News

@inproceedings{nm2018acc,
  abstract = {Achieving optimal steady-state performance in real-time is an increasingly  necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. The proposed solution can be logically divided into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component computes an input to the LTI system that aims to drive the system toward the optimal steady-state.
We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using integral quadratic constraints (IQCs), the proposed framework is able to translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed loop system. We illustrate the versatility of our framework using several examples.},
  author = {Nelson, Zachary and Mallada, Enrique},
  booktitle = {American Control Conference (ACC)},
  doi = {10.23919/ACC.2018.8431231},
  grants = {1544771, W911NF-17-1-0092, 1711188},
  issn = {2378-5861},
  keywords = {Optimization, IQCs},
  month = {06},
  title = {An integral quadratic constraint framework for steady state optimization of linear time invariant systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-ACC-NM.pdf},
  year = {2018}
}

@inproceedings{lnms2018cdc,
  abstract = {We consider the problem of designing a feedback
controller that guides the input and output of a linear timeinvariant
system to a minimizer of a convex optimization
problem. The system is subject to an unknown disturbance,
piecewise constant in time, which shifts the feasible set defined
by the system equilibrium constraints. Our proposed design
combines proportional-integral control with gradient feedback,
and enforces the Karush-Kuhn-Tucker optimality conditions
in steady-state without incorporating dual variables into the
controller. We prove that the input and output variables achieve
optimality in steady-state, and provide a stability criterion
based on absolute stability theory. The effectiveness of our
approach is illustrated on a simple example system.},
  author = {Lawrence, Liam S. P. and Nelson, Zachary and Mallada, Enrique and Simpson-Porco, John W.},
  booktitle = {57th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2018.8619812},
  grants = {CPS:1544771, ARO:W911NF-17-1-0092, CAREER-1752362},
  issn = {2576-2370},
  month = {12},
  pages = {3251-3257},
  title = {Optimal Steady-State Control for Linear Time-Invariant Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-LNMS.pdf},
  year = {2018}
}

@misc{jhgm2018ferc-taic,
  author = {Ji, Chengda and Hajiesmaili, Mohammad H. and Gayme, Dennice F. and Mallada, Enrique},
  grants = {CAREER-1752362, ENERGISE-DE-EE0008006, EPCN-1711188},
  howpublished = {FERC Trans-Atlantic Infraday Workshop},
  month = {11},
  title = {Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets},
  url = {https://mallada.ece.jhu.edu/pubs/2018-FERC-TAIC-JHGM.pdf},
  year = {2018}
}

@article{pm2020tac,
  abstract = {The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.},
  author = {Paganini, Fernando and Mallada, Enrique},
  doi = {10.1109/TAC.2019.2942536},
  grants = {CPS-1544771, AMPS-1736448, EPCN-1711188, CAREER-1752362, ENERGISE-DE-EE0008006},
  journal = {IEEE Transactions on Automatic Control},
  month = {7},
  number = {7},
  pages = {3007-3022},
  title = {Global analysis of synchronization performance for power systems: bridging the theory-practice gap},
  url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-PM.pdf},
  volume = {67},
  year = {2020}
}

@article{pm2019tcns,
  abstract = {This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.},
  author = {Pates, Richard and Mallada, Enrique},
  doi = {10.1109/TCNS.2019.2922503},
  grants = {CPS:1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362},
  journal = {IEEE Transactions on Control of Network Systems},
  keywords = {Network Control; Power Networks},
  month = {9},
  number = {3},
  pages = {1174-1184},
  title = {Robust Scale Free Synthesis for Frequency Regulation in Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2019-TCNS-PM.pdf},
  volume = {6},
  year = {2019}
}

@inproceedings{jpm2017cdc,
  abstract = {Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters. 
Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.},
  author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
  booktitle = {56th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2017.8264414},
  grants = {1544771, 1711188, W911NF-17-1-0092},
  keywords = {Power Networks},
  month = {12},
  pages = {5098-5105},
  title = {Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems},
  url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-JPM.pdf},
  year = {2017}
}

@inproceedings{zkvrm2018cdc,
  abstract = {Classical results in sparse representation guarantee
the exact recovery of sparse signals under assumptions on
the dictionary that are either too strong or NP hard to check.
Moreover, such results may be too pessimistic in practice since
they are based on a worst-case analysis. In this paper, we
consider the sparse recovery of signals defined over a graph,
for which the dictionary takes the form of an incidence matrix.
We show that in this case necessary and sufficient conditions
can be derived in terms of properties of the cycles of the
graph, which can be checked in polynomial time. Our analysis
further allows us to derive location dependent conditions for
recovery that only depend on the cycles of the graph that
intersect this support. Finally, we exploit sparsity properties on
the measurements to a specialized sub-graph-based recovery
algorithm that outperforms the standard $l_1$-minimization.},
  author = {Zhao, Mengnan and Kaba, Mustafa Devrim and Vidal, Rene and Robinson, Daniel R. and Mallada, Enrique},
  booktitle = {57th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2018.8619666},
  grants = {AMPS:1736448},
  issn = {2576-2370},
  month = {12},
  pages = {364-371},
  title = {Sparse Recovery over Graph Incidence Matrices},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-ZKVRM.pdf},
  year = {2018}
}

@inproceedings{lnms2018cdc,
  abstract = {We consider the problem of designing a feedback
controller that guides the input and output of a linear timeinvariant
system to a minimizer of a convex optimization
problem. The system is subject to an unknown disturbance,
piecewise constant in time, which shifts the feasible set defined
by the system equilibrium constraints. Our proposed design
combines proportional-integral control with gradient feedback,
and enforces the Karush-Kuhn-Tucker optimality conditions
in steady-state without incorporating dual variables into the
controller. We prove that the input and output variables achieve
optimality in steady-state, and provide a stability criterion
based on absolute stability theory. The effectiveness of our
approach is illustrated on a simple example system.},
  author = {Lawrence, Liam S. P. and Nelson, Zachary and Mallada, Enrique and Simpson-Porco, John W.},
  booktitle = {57th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2018.8619812},
  grants = {CPS:1544771, ARO:W911NF-17-1-0092, CAREER-1752362},
  issn = {2576-2370},
  month = {12},
  pages = {3251-3257},
  title = {Optimal Steady-State Control for Linear Time-Invariant Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-LNMS.pdf},
  year = {2018}
}

@inproceedings{jmg2018cdc,
  abstract = {Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second order integrator systems under a parameterized family of controllers (homotopy) that continuously trade between relative and absolute feedback interconnections in terms of the H2 norm an appropriately defined inputoutput system. Our approach extends the previous H2 norm based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H2 norm but that purely relative feedback can only achieve finite norms when the measurement error is not exciting subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of relative feedback in double integrator systems smoothly decreases the system performance and that this performance degradation is more rapid systems with relative feedback in only the first state (position).},
  author = {Ji, Chengda and Mallada, Enrique and Gayme, Dennice},
  booktitle = {57th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2018.8619283},
  grants = {CPS:1544771, ARO:W911NF-17-1-0092, CAREER-1752362},
  issn = {2576-2370},
  month = {12},
  pages = {1238-1244},
  title = {Evaluating Robustness of Consensus Algorithms Under Measurement Error over Digraph},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-JMG.pdf},
  year = {2018}
}

@inproceedings{pm2018mtns,
  abstract = {Electro-mechanical oscillations in power systems
are typically controlled by simple decentralised controllers.
We derive a formula for computing the delay margin of such
controllers when the power system is represented by a simple
mechanical network. This formula reveals a clear trade-off
between system damping, inertia, and robustness to delays. In
particular, it shows that reducing system inertia, which is a
common consequence of increased renewable generation, can
reduce robustness to unmodelled dynamics.},
  author = {Pates, Richard and Mallada, Enrique},
  booktitle = {23rd International Symposium on Mathematical Theory of Networks and Systems},
  grants = {CPS:1544771, ARO:W911NF-17-1-0092, 1711188, CAREER-1752362},
  month = {7},
  title = {Damping, Inertia, and Delay Robustness Trade-offs in Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-MTNS-PM.pdf},
  year = {2018}
}

@inproceedings{arspm2019acc,
  abstract = {Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization.

More precisely, for a DC network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a dynamic game, where each player (load) seeks to myopically maximize their utility, and where every stable power flow solution amounts to a Local Nash Equilibrium.

Using this framework, we show that voltage collapse is equivalent to the non-existence of a Local Nash Equilibrium in the game and, as a result, it is caused by the lack of cooperation
between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers.},
  author = {Avraam, Charalampos and Rines, Jesse and Sarker, Aurik and Paganini, Fernando and Mallada, Enrique},
  booktitle = {American Control Conference (ACC)},
  doi = {10.23919/ACC.2019.8814708},
  grants = {CAREER-1752362,EPCN-1711188,ENERGISE-DE-EE0008006,ARO-W911NF-17-1-0092,EPCN-1711188,CPS-1544771},
  keywords = {Power Networks},
  month = {06},
  pages = {1957-1964},
  title = {Voltage Collapse Stabilization in Star DC Networks},
  url = {https://mallada.ece.jhu.edu/pubs/2019-ACC-ARSPM.pdf},
  year = {2019}
}

@article{pm2020tac,
  abstract = {The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance, and analyzed under highly simplified assumptions. In this paper we extend this approach to more realistic network scenarios, and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.},
  author = {Paganini, Fernando and Mallada, Enrique},
  doi = {10.1109/TAC.2019.2942536},
  grants = {CPS-1544771, AMPS-1736448, EPCN-1711188, CAREER-1752362, ENERGISE-DE-EE0008006},
  journal = {IEEE Transactions on Automatic Control},
  month = {7},
  number = {7},
  pages = {3007-3022},
  title = {Global analysis of synchronization performance for power systems: bridging the theory-practice gap},
  url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-PM.pdf},
  volume = {67},
  year = {2020}
}

@article{pm2019tcns,
  abstract = {This paper develops a framework for power system stability analysis, that allows for the decentralised design of frequency controllers. The method builds on a novel decentralised stability criterion, expressed as a positive real requirement, that depends only on the dynamics of the components at each individual bus, and the aggregate susceptance of the transmission lines connected to it. The criterion is both robust to network uncertainties as well as heterogeneous network components, and it can be verified using several standard frequency response, state space, and circuit theory analysis tools. Moreover, it allows to formulate a scale free synthesis problem, that depends on individual bus dynamics and leverages tools from Hinf optimal control. Notably, unlike similar passivity methods, our framework certifies the stability of several existing (non-passive) power system control schemes and allows to study robustness with respect to delays.},
  author = {Pates, Richard and Mallada, Enrique},
  doi = {10.1109/TCNS.2019.2922503},
  grants = {CPS:1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362},
  journal = {IEEE Transactions on Control of Network Systems},
  keywords = {Network Control; Power Networks},
  month = {9},
  number = {3},
  pages = {1174-1184},
  title = {Robust Scale Free Synthesis for Frequency Regulation in Power Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2019-TCNS-PM.pdf},
  volume = {6},
  year = {2019}
}

@inproceedings{jpm2017cdc,
  abstract = {Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, delayed actions, and power disturbances are considered in the design of dynamic controllers for grid-connected inverters. 
Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters that is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.},
  author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
  booktitle = {56th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2017.8264414},
  grants = {1544771, 1711188, W911NF-17-1-0092},
  keywords = {Power Networks},
  month = {12},
  pages = {5098-5105},
  title = {Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems},
  url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-JPM.pdf},
  year = {2017}
}

@article{zmlb2018ijepes,
  abstract = {A distributed control scheme, which can be implemented on generators and controllable loads in a plug-and-play manner, is proposed for power system frequency regulation. The proposed scheme is based on local measurements, local computation, and neighborhood information exchanges over a communication network with an arbitrary (but connected) topology. In the event of a sudden change in generation or load, the proposed scheme can restore the nominal frequency and the reference inter-area power flows, while minimizing the total cost of control for participating generators and loads. Power network stability under the proposed control is proved with a relatively realistic model which includes nonlinear power flow and a generic (potentially nonlinear or high-order) turbine-governor model, and further with first- and second-order turbine-governor models as special cases. In simulations, the proposed control scheme shows a comparable performance to the existing automatic generation control (AGC) when implemented only on the generator side, and demonstrates better dynamic characteristics that AGC when each scheme is implemented on both generators and controllable loads.},
  author = {Zhao, Changhong and Mallada, Enrique and Low, Steven H and Bialek, Janusz W},
  doi = {https://doi.org/10.1016/j.ijepes.2018.03.014},
  grants = {W911NF-17-1-0092, 1544771, 1711188, 1736448, 1752362},
  issn = {0142-0615},
  journal = {International Journal of Electric Power and Energy Systems},
  keywords = {Power Networks; Frequency Control},
  month = {10},
  pages = {1 -12},
  title = {Distributed plug-and-play optimal generator and load control for power system frequency regulation},
  url = {https://mallada.ece.jhu.edu/pubs/2018-IJEPES-ZMLB.pdf},
  volume = {101},
  year = {2018}
}

@inproceedings{nm2018acc,
  abstract = {Achieving optimal steady-state performance in real-time is an increasingly  necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. The proposed solution can be logically divided into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component computes an input to the LTI system that aims to drive the system toward the optimal steady-state.
We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using integral quadratic constraints (IQCs), the proposed framework is able to translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed loop system. We illustrate the versatility of our framework using several examples.},
  author = {Nelson, Zachary and Mallada, Enrique},
  booktitle = {American Control Conference (ACC)},
  doi = {10.23919/ACC.2018.8431231},
  grants = {1544771, W911NF-17-1-0092, 1711188},
  issn = {2378-5861},
  keywords = {Optimization, IQCs},
  month = {06},
  title = {An integral quadratic constraint framework for steady state optimization of linear time invariant systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-ACC-NM.pdf},
  year = {2018}
}