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Enrique Mallada

Assistant Professor Electrical & Computer Engineering (he/him/his)

Barton Hall 312 3400 N Charles St  Baltimore MD 21218
phone: 410-516-7018 fax: 410-516-5566 mallada [at] jhu [dot] edu

I am an assistant professor in Electrical and Computer Engineering (ECE) at Johns Hopkins University (JHU) since Jan 2016. I earned my Ph.D. in ECE with a minor in Applied Mathematics from Cornell University in Jan 2014. Before joining JHU, I was a postdoctoral scholar at the Center for the Mathematics of Information (CMI) in the Computational and Mathematical Sciences (CMS) department at Caltech from 2013 to 2015.


Research Interests

  • Networked Systems: coupled oscillators, clock synchronization, saddle-flows, network coherence, distributed coordination, consensus
  • Power Systems: frequency control, inverter-based control, real-time congestion management, electricity markets, reduced-order models
  • Optimization: time-varying optimization, primal-dual algorithms, semidefinite programming, sum-of-squares optimization
  • Machine Learning: reinforcement learning, sparse recovery, subspace preserving recovery, network tomography, multi-armed bandits

Preprints

  1. C. Avraam and E. Mallada, Voltage Collapse Stabilization in Star DC Networks, 2021, submitted.
    [BibTeX] [Abstract] [Download PDF]

    Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

    @unpublished{am2021a-preprint,
      abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE
    24-bus reliability test system.},
      author = {Avraam, Charalampos and Mallada, Enrique},
      author+an = {2=first},
      month = {4},
      pages = {1-12},
      title = {Voltage Collapse Stabilization in Star DC Networks},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-AM.pdf},
      year = {2021, submitted}
    }

  2. R. K. Bansal, P. You, D. F. Gayme, and E. Mallada, A Market Mechanism for Truthful Bidding with Energy Storage, 2021, submitted.
    [BibTeX] [Abstract] [Download PDF]

    This paper proposes a market mechanism for multiinterval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energycycling functions that map prices to cycle depths. The resulting market-clearing process–implemented via convex programming–yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumerbased approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful cost, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.

    @unpublished{bygm2021a-preprint,
      abstract = {This paper proposes a market mechanism for multiinterval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energycycling functions that map prices to cycle depths. The resulting market-clearing process--implemented via convex programming--yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumerbased approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful cost, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.},
      author = {Bansal, Rajni Kant and You, Pengcheng and Gayme, Dennice F. and Mallada, Enrique},
      grants = {CAREER-1752362, TRIPODS-1934979, CPS-2136324},
      month = {10},
      pages = {1-9},
      record = {submitted Oct. 2021},
      title = {A Market Mechanism for Truthful Bidding with Energy Storage},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-BYGM.pdf},
      year = {2021, submitted}
    }

  3. A. Castellano, H. Min, J. Bazerque, and E. Mallada, Learning to Act Safely with Limited Exposure and Almost Sure Certainty, 2021, submitted.
    [BibTeX] [Abstract] [Download PDF]

    This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to navigate trade-offs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We illustrate this concept in two complementary settings. We first focus on the canonical multi-armed bandit problem and seek to study the intrinsic trade-offs of learning safety in the presence of uncertainty. Under mild assumptions on sufficient exploration, we provide an algorithm that provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines. We then consider the problem of finding optimal policies for a Markov Decision Process (MDP) with almost sure constraints. We show that the (action) value function satisfies a barrier-based decomposition which allows for the identification of feasible policies independently of the reward process. Using this decomposition, we develop a Barrier-learning algorithm, that identifies such unsafe state-action pairs in a finite expected number of steps. Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events. Simulations corroborate our theoretical findings, further illustrating the aforementioned trade-offs, and suggesting that safety constraints can further speed up the learning process.

    @unpublished{cmbm2021a-preprint,
      abstract = {This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to navigate trade-offs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We illustrate this concept in two complementary settings. We first focus on the canonical multi-armed bandit problem and seek to study the intrinsic trade-offs of learning safety in the presence of uncertainty.  Under mild assumptions on sufficient exploration, we provide an algorithm that provably detects all unsafe machines in an (expected) finite number of rounds. The analysis also unveils a trade-off between the number of rounds needed to secure the environment and the probability of discarding safe machines.  We then consider the problem of finding optimal policies for a Markov Decision Process (MDP) with almost sure constraints. 
    We show that the (action) value function satisfies a barrier-based decomposition which allows for the identification of feasible policies independently of the reward process. Using this decomposition, we develop a Barrier-learning algorithm, that identifies such unsafe state-action pairs in a finite expected number of steps. Our analysis further highlights a trade-off between the time lag for the underlying MDP necessary to detect unsafe actions, and the level of exposure to unsafe events. Simulations corroborate our theoretical findings, further illustrating the aforementioned trade-offs, and suggesting that safety constraints can further speed up the learning process.},
      author = {Castellano, Agustin and Min, Hancheng and Bazerque, Juan and Mallada, Enrique},
      month = {5},
      pages = {1-16},
      title = {Learning to Act Safely with Limited Exposure and Almost Sure Certainty},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-CMBM.pdf},
      year = {2021, submitted}
    }

  4. J. Guthrie, M. Kobilarov, and E. Mallada, Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance, 2021, submitted.
    [BibTeX] [Abstract] [Download PDF]

    Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming solvers in the canonical setting of a circular robot navigating around $M$ convex polytopes over $N$ time steps. However, it requires introducing $(2+L)MN$ additional constraints and $LMN$ additional variables, with $L$ being the number of halfplanes per polytope, leading to larger nonlinear programs with slower and less reliable solving time. In this paper, we overcome this issue by building closed-form representations of the collision avoidance conditions by outer-approximating the Minkowski sum conditions for collision. Our solution requires only $MN$ constraints (and no additional variables), leading to a smaller nonlinear program. On motion planning problems for an autonomous car and quadcopter in cluttered environments, we achieve speedups of 4.0x and 10x respectively with significantly less variance in solve times and negligible impact on performance arising from the use of outer approximations.

    @unpublished{gkm2022a-preprint,
      abstract = {Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming solvers in the canonical setting of a circular robot navigating around $M$ convex polytopes over $N$ time steps. However, it requires introducing $(2+L)MN$ additional constraints and $LMN$ additional variables, with $L$ being the number of halfplanes per polytope, leading to larger nonlinear programs with slower and less reliable solving time. In this paper, we overcome this issue by building closed-form representations of the collision avoidance conditions by outer-approximating the Minkowski sum conditions for collision. Our solution requires only $MN$ constraints (and no additional variables), leading to a smaller nonlinear program. On motion planning problems for an autonomous car and quadcopter in cluttered environments, we achieve speedups of 4.0x and 10x respectively with significantly less variance in solve times and negligible impact on performance arising from the use of outer approximations.},
      author = {Guthrie, James and Kobilarov, Marin and Mallada, Enrique},
      month = {10},
      pages = {1-7},
      title = {Closed-Form Minkowski Sum Approximations for Efficient Optimization-Based Collision Avoidance},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-GKM.pdf},
      year = {2021, submitted}
    }

  5. H. Min and E. Mallada, Coherence and Concentration in Tightly-Connected Networks, 2021, submitted.
    [BibTeX] [Abstract] [Download PDF]

    Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE 24-bus reliability test system.

    @unpublished{mm2021a-preprint,
      abstract = {Economic dispatch and frequency regulation are typically viewed as fundamentally different problems in power systems and, hence, are typically studied separately. In this paper, we frame and study a joint problem that co-optimizes both slow timescale economic dispatch resources and fast timescale frequency regulation resources. We show how the joint problem can be decomposed without loss of optimality into slow and fast timescale sub-problems that have appealing interpretations as the economic dispatch and frequency regulation problems respectively. We solve the fast timescale sub-problem using a distributed frequency control algorithm that preserves the stability of the network during transients. We solve the slow timescale sub-problem using an efficient market mechanism that coordinates with the fast timescale sub-problem. We investigate the performance of the decomposition on the IEEE
    24-bus reliability test system.},
      author = {Min, Hancheng and Mallada, Enrique},
      grants = {CAREER-1752362;EPCN-1711188;AMPS-1736448;TRIPODS-1934979},
      month = {1},
      pages = {1-16},
      title = {Coherence and Concentration in Tightly-Connected Networks},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-MM.pdf},
      year = {2021, submitted}
    }

  6. G. H. Oral, E. Mallada, and D. Gayme, On the Role of Interconnection Directionality in the Quadratic Performance of Double-Integrator Networks, 2021, under review.
    [BibTeX] [Abstract] [Download PDF]

    This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of position and velocity based response functions given impulsive inputs to each vehicle. We exploit the spectral properties of weighted graph Laplacians and output performance matrices to derive a novel method of computing the closed-form solutions for this general class of performance metrics, which include H2-norm based quantities as special cases. We then explore the effect of the interplay between network properties (such as edge directionality and connectivity) and the control strategy on the overall network performance. More precisely, for systems whose interconnection is described by graphs with normal Laplacian L, we characterize the role of directionality by comparing their performance with that of their undirected counterparts, represented by the Hermitian part of L. We show that, for single-integrator networks, directed and undirected graphs perform identically. However, for double-integrator networks, graph directionality -expressed by the eigenvalues of L with nonzero imaginary part- can significantly degrade performance. Interestingly, in many cases, well-designed feedback can also exploit directionality to mitigate degradation or even improve the performance to exceed that of the undirected case. Finally we focus on a system coherence metric -aggregate deviation from the state average- to investigate the relationship between performance and degree of connectivity, leading to somewhat surprising findings. For example, increasing the number of neighbors on a ω-nearest neighbor directed graph does not necessarily improve performance. Similarly, we demonstrate equivalence in performance between all-to-one and all-to-all communication graphs.

    @unpublished{omg2021a-preprint,
      abstract = {This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of position and velocity based response functions given impulsive inputs to each vehicle. We exploit the spectral properties of weighted graph Laplacians and output performance matrices to derive a novel method of computing the closed-form solutions for this general class of performance metrics, which include H2-norm based quantities as special cases. We then explore the effect of the interplay between network properties (such as edge directionality and connectivity) and the control strategy on the overall network performance. More precisely, for systems whose interconnection is described by graphs with normal Laplacian L, we characterize the role of directionality by comparing their performance with that of their undirected counterparts, represented by the Hermitian part of L. We show that, for single-integrator networks, directed and undirected graphs perform identically. However, for double-integrator networks, graph directionality -expressed by the eigenvalues of L with nonzero imaginary part- can significantly degrade performance. Interestingly, in many cases, well-designed feedback can also exploit directionality to mitigate degradation or even improve the performance to exceed that of the undirected case. Finally we focus on a system coherence metric -aggregate deviation from the state average- to investigate the relationship between performance and degree of connectivity, leading to somewhat surprising findings. For example, increasing the number of neighbors on a ω-nearest neighbor directed graph does not necessarily improve performance. Similarly, we demonstrate equivalence in performance between all-to-one and all-to-all communication graphs.},
      author = {Oral, H. Giray and Mallada, Enrique and Gayme, Dennice},
      grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092},
      month = {4},
      pages = {1-8},
      record = {revised Nov. 2020, submitted Nov. 2019},
      title = {On the Role of Interconnection Directionality in the Quadratic Performance of Double-Integrator Networks},
      url = {https://mallada.ece.jhu.edu/pubs/2019-Preprint-OMG.pdf},
      year = {2021, under review}
    }

  7. R. Pates, A. Ferragut, E. Pivo, P. You, F. Paganini, and E. Mallada, Respect the Unstable: Delays and Saturation in Contact Tracing for Disease Control, 2020, submitted.
    [BibTeX] [Abstract] [Download PDF]

    Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein’s cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints in the TeTrIs process have on preventing exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, having a delay in the TeTrIs process smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.

    @unpublished{pfpypm2021a-preprint,
      abstract = {Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein's cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints in the TeTrIs process have on preventing exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, having a delay in the TeTrIs process  smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.},
      author = {Pates, Richard and Ferragut, Andres and Pivo, Elijah and You, Pengcheng and Paganini, Fernando and Mallada, Enrique},
      grants = {CAREER-1752362, EPCN-1711188, AMPS-1736448, TRIPODS-1934979},
      month = {11},
      pages = {1-25},
      title = {Respect the Unstable: Delays and Saturation in Contact Tracing for Disease Control},
      url = {https://mallada.ece.jhu.edu/pubs/2021-Preprint-PFPYPM.pdf},
      year = {2020, submitted}
    }

Recent Publications

  1. Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 6, pp. 1988-1993, 2021. doi:10.1109/LCSYS.2020.3044551
    [BibTeX] [Abstract] [Download PDF]

    We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.

    @article{jbvm2021lcss,
      abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.},
      author = {Jiang, Yan and Bernstein, Andrey and Vorobev, Petr and Mallada, Enrique},
      doi = {10.1109/LCSYS.2020.3044551},
      grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188},
      journal = {IEEE Control Systems Letters (L-CSS)},
      month = {12},
      note = {also in ACC 2021},
      number = {6},
      pages = {1988-1993},
      record = {early access Dec 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020},
      title = {Grid-forming frequency shaping control in low inertia power systems},
      url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-JBVM.pdf},
      volume = {5},
      year = {2021}
    }

  2. H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” IEEE Control Systems Letters (L-CSS), vol. 5, iss. 5, pp. 1741-1746, 2021. doi:10.1109/LCSYS.2020.3043733
    [BibTeX] [Abstract] [Download PDF]

    We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models –based on frequency weighted balanced truncation– that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.

    @article{mpm2021lcss,
      abstract = {We introduce a novel framework to approximate the aggregate frequency dynamics of coherent synchronous generators. By leveraging recent results on dynamics concentration of tightly connected networks, we develop a hierarchy of reduced order models --based on frequency weighted balanced truncation-- that accurately approximate the aggregate system response. Our results outperform existing aggregation techniques and can be shown to monotonically improve the approximation as the hierarchy order increases.},
      author = {Min, Hancheng and Paganini, Fernando and Mallada, Enrique},
      doi = {10.1109/LCSYS.2020.3043733},
      grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
      journal = {IEEE Control Systems Letters (L-CSS)},
      month = {11},
      note = {also in ACC 2021},
      number = {5},
      pages = {1741-1746},
      record = {early accesss Nov 2020, accepted Nov 2020, revised Nov 2020, submitted Sep 2020},
      title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators},
      url = {https://mallada.ece.jhu.edu/pubs/2021-LCSS-MPM.pdf},
      volume = {5},
      year = {2021}
    }

  3. Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, pp. 1-13, 2021. doi:10.1109/TPWRS.2021.3072833
    [BibTeX] [Abstract] [Download PDF]

    With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage — frequency shaping control — that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.

    @article{jcvm2021tps,
      abstract = {With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of frequency response following major contingencies. In this manuscript, we propose a new strategy for energy storage -- frequency shaping control -- that allows to completely eliminate the frequency Nadir, one of the main issue in frequency security, and at the same time tune the rate of change of frequency (RoCoF) to a desired value. With Nadir eliminated, the frequency security assessment can be performed via simple algebraic calculations, as opposed to dynamic simulations for conventional control strategies. Moreover, our proposed control is also very efficient in terms of the requirements on storage peak power, requiring up to 40% less power than conventional virtual inertia approach for the same performance.},
      author = {Jiang, Yan and Cohn, Eliza and Vorobev, Petr and Mallada, Enrique},
      doi = {10.1109/TPWRS.2021.3072833},
      journal = {IEEE Transactions on Power Systems},
      month = {4},
      pages = {1-13},
      pubstate = {early access},
      record = {accepted Mar 2021, revised Oct 2020, submitted May 2020},
      title = {Storage-Based Frequency Shaping Control},
      url = {https://mallada.ece.jhu.edu/pubs/2021-TPS-JCVM.pdf},
      year = {2021}
    }

  4. Y. Jiang, R. Pates, and E. Mallada, “Dynamic Droop Control in Low Inertia Power Systems,” IEEE Transactions on Automatic Control, vol. 66, iss. 8, pp. 3518-3533, 2021. doi:10.1109/TAC.2020.3034198
    [BibTeX] [Abstract] [Download PDF]

    A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid’s stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies –droop control (DC) and virtual inertia (VI)– on several performance metrics induced by L2 and L∞ signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c Droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumptions are not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

    @article{jpm2021tac,
      abstract = {A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore
    the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverterbased frequency control. With this aim, we perform a qualitative
    and quantitative study comparing the effect of conventional
    control strategies --droop control (DC) and virtual inertia (VI)--
    on several performance metrics induced by L2 and L∞ signal
    norms. By extending a recently proposed modal decomposition
    method, we capture the effect of step and stochastic power
    disturbances, and frequency measurement noise, on the overall
    transient and steady-state behavior of the system. Our analysis
    unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without
    increasing steady-state control effort, or the large frequency
    variance that VI introduces in the presence of measurement
    noise. We further propose a novel dynam-i-c Droop controller
    (iDroop) that overcomes the limitations of DC and VI. More
    precisely, we show that iDroop can be tuned to achieve high
    noise rejection, fast system-wide synchronization, or frequency
    overshoot (Nadir) elimination without affecting the steady-state
    control effort share, and propose a tuning recommendation that
    strikes a balance among these objectives. Extensive numerical
    experimentation shows that the proposed tuning is effective even
    when our proportionality assumptions are not valid, and that
    the particular tuning used for Nadir elimination strikes a good
    trade-off among various performance metrics.},
      author = {Jiang, Yan and Pates, Richard and Mallada, Enrique},
      doi = {10.1109/TAC.2020.3034198},
      grants = {ENERGISE-DE-EE0008006, EPCN-1711188,AMPS-1736448, CPS-1544771, CAREER-1752362, AMPS-1736448, ARO-W911NF-17-1-0092},
      journal = {IEEE Transactions on Automatic Control},
      month = {8},
      number = {8},
      pages = {3518-3533},
      record = {available online Nov. 2020, accepted Aug. 2020, revised Mar. 2020, submitted Aug. 2019},
      title = {Dynamic Droop Control in Low Inertia Power Systems},
      url = {https://mallada.ece.jhu.edu/pubs/2021-TAC-JPM.pdf},
      volume = {66},
      year = {2021}
    }

  5. M. D. Kaba, M. Zhao, R. Vidal, D. R. Robinson, and E. Mallada, “What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?,” IEEE Transactions on Information Theory, vol. 67, iss. 5, pp. 3060-3074, 2021. doi:10.1109/TIT.2021.3067280
    [BibTeX] [Abstract] [Download PDF]

    We propose a new framework for studying the recovery of signals with structured sparsity patterns via $l_1$-minimization. We achieve this by generalizing the well-known nullspace property for sparse recovery. We show that for each dictionary there is a maximum sparsity pattern—described by a mathematical object called an abstract simplicial complex—that can be recovered via $l_1$-minimization. We provide two different characterizations of this maximum sparsity pattern. In addition, we show how this new framework is useful in the study of sparse recovery problems when the dictionary takes the form of a graph incidence matrix or a partial Discrete Fourier Transform. In both cases we successfully characterize the collection of all support sets for which exact recovery via $l_1$-minimization is possible. When the dictionary is an incidence matrix, we show that the success of exact recovery can be certified in polynomial time, although this is known to be NP-hard for general matrices.

    @article{kzvrm2021tit,
      abstract = {We propose a new framework for studying the recovery of signals with structured sparsity patterns via $l_1$-minimization. We achieve this by generalizing the well-known nullspace property for sparse recovery. We show that for each dictionary there is a maximum sparsity pattern---described by a mathematical object called an abstract simplicial complex---that can be recovered via $l_1$-minimization.  We provide two different characterizations of this maximum sparsity pattern. In addition, we show how this new framework is useful in the study of sparse recovery problems when the dictionary takes the form of a graph incidence matrix or a partial Discrete Fourier Transform. In both cases we successfully characterize the collection of all support sets for which exact recovery via $l_1$-minimization is possible. When the dictionary is an incidence matrix, we show that the success of exact recovery can be certified in polynomial time, although this is known to be NP-hard for general matrices.},
      author = {Kaba, Mustafa Devrim and Zhao, Mengnan and Vidal, Rene and Robinson, Daniel R. and Mallada, Enrique},
      doi = {10.1109/TIT.2021.3067280},
      grants = {AMPS:1736448;CAREER-1752362},
      journal = {IEEE Transactions on Information Theory},
      month = {5},
      number = {5},
      pages = {3060-3074},
      record = {early access Mar. 2021, accepted Jan. 2021, revised Apr. 2020, submitted Oct. 2019},
      title = {What is the Largest Sparsity Pattern that Can Be Recovered by 1-Norm Minimization?},
      url = {https://mallada.ece.jhu.edu/pubs/2021-TIT-KZVRM.pdf},
      volume = {67},
      year = {2021}
    }

  6. M. Almassalkhi, S. Brahma, N. Nazir, H. Ossareh, P. Racherla, S. Kundu, S. P. Nandanoori, T. Ramachandran, A. Singhal, D. Gayme, C. Ji, E. Mallada, Y. Shen, P. You, and D. Anand, “Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems,” Energies, vol. 13, iss. 23, pp. 1-35, 2020. doi:10.3390/en13236399
    [BibTeX] [Abstract] [Download PDF]

    Forward-looking renewable portfolio standards will lead to extreme levels of variable solar PV in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliablymanage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimize the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

    @article{abetal2020energies,
      abstract = {Forward-looking renewable portfolio standards will lead to extreme levels of variable solar PV in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliablymanage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimize the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.},
      author = {Almassalkhi, Mads and Brahma, Sarnaduti and Nazir, Nawaf and Ossareh, Hamid and Racherla, Pavan and Kundu, Soumya and Nandanoori, Sai P. and Ramachandran, Thiagarajan and Singhal, Ankit and Gayme, Dennice and Ji, Chengda and Mallada, Enrique and Shen, Yue and You, Pengcheng and Anand, Dhananjay},
      doi = {10.3390/en13236399},
      grants = {CAREER-1752362,EPCN-1711188,AMPS-1736448,TRIPODS-1934979},
      journal = {Energies},
      month = {12},
      number = {23},
      pages = {1-35},
      title = {Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems},
      url = {https://mallada.ece.jhu.edu/pubs/2020-ENERGIES-ABetal.pdf},
      volume = {13},
      year = {2020}
    }

  7. L. S. P. Lawrence, J. W. Simpson-Porco, and E. Mallada, “Linear-Convex Optimal Steady-State Control,” IEEE Transactions on Automatic Control, pp. 1-8, 2020. doi:10.1109/TAC.2020.3044275
    [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.

    @article{lsm2020tac,
      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},
      doi = {10.1109/TAC.2020.3044275},
      journal = {IEEE Transactions on Automatic Control},
      month = {12},
      pages = {1-8},
      pubstate = {early access},
      record = {accepted Nov 2020, conditionally accepted Aug. 2020, 2nd revision May 2020, revised Sept 2019, submitted Oct. 2018},
      title = {Linear-Convex Optimal Steady-State Control},
      url = {https://mallada.ece.jhu.edu/pubs/2020-TAC-LSM.pdf},
      year = {2020}
    }

  8. A. Bahram, M. H. Hajiesmaili, Z. Lee, N. Crespi, and E. Mallada, “Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints,” IEEE Transactions on Sustainable Computing, 2020. doi:10.1109/TSUSC.2020.2979854
    [BibTeX] [Abstract] [Download PDF]

    Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.

    @article{bhlcm2019tsusc,
      abstract = {Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This paper focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.},
      author = {Bahram, Alina and Hajiesmaili, Mohammad H. and Lee, Zachary and Crespi, Noel and Mallada, Enrique},
      doi = {10.1109/TSUSC.2020.2979854},
      grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979,EPCN-1711188,},
      journal = {IEEE Transactions on Sustainable Computing},
      month = {1},
      title = {Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints},
      url = {https://mallada.ece.jhu.edu/pubs/2020-TSUSC-BHLCM.pdf},
      year = {2020}
    }


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