ECE Seminar @ University of Iowa

I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Dynamic Droop Approach” at ECE Seminar, University of Iowa (Host: Weiyu Xu). 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] Unknown bibtex entry with key [jpm2020tac]
[Bibtex]
[3] [doi] Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, pp. 1-13, 2021.
[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}
}

6 papers accepted to ACC 21

6 papers [1, 2, 3, 4, 5, 6] have been accepted to American Control Conference(ACC) 2021!

[1] [doi] J. Guthrie and E. Mallada, “Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization,” in American Control Conference, 2021, pp. 1-7.
[Bibtex] [Abstract] [Download PDF]

We study the problem of finding closed-form outerapproximations of Minkowski sums and products of sets inthe complex plane. Using polar coordinates, we pose this asan optimization problem in which we find a pair of contoursthat give lower and upper bounds on the radial distance ata given angle. Through a series of variable transformationswe rewrite this as a sum-of-squares optimization problem.Numerical examples are given to demonstrate the performance.

@inproceedings{gm2021acc,
  abstract = {We study the problem of finding closed-form outerapproximations  of  Minkowski  sums  and  products  of  sets  inthe  complex  plane.  Using  polar  coordinates,  we  pose  this  asan  optimization  problem  in  which  we  find  a  pair  of  contoursthat  give  lower  and  upper  bounds  on  the  radial  distance  ata  given  angle.  Through  a  series  of  variable  transformationswe  rewrite  this  as  a  sum-of-squares  optimization  problem.Numerical examples are given to demonstrate the performance.},
  author = {Guthrie, James and Mallada, Enrique},
  booktitle = {American Control Conference},
  doi = {10.23919/ACC50511.2021.9482940},
  grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
  month = {5},
  pages = {1-7},
  record = {submitted Sep. 2020, accepted Jan. 2021},
  title = {Outer Approximations of Minkowski Operations on Complex Sets via Sum-of-Squares Optimization},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-GM.pdf},
  year = {2021}
}
[2] P. You and E. Mallada, “Saddle Flow Dynamics: Observable Certificates and Separable Regularization,” in American Control Conference, 2021, pp. 1-7.
[Bibtex] [Abstract] [Download PDF]

This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexityconcavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.

@inproceedings{ym2021acc,
  abstract = {This paper proposes a certificate, rooted in observability,
for asymptotic convergence of saddle flow dynamics
of convex-concave functions to a saddle point. This observable
certificate directly bridges the gap between the invariant set
and the equilibrium set in a LaSalle argument, and generalizes
conventional conditions such as strict convexity-concavity and
proximal regularization. We further build upon this certificate
to propose a separable regularization method for saddle flow
dynamics that makes minimal requirements on convexityconcavity
and yet still guarantees asymptotic convergence to
a saddle point. Our results generalize to saddle flow dynamics
with projections on the vector field and have an immediate
application as a distributed solution to linear programs.},
  author = {You, Pengcheng and Mallada, Enrique},
  booktitle = {American Control Conference},
  grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
  month = {1},
  pages = {1-7},
  pubstate = {accepted},
  record = {submitted Sep. 2020},
  title = {Saddle Flow Dynamics: Observable Certificates and Separable Regularization},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-YM.pdf},
  year = {2021}
}
[3] H. Min, F. Paganini, and E. Mallada, “Accurate Reduced Order Models for Coherent Heterogeneous Generators,” in American Control Conference, 2021, pp. 1-6.
[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.

@inproceedings{mpm2021acc,
  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},
  booktitle = {American Control Conference},
  grants = {CAREER-1752362, CPS-1544771, ENERGISE-DE-EE0008006, AMPS-1736448, TRIPODS-1934979, EPCN-1711188, ARO-W911NF-17-1-0092},
  month = {1},
  pages = {1-6},
  pubstate = {accepted},
  record = {submitted Sep. 2020},
  title = {Accurate Reduced Order Models for Coherent Heterogeneous Generators},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-MPM.pdf},
  year = {2021}
}
[4] Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control in low inertia power systems,” in American Control Conference, 2021, pp. 1-6.
[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.

@inproceedings{jbvm2021acc,
  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},
  booktitle = {American Control Conference},
  grants = {CAREER-1752362, AMPS-1736448, TRIPODS-1934979, EPCN-1711188},
  month = {1},
  pages = {1-6},
  pubstate = {accepted},
  record = {submitted Sep. 2020},
  title = {Grid-forming frequency shaping control in low inertia power systems},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-JBVM.pdf},
  year = {2021}
}
[5] A. Castellano, J. Bazerque, and E. Mallada, “Learning to be safe, in finite time,” in American Control Conference, 2021, pp. 1-8.
[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 relax its optimality requirements mildly. We focus on the canonical multi-armed bandit problem and seek to study the exploration-preservation trade-off intrinsic within safe learning. More precisely, by defining a handicap metric that counts the number of unsafe actions, we provide an algorithm for discarding unsafe machines (or actions), with probability one, that achieves constant handicap. Our algorithm is rooted in the classical sequential probability ratio test, redefined here for continuing tasks. Under standard assumptions on sufficient exploration, our rule 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. Our decision rule can wrap around any other algorithm to optimize a specific auxiliary goal since it provides a safe environment to search for (approximately) optimal policies. Simulations corroborate our theoretical findings and further illustrate the aforementioned trade-offs.

@inproceedings{cbm2021acc,
  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 relax its optimality requirements mildly. We focus on the canonical multi-armed bandit problem and seek to study the exploration-preservation trade-off intrinsic within safe learning. More precisely, by defining a handicap metric that counts the number of unsafe actions, we provide an algorithm for discarding unsafe machines (or actions), with probability one, that achieves constant handicap.
Our algorithm is rooted in the classical sequential probability ratio test, redefined here for continuing tasks.  Under standard assumptions on sufficient exploration, our rule 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. Our decision rule can wrap around any other algorithm to optimize a specific auxiliary goal since it provides a safe environment to search for (approximately) optimal policies. Simulations corroborate our theoretical findings and further illustrate the aforementioned trade-offs.},
  author = {Castellano, Agustin and Bazerque, Juan and Mallada, Enrique},
  booktitle = {American Control Conference},
  grants = {CPS-1544771, CAREER-1752362, TRIPODS-1934979},
  month = {1},
  pages = {1-8},
  pubstate = {accepted},
  record = {submitted Sep. 2020},
  title = {Learning to be safe, in finite time},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-CBM.pdf},
  year = {2021}
}
[6] R. K. Bansal, P. You, D. F. Gayme, and E. Mallada, “Storage Degradation Aware Economic Dispatch,” in American Control Conference, 2021, pp. 1-6.
[Bibtex] [Abstract] [Download PDF]

In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual participants in the sense that it maximizes the profit of generators and storage units, under price taking assumptions. We further provide a condition under which the optimal storage response is unique for given market clearing prices. Simulations using data from the New York Independent System Operator (NYISO) illustrate the optimization framework. In particular, they show that the generation-centric dispatch that does not account for storage degradation is insufficient to guarantee storage profitability.

@inproceedings{bygm2021acc,
  abstract = {In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual participants in the sense that it maximizes the profit of generators and storage units, under price taking assumptions. We further provide a condition under which the optimal storage response is unique for given market clearing prices. Simulations using data from the New York Independent System Operator (NYISO) illustrate the optimization framework. In particular, they show that the generation-centric dispatch that does not account for storage degradation is insufficient to guarantee storage profitability. },
  author = {Bansal, Rajni Kant and You, Pengcheng and Gayme, Dennice F. and Mallada, Enrique},
  booktitle = {American Control Conference},
  grants = {CPS-1544771, EPCN-1711188, CAREER-1752362, TRIPODS-1934979},
  month = {1},
  pages = {1-6},
  pubstate = {accepted},
  record = {submitted Sep. 2020},
  title = {Storage Degradation Aware Economic Dispatch},
  url = {https://mallada.ece.jhu.edu/pubs/2021-ACC-BYGM.pdf},
  year = {2021}
}

1 paper accepted to TIT


Our paper on sparse recovery by 1-norm minimization [1] has been accepted to IEEE Transactions on Information Theory!

[1] [doi] 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.
[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}
}

1 paper accepted to ENERGIES


Our paper on optimal coordination of Distributed Energy Resources [1] has been accepted to Energies!

[1] [doi] 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.
[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}
}

1 paper accepted to TAC


Our paper on linear-convex optimal steady-state control [1] has been accepted to IEEE Transactions on Automatic Control!

[1] Unknown bibtex entry with key [lsm2021tac]
[Bibtex]

2 papers accepted to L-CSS

Our papers on grid-forming frequency shaping control [1] and on reduced order model for coherent generators [2] have been accepted to the IEEE Control Systems Letters (L-CSS)!

[1] [doi] 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.
[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] [doi] 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.
[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}
}

1 paper accepted to TAC

Our paper on Dynamic Droop Control in Low-inertia Power Systems [1] has been accepted to IEEE Transactions on Automatic Control!

[1] [doi] 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.
[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}
}

Seminar @ Oxford Univerisity

I gave a talk on “Embracing Low Inertia in Power System Frequency Control: A Dynamic Droop Approach” at Oxford Univerisity (Host: Antonis Papachristodoulou). 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] Unknown bibtex entry with key [jpm2020tac]
[Bibtex]
[3] [doi] Y. Jiang, E. Cohn, P. Vorobev, and E. Mallada, “Storage-Based Frequency Shaping Control,” IEEE Transactions on Power Systems, pp. 1-13, 2021.
[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}
}