arXiv subjects

Prabir Barooah

Publications and source records attributed to Prabir Barooah.

32 records · Page 2Linked to original sources

arXiv2019

Differentially Private Smart Metering: Implementation, Analytics, and Billing

Smart power grids offer to revolutionize power distribution by sharing granular power usage data, though this same data sharing can reveal a great deal about users, and there are serious privacy concerns for customers. In this paper, we address these concerns using differential privacy. Differential privacy is a statistical notion of privacy that adds carefully-calibrated noise to sensitive data before sharing it, and we apply it to provide strong privacy guarantees to individual customers. Under this implementation, we quantify the impact of privacy upon smart grid analytics, which are of interest to utilities, to quantify the loss in accuracy incurred by privacy. Simultaneously, we quantify the financial impact of privacy through bounding deviations in customers' utility bills. Simulation results are provided using actual power usage data, demonstrating the viability of this approach in practice.

math.OC↗

arXiv2018

On the round-trip efficiency of an HVAC-based virtual battery

Flexible loads, especially heating, ventilation, and air-conditioning (HVAC) systems can be used to provide a battery-like service to the power grid by varying their demand up and down over a baseline. Recent work has reported that providing virtual energy storage with HVAC systems lead to a net loss of energy, akin to a low round-trip efficiency (RTE) of a battery. In this work we rigorously analyze the RTE of a virtual battery through a simplified physics-based model. We show that the low RTEs reported in recent experimental and simulation work are an artifact of the experimental/simulation setup. When the HVAC system is repeatedly used as a virtual battery, the asymptotic RTE is 1. Robustness of the result to assumptions made in the analysis is illustrated through a simulation case study.

eess.SY↗

arXiv2017

Distributed demand-side contingency-service provisioning while minimizing consumer disutility through local frequency measurements and inter-load communication

We consider the problem of smart and flexible loads providing contingency reserves to the electric grid and provide a Distributed Gradient Projection (DGP) algorithm to minimize loads' disutility while providing contingency services. Each load uses locally obtained grid-frequency measurements and inter-load communication to coordinate their actions, and the privacy of each load is preserved: only gradient information is exchanged---not disutility or consumption information. We provide a proof of convergence of the proposed DGP algorithm, and we compare its performance through simulations to that of a "dual algorithm" previously proposed in the literature that solved the dual optimization problem. The DGP algorithm solves the primal problem. Its main advantage over the dual algorithm is that it is applicable to convex---but not necessarily strictly convex---consumer disutility functions, such as a model of consumer behavior that is insensitive to small changes in consumption, while the dual algorithm is not. Simulations show the DGP algorithm aids in arresting grid-frequency deviations in response to contingency events and performs better or similarly to the dual algorithm in cases where the two can be compared.

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arXiv2014

Accurate Distributed Time Synchronization in Mobile Wireless Sensor Networks from Noisy Difference Measurements

We propose a distributed algorithm for time synchronization in mobile wireless sensor networks. Each node can employ the algorithm to estimate the global time based on its local clock time. The problem of time synchronization is formulated as nodes estimating their skews and offsets from noisy difference measurements of offsets and logarithm of skews; the measurements acquired by time-stamped message exchanges between neighbors. A distributed stochastic approximation based algorithm is proposed to ensure that the estimation error is mean square convergent (variance converging to 0) under certain conditions. A sequence of scheduled update instants is used to meet the requirement of decreasing time-varying gains that need to be synchronized across nodes with unsynchronized clocks. Moreover, a modification on the algorithm is also presented to improve the initial convergence speed. Simulations indicate that highly accurate global time estimates can be achieved with the proposed algorithm for long time durations, while the errors in competing algorithms increase over time.

eess.SY↗

arXiv2014

Ancillary Service to the Grid Using Intelligent Deferrable Loads

Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads. Introduced in this paper is a technique for decentralized control for automated demand response that can be used by grid operators as ancillary service for maintaining demand-supply balance. A Markovian Decision Process (MDP) model is introduced for an individual load. A randomized control architecture is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand. An aggregate model for a large number of loads is then developed by examining the mean field limit. A key innovation is an LTI-system approximation of the aggregate nonlinear model, with a scalar signal as the input and a measure of the aggregate demand as the output. This makes the approximation particularly convenient for control design at the grid level. The second half of the paper contains a detailed application of these results to a network of residential pools. Simulations are provided to illustrate the accuracy of the approximations and effectiveness of the proposed control approach.

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arXiv2013

Estimation from Relative Measurements in Mobile Networks with Markovian Switching Topology: Clock Skew and Offset Estimation for Time Synchronization

We analyze a distributed algorithm for estimation of scalar parameters belonging to nodes in a mobile network from noisy relative measurements. The motivation comes from the problem of clock skew and offset estimation for the purpose of time synchronization. The time variation of the network was modeled as a Markov chain. The estimates are shown to be mean square convergent under fairly weak assumptions on the Markov chain, as long as the union of the graphs is connected. Expressions for the asymptotic mean and correlation are also provided. The Markovian switching topology model of mobile networks is justified for certain node mobility models through empirically estimated conditional entropy measures.

eess.SY↗

arXiv2012

Improving Convergence Rate of Distributed Consensus Through Asymmetric Weights

We propose a weight design method to increase the convergence rate of distributed consensus. Prior work has focused on symmetric weight design due to computational tractability. We show that with proper choice of asymmetric weights, the convergence rate can be improved significantly over even the symmetric optimal design. In particular, we prove that the convergence rate in a lattice graph can be made independent of the size of the graph with asymmetric weights. We then use a Sturm-Liouville operator to approximate the graph Laplacian of more general graphs. A general weight design method is proposed based on this continuum approximation. Numerical computations show that the resulting convergence rate with asymmetric weight design is improved considerably over that with symmetric optimal weights and Metropolis-Hastings weights.

math.OC↗

arXiv2012

On achieving size-independent stability margin of vehicular lattice formations with distributed control

We study the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as O(1/N^2), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to O(1/N). In this paper, we show that, with judicious choice of non-vanishing asymmetry in control, the stability margin of the closed loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case.

nlin.AO↗

arXiv2011

Control of large 1D networks of double integrator agents: role of heterogeneity and asymmetry on stability margin

We consider the distributed control of a network of heterogeneous agents with double integrator dynamics to maintain a rigid formation in 1D Euclidean space. The control signal at a vehicle is allowed to use relative position and velocity with its two nearest neighbors. Most of the work on this problem, though extensive, has been limited to homogeneous networks, in which agents have identical masses and control gains, and symmetric control, in which information from front and back neighbors are weighted equally. We examine the effect of heterogeneity and asymmetry on the closed loop stability margin, which is measured by the real part of the least stable pole of the closed-loop system. By using a PDE (partial differential equation) approximation in the limit of large number of vehicles, we show that heterogeneity has little effect while asymmetry has a significant effect on the stability margin. When control is symmetric, the stability margin decays to 0 as $O(1/N^2)$, where $N$ is the number of agents, even when the agents are heterogeneous in their masses and control gains. In contrast, we show that arbitrarily small amount of asymmetry in the velocity feedback gains can improve the decay of the stability margin to $O(1/N)$. Poor design of such asymmetry makes the closed loop unstable for sufficiently large $N$. With equal amount of asymmetry in both position and velocity feedback gains, the closed loop is stable for arbitrary $N$ and the stability margin scaling trend can also be improved to $O(1/N)$, but the sensitivity to disturbance becomes worse. Effect of asymmetry in position feedback gains alone and unequal amount of asymmetry in position and velocity feedback are open problems. Numerical computations are provided to corroborate the analysis.

nlin.AO↗

arXiv2011

Decentralized control of large vehicular formations: stability margin and sensitivity to external disturbances

We study the stability and robustness of large-scale vehicular formations, in which each vehicle is modeled as a double-integrator. Two types of information graphs are considered: directed trees and undirected graphs. We prove stability of the formation with arbitrary number of vehicles for linear as well as a class of nonlinear controllers. In the case of linear control, we provide quantitative scaling laws of the stability margin and sensitivity to external disturbances (H-infinity norm) with respect to the number of vehicles $N$ in the formation. It is shown that the formation with directed tree graph achieves size-independent stability margin but suffers from high algebraic growth of initial errors. The stability margin in case of the undirected graph decays to 0 as at least $O(1/N)$. In addition, we show that the sensitivity to external disturbances in directed tree graphs is geometric in $k$ where $k <= N$ is the number of generations of the directed tree, while that of the undirected graph is only quadratic in $N$. In particular, for 1-D vehicular platoons, we obtain precise formulae for the H-infinity norm of the transfer function from the disturbances to the position errors. It is shown that the H-infinity norm scales as $O(α^N) (α>1)$ for predecessor-following architecture, but only as $O(N^3)$ for symmetric bidirectional architectures. For a class of nonlinear controllers, numerical simulations show that the transient response due to initial errors and sensitivity to external disturbances are improved considerably for the formation with directed tree graphs. However, by using the nonlinear controller considered, little improvement can be made for that with undirected graphs.

nlin.AO↗

arXiv2011

Detecting Separation in Robotic and Sensor Networks

In this paper we consider the problem of monitoring detecting separation of agents from a base station in robotic and sensor networks. Such separation can be caused by mobility and/or failure of the agents. While separation/cut detection may be performed by passing messages between a node and the base in static networks, such a solution is impractical for networks with high mobility, since routes are constantly changing. We propose a distributed algorithm to detect separation from the base station. The algorithm consists of an averaging scheme in which every node updates a scalar state by communicating with its current neighbors. We prove that if a node is permanently disconnected from the base station, its state converges to $0$. If a node is connected to the base station in an average sense, even if not connected in any instant, then we show that the expected value of its state converges to a positive number. Therefore, a node can detect if it has been separated from the base station by monitoring its state. The effectiveness of the proposed algorithm is demonstrated through simulations, a real system implementation and experiments involving both static as well as mobile networks.

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arXiv2010

Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure

We consider the problem of distributed formation control of a large number of vehicles. An individual vehicle in the formation is assumed to be a fully actuated point mass. A distributed control law is examined: the control action on an individual vehicle depends on (i) its own velocity and (ii) the relative position measurements with a small subset of vehicles (neighbors) in the formation. The neighbors are defined according to an information graph. In this paper we describe a methodology for modeling, analysis, and distributed control design of such vehicular formations whose information graph is a D-dimensional lattice. The modeling relies on an approximation based on a partial differential equation (PDE) that describes the spatio-temporal evolution of position errors in the formation. The analysis and control design is based on the PDE model. We deduce asymptotic formulae for the closed-loop stability margin (absolute value of the real part of the least stable eigenvalue) of the controlled formation. The stability margin is shown to approach 0 as the number of vehicles N goes to infinity. The exponent on the scaling law for the stability margin is influenced by the dimension and the structure of the information graph. We show that the scaling law can be improved by employing a higher dimensional information graph. Apart from analysis, the PDE model is used for a mistuning-based design of control gains to maximize the stability margin. Mistuning here refers to small perturbation of control gains from their nominal symmetric values. We show that the mistuned design can have a significantly better stability margin even with a small amount of perturbation. The results of the analysis with the PDE model are corroborated with numerical computation of eigenvalues with the state-space model of the formation.

nlin.AO↗

arXiv2009

Error Scaling Laws for Linear Optimal Estimation from Relative Measurements

We study the problem of estimating vector-valued variables from noisy "relative" measurements. This problem arises in several sensor network applications. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables and edges to noisy measurements of the difference between two variables. We take an arbitrary variable as the reference and consider the optimal (minimum variance) linear unbiased estimate of the remaining variables. We investigate how the error in the optimal linear unbiased estimate of a node variable grows with the distance of the node to the reference node. We establish a classification of graphs, namely, dense or sparse in Rd,1<= d <=3, that determines how the linear unbiased optimal estimation error of a node grows with its distance from the reference node. In particular, if a graph is dense in 1,2, or 3D, then a node variable's estimation error is upper bounded by a linear, logarithmic, or bounded function of distance from the reference, respectively. Corresponding lower bounds are obtained if the graph is sparse in 1, 2 and 3D. Our results also show that naive measures of graph density, such as node degree, are inadequate predictors of the estimation error. Being true for the optimal linear unbiased estimate, these scaling laws determine algorithm-independent limits on the estimation accuracy achievable in large graphs.

cs.IT↗

arXiv2008

Mistuning-based Control Design to Improve Closed-Loop Stability of Vehicular Platoons

We consider a decentralized bidirectional control of a platoon of N identical vehicles moving in a straight line. The control objective is for each vehicle to maintain a constant velocity and inter-vehicular separation using only the local information from itself and its two nearest neighbors. Each vehicle is modeled as a double integrator. To aid the analysis, we use continuous approximation to derive a partial differential equation (PDE) approximation of the discrete platoon dynamics. The PDE model is used to explain the progressive loss of closed-loop stability with increasing number of vehicles, and to devise ways to combat this loss of stability. If every vehicle uses the same controller, we show that the least stable closed-loop eigenvalue approaches zero as O(1/N^2) in the limit of a large number (N) of vehicles. We then show how to ameliorate this loss of stability by small amounts of "mistuning", i.e., changing the controller gains from their nominal values. We prove that with arbitrary small amounts of mistuning, the asymptotic behavior of the least stable closed loop eigenvalue can be improved to O(1/N) All the conclusions drawn from analysis of the PDE model are corroborated via numerical calculations of the state-space platoon model.

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