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• 1.
KTH, School of Electrical Engineering (EES), Communication Networks.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Automatic Control.
Power-system state-estimation security: Attacks and protection schemes2010In: Smart Grid Communications and Networking, Cambridge University Press, 2010, p. 388-412Chapter in book (Other academic)

Introduction Supervisory control and data acquisition (SCADA) systems are widely used to monitor and control large-scale transmission power grids. Monitoring traditionally involves the measurement of voltage magnitudes and power flows; these data are collected by meters located in substations. In order to deliver the measured data from the substations to the control centre, the measurement data measured by meters in the same substation are multiplexed by a remote terminal unit (RTU) [1, 2]. Because electric power transmission systems extend over large geographical areas, typically entire countries, wide-area networks (WANs) are used to deliver the multiplexed measurement data from the substations to the control centre. For large-scale transmission grids it is often not feasible to measure all power flows and voltages of interest. Furthermore, the measurements are often noisy. Therefore the measurement data are usually fed into a model-based state estimator (SE) at the control centre, which is used to estimate the complete physical state (complex bus voltages) of the power grid. The SE is used to identify faulty equipment and corrupted measurement data through the so-called bad-data detection (BDD) system. Apart from BDD, the state estimate is used by the human operators and by the energy-management systems (EMS) found in modern SCADA systems, such as optimal power flow analysis, and contingency analysis (CA), see for example [1]. Future power grids will be even more dependent on accurate state estimators to fulfil their task of optimally and dynamically routing power flows, because clean renewable power generation tends to be less predictable than nonrenewable power generation.

• 2.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Chalmers University of Technology. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
A graph-theoretic approach on optimizing informed-node selection in multi-agent tracking control2014In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 267, p. 104-111Article in journal (Refereed)

A graph optimization problem for a multi-agent leader follower problem is considered. In a multi-agent system with n followers and one leader, each agent's goal is to track the leader using the information obtained from its neighbors. The neighborhood relationship is defined by a directed communication graph where k agents, designated as informed agents, can become neighbors of the leader. This paper establishes that, for any given strongly connected communication graph with k informed agents, all agents will converge to the leader. In addition, an upper bound and a lower bound of the convergence rate are obtained. These bounds are shown to explicitly depend on the maximal distance from the leader to the followers. The dependence between this distance and the exact convergence rate is verified by empirical studies. Then we show that minimizing the maximal distance problem is a metric k-center problem in classical combinatorial optimization studies, which can be approximately solved. Numerical examples are given to illustrate the properties of the approximate solutions.

• 3.
Automatic Control, Lund University.
Automatic Control, Lund University.
Frequency Domain Model Reduction Method for Parameter-dependent Systems2010In: American Control Conference (ACC), 2010, 2010, p. 3082-3087Conference paper (Refereed)

In this paper a modification of a recently proposedmodel simplification method for linear time invariant parameterizedmodels is presented. It is able to obtain models withexplicit parameter dependence. The method is based on convexoptimization with semidefinite constraints. Computation of thereduced model requires only the frequency samples of the fullone, hence it is possible to apply the methods to large-scalemodels. Numerical examples showing the drawbacks and theadvantages of the method are also presented.

• 4.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology. Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction2005In: 42nd Design Automation Conference, Proceedings 2005, 2005, p. 933-938Conference paper (Refereed)

In this paper an optimization based model order reduction (MOR) framework is proposed. The method involves setting up a quasiconvexprogram that explicitly minimizes a relaxation of the optimal H∞ norn MOR problem. The method generates guaranteedstable and passive reduced models and it is very flexible in imposingadditional constraints. The proposed optimization approach isalso extended to parameterized model reduction problem (PMOR).The proposed method is compared to existing moment matchingand optimization based MOR methods in several examples. APMOR model for a large RF inductor is also constructed.

• 5.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology. Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction2008In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, ISSN 0278-0070, E-ISSN 1937-4151, Vol. 27, no 3, p. 456-469Article in journal (Refereed)

In this paper, an optimization-based model orderreduction (MOR) framework is proposed. The method involvessetting up a quasi-convex program that solves a relaxation of theoptimal H∞ norm MOR problem. The method can generate guaranteedstable and passive reduced models and is very flexible inimposing additional constraints such as exact matching of specificfrequency response samples. The proposed optimization-basedapproach is also extended to solve the parameterized modelreductionproblem (PMOR). The proposed method is compared to existing moment matching and optimization-basedMOR methodsin several examples. PMOR models for large RF inductors oversubstrate and power-distribution grid are also constructed.

• 6.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology. Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Bounding L2 Gain System Error Due to Approximations of the Nonlinear Vector Field2007In: Proceedings of the IEEE Conference on Computer-Aided Design, 2007, p. 879-886Conference paper (Refereed)

Typical nonlinear model order reduction approachesneed to address two issues: reducing the order ofthe model, and approximating the vector field. In this paperwe focus exclusively on the second issue, and present resultscharacterizing the repercussions at the system level of vector fieldapproximations. The error assessment problem is formulatedas the L2 gain upper bounding problem of a scaled feedbackinterconnection. Applying the small gain theorem in the proposedsetup, we prove that the L2 gain of the error system is upperbounded by the L2 gain of the vector field approximationerror, provided it is small. In addition, the paper also presentsa numerical procedure, based on the IQC/LMI approach, toperform the error estimation task with less conservatism. Anumerical example is given in this paper to demonstrate thepractical implications of the presented results.

• 7.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Convex Relaxation Approach to the Identification of the Wiener-Hammerstein Model2008In: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, p. 1375-1382Conference paper (Refereed)

In this paper, an input/output system identificationtechnique for the Wiener-Hammerstein model and its feedbackextension is proposed. In the proposed framework, the identificationof the nonlinearity is non-parametric. The identificationproblem can be formulated as a non-convex quadratic program(QP). A convex semidefinite programming (SDP) relaxation isthen formulated and solved to obtain a sub-optimal solution tothe original non-convex QP. The convex relaxation turns out tobe tight in most cases. Combined with the use of local search,high quality solutions to the Wiener-Hammerstein identificationcan frequently be found. As an application example, randomlygenerated Wiener-Hammerstein models are identified.

• 8.
Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Aeronautics and Astronautics, Massachusetts Institute of Technology.
Fast time-domain simulation for large-order linear time-invariant state space systems2005In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 63, no 5, p. 681-708Article in journal (Refereed)

Time-domain simulation is essential for both analysis and design of complex systems. Unfortunately, high model fidelity leads to large system size and bandwidths, often causing excessive computation and memory saturation. In response we develop an efficient scheme for large-order linear time-invariant systems. First, the A matrix is block diagonalized. Then, subsystems of manageable dimensions and bandwidth are formed, allowing multiple sampling rates. Each subsystem is then discretized using a O(n(s)) scheme, where n(s) is the number of states. Subsequently, a sparse matrix O(n(s)) discrete-time system solver is employed to compute the history of the state and output. Finally, the response of the original system is obtained by superposition. In practical engineering applications, closing feedback loops and cascading filters can hinder the efficient use of the simulation scheme. Solutions to these problems are addressed in the paper. The simulation scheme, implemented as a MATLAB function fast1sim, is benchmarked against the standard LTI system simulator 1sim and is shown to be superior for medium to large systems. The algorithm scales close to O(n(s)(2)) for a set of benchmarked systems. Simulation of a high-fidelity model (n &AP; 2200) of the Space Interferometry Mission spacecraft illustrates real world application of the method.

• 9.
Automatic Control, Lund University.
Automatic Control, Lund University.
A Singular Value Decomposition Based Closed Loop Stability Preserving Controller Reduction Method2010In: 2010 AMERICAN CONTROL CONFERENCE, 2010, p. 1079-1084Conference paper (Refereed)

In this paper a controller reduction method whichpreserves closed loop stability is described. A Lyapunov inequalitybased sufficient condition is proposed in the search ofthe reduced controller. The reduced controller leads to a stableclosed loop system with guaranteed approximation quality. Furthermore,the proposed problem can be formulated as a matrixapproximation problem which can be solved efficiently usingsingular value decomposition. Numerical application examplesare shown in the end to evaluate the generality of the proposedreduction method.

• 10.
Automatic Control, Lund University.
Automatic Control, Lund University.
A SVD Based Controller Reduction Method2010In: SICE Annual Conference 2010, SICE 2010, 2010, p. 2564-2569Conference paper (Refereed)

In this paper an efficient controller reduction method which guarantees closed loop stability is described. The reduced controller is obtained by solving a generalized controllability Grammian type Lyapunov inequality. This Lyapunov inequality based reduced controller search can be formulated as a generalized minimum rank matrix approximation problem to which an efficient singular value decomposition based solution procedure is available. This paper contains theoretical and numerical results on the merit of the proposed reduction method.

• 11.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Automatic Control, Lund University.
Controller reduction via minimum rank matrix approximation2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 6, p. 1069-1076Article in journal (Refereed)

In this paper a controller reduction method for discrete-time linear time-invariant systems is described. Using the bounded-real lemma, the proposed method generates reduced controllers with closed loop stability and H∞ norm performance guarantee. Information of the full controller is used as a basis for reduction using singular value decomposition. This is different from traditional model reduction schemes such as weighted balanced truncation. Numerical assessment of the proposed method is given in the end of the paper.

• 12.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
Automatic Control, Lund University.
Controller Reduction with Closed Loop Performance Guarantee2010In: IEEE Conference on Decision and Control, 2010, p. 6207-6212Conference paper (Refereed)

This paper describes a modification of a singular value decomposition (SVD) based controller reduction method recently proposed in \cite{SR10}. Instead of formulating a $\mathcal{H}_2$ norm characterizing generalized controllability Gramian inequality as in the previous case, the current method applies the bounded-real lemma to certify the closed loop performances in $\mathcal{H}_\infty$ norm. In addition, unlike the previous method, the current one does not suffer from the lack of symmetry that all the data from the plant is not utilized. Yet, the current method inherits the same merit as the previous one that the formulated problem can be solved as a generalized minimum rank matrix approximation problem which can be solved efficiently using SVD. Extensions and numerical examples are shown in the end.

• 13.
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
Automatic Control, Lund University.
On a Generalized Matrix Approximation Problem in the Spectral Norm2012In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, no 7, p. 2331-2341Article in journal (Refereed)

In this paper theoretical results regarding a generalized minimumrank matrix approximation problem in the spectral norm are presented.An alternative solution expression for the generalized matrixapproximation problem is obtained. This alternative expressionprovides a simple characterization of the achievableminimum rank,which is shown to be the same as the optimal objective value of theclassical problem considered by Eckart–Young–Schmidt–Mirsky, aslong as the generalized problem is feasible. In addition, this paperprovides a result on a constrained version of the matrix approximationproblem, establishing that the later problem is solvable viasingular value decomposition.

• 14.
Automatic Control, Lund University.
Automatic Control, Lund University.
On the Minimum Rank of a Generalized Matrix Approximation Problem in the Maximum Singular Value Norm2010In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, 2010, p. 227-234Conference paper (Refereed)

In this paper theoretical results regarding a generalizedminimum rank matrix approximation problem in themaximum singular value norm are presented. Using the idea ofprojection, the considered problem can be shown to be equivalentto a classical minimum rank matrix approximation whichcan be solved efficiently using singular value decomposition. Inaddition, as long as the generalized problem is feasible, it isshown to have exactly the same optimal objective value as thatof the classical problem. Certain comments and extensions ofthe presented theorem are included in the end of the paper.

• 15.
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Automatic Control.
Computing critical k-tuples in power networks2012In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 27, no 3, p. 1511-1520Article in journal (Refereed)

In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical k-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the measurement set, or aid the placement of new meters. The critical k-tuple problem is a combinatorial generalization of the critical measurement calculation problem. Using topological network observability results, this paper proposes an efficient and accurate approximate solution procedure for the considered problem based on solving a minimum-cut (Min-Cut) problem and enumerating all its optimal solutions. It is also shown that the sparsest critical k -tuple problem can be formulated as a mixed integer linear programming (MILP) problem. This MILP problem can be solved exactly using available solvers such as CPLEX and Gurobi. A detailed numerical study is presented to evaluate the efficiency and the accuracy of the proposed Min-Cut and MILP calculations.

• 16.
KTH, School of Electrical Engineering (EES), Automatic Control. Chalmers University of Technology.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Data Attack Isolation in Power Networks Using Secure Voltage Magnitude Measurements2014In: IEEE Transactions on Smart Grid, ISSN 1949-3053, E-ISSN 1949-3061, Vol. 5, no 1, p. 14-28Article in journal (Refereed)

In this paper a procedure to detect and isolate data attacks on power network power flow measurements is proposed. This method can be used in conjunction with available bad data detection (BDD) methods to isolate multiple bad data which are otherwise difficult to handle. The proposed procedure relies on secure measurements of bus voltage magnitudes to define a measurement residual using potentially compromised active and reactive power flow measurements on transmission lines. The proposed residual can be calculated in real-time. In addition, the component of the proposed residual on any particular line depends only locally on the component of the data attack on the same line. This makes the proposed residual well-suited for distributed data attack isolation in large-scale power networks. Furthermore, it can be shown that the proposed procedure becomes more effective when measurements from multiple time instances can be utilized. A detailed numerical case study on the IEEE 14-bus benchmark system demonstrates the effectiveness of the proposed procedure.

• 17.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Detection and identification of data attacks in power system2012In: American Control Conference (ACC), 2012, IEEE Computer Society, 2012, p. 3651-3656Conference paper (Refereed)

In this paper a power system state estimator cyber-attack detection and identification scheme is presented. The proposed scheme considers the information from both the active power measurements and the reactive power measurements. Under the scenario that the network operator can take multiple different samples of measurements and the attackers can attack only once, the proposed scheme can detect the presence of what has been described as stealth (or unobservable) attacks. The detection is provably correct. Furthermore, if an attack is present, the proposed scheme can identify exactly the attacked transmission lines.

• 18.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Electric Power Network Security Analysis via Minimum Cut Relaxation2011In: 50th IEEE Conference on Decision and Control and European Control Conference, 2011Conference paper (Refereed)

In this paper an efficient computation schemefor analyzing the security of power transmission networks ispresented. In order to strategically allocate protection devicesin the network, the problem of finding the sparsest stealthy falsedata attack to the state estimator is studied. While the attacksearch problem is traditionally solved as a generic constrainedcardinality minimization problem, this paper exploits the problemstructure intrinsic to the power network application toobtain a polynomial time approximate algorithm based on aminimum cut relaxation. Experiment results from realistic testcases are presented to demonstrate the efficiency and accuracyof the proposed algorithm.

• 19.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Exact LASSO solutions for a class of constrained cardinality minimization problemsArticle in journal (Refereed)

This paper shows that the least absolute shrinkage and selection operator (LASSO) can provide an exact optimal solution to a special type of constrained cardinality minimization problem, which is motivated from a sensor network measurement robustness analysis problem. The constraint matrix of the considered problem is totally unimodular. This is shown to imply that LASSO leads to a tight linear programming relaxation of the considered cardinality minimization problem. The presented result is based on a deterministic argument, which differs from other well-known deterministic results for LASSO such as mutual incoherence and restricted isometry property. There exist cases given in this paper where the proposed result is applicable, while mutual incoherence and restricted isometry property are not.

• 20.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
On the Exact Solution to a Smart Grid Cyber-Security Analysis Problem2013In: IEEE Transactions on Smart Grid, ISSN 1949-3053, E-ISSN 1949-3061, Vol. 4, no 2, p. 856-865Article in journal (Refereed)

This paper considers a smart grid cyber-security problem analyzing the vulnerabilities of electric power networks to false data attacks. The analysis problem is related to a constrained cardinality minimization problem. The main result shows that an l1 relaxation technique provides an exact optimal solution to this cardinality minimization problem. The proposed result is based on a polyhedral combinatorics argument. It is different from well-known results based on mutual coherence and restricted isometry property. The results are illustrated on benchmarks including the IEEE 118-bus, IEEE 300-bus and the Polish 2383-bus and 2736-bus systems.

• 21.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Scheduling Smart Home Appliances Using Mixed Integer Linear Programming2011In: 50th IEEE Conference on Decsion and Control and European Control Conference, IEEE , 2011Conference paper (Refereed)

This paper considers the minimum electricity costscheduling problem of smart home appliances. Operation characteristics,such as expected duration and peak power consumptionof the smart appliances, can be adjusted through a powerprofile signal. The optimal power profile signal minimizes cost,while satisfying technical operation constraints and consumerpreferences. Constraints such as enforcing uninterruptible andsequential operations are modeled in the proposed frameworkusing mixed integer linear programming (MILP). Several realisticscenarios based on actual spot price are considered,and the numerical results provide insight into tariff design.Computational issues and extensions of the proposed schedulingframework are also discussed.

• 22.
KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Network-Aware Mitigation of Data Integrity Attacks on Power System State Estimation2012In: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 30, no 6, p. 1108-1118Article in journal (Refereed)

Critical power system applications like contingency analysis and optimal power flow calculation rely on the power system state estimator. Hence the security of the state estimator is essential for the proper operation of the power system. In the future more applications are expected to rely on it, so that its importance will increase. Based on realistic models of the communication infrastructure used to deliver measurement data from the substations to the state estimator, in this paper we investigate the vulnerability of the power system state estimator to attacks performed against the communication infrastructure. We define security metrics that quantify the importance of individual substations and the cost of attacking individual measurements. We propose approximations of these metrics, that are based on the communication network topology only, and we compare them to the exact metrics. We provide efficient algorithms to calculate the security metrics. We use the metrics to show how various network layer and application layer mitigation strategies, like single and multi-path routing and data authentication, can be used to decrease the vulnerability of the state estimator. We illustrate the efficiency of the algorithms on the IEEE 118 and 300 bus benchmark power systems.

• 23.
KTH, School of Electrical Engineering (EES), Communication Networks.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
Network-layer protection schemes against stealth attacks on state estimators in power systems2011In: IEEE SmartGridComm 2011, IEEE , 2011Conference paper (Refereed)

The power system state estimator is an important application used to calculate optimal power flows, to maintain the system in a secure state, and to detect faulty equipment. Its importance in the operation of the smart grid is expected to increase, and therefore its security is an important concern. Based on a realistic model of the communication infrastructure used to deliver measurement data from the substations to the state estimator, in this paper we investigate the vulnerability of the power system state estimator to attacks performed against the communication infrastructure. We define security metrics that quantify the importance of individual substations and the cost of attacking individual measurements. We provide efficient algorithms to calculate these metrics, and use the metrics to show how various network layer and application layer mitigation strategies can be used to decrease the vulnerability of the state estimator. We illustrate the efficiency of the algorithms on the IEEE 118 and 300 bus benchmark power systems.

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