controller design, along with simulations of extended scenarios. Our results hold without assumptions on uniform line admittances, inverter power ratings, or voltage magnitudes.

关键词： Inverters Frequency control Microgrids Steady-state Voltage control Synchronization Power system stability

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Finite-Field Consensus

Finite-Field Consensus

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IEEE Annual Conference on Decision and control

作者： Fabio Pasqualetti Domenica Borra Francesco Bullo Mechanical Engineering Department University of California Riverside Dipartimento di Scienze Matematiche Politecnico di Torino Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara

ISBN: (纸本)9781467357159

This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,...,p - 1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. For instance we show that, differently from the case of consensus networks over the field of real numbers, consensus networks over finite fields converge in finite time, and that properties of the agents interaction graph are not sufficient to ensure finite-field consensus. Finally, we discuss the application of finite-field consensus to distributed averaging in sensor networks.

关键词： Galois fields Network topology Prime number Converge Sufficient conditions

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Sparse and Optimal Wide-Area Damping control in Power Networks

Sparse and Optimal Wide-Area Damping Control in Power Networ...

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American control Conference

作者： Florian Dorfler Mihailo R. Jovanovic Michael Chertkov Francesco Bullo Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa Barbara CA 93106 Department of Electrical and Computer Engineering University of Minnesota Minneapolis MN 55455 Theory Division & Center for Nonlinear Studies at LANL and with New Mexico Consortium Los Alamos NM 87544

ISBN: (纸本)9781479901777

Inter-area oscillations in power networks are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide-area control strategies that involve communication of remote signals. In conventional wide-area control strategies the control structure is fixed a priori typically based on modal criteria. In contrast, here we employ the recently introduced paradigm of sparsity-promoting optimal control to simultaneously identify the control structure and optimize the closed-loop performance. To induce a sparse control architecture, we regularize the standard quadratic performance index with an l_1-penalty on the feedback matrix. The quadratic objective functions are inspired by the classic slow coherency theory and are aimed at imitating homogeneous networks without interarea oscillations. We use a compelling example to demonstrate that the proposed combination of the sparsity-promoting optimal control design with the slow coherency objective functions performs almost as well as the optimal centralized controllers.

关键词： Power grids control Architecture damped control design control Objective function Optimal control quadratic performance index homogeneous network

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Droop-controlled inverters are Kuramoto oscillators

Droop-controlled inverters are Kuramoto oscillators

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3rd IFAC Workshop on Distributed Estimation and control in Networked systems, NECSYS 2012

作者： Simpson-Porco, John W. Dörfler, Florian Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa Barbara CA 93106 United States

ISBN: (纸本)9783902823229

Motivated by the recent interest in smart grid technology and by the push towards distributed and renewable energy, we study the parallel operation of DC/AC inverters in a lossless microgrid. We show that the parallel interconnection of DC/AC inverters equipped with conventional droop controllers is precisely described by the Kuramoto model of coupled phase oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and exponentially stable. Remarkably, we find that the existence of such a synchronized solution does not depend on the selection of droop coefficients. We prove that the inverters share the network power demand in proportion to their power ratings if and only if the droop coefficients are selected proportionally, and we characterize the set of feasible loads which can be serviced. These results hold without assumptions on identical line characteristics or voltage magnitudes. © 2012 IFAC.

关键词： Synchronization

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Eulerian opinion dynamics with bounded confidence and exogenous inputs

Eulerian opinion dynamics with bounded confidence and exogen...

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3rd IFAC Workshop on Distributed Estimation and control in Networked systems, NECSYS 2012

作者： Mirtabatabaei, Anahita Jia, Peng Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara Santa Barbara CA 93106 United States

ISBN: (纸本)9783902823229

The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with non-Bayesian "rule of thumb" methods. This paper focuses on an Eulerian bounded-confidence model of opinion dynamics with a potential time-varying exogenous input. First, we prove some properties of this system's dynamics with time-varying input. Second, we prove the convergence of the population's distribution with no input to a sum of Dirac Delta measures. Finally, we define an input's attraction range, and for a normally distributed input and uniformly distributed initial population, we conjecture that the length of attraction range is an increasing affine function of population's confidence bound and input's variance. © 2012 IFAC.

关键词： Dynamics

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