1 paper accepted to TAC


Our paper [1] on a leaky integrator approach for robust decentralized secondary frequency control has been accepted to IEEE Transactions on Automatic Control!

[1] [doi] E. Weitenberg, Y. Jiang, C. Zhao, E. Mallada, C. De Persis, and F. Dorfler, “Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs,” IEEE Transactions on Automatic Control, vol. 64, iss. 10, pp. 3967-3982, 2019.
[Bibtex] [Abstract] [Download PDF]
Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.
@article{wjzmdd2019tac,
  abstract = {Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers.
In this paper we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.},
  author = {Weitenberg, Erik and Jiang, Yan and Zhao, Changhong and Mallada, Enrique and De Persis, Claudio and Dorfler, Florian},
  doi = {10.1109/TAC.2018.2884650},
  grants = {CPS-1544771, EPCN-1711188, AMPS-1736448, CAREER-1752362, ENERGISE-DE-EE0008006},
  issn = {0018-9286},
  journal = {IEEE Transactions on Automatic Control},
  keywords = {Power Networks},
  month = {10},
  number = {10},
  pages = {3967-3982},
  title = {Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs},
  url = {https://mallada.ece.jhu.edu/pubs/2019-TAC-WJZMDD.pdf},
  volume = {64},
  year = {2019}
}

Control Seminar @ University of Michigan

I gave a talk on “Inverter-based Control for Low Inertia Power Systems” in the Control Seminar at the University of Michigan. Related publications include [1, 2, 3].

[1] [doi] F. Paganini and E. Mallada, “Global analysis of synchronization performance for power systems: bridging the theory-practice gap,” IEEE Transactions on Automatic Control, vol. 67, iss. 7, pp. 3007-3022, 2020.
[Bibtex] [Abstract] [Download PDF]

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.

@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}
}
[2] [doi] R. Pates and E. Mallada, “Robust Scale Free Synthesis for Frequency Regulation in Power Systems,” IEEE Transactions on Control of Network Systems, vol. 6, iss. 3, pp. 1174-1184, 2019.
[Bibtex] [Abstract] [Download PDF]

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.

@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}
}
[3] [doi] Y. Jiang, R. Pates, and E. Mallada, “Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 5098-5105.
[Bibtex] [Abstract] [Download PDF]

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.

@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}
}

Invited Session @ INFORMS Annual Meeting


I co-organized with John Simpson-Porco an invited session on Real-time Optimization of Power Systems at INFORMS Annual Meeting. This session is motivated by our recent work on the topic [1, 2, 3]

[1] [doi] Z. Nelson and E. Mallada, “An integral quadratic constraint framework for steady state optimization of linear time invariant systems,” in American Control Conference, 2018.
[Bibtex] [Abstract] [Download PDF]
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.
@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},
  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}
}
[2] [doi] L. S. P. Lawrence, Z. Nelson, E. Mallada, and J. W. Simpson-Porco, “Optimal Steady-State Control for Linear Time-Invariant Systems,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 3251-3257.
[Bibtex] [Abstract] [Download PDF]
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.
@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},
  pubstate = {presented, submitted Mar. 2018.},
  title = {Optimal Steady-State Control for Linear Time-Invariant Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-LNMS.pdf},
  year = {2018}
}
[3] L. S. P. Lawrence, J. W. Simpson-Porco, and E. Mallada, Linear-Convex Optimal Steady-State Control, 2020, under review.
[Bibtex] [Abstract] [Download PDF]
We consider the problem of designing a feedback controller for a multivariable nonlinear system that regulates an arbitrary subset of the system states and inputs to the solution of a constrained optimization problem, despite parametric modelling uncertainty and time-varying exogenous disturbances; we term this the optimal steady-state (OSS) control problem. We derive necessary and sufficient conditions for the existence of an OSS controller by formulating the OSS control problem as an output regulation problem wherein the regulation error is unmeasurable. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to an output regulation problem with measurable error. This yields a design framework for OSS control that unifies and extends many existing designs in the literature. We present a complete and constructive solution of the OSS control problem for the case where the plant is linear time-invariant with structured parametric uncertainty, and disturbances are constant in time. We illustrate these results via an application to optimal frequency control of power networks, and show that our design procedure recovers several frequency controllers from the recent literature.
@unpublished{lsm2019a-preprint,
  abstract = {We consider the problem of designing a feedback controller for a multivariable nonlinear system that regulates an arbitrary subset of the system states and inputs to the solution of a constrained optimization problem, despite parametric modelling uncertainty and time-varying exogenous disturbances; we term this the optimal steady-state (OSS) control problem. We derive necessary and sufficient conditions for the existence of an OSS controller by formulating the OSS control problem as an output regulation problem wherein the regulation error is unmeasurable. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to an output regulation  problem with measurable error. This yields a design framework for OSS control that unifies and extends many existing designs in the literature. We present a complete and constructive solution of the OSS control problem for the case where the plant is linear time-invariant with structured parametric uncertainty, and disturbances are constant in time. We illustrate these results via an application to optimal frequency control of power networks, and show that our design procedure recovers several frequency controllers from the recent literature.},
  author = {Lawrence, Liam S. P. and Simpson-Porco, John W. and Mallada, Enrique},
  month = {8},
  pages = {1-8},
  title = {Linear-Convex Optimal Steady-State Control},
  url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-LSM.pdf},
  year = {2020, under review}
}

1 abstract accepted to FERC’s TAIC


An abstract on our work on Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets [1] was accepted to the FERC Trans-Atlantic INFRADAY Conference.

[1] C. Ji, M. H. Hajiesmaili, D. F. Gayme, and E. Mallada, Coordinating Distribution System Resources for Co-optimized Participation in Energy and Ancillary Service Transmission System Markets, 2018.
[Bibtex] [Download PDF]
@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}
}

ECE Seminar @ University of Waterloo


I gave a talk on “Inverter-based Control for Low Inertia Power Systems” in the ECE Seminar at the University of Waterloo. Related publications include [1, 2, 3].

[1] [doi] F. Paganini and E. Mallada, “Global analysis of synchronization performance for power systems: bridging the theory-practice gap,” IEEE Transactions on Automatic Control, vol. 67, iss. 7, pp. 3007-3022, 2020.
[Bibtex] [Abstract] [Download PDF]
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.
@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}
}
[2] [doi] R. Pates and E. Mallada, “Robust Scale Free Synthesis for Frequency Regulation in Power Systems,” IEEE Transactions on Control of Network Systems, vol. 6, iss. 3, pp. 1174-1184, 2019.
[Bibtex] [Abstract] [Download PDF]
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.
@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}
}
[3] [doi] Y. Jiang, R. Pates, and E. Mallada, “Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems,” in 56th IEEE Conference on Decision and Control (CDC), 2017, pp. 5098-5105.
[Bibtex] [Abstract] [Download PDF]
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.
@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}
}

3 papers accepted to CDC 18

Our papers on sparse recovery on graph incidence matrices [1], optimal steady-state control [2], and robustness of consensus algorithms under measurement errors [3] have been accepted to IEEE Conference on Decision and Control. See you in Miami!

[1] [doi] M. Zhao, M. D. Kaba, R. Vidal, D. R. Robinson, and E. Mallada, “Sparse Recovery over Graph Incidence Matrices,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 364-371.
[Bibtex] [Abstract] [Download PDF]

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.

@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}
}
[2] [doi] L. S. P. Lawrence, Z. Nelson, E. Mallada, and J. W. Simpson-Porco, “Optimal Steady-State Control for Linear Time-Invariant Systems,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 3251-3257.
[Bibtex] [Abstract] [Download PDF]

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.

@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},
  pubstate = {presented, submitted Mar. 2018.},
  title = {Optimal Steady-State Control for Linear Time-Invariant Systems},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-LNMS.pdf},
  year = {2018}
}
[3] [doi] C. Ji, E. Mallada, and D. Gayme, “Evaluating Robustness of Consensus Algorithms Under Measurement Error over Digraph,” in 57th IEEE Conference on Decision and Control (CDC), 2018, pp. 1238-1244.
[Bibtex] [Abstract] [Download PDF]

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).

@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},
  pubstate = {presented, submitted Mar. 2018.},
  title = {Evaluating Robustness of Consensus Algorithms Under Measurement Error over Digraph},
  url = {https://mallada.ece.jhu.edu/pubs/2018-CDC-JMG.pdf},
  year = {2018}
}

1 paper accepted to MTNS

Our paper exploring robustness tradeoffs of the swing equations [1] has been accepted to the 23rd International Symposium on Mathematical Theory of Networks and Systems.

[1] R. Pates and E. Mallada, “Damping, Inertia, and Delay Robustness Trade-offs in Power Systems,” in 23rd International Symposium on Mathematical Theory of Networks and Systems, 2018.
[Bibtex] [Abstract] [Download PDF]

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.

@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:},
  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}
}

Jesse and Aurik received Honorable Mention

Jesse Rines and Aurik Sarker, co-authors of the paper [1], received an honorable mention of the The Muly Family Undergraduate Research Award. Congrats!

[1] [doi] C. Avraam, J. Rines, A. Sarker, F. Paganini, and E. Mallada, “Voltage Collapse Stabilization in Star DC Networks,” in American Control Conference, 2019, pp. 1957-1964.
[Bibtex] [Abstract] [Download PDF]
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.
@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, C. and Rines, J. and Sarker, A. and Paganini, F. and Mallada, E.},
  booktitle = {American Control Conference},
  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},
  pubstate = {presented, submitted Sep. 2018},
  title = {Voltage Collapse Stabilization in Star DC Networks},
  url = {https://mallada.ece.jhu.edu/pubs/2019-ACC-ARSPM.pdf},
  year = {2019}
}