A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 3) Distributed Control Based on Angle Droop Characteris- <s> Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes. <s> BIB001 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 3) Distributed Control Based on Angle Droop Characteris- <s> Modeled after the hierarchical control architecture of power transmission systems, a layering of primary, secondary, and tertiary control has become the standard operation paradigm for islanded microgrids. Despite this superficial similarity, the control objectives in microgrids across these three layers are varied and ambitious, and they must be achieved while allowing for robust plug-and-play operation and maximal flexibility, without hierarchical decision making and time-scale separations. In this work, we explore control strategies for these three layers and illuminate some possibly-unexpected connections and dependencies among them. Building from a first-principle analysis of decentralized primary droop control, we study centralized, decentralized, and distributed architectures for secondary frequency regulation. We find that averaging-based distributed controllers using communication among the generation units offer the best combination of flexibility and performance. We further leverage these results to study constrained AC economic dispatch in a tertiary control layer. Surprisingly, we show that the minimizers of the economic dispatch problem are in one-to-one correspondence with the set of steady-states reachable by droop control. In other words, the adoption of droop control is necessary and sufficient to achieve economic optimization. This equivalence results in simple guidelines to select the droop coefficients, which include the known criteria for power sharing. We illustrate the performance and robustness of our designs through simulations. <s> BIB002 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 3) Distributed Control Based on Angle Droop Characteris- <s> This note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors. <s> BIB003 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 3) Distributed Control Based on Angle Droop Characteris- <s> This paper presents a new distributed control framework to coordinate inverter-interfaced distributed energy resources (DERs) in island microgrids. We show that under bounded load uncertainties, the proposed control method can steer the microgrid to a desired steady state with synchronized inverter frequency across the network and proportional sharing of both active and reactive powers among the inverters. We also show that such convergence can be achieved while respecting constraints on voltage magnitude and branch angle differences. The controller is robust under various contingency scenarios, including loss of communication links and failures of DERs. The proposed controller is applicable to lossy mesh microgrids with heterogeneous R/X distribution lines and reasonable parameter variations. Simulations based on various microgrid operation scenarios are also provided to show the effectiveness of the proposed control method. <s> BIB004 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 3) Distributed Control Based on Angle Droop Characteris- <s> Abstract In this paper we study theoretical properties of the frequency control problem in inverter-based microgrids with primary and decentralised/distributed secondary control loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of attraction is guaranteed under a condition on the power mismatch between demand and generation at each inverter bus. An estimate of the region of attraction is obtained from which an ultimate bound set for the state trajectories can be determined by recursive iterations of a nonlinear mapping. The derived results provide a certificate of the overall stability and performance of the controlled microgrid. <s> BIB005
tics: Similar to the above-mentioned droop control scheme, one has the following angle droop control model for a microgrid BIB005 , BIB001 with purely inductive lines where d p i > 0, θ i , u i , and l ij denote, respectively, the droop coefficient, the bus phase angle, the control input determined by a secondary control loop, and the magnitude of pure imaginary admittance of the interconnecting line between inverters i and j. ΔP * i represents the inverter power mismatch between the nominal injection setpoint of inverters and the load demand of buses. To eliminate this angle deviation, a typical distributed secondary controller is where κ > 0 is the coefficient and α ij is the same with one in BIB003 . This distributed controller is employed in BIB002 to offer the best combination of flexibility and performance by using communication among generation units. Especially, when θ i θ j , the above control model can be simplified as BIB003 . Lately, stability and convergence properties receive considerable research efforts (see, e.g., BIB001 and BIB004 ). Specially, a necessary and sufficient condition is derived in BIB001 to disclose the existence and uniqueness of locally exponentially stable equilibrium. In addition, frequency regulation without assuming time-scale separation can be ensured and ultimate boundedness can also be satisfied under a condition on power mismatch BIB005 . In particular, a simplified distributed controller is designed in BIB004 to steer the microgrid with security constraints to a desired steady state. The designed controller is also robust for loss of communication links and failures of distributed energy resources.