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Phasor measurement units (PMUs) have become instrumental in modern power systems for enabling real time, wide-area monitoring and control. Accordingly, many studies have investigated efficient and robust dynamic state estimation (DSE) methods in order to accurately compute the dynamic states of generation units. Nonetheless, most of them forego the dynamic-algebraic nature of power networks and only consider their nonlinear dynamic representations. Motivated by the lack of DSE methods based on power network’s differential-algebraic equations (DAEs), this article develops a novel observer-based DSE framework in order to perform simultaneous estimation of the dynamic and algebraic states of multimachine power networks. Specifically, we leverage the DAE dynamics of a power network around an operating point and combine them with a PMU-based measurement model capable of capturing bus voltages and line currents. The proposed $\mathcal {H}_{\infty }$ observer, which only requires detectability and impulse observability conditions that are satisfied for various power networks, is designed to handle various noise, unknown inputs, and input sensor failures. The results obtained from performing extensive numerical simulations on IEEE 9-bus and 39-bus systems showcase the effectiveness of the proposed approach for DSE purposes.

Optimal, network-driven control of water distribution networks (WDNs) is very difficult: valve and pump models form nontrivial, combinatorial logic; hydraulic models are nonconvex; water demand patterns are uncertain; and WDNs are naturally of large scale. Prior research on control of WDN addressed major research challenges, yet either i) adopted simplified hydraulic models, WDN topologies, and rudimentary valve/pump modeling or ii) used mixed-integer, nonconvex optimization to solve WDN control problems. The objective of this article is to develop tractable computational algorithms to manage WDN operation, while considering arbitrary topology, flow direction, an abundance of valve types, control objectives, hydraulic models, and operational constraints—all while only using convex, continuous optimization. Specifically, we propose new geometric programming (GP)-based model predictive control (MPC) algorithms, designed to solve the water flow equations and obtain WDN controls, i.e., pump/valve schedules alongside heads and flows. The proposed approach amounts to solving a series of convex optimization problems that graciously scale to large networks. The proposed approach is tested using a 126-node network with many valves and pumps and is shown to outperform traditional, rule-based control. The developed GP-based MPC algorithms, as well as the numerical test results, are all included on Github.

Uncertainty from renewable energy and loads is one of the major challenges for stable grid operation. Various approaches have been explored to remedy these uncertainties. In this paper, we design centralized or decentralized state-feedback controllers for generators while considering worst case uncertainty. Specifically, this paper introduces the notion of $\mathcal {L}_{\infty }$ robust control and stability for uncertain power networks. An uncertain and nonlinear differential algebraic equation model of the network is presented. The model includes unknown disturbances from renewables and loads. Given an operating point, the linearized state-space presentation is given. Then, the notion of $\mathcal {L}_{\infty }$ robust control and stability is discussed, resulting in a nonconvex optimization routine that yields a state feedback gain mitigating the impact of disturbances. The developed routine includes explicit input-bound constraints on generators’ inputs and a measure of the worst case disturbance. The feedback control architecture can be centralized, distributed, or decentralized. Algorithms based on successive convex approximations are then given to address the nonconvexity. Case studies are presented showcasing the performance of the $\mathcal {L}_{\infty }$ controllers in comparison with automatic generation control and $\mathcal {H}_{\infty }$ control methods.

We propose methods to solve time-varying, sensor and actuator (SaA) selection problems for uncertain cyber-physical systems. We show that many SaA selection problems for optimizing a variety of control and estimation metrics can be posed as semidefinite optimization problems with mixed-integer bilinear matrix inequalities (MIBMIs). Although this class of optimization problems is computationally challenging, we present tractable approaches that directly tackle MIBMIs, providing both upper and lower bounds, and that lead to effective heuristics for SaA selection. The upper and lower bounds are obtained via successive convex approximations and semidefinite programming relaxations, respectively, and selections are obtained with a slicing algorithm from the solutions of the bounding problems. Custom branch-and-bound and combinatorial greedy approaches are also developed for a broad class of systems for comparison. Finally, comprehensive numerical simulations are performed to compare the different methods and illustrate their effectiveness.