Enrique Mallada

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

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

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

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

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

@article{cmlc2018tac,
  abstract = {This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit  set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.},
  author = {Cherukuri, Ashish and Mallada, Enrique and Steven H. Low and Jorge Cortes},
  doi = {10.1109/TAC.2017.2778689},
  grants = {W911NF-17-1-0092},
  journal = {IEEE Transactions on Automatic Control},
  keywords = {Saddle-Point Dynamics; Caratheodory solutions},
  month = {08},
  number = {8},
  pages = {2449-2464},
  title = {The role of convexity on saddle-point dynamics: Lyapunov function and robustness},
  url = {https://mallada.ece.jhu.edu/pubs/2018-TAC-CMLC.pdf},
  volume = {63},
  year = {2018}
}

@inproceedings{pm2017allerton,
  abstract = {A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations.

We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine's rating); we characterize Nadir and RoCoF by the Linf norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the L2 norm of the error of the vector of bus frequencies w.r.t. the system frequency.

For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.},
  author = {Paganini, Fernando and Mallada, Enrique},
  booktitle = {55th Allerton Conference on Communication, Control, and Computing},
  doi = {10.1109/ALLERTON.2017.8262755},
  grants = {1544771, 1711188, 1736448},
  keywords = {Power Networks; Synchronization},
  month = {10},
  pages = {324-331},
  title = {Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia},
  url = {https://mallada.ece.jhu.edu/pubs/2017-Allerton-PM.pdf},
  year = {2017}
}

@inproceedings{hcm2017cdc,
  abstract = {The security-constrained economic dispatch (SCED) problem tries to maintain the reliability of a power network by ensuring that a single failure does not lead to a global outage. The previous research has mainly investigated SCED by formulating the problem in different modalities, e.g. preventive or corrective, and devising efficient solutions for SCED. In this paper, we tackle a novel and important direction, and analyze the economic cost of incorporating security constraints in economic dispatch. Inspired by existing inefficiency metrics in game theory and computer science, we introduce notion of price of security as a metric that formally characterizes the economic inefficiency of security-constrained economic dispatch as compared to the original problem without security constraints. Then, we focus on the preventive approach in a simple topology comprising two buses and two lines, and investigate the impact of generation availability and demand distribution on the price of security. Moreover, we explicitly derive the worst-case input instance that leads to the maximum price of security. By extensive experimental study on two test-cases, we verify the analytical results and provide insights for characterizing the price of security in general networks.},
  author = {Hajiesmaili, Mohammad H. and Cai, Desmond and Mallada, Enrique},
  booktitle = {56th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2017.8263947},
  grants = {1544771, 1711188, 1736448},
  keywords = {Power Networks},
  month = {12},
  pages = {2035-2040},
  title = {Understanding the Inefficiency of Security-Constrained Economic Dispatch},
  url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-HCM.pdf},
  year = {2017}
}

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

@inproceedings{omg2017cdc,
  abstract = {In this paper we investigate the performance of linear networked dynamical systems over strongly connected digraphs. We consider first and second order systems subject to distributed disturbance inputs, and define an appropriate system output so that the performance measure is quantified through the input-output $\mathcal H_2$ norm of the system. We first develop a generalized framework for the computation of the $\mathcal H_2$ norm. We apply this framework to systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We consider two performance metrics and find closed form solutions for the first and bounds for the other; which both depend on the eigenvalues of these graph Laplacians.
Numerical examples indicate that: (i) the tightness of the bounds are highly dependent on the graph structure, (ii) the $\mathcal H_2$ norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.},
  author = {Oral, H. Giray and Mallada, Enrique and Gayme, Dennice},
  booktitle = {56th IEEE Conference on Decision and Control (CDC)},
  doi = {10.1109/CDC.2017.8263893},
  grants = {1544771, W911NF-17-1-0092},
  keywords = {Power Networks},
  month = {12},
  pages = {1688-1694},
  title = {Performance of first and second order linear networked systems over digraphs},
  url = {https://mallada.ece.jhu.edu/pubs/2017-CDC-OMG.pdf},
  year = {2017}
}

@article{dms2017ieee-csl,
  abstract = {The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this paper, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: fixed point iterations, convex relaxations, and energy functions - we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that (i) voltage magnitudes are increasing functions of the reactive power injections, (ii) the solution is a continuous function of the injections, and (iii) the solution is the last one to vanish as the system is loaded past the feasibility boundary.},
  author = {Dvijotham, Krishnamurthy and Mallada, Enrique and Simpson-Porco, John W.},
  doi = {10.1109/LCSYS.2017.2717578},
  grants = {1544771},
  journal = {IEEE Control Systems Letters},
  keywords = {Power Networks; Power Flow Solutions},
  month = {10},
  number = {2},
  pages = {322-327},
  title = {High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms},
  url = {https://mallada.ece.jhu.edu/pubs/2017-IEEE-CSL-DMS.pdf},
  volume = {1},
  year = {2017}
}