@article{teranishi_sadamoto_chakrabortty_kogiso_2023, title={Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems Based on Sample Identifying Complexity and Deciphering Time}, volume={68}, ISSN={["1558-2523"]}, DOI={10.1109/TAC.2022.3174691}, abstractNote={In the state-of-the-art literature on cryptography and control theory, there has been no systematic methodology of constructing cyber–physical systems that can achieve the desired control performance while being protected against eavesdropping attacks. In this article, we tackle this challenging problem. We first propose two novel notions referred to as sample identifying complexity and sample deciphering time in an encrypted control framework. The former explicitly captures the relation between the dynamical characteristics of control systems and the level of identifiability of the systems while the latter shows the relation between the computation time for the identification and the key length of a cryptosystem. Based on these two tractable new notions, we propose a systematic method for designing both of an optimal key length to prevent system identification with a given precision within a given life span of systems and of an optimal controller to maximize both of the control performance and the difficulty of the identification. The efficiency of the proposed method in terms of security level and realtime-ness is investigated through numerical simulations. To the best of our knowledge, this article first connects the relationship between the security of cryptography and dynamical systems from a control-theoretic perspective.}, number={4}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Teranishi, Kaoru and Sadamoto, Tomonori and Chakrabortty, Aranya and Kogiso, Kiminao}, year={2023}, month={Apr}, pages={2183–2198} }
 @article{lian_chakrabortty_duel-hallen_2023, title={Game-Theoretic Mixed H<sub>2</sub>/H<sub>∞</sub> Control with Sparsity Constraint for Multi-Agent Control Systems}, ISSN={["2576-2370"]}, DOI={10.1109/CDC49753.2023.10384040}, abstractNote={A mixed $H_{2}/H_{\infty}$ control problem under a sparsity constraint is investigated for multi-agent control systems (MAS) to provide robustness against model uncertainty and to reduce the communication cost. First, proximal alternating linearized minimization (PALM) is employed to develop a centralized social optimization algorithm, which is guaranteed to converge to a globally optimal sparse controller. Next, we investigate a noncooperative game that accommodates different control performance criteria of the agents and propose a best-response dynamics algorithm based on PALM. A special case of this game produces a partially distributed social optimization solution. We validate the proposed algorithms using a network with open-loop-unstable nodes and demonstrate superiority of the PALM-based method to a previously investigated sparsity-constrained mixed $H_{2}/H_{\infty}$ controller.}, journal={2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC}, author={Lian, Feier and Chakrabortty, Aranya and Duel-Hallen, Alexandra}, year={2023}, pages={5526–5531} }
 @article{chakraborty_chakrabortty_farantatos_patel_hooshyar_darvishi_2023, title={Hierarchical frequency and voltage control using prioritized utilization of inverter based resources}, volume={144}, ISSN={["1879-3517"]}, DOI={10.1016/j.ijepes.2022.108527}, abstractNote={We propose a novel hierarchical frequency and voltage control design for multi-area power system integrated with inverter-based resources (IBRs). The design is based on the idea of prioritizing the use of IBRs over conventional generator-based control in compensating for sudden and unpredicted changes in loads and generations, and thereby mitigate any undesired dynamics in the frequency or the voltage by exploiting their fast actuation time constants. A new sequential optimization problem, referred to as Area Prioritized Power Flow (APPF), is formulated to model this prioritization. It is shown that compared to conventional power flow APPF not only leads to a fairer balance between the dispatch of active and reactive power from the IBRs and the synchronous generators, but also limits the impact of any contingency from spreading out beyond its respective control area, thereby guaranteeing a better collective dynamic performance of the grid. This improvement, however, comes at the cost of adding an extra layer of communication needed for executing APPF in a hierarchical way. Results are validated using simulations of a 9-machine, 6-IBR, 33-bus, 3-area power system model, illustrating how APPF can mitigate a disturbance faster and more efficiently by prioritizing the use of local area-resources.}, journal={INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS}, author={Chakraborty, Rahul and Chakrabortty, Aranya and Farantatos, Evangelos and Patel, Mahendra and Hooshyar, Hossein and Darvishi, Atena}, year={2023}, month={Jan} }
 @article{chakraborty_chakrabortty_osipov_chow_2023, title={Power Flow Optimization Redesign for Transient Stability Enhancement}, ISSN={["2167-9665"]}, DOI={10.1109/ISGT51731.2023.10066339}, abstractNote={We develop an optimization program referred to as the $H_{2}$ -power flow modification $(H_{2}$-pfm) that utilizes the potential of inverter-based resources (IBRs) for improving damping of the electro-mechanical dynamics of a power system, and, in turn, enhances its transient stability radius as well. The method tunes the active and reactive power setpoints of the IBRs generated from the standard AC-OPF solution to optimize the $\mathbf{H}_{2}$ -norm of the transfer function of the grid model considering any incoming disturbance as the input and the generator rotor speeds as the outputs. Power transfer distribution factors (PTDFs) are used to identify the most relevant sets of tunable setpoints to reduce the search space, thereby making the problem solvable online. Simulation results are shown using a 16-machine, 68-bus New York power system model integrated with 7 wind farms. Results indicate that $H_{2}$ - PFM leads to notable improvement in transient stability compared to that for nominal AC-OPF.}, journal={2023 IEEE POWER & ENERGY SOCIETY INNOVATIVE SMART GRID TECHNOLOGIES CONFERENCE, ISGT}, author={Chakraborty, Rahul and Chakrabortty, Aranya and Osipov, Denis and Chow, Joe H.}, year={2023} }
 @article{kar_bai_chakrabortty_2023, title={Reinforcement Learning based Approximate Optimal Control of Nonlinear Systems using Carleman Linearization}, ISSN={["2378-5861"]}, DOI={10.23919/ACC55779.2023.10156057}, abstractNote={We develop a policy iteration-based model-free reinforcement learning (RL) control for nonlinear systems with single input. First, Carleman linearization, a commonly used linearization technique in the Hilbert space, is applied to express the nonlinear system as an infinite-dimensional Carleman state-space model, followed by derivation of an online state-feedback RL controller using state and input data in this infinite-dimensional space. Next, the practicality of using any finite-order truncation of this controller, and the corresponding closed-loop stability of the nonlinear plant is established. Results are validated using two numerical examples, where we show how our proposed method provides solutions close to the optimal control resulting from the model-based Carleman controllers. We also compare our controller to alternative data-driven methods, showing its advantage in terms of shorter learning time.}, journal={2023 AMERICAN CONTROL CONFERENCE, ACC}, author={Kar, Jishnudeep and Bai, He and Chakrabortty, Aranya}, year={2023}, pages={3362–3367} }
 @article{an_shukla_chakrabortty_duel-hallen_2023, title={Robust and Scalable Game-theoretic Security Investment Methods for Voltage Stability of Power Systems}, ISSN={["2576-2370"]}, DOI={10.1109/CDC49753.2023.10383722}, abstractNote={We develop investment approaches to secure electric power systems against load attacks where a malicious intruder (the attacker) covertly changes reactive power setpoints of loads to push the grid towards voltage instability while the system operator (the defender) employs reactive power compensation (RPC) to prevent instability. Extending our previously reported Stackelberg game formulation for this problem, we develop a robust-defense sequential algorithm and a novel genetic algorithm that provides scalability to large-scale power system models. The proposed methods are validated using IEEE prototype power system models with time-varying load uncertainties, demonstrating that reliable and robust defense is feasible unless the operator's RPC investment resources are severely limited relative to the attacker's resources.}, journal={2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC}, author={An, Lu and Shukla, Pratishtha and Chakrabortty, Aranya and Duel-Hallen, Alexandra}, year={2023}, pages={7061–7066} }
 @article{shukla_an_chakrabortty_duel-hallen_2022, title={A Robust Stackelberg Game for Cyber-Security Investment in Networked Control Systems}, volume={9}, ISSN={["1558-0865"]}, url={https://doi.org/10.1109/TCST.2022.3207671}, DOI={10.1109/TCST.2022.3207671}, abstractNote={We present a resource-planning game for cyber-security of networked control systems (NCSs). The NCS is assumed to be operating in closed loop using a linear state feedback $\mathcal {H}_{2}$ -controller. A zero-sum, two-player Stackelberg game (SG) is developed between an attacker and a defender for this NCS. The attacker aims to disable communication of selected nodes and thereby render the feedback gain matrix to be sparse, leading to degradation of closed-loop performance, while the defender aims to prevent this loss by investing in the protection of targeted nodes. Both the players trade their $\mathcal {H}_{2}$ -performance objectives for the costs of their actions. The standard backward induction (BI) method is modified to determine a cost-based Stackelberg equilibrium (CBSE) that saves the players’ costs without degrading the control performance. We analyze the dependence of a CBSE on the relative budgets of the players and on the node “importance” order. Moreover, a robust defense (RD) method is developed for the realistic case when the defender is not informed about the attacker’s resources. The proposed algorithms are validated using examples from wide-area control of electric power systems. It is demonstrated that reliable and RD is feasible unless the defender’s resources are severely limited relative to the attacker’s resources. We also show that the proposed methods are robust to time-varying model uncertainties and thus are suitable for long-term security investment in realistic NCSs. Finally, we use computationally efficient genetic algorithms (GAs) to compute the optimal strategies of the attacker and the defender in realistic large power systems.}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Shukla, Pratishtha and An, Lu and Chakrabortty, Aranya and Duel-Hallen, Alexandra}, year={2022}, month={Sep} }
 @article{ishizaki_ito_kawaguchi_chakrabortty_2022, title={Data-Adaptive Retrofit Control for Power System Stabilizer Design}, ISSN={["2576-2370"]}, DOI={10.1109/CDC51059.2022.9992890}, abstractNote={In this paper, we propose a design procedure of data-adaptive power system stabilizers (PSSs) in the framework of retrofit control. The proposed procedure is modular in the sense that both design and implementation processes of PSSs can be performed using only a local subsystem model and local measurement. In particular, we consider online identification of a dynamical feedback effect between the states of a generator of interest and the main grid to make the PSS adaptive to the variation of grid characteristics depending on power flow distributions. The main theoretical contribution is to show that the same retrofit controller as that developed for linear systems in the literature works properly even for nonlinear power systems where an operating point of interest varies depending on power flow distributions. In addition, we propose an online identification algorithm of the grid characteristics that makes use of the physical structure of power systems. We demonstrate the efficacy of the proposed data-adaptive PSS by a numerical simulation on the IEEE 9-bus test power system.}, journal={2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC)}, author={Ishizaki, Takayuki and Ito, Masahiro and Kawaguchi, Takahiro and Chakrabortty, Aranya}, year={2022}, pages={2210–2215} }
 @article{jing_bai_george_chakrabortty_sharma_2022, title={Learning Distributed Stabilizing Controllers for Multi-Agent Systems}, volume={6}, ISSN={["2475-1456"]}, DOI={10.1109/LCSYS.2021.3072007}, abstractNote={We address model-free distributed stabilization of heterogeneous continuous-time linear multi-agent systems using reinforcement learning (RL). Two algorithms are developed. The first algorithm solves a centralized linear quadratic regulator (LQR) problem without knowing any initial stabilizing gain in advance. The second algorithm builds upon the results of the first algorithm, and extends it to distributed stabilization of multi-agent systems with predefined interaction graphs. Rigorous proofs are provided to show that the proposed algorithms achieve guaranteed convergence if specific conditions hold. A simulation example is presented to demonstrate the theoretical results.}, journal={IEEE CONTROL SYSTEMS LETTERS}, author={Jing, Gangshan and Bai, He and George, Jemin and Chakrabortty, Aranya and Sharma, Piyush K.}, year={2022}, pages={301–306} }
 @article{negi_chakrabortty_2022, title={Optimal co-designs of communication and control in bandwidth-constrained cyber-physical systems}, volume={142}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2022.110288}, abstractNote={We address the problem of sparsity-promoting optimal control of cyber–physical systems (CPSs) in the presence of communication delays. The delays are categorized into two types — namely, an inter-layer delay for passing state and control information between the physical layer and the cyber layer, and an intra-layer delay that operates between the computing agents, referred to here as control nodes (CNs), within the cyber-layer. Our objective is to minimize the closed-loop H2-norm of the physical system by co-designing an optimal combination of these two delays and a sparse state-feedback controller while respecting a given bandwidth cost constraint. We propose a two-loop optimization algorithm for this. Based on the alternating directions method of multipliers (ADMM), the inner loop handles the conflicting directions between the decreasing H2-norm and the increasing sparsity level of the controller. The outer loop comprises a semidefinite program (SDP)-based relaxation of non-convex inequalities necessary for closed-loop stability. Moreover, for CPSs where the state and control information assigned to the CNs are not private, we derive an additional algorithm that further sparsifies the communication topology by modifying the row and column structures of the obtained controller, resulting in a reassignment of the communication map between the cyber and physical layers, and determining which physical agent should send its state information to which CN. Proofs for closed-loop stability and optimality are provided for both algorithms, followed by numerical simulations.}, journal={AUTOMATICA}, author={Negi, Nandini and Chakrabortty, Aranya}, year={2022}, month={Aug} }
 @article{jing_bai_george_chakrabortty_2021, title={Decomposability and Parallel Computation of Multi-Agent LQR}, ISSN={["2378-5861"]}, DOI={10.23919/ACC50511.2021.9483338}, abstractNote={Individual agents in a multi-agent system (MAS) may have decoupled open-loop dynamics, but a cooperative control objective usually results in coupled closed-loop dynamics thereby making the control design computationally expensive. The computation time becomes even higher when a learning strategy such as reinforcement learning (RL) needs to be applied to deal with the situation when the agents dynamics are not known. To resolve this problem, we propose a parallel RL scheme for a linear quadratic regulator (LQR) design in a continuous-time linear MAS. The idea is to exploit the structural properties of two graphs embedded in the $Q$ and $R$ weighting matrices in the LQR objective to define an orthogonal transformation that can convert the original LQR design to multiple decoupled smaller-sized LQR designs. We show that if the MAS is homogeneous then this decomposition retains closed-loop optimality. Conditions for decomposability, an algorithm for constructing the transformation matrix, a parallel RL algorithm, and robustness analysis when the design is applied to non-homogeneous MAS are presented. Simulations show that the proposed approach can guarantee significant speed-up in learning without any loss in the cumulative value of the LOR cost.}, journal={2021 AMERICAN CONTROL CONFERENCE (ACC)}, author={Jing, Gangshan and Bai, He and George, Jemin and Chakrabortty, Aranya}, year={2021}, pages={4527–4532} }
 @article{minster_saibaba_kar_chakrabortty_2021, title={EFFICIENT ALGORITHMS FOR EIGENSYSTEM REALIZATION USING RANDOMIZED SVD}, volume={42}, ISSN={["1095-7162"]}, DOI={10.1137/20M1327616}, abstractNote={Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the singular value decomposition (SVD) of a large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix. We provide a detailed analysis of the error in the identified system matrices and the computational cost of the proposed algorithms. We demonstrate the accuracy and computational benefits of our algorithms on two test problems: the first involves a partial differential equation that models the cooling of steel rails, and the second is an application from power systems engineering.}, number={2}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Minster, Rachel and Saibaba, Arvind K. and Kar, Jishnudeep and Chakrabortty, Aranya}, year={2021}, pages={1045–1072} }
 @article{sadamoto_chakrabortty_2021, title={Enhancing Controllability of Wind Farms Against Parametric Resonance: A Series Compensation Approach}, volume={5}, ISSN={["2475-1456"]}, DOI={10.1109/LCSYS.2020.3040339}, abstractNote={A critical factor deciding the controllability of a doubly-fed induction generator (DFIG) in a wind power system is the ratio of its leakage reactance to resistance. If this ratio is high then the DFIG has two uncontrollable slow resonant modes. The emergence of these modes, often referred to as parametric resonance, can cause the wind farm to exhibit poorly damped transient behavior, irrespective of any control action. In this letter we resolve this problem by presenting a new series compensation strategy in the stator line of the DFIG that prevents this uncontrollability. By tuning the compensation and the controller gains of the DFIG, the controllability of the wind farm is shown to be improved drastically, and accordingly the inter-area oscillations on the grid side to be damped significantly. We illustrate various implementation aspects of the proposed approach via numerical simulations of the IEEE 68-bus power system model with one wind farm.}, number={4}, journal={IEEE CONTROL SYSTEMS LETTERS}, author={Sadamoto, Tomonori and Chakrabortty, Aranya}, year={2021}, month={Oct}, pages={1447–1452} }
 @article{sadamoto_chakrabortty_imura_2021, title={Fast Online Reinforcement Learning Control Using State-Space Dimensionality Reduction}, volume={8}, ISSN={["2372-2533"]}, DOI={10.1109/TCNS.2020.3027780}, abstractNote={In this article, we propose a fast reinforcement learning (RL) control algorithm that enables online control of large-scale networked dynamic systems. RL is an effective way of designing model-free linear quadratic regulator (LQR) controllers for linear time-invariant (LTI) networks with unknown state-space models. However, when the network size is large, conventional RL can result in unacceptably long learning times. The proposed approach is to construct a compressed state vector by projecting the measured state through a projective matrix. This matrix is constructed from online measurements of the states in a way that it captures the dominant controllable subspace of the open-loop network model. Next, an RL controller is learned using the reduced-dimensional state instead of the original state such that the resulting cost is close to the optimal LQR cost. Numerical benefits as well as the cyber–physical implementation benefits of the approach are verified using illustrative examples including an example of wide-area control of the IEEE 68-bus benchmark power system.}, number={1}, journal={IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS}, author={Sadamoto, Tomonori and Chakrabortty, Aranya and Imura, Jun-ichi}, year={2021}, month={Mar}, pages={342–353} }
 @article{kar_chakrabortty_2021, title={LSTM based Denial-of-Service Resiliency for Wide-Area Control of Power Systems}, ISSN={["2165-4816"]}, DOI={10.1109/ISGTEUROPE52324.2021.9640193}, abstractNote={Denial-of-Service (DoS) attacks in wide-area control loops of electric power systems can cause temporary halting of information flow between the generators, leading to closed-loop instability. One way to counteract this issue would be to recreate the missing state information at the impacted generators by using the model of the entire system. However, that not only violates privacy but is also impractical from a scalability point of view. In this paper, we propose to resolve this issue by using a model-free technique employing neural networks. Specifically, a long short-term memory network (LSTM) is used. Once an attack is detected and localized, the LSTM at the impacted generator(s) predicts the magnitudes of the corresponding missing states in a completely decentralized fashion using offline training and online data updates. These predicted states are thereafter used in conjunction with the healthy states to sustain the wide-area feedback until the attack is cleared. The approach is validated using the IEEE 68-bus, 16-machine power system.}, journal={2021 IEEE PES INNOVATIVE SMART GRID TECHNOLOGY EUROPE (ISGT EUROPE 2021)}, author={Kar, Jishnudeep and Chakrabortty, Aranya}, year={2021}, pages={313–317} }
 @article{jing_bai_george_chakrabortty_2021, title={Model-Free Optimal Control of Linear Multiagent Systems via Decomposition and Hierarchical Approximation}, volume={8}, ISSN={["2372-2533"]}, DOI={10.1109/TCNS.2021.3074256}, abstractNote={Designing the optimal linear quadratic regulator (LQR) for a large-scale multiagent system is time consuming since it involves solving a large-size matrix Riccati equation. The situation is further exasperated when the design needs to be done in a model-free way using schemes such as reinforcement learning (RL). To reduce this computational complexity, we decompose the large-scale LQR design problem into multiple small-size LQR design problems. We consider the objective function to be specified over an undirected graph, and cast the decomposition as a graph clustering problem. The graph is decomposed into two parts, one consisting of independent clusters of connected components, and the other containing edges that connect different clusters. Accordingly, the resulting controller has a hierarchical structure, consisting of two components. The first component optimizes the performance of each independent cluster by solving the small-size LQR design problem in a model-free way using an RL algorithm. The second component accounts for the objective coupling different clusters, which is achieved by solving a least-squares problem in one shot. Although suboptimal, the hierarchical controller adheres to a particular structure as specified by interagent couplings in the objective function and by the decomposition strategy. Mathematical formulations are established to find a decomposition that minimizes the number of required communication links or reduces the optimality gap. Numerical simulations are provided to highlight the pros and cons of the proposed designs.}, number={3}, journal={IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS}, author={Jing, Gangshan and Bai, He and George, Jemin and Chakrabortty, Aranya}, year={2021}, month={Sep}, pages={1069–1081} }
 @article{mukherjee_bai_chakrabortty_2021, title={Model-based and model-free designs for an extended continuous-time LQR with exogenous inputs}, volume={154}, ISSN={["1872-7956"]}, DOI={10.1016/j.sysconle.2021.104983}, abstractNote={We present an extended linear quadratic regulator (LQR) design for continuous-time linear time invariant (LTI) systems in the presence of exogenous inputs with a novel feedback control structure. We first propose a model-based solution with cost minimization guarantees for states and inputs using dynamic programming (DP) that out-performs classical LQR with exogenous inputs. The control law consists of a combination of the optimal state feedback and an additional optimal term which is dependent on the exogenous inputs. The control gains for the two components are obtained by solving a set of matrix differential equations. We provide these solutions for both finite horizons and steady state cases. In the second part of the paper, we formulate a reinforcement learning (RL) based algorithm which does not need any model information except the input matrix, and can compute approximate steady-state extended LQR gains using measurements of the states, the control inputs, and the exogenous inputs. Both model-based and data-driven optimal control algorithms are tested with a numerical example under different exogenous inputs showcasing the effectiveness of the designs.}, journal={SYSTEMS & CONTROL LETTERS}, author={Mukherjee, Sayak and Bai, He and Chakrabortty, Aranya}, year={2021}, month={Aug} }
 @article{mukherjee_chakrabortty_babaei_2021, title={Modeling and Quantifying the Impact of Wind Penetration on Slow Coherency of Power Systems}, volume={36}, ISSN={["1558-0679"]}, DOI={10.1109/TPWRS.2020.3022832}, abstractNote={This paper presents a mathematical analysis of how wind generation impacts the slow coherency property of power systems. Slow coherency arises from time-scale separation in the dynamics of synchronous generators, where generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time-scale due to weaker coupling. This time-scale separation is reflected in the form of a spectral separation in the weighted Laplacian matrix describing the swing dynamics of the generators. However, when wind farms with doubly-fed induction generators (DFIG) are integrated into the system then this Laplacian matrix changes based on both the level of wind penetration and the location of the wind farms. The modified Laplacian changes the effective slow eigenspace of the generators. Depending on the penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and propose an equivalent Laplacian matrix to compute the modified coherent areas. Results are validated using the IEEE 68-bus test system with one and multiple wind farms. The model-based slow coherency results are compared with measurement-based principal component analysis to substantiate our derivations.}, number={2}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Mukherjee, Sayak and Chakrabortty, Aranya and Babaei, Saman}, year={2021}, month={Mar}, pages={1002–1012} }
 @article{mukherjee_chakrabortty_babaei_2021, title={Modeling and Quantifying the Impact of Wind Penetration on Slow Coherency of Power Systems}, ISSN={["1944-9925"]}, DOI={10.1109/PESGM46819.2021.9637872}, abstractNote={This paper presents a mathematical analysis of how wind generation impacts the slow coherency property of power systems. Slow coherency arises from time-scale separation in the dynamics of synchronous generators, where generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time-scale due to weaker coupling. This time-scale separation is reflected in the form of a spectral separation in the weighted Laplacian matrix describing the swing dynamics of the generators. However, when wind farms with doubly-fed induction generators (DFIG) are integrated into the system then this Laplacian matrix changes based on both the level of wind penetration and the location of the wind farms. The modified Laplacian changes the effective slow eigenspace of the generators. Depending on the penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and propose an equivalent Laplacian matrix to compute the modified coherent areas. Results are validated using the IEEE 68-bus test system with one and multiple wind farms. The model-based slow coherency results are compared with measurement-based principal component analysis to substantiate our derivations.}, journal={2021 IEEE POWER & ENERGY SOCIETY GENERAL MEETING (PESGM)}, author={Mukherjee, Sayak and Chakrabortty, Aranya and Babaei, Saman}, year={2021} }
 @article{ishizaki_chakrabortty_2021, title={Necessity of Lossless Transmission and Convexity of Potential Energy Function for Equilibrium Independent Passivity of Power Systems}, ISSN={["0743-1546"]}, DOI={10.1109/CDC45484.2021.9683357}, abstractNote={This paper shows that the losslessness of transmission networks is necessary for equilibrium independent passivity of a nonlinear power system model. Furthermore, it is shown that a domain over which a classical potential energy function is convex captures the largest set of equilibria whose asymptotic stability can be proven by passivity. Both results are found via linearization at each of all possible equilibria, depending on external inputs. In particular, the first result is shown based on the fact that the positive realness of the transfer matrix of a linearized electrical dynamics can be proven without finding a specific storage function. The second is shown by the fact that the Hessian of the potential energy function is positive semidefinite, or equivalently, a storage function for the nonlinear model is positive definite over a relevant state space if and only if the linearized version of the exciter dynamics is stable, and a Laplacian matrix of the linearized model is positive semidefinite. A numerical example demonstrates that the eigenvalues of this Laplacian matrix can be used as a good index for stability analysis.}, journal={2021 60TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC)}, author={Ishizaki, Takayuki and Chakrabortty, Aranya}, year={2021}, pages={4242–4247} }
 @article{alfredo hernandez-ortega_chakrabortty_roman messina_morales rergis_2021, title={Nonlinear Koopman Observability Measures on Subsets of Power System State Variables}, ISSN={["0743-1546"]}, DOI={10.1109/CDC45484.2021.9682953}, abstractNote={Recently, the perturbed Koopman mode analysis (PKMA) was proposed for analyzing oscillations arising from power system models under stressed operating conditions, using both linear and nonlinear Koopman eigenfunctions. A question of current interest is how one can use the information provided by these PKMA models to complement and enhance estimations obtained through data-driven Koopman operator-based approaches. Motivated by this question, in this paper we derive nonlinear Koopman measures of observability for a third-order PKMA model to assess the most dominant global dynamics underlying a selected set of observables. These nonlinear measures are generic by formulation; however, the focus is on a subset of the state variables of a power system. With the selected observables, we illustrate the usefulness of our approach in identifying a relatively small subset of dominant Koopman modes that closely mimic the global dynamical behavior. We validate our results on a test system, followed by a comparison with the extended dynamic mode decomposition (EDMD). The simulations demonstrate how the proposed model-based approach is complementary to these data-driven approaches. Utility of this method for model-order reduction, wide-area monitoring, and optimal sensor placement are also highlighted.}, journal={2021 60TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC)}, author={Alfredo Hernandez-Ortega, Marcos and Chakrabortty, Aranya and Roman Messina, Arturo and Morales Rergis, Carlos}, year={2021}, pages={4222–4227} }
 @article{inoue_sadamoto_arahata_chakrabortty_2021, title={Optimal Power Flow Design for Enhancing Dynamic Performance: Potentials of Reactive Power}, volume={12}, ISSN={["1949-3061"]}, DOI={10.1109/TSG.2020.3019417}, abstractNote={We present a new optimal power flow (OPF) design that not only optimizes fuel cost but also enhances dynamic performance of a power system. Performance is quantified by the <inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math></inline-formula>-norm of the transfer matrix from any disturbance input to a set of performance outputs, which in this case are chosen as the frequencies of the generators. The <inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math></inline-formula>-norm models the attenuation of the frequency amplitudes following the disturbance, and thereby quantifies the amount of damping torque induced on the tie-line flows. The method, referred to as <inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math></inline-formula>-power flow modification (<inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math></inline-formula>-PFM) is carried out in two steps. First, the regular OPF is solved to obtain the optimal generator setpoints for active and reactive power dispatch. Second, the load setpoints are re-tuned to minimize the aforesaid <inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math></inline-formula>-norm while keeping the generator setpoints fixed. In particular, manipulating the load reactive power in this way is found to reduce the norm remarkably, improving disturbance attenuation and damping. A gradient descent algorithm is proposed for this minimization. Results are validated using the 68-bus test system with a solar farm.}, number={1}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Inoue, Masaki and Sadamoto, Tomonori and Arahata, Mitsuru and Chakrabortty, Aranya}, year={2021}, month={Jan}, pages={599–611} }
 @article{mukherjee_bai_chakrabortty_2021, title={Reduced-dimensional reinforcement learning control using singular perturbation approximations}, volume={126}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2020.109451}, abstractNote={We present a set of model-free, reduced-dimensional reinforcement learning (RL) based optimal control designs for linear time-invariant singularly perturbed (SP) systems. We first present a state-feedback and output-feedback based RL control design for a generic SP system with unknown state and input matrices. We take advantage of the underlying time-scale separation property of the plant to learn a linear quadratic regulator (LQR) for only its slow dynamics, thereby saving a significant amount of learning time compared to the conventional full-dimensional RL controller. We analyze the sub-optimality of the design using SP approximation theorems and provide sufficient conditions for closed-loop stability. Thereafter, we extend both designs to clustered multi-agent consensus networks, where the SP property reflects through clustering. We develop both centralized and cluster-wise block-decentralized RL controllers for such networks, in reduced dimensions. We demonstrate the details of the implementation of these controllers using simulations of relevant numerical examples and compare them with conventional RL designs to show the computational benefits of our approach.}, journal={AUTOMATICA}, author={Mukherjee, Sayak and Bai, He and Chakrabortty, Aranya}, year={2021}, month={Apr} }
 @article{mukherjee_chakrabortty_bai_darvishi_fardanesh_2021, title={Scalable Designs for Reinforcement Learning-Based Wide-Area Damping Control}, volume={12}, ISSN={["1949-3061"]}, DOI={10.1109/TSG.2021.3050419}, abstractNote={This article discusses how techniques from reinforcement learning (RL) can be exploited to transition to a model-free and scalable wide-area oscillation damping control of power grids. We present two control architectures with distinct features. Performing full-dimensional RL control designs for any practical grid would require an unacceptably long learning time and result in a dense communication architecture. Our designs avoid the curse of dimensionality by employing ideas from model reduction. The first design exploits time-scale separation in the generator electro-mechanical dynamics arising from coherent clustering, and learns a controller using both electro-mechanical and non-electro-mechanical states while compensating for the error in incorporating the latter through the RL loop. The second design presents an output-feedback approach enabled by a neuro-adaptive observer using measurements of only the generator frequencies. The controller exhibits an adaptive behavior that updates the control gains whenever there is a notable change in the loads. Theoretical guarantees for closed-loop stability and performance are provided for both designs. Numerical simulations are shown for the IEEE 68-bus power system model.}, number={3}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Mukherjee, Sayak and Chakrabortty, Aranya and Bai, He and Darvishi, Atena and Fardanesh, Bruce}, year={2021}, month={May}, pages={2389–2401} }
 @article{chakrabortty_2021, title={Wide-Area Control of Power Systems}, volume={9}, ISSN={["2325-5889"]}, DOI={10.1109/MELE.2020.3047165}, abstractNote={In the foreseeable future, the north American power transmission system is expected to evolve into the largest and most complex Internet of Things (IoT) technology, encompassing the use of massive volumes of data from phasor measurement units (PMUs) to make control decisions in the face of major disturbances without jeopardizing grid stability or the quality of service. In this modern grid, besides conventional generation, distributed energy resources (DERs) in the form of renewables, smart loads, and power electronic converters, will serve as active end points that not only consume, but can also generate, store, sense, compute, communicate, and react to datadriven commands. They will turn the grid into a large network of active nodes, introducing rapid, large, frequent, and random fluctuations in power flow, voltage, and frequency with a huge amount of model uncertainty while at the same time increasing our capability to learn and control them through a massive, data-driven IoT platform.}, number={1}, journal={IEEE ELECTRIFICATION MAGAZINE}, author={Chakrabortty, Aranya}, year={2021}, month={Mar}, pages={45–52} }
 @article{katewa_chakrabortty_gupta_2020, title={Differential Privacy for Network Identification}, volume={7}, ISSN={["2372-2533"]}, DOI={10.1109/TCNS.2019.2922169}, abstractNote={We consider a multiagent linear time-invariant system whose dynamical model may change from one disturbance event to another. The system is monitored by a control center that collects output measurements from the agents after every event and estimates the eigenvalues of the model to keep track of any adverse impact of the disturbance on its spectral characteristics. Sharing measurements in this way, however, can be susceptible to privacy breaches. If an intruder gains access to these measurements, she may estimate the values of sensitive model parameters and launch more severe attacks. To prevent this, we employ a differential privacy framework by which agents can add synthetic noise to their measurements before sending them to the control center. The noise is designed carefully by characterizing the sensitivity of the system so that it limits the intruder from inferring any incremental change in the sensitive parameters, thereby protecting their privacy. Our numerical results show that the proposed design results in marginal degradation in eigenvalue estimation when compared to the error incurred by the intruder in identifying the sensitive parameters.}, number={1}, journal={IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS}, author={Katewa, Vaibhav and Chakrabortty, Aranya and Gupta, Vijay}, year={2020}, month={Mar}, pages={266–277} }
 @article{zhao_srivastava_chakrabortty_terzija_kamwa_bi_zhang_2020, title={Guest Editorial: Next Generation of Synchrophasor-based Power System Monitoring, Operation and Control}, volume={14}, ISSN={["1751-8695"]}, DOI={10.1049/iet-gtd.2020.1315}, number={19}, journal={IET GENERATION TRANSMISSION & DISTRIBUTION}, author={Zhao, Junbo and Srivastava, Anurag and Chakrabortty, Aranya and Terzija, Vladimir and Kamwa, Innocent and Bi, Tianshu and Zhang, Yingchen}, year={2020}, month={Oct}, pages={3943–3944} }
 @article{sadamoto_chakrabortty_2020, title={Improving Controllability and Plug-and-Play Operation of Wind Farms Using B2B Converters}, volume={4}, ISSN={["2475-1456"]}, DOI={10.1109/LCSYS.2019.2931822}, abstractNote={We show that a critical factor deciding the controllability of a doubly fed induction generator (DFIG) in a wind power system is the ratio of its leakage reactance to resistance. If this ratio is high then the DFIG has two uncontrollable slow resonant modes. In that situation any type of control action for attenuating disturbances inside the wind farm becomes impossible. In order to prevent this uncontrollability, we propose to add a back-to-back (B2B) converter in the stator line of the DFIG. This new converter has two benefits: 1) it improves the controllability of the wind farm significantly and 2) its signal-flow diagram reveals a cascade structure where the grid is shown to impact the DFIG dynamics, but not vice versa. The cascade structure also enables one to design controllers for regulating the DFIG currents and its dc-link voltages in a completely modular and plug-and-play fashion. We illustrate various implementation aspects of this control mechanisms via numerical simulations of the IEEE 68-bus power system model with one wind farm.}, number={2}, journal={IEEE CONTROL SYSTEMS LETTERS}, author={Sadamoto, Tomonori and Chakrabortty, Aranya}, year={2020}, month={Apr}, pages={379–384} }
 @article{mukherjee_babaei_chakrabortty_fardanesh_2020, title={Measurement-driven optimal control of utility-scale power systems: A New York State grid perspective}, volume={115}, ISSN={["1879-3517"]}, DOI={10.1016/j.ijepes.2019.105470}, abstractNote={This paper focuses on designing and testing a supplementary controller for an ultra-large, utility-scale power system, namely the New York State (NYS) Power Grid from a completely measurement-based perspective. We present the control design using the Flexible AC Transmission System (FACTS) facility at the NYS grid. We use the utility-scale Eastern Interconnection (EI) model consisting of over 70,000 buses in the PSS/E platform for this research. The coherency structure of the NYS grid is analyzed by performing Principal Component Analysis (PCA) on frequency measurements obtained from multiple contingency simulations. Thereafter, we use the frequency measurements from PMU-enabled buses to identify a reduced-order state space model of the grid such that it matches the input-output characteristics along with identifying the inter-area modes. This model is then used to design the Linear Quadratic Gaussian (LQG) based optimal FACTS controller. Then the controller is implemented in the PSS/E model of the Eastern Interconnection (EI) as a PSS/E-FORTRAN based user defined module. The effectiveness of the control performance is shown using the non-linear simulations under different contingencies provided by the New York Independent System Operator (NYISO).}, journal={INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS}, author={Mukherjee, Sayak and Babaei, Saman and Chakrabortty, Aranya and Fardanesh, Bruce}, year={2020}, month={Feb} }
 @article{jing_bai_george_chakrabortty_2020, title={Model-Free Reinforcement Learning of Minimal-Cost Variance Control}, volume={4}, ISSN={["2475-1456"]}, DOI={10.1109/LCSYS.2020.2995547}, abstractNote={This letter proposes two reinforcement learning (RL) algorithms for solving a class of coupled algebraic Riccati equations (CARE) for linear stochastic dynamic systems with unknown state and input matrices. The CARE are formulated for a minimal-cost variance (MCV) control problem that aims to minimize the variance of a cost function while keeping its mean at an acceptable range using a noisy infinite-horizon full-state feedback linear quadratic regulator (LQR). We propose two RL algorithms where the input matrix can be estimated at the very first iteration. This, in turn, frees up significant amount of computational complexity in the intermediate steps of the learning phase by avoiding repeated matrix inversion of a high-dimensional data matrix. The overall complexity is shown to be less than RL for both stochastic and deterministic LQR. Additionally, the disturbance noise entering the model is not required to satisfy any condition for ensuring efficiency of either RL algorithms. Simulation examples are presented to illustrate the effectiveness of the two designs.}, number={4}, journal={IEEE CONTROL SYSTEMS LETTERS}, author={Jing, Gangshan and Bai, He and George, Jemin and Chakrabortty, Aranya}, year={2020}, month={Oct}, pages={916–921} }
 @article{negi_chakrabortty_2020, title={Sparsity-promoting optimal control of cyber-physical systems over shared communication networks}, volume={122}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2020.109217}, abstractNote={Recent years have seen several new directions in the design of sparse control of cyber–physical systems (CPSs) driven by the objective of reducing communication costs. One common assumption made in these designs is that the communication happens over a dedicated network. For many practical applications, however, communication must occur over shared networks, leading to two critical design challenges, namely — time-delays in the feedback and fair sharing of bandwidth among users. In this paper, we present a set of sparse H2 control designs under these two design constraints. An essential aspect of our design is that the delay itself can be a function of sparsity, which leads to an interesting pattern of trade-offs in the H2 performance. We present three distinct algorithms. The first algorithm preconditions the assignable bandwidth to the network and produces an initial guess for a stabilizing controller. This is followed by our second algorithm, which sparsifies this controller while simultaneously adapting the feedback delay and optimizing the H2 performance using alternating directions method of multipliers (ADMM). The third algorithm extends this approach to a multiple user scenario where an optimal number of communication links, whose total sum is fixed, is distributed fairly among users by minimizing the variance of their H2 performances. The problem is cast as a difference-of-convex (DC) program with mixed-integer linear program (MILP) constraints. We provide theorems to prove the convergence of these algorithms, followed by validation through numerical simulations.}, journal={AUTOMATICA}, author={Negi, Nandini and Chakrabortty, Aranya}, year={2020}, month={Dec} }
 @inproceedings{shukla_chakrabortty_duel-hallen_2019, place={Philadelphia}, title={A Cyber-Security Investment Game for Networked Control Systems}, publisher={American Control Conference}, author={Shukla, P. and Chakrabortty, A. and Duel-Hallen, A.}, year={2019} }
 @inproceedings{mukherjee_chakrabortty_bai_2019, place={Atlanta, GA}, title={A Measurement-based Adaptive Power System Damping Control Design using ERA-driven Neural Observer and Reinforcement Learning}, booktitle={IEEE PES General Meeting}, author={Mukherjee, S. and Chakrabortty, A. and Bai, H.}, year={2019} }
 @inproceedings{milani_cisneros_chakrabortty_husain_2019, place={Philadelphia}, title={A passivity-based globally stabilizing PI controller for primary control of radial power distribution systems}, publisher={American Control Conference}, author={Milani, A. and Cisneros, R. and Chakrabortty, A. and Husain, I.}, year={2019} }
 @misc{dibaji_pirani_flamholz_annaswamy_johansson_chakrabortty_2019, title={A systems and control perspective of CPS security}, volume={47}, ISSN={["1367-5788"]}, DOI={10.1016/j.arcontrol.2019.04.011}, abstractNote={The comprehensive integration of instrumentation, communication, and control into physical systems has led to the study of Cyber-Physical Systems (CPSs), a field that has recently garnered increased attention. A key concern that is ubiquitous in CPS is a need to ensure security in the face of cyber attacks. In this paper, we carry out a survey of systems and control methods that have been proposed for the security of CPS. We classify these methods into three categories based on the type of defense proposed against the cyberattacks: prevention, resilience, and detection & isolation. A unified threat assessment metric is proposed in order to evaluate how CPS security is achieved in each of these three cases. Also surveyed are the risk assessment tools and the effect of network topology on CPS security. Furthermore, an emphasis has been placed on power and transportation applications in the overall survey.}, journal={ANNUAL REVIEWS IN CONTROL}, author={Dibaji, Seyed Mehran and Pirani, Mohammad and Flamholz, David Bezalel and Annaswamy, Anuradha M. and Johansson, Karl Henrik and Chakrabortty, Aranya}, year={2019}, pages={394–411} }
 @inproceedings{mukherjee_chakrabortty_bai_2019, place={Philadelphia}, title={Block-Decentralized Model-Free Reinforcement Learning Control of Two Time-Scale Networks}, publisher={American Control Conference}, author={Mukherjee, S. and Chakrabortty, A. and Bai, H.}, year={2019} }
 @inproceedings{khan_cisneros_chakrabortty_husain_2019, place={Philadelphia}, title={Coordinated Control of Energy Storage in Networked Microgrids under Unpredicted Load Demands}, publisher={American Control Conference}, author={Khan, M.T. and Cisneros, R. and Chakrabortty, A. and Husain, I.}, year={2019} }
 @article{sadamoto_chakrabortty_ishizaki_imura_2019, title={Dynamic Modeling, Stability, and Control of Power Systems with Distributed Energy Resources}, volume={39}, ISSN={["1941-000X"]}, DOI={10.1109/MCS.2018.2888680}, abstractNote={Significant infrastructure changes are currently being implemented in power system networks around the world by maximizing the penetration of renewable energy, installing new transmission lines, adding flexible loads, and promoting independence in power production by disintegrating the grid into microgrids [1]. The shift of energy supply from large central generating stations to smaller producers, such as wind farms, solar photovoltaic (PV) farms, rooftop PV systems, and energy-storage systems collectively known as distributed energy resources (DERs) or inverter-based resources, is accelerating at a rapid pace. Hundreds of power electronic devices are being added, creating hundreds of new control points in the grid.}, number={2}, journal={IEEE Control Systems Magazine}, author={Sadamoto, T. and Chakrabortty, A. and Ishizaki, T. and Imura, J.}, year={2019}, month={Apr}, pages={34–65} }
 @inproceedings{mukherjee_darvishi_chakrabortty_fardanesh_2019, place={Atlanta, GA}, title={Learning Power System Dynamic Signatures using LSTM-Based Deep Neural Network : A Prototype Study on the New York State Grid}, booktitle={IEEE PES General Meeting}, author={Mukherjee, S. and Darvishi, A. and Chakrabortty, A. and Fardanesh, B.}, year={2019} }
 @inproceedings{ni_chakrabortty_xin_2019, place={Atlanta, GA}, title={Online Tuning of Cloud-based Wide-Area Controllers with Variations in Network Traffic}, booktitle={IEEE PES General Meeting}, author={Ni, H. and Chakrabortty, A. and Xin, Y.}, year={2019} }
 @article{chakrabortty_2019, title={Research Challenges for Design and Implementation of Wide-Area Control}, ISBN={["978-3-319-98309-7"]}, DOI={10.1007/978-3-319-98310-3_10}, abstractNote={The 2003 Northeast blackout uncovered the vulnerability of the US power system, and manifested the urgent need for real-time state monitoring and control of the grid leading to the development of the wide-area measurement systems (WAMS) technology.}, journal={SMART GRID CONTROL: OVERVIEW AND RESEARCH OPPORTUNITIES}, author={Chakrabortty, Aranya}, year={2019}, pages={165–172} }
 @book{stoustrup_annaswamy_chakrabortty_qu_2019, title={Smart Grid Control: Overview and Research Opportunities}, ISBN={["978-3-319-98309-7"]}, DOI={10.1007/978-3-319-98310-3}, abstractNote={This book focuses on the role of systems and control, provides an overview of the smart grid control landscape, and helps to promote smart grids by demonstrating how it can deal with customer demand and other practical market-related issues such as pricing}, journal={SMART GRID CONTROL: OVERVIEW AND RESEARCH OPPORTUNITIES}, author={Stoustrup, Jakob and Annaswamy, Anuradha and Chakrabortty, Aranya and Qu, Zhihua}, year={2019}, pages={1–288} }
 @inbook{chakrabortty_bose_2019, title={Smart Grid Simulation and Control}, booktitle={Power Electronics in Renewable Energy Systems and Smart Grid}, publisher={IEEE Press}, author={Chakrabortty, A. and Bose, A.}, year={2019} }
 @inproceedings{dizche_chakrabortty_duel-hallen_2019, place={Philadelphia}, title={Sparse Wide-Area Control of Power Systems using Data-driven Reinforcement Learning}, publisher={American Control Conference}, author={Dizche, A. Fallah and Chakrabortty, A. and Duel-Hallen, A.}, year={2019} }
 @inproceedings{mukherjee_xue_chakrabortty_2018, title={A Hierarchical Design for Damping Control of Wind-Integrated Power Systems Considering Heterogeneous Wind Farm Dynamics}, ISBN={9781538676981}, url={http://dx.doi.org/10.1109/ccta.2018.8511456}, DOI={10.1109/ccta.2018.8511456}, abstractNote={The majority of control designs for wind power systems rest upon the simplifying assumption that every wind turbine and generator (WTG) inside a wind farm has identical dynamics, and, hence, can be aggregated into a single WTG admitting a single controller. In reality, however, this assumption does not hold because of wake effect due to which the small-signal models of turbines in a given row may be similar, but those between different rows can be significantly dissimilar. In this paper we propose a hierarchical control design to address these types of heterogeneous models of WTGs in a wind farm. Our approach is to group all turbines in a row as a cluster, design a cluster-level aggregate controller by averaging of states, make these aggregate controllers exchange average state information through a local communication network, and thereafter project the aggregate controller back to the original WTGs for implementation. Simulations validating the effectiveness of this hierarchical controller are shown for the IEEE 68-bus benchmark power system with one wind farm.}, booktitle={2018 IEEE Conference on Control Technology and Applications (CCTA)}, publisher={IEEE}, author={Mukherjee, Sayak and Xue, Nan and Chakrabortty, Aranya}, year={2018}, month={Aug} }
 @inproceedings{mukherjee_babaei_chakrabortty_2018, title={A Measurement-Based Approach for Optimal Damping Control of the New York State Power Grid}, ISBN={9781538677032}, url={http://dx.doi.org/10.1109/pesgm.2018.8586338}, DOI={10.1109/pesgm.2018.8586338}, abstractNote={This paper presents a supplementary controller design for the state-of-the-art Flexible AC Transmission System (FACTS) facility in New York State (NYS) power grid from a completely measurement based perspective. We first carry out coherency analysis using measurements from multiple offline contingency simulations, and obtain coherent areas using Principal Component Analysis (PCA). Thereafter, we choose all the buses containing Phasor Measurement Units (PMUs) from each coherent zone, and use bus measurements to identify a highly reduced-order state space model of the grid using Eigensystem Realization Algorithm (ERA) such that it retains dominant inter-area modes and matches the input-output characteristics. We use this model to design a Linear Quadratic Gaussian (LQG) based optimal controller for FACTS-based actuator. The closed-loop response is simulated using PSS/E model of the Eastern Interconnection (EI). Effectiveness of the control performance is verified by non-linear simulations under different contingency scenarios specified by New York Independent System Operator (NYISO).}, booktitle={2018 IEEE Power & Energy Society General Meeting (PESGM)}, publisher={IEEE}, author={Mukherjee, Sayak and Babaei, Saman and Chakrabortty, Aranya}, year={2018}, month={Aug} }
 @article{xue_chakrabortty_2018, title={Control Inversion: A Clustering-Based Method for Distributed Wide-Area Control of Power Systems}, ISSN={2325-5870 2372-2533}, url={http://dx.doi.org/10.1109/tcns.2018.2888997}, DOI={10.1109/tcns.2018.2888997}, abstractNote={Wide-area control (WAC) has been shown to be an effective tool for damping low-frequency oscillations in power systems. In the current state of art, WAC is challenged by two main factors, namely, scalability of design and complexity of implementation. In this paper, we present a control design called control inversion that bypasses both of these challenges using the idea of clustering. The basic philosophy behind this method is to project the original power system model into a lower-dimensional state space through clustering and aggregation of generator states, and then designing a linear-quadratic regulator (LQR) controller for the lower-dimensional model. This controller is finally projected back to the original coordinates for wide-area implementation. The main problem is, therefore, posed as finding the projection which best matches the closed-loop performance of the WAC controller with that of a reference LQR controller for damping low-frequency oscillations. We verify the effectiveness of the proposed design using the IEEE 48-machine power system model of the Northeastern Power Coordinating Council.}, journal={IEEE Transactions on Control of Network Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Xue, Nan and Chakrabortty, Aranya}, year={2018}, pages={1–1} }
 @inproceedings{gusrialdi_chakrabortty_qu_2018, title={Distributed Learning of Mode Shapes in Power System Models}, ISBN={9781538613955}, url={http://dx.doi.org/10.1109/cdc.2018.8618949}, DOI={10.1109/cdc.2018.8618949}, abstractNote={We address the problem of distributed estimation of eigenvectors for power system models using online phasor measurements. The power system is considered to be divided into a set of non-overlapping areas, each of which is equipped with a local estimator. Online measurements of bus voltage and current phasors are first used to generate estimates of the generator states in each area using decentralized Kalman filters. Thereafter, these estimates are used for identifying a reduced-order model of the system in a completely distributed way by sharing state information between the estimators over a strongly connected communication graph. The identified model is then utilized to estimate its right eigenvectors over the same distributed graph. Results are validated using a 50-bus power system model with four areas.}, booktitle={2018 IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Gusrialdi, Azwirman and Chakrabortty, Aranya and Qu, Zhihua}, year={2018}, month={Dec} }
 @article{jain_chakrabortty_biyik_2018, title={Distributed wide-area control of power system oscillations under communication and actuation constraints}, volume={74}, ISSN={["1873-6939"]}, DOI={10.1016/j.conengprac.2018.03.003}, abstractNote={In this paper a distributed Model Predictive Control design is presented for inter-area oscillation damping in power systems under two critical cyber–physical constraints — namely, communication constraints that lead to sparsification of the underlying communication network, and actuation constraints that respect the saturation limits of generator controllers. In the current state-of-art, distributed controllers in power systems are executed over fixed communication topologies that are most often agnostic of the magnitude and location of the incoming disturbance signals. This often leads to a sub-optimal closed-loop performance. In contrast, the communication topology for the proposed controller is selected in real-time after a disturbance event based on event-specific correlations of the generator states with the dominant oscillation modes that are excited by that event. Since these correlations can differ from one event to another, so can the choice of the communication topology. These correlations are used to identify the most important sets of generators that must exchange state information for enhancing closed-loop damping of the inter-area modal frequencies. Effectiveness of this strategy is shown via simulations on the 48-machine, 140-bus model for the Northeast Power Coordinating Council.}, journal={CONTROL ENGINEERING PRACTICE}, author={Jain, Abhishek and Chakrabortty, Aranya and Biyik, Emrah}, year={2018}, month={May}, pages={132–143} }
 @article{khan_milani_chakrabortty_husain_2018, title={Dynamic Modeling and Feasibility Analysis of a Solid-State Transformer-Based Power Distribution System}, volume={54}, ISSN={["1939-9367"]}, DOI={10.1109/tia.2017.2757450}, abstractNote={This paper presents a comprehensive state-space dynamic model of a future power distribution system for plug-and-play interface of distributed renewable energy resources and distributed energy storage devices. The system, called the future renewable electric energy delivery and management (FREEDM) system, comprises of multiple solid-state transformers (SSTs), and load, generation, and storage connected to each SST in a distributed network. The system allows for high penetration of renewable generation with energy storage at the distribution level. A physics-based 70th-order state-space average model is first developed considering the physical and controller properties of a single-SST FREEDM system along with its distribution components. This fundamental model is then extended to build a multi-SST FREEDM system for feasibility and dynamics behavior analysis of the entire system, which is essential to ensure system power balance. The full average model with multiple SSTs has been incorporated in an IEEE 34 bus distribution testbed for a scaled analysis of the system.}, number={1}, journal={IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS}, author={Khan, Md Tanvir Arafat and Milani, Alireza Afiat and Chakrabortty, Aranya and Husain, Iqbal}, year={2018}, pages={551–562} }
 @article{milani_khan_chakrabortty_husain_2018, title={Equilibrium Point Analysis and Power Sharing Methods for Distribution Systems Driven by Solid-State Transformers}, volume={33}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2017.2720540}, abstractNote={The feasible equilibria of operation of distribution-level power system models interfaced with solid-state transformers (SST) are analyzed and presented through a set of analytical relationships. The active and reactive power balances in the SST are realized through control of power electronic converters with appropriate choices for voltage and current setpoints. These setpoints parameterize the nonlinear model of the SST. Therefore, choosing them appropriately in sync with the generation and load profiles in the system is critical for maintaining a feasible equilibrium. These equilibrium sets are derived by first considering a fundamental physics-based model of a single-SST system, and thereafter, by extending them to systems with multiple SSTs connected to a radial distribution feeder. Power sharing methods are developed by which multiple SSTs can share a given change in load by generating an appropriate set of feasible setpoints for their input stage rectifiers. A control architecture is proposed for executing these load-sharing methods for both instantaneous and predictive load commands. The algorithms are verified by simulations on a representative distribution test system with nine SSTs.}, number={2}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Milani, Alireza Afiat and Khan, Md Tanvir Arafat and Chakrabortty, Aranya and Husain, Iqbal}, year={2018}, month={Mar}, pages={1473–1483} }
 @article{ishizaki_chakrabortt_imura_2018, title={Graph-Theoretic Analysis of Power Systems}, volume={106}, ISSN={["1558-2256"]}, DOI={10.1109/jproc.2018.2812298}, abstractNote={In this paper, we present an overview of the applications of graph theory in power system modeling, dynamics, coherency, and control. First, we study synchronization of generator dynamics using both nonlinear and small-signal representations of classical structure-preserving models of power systems in light of their network structure and the weights associated with the nodes and edges of the network graph. We overview important necessary and sufficient conditions for both phase and frequency synchronization. We highlight the role of graph structure in coherency properties, and introduce the idea of generator and bus aggregation whereby dynamic equivalent models of large power grids can be developed while retaining the concept of a “bus” in the network graph of the equivalent model. We also discuss several new results on graph sparsification for designing distributed controllers for power flow oscillation damping.}, number={5}, journal={PROCEEDINGS OF THE IEEE}, author={Ishizaki, Takayuki and Chakrabortt, Aranya and Imura, Jun-Ichi}, year={2018}, month={May}, pages={931–952} }
 @inproceedings{xue_chakrabortty_2018, title={Hierarchical H 2 Control of Large-Scale Network Dynamic Systems}, ISBN={9781538654286}, url={http://dx.doi.org/10.23919/acc.2018.8431640}, DOI={10.23919/acc.2018.8431640}, abstractNote={Standard $\mathcal{H}_{2}$ optimal control of networked dynamic systems tend to become unscalable with network size. Structural constraints can be imposed on the design to counteract this problem albeit at the risk of making the solution nonconvex. In this paper, we present a special class of structural constraints such that the $\mathcal{H}_{2}$ design satisfies a quadratic invariance condition, and therefore can be reformulated as a convex problem. This special class consists of structured and weighted projections of the input and output spaces. The choice of these projections can be optimized to match the closed-loop performance of the reformulated controller with that of the standard $\mathcal{H}_{2}$ controller. The advantage is that unlike the latter, the reformulated controller results in a hierarchical implementation which requires significantly lesser number of communication links. We illustrate our design with simulations of a 500-node network.}, booktitle={2018 Annual American Control Conference (ACC)}, publisher={IEEE}, author={Xue, Nan and Chakrabortty, Aranya}, year={2018}, month={Jun} }
 @article{susuki_chakrabortty_2018, title={Introduction to Koopman Mode Decomposition for Data-Based Technology of Power System Nonlinear Dynamics}, volume={51}, ISSN={["2405-8963"]}, DOI={10.1016/j.facol.2018.11.723}, number={28}, journal={IFAC PAPERSONLINE}, author={Susuki, Yoshihiko and Chakrabortty, Aranya}, year={2018}, pages={327–332} }
 @article{susuki_chakrabortty_2018, title={Introduction to Koopman Mode Decomposition for Data-Based Technology of Power System Nonlinear Dynamics}, volume={51}, ISSN={2405-8963}, url={http://dx.doi.org/10.1016/J.IFACOL.2018.11.723}, DOI={10.1016/J.IFACOL.2018.11.723}, abstractNote={Abstract Data-based technology of power system dynamics has attracted a lot of interest in the modern power system with the so-called Wide-Area Measurement System (WAMS). Concerted efforts are currently being made to develop the technology based on linearized dynamic models. In contrast, the full nonlinear models have received less attention in this research community. We present the research challenges to go beyond the conventional linear framework by focusing on Koopman Mode Decomposition (KMD), which is a nonlinear generalization of linear oscillatory modes guided by operator theory of nonlinear dynamical systems. Our discussion begins with a review of the main tools—Koopman operator and Prony approximation of KMD. We pose several distinct problems on data analysis, computation, monitoring, situational awareness, and control for the future power system architecture. Our idea is then illustrated on how the Prony approximation of KMD is distributed in WAMS.}, number={28}, journal={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Susuki, Yoshihiko and Chakrabortty, Aranya}, year={2018}, pages={327–332} }
 @inproceedings{mukherjee_bai_chakrabortty_2018, title={On Model-Free Reinforcement Learning of Reduced-Order Optimal Control for Singularly Perturbed Systems}, ISBN={9781538613955}, url={http://dx.doi.org/10.1109/cdc.2018.8619022}, DOI={10.1109/cdc.2018.8619022}, abstractNote={We propose a model-free reduced-order optimal control design for linear time-invariant singularly perturbed (SP) systems using reinforcement learning (RL). Both the state and input matrices of the plant model are assumed to be completely unknown. The only assumption imposed is that the model admits a similarity transformation that results in a SP representation. We propose a variant of Adaptive Dynamic Programming (ADP) that employs only the slow states of this SP model to learn a reduced-order adaptive optimal controller. The method significantly reduces the learning time, and complexity required for the feedback control by taking advantage of this model reduction. We use approximation theorems from singular perturbation theory to establish sub-optimality of the learned controller, and to guarantee closed-loop stability. We validate our results using two representative examples - one with a standard singularly perturbed dynamics, and the other with clustered multi-agent consensus dynamics. Both examples highlight various implementation details and effectiveness of the proposed approach.}, booktitle={2018 IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Mukherjee, Sayak and Bai, He and Chakrabortty, Aranya}, year={2018}, month={Dec} }
 @inproceedings{gubitz_sico_chakrabortty_2018, title={Online Detection and Quantification of Transient Instability using Lyapunov Exponents from PMU Data}, ISBN={9781538671382}, url={http://dx.doi.org/10.1109/naps.2018.8600586}, DOI={10.1109/naps.2018.8600586}, abstractNote={Lyapunov Exponents (LE) have been shown to be an effective tool in predicting short-term voltage instability in power systems by determining if their voltage trajectories indicate that a system is stable or unstable. This paper provides an improved LE algorithm for use in real-time streaming applications for short-term voltage instability detection. Additionally, this paper proposes three variants to the traditional LE calculation, which estimate the final value of the LE and accurately quantify the stability of a stable power system. The proposed modifications to the LE calculation are applied to voltages sampled at Phasor Measurement Unit (PMU) data rates. The streaming algorithm presented is used to activate a Battery Energy Storage System (BESS) to improve power system stability. Results are validated by using the IEEE 39 Bus model, a Duke Energy system model, and historical events recorded by Duke Energy PMUs.}, booktitle={2018 North American Power Symposium (NAPS)}, publisher={IEEE}, author={Gubitz, Timothy and Sico, Kathleen and Chakrabortty, Aranya}, year={2018}, month={Sep} }
 @article{liao_chakrabortty_2018, title={Optimization Algorithms for Catching Data Manipulators in Power System Estimation Loops}, ISSN={1063-6536 1558-0865}, url={http://dx.doi.org/10.1109/tcst.2018.2805294}, DOI={10.1109/tcst.2018.2805294}, abstractNote={In this paper, we develop a set of algorithms that can detect the identities of malicious data manipulators in distributed optimization loops for estimating oscillation modes in large-power system models. The estimation is posed in terms of a consensus problem among multiple local estimators that jointly solve for the characteristic polynomial of the network model. If any of these local estimates is compromised by a malicious attacker, resulting in an incorrect value of the consensus variable, then the entire estimation loop can be destabilized. We present four iterative algorithms by which this instability can be quickly detected, and the identities of the compromised estimators can be revealed. The algorithms are solely based on the computed values of the estimates, and do not need any information about the model of the power system. Both large and covert attacks are considered. The results are illustrated using simulations of the IEEE 68-bus power system model.}, journal={IEEE Transactions on Control Systems Technology}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Liao, Mang and Chakrabortty, Aranya}, year={2018}, pages={1–16} }
 @article{sadamoto_chakrabortty_ishizaki_imura_2018, title={Retrofit Control of Wind-Integrated Power Systems}, volume={33}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2017.2750411}, abstractNote={In this paper, we address several growing concerns of wind power integration from the perspective of power system dynamics and stability. We propose a new control design technique called retrofit control, by which one can control the rotor voltages of doubly fed induction generators to suppress the oscillations in the tie-line power flows caused by a disturbance inside the wind farm. The controller can be designed in a modular way, and also implemented in a completely decentralized fashion using only local feedback from the wind generator states and the voltage at the point of common coupling without depending on the states of any of the synchronous machines in the rest of the system. We show the effectiveness of the design using simulations of the IEEE 68- bus, 16-machine power system model with two wind farms.}, number={3}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Sadamoto, Tomonori and Chakrabortty, Aranya and Ishizaki, Takayuki and Imura, Jun-ichi}, year={2018}, month={May}, pages={2804–2815} }
 @inproceedings{ni_rahouti_chakrabortty_xiong_xin_2018, place={Portland, OR}, title={Routing Path Optimization for Regulating Delays in Wide-Area Controllers Implemented over Cloud Networks}, booktitle={IEEE PES General Meeting}, author={Ni, H. and Rahouti, M. and Chakrabortty, A. and Xiong, K. and Xin, Y.}, year={2018} }
 @inproceedings{dibaji_pirani_annaswamy_johansson_chakrabortty_2018, title={Secure Control of Wide-Area Power Systems: Confidentiality and Integrity Threats}, ISBN={9781538613955}, url={http://dx.doi.org/10.1109/cdc.2018.8618862}, DOI={10.1109/cdc.2018.8618862}, abstractNote={A cyber-physical model for wide-area control of power systems is considered, where the state variables of each generator are measured and sent to the cyber-network and the corresponding control inputs are computed distributively. The secure control of such wide-area power systems is considered in the presence of cyber attacks that introduce threats that compromise their integrity and confidentiality. Detection, prevention, and resilience for these attacks and algorithms for accomplishing these goals are proposed. In particular, an algorithm to overcome confidentiality attacks of the underlying control gains is presented. Also proposed is an algorithm for defense against integrity attacks that might take place on the cyber-network. For this purpose, a resilient information retrieval approach is leveraged which recovers the true state variables despite the malicious attacks on both virtual machines and communication links. The retrieved states are then used to detect possible attacks on phasor measurement units (PMU) in the next time-step. Simulation studies are included to validate our proposed approaches.}, booktitle={2018 IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Dibaji, S. M. and Pirani, M. and Annaswamy, A. M. and Johansson, K. H. and Chakrabortty, A.}, year={2018}, month={Dec} }
 @book{annaswamy_stoustrup_chakrabortty_qu_2018, place={MA}, title={Smart Grid Control: Opportunities and Research Challenges}, publisher={Springer}, year={2018}, month={Oct} }
 @inproceedings{negi_chakrabortty_2018, title={Sparse Optimal Control of LTI Systems under Sparsity-Dependent Delays}, ISBN={9781538654286}, url={http://dx.doi.org/10.23919/acc.2018.8431138}, DOI={10.23919/acc.2018.8431138}, abstractNote={We address the problem of sparse $\mathcal{H}_{2}$ control design for linear time invariant (LTI) systems in the presence of feedback delays. Depending on the network configuration, the delays may be constant, or an explicit function of the sparsity itself. We first state a sufficient condition for delay stability, and show that it appears as a non-convex bilinear matrix inequality (BMI) constraint for the $\mathcal{H}_{2}$-minimization problem. We relax this BMI as a set of convex semidefinite programs that result in a two loop optimization algorithm. The inner-loop promotes sparsity of the state feedback matrix constrained by the set of stabilizing gains for the delayed system. The outer-loop aligns the direction of sparsity with the minimizing $\mathcal{H}_{2}$ norm direction. We solve this two loop optimization using the alternating direction method of multipliers (ADMM). Simulation results illustrate the effectiveness of the proposed approach in finding sparse feedback matrices that achieve a low $\mathcal{H}_{2}$ norm while guaranteeing stability of the closed-loop delayed system.}, booktitle={2018 Annual American Control Conference (ACC)}, publisher={IEEE}, author={Negi, Nandini and Chakrabortty, Aranya}, year={2018}, month={Jun} }
 @inproceedings{dibaji_annaswamy_chakrabortty_hussain_2018, title={Sparse and Distributed Control of Wide-Area Power Systems with Large Communication Delays}, ISBN={9781538654286}, url={http://dx.doi.org/10.23919/acc.2018.8431309}, DOI={10.23919/acc.2018.8431309}, abstractNote={A sparse and distributed optimal control strategy is proposed for wide-area control of power systems in the presence of large network delays. Sparsity is introduced in the underlying communication network on the basis of dominant participation of the state variables in the inter-area oscillation modes that decides which generators should communicate with which other generators, and included in the control design. In addition, the controller accommodates large network delays that are of values four to five times greater than the sampling period. A virtual sparsity concept is introduced to accommodate these delays by zeroing out the gains that correspond to measurements that are yet to arrive. Results are verified through a simulation study of the IEEE-39 bus power system model, where it is shown that with 86% less communication channels, we can obtain nearly 89% of the performance compared to the case with a non-sparse controller.}, booktitle={2018 Annual American Control Conference (ACC)}, publisher={IEEE}, author={Dibaji, Seyed Mehran and Annaswamy, Anuradha and Chakrabortty, Aranya and Hussain, Alefiya}, year={2018}, month={Jun} }
 @inproceedings{lian_chakrabortty_wu_duel-hallen_2018, title={Sparsity-Constrained Mixed H 2 /H ∞ Control}, ISBN={9781538654286}, url={http://dx.doi.org/10.23919/acc.2018.8431378}, DOI={10.23919/acc.2018.8431378}, abstractNote={We propose an algorithm for designing sparsity-constrained controllers for linear time-invariant systems with model uncertainties using a mixed $H_{2}/H_{\infty}$ objective. We first improve a previously proposed descent algorithm for mixed $H_{2}/H_{\infty}$ control using a modified Zoutendijk's method. Thereafter, we impose a sparsity constraint on this design by combining it with a greedy gradient support pursuit (GraSP) method. The proposed algorithm guarantees a predetermined level of sparsity while maintaining acceptable $H_{2}$ performance as well as $H_{\infty}$ robustness to uncertainties in the open-loop model. The effectiveness of the proposed method is illustrated through simulations.}, booktitle={Proceedings of the Annual American Control Conference (ACC)}, publisher={IEEE}, author={Lian, Feier and Chakrabortty, Aranya and Wu, Fen and Duel-Hallen, Alexandra}, year={2018}, month={Jun}, pages={6253–6258,} }
 @inproceedings{jain_chakrabortty_biyik_2018, title={Structurally Constrained `1-Sparse Control of Power Systems: Online Design and Resiliency Analysis}, ISBN={9781538654286}, url={http://dx.doi.org/10.23919/acc.2018.8431667}, DOI={10.23919/acc.2018.8431667}, abstractNote={This paper presents a sparse Linear Quadratic Regulator (LQR) design for damping oscillations in wide-area power system networks. We first show how, depending on the severity and location of a fault, different sets of generators can have different contributions to the inter-area oscillation modes. This information is used to construct the communication topology for feedback control. An additional layer of sparsity is imposed on top of this communication structure by posing an $\ell_{1}$-sparsification of the generator states that are transmitted through each communication link. An algorithm is provided where the designed sparse controller is also used to enhance the resiliency of the closed-loop system against denial-of-service (DoS) attacks. Results are validated using simulations on the IEEE 39-bus New England power system model.}, booktitle={2018 Annual American Control Conference (ACC)}, publisher={IEEE}, author={Jain, Abhishek and Chakrabortty, Aranya and Biyik, Emrah}, year={2018}, month={Jun} }
 @inproceedings{mlinaric_ishizaki_chakrabortty_grundel_benner_imura_2018, title={Synchronization and Aggregation of Nonlinear Power Systems with Consideration of Bus Network Structures}, ISBN={9783952426982}, url={http://dx.doi.org/10.23919/ecc.2018.8550528}, DOI={10.23919/ecc.2018.8550528}, abstractNote={We study nonlinear power systems consisting of generators, generator buses, and non-generator buses. First, looking at a generator and its bus' variables jointly, we introduce a synchronization concept for a pair of such joint generators and buses. We show that this concept is related to graph symmetry. Next, we extend, in two ways, the synchronization from a pair to a partition of all generators in the networks and show that they are related to either graph symmetry or equitable partitions. Finally, we show how an exact reduced model can be obtained by aggregating the generators and associated buses in the network when the original system is synchronized with respect to a partition, provided that the initial condition respects the partition. Additionally, the aggregation-based reduced model is again a power system.}, booktitle={2018 European Control Conference (ECC)}, publisher={IEEE}, author={Mlinaric, Petar and Ishizaki, Takayuki and Chakrabortty, Aranya and Grundel, Sara and Benner, Peter and Imura, Jun-ichi}, year={2018}, month={Jun} }
 @inbook{chakrabortty_2018, title={Wide-Area Communication and Control: A Cyber-Physical Perspective}, ISBN={9783319983097 9783319983103}, ISSN={2196-3185 2196-3193}, url={http://dx.doi.org/10.1007/978-3-319-98310-3_9}, DOI={10.1007/978-3-319-98310-3_9}, abstractNote={For several decades, the traditional mindset for controlling large-scale power systems has been limited to local output feedback control, which means that controllers installed within the operating region of any utility company typically use measurements available only from inside that region for feedback, and, in fact, more commonly only from the vicinity of the controller location. Examples of such controllers include Automatic Voltage Regulators (AVR), Power System Stabilizers (PSS), Automatic Generation Control (AGC), FACTS control, HVDC, and so on.}, booktitle={Smart Grid Control}, publisher={Springer International Publishing}, author={Chakrabortty, Aranya}, year={2018}, month={Sep}, pages={139–164} }
 @article{soudbakhsh_chakrabortty_annaswamy_2017, title={A delay-aware cyber-physical architecture for wide-area control of power systems}, volume={60}, ISSN={["1873-6939"]}, DOI={10.1016/j.conengprac.2016.12.012}, abstractNote={In this paper we address the problem of wide-area control of power systems using Synchrophasor measurements in the presence of network delays. We propose a novel cyber-physical architecture that uses an arbitrated network control systems approach for mitigating the destabilizing effects of delays in power systems. The approach consists of: (1) utilization of Synchrophasor measurements from distributed measurements across different buses in the power network, (2) estimation of delays that control messages experience, (3) a delay-aware control design that explicitly accommodates the delays and judiciously utilizes estimated system states when needed, and (4) a switching control strategy that aborts the computation of control signals when delays exceed a certain threshold to improve resource utilization. While the control gains are determined using a centralized power system model and state feedback, it is shown that the delay-aware aspects of the proposed architecture allow both distributed measurements and distributed implementation of the control law. The results are illustrated using a 50-bus, 14-generator, 4-area power system model. The results clearly demonstrate that the proposed controller recovers the ideal system performance (such as deviations in frequency<3mHz) even in the presence of large intra-area and inter-area delays with a small amount of additional control effort. Using the proposed overrun strategy, the results also confirm that about 30% drops can be accommodated with the proposed arbitrated network control systems approach.}, journal={CONTROL ENGINEERING PRACTICE}, author={Soudbakhsh, Damoon and Chakrabortty, Aranya and Annaswamy, Anuradha M.}, year={2017}, month={Mar}, pages={171–182} }
 @inproceedings{sadamoto_chakrabortty_ishizaki_imura_2017, title={A retrofitting-based supplementary controller design for enhancing damping performance of wind power systems}, ISBN={9781509059928}, url={http://dx.doi.org/10.23919/acc.2017.7963368}, DOI={10.23919/acc.2017.7963368}, abstractNote={In this paper we address the growing concerns of wind power integration from the perspective of power system dynamics and stability. We propose a new retrofit control technique where an additional controller is designed at the doubly-fed induction generator site inside the wind power plant. This controller cancels the adverse impacts of the power flow from the wind side to the grid side on the dynamics of the overall power system. The main advantage of this controller is that it can be implemented by feeding back only the wind states and wind bus voltage without depending on any of the other synchronous machines in the rest of the system. Through simulations of a 4-machine Kundur power system model we show that the retrofit can efficiently enhance the damping performance of the system variable despite very high values of wind penetration.}, booktitle={2017 American Control Conference (ACC)}, publisher={IEEE}, author={Sadamoto, Tomonori and Chakrabortty, Aranya and Ishizaki, Takayuki and Imura, Jun-ichi}, year={2017}, month={May} }
 @inproceedings{jain_chakrabortty_biyik_2017, title={An online structurally constrained LQR design for damping oscillations in power system networks}, ISBN={9781509059928}, url={http://dx.doi.org/10.23919/acc.2017.7963261}, DOI={10.23919/acc.2017.7963261}, abstractNote={This paper presents an online distributed control design for suppressing inter-area oscillations in large power systems under structural constraints posed on the underlying communication network. The presence of multiple clusters of generators in a power system results in several inter-area oscillation modes. By modal analysis, we first show that the contribution of each inter-area mode on the electromechanical state response of the generators is heavily dependent on the perturbed initial state of the system. We then take advantage of this observation to design structural constraints on the communication graph. A parallelized constrained linear quadratic regulator (LQR) design is then proposed to balance the tradeoff between performance and the level of sparsity induced in the network. Algorithms for practical implementation of the design are provided. Results are compared with the full order LQR, and illustrated on the New England 39-bus power system model.}, booktitle={2017 American Control Conference (ACC)}, publisher={IEEE}, author={Jain, Abhishek and Chakrabortty, Aranya and Biyik, Emrah}, year={2017}, month={May} }
 @article{dibaji_yildiz_annaswamy_chakrabortty_soudbakhsh_2017, title={Delay-Aware Control Designs of Wide-Area Power Networks * *This work was supported in part by NSF grant ECS 1054394.}, volume={50}, ISSN={2405-8963}, url={http://dx.doi.org/10.1016/j.ifacol.2017.08.014}, DOI={10.1016/j.ifacol.2017.08.014}, abstractNote={A co-design of the implementation platform and control strategies for wide-area power networks is addressed. Limited and shared resources among control and non-control applications introduce delays in transmitted messages. The design is based on a delay-aware architecture and cloud computing has been proposed for damping wide-area oscillations. We accommodate possibly large delays in the network and take into account their values in the designs. Moreover, we design output feedbacks for the cases that some state variables are not accessible. The designs are verified through a simulation on 50-bus Australian model.}, number={1}, journal={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Dibaji, Seyed Mehran and Yildiz, Yildiray and Annaswamy, Anuradha and Chakrabortty, Aranya and Soudbakhsh, Damoon}, year={2017}, month={Jul}, pages={79–84} }
 @inproceedings{chakrabortty_2017, title={Distributed cyber-physical algorithms for wide-area control of power systems}, DOI={10.1109/ciss.2017.7926090}, abstractNote={With the number of Phasor Measurement Units (PMUs) in the North American power grid scaling up into the thousands, system operators are gradually inclining towards distributed cyber-physical architectures for executing wide-area monitoring and control operations using Synchrophasors. Traditional centralized approaches, in fact, are anticipated to become untenable soon due to various factors such as data volume, security against single point of failure, communication overhead, and failure to adhere to real-time deadlines. In this talk I will propose a distributed communication and computational architecture, and its associated distributed optimal control algorithms, for one of the most critical applications run by utility companies - namely, wide-area control of power flow oscillations following small-signal and large-signal disturbances in the grid. In this architecture, Synchrophasor data from PMUs located at the terminal buses of generators are first transmitted to the local control center for that particular balancing region, and thereafter to a set virtual computers in a local cloud computing network. Depending on the correlation between the generator states in terms of the modal content of the measured signals, a distributed communication strategy is chosen and established between these virtual computers in the cloud. A real-time model-predictive control design is then implemented using this distributed communication network, assuming synchronous communication. I will present simulations that highlight some interesting convergence and accuracy trade-offs for the real-time implementation of the wide-area controller, and also illustrate their architectural resiliency against denial-of-service and data-manipulation attacks using case studies from the recently federated DETER-WAMS testbed between NC State and University of Southern California.}, booktitle={2017 51st Annual Conference on Information Sciences and Systems (CISS)}, author={Chakrabortty, Aranya}, year={2017} }
 @article{lian_chakrabortty_duel-hallen_2017, place={USA}, title={Game-Theoretic Multi-Agent Control and Network Cost Allocation Under Communication Constraints}, volume={35}, ISSN={["1558-0008"]}, DOI={10.1109/jsac.2017.2659338}, abstractNote={Multi-agent networked linear dynamic systems have attracted the attention of researchers in power systems, intelligent transportation, and industrial automation. The agents might cooperatively optimize a global performance objective, resulting in social optimization, or try to satisfy their own selfish objectives using a noncooperative differential game. However, in these solutions, large volumes of data must be sent from system states to possibly distant control inputs, thus resulting in high cost of the underlying communication network. To enable economically viable communication, a game-theoretic framework is proposed under the communication cost, or sparsity, constraint, given by the number of communicating state/control input pairs. As this constraint tightens, the system transitions from dense to sparse communication, providing the tradeoff between dynamic system performance and information exchange. Moreover, using the proposed sparsity-constrained distributed social optimization and noncooperative game algorithms, we develop a method to allocate the costs of the communication infrastructure fairly and according to the agents’ diverse needs for feedback and cooperation. Numerical results illustrate utilization of the proposed algorithms to enable and ensure economic fairness of wide-area control among power companies.}, number={2}, journal={IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS}, author={Lian, Feier and Chakrabortty, Aranya and Duel-Hallen, Alexandra}, year={2017}, month={Feb}, pages={330–340} }
 @article{chavan_weiss_chakrabortty_bhattacharya_salazar_ashrafi_2017, title={Identification and Predictive Analysis of a Multi-Area WECC Power System Model Using Synchrophasors}, volume={8}, ISSN={1949-3053 1949-3061}, url={http://dx.doi.org/10.1109/tsg.2016.2531637}, DOI={10.1109/tsg.2016.2531637}, abstractNote={This paper describes the construction of a reduced-order five-machine dynamic equivalent electro-mechanical model of the Western Electricity Coordinating Council (WECC) 500 kV power system network using slow mode oscillations of power flows derived from phasor measurement unit data. We first extract the slow oscillations using modal decomposition, and use them to estimate four key parameters of the reduced-order system, namely, the inter-area transmission line impedances, intra-area Thevenin reactances, rotational inertia, and damping of the aggregated synchronous generators. The resulting five-machine equivalent model is validated using different ranges of contingencies such as generation loss and line loss, and thereafter used for accurate prediction of oscillation mode frequencies and their damping factors. Finally, we present an algorithm by which this reduced-order model can be used to determine the criticality of line loss events within any area based on the divergence of load flow. The conclusions are drawn with the possible applications of the model for transient stability assessment, and prediction of stability limits needed to sustain increasing wind power penetration in the WECC.}, number={4}, journal={IEEE Transactions on Smart Grid}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chavan, Govind and Weiss, Matthew and Chakrabortty, Aranya and Bhattacharya, Subhashish and Salazar, Armando and Ashrafi, Farrokh-Habibi}, year={2017}, month={Jul}, pages={1977–1986} }
 @inproceedings{liao_chakrabortty_2017, title={Identifying data-manipulators in power system mode estimation loops with noisy measurements}, ISBN={9781509059928}, url={http://dx.doi.org/10.23919/acc.2017.7963371}, DOI={10.23919/acc.2017.7963371}, abstractNote={We develop an algorithm that can detect the identity of false data-injection attackers in distributed optimization loops for estimating oscillation modes in power system models when the measurements used for the estimation are noisy. The fundamental set-up for the optimization is based on a distributed version of total least-squares (TLS) executed via Alternating Direction Multiplier Method (ADMM). The algorithm is implemented via message passing between a set of local estimators and a central coordinator. Some of these local estimators are assumed to be compromised by malicious attackers that send incorrect values of their local estimates to the coordinator. We show that if the central supervisor, instead of computing the average of the local estimates as is the usual approach in ADMM, employs a deterministic ordered Round-Robbin technique to generate the consensus variable, then it is possible to catch the identity of the manipulators by simply observing the evolution of the consensus variable. We also show that choosing the right order based on the TLS estimates can amplify the attack signatures, which helps in reducing false alarms in presence of noise. We illustrate the results using simulations of the IEEE 68-bus power system model.}, booktitle={2017 American Control Conference (ACC)}, publisher={IEEE}, author={Liao, Mang and Chakrabortty, Aranya}, year={2017}, month={May} }
 @inproceedings{chakrabortty_2017, title={Infusing Autonomy in Power Distribution Networks using Smart Transformers}, DOI={10.1109/ccta.2017.8062607}, abstractNote={In this tutorial we describe a list of analytical methods from optimization, control theory, and machine learning that can be used for infusing autonomy in large-scale interconnected networks of microgrids with as little human intervention in their control loops as possible. The cornerstone medium for promoting this autonomy is smart transformers made out of solid-state technology, which serve the dual role of a power-electronic transformer with very fast switching capability, and, hence, with significantly smaller size than conventional magnetic transformers, as well as of a powerful computer or logic-machine that can make intelligent decisions via communication. Solid-state transformers (SSTs) are, in fact, being anticipated to be the backbone of tomorrow's modern distribution grid. Microgrids typically have three layers of controllers — namely, primary control (for switching and circuit-breaking decisions), secondary control (for voltage and frequency regulation, and synchronization), and tertiary control (where a centralized supervisory controller communicates with energy management centers for updating setpoints according to load demands, and other changes in the circuit). Operating these control layers in today's microgrids require professional knowledge of the system, and calls for the operators to manually configure each of the components. With technology advancing to low-cost microprocessor driven devices such as SSTs, we propose a suite of new control and learning approaches that exploit different ‘Internet of things’ functionalities embedded inside the SSTs, and thereby guarantee at-scale resilience, reliability, fault-tolerance, and autonomy for tomorrow's distribution networks.}, booktitle={2017 IEEE conference on control technology and applications (CCTA 2017)}, author={Chakrabortty, Aranya}, year={2017}, pages={1110–1116} }
 @inproceedings{xue_chakrabortty_2017, title={LQG control of large networks: A clustering-based approach}, ISBN={9781509059928}, url={http://dx.doi.org/10.23919/acc.2017.7963301}, DOI={10.23919/acc.2017.7963301}, abstractNote={In this paper we present a Linear Quadratic Gaussian (LQG) control design for large-dimensional network dynamic systems using the idea of network clustering. When networks have tens of thousands of nodes spread over a wide geographical span, the design of conventional output feedback controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithm bypasses these difficulties by clustering the network nodes using structural properties of its closed-loop transfer matrix. The cluster assignment is applied for constructing a structured projection matrix P, which is used to pose a significantly lower-dimensional controller design. The problem is, therefore, posed in terms of finding the optimal set of clusters or P that minimizes the ℋ2-norm of the error between the transfer matrices of the full-order network with a conventional LQG controller and that with the projected LQG controller. We derive an upper bound on this error as a function of P, and design a P that minimizes this bound.}, booktitle={2017 American Control Conference (ACC)}, publisher={IEEE}, author={Xue, Nan and Chakrabortty, Aranya}, year={2017}, month={May} }
 @misc{chakrabortty_bose_2017, title={Smart Grid Simulations and Their Supporting Implementation Methods}, volume={105}, ISSN={["1558-2256"]}, DOI={10.1109/jproc.2017.2737635}, abstractNote={In this tutorial we present the state-of-the-art as well as new methods for simulating various planning, operation, stability, reliability, and economic models of electric power systems. The discussion is driven by both first-principle models and empirical models. First-principle models result from the fundamental physics and engineering principles that govern the behavior of various components of a grid. Empirical models, on the other hand, are models that result from statistics and data analysis. We overview a wide spectrum of applications starting from planning models with a time-scale of simulation in years to real-time models where the time-scale can be in the order of milliseconds. We present a list of simulation software popularly used by the power engineering research community across the world. The increasingly important roles of power electronics, communication and computing, model aggregation, hybrid simulation, faster-than-real-time simulation, and co-simulation in emulating the daily operation of a grid are enumerated. The importance of research testbeds for testing, verification and validation of complex grid models at various temporal and spatial scales is also highlighted. The overall goal is to provide a vision on how simulations and their supporting implementation methods can help us in understanding the evolving behavior of tomorrow’s power networks as a truly intelligent cyber-physical system.}, number={11}, journal={PROCEEDINGS OF THE IEEE}, author={Chakrabortty, Aranya and Bose, Anjan}, year={2017}, month={Nov}, pages={2220–2243} }
 @article{nabavi_chakrabortty_2017, title={Structured Identification of Reduced-Order Models of Power Systems in a Differential-Algebraic Form}, volume={32}, ISSN={0885-8950 1558-0679}, url={http://dx.doi.org/10.1109/tpwrs.2016.2554154}, DOI={10.1109/tpwrs.2016.2554154}, abstractNote={In a recent paper, we proposed a system identification method for constructing reduced-order models for the electro-mechanical dynamics of large power systems, divided into multiple coherent clusters, using Synchrophasors. Every cluster in the actual model was represented as an aggregate generator in the reduced-order model. An aggregate network graph connected one aggregate generator to another. In this paper, we extend this identification approach to differential-algebraic (DAE) models. First, every cluster is associated with a unique terminal bus, referred to as the pilot bus, that couples its internal network to the rest of the system. The proposed algorithm uses Synchrophasor measurements from the pilot buses to identify the dynamic model of the aggregate generator for each cluster using nonlinear least squares while retaining the identity of all the pilot buses. The resulting reduced-order model is in the form of a nonlinear electric circuit described by aggregate differential and algebraic equations. We illustrate our results using two case studies, one for the IEEE 9-bus power system and another for the IEEE 39-bus power system. We also discuss how these reduced-order DAE models may be useful for designing shunt controllers at the pilot buses by using Synchrophasor feedback.}, number={1}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Nabavi, Seyedbehzad and Chakrabortty, Aranya}, year={2017}, month={Jan}, pages={198–207} }
 @article{nabavi_chakrabortty_2016, title={A Graph-Theoretic Condition for Global Identifiability of Weighted Consensus Networks}, volume={61}, ISSN={["1558-2523"]}, DOI={10.1109/tac.2015.2438425}, abstractNote={In this technical note, we present a sufficient condition that guarantees identifiability for a class of linear network dynamic systems exhibiting continuous-time weighted consensus protocols. Each edge of the underlying network graph G of the system is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definition of output distinguishability, we first derive a condition that ensures the identifiability of the edge-weights of G in terms of the associate transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge-weights. We describe our results using illustrative examples.}, number={2}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Nabavi, Seyedbehzad and Chakrabortty, Aranya}, year={2016}, month={Feb}, pages={497–502} }
 @inproceedings{liao_chakrabortty_2016, title={A Round-robin ADMM algorithm for identifying data-manipulators in power system estimation}, DOI={10.1109/acc.2016.7525462}, abstractNote={In this paper we develop an algorithm that can detect the identity of false data-injection attackers in distributed optimization loops for estimating oscillation modes in large power system models. The fundamental set-up for this distributed optimization is based on Alternating Direction Multiplier Method (ADMM). The power system is divided into multiple non-overlapping areas, each equipped with a local estimator. These local estimators use local sensor measurements to carry out a local regression algorithm for generating a local estimate for the characteristic polynomial for the system transfer function, and, thereafter, communicate this estimate to a central supervisor. The supervisor computes the average of all estimates, and broadcasts this average or consensus variable back to each local estimator to be used in the next round of regression. However, if one of the local estimators is compromised by a malicious attacker that may send corrupted values of its local estimate to the central supervisor, then it is difficult to detect the identity of this attacked estimator from the algorithm stated above. In this paper we propose an alternative algorithm where the central supervisor, instead of computing the average, employs a Round-Robin technique to generate the consensus variable, and show that by tracking the evolution of this consensus variable it is possible to identify which estimator is malicious. We analyze the convergence properties of this modified ADMM algorithm, and illustrate its effectiveness using simulation results.}, booktitle={2016 american control conference (acc)}, author={Liao, M. and Chakrabortty, Aranya}, year={2016}, pages={3539–3544} }
 @inproceedings{qian_xu_zhang_chakrabortty_mueller_xin_2016, title={A resilient software infrastructure for wide-area measurement systems}, DOI={10.1109/pesgm.2016.7741949}, abstractNote={To support the scalability and resilience requirements of distributed Wide-Area Measurement System (WAMS) architectures, we design and implement a software infrastructure to estimate power grid oscillation modes based on real-time data collected from Phasor Measurement Units (PMUs). This estimation algorithm can be deployed on a hierarchical structure of Phasor Data Concentrators (PDCs), which calculate local estimates and communicate with each other to calculate the global estimate. This work contributes a resilient system to WAMS with guarantees for (1) Quality of Service in network delay, (2) network failure tolerance, and (3) self-recoverability. The core component of the infrastructure is a distributed storage system. Externally, the storage system provides a cloud data lookup service with bounded response times and resilience, which decouples the data communication between PMUs, PDCs, and power-grid monitor/control applications. Internally, the storage system organizes PDCs as storage nodes and employs a real-time task scheduler to order data lookup requests so that urgent requests can be served earlier. To demonstrate the resilience of our distributed system, we deploy the system on a (1) virtual platform and (2) bare-metal machines, where we run a distributed algorithm on the basis of the Prony algorithm and the Alternating Directions Method of Multipliers (ADMM) to estimate the electro-mechanical oscillation modes. We inject different failures into the system to study their impact on the estimation algorithm. Our experiments show that temporary failures of a PDC or a network link do not affect the estimation result since the historical PMU data are cached in the storage system and PDCs can obtain the data on demand.}, booktitle={2016 ieee power and energy society general meeting (pesgm)}, author={Qian, T. and Xu, H. and Zhang, J. H. and Chakrabortty, Aranya and Mueller, F. and Xin, Y. F.}, year={2016} }
 @article{weiss_abu-jaradeh_chakrabortty_jamehbozorg_habibi-ashrafi_salazar_2016, title={A wide-area SVC controller design for inter-area oscillation damping in WECC based on a structured dynamic equivalent model}, volume={133}, ISSN={["1873-2046"]}, DOI={10.1016/j.epsr.2015.11.009}, abstractNote={In our recent work [1], we constructed a reduced-order model of the Western Electricity Coordinating Council (WECC) power system using mathematically derived parameters from real Synchrophasor data. These parameters include inter and intra-area impedances, inertias, and damping factors for aggregate synchronous generators representing five geographical, and yet coherent, areas of WECC. In this paper, we use this reduced-order model as a tool to design a supplementary controller for a Static VAr Compensator (SVC), located at the terminal bus of one of the aggregate generators. Wide-area feedback consisting of phase angle and frequency measurements from Phasor Measurement Units (PMUs) in the other areas is used to design this controller. The objective is to damp the inter-machine oscillation modes of the reduced-order model, which in the full-order system corresponds to inter-area oscillations. The controller input is chosen via statistical variance analysis, and its parameters are tuned to improve the damping factors of the slow modes. The model is implemented in a real-time digital simulator, and validated using a wide range of disturbance scenarios. The closed-loop system is observed to be highly robust to all of these disturbances as well as the choice of operating points. Detailed experimental analyses of the capacity of the SVC to satisfy the damping specifications of supplementary control are also presented via multiple contingencies. The results are promising in aiding damping of inter-area modes in WECC, especially at a time of increasing penetration of wind and other renewable resources.}, journal={ELECTRIC POWER SYSTEMS RESEARCH}, author={Weiss, Matthew and Abu-Jaradeh, Backer N. and Chakrabortty, Aranya and Jamehbozorg, Arash and Habibi-Ashrafi, Farrokh and Salazar, Armando}, year={2016}, month={Apr}, pages={1–11} }
 @article{zhang_nabavi_chakrabortty_xin_2016, title={ADMM Optimization Strategies for Wide-Area Oscillation Monitoring in Power Systems Under Asynchronous Communication Delays}, volume={7}, ISSN={["1949-3061"]}, DOI={10.1109/tsg.2016.2547939}, abstractNote={In this paper, we present a suite of asynchronous distributed optimization algorithms for wide-area oscillation estimation in power systems using alternating direction method of multipliers (ADMMs). We first pose the estimation problem as a real-time, iterative, and distributed consensus problem. Thereafter, we consider a probabilistic traffic model for modeling delays in any typical wide-area communication network, and study how the delays enter the process of information exchange between distributed phasor data concentrators that are employed to execute this consensus algorithm in a coordinated fashion. Finally, we propose four different strategies by which the convergence rate and accuracy of this consensus algorithm can be made immune to the asynchrony resulting from the network traffic. We carry out extensive simulations to show possible numerical instabilities and sensitivities of the ADMM convergence on our proposed strategies. Our results exhibit a broad view of how the convergence of any distributed estimation algorithm in a generic cyber-physical system depends strongly on the uncertainties of the underlying communication models.}, number={4}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Zhang, Jianhua and Nabavi, Seyedbehzad and Chakrabortty, Aranya and Xin, Yufeng}, year={2016}, month={Jul}, pages={2123–2133} }
 @inproceedings{boker_yuan_wu_chakrabortty_2016, title={Aggregate control of clustered networks with inter-cluster time delays}, DOI={10.1109/acc.2016.7526506}, abstractNote={We address a control problem for networks that have multiple dense clusters with sparse interconnection structure. By making use of the time-scale separation properties of such networks, we design state-feedback controllers at the cluster level to guarantee stability in the presence of time varying delays in the inter-cluster feedback channels. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network model, the closed-loop response is close to that obtained from the approximate models, provided that the clustering is strong and the time delay is below the maximum limit. The design procedure is demonstrated by a simulation example.}, booktitle={2016 american control conference (acc)}, author={Boker, A. M. and Yuan, C. Z. and Wu, F. and Chakrabortty, Aranya}, year={2016}, pages={5340–5345} }
 @article{caramanis_ntakou_hogan_chakrabortty_schoene_2016, title={Co-Optimization of Power and Reserves in Dynamic T&D Power Markets With Nondispatchable Renewable Generation and Distributed Energy Resources}, volume={104}, ISSN={["1558-2256"]}, DOI={10.1109/jproc.2016.2520758}, abstractNote={Marginal-cost-based dynamic pricing of electricity services, including real power, reactive power, and reserves, may provide unprecedented efficiencies and system synergies that are pivotal to the sustainability of massive renewable generation integration. Extension of wholesale high-voltage power markets to allow distribution network connected prosumers to participate, albeit desirable, has stalled on high transaction costs and the lack of a tractable market clearing framework. This paper presents a distributed, massively parallel architecture that enables tractable transmission and distribution locational marginal price (T&DLMP) discovery along with optimal scheduling of centralized generation, decentralized conventional and flexible loads, and distributed energy resources (DERs). DERs include distributed generation; electric vehicle (EV) battery charging and storage; heating, ventilating, and air conditioning (HVAC) and combined heat & power (CHP) microgenerators; computing; volt/var control devices; grid-friendly appliances; smart transformers; and more. The proposed iterative distributed architecture can discover T&DLMPs while capturing the full complexity of each participating DER's intertemporal preferences and physical system dynamics.}, number={4}, journal={PROCEEDINGS OF THE IEEE}, author={Caramanis, Michael and Ntakou, Elli and Hogan, William W. and Chakrabortty, Aranya and Schoene, Jens}, year={2016}, month={Apr}, pages={807–836} }
 @inproceedings{chakrabortty_2016, title={Co-designing communication and control systems for wide-area control of power systems}, DOI={10.1109/acc.2016.7525319}, abstractNote={Summary form only given. Following the Northeast blackout of 2003, the Wide-Area Measurement Systems (WAMS) technology using Phasor Measurement Units (PMUs) has tremendously matured for the North American grid. However, with the rapidly increasing number of deployed PMUs, the design and deployment of an efficient wide-area communication and computing infrastructure remains one of the greatest challenges to harvest the gigantic volumes of PMU data in real-time. Neither the architecture of such networks nor the impacts of their operational uncertainties such as delays and data losses on the envisioned control actions are well understood in the current state of art. This tutorial talk will address this gap, and propose a highly resilient, fault-tolerant, and reliable distributed network control system for tomorrow's power grids using cutting-edge emerging technologies such as cloud computing and software defined networks. The proposed architecture will be realized via three interactive layers. Layer 1 will consist of physics-based controllers for power oscillation damping. Layer 2 will contain delay control rules for the communication network that work in tandem with the grid controllers. Layer 3 will consist of a supervisory controller realized through embedding and reconfiguration rules in a distributed cloud environment that continuously monitors the system status, and ensures fault-tolerance, resilience, and reliability of the overall closed-loop control system.}, booktitle={2016 american control conference (acc)}, author={Chakrabortty, Aranya}, year={2016}, pages={2667–2667} }
 @inproceedings{khan_milani_chakrabortty_husain_2016, title={Comprehensive dynamic modeling of a solid-state transformer based power distribution system}, DOI={10.1109/ecce.2016.7854949}, abstractNote={This paper presents a physics based comprehensive dynamic model of a future power distribution system, termed as the FREEDM system, for plug-and-play interface of distributed renewable energy resources and distributed energy storage devices. The system allows for high penetration of renewable generation with energy storage at the distribution level. FREEDM system consists of an energy router, which is the power electronics based solid-state transformer (SST) that interfaces distributed generation, storage and local loads on the low voltage side with the medium voltage node of the distribution grid. In this paper, state-space modeling and dynamic performance of the SST is analyzed along with the renewable generation sources and storage components with the goal of studying the feasible operating points of the FREEDM system. The actual model of the single-SST system amounts to highly complex dynamics with more than hundred state variables. Singular perturbation based model reduction techniques are applied, thereby leading to a 70th order state-space average model suitable for AC and DC energy cell system sizing, stability analysis, and controller design. The analysis with the system model revealed the SST input stage system parameters have the dominant effect on the feasible operation region.}, booktitle={2016 ieee energy conversion congress and exposition (ecce)}, author={Khan, M. T. A. and Milani, A. A. and Chakrabortty, Aranya and Husain, I.}, year={2016} }
 @article{chakrabortty_2016, title={Distributed Cyber-Physical Algorithms for Wide-Area Monitoring of Power Systems}, number={Special issue on Design of Cooperative Distributed Energy Management Systems}, journal={Journal of the Society of Instrument and Control Engineers (SICE), Japan}, author={Chakrabortty, A.}, editor={Namerikawa, T. and Fujita, M.Editors}, year={2016} }
 @inbook{nabavi_zhang_chakrabortty_2016, title={Distributed algorithms for wide-area monitoring of power systems: a cyber-physical perspective}, ISBN={9781849199360 9781849199377}, url={http://dx.doi.org/10.1049/pbpo081e_ch3}, DOI={10.1049/pbpo081e_ch3}, abstractNote={This chapter develops a distributed algorithmic framework for executing critical transmission-level operations of power systems using Synchrophasor data. As the number of phasor measurement units continues to increase exponentially, it is rather intuitive that the current state-of-the-art centralized communication and information processing architecture of wide-area measurement system will no longer be sustainable under such data-explosion, and a completely distributed cyber-physical architecture will need to be developed. Very little attention has yet been paid to the most critical consequence of this envisioned distributed architecture - namely, distributed algorithms. Our primary task in this chapter is to describe how one can develop distributed optimization methods for solving real-time wide-area monitoring problems with investigation of their convergence, robustness, and implementation issues.}, booktitle={Cyber-Physical-Social Systems and Constructs in Electric Power Engineering}, publisher={Institution of Engineering and Technology}, author={Nabavi, S. and Zhang, J. and Chakrabortty, A.}, editor={Suryanarayanan, Siddharth and Roche, Robin and Hansen, Timothy M.Editors}, year={2016}, month={Oct}, pages={39–73} }
 @inproceedings{wang_chakrabortty_2016, title={Distributed monitoring of wide-area oscillations in the presence of GPS spoofing attacks}, ISBN={9781509041688}, url={http://dx.doi.org/10.1109/pesgm.2016.7741175}, DOI={10.1109/pesgm.2016.7741175}, abstractNote={Phasor Measurement Units (PMU) are playing an increasingly important role in wide-area monitoring and control of power systems. PMUs allow synchronous real-time measurements of voltage, phase angle and frequency from multiple remote locations in the grid, enabled by their ability to align to Global Position System (GPS) clocks. Given that this ability is vulnerable to GPS spoofing attacks, which have been confirmed easy to launch, this paper proposes a distributed real-time wide-area oscillation estimation approach that is robust to GPS spoofing on PMUs and their associated Phasor Data Concentrators (PDCs). The approach employs the idea of checking update consistency across distributed nodes and can tolerate up to one third of compromised nodes. Numerical simulations confirmed the effectiveness of the proposed approach.}, booktitle={2016 IEEE Power and Energy Society General Meeting (PESGM)}, publisher={IEEE}, author={Wang, Yongqiang and Chakrabortty, Aranya}, year={2016}, month={Jul} }
 @inproceedings{lian_duel-hallen_chakrabortty_2016, title={Ensuring economic fairness in wide-area control for power systems via game theory}, DOI={10.1109/acc.2016.7525415}, abstractNote={Wide-area control helps in suppression of interarea oscillations in electric power systems, but potentially requires a substantial investment into the communication network needed to exchange state information. To provide companies with incentives to subsidize the wide-area communication links, a fair cost-allocation method based on the theory of cooperative network-formation games (NFG) is developed. The Nash Bargaining Solution (NBS) is utilized to fairly allocate the communication cost to the companies, which act as game-players. First, the wide-area control problem is formulated using the state-feedback-based LQR minimization approach, and the social communication cost is computed using a sparsity-promoting algorithm. Second, the disagreement point, which determines the maximum cost each area is willing to pay, is computed. This selfish cost is proportional to the energy an area saves by utilizing wide-area feedback and is derived from the Nash Equilibria (NEs) of two noncooperative NFGs, with and without wide-area feedback, respectively. Finally, the social cost is divided optimally among the companies, with all players benefiting from cooperation. The proposed cost allocation is illustrated for the Australian 50-bus power system example.}, booktitle={2016 american control conference (acc)}, author={Lian, F. and Duel-Hallen, A. and Chakrabortty, Aranya}, year={2016}, pages={3231–3236} }
 @article{braswell_cahoon_york_jordan_seagroves_2016, title={Fluridone and Encapsulated Acetochlor Reduce Protoporphyrinogen Oxidase Inhibitor Use in a Glufosinate-Based Palmer Amaranth Management Program for Cotton}, volume={30}, ISSN={["1550-2740"]}, DOI={10.1614/wt-d-16-00025.1}, abstractNote={Flumioxazin and fomesafen are commonly used to control glyphosate-resistant Palmer amaranth in cotton and other crops, thus increasing risk to select for Palmer amaranth biotypes resistant to protoporphyrinogen oxidase (PPO) inhibitors. A field experiment was conducted to determine the potential for fluridone and acetochlor to substitute for soil-applied PPO inhibitors in a Palmer amaranth management system with glufosinate applied twice POST and diuron plus MSMA POST-directed in conservation tillage cotton. Fluridone and flumioxazin applied preplant 23 to 34 d prior to planting were similarly effective. Fluridone and acetochlor plus diuron applied PRE controlled Palmer amaranth as well as fomesafen plus diuron PRE. All systems with preplant and PRE herbicides followed by glufosinate POST and diuron plus MSMA layby controlled Palmer amaranth well. Cotton yield did not differ among herbicide treatments. This research demonstrates that fluridone and acetochlor can substitute for soil-applied PPO-inhibiting herbicides in management systems for Palmer amaranth. Nomenclature: Acetochlor; diuron; flumioxazin; fluridone; fomesafen; glufosinate; MSMA; Palmer amaranth, Amaranthus palmeri S. Watts.; cotton, Gossypium hirsutum L.}, number={4}, journal={WEED TECHNOLOGY}, author={Braswell, Lewis R. and Cahoon, Charles W., Jr. and York, Alan C. and Jordan, David L. and Seagroves, Richard W.}, year={2016}, pages={838–847} }
 @inproceedings{annaswamy_hussain_chakrabortty_cvetkovic_2016, title={Foundations of Infrastructure-CPS}, DOI={10.1109/acc.2016.7525316}, abstractNote={Cyber-physical systems are now becoming increasingly prevalent and possibly even mainstream. Infrastructures have been around as long as urban centers, supporting a society's needs for its planning, operation, and safety. As we move deeper into the 21st century, these infrastructures are becoming smart - they monitor themselves through sensor-networks, communicate through a layered architecture, and most importantly self-govern through multiple agents, resulting in a complex integration and interaction between cyber and physical components. With the basics of CPS in place, such as stability, robustness, and reliability properties at a systems level, and hybrid, switched, and event-triggered properties at a network level, we believe that the time is right to go to the next step, of the analysis and synthesis of cyber-physical systems that are present in an infrastructure. We denote such systems as Infrastructure-CPS, which form the focus of the proposed tutorial. We discuss three different foundations of Infrastructure-CPS, (i) Human Empowerment, (ii) Transactive Control, and (iii) Resilience. This will be followed by two examples, one on the nexus between power and communication infrastructure, and the other between natural gas and electricity, both of which have been investigated extensively of late, and are emerging to be apt illustrations of Infrastructure-CPS.}, booktitle={2016 american control conference (acc)}, author={Annaswamy, A. M. and Hussain, A. and Chakrabortty, Aranya and Cvetkovic, M.}, year={2016}, pages={2649–2664} }
 @inproceedings{xue_chakrabortty_2016, title={H-2-clustering of closed-loop consensus networks under a class of LQR design}, DOI={10.1109/acc.2016.7526799}, abstractNote={Given any positive integer r, our objective is to develop a strategy for grouping the states of a n-node network into r ≤ n distinct non-overlapping groups. The criterion for this partitioning is defined as follows. First, a LQR controller is defined for the original n-node network. Then, a r-dimensional reduced-order network is created by imposing a projection matrix P on the n-node open-loop network, and a reduced-order r-dimensional LQR controller is constructed. The resulting controller is, thereafter, projected back to its original coordinates, and implemented in the n-node network. The problem, therefore, is to find a grouping strategy or P that will minimize the difference between the closed-loop transfer matrix of the original network with the full-order controller and that with the projected controller, in the sense of H2 norm. We derive an upper bound on this difference in terms of P, and, thereby propose a design for P using K-means that tightens the bound while guaranteeing numerical feasibility.}, booktitle={2016 american control conference (acc)}, author={Xue, N. and Chakrabortty, Aranya}, year={2016}, pages={7141–7146} }
 @inproceedings{xue_chakrabortty_2016, title={H-2-clustering of closed-loop consensus networks under generalized LQR designs}, DOI={10.1109/cdc.2016.7799051}, abstractNote={In this paper we present a Linear Quadratic Regulator (LQR) control design for large-scale consensus networks. When such networks have tens of thousands of nodes spread over a wide geographical span, the design and implementation of conventional LQR controllers become very challenging. Consider an n-node consensus network with both node and edge weights. Given any positive integer r, our objective is to develop a strategy for grouping the states of this network into r distinct non-overlapping groups. The criterion for this partitioning is defined as follows. First, an LQR state-feedback controller is defined over the n-node network for any given Q ≥ 0. Then, an r-dimensional reduced-order network is created by imposing a projection matrix P on the open-loop network, and a reduced-order r-dimensional LQR controller is constructed. The resulting controller is, thereafter, projected back to its original coordinates, and implemented in the n-node network. The problem, therefore, is to find a grouping strategy or P that will minimize the difference between the closed-loop transfer matrix of the original network with the full-order controller and that with the projected controller in the sense of ℋ2 norm. We derive an upper bound on this difference in terms of P, and, thereby propose a design for P using weighted k-means that tightens the bound. The weighting of k-means arises due to the node weights in the network, and the resulting asymmetry in its Laplacian matrix.}, booktitle={2016 ieee 55th conference on decision and control (cdc)}, author={Xue, N. and Chakrabortty, Aranya}, year={2016}, pages={5116–5121} }
 @inproceedings{liao_chakrabortty_2016, title={Identifying covert data-manipulators in power system estimation loops}, DOI={10.1109/cdc.2016.7798441}, abstractNote={We develop a set of algorithms for identifying covert data manipulators in distributed optimization loops for estimating oscillation modes in power systems. The fundamental set-up for the optimization is based on Alternating Direction Multiplier Method (ADMM), implemented via message passing between a set of local estimators and a central coordinator. Some of these local estimators are assumed to be compromised by malicious attackers that send incorrect values of their local estimates to the coordinator. Even a small amount of such bias can easily destabilize the ADMM loop. In our first algorithm, we catch the identity of these attackers by employing the standard ADMM but adjusting the value of the penalty factor used in the update of the primal variable. We show that this adjustment can amplify the attack signature, and help in identification, especially when the attack magnitude is small. In our second algorithm, we employ a Round-Robbin variant of ADMM, and catch the manipulators by simply observing the evolution of the dual variable. We illustrate the results using simulations of the IEEE 68-bus power system model.}, booktitle={2016 ieee 55th conference on decision and control (cdc)}, author={Liao, M. and Chakrabortty, Aranya}, year={2016}, pages={1273–1278} }
 @inproceedings{chockalingam_chakrabortty_hussain_2016, title={Mitigating denial-of-service attacks in wide-area LQR control}, DOI={10.1109/pesgm.2016.7741285}, abstractNote={In this work we study the impacts of Denial-of-Service (DoS) attacks on the cyber-physical implementation of wide-area control. The controller is desgined as a Linear Quadratic Regulator (LQR) for damping power flow oscillations. We first derive a nominal mathematical model of the power system network considering a delay-aware LQR controller without any DoS. Thereafter, we model how DoS enters the closed-loop dynamics of this system by considering the Hadamard product of the LQR gain matrix with a matrix of attacked links. We propose two mitigation strategies to compensate for the loss of missing states in the feedback path, and test their effectiveness against three variables of interest - namely, location of attack, time of attack, and duration of attack. We design a decision tree classifier for each strategy based on these parameters to predict the severity of an attack. The results are illustrated with a DoS simulation on the standard IEEE 4-machine Kundur model.}, booktitle={2016 ieee power and energy society general meeting (pesgm)}, author={Chockalingam, N. and Chakrabortty, Aranya and Hussain, A.}, year={2016} }
 @article{xue_chakrabortty_2016, title={Parallel Identification of Power System Dynamic Models Under Scheduling Constraints}, volume={31}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2015.2504453}, abstractNote={In this paper we present two sets of parallel algorithms for identifying real-time, small-signal dynamic models of power systems using multiple sources of Synchrophasor data. The first problem is posed in terms of identifying the transfer matrix of single-input multiple-output (SIMO) power system models using linear least-squares (LLS), where parallelism can be implemented through parallel execution of matrix multiplications using multiple processors or workers. Given the constraints of sequential communication and limited local memory, which may arise due to multiple applications running in the workers at the same time, a novel scheduling algorithm is proposed to enable flexible deadlines that meet these constraints. The scheduling algorithm minimizes the total time of execution under constraints, and can be solved via integer programming. The second problem is posed as a similar parallel algorithm for identifying a linearized state-variable (SV) model of a power system using both linear and nonlinear least-squares (NLS) in presence of scheduling. The performance of all the algorithms are studied via simulations of an IEEE 145-bus, 50-machine power system model, and compared with their centralized, non-parallel implementation.}, number={6}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Xue, Nan and Chakrabortty, Aranya}, year={2016}, month={Nov}, pages={4584–4594} }
 @article{chandra_gayme_chakrabortty_2016, title={Time-Scale Modeling of Wind-Integrated Power Systems}, volume={31}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2016.2521403}, abstractNote={This paper describes time-scale separation properties of dynamic models of wind-integrated power systems. We first derive a mathematical model for the dynamics of a power network consisting of synchronous generators, loads and a wind power plant modeled by a wind turbine and a controlled doubly-fed induction generator. We then aggregate this system into multiple coherent areas, and apply a linear transformation to represent the model in terms of slow and fast states. Using this transformed system we show that the ratio of the time constant associated with the swing states to that of the wind plant can be used to characterize conditions under which the slow time-scale of the power system changes with increasing wind penetration. We further demonstrate that these modal responses depend on the relative locations of the synchronous generators, the loads and the wind generator in the power system. We illustrate these observations through simulations of a two-area 8-bus power system and a five-area 68-bus power system.}, number={6}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Chandra, Souvik and Gayme, Dennice F. and Chakrabortty, Aranya}, year={2016}, month={Nov}, pages={4712–4721} }
 @inproceedings{weiss_zhang_chakrabortty_2016, title={Wide-area control of power systems using cloud-in-the-loop feedback}, ISBN={9781509045457}, url={http://dx.doi.org/10.1109/globalsip.2016.7905959}, DOI={10.1109/globalsip.2016.7905959}, abstractNote={We propose the use of cloud-computing platforms and virtual network laboratories such as GENI (Global Environment for Network Innovations), together with high-speed software defined networks such as Internet2 to combat various cyber-physical implementation challenges for wide-area control of large power systems using Synchrophasors. Experimental results from a cloud-in-the-loop testbed environment are reported to support our proposed architecture.}, booktitle={2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, publisher={IEEE}, author={Weiss, Matthew and Zhang, Jianhua and Chakrabortty, Aranya}, year={2016}, month={Dec} }
 @article{nudell_nabavi_chakrabortty_2015, title={A Real-Time Attack Localization Algorithm for Large Power System Networks Using Graph-Theoretic Techniques}, volume={6}, ISSN={["1949-3061"]}, DOI={10.1109/tsg.2015.2406571}, abstractNote={We develop a graph-theoretic algorithm for localizing the physical manifestation of attacks or disturbances in large power system networks using real-time synchrophasor measurements. We assume the attack enters through the electro-mechanical swing dynamics of the synchronous generators in the grid as an unknown additive disturbance. Considering the grid to be divided into coherent areas, we pose the problem as to localize which area the attack may have entered using relevant information extracted from the phasor measurement data. Our approach to solve this problem consists of three main steps. We first run a phasor-based model reduction algorithm by which a dynamic equivalent of the clustered network can be identified in real-time. Second, in parallel, we run a system identification in each area to identify a transfer matrix model for the full-order power system. Thereafter, we exploit the underlying graph-theoretic properties of the identified reduced-order topology, create a set of localization keys, and compare these keys with a selected set of transfer function residues. We validate our results using a detailed case study of the two-area Kundur model and the IEEE 39-bus power system.}, number={5}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Nudell, Thomas R. and Nabavi, Seyedbehzad and Chakrabortty, Aranya}, year={2015}, month={Sep}, pages={2551–2559} }
 @inproceedings{weiss_chakrabortty_ashrafi_jamehbozorg_ahu-jaradeh_2015, title={A Wide-area SVC controller design using a dynamic equivalent model of WECC}, DOI={10.1109/pesgm.2015.7286605}, abstractNote={In our recent work [1] we constructed a reduced-order five-area model of the Western Electricity Coordinating Council (WECC) power system using mathematically derived parameters from real PMU data. These parameters include inter and intra-area impedances, inertias, and damping values for aggregate machines representing five geographic areas. In this paper we use this reduced-order model as a tool to design an SVC controller to damp the inter-machine oscillation modes, which in the full-order model corresponds to inter-area oscillations. The controller input is chosen via statistical variance analysis, and its parameters are tuned to improve slow mode damping. The model is implemented in a real-time digital simulator, and emulated for various disturbance scenarios to illustrate the effectiveness of the SVC using a metric for dynamic performance. The resulting closed-loop response is promising in aiding damping of inter-area modes in the WECC, especially at a time of increasing penetration of wind and other renewable resources.}, booktitle={2015 ieee power & energy society general meeting}, author={Weiss, M. and Chakrabortty, Aranya and Ashrafi, F. H. and Jamehbozorg, A. and Ahu-Jaradeh, B. N.}, year={2015} }
 @inproceedings{nabavi_chakrabortty_khargonekar_2015, title={A global identifiability condition for consensus networks on tree graphs}, DOI={10.1109/acc.2015.7170999}, abstractNote={In this paper we present a sufficient condition that guarantees identifiability of linear network dynamic systems exhibiting continuous-time weighted consensus protocols with acyclic structure. Each edge of the underlying network graph G is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definitions of identifiability and indistinguishability, we first derive a condition that ensures the identifiability of the edge weights of G in terms of the associated transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge weights. We describe our results using illustrative examples.}, booktitle={2015 american control conference (acc)}, author={Nabavi, S. and Chakrabortty, Aranya and Khargonekar, P. P.}, year={2015}, pages={1830–1835} }
 @inproceedings{jain_biyik_chakrabortty_2015, title={A model predictive control design for selective modal damping in power systems}, DOI={10.1109/acc.2015.7172007}, abstractNote={This paper presents a novel real-time predictive control technique to damp dominant inter-area oscillation modes in power systems. We first show that conventional Power System Stabilizers (PSS) in synchronous generators are best suited to damp only the intra-area oscillation modes, and participate poorly in inter-area damping. We then design a centralized Model Predictive Controller (MPC) to provide supplementary control to these conventional PSSs based on a Selective Discrete Fourier Transform (SDFT) approach. The SDFT extracts the energies associated with the inter-area frequency components in the output spectrum of the system, and uses this information to construct a weighting matrix Q. The MPC is then formulated as a quadratic minimization of the outputs using Q, resulting in damping only the inter-area modes of interest. In reality, however, the most dominant DFT magnitudes will not be known ahead of time since they are decided by the location of the disturbance. Therefore, we next augment the MPC design by predicting the dominant DFT magnitudes in the desired low frequency range using online measured data, and tuning Q accordingly. We illustrate the effectiveness of the proposed approach using an IEEE 39-bus prototype power system model for the New England system.}, booktitle={2015 american control conference (acc)}, author={Jain, A. and Biyik, E. and Chakrabortty, Aranya}, year={2015}, pages={4314–4319} }
 @inproceedings{nabavi_chakrabortty_2015, title={An intrusion-resilient distributed optimization algorithm for modal estimation in power systems}, DOI={10.1109/cdc.2015.7402084}, abstractNote={In this paper we present an intrusion-resilient distributed algorithmic approach to estimate the electro-mechanical oscillation modes of a large power system using Synchrophasor measurements. For this, we first show how to distribute the centralized Prony method over a network consisting of several computational areas using a distributed variant of alternating direction method of multipliers (D-ADMM). We then add a cross-verification step to show the resiliency of this algorithm against the cyber-attacks that may happen in the form of data manipulation. We illustrate the robustness of our method in face of intrusion for a case study on IEEE 68-bus power system.}, booktitle={2015 54th IEEE conference on decision and control (CDC)}, author={Nabavi, S. and Chakrabortty, Aranya}, year={2015}, pages={39–44} }
 @inproceedings{zhang_nabavi_chakrabortty_xin_2015, title={Convergence analysis of ADMM-based power system mode estimation under asynchronous wide-area communication delays}, DOI={10.1109/pesgm.2015.7286038}, abstractNote={In our recent paper [1], we proposed a distributed PMU-PDC architecture for estimating power system oscillation modes by integrating a Prony-based algorithm with Alternating Direction Method of Multipliers (ADMM). A critical assumption behind the proposed method was that the communication between local PDCs and the central averager is completely synchronized. In realistic wide-area networks, however, such synchronous communication may not always be possible. In this paper we address this issue of asynchronous communication, and its impact on the convergence of the distributed estimation. We first impose a probability model for the communication delays between the central PDC and the local PDCs, and then implement two strategies of averaging at the central PDC based on a chosen delay threshold. We carry out simulations to show possible instabilities and sensitivities of the ADMM convergence on delay distribution parameters under these two averaging strategies. Our results exhibit a broad view of how the convergence of distributed estimation algorithms in physical processes depends strongly on the uncertainties in the underlying communications in a generic cyber-physical system.}, booktitle={2015 ieee power & energy society general meeting}, author={Zhang, J. H. and Nabavi, S. and Chakrabortty, Aranya and Xin, Y. F.}, year={2015} }
 @article{nabavi_zhang_chakrabortty_2015, title={Distributed Optimization Algorithms for Wide-Area Oscillation Monitoring in Power Systems Using Interregional PMU-PDC Architectures}, volume={6}, ISSN={["1949-3061"]}, DOI={10.1109/tsg.2015.2406578}, abstractNote={In this paper, we present a set of distributed algorithms for estimating the electro-mechanical oscillation modes of large power system networks using synchrophasors. With the number of phasor measurement units (PMUs) in the North American grid scaling up to the thousands, system operators are gradually inclining toward distributed cyber-physical architectures for executing wide-area monitoring and control operations. Traditional centralized approaches, in fact, are anticipated to become untenable soon due to various factors such as data volume, security, communication overhead, and failure to adhere to real-time deadlines. To address this challenge, we propose three different communication and computational architectures by which estimators located at the control centers of various utility companies can run local optimization algorithms using local PMU data, and thereafter communicate with other estimators to reach a global solution. Both synchronous and asynchronous communications are considered. Each architecture integrates a centralized Prony-based algorithm with several variants of alternating direction method of multipliers (ADMM). We discuss the relative advantages and bottlenecks of each architecture using simulations of IEEE 68-bus and IEEE 145-bus power system, as well as an Exo-GENI-based software defined network.}, number={5}, journal={IEEE TRANSACTIONS ON SMART GRID}, author={Nabavi, Seyedbehzad and Zhang, Jianhua and Chakrabortty, Aranya}, year={2015}, month={Sep}, pages={2529–2538} }
 @inproceedings{nudell_chakrabortty_2015, title={Ensuring localizability of node attacks in consensus networks via feedback graph design}, ISBN={9781479986842}, url={http://dx.doi.org/10.1109/acc.2015.7170759}, DOI={10.1109/acc.2015.7170759}, abstractNote={In this paper we consider the problem of localizability of attacks in continuous-time consensus networks. In our previous work [1] we showed that if a consensus network is divided into clusters, then a supervisor can successfully localize the cluster in which an attack may have been launched by simply inspecting the sign patterns of the residues corresponding to the slow poles of its input-output transfer function (TF). A necessary condition for localizability, however, was that the attack must enter through a node that guarantees this TF to be minimal. In case the attacker knows the identity of the so-called zero nodes from where the TFs are non-minimal, and chooses to launch the attack at any of them, then the supervisor cannot localize the attack.We show that this problem can be bypassed by designing a state-feedback controller that equivalently changes the algebraic properties of the underlying network graph, and thereby restores minimality of the TF. We illustrate the approach by simulating a three-area, 30-node graph, and highlighting the performance trade-offs that come as a price of localizability.}, booktitle={2015 American Control Conference (ACC)}, publisher={IEEE}, author={Nudell, Thomas R. and Chakrabortty, Aranya}, year={2015}, month={Jul} }
 @inproceedings{chandra_mehta_chakrabortty_2015, title={Equilibria analysis of power systems using a numerical homotopy method}, DOI={10.1109/pesgm.2015.7285823}, abstractNote={In this paper, we present a homotopy based numerical continuation algorithm to efficiently compute all feasible equilibria of a complex power system model. The dynamic characteristics of conventional power systems are undergoing a sea change due to the impact of large-scale integration of renewables, storage elements, new type of loads etc. Several parameters of these components affect the power system operation leading to multiple feasible equilibria which may be intractable by the traditional load flow techniques. In contrast, our algorithm finds all the feasible solutions over a certain parameter space. We illustrate the results through the simulation of a 5-machine power system model with wind, storage elements, and dynamic loads. We observed that the wind velocity and the reference to the wind bus voltage strongly affect the number and the stability of the system equilibria. Knowledge of these equilibria can benefit small-signal stability assessment and system level planning.}, booktitle={2015 ieee power & energy society general meeting}, author={Chandra, S. and Mehta, D. and Chakrabortty, Aranya}, year={2015} }
 @inproceedings{chandra_mehta_chakrabortty_2015, title={Exploring the impact of wind penetration on power system equilibrium using a numerical continuation approach}, DOI={10.1109/acc.2015.7172011}, abstractNote={In this paper we investigate how the equilibrium characteristics of conventional power systems may change with an increase in wind penetration. We first derive a differentialalgebraic model of a power system network consisting of synchronous generators, loads and a wind power plant modeled by wind turbines and doubly-fed induction generators (DFIG). The models of these three components are coupled via nonlinear power flow equations. In contrast to the traditional approach for solving the power flows via iterative methods that often lead to a local solution, we apply a recently developed parameterhomotopy based numerical continuation algorithm to compute all possible solutions. The method obtains all the solutions of the power flow equations over multiple values of the wind penetration. We observe that depending on the penetration limit and the setpoint value for the magnitude of the wind bus voltage, the system may exhibit several undesired or even unstable equilibria. We illustrate these results through a detailed simulation of a 5-machine power system model with wind injection, and highlight how the solutions may be helpful for small-signal stability assessment.}, booktitle={2015 american control conference (acc)}, author={Chandra, S. and Mehta, D. and Chakrabortty, Aranya}, year={2015}, pages={4339–4344} }
 @article{nudell_chakrabortty_2015, title={Graph-Theoretic Methods for Measurement-Based Input Localization in Large Networked Dynamic Systems}, volume={60}, ISSN={["1558-2523"]}, DOI={10.1109/tac.2015.2398911}, abstractNote={In this paper, we consider the problem of localizing disturbance inputs in first-order linear time-invariant (LTI) consensus networks using measurement-based graph-theoretic methods. We consider every node and edge of the network graph to be characterized with physical weights, and show that the resulting system dynamics can be represented in terms of an asymmetric Laplacian matrix Lm. Assuming the network graph to be divided into p coherent clusters, we next propose an input localization algorithm based on the properties of the weak nodal domains corresponding to the first p-1 slow eigenvalues of Lm. The algorithm takes in sensor measurements of the states from selected nodes, runs a system identification routine to construct the input-output transfer matrix, and compares the signs of the residues of the component transfer functions to a nominal localization key to determine in which cluster(s)the disturbance input may have entered. We prove that for systems defined over a specific class of graphs, referred to as p-area complete graphs, the localization is unique. We also state the extension of this result for second-order synchronization networks. We illustrate the algorithms by applying them to large-scale power system networks.}, number={8}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Nudell, Thomas R. and Chakrabortty, Aranya}, year={2015}, month={Aug}, pages={2114–2128} }
 @inproceedings{boker_nudell_chakrabortty_2015, title={On aggregate control of clustered consensus networks}, DOI={10.1109/acc.2015.7172204}, abstractNote={In this paper we address the problem of controlling the slow-time-scale dynamics of clustered consensus networks. Using time-scale separation arising from clustering, we first decompose the actual network model into an approximate model, and define the controller at every node as the sum of two independent state-feedback controls, one for the fast dynamics and another for the slow. We show that the slow controller is identical for every node belonging to the same cluster, indicating that only a single aggregate slow controller needs to be designed per area. This reduces the computational complexity of the design significantly. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network, the closed-loop response is close to that obtained from the approximate models, provided that the clustering is strong. The design procedure is demonstrated by a simulation example.}, booktitle={2015 american control conference (acc)}, author={Boker, A. M. and Nudell, T. R. and Chakrabortty, Aranya}, year={2015}, pages={5527–5532} }
 @inproceedings{katewa_chakrabortty_gupta_2015, title={Protecting privacy of topology in consensus networks}, DOI={10.1109/acc.2015.7171103}, abstractNote={Consider a set of agents implementing the discrete time consensus algorithm. At each time step, all agents also transmit their states to a central estimator that wishes to identify the underlying topology and eigenvalues of the network. It does so by using a nonlinear least squares (NLS) algorithm to identify the state evolution matrix used in the consensus algorithm. We present a mechanism to protect the differential privacy of this topology from an eavesdropper who may have unauthorized access to the estimator. In this mechanism, every agent purposely adds noise to its measurements before transmission to the estimator. The noise is designed to ensure that the eavesdropper cannot uniquely identify the topology with a specified confidence level. Numerical results are presented to describe the corresponding trade-off in estimation accuracy as a function of the level of differential privacy achieved.}, booktitle={2015 american control conference (acc)}, author={Katewa, V. and Chakrabortty, Aranya and Gupta, V.}, year={2015}, pages={2476–2481} }
 @article{gayme_chakrabortty_2014, title={A Spatio-Temporal Framework for Spectral Analysis and Control of Interarea Oscillations in Wind-Integrated Power Systems}, volume={22}, ISSN={["1558-0865"]}, DOI={10.1109/tcst.2013.2278977}, abstractNote={This brief presents an analytical method to study the effects of wind farm location on the interarea oscillation spectrum of large radial power systems along with a means to shape this spectrum. We consider a continuum representation of the electromechanical swing equations for the power system with the wind power injection modeled as a spatial point source forcing applied at a certain electrical distance from one end of the transfer path. The resulting forced hyperbolic wave equation for the rotor phase angle is used to derive an analytical expression for the spectrum of the power flow as a function of the wind power injection location. A simulation study shows that judicious siting of the wind farm can provide effective damping to a particular set of modes. Finally, we show how the analysis framework can be extended to provide a means of shaping the interarea oscillation spectrum for a grid with a wind farm at an arbitrary location using a simple optimal control design for the wind power output.}, number={4}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Gayme, Dennice F. and Chakrabortty, Aranya}, year={2014}, month={Jul}, pages={1658–1665} }
 @inproceedings{zhang_jaipuria_chakrabortty_hussain_2014, title={A distributed optimization algorithm for attack-resilient wide-area monitoring of power systems: Theoretical and experimental methods}, volume={8840}, DOI={10.1007/978-3-319-12601-2_21}, abstractNote={In this paper we present a real-time distributed optimization algorithm based on Alternating Directions Method of Multipliers (ADMM) for resilient monitoring of power flow oscillation patterns in large power system networks. We pose the problem as a least squares (LS) estimation problem for the coefficients of the characteristic polynomial of the transfer function, and combine a centralized Prony algorithm with ADMM to execute this estimation via distributed consensus. We consider the network topology to be divided into multiple clusters, with each cluster equipped with a local estimator at the local control center. At any iteration, the local estimators receive Synchrophasor measurements from within their own respective areas, run a local consensus algorithm, and communicate their estimates to a central estimator. The central estimator averages all estimates, and broadcasts the average back to each local estimator as the consensus variable for their next iteration. By imposing a redundancy strategy between the local and the global estimators via mutual coordination, we show that the distributed algorithm is more resilient to communication failures as compared to alternative centralized methods. We illustrate our results using a hardware-in-loop power system testbed at NC State federated with a networking and cyber-security testbed at USC/ISI.}, booktitle={Decision and game theory for security, gamesec 2014}, author={Zhang, J. H. and Jaipuria, P. and Chakrabortty, Aranya and Hussain, A.}, year={2014}, pages={350–359} }
 @inproceedings{nudell_chakrabortty_2014, title={A graph-theoretic algorithm for localization of forced harmonic oscillation inputs in power system networks}, DOI={10.1109/acc.2014.6859401}, abstractNote={In this paper we consider the problem of localizing inputs in swing dynamic models of large power system networks in the form of forced oscillations with unknown amplitude and frequency. Such harmonic oscillations commonly result from internal failures of control actuators in synchronous machines, and are particularly dangerous because their frequency often lies in the range of the inter-area oscillation modes of the system, resulting in an unwanted sub-synchronous resonance phenomena. We first develop the concept of discrete nodal domains for second-order network dynamic systems, and relate these nodal domains to the residues of the system transfer function. Thereafter, we develop a graph-theoretic algorithm based on the magnitude as well as the sign of these residues that detects the location of the forced oscillation input. We simulate a 60-generator 4-area power system to illustrate the different steps of our algorithm.}, booktitle={2014 american control conference (acc)}, author={Nudell, T. R. and Chakrabortty, Aranya}, year={2014}, pages={1334–1340} }
 @inproceedings{nabavi_chakrabortty_2014, title={A real-time distributed prony-based algorithm for modal estimation of power system oscillations}, DOI={10.1109/acc.2014.6859381}, abstractNote={In this paper, we present a set of distributed algorithms to estimate the oscillatory electro-mechanical eigenvalues of large power system networks using real-time measurements of phase angles and frequencies. We consider the underlying network to exhibit a strong coherency structure resulting in a two-time-scale behavior of the states. Our goal is to develop a distributed strategy by which only the slow eigenvalues, or the inter-area oscillation modes, can be estimated. Assuming a reliable bound for the slow frequencies, we first pass the actual measurements from the full-order network through a bandpass filter, and use the filter outputs as the effective inputs to our distributed estimation routine. We integrate the centralized Prony method for modal extraction with two commonly-used distributed optimization algorithms, namely, distributed subgradient method (DSM), and alternating direction method of multipliers (ADMM), and show how the filtered outputs can be used in each case to asymptotically estimate the slow eigenvalues of interest. We illustrate our results using a IEEE 39-bus power system, and show the robustness of our methods in face of communication failures.}, booktitle={2014 american control conference (acc)}, author={Nabavi, S. and Chakrabortty, Aranya}, year={2014}, pages={729–734} }
 @inproceedings{qian_chakrabortty_mueller_xin_2014, title={A real-time distributed storage system for multi-resolution virtual synchrophasor}, ISBN={9781479964154}, url={http://dx.doi.org/10.1109/pesgm.2014.6939832}, DOI={10.1109/pesgm.2014.6939832}, abstractNote={With the continuing large-scale deployment of Phasor Measurement Units (PMU), the Wide-Area Measurement System (WAMS) technology is envisioned to evolve towards a distributed architecture where multiple sets of distributed Phasor Data Concentrators (PDCs) collectively process PMU data to achieve real-time distributed intelligence. Emerging applications developed under this vision will pose stringent but heterogeneous real-time requirements on throughput, delay, and reliability performance of the underlying communication and computing infrastructure. To address this problem, we present a novel virtual PMU (vPMU) architecture that decomposes phasor samples into multiple resolution layers. For a particular receiver with a certain resolution requirement, a complete set of PMU data can be composed by combining samples from the lower layers, without the need for samples from higher layers. We design and implement a real-time distributed storage system to support the virtual PMU data communication. We extend the Chord algorithm so that the response time of data communication can be bounded by our storage system. In addition, we use queuing theory to analyze the response time of requests with our stochastic model.}, booktitle={2014 IEEE PES General Meeting | Conference & Exposition}, publisher={IEEE}, author={Qian, Tao and Chakrabortty, Aranya and Mueller, Frank and Xin, Yufeng}, year={2014}, month={Jul} }
 @article{chandra_gayme_chakrabortty_2014, title={Coordinating Wind Farms and Battery Management Systems for Inter-Area Oscillation Damping: A Frequency-Domain Approach}, volume={29}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2013.2282367}, abstractNote={This paper presents a set of linear control designs for shaping the inter-area oscillation spectrum of a large radial power system through coordinated control of a wind farm and a battery energy system (BES). We consider a continuum representation of the power system with the wind and battery power modeled as point-source forcings. A spectral analysis of the system demonstrates that its oscillation spectrum strongly depends on the locations of these power injections, implying that there are siting locations that produce more favorable spectral responses. However, the ability to site a wind farm or BES at a specific location may be limited by geographic, environmental, economic or other considerations. Our work provides a means to circumvent this problem by designing co-ordinated controllers for the power outputs of the wind farm and the BES by which one can shape the spectral response of the system to a desired response. The design is posed as a parametric optimization problem that minimizes the error between the two spectral responses over a finite range of frequencies. The approach is independent of the locations of the wind farm and the BES, and can be implemented in a decentralized fashion.}, number={3}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Chandra, Souvik and Gayme, Dennice F. and Chakrabortty, Aranya}, year={2014}, month={May}, pages={1454–1462} }
 @inproceedings{lian_duel-hallen_chakrabortty_2014, place={Piscataway, NJ, USA}, title={Cost allocation strategies for wide-area control of power systems using Nash Bargaining Solution}, ISBN={9781467360906 9781479977468 9781479977451}, url={http://dx.doi.org/10.1109/cdc.2014.7039644}, DOI={10.1109/cdc.2014.7039644}, abstractNote={In this paper we present a novel game-theoretic strategy that guarantees fair cost allocation incurred by communication links in wide-area control for electric power systems. The underlying transmission network topology results in vastly diverse requirements for inter-area feedback for operating areas owned by different utility companies. Thus, it is unfair to divide the total communication cost equally among all companies. Our objective is to quantify these requirements and incorporate them into a fair cost distribution scheme. We formulate the wide-area control problem as a state-feedback based LQR minimization problem and cast it as a cooperative game with companies acting as game-players. We first apply sparsity-promoting optimization algorithms to construct the feedback gain matrix such that its off-diagonal blocks that characterize the inter-area feedback are as sparse as possible under a desired energy constraint. Assigning a fixed cost to every non-zero element in these off-diagonal blocks, we apply the Nash Bargaining Solution (NBS) to fairly allocate the total cost among the various game-players. Resulting insights into the wide-area communication requirements for different areas over a range of energy constraints are discussed.}, booktitle={53rd IEEE Conference on Decision and Control}, publisher={IEEE}, author={Lian, Feier and Duel-Hallen, Alexandra and Chakrabortty, Aranya}, year={2014}, month={Dec}, pages={1701–6} }
 @inproceedings{soudbakhsh_chakrabortty_annaswamy_2014, title={Delay-aware co-designs for wide-area control of power grids}, ISBN={9781467360906 9781479977468 9781479977451}, url={http://dx.doi.org/10.1109/cdc.2014.7039769}, DOI={10.1109/cdc.2014.7039769}, abstractNote={In this paper we address the problem of wide-area control of power systems in presence of different classes of network delays. We pose the control objective as an LQR minimization of the electro-mechanical states of the swing equations, and present a so-called arbitration approach by which the flexibilities of the communication network such as scheduling policies, bandwidth, etc., can be exploited to co-design a delay-aware state feedback control law. A key feature of our method is that it retain the samples of the control input until a desired time instant using shapers before releasing them for actuation. This essentially means that we regulate the delays entering our controller. Hence, unlike the traditional robust control designs reported in the power system literature, our design is delay-aware, not delay-tolerant. They are, therefore, much more reliable and practical to implement. We illustrate our results using a 50-bus, 14-generator, 4-area power system model, and show how the proposed arbitrated controller can guarantee significantly better closed-loop performance than traditional robust controllers.}, booktitle={53rd IEEE Conference on Decision and Control}, publisher={IEEE}, author={Soudbakhsh, Damoon and Chakrabortty, Aranya and Annaswamy, Anuradha M.}, year={2014}, month={Dec} }
 @book{phillips_nagle_chakrabortty_2014, title={Digital Control System Analysis and Design}, publisher={Prentice Hall}, author={Phillips, C.L. and Nagle, H.T. and Chakrabortty, A.}, year={2014}, month={Feb} }
 @article{zhang_chakrabortty_xin_2014, title={Distributed Implementation of Wide-Area Monitoring Algorithms for Power Systems Using a US-Wide ExoGENI-WAMS Testbed (Invited Paper)}, ISSN={["1530-0889"]}, DOI={10.1109/dsn.2014.79}, abstractNote={In this paper we address the problem of implementing wide-area oscillation monitoring algorithms for large power system networks using distributed processing of Synchrophasor measurements. We consider two computational approaches, namely decentralized least squares (DLS) and its recursive implementation (RLS). Both algorithms are executed using multiple phasor data concentrators (PDC), deployed as virtual computing machines communicating over a fiber-optic communication network. Results are demonstrated using the US-Wide ExoGENI communication network connected to a PMU test bed at NC State University, and analyze the end-to-end computational and communication delays for both algorithms.}, journal={2014 44TH ANNUAL IEEE/IFIP INTERNATIONAL CONFERENCE ON DEPENDABLE SYSTEMS AND NETWORKS (DSN)}, author={Zhang, Jianhua and Chakrabortty, Aranya and Xin, Yufeng}, year={2014}, pages={762–767} }
 @article{chakrabortty_2014, title={Distributed Optimization Methods for Wide-Area Damping Control of Power System Oscillations}, volume={47}, ISSN={1474-6670}, url={http://dx.doi.org/10.3182/20140824-6-za-1003.00603}, DOI={10.3182/20140824-6-za-1003.00603}, abstractNote={Abstract This paper presents a distributed optimization algorithm to address the problem of wide-area damping control of large-scale electric power systems using Synchrophasors. Our approach consists of a three-step strategy First, Synchrophasors from selected nodes in a power network are used to identify offline dynamic models of the dominant areas of the network. Thereafter, a linear controller is designed for this reduced-order model to shape the inter-machine oscillation dynamics. Finally, algorithms are developed to invert this design to realistic local controllers in each area by optimizing the controller parameters until their interarea response matches the closed-loop inter-machine response achieved in the second step. A model reference control design following this three-step strategy was recently proposed in [1] using a centralized controller. Our results in this paper extend that design by posing the problem purely from a perspective of distributed optimization.}, number={3}, journal={IFAC Proceedings Volumes}, publisher={Elsevier BV}, author={Chakrabortty, Aranya}, year={2014}, pages={1861–1866} }
 @inproceedings{nabavi_chakrabortty_2014, title={Distributed estimation of inter-area oscillation modes in large power systems using alternating direction multiplier method}, DOI={10.1109/pesgm.2014.6939475}, abstractNote={In this paper we present a distributed algorithmic approach to estimate the electro-mechanical oscillation modes of a large power system network using real-time Synchrophasor measurements of phase angles and frequencies. Considering the underlying network to exhibit strong coherency, we are particularly interested in estimating the inter-area oscillation frequencies and their damping factors in a distributed fashion. For this we first integrate the centralized Prony method with a commonly used distributed optimization algorithm, namely, alternating direction method of multipliers (ADMM), and show how the resulting approach can utilize PMU data to identify the modes of interest asymptotically. We illustrate our results using IEEE 39-bus, and 68-bus power systems, and also show the robustness of our method in face of communication failures.}, booktitle={2014 ieee pes general meeting - conference & exposition}, author={Nabavi, S. and Chakrabortty, Aranya}, year={2014} }
 @inproceedings{chandra_weiss_chakrabortty_gayme_2014, title={Impact analysis of wind power injection on time-scale separation of power system oscillations}, DOI={10.1109/pesgm.2014.6938975}, abstractNote={In this work, we present an analytical relationship between the two time-scale behavior of coherent power system networks with increasing levels of wind penetration. We first derive a mathematical model coupling the electro-mechanical swing dynamics of the grid integrated with the dynamics of a doubly-fed induction machine via power flow. We then consider the system to be comprised of r coherent areas and apply a similarity transformation to explicitly show that the integrated system may exhibit a three time-scale behavior depending on the amount of wind power injection. This effect is illustrated using simulations of a model of the US Western Interconnection.}, booktitle={2014 ieee pes general meeting - conference & exposition}, author={Chandra, S. and Weiss, M. D. and Chakrabortty, Aranya and Gayme, D. F.}, year={2014} }
 @article{chakrabortty_martin_2014, title={Optimal Measurement Allocation Algorithms for Parametric Model Identification of Power Systems}, volume={22}, ISSN={["1558-0865"]}, DOI={10.1109/tcst.2014.2299437}, abstractNote={In this paper, we present an optimization algorithm that selects the optimal sets of points for placing phasor measurement units (PMUs) on the transmission lines of a multimachine power system for the purpose of identifying the best model fit for its wide-area swing dynamics. Alternatively, the method can also be viewed as a way to select the optimal set of points at which phasor values should be computed using measurements available from PMUs such that these computed values, also referred to here as pseudo-measurements, can generate the best estimate of the swing model, especially when the measurements are noisy. We pose the identification problem as an equivalent parameter estimation problem for the admittance of each tie-line and the inertia of each machine using phasor measurements of voltage magnitude, phase angle and frequency, corrupted with high-frequency measurement noise. We then formulate the Cramer-Rao bounds (CRBs) for the estimates of these unknown parameters, and show that the bounds are functions of the PMU locations and of the contribution of each measurement variable in the combined output. We finally state the condition for finding the optimal PMU location that guarantees the tightest CRB, and, therefore, the most accurate swing model for the system.}, number={5}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Chakrabortty, Aranya and Martin, Clyde F.}, year={2014}, month={Sep}, pages={1801–1812} }
 @article{anderson_chakrabortty_2014, title={PMU placement for dynamic equivalencing of power systems under flow observability constraints}, volume={106}, ISSN={["1873-2046"]}, DOI={10.1016/j.epsr.2013.08.002}, abstractNote={In this paper we develop two graph-theoretic algorithms for placing Phasor Measurement Units (PMUs) in a multi-area power system network with the objective of identifying its dynamic equivalent model. The system is considered to be divided into clusters of synchronous generators and loads, with each area connected to other sets of areas through designated transmission networks. We first show that in order to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising from the boundary buses of these areas. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive two sets of algorithms to compute the sub-optimal minimum cover, first for a bipartite graph and then for any general topology. The respective algorithms are referred to as CONPLAC and CONITPLAC. Results are illustrated using a IEEE 34-bus system pointing to the robustness of the proposed algorithms against time-varying network topology. Finally, we present statistical analyses to describe how the final set of chosen PMU locations and the computational time of these algorithms depend on network size, complexity and measurement constraints.}, journal={ELECTRIC POWER SYSTEMS RESEARCH}, author={Anderson, Joel E. and Chakrabortty, Aranya}, year={2014}, month={Jan}, pages={51–61} }
 @inproceedings{chakrabortty_khan_2014, title={Spatio-temporal oscillation monitoring in spatially distributed power system networks using energy functions}, DOI={10.1109/acc.2014.6859496}, abstractNote={In this paper we consider continuum models of power system networks divided into clusters, and present a model reduction method to derive the analytical expressions for frequency waves propagating from one cluster to another depending on the network topology. Previous results have modeled such electromechanical waves mostly for two-area radial transfer paths, i.e., for two-node line graphs. Our results extend this approach to a network of areas connected by equivalent transfer paths by defining an equivalent Sturm-Liouville eigenvalue equation for the clustered network. We derive analytical expressions for the equivalent damping and power spectrum of this eigenvalue problem, as well for the spatio-temporal kinetic and potential energy functions that may used for transient stability assessment of the clustered network model following a disturbance.}, booktitle={2014 american control conference (acc)}, author={Chakrabortty, Aranya and Khan, T. R.}, year={2014}, pages={753–758} }
 @inproceedings{nudell_chakrabortty_2013, title={A graph-theoretic algorithm for disturbance localization in large power grids using residue estimation}, ISBN={9781479901784 9781479901777 9781479901753}, url={http://dx.doi.org/10.1109/acc.2013.6580367}, DOI={10.1109/acc.2013.6580367}, abstractNote={In this paper we consider the problem of localizing unknown disturbances in large power systems using a measurement-based graph theoretic method. We first show that the aggregate electro-mechanical model of the power system, under certain assumptions, can be analyzed analogously to a generic nth-order asymmetric networked dynamic system. Considering that the network exhibits a clustering structure leading to slow and fast eigenvalues, we propose an input localization method based on the properties of the weak nodal domains corresponding to the first p dominant slow eigenvalues. In particular, we prove that for systems defined over p-area complete graphs the input localization is unique. We provide simulation results to illustrate our algorithm.}, booktitle={2013 American Control Conference}, publisher={IEEE}, author={Nudell, Thomas R. and Chakrabortty, Aranya}, year={2013}, month={Jun} }
 @inproceedings{weiss_chakrabortty_xin_2013, title={A multi-user network testbed for wide-area monitoring and control of power systems using distributed synchrophasors}, ISBN={9781450320528}, url={http://dx.doi.org/10.1145/2487166.2487212}, DOI={10.1145/2487166.2487212}, abstractNote={In this poster we describe an advanced hardware-in-loop simulation facility for real-time demonstration and validation of power system monitoring and control algorithms, currently under construction at NC State University. This facility integrates a real-time power system emulation lab with the GENI network and its associated cloud testbeds. The dynamic responses from the power system emulator are captured via real hardware Phasor Measurement Units (PMU) that are synchronized with the time-scale of the simulations via a common GPS reference. These responses are then sent to the computing and storage resource in GENI using the IEEE C37.118 protocol, running the smart grid control and management application simulations via QoS-guaranteed communications channels, all provisioned in a dynamic fashion.}, booktitle={Proceedings of the the fourth international conference on Future energy systems - e-Energy '13}, publisher={ACM Press}, author={Weiss, Matthew and Chakrabortty, Aranya and Xin, Yufeng}, year={2013} }
 @inproceedings{xin_chakrabortty_2013, title={A study on group communication in distributed wide-area measurement system networks in large power systems}, ISBN={9781479902484}, url={http://dx.doi.org/10.1109/globalsip.2013.6736935}, DOI={10.1109/globalsip.2013.6736935}, abstractNote={Future wide-area measurement and control applications in large electric power systems will require a new decentralized architecture that scales up with the rapidly growing deployment of Phasor Measurement Units (PMUs). The emerging cloud computing paradigm that allows dynamic creation of virtual machines to form virtual data centers would help better support this new architecture through more efficient and flexible use of the networking and computing resources. However, this paradigm shift poses new technical challenges to the underneath communication and computing infrastructure leading to new problem formulations and solution approaches. Given that the primary communication pattern in the decentralized system will consist of various types of real-time group communication methods, in this paper we present a preliminary study on two problems, namely communication group formation and routing, that are fundamental to the envisioned new communication architecture.}, booktitle={2013 IEEE Global Conference on Signal and Information Processing}, publisher={IEEE}, author={Xin, Yufeng and Chakrabortty, Aranya}, year={2013}, month={Dec} }
 @article{chakrabortty_xin_2013, title={Hardware-in-the-Loop Simulations and Verifications of Smart Power Systems Over an Exo-GENI Testbed}, DOI={10.1109/gree.2013.12}, abstractNote={In this paper we describe an advanced hardware-in- loop simulation facility for real-time demonstration and validation of power system monitoring and control algorithms, currently under construction at NC State University. This facility integrates a real-time power system emulation lab with the GENI network and its associated cloud testbeds. The dynamic responses from the power system emulator are captured via real hardware Phasor Measurement Units (PMU) that are synchronized with the time-scale of the simulations via a common GPS reference. These responses are then sent to the computing and storage resource in GENI using the IEEE C37.118 protocol, running the smart grid control and management application simulations via QoS-guaranteed communications channels, all provisioned in a dynamic fashion.}, journal={2013 SECOND GENI RESEARCH AND EDUCATIONAL EXPERIMENT WORKSHOP (GREE)}, author={Chakrabortty, Aranya and Xin, Yufeng}, year={2013}, pages={16–19} }
 @inproceedings{chakrabortty_khargonekar_2013, title={Introduction to wide-area control of power systems}, DOI={10.1109/acc.2013.6580901}, abstractNote={A key element in the development of smart power transmission systems over the past decade is the tremendous advancement of the Wide-Area Measurement System (WAMS) technology, also commonly referred to as the Synchrophasor technology. Sophisticated digital recording devices called Phasor Measurement Units or PMUs are currently being installed at different points in the North American grid, especially under the smart grid initiatives of the US Department of Energy, to record and communicate GPS-synchronized, high sampling rate (6-60 samples/sec), dynamic power system data. Significant research efforts have been made on techniques to useWAMS for monitoring and situational awareness of large power networks dispersed across wide geographical areas. In contrast, use of WAMS for automatic feedback control has received less attention from the research community. The objective of this paper is to bridge this gap by formulating wide-area control problems for oscillation damping, voltage control, wide-area protection, and disturbance localization. We present the main research challenges that need to be overcome to realize the benefits of wide area control in power systems. Our discussion begins with a review of the fundamental physical models of different characteristic components of a large transmission-level power grid such as synchronous generators, transmission lines, and loads, followed by a description of how these subsystem-level models can be integrated to form the overall system model. We pose ten distinct control-theoretic problems. The first two problems are on using PMU measurements from selected nodes in the system to identify such system models in different resolutions in real-time, and the remaining on how the identified models can be used for designing output-feedback based damping controllers, for understanding voltage fluctuations at different nodes of the network graph, and for detecting malicious inputs entering the system dynamics via faults or extraneous attacks. We also propose two new control paradigms, namely a scheduling approach for appropriate controller selection based on online estimation of oscillation modes, and distributed phasor-based control using model estimation. We illustrate our ideas via representative examples, many of which are inspired by well-known power transfer paths in the US west coast grid, also referred to as the Western Electricity Coordinating Council (WECC).}, booktitle={2013 american control conference (acc)}, author={Chakrabortty, Aranya and Khargonekar, P. P.}, year={2013}, pages={6758–6770} }
 @inbook{chakrabortty_chow_2013, title={Measurement-Based Methods for Model Reduction of Power Systems Using Synchrophasors}, ISBN={9781461418023 9781461418030}, ISSN={2196-3185 2196-3193}, url={http://dx.doi.org/10.1007/978-1-4614-1803-0_8}, DOI={10.1007/978-1-4614-1803-0_8}, abstractNote={Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how “Northern Washington” oscillates against “Southern California” in response to various disturbance events. The main question here is whether we can analytically construct dynamic electromechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of hundreds of actual generators. In this chapter we present an overview of several new results on how to construct such simplified interarea models of large power systems by using dynamic measurements available from phasor measurement units (PMUs) installed at limited points on the transmission lines. Our examples of study are motivated by widely encountered power transfer paths in the Western Electricity Coordinating Council (WECC), namely a two-area radial system representing the WA-MT flow, a star-connected three-area system resembling the Pacific AC Intertie, and a generic multi-area system with more than one dominant slow mode of oscillation.}, booktitle={Power Electronics and Power Systems}, publisher={Springer New York}, author={Chakrabortty, Aranya and Chow, J.}, year={2013}, pages={159–197} }
 @inproceedings{thakur_chakrabortty_2013, title={Multi-dimensional wide-area visualization of power system dynamics using Synchrophasors}, ISBN={9781479913039}, url={http://dx.doi.org/10.1109/pesmg.2013.6672612}, DOI={10.1109/pesmg.2013.6672612}, abstractNote={Majority of the traditional visualization techniques for Synchrophasor-based wide-area monitoring of large power grids are based on displaying measured values of voltage, phase angle, currents, and frequencies at discrete points in space, thereby providing only limited insight into the spatio-temporal relationships between the dynamic features embedded in the measured signals. To bridge this gap, we present several geospatial and multi-dimensional visualization methods that correlate various dynamic attributes of phase angle and power oscillations, and explicitly quantify their spatio-temporal couplings, on both absolute and relative scales. In particular, we focus on four main attributes, namely, modal frequency, damping factor, residues, and modal energy. We show how the proposed methods can interpret the interdependencies of these respective features over space and time leading to more global situational awareness, how they can be visualized in real-time using 3-dimensional plots, and, most importantly, how they can be used for robust outlier detection and baseline modification in large PMU datasets.}, booktitle={2013 IEEE Power & Energy Society General Meeting}, publisher={IEEE}, author={Thakur, Sidharth and Chakrabortty, Aranya}, year={2013} }
 @inproceedings{nabavi_chakrabortty_2013, title={Topology identification for dynamic equivalent models of large power system networks}, DOI={10.1109/acc.2013.6579989}, abstractNote={In this paper we propose two algorithms to identify the equivalent topology of reduced-order models of power systems using measurements of phase angles and frequencies available from Phasor Measurement Units (PMUs). We first show that the topology identification problem can be posed as a parameter estimation problem. Thereafter, we extract the slow oscillatory component of the PMU measurements using subspace identification methods and use them for identifying the topological parameters via conventional ℓ2 minimization approach. Next, we consider the problem of identifying a sparse equivalent network topology using a ℓ1/ℓ2 minimization technique. We illustrate our results using a IEEE 39-bus model.}, booktitle={2013 american control conference (acc)}, author={Nabavi, S. and Chakrabortty, Aranya}, year={2013}, pages={1138–1143} }
 @inproceedings{chandra_gayme_chakrabortty_2013, title={Using battery management systems to augment inter-area oscillation control in wind-integrated power systems}, DOI={10.1109/acc.2013.6580748}, abstractNote={This paper presents a control design for shaping the inter-area oscillations of a wind-integrated power system through coordination between a wind power controller and a controlled battery energy system (BES). We consider a continuum representation of the power system dynamics subject to two point source forcings from wind and battery power, each injected at specified electrical distances along the transfer path. The inter-area oscillation modes of a wind-integrated power system have previously been shown to be highly dependent on the location where wind power is injected, as a result of which a particular injection site may produce a desired spectral response. A wind power controller may be used to achieve the response in an arbitrary location but the effect is limited to small frequency ranges. In the present work, we design co-dependent linear controllers for the wind power and the BES in charging mode, and show that the addition of this controlled BES greatly improves the spectral matching within the inter-area oscillation range. We illustrate the performance of our controllers using power system models inspired by US west coast transfer paths such as the Pacific AC Inter-tie.}, booktitle={2013 american control conference (acc)}, author={Chandra, S. and Gayme, D. F. and Chakrabortty, Aranya}, year={2013}, pages={5809–5814} }
 @inproceedings{chakrabortty_michailidis_xin_2012, title={A decentralized ID algorithm for detecting slow-fast oscillations in power systems from overwhelming volumes of phasor data}, DOI={10.1109/cdc.2012.6426669}, abstractNote={As the number of sensors, namely Phasor Measurement Units or PMUs, in the US power transmission grid scales up into the thousands within the next few years, the current state-of-the-art centralized data processing architecture will no longer be sustainable, and decentralized algorithms must be developed instead. In this paper we propose such an algorithm for one of the most critical applications in power system monitoring- namely, modal decomposition of swing dynamics for detecting slow and fast oscillation modes in the system with evaluation of their respective damping factors. Given a multiple set of coherent generation clusters in the system, we first use data from all PMU sources to calculate the oscillatory modes, their damping and participation in a centralized fashion. Next, we categorize the PMUs into several disjoint sets, and use the data from each of these sets to evaluate the modal frequencies for the entire system individually, assuming that the network has a connected topology guaranteeing system observability. A global estimate for any specific eigenvalue of interest is then computed from the geometric mean of those obtained from the disjoint estimation, and analytical expressions are derived to indicate how this geometric mean, representing the `fused distributed solution' compares to the centralized solution. A discussion on how the output nodes in the network should be chosen appropriately contingent on the topological structure of the network, in order to minimize the error between the two estimates is also presented. We illustrate our results with prototype power system network models inspired by two well-known transfer paths in the US west coast grid.}, booktitle={2012 ieee 51st annual conference on decision and control (cdc)}, author={Chakrabortty, Aranya and Michailidis, G. and Xin, Y. F.}, year={2012}, pages={5010–5015} }
 @inproceedings{anderson_chakrabortty_2012, title={A minimum cover algorithm for PMU placement in power system networks under line observability constraints}, DOI={10.1109/pesgm.2012.6345002}, abstractNote={In this paper we develop a graph-theoretic PMU placement algorithm for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. The system is considered to be divided into clusters or areas of synchronous generators, with each area connected to other sets of areas through designated transmission networks. The buses in the system are accordingly divided into two types, namely - boundary buses of the areas and boundary buses of the transmission networks. We first show that in order to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising out of the boundary buses of the areas and those of the corresponding transmission networks they are connected to. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive an algorithm to compute the sub-optimal minimum cover for the multi-area system. The method is illustrated via a 4-6 bipartite network, as well as with two small examples from the WECC system. Statistical analyses of the algorithm are also presented describing how the final set of chosen PMU locations as well as the computational time needed to run the algorithm are dependent on the size, complexity and measurement constraints of the network.}, booktitle={2012 IEEE Power and Energy Society General Meeting}, author={Anderson, J. E. and Chakrabortty, Aranya}, year={2012} }
 @book{libraries_2012, title={Control and Optimization Methods for Electric Smart Grids}, DOI={10.1007/978-1-4614-1605-0}, abstractNote={Control and Optimization Methods for Electric Smart Grids brings together leading experts in power, control and communication systems, and consolidates some of the most promising recent research in sm}, journal={CONTROL AND OPTIMIZATION METHODS FOR ELECTRIC SMART GRIDS}, publisher={New York: Springer}, author={Libraries, NC State University}, year={2012}, pages={1–371} }
 @inproceedings{felder_chakrabortty_2012, title={Evaluating the computation times of real-time algorithms for power system modeling and state prediction}, DOI={10.1109/smartgridcomm.2012.6485956}, abstractNote={This paper presents a comparative study of three real-time algorithms for power system model identification, parameter estimation and state prediction using real-time Phasor Measurement (PMU) data available from various selected nodes in a power system. Current modeling and state estimation algorithms in power control centers only use limited amount of data, leading to local observability. Our approach, on the other hand, is to use data from wide regions in the grid to gain insight on the global health of the system. The two main challenges for our approach are, therefore, the large size of the system and the large amount of measured data. Three specific algorithms, namely the Eigenvalue Realization Algorithm, linear least squares and state observer method, are used for this purpose. The first algorithm identifies the global system dynamics from PMU data in real-time, the second relaxes the identification problem as a parameter estimation problem, while the third generates estimate of the global state and, thereafter, computes the impulse response of a selected oscillation mode depending on the participation of that mode on the chosen output. The performance of these three methods is then compared in terms of their computational time delays and accuracy of prediction.}, booktitle={2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm)}, author={Felder, J. and Chakrabortty, Aranya}, year={2012}, pages={37–42} }
 @inproceedings{anderson_chakrabortty_2012, title={Graph-theoretic algorithms for PMU placement in power systems under measurement observability constraints}, DOI={10.1109/smartgridcomm.2012.6486054}, abstractNote={In this paper we develop two graph-theoretic PMU placement algorithms for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. We first show that to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising out of the boundary buses of the areas. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive an algorithm to compute the sub-optimal minimum cover, first for a bipartite graph and then for any general topology. We illustrate our results using a IEEE 34-bus model.}, booktitle={2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm)}, author={Anderson, J. E. and Chakrabortty, Aranya}, year={2012}, pages={617–622} }
 @inproceedings{chakrabortty_khan_2012, title={Graph-theoretic model reduction of oscillation propagation in spatially distributed power system networks}, ISBN={9781467320665 9781467320658 9781467320634 9781467320641}, url={http://dx.doi.org/10.1109/cdc.2012.6426348}, DOI={10.1109/cdc.2012.6426348}, abstractNote={In this paper we consider continuum models of large distributed power systems defined over dynamic equivalent clusters, and derive a model reduction method to illustrate how oscillations can propagate from one cluster to another in the form of equivalent frequency waves depending on the topology of their interconnections. Previous results in [1], [2] have modeled such electromechanical waves mostly for two-area radial transfer paths (or, equivalently for a two-node line graph) by representing the swing dynamics in terms of partial differential equations (PDEs). Our results extend this approach to a network of areas connected by equivalent transfer paths, and defines an equivalent Sturm-Liouville eigenvalue equation for the entire network. We show that depending on the network topology the solutions of this eigenvalue problem can be significantly different from those for the individual paths. Simulation results for several representative power system network structures confirm our hypothesis.}, booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Chakrabortty, Aranya and Khan, Taufiquar R.}, year={2012}, month={Dec} }
 @inproceedings{gayme_chakrabortty_2012, title={Impact of wind farm placement on inter-area oscillations in large power systems}, ISBN={9781457710964 9781457710957 9781457710940 9781467321020}, url={http://dx.doi.org/10.1109/acc.2012.6315617}, DOI={10.1109/acc.2012.6315617}, abstractNote={This paper presents an analytical method for evaluating how the placement of wind farms in a large, geographically dispersed power system may affect its inter-area oscillation dynamics. We consider a continuum representation of the electro-mechanical swing dynamics for the power system leading to a linear hyperbolic wave equation for the rotor phase angle across the transfer path. The wind power is modeled as the output of a dynamic system entering the wave equation as a point source in space located at a certain electrical distance from one end of the path. We then derive the spectrum of the line power flow for this forced system using a Fourier analysis, and show how its frequency response, especially for the inter-area or low-frequency modes, is parameterized by this distance variable. We finally pose this parametric dependence as a planning problem in light of finding the optimal distance for placing the wind farm such that a specified set of inter-area modes are damped. We illustrate our results using simulations based on a two-area power system model inspired by US west coast transfer paths such as the Pacific AC Inter-tie.}, booktitle={2012 American Control Conference (ACC)}, publisher={IEEE}, author={Gayme, D. F. and Chakrabortty, A.}, year={2012}, month={Jun} }
 @inproceedings{gayme_chakrabortty_2012, title={Shaping power system inter-area oscillations through control loops of grid integrated wind farms}, ISBN={9781467320665 9781467320658 9781467320634 9781467320641}, url={http://dx.doi.org/10.1109/cdc.2012.6426125}, DOI={10.1109/cdc.2012.6426125}, abstractNote={This paper presents a control design for shaping the inter-area oscillation spectrum of a large wind-integrated power system. The power system is modeled using a continuum representation of the electro-mechanical swing dynamics with the wind power entering as a spatial point source at a specific electrical distance along the transfer path. The frequency response, particularly that of inter-area oscillations, has previously been shown to be highly sensitive to this location. However, in many situations, it may not be possible to site a wind farm at the location with the most desirable frequency response. Here, we show that one can design a wind farm controller to shape the frequency response of the power system with a wind farm at an arbitrary location to closely resemble that of a system with a more favorable wind injection site. The results are illustrated using simulations based on power system models inspired by US west coast transfer paths such as the Pacific AC Inter-tie.}, booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Gayme, Dennice F. and Chakrabortty, Aranya}, year={2012}, month={Dec} }
 @article{chakrabortty_2012, title={Wide-Area Damping Control of Power Systems Using Dynamic Clustering and TCSC-Based Redesigns}, volume={3}, ISSN={1949-3053 1949-3061}, url={http://dx.doi.org/10.1109/tsg.2012.2197029}, DOI={10.1109/tsg.2012.2197029}, abstractNote={In this paper we present a FACTS (Flexible AC Transmission Systems)-based control design for electromechanical oscillation damping in large power systems, facilitated by aggregate models that can be constructed using Synchronized phasor measurements. Our approach consists of three steps, namely-1. Model Reduction, where Synchrophasors are used to identify second-order models of the oscillation clusters of the power system retaining the inter-ties on which FACTS devices such as Thyristor Controlled Series Compensators (TCSC) are installed, 2. Aggregate Control, where feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally 3. Control Inversion, where the aggregate control design is distributed and tuned to actual TCSC controllers in the full-order model until its inter-area responses match the respective inter-machine responses of the reduced-order system. It is shown that the inversion problem can be posed equivalently as decomposing the swing dynamics into fast and slow states, and designing the controllers such that the slow dynamics can optimally track a desired closed-loop signal designed for the aggregate model. Application of the approach to two-area power systems is demonstrated through topological examples inspired by the US west coast grid.}, number={3}, journal={IEEE Transactions on Smart Grid}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chakrabortty, Aranya}, year={2012}, month={Sep}, pages={1503–1514} }
 @inproceedings{chakrabortty_2012, title={Wide-Area Damping Control of Power Systems Using Inversion Techniques: A TCSC-Based Model Reference Approach}, booktitle={Proceedings of IEEE PES General Meeting}, author={Chakrabortty, A.}, year={2012} }
 @inproceedings{chakrabortty_2012, title={Wide-area damping control of power systems using clustering and FACTS-based redesigns}, ISBN={9781457710964 9781457710957 9781457710940 9781467321020}, url={http://dx.doi.org/10.1109/acc.2012.6315533}, DOI={10.1109/acc.2012.6315533}, abstractNote={In this paper we present a FACTS (Flexible AC Transmission Systems)-based control design for electromechanical oscillation damping in large power systems, facilitated by aggregate models that can be constructed using Synchronized phasor measurements. Our approach consists of three steps, namely - 1. Model Reduction, where Synchrophasors are used to identify second-order models of the oscillation clusters of the power system retaining the inter-ties on which FACTS devices such as Thyristor Controlled Series Compensators (TCSC) are installed, 2. Aggregate Control, where feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally 3. Control Inversion, where the aggregate control design is distributed and tuned to actual TCSC controllers in the full-order model until its inter-area responses match the respective inter-machine responses of the reduced-order system. It is shown that the inversion problem can be posed equivalently as decomposing the swing dynamics into fast and slow states, and designing the controllers such that the slow dynamics can optimally track a desired closed-loop signal designed for the aggregate model.}, booktitle={2012 American Control Conference (ACC)}, publisher={IEEE}, author={Chakrabortty, A.}, year={2012}, month={Jun} }
 @article{chakrabortty_chow_salazar_2011, title={A Measurement-Based Framework for Dynamic Equivalencing of Large Power Systems Using Wide-Area Phasor Measurements}, volume={2}, ISSN={1949-3053 1949-3061}, url={http://dx.doi.org/10.1109/tsg.2010.2093586}, DOI={10.1109/tsg.2010.2093586}, abstractNote={Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how northern Washington oscillates against southern California in response to various disturbance events. The main question here is whether we can analytically construct dynamic electromechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of thousands of actual generators. In this paper we address this problem, and present a concise overview of several new results on how to construct simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our examples of study are motivated by widely encountered power transfer paths in the Western Electricity Coordinating Council (WECC), namely, a two-area radial system representing the WA-MT flow, and a star-connected three-area system resembling the Pacific AC Intertie.}, number={1}, journal={IEEE Transactions on Smart Grid}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chakrabortty, Aranya and Chow, Joe H. and Salazar, Armando}, year={2011}, month={Mar}, pages={68–81} }
 @article{chakrabortty_salazar_2011, title={Building a dynamic electro-mechanical model for the Pacific AC intertie using distributed synchrophasor measurements}, volume={21}, ISSN={["1430-144X"]}, DOI={10.1002/etep.586}, abstractNote={In this paper, we present a novel algorithm for constructing simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our example of study in this paper is a widely encountered realistic system, namely the Pacific AC intertie, which closely resembles a star-connected three-area power system. We derive analytical results showing how the voltage, phase angle, and frequency oscillations at different buses on the transfer path of this intertie can be used to estimate the essential parameters of the three-machine equivalent model of this three-area system. We illustrate the results with actual disturbance event data from the Western Electricity Coordinating Council. Copyright © 2011 John Wiley & Sons, Ltd.}, number={4}, journal={EUROPEAN TRANSACTIONS ON ELECTRICAL POWER}, author={Chakrabortty, Aranya and Salazar, Armando}, year={2011}, month={May}, pages={1657–1672} }
 @inproceedings{chakrabortty_khan_2011, title={Modeling and Analysis of Oscillation Propagation in Complex Power System Networks}, ISBN={9781457710001}, url={http://dx.doi.org/10.1109/pes.2011.6039918}, DOI={10.1109/pes.2011.6039918}, abstractNote={American Electric Power (AEP) will provide a presentation, “Community Energy Storage (CES) at AEP”, which will include a discussion of AEP's evolution from substation scale NaS Batteries to smaller energy units located closer to the customer but operated as a fleet to achieve system benefits comparable to the larger battery systems. AEP Ohio is installing 80–25 KW units on a distribution circuit as part of a Department of Energy Stimulus Demonstration Project. CES utilizes individual battery controls and a control hub to provide peak shaving ability at a system level and the ability island small groups of customers during outages of their primary circuit. The presentation will cover reasons for moving to CES, basic specifications, and experience to date in testing and installing units in the Columbus, OH area.}, booktitle={Proceedings of the IEEE Power & Energy Society General Meeting}, author={Chakrabortty, A. and Khan, T.R.}, year={2011}, month={Jul} }
 @article{chakrabortty_martin_2011, title={Optimal measurement allocation for parametric model identification of electrical networks}, volume={2}, ISSN={2185-4106}, url={http://dx.doi.org/10.1587/nolta.2.302}, DOI={10.1587/nolta.2.302}, abstractNote={In this paper we develop optimal sensor siting methods along the edges of a large network of electrical oscillators to identify a parametric model for the network using dynamic measurements of electrical signals corrupted with Gaussian noise. We pose the identification problem as estimation of four essential parameters for each edge in the network, namely the real and imaginary components of the edge-weight, or equivalently, the resistance and reactance of the tie-line connecting any two oscillators, and the inertias of the oscillators connected by this edge. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters using three fundamental outputs - namely, the magnitude, the phase angle and the frequency of the voltage phasor along each edge, and show that the bounds are functions of the sensor locations on the edges as well as of the contribution of each variable in the combined output. We finally state the condition for finding the optimal sensor location and the optimal signal combination to achieve the tightest Cramer-Rao bound. The problem is first addressed for open-loop networks and, thereafter, for networks where outputs measured at desired locations on the edges are fed back to the nodes to improve transient performance. We show that unlike the first case where the open-loop configuration allows us to optimize the bounds in a distributed fashion for each individual edge, for the latter situation the problem no longer has a decoupled structure under the influence of feedback, and must be carried out in a centralized fashion.}, number={3}, journal={Nonlinear Theory and Its Applications, IEICE}, publisher={Institute of Electronics, Information and Communications Engineers (IEICE)}, author={Chakrabortty, Aranya and Martin, Clyde F.}, year={2011}, pages={302–319} }
 @inproceedings{chakrabortty_2011, title={Optimal sensor placement for parametric identification of electrical networks using mixed phasor measurements}, DOI={10.1109/acc.2011.5991539}, abstractNote={In this paper we present an algorithm for placing sensors optimally along the edges of a large network of electrical oscillators to identify a parametric model for the network using a linear combination of three fundamental electrical signals- namely, the magnitude, the phase angle and the frequency of the voltage phasor along each edge, corrupted with Gaussian noise. We pose the identification problem as estimation of four essential parameters for each edge, namely the real and imaginary components of the edge-weight (or, equivalently the resistance and reactance along the transmission line), and the inertias of the two machines connected by this edge. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters, and show that the bounds are functions of the sensor locations and of the contribution of each variable in the combined output. We Anally state the condition for finding the optimal sensor location and the optimal signal combination to achieve the tightest Cramer-Rao bound.}, booktitle={2011 american control conference}, author={Chakrabortty, Aranya}, year={2011}, pages={4540–4545} }
 @article{chakrabortty_scholtz_2011, title={Time-Scale Separation Designs for Performance Recovery of Power Systems With Unknown Parameters and Faults}, volume={19}, ISSN={1063-6536 1558-0865}, url={http://dx.doi.org/10.1109/tcst.2010.2043105}, DOI={10.1109/tcst.2010.2043105}, abstractNote={In this brief we apply several time-scale separation designs for robust stabilization and performance recovery to multimachine power systems with two commonly encountered classes of uncertainties, namely matched additive uncertainty (e.g., line outage) and input multiplicative uncertainty (e.g., load or generation changes). We illustrate the effectiveness of the designs in eliminating undesired performance such as the possibilities of a Hopf bifurcation and subsequent voltage collapse in a single machine infinite bus power system. We also demonstrate the application of one of the designs to fault recovery of a classical 9-bus system.}, number={2}, journal={IEEE Transactions on Control Systems Technology}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chakrabortty, Aranya and Scholtz, Ernst}, year={2011}, month={Mar}, pages={382–390} }
 @inbook{chakrabortty_2011, title={Transient Stability Assessment Using Synchronized Phasor Measurements}, booktitle={Electric Power Engineering Handbook}, publisher={CRC Press}, author={Chakrabortty, A.}, year={2011} }
 @inproceedings{xin_baldine_chase_beyene_parkhurst_chakrabortty_2011, title={Virtual smart grid architecture and control framework}, ISBN={9781457717024 9781457717048 9781457717024}, url={http://dx.doi.org/10.1109/smartgridcomm.2011.6102318}, DOI={10.1109/smartgridcomm.2011.6102318}, abstractNote={In this paper, we present a cloud based virtual Smart Grid (vSG) architecture and its concept design. This novel architecture extends the pervasive virtualization principle to the wide area smart grid sensory, communication, and control systems, and essentially embeds the Smart Grid (SG) into a cloud environment. We particularly design a systematic virtualization mechanism for SG system in three levels: sensors (PMU), substation, and inter-substation. The resulted unified virtualization allows us to extend our existing work in cloud computing to design a vSG control framework. The goal is to provision on-demand virtual real-time systems to support various smart grid applications with guaranteed Quality of Service (QoS) while achieving economies of scale by decoupling the logical systems from the physical infrastructure. Future research will present typical transmission level applications using Synchrophasors that this vSG framework can encompass.}, booktitle={2011 IEEE International Conference on Smart Grid Communications (SmartGridComm)}, publisher={IEEE}, author={Xin, Yufeng and Baldine, Ilia and Chase, Jeff and Beyene, Tsegereda and Parkhurst, Bill and Chakrabortty, Aranya}, year={2011}, month={Oct} }
 @inproceedings{chakrabortty_2011, title={Wide-area damping control of large power systems using a model reference approach}, ISBN={9781612848013 9781612848006 9781467304573 9781612847993}, url={http://dx.doi.org/10.1109/cdc.2011.6161353}, DOI={10.1109/cdc.2011.6161353}, abstractNote={In this paper we present some initial results on the design of dynamic controllers for electromechanical oscillation damping in large power systems using Synchronized Phasor Measurements. Our approach consists of three steps, namely - 1. Model Reduction, where phasor data are used to identify second-order models of the oscillation clusters of the system, 2. Aggregate Control, where state-feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally 3. Control Inversion, where the aggregate control design is distributed and tuned to actual realistic controllers at the generator terminals until the inter-area responses of the full-order power system matches the respective inter-machine responses of the reduced-order system. Although a general optimization framework is needed to formulate these three steps for any n-area power system, we specifically show that model reference control (MRC) can be an excellent choice to solve this damping problem when the power system consists of two dominant areas, or equivalently one dominant interarea mode.}, booktitle={IEEE Conference on Decision and Control and European Control Conference}, publisher={IEEE}, author={Chakrabortty, Aranya}, year={2011}, month={Dec} }
 @inproceedings{chakrabortty_salazar_2010, title={Building a dynamic electromechanical model for the pacific AC intertie using PMU measurements}, ISBN={9781424465491}, url={http://dx.doi.org/10.1109/pes.2010.5589513}, DOI={10.1109/pes.2010.5589513}, abstractNote={In this paper we present several new results on how to construct simplified inter-area models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our example of study in this paper is a widely encountered realistic system, namely the Pacific AC intertie, which closely resembles a star-connected three-area power system. We derive analytical results showing how the voltage, phase angle and frequency oscillations at different buses on the transfer path of this intertie can be used to estimate the essential parameters of the three-machine equivalent model of this three-area system. We illustrate the results with actual disturbance event data from the WECC.}, booktitle={IEEE PES General Meeting}, publisher={IEEE}, author={Chakrabortty, A and Salazar, A}, year={2010}, month={Jul} }
 @inproceedings{chakrabortty_chow_2010, title={Macroscopic modeling of large power systems using distributed dynamic measurements with dependence on network topology}, ISBN={9781424477456}, url={http://dx.doi.org/10.1109/cdc.2010.5717012}, DOI={10.1109/cdc.2010.5717012}, abstractNote={Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how ‘Northern Washington’ oscillates against ‘Southern California’ in response to various disturbance events. The main question here is whether we can analytically construct dynamic electro-mechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of thousands of actual generators. We address this problem in this paper and present several new results on how to construct simplified macroscopic models of large power networks by using dynamic measurements available from specific points on the network edges. Our examples of study are motivated by widely encountered power transfer paths in the US west coast power system, namely, a two-node radial network and a star-connected three-node system.}, booktitle={49th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Chakrabortty, Aranya and Chow, Joe H.}, year={2010}, month={Dec} }
 @inproceedings{chakrabortty_szczodrak_2010, title={Optimal placement of PMUs for identification of power system models using noisy measurement data}, ISBN={9781424465491}, url={http://dx.doi.org/10.1109/pes.2010.5589445}, DOI={10.1109/pes.2010.5589445}, abstractNote={In this paper we address the problem of placing Phasor Measurement Units (PMUs) on a long transmission line connecting two areas of a power system network. Dynamic measurements of electrical signals such as magnitudes and phases of bus voltages and line currents, corrupted with Gaussian noise, are available from these PMUs. Our objective is to determine the best locations for their placement such that, given a particular measured noisy signal, the error in identifying a two-machine interarea equivalent model of the two-area power system is minimum. We first show that the identification problem is equivalent to estimating four essential model parameters, namely the two intra-area reactances, and the inertias of the two aggregated machines. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters, and show that the bounds are functions of the PMU location. We finally state the condition for finding the optimal PMU location to achieve the tightest Cramer-Rao bound.}, booktitle={IEEE PES General Meeting}, publisher={IEEE}, author={Chakrabortty, Aranya and Szczodrak, Marta A}, year={2010}, month={Jul} }
 @inproceedings{chakrabortty_martin_2010, title={Optimal sensor placement for parametric model identification of electrical networks, Part II: Estimation under output feedback}, ISBN={9781424477456}, url={http://dx.doi.org/10.1109/cdc.2010.5717928}, DOI={10.1109/cdc.2010.5717928}, abstractNote={In this paper we present an algorithm for choosing optimal measurement points on the edges of a network of dynamic electrical oscillators such that the noise-corrupted electrical signals measured by sensors at that point can be used for generating the most accurate estimates for the network model. Assuming that the measured outputs are fed back to the network nodes to increase system damping we show that the Cramer-Rao bounds for the model estimates are functions of the sensor locations on every edge in the network. We finally state the condition for finding the optimal sensor locations to achieve the tightest Cramer-Rao bounds. An interesting observation is that unlike the algorithm derived in Part-I of this paper [1], where the open-loop configuration of the system allows us to optimize the bounds in a distributed fashion for each individual edge, here the problem no longer has that decoupled structure under the influence of feedback and must be carried out in a centralized way.}, booktitle={49th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Chakrabortty, Aranya and Martin, Clyde F.}, year={2010}, month={Dec} }
 @inproceedings{chakrabortty_martin_2010, title={Optimal sensor placement for parametric model identification of electrical networks, part I: Open loop estimation}, ISBN={9781424477456}, url={http://dx.doi.org/10.1109/cdc.2010.5717926}, DOI={10.1109/cdc.2010.5717926}, abstractNote={In this paper we present an algorithm for placing sensors optimally along the edges of a large network of electrical oscillators to identify a parametric model for the network using dynamic measurements of electrical signals such as magnitudes and phase angles of voltages and currents, corrupted with Gaussian noise. We pose the identification problem as estimation of four essential parameters for each edge, namely the real and imaginary components of the edge-weight (or, equivalently the resistance and reactance along the transmission line), and the inertias of the two machines connected by this edge. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters, and show that the bounds are functions of the sensor locations. We finally state the condition for finding the optimal sensor location to achieve the tightest Cramer-Rao bound.}, booktitle={49th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Chakrabortty, Aranya and Martin, Clyde F.}, year={2010}, month={Dec} }
 @article{chakrabortty_chow_salazar_2009, title={Interarea Model Estimation for Radial Power System Transfer Paths With Intermediate Voltage Control Using Synchronized Phasor Measurements}, volume={24}, ISSN={0885-8950 1558-0679}, url={http://dx.doi.org/10.1109/tpwrs.2009.2022995}, DOI={10.1109/tpwrs.2009.2022995}, abstractNote={In this paper we develop measurement-based methods for estimating a two-machine reduced model to represent the interarea dynamics of a radial, two-area power system with intermediate dynamic voltage control. Two types of voltage control equipment are considered, namely, a static VAr compensator (SVC), and a synchronous condenser. The methods use synchronized bus voltage phasor data at several buses including the voltage control bus, and the line currents on the power transfer path.}, number={3}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chakrabortty, A. and Chow, J.H. and Salazar, A.}, year={2009}, month={Aug}, pages={1318–1326} }
 @inproceedings{chakrabortty_mesbahi_2009, title={Performance oriented high gain redesigns for FACTS-controlled SMIB power systems}, ISBN={9781424438716}, url={http://dx.doi.org/10.1109/cdc.2009.5399567}, DOI={10.1109/cdc.2009.5399567}, abstractNote={In this paper we apply the singular perturbation based nonlinear control redesign of [1] to guarantee a desired transient performance of Single Machine Infinite Bus (SMIB) electric power systems with dynamic Flexible AC Transmission System (FACTS) control. We illustrate the design by two different case studies, namely, a SMIB system with a thyristor controlled series compensator (TCSC) installed on the transmission line, and a system feeding an induction motor load controlled by a static VAr compensator (SVC). For both of these plants, we redesign the mechinical power input to the main generator to guarantee a desired closed loop transient performance even in the presence of the FACTS dynamics. The effectiveness of the redesigns in recovering desired system trajectories is then illustrated through simulations.}, booktitle={Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference}, publisher={IEEE}, author={Chakrabortty, Aranya and Mesbahi, Mehran}, year={2009}, month={Dec} }
 @article{chakrabortty_arcak_2009, title={Robust Stabilization and Performance Recovery of Nonlinear Systems With Unmodeled Dynamics}, volume={54}, ISSN={0018-9286 1558-2523}, url={http://dx.doi.org/10.1109/tac.2009.2015554}, DOI={10.1109/tac.2009.2015554}, abstractNote={In this technical note we present a time-scale separation redesign for stabilization and performance recovery of nonlinear systems with unmodeled dynamics. The unmodeled dynamics studied do not change the relative degree of the plant and are minimum phase. We design two sets of high gain filters-the first to estimate the uncertain input to the plant over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. The control input then acts over the slow time-scale and guarantees that the closed-loop trajectories approach those of the nominal system.}, number={6}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chakrabortty, A. and Arcak, M.}, year={2009}, month={Jun}, pages={1351–1356} }
 @inproceedings{chakrabortty_2009, title={Some new results on the identification of two-area power system models with SVC control}, ISBN={9781424445233}, url={http://dx.doi.org/10.1109/acc.2009.5159918}, DOI={10.1109/acc.2009.5159918}, abstractNote={In this paper we study a measurement-based model identification problem for constructing dynamic equivalent models of two-area radial power systems with intermediate voltage control by Static VAr Compensators (SVC).We consider two types of feedback mechanisms, namely, combined voltage and current feedback from the SVC bus, and supplementary current feedback from the transmission line. Given these system configurations, we first derive expressions for the aggregated equivalent reactance and machine inertias in each area, and then show how these parameters can be computed from the voltage and frequency measurements at three buses in the transfer path including the SVC bus.}, booktitle={2009 American Control Conference}, publisher={IEEE}, author={Chakrabortty, Aranya}, year={2009} }
 @inproceedings{chakrabortty_chow_2009, place={Belem, Brazil}, title={Synchronized Phasor Data Estimation of Dynamic Parameters for Radial Power System Transfer Path with Voltage Reinforcement}, booktitle={11th Symposium of Specialists in Electric Operational and Expansion Planning (SEPOPE)}, author={Chakrabortty, A. and Chow, J.H.}, year={2009}, month={Mar} }
 @article{chakrabortty_arcak_2009, title={Time-scale separation redesigns for stabilization and performance recovery of uncertain nonlinear systems}, volume={45}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/j.automatica.2008.06.004}, DOI={10.1016/j.automatica.2008.06.004}, abstractNote={In this paper we propose two different time-scale separation based robust redesign techniques which recover the trajectories of a nominal control design in the presence of uncertain nonlinearities. We first consider additive input uncertainties and design a high-gain filter to estimate the uncertainty. We then employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. We next extend this design to systems with uncertain input nonlinearities in which case we design two sets of high gain filters—the first to estimate the input uncertainty over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. Using singular perturbation theory we prove that the trajectories of the respective two-time-scale and three-time scale redesigned systems approach those of the nominal system when the filter gains are increased. We illustrate the redesigns by applying them to various physically motivated examples.}, number={1}, journal={Automatica}, publisher={Elsevier BV}, author={Chakrabortty, Aranya and Arcak, Murat}, year={2009}, month={Jan}, pages={34–44} }
 @article{chow_chakrabortty_vanfretti_arcak_2008, title={Estimation of Radial Power System Transfer Path Dynamic Parameters Using Synchronized Phasor Data}, volume={23}, ISSN={0885-8950 1558-0679}, url={http://dx.doi.org/10.1109/tpwrs.2008.919315}, DOI={10.1109/tpwrs.2008.919315}, abstractNote={This paper develops a measurement-based method for estimating a two-machine reduced model to represent the interarea dynamics of a radial, multimachine power system. The method uses synchronized bus voltage phasor measurements at two buses and the line current on the power transfer path. The innovation is the application of the interarea oscillation components in the voltage variables resulting from disturbances for extrapolating system impedances and inertias beyond the measured buses. Expressions for the amplitudes of the bus voltage and bus frequency oscillations as functions of the location on the transmission path are derived from a small-signal perturbation approach. The reduced model provides approximate response to disturbances on the transfer path and offers an alternative to model reduction techniques based on detailed system models and data.}, number={2}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chow, J.H. and Chakrabortty, A. and Vanfretti, L. and Arcak, M.}, year={2008}, month={May}, pages={564–571} }
 @inproceedings{chakrabortty_chow_2008, title={Interarea model estimation for radial power system transfer paths with voltage support using synchronized phasor measurements}, ISBN={9781424419050}, url={http://dx.doi.org/10.1109/pes.2008.4596292}, DOI={10.1109/pes.2008.4596292}, abstractNote={In this paper we develop a measurement-based method for estimating a two-machine reduced model to represent the interarea dynamics of a radial, two-area power system with intermediate voltage support. The method uses synchronized bus voltage phasor measurements at three buses including the voltage control bus, and the line currents on the power transfer path.}, booktitle={2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century}, publisher={IEEE}, author={Chakrabortty, Aranya and Chow, Joe H.}, year={2008}, month={Jul} }
 @inproceedings{chakrabortty_arcak_tsiotras_2008, title={Robust design of a spacecraft attitude tracking control system with actuator uncertainties}, ISBN={9781424431236}, url={http://dx.doi.org/10.1109/cdc.2008.4738803}, DOI={10.1109/cdc.2008.4738803}, abstractNote={In this paper we apply the robust redesign for transient performance recovery of nonlinear systems with input uncertainties developed in [2] to a spacecraft attitude tracking problem with actuator uncertainties. We first extend the robust design of [2] to a generalized uncertainty structure. Next, we show that when the spin and transverse axis directions and/or the gains of the flywheel actuators are uncertain, the kinematic model of a spacecraft can be expressed in this structure. We apply the extended design to this spacecraft model, illustrate it with a simulation example, and numerically compute the permissible range of the uncertainties for which this design guarantees stability.}, booktitle={2008 47th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Chakrabortty, Aranya and Arcak, Murat and Tsiotras, Panagiotis}, year={2008} }
 @inproceedings{chakrabortty_arcak_2008, title={Robust stabilization and performance recovery of nonlinear systems with input unmodeled dynamics}, ISBN={9781424431236}, url={http://dx.doi.org/10.1109/cdc.2008.4738805}, DOI={10.1109/cdc.2008.4738805}, abstractNote={In this paper we extend the time-scale separation redesign for stabilization and performance recovery of uncertain nonlinear systems proposed in and to systems with input unmodeled dynamics. The class of unmodeled dynamics studied are relative degree zero and minimum phase. We design two sets of high gain filters - the first to estimate the uncertain input to the plant over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. The control input then acts over the slow time-scale and guarantees that the closed-loop trajectories approach those of the nominal system.}, booktitle={2008 47th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Chakrabortty, Aranya and Arcak, Murat}, year={2008} }
 @inproceedings{chakrabortty_arcak_2007, title={A Three-time-scale redesign for robust stabilization and performance recovery of nonlinear systems with input uncertainties}, ISBN={9781424414970}, url={http://dx.doi.org/10.1109/cdc.2007.4434118}, DOI={10.1109/cdc.2007.4434118}, abstractNote={In this paper we propose a robust redesign technique which recovers the trajectories of a nominal control design in the presence of input uncertainties. We design two sets of high gain filters - the first to estimate the input uncertainty over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time- scale. Using singular perturbation theory we prove that the trajectories of the resulting three-time scale redesigned system approach those of the nominal system when the filter gains are increased.}, booktitle={2007 46th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Chakrabortty, Aranya and Arcak, Murat}, year={2007} }
 @inproceedings{chakrabortty_arcak_2007, title={A Two-Time-Scale Redesign for Robust Stabilization and Performance Recovery of Uncertain Nonlinear Systems}, ISBN={1424409888 1424409896}, ISSN={0743-1619}, url={http://dx.doi.org/10.1109/acc.2007.4282348}, DOI={10.1109/acc.2007.4282348}, abstractNote={In this paper we propose a robust redesign technique which recovers the trajectories of a nominal control design in the presence of additive input uncertainties. We design a high-gain filter and employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. Using singular perturbation theory we prove that the trajectories of the redesigned system approach those of the nominal system when the filter gain is increased. We illustrate the redesign by applying it to two physically motivated examples.}, booktitle={2007 American Control Conference}, publisher={IEEE}, author={Chakrabortty, Aranya and Arcak, Murat}, year={2007}, month={Jul} }
 @inproceedings{chakrabortty_scholtz_arcak_2007, title={Performance recovery of power systems with unknown parameters and faults}, ISBN={9781424414970}, url={http://dx.doi.org/10.1109/cdc.2007.4434119}, DOI={10.1109/cdc.2007.4434119}, abstractNote={In this paper we apply the time-scale separation design developed by Chakrabortty and Arcak (2007) for robust stabilization and performance recovery to power systems with unknown load power demands and unexpected line outages. We estimate the unknown over a fast time-scale using a high-gain filter and then employ this estimate to cancel the unknown so that over a slower time-scale the trajectories of the closed loop system approach those of the nominal system. We illustrate the effectiveness of the design in eliminating the possibilities of a Hopf bifurcation and subsequent voltage collapse in a single machine infinite bus (SMIB) power system. We then demonstrate the application of the design to fault recovery of a classical 9-bus system.}, booktitle={2007 46th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Chakrabortty, Aranya and Scholtz, Ernst and Arcak, Murat}, year={2007} }
 @article{chow_chakrabortty_arcak_bhargava_salazar_2007, title={Synchronized Phasor Data Based Energy Function Analysis of Dominant Power Transfer Paths in Large Power Systems}, volume={22}, ISSN={0885-8950}, url={http://dx.doi.org/10.1109/tpwrs.2007.895162}, DOI={10.1109/tpwrs.2007.895162}, abstractNote={Many large interconnected power systems such as the U.S. eastern interconnection and the U.S. western power system are characterized by many power transfer paths or interfaces with high loading. Disruptions of these transfer paths frequently lead to increased loading on neighboring transfer paths, which themselves will become less secure and could cause further disruptions. State estimators have limited performance under large system disruptions, because of low sampling rates and potentially poor solution quality due to topology errors. Furthermore, disruptions in external power systems cannot be readily seen by control room operators because most state estimators only use reduced models for external systems. A system of well-placed phasor measurement units (PMUs) that provide voltage and current magnitude and phase at a high sampling rate can provide useful system dynamic security information. In this paper we apply energy function analysis using phasor data to monitor the dynamic status of power transfer paths. The ideas will be illustrated using actual data captured by several PMUs in the U.S. western power system}, number={2}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Chow, Joe H. and Chakrabortty, Aranya and Arcak, Murat and Bhargava, Bharat and Salazar, Armando}, year={2007}, month={May}, pages={727–734} }
 @inproceedings{chow_chakrabortty_arcak_bhargava_salazar_2006, title={Synchronized phasor data based energy function analysis of power transfer paths}, ISBN={1424404932}, url={http://dx.doi.org/10.1109/pes.2006.1709043}, DOI={10.1109/pes.2006.1709043}, abstractNote={Many large interconnected power systems such as the US eastern interconnection and the US western power system are characterized by many power transfer paths with high loading. Disruptions of these transfer paths frequently lead to increased loading on neighboring transfer paths, which themselves become less secure and could cause further disruptions. State estimators have limited performance under large system disruptions, because of low sampling rates and potentially poor solution quality due to topology errors. Furthermore, disruptions in external power systems cannot be readily seen by control room operators because most state estimators only use reduced models for external systems. A system of well-placed phasor measurement units (PMUs) that provide voltage and current magnitude and phase at a high sampling rate can provide useful system dynamic security information. In this paper we apply energy function analysis using phasor data to monitor the dynamic status of power transfer paths. The ideas are illustrated for a power transfer path using actual PMU data in the US western power system}, booktitle={2006 IEEE Power Engineering Society General Meeting}, publisher={IEEE}, author={Chow, J.H. and Chakrabortty, A. and Arcak, M. and Bhargava, B. and Salazar, A.}, year={2006} }