A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper proposes a secondary voltage control of microgrids based on the distributed cooperative control of multi-agent systems. The proposed secondary control is fully distributed; each distributed generator only requires its own information and the information of some neighbors. The distributed structure obviates the requirements for a central controller and complex communication network which, in turn, improves the system reliability. Input-output feedback linearization is used to convert the secondary voltage control to a linear second-order tracker synchronization problem. The control parameters can be tuned to obtain a desired response speed. The effectiveness of the proposed control methodology is verified by the simulation of a microgrid test system. <s> BIB001 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> Existing electric power distribution networks are operating near full capacity and facing rapid changes to address environmental concerns and improve their reliability and sustainability. These concerns are satisfied through the effective integration and coordination of distributed generators (DGs), which facilitate the exploitation of renewable energy resources, including wind power, photovoltaics, and fuel cells [1]. Although DGs can be of rotating machinery type, more recently, DGs have been designed to support renewable energy resources by electronic interfacing through voltage source inverters (VSI). Each DG corresponds to one energy source, and its control inputs are given to the interface VSI [1]-[5]. The successful coordination of DGs can be realized through microgrids, which are small-scale power systems consisting of local generation, local loads, and energy storage systems. Microgrids are autonomous subsystems with dedicated control systems that provide guaranteed power quality for local loads such as hospitals, economic centers, apartments, and universities. The microgrid concept, with its local control and power quality support, allows for the scalable integration of local power resources and loads into the existing power grid and enables a high penetration of distributed generation [5]-[10]. <s> BIB002 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> Motivated by the fact that the location(s) and structural properties of the pinning node(s) affect the algebraic connectivity of a network with respect to the reference value, and thereby its dynamic performance, this paper studies the application of single and multiple pinning of distributed cooperative secondary control of distributed generators (DGs) in an islanded microgrid operation. It is shown that the selection of a pinning set based on the degree of connectivity and distance of leader DG(s) from the rest of the network improves the transient performance for microgrid voltage and frequency regulation. The efficacy of the distributed control strategy based on the proposed algorithms is illustrated via numerical results simulating typical scenarios for a variety of microgrid configurations. <s> BIB003 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper proposes a new distributed cooperative secondary control for both frequency and voltage restoration of an islanded microgrid with droop-controlled, inverter-based distributed generations (DGs). Existing distributed methods commonly design secondary control based on the minimum real part of the nonzero Laplacian matrix eigenvalues related to the microgrid communication graph, which, however, is global information. In contrast to the existing distributed methods, in this paper we design a fully distributed adaptive control based on the dynamic model of DG units and on information from neighboring units. Therefore, the proposed control scheme increases the system reliability, decreases its sensitivity to failures, and eliminates the need for a central processing unit. The fully distributed controllers restore the islanded microgrid frequency and voltage magnitudes to their reference values for all DG units irrespective of parametric uncertainties and disturbances while providing accurate real power sharing. Furthermore, the proposed method considers the coupling between the islanded microgrid frequency and voltages. Finally, we have conducted comprehensive simulation studies in the MATLAB/SimPowerSystems toolbox to verify the proposed control strategy performance. <s> BIB004 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox. <s> BIB005 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper presents a robust distributed secondary control (DSC) scheme for inverter-based microgrids (MGs) in a distribution sparse network with uncertain communication links. By using the iterative learning mechanics, two discrete-time DSC controllers are designed, which enable all the distributed energy resources (DERs) in an MG to achieve the voltage/frequency restoration and active power sharing accuracy, respectively. In special, the secondary control inputs are merely updated at the end of each round of iteration, and thus, each DER only needs to share information with its neighbors intermittently in a low-bandwidth communication manner. This way, the communication costs are greatly reduced, and some sufficient conditions on the system stability and robustness to the uncertainties are also derived by using the tools of Lyapunov stability theory, algebraic graph theory, and matrix inequality theory. The proposed controllers are implemented on local DERs, and thus, no central controller is required. Moreover, the desired control objective can also be guaranteed even if all DERs are subject to internal uncertainties and external noises including initial voltage and/or frequency resetting errors and measurement disturbances, which then improves the system reliability and robustness. The effectiveness of the proposed DSC scheme is verified by the simulation of an islanded MG in MATLAB/SimPowerSystems. <s> BIB006 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> One of the fundamental and challenging issues in microgrids is to guarantee fairness of load sharing while realizing voltage regulation of distributed generations. In order to address this issue, a new multiobjective optimization problem with tunable weighting coefficients is first formulated for dc microgrids. Second, a new distributed control scheme, which only requires local communications among neighbors, is proposed to solve the optimization problem. It is theoretically proved that the distributed control scheme can exponentially achieve the global optimal outputs of voltages and currents at distributed generations. Compared with a centralized control scheme, the proposed distributed control scheme provides remarkable advantages in improving reliability and scalability of microgrids. Third, the distributed control scheme is extended to accommodate a constant communication delay. The effects of the communication delay on the stability of microgrids are explicitly characterized. Finally, the performance of the proposed control schemes is evaluated by a modified six-bus microgrid with dc-powered trolleybus systems in terms of their convergence, robustness to load variations, plug-and-play functionality, tradeoff ability, and effects of communication delays. <s> BIB007 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper presents a novel secondary frequency and voltage control method for islanded microgrids based on distributed cooperative control. The proposed method utilizes a sparse communication network where each DG unit only requires local and its neighbors’ information to perform control actions. The frequency controller restores the system frequency to the nominal value while maintaining the equal generation cost increment value among DG units. The voltage controller simultaneously achieves the critical bus voltage restoration and accurate reactive power sharing. Subsequently, the case when the DG unit ac-side voltage reaches its limit value is discussed and a controller output limitation method is correspondingly provided to selectively realize the desired control objective. This paper also provides a small-signal dynamic model of the microgrid with the proposed controller to evaluate the system dynamic performance. Finally, simulation results on a microgrid test system are presented to validate the effectiveness of the proposed method. <s> BIB008 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper proposes a distributed noise resilient control technique for voltage and frequency synchronization in inverter-based ac microgrids. Existing cooperative control techniques assume ideal communication among inverters. The effect of additive noise in communication links among inverters, and between the reference signal and inverters, on the synchronization process, is studied. Distributed least mean-square solutions estimate the reference set points, and a local least mean-square algorithm estimates neighboring inverter frequencies and voltages. The efficacy of the proposed solution, for an islanded microgrid test system under the additive noise in reference communication links and links connecting neighboring inverters, is evaluated for a modified IEEE 34-bus feeder system. An upper bound for the noise-induced deviation in the consensus parameter is analytically derived and verified by the simulated testbed. <s> BIB009 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> C. Distributed Control of Microgrids via Droop Characteristic <s> This paper is concerned with active power sharing and frequency regulation in an islanded microgrid under event-triggered communication. A distributed secondary control scheme with a sampled-data-based event-triggered communication mechanism is proposed to achieve active power sharing and frequency regulation in a unified framework, where neighborhood sampled-data exchange occurs only when the predefined triggering condition is violated. Compared with traditional periodic communication mechanisms, the proposed event-triggered communication mechanism shows some prominent ability in reducing the number of communication among neighbors while guaranteeing the desired performance level of microgirds. By employing the Lyapunov–Kravovskii functional method, some sufficient conditions are derived to characterize the effects of control gains, system parameters, and sampling period on stability of microgrids. Finally, case studies on a modified IEEE 34-bus test system are conducted to evaluate the performance of the proposed distributed control scheme, showcasing its effectiveness, robustness against load changes, and plug-and-play ability. <s> BIB010
Microgrids, a kind of typical industrial CPSs, are usually an aggregation of distributed generators (such as renewable energy sources and conventional generators), energy storage systems, and other equipment. Their upcoming, large-scale interconnection with the national primary grid requires urgent research attention to focus on highly reliable distributed regulation technologies. Especially, at the forefront of the field, a hierarchical control scheme, including the primary control and the secondary control, is conventionally adopted for this operation. The purpose of primary control, a decentralized control approach realized through a droop mechanism, is to stabilize microgrids and handle proportional load sharing among inverters. This control forces the bus voltages and frequency to deviate from their nominal values and could lead to poor reactive power sharing in the presence of unequal bus voltages. To overcome these shortcomings, secondary control under a distributed architecture is necessary to update the set points of the local primary control BIB007 , BIB010 . BIB004 , BIB005 can be described in a compact form ⎧ ⎨ where y T and other parameters can be found in BIB001 . Here, i Ldi , i Lqi , v odi , v oq i , i odi , and i oq i are the quadratic and direct components of converter current i Li , LC filter voltage v di , and output connector current i oi . Furthermore, a more general 13th-order nonlinear model can be found in BIB002 . According to the partial feedback linearizing scheme, an auxiliary controller based on consensus errors constructed in BIB004 is for voltage control, where there exists at least one pinning gain p i > 0 for voltage source converter i. In addition, taking proportional real power sharing into account, one has BIB008  for frequency control. It should be pointed out that the regulating error of active power allocation is embedded in the control strategy with intent to maintain the equal cost increment achieved in the primary control BIB008 . By utilizing iterative learning approaches, a robust distributed secondary control is presented in BIB006 to achieve both active power sharing accuracy and voltage/frequency restoration of microgrids with uncertain communication links. Furthermore, an improved controller by combining tracking performance and regulator synchronization is developed in BIB008 for islanded microgrids with a sparse communication network, and in BIB009 for inverter-based ac microgrids with additive channel noises. A consensus-based distributed controller is designed in BIB005 to provide more robustness to unmodeled dynamics, unknown disturbances, and uncertainties while restoring the desired voltage magnitude and frequency within finite time. Generally speaking, the controller gain usually depends on the eigenvalues of a Laplacian matrix, which are essentially global information. In contrast to these existing distributed methods, a fully distributed adaptive controller designed in BIB004 only utilizes the dynamics model of distributed generation (DG) units and neighbors' information and therefore eliminates the need of a central computing and communication unit. Furthermore, both single and multiple pinning schemes are discussed in BIB003 and it is disclosed that the selection of a pinning set depends on both the degree of algebraic connectivity and the distance of leaders. However, the problems on the selection of pinning nodes and the design of pinning strength are not solved effectively, especially for the cases with network-induced phenomena and communication protocols.