Dynamic Average Consensus Algorithm Research Articles

A novel dynamic event-triggered mechanism for dynamic average consensus

This paper studies a challenging issue introduced in a recent survey, namely designing a distributed event-based scheme to solve the dynamic average consensus (DAC) problem. First, a robust adaptive distributed event-based DAC algorithm is designed without imposing specific initialization criteria to perform estimation task under intermittent communication. Second, a novel adaptive distributed dynamic event-triggered mechanism is proposed to determine the triggering time when neighboring agents broadcast information to each other. Compared to the existing event-triggered mechanisms, the novelty of the proposed dynamic event-triggered mechanism lies in that it guarantees the existence of a positive and uniform minimum inter-event interval without sacrificing any accuracy of the estimation, which is much more practical than only ensuring the exclusion of the Zeno behavior or the boundedness of the estimation error. Third, a composite adaptive law is developed to update the adaptive gain employed in the distributed event-based DAC algorithm and dynamic event-triggered mechanism. Using the composite adaptive update law, the distributed event-based solution proposed in our work is implemented without requiring any global information. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

A voltage-shifting-based state-of-charge balancing control for distributed energy storage systems in islanded DC microgrids

This paper presents a distributed secondary level control strategy for battery energy units (BEUs) parallel in a DC microgrid. The control structure is divided into two layers. The primary control layer is implemented with a droop control. The voltage-shifting term is generated by the secondary control layer, where an information state factor λ is introduced to meet the bus voltage restoration, state-of-charge (SOC) balancing and accurate current sharing. A sigmoid function with a balancing adjustment factor is adopted to improve both SOC balancing accuracy and speed. When each information state factor in the system converges to the average value, accurate current sharing according to the SOC values of BEUs and capacities is attained, and the average output voltage is consistent with the nominal voltage of microgrid. Compared with existing methods, the proposed method has no requirement on a complex control structure and only two variables need to be transferred between adjacent converters, which reduces the information traffic and the communication burden. Moreover, the proposed nonlinear control strategy effectively avoids unnecessary cyclic charge or discharge between BEUs and inhibits circulating currents. The proposed method also has the ability of plug and play, since SOC balancing among BEUs with different capacities is considered, and, in the communication layer, the dynamic average consensus algorithm is utilized to obtain both average SOC and average λ. The performance of the proposed control method is confirmed in simulation and experiment.

Privacy-Preserving Dynamic Average Consensus via Random Number Perturbation

This brief focuses on the study of privacy preservation of dynamic average consensus (DAC) in multi-agent networks. A privacy-preserving DAC (PP-DAC) algorithm is proposed based on a carefully designed random number perturbation mechanism. The PP-DAC algorithm is able to protect agents from the leakage of sensitive information without compromising their tracking accuracy. Furthermore, the privacy analysis for different scenarios is given to show that the PP-DAC algorithm works well unless all neighbors of the target agent collude with each other to attack this agent. Also, some numerical simulations are given to illustrate the validity of the proposed algorithm.

An Operator-Theoretic Approach to Robust Event-Triggered Control of Network Systems With Frequency-Domain Uncertainties

In this paper, we study the robustness of the event-triggered consensus algorithms against frequency- domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain L2-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicative uncertainties are considered, respectively. In both cases, quantitative relationships among the parameters of the controllers, the Laplacian matrix of the network topology, and the robustness against aperiodic event triggering and frequency-domain uncertainties are unveiled. Furthermore, the event-triggered dynamic average consensus (DAC) problem is also investigated, wherein the sampling errors are shown to be images of nonlinear finite-gain operators. The robust performance of the proposed DAC algorithm is analyzed, which indicates that the robustness and the performance are negative

A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback

This article studies accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into a weighted summation of current and outdated terms. When determining the weighted sum, there is a range of time delay that results in a higher convergence rate for the algorithm. For such weights, using the Lambert <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$W$</tex-math></inline-formula> function, we obtain the rate-increasing range of the time delay, obtain the maximum reachable rate, and characterize the value of the corresponding maximizer delay. We also study the effect of using the outdated feedback on the control effort of the agents. We show that only for some specific affine combination of the immediate and outdated feedback, the control effort of the agents does not go beyond that of the delay-free algorithm. In addition, we demonstrate that using outdated feedback does not increase the steady-state tracking error of the average consensus algorithm. Finally, we determine the optimum combination of the current and the outdated feedback weights to achieve the maximum increase in the rate of convergence without increasing the control effort of the agents. We demonstrate our results through a numerical example.

Distributed control strategy for voltage and frequency restoration and accurate reactive power-sharing for islanded microgrid

For a conventional droop-controlled islanded microgrid, the poor reactive power-sharing and drop of bus voltage and frequency caused by line impedance mismatch and droop characteristics are inevitable. So far, consensus-based distributed control algorithms, in which a secondary control layer with the integration of voltage and frequency restoration and reactive power-sharing compensation mechanisms, has been treated as a promising solution. However, for most of the currently available distributed algorithms, it is the active power-sharing rather than the reactive power-sharing that was made the control goal, which is opposite to the fact that accurate power-sharing could always hold considering the integration effect in the active power control loop. Although a few recently published distributed algorithms added the reactive power-sharing goal in the second control layer, the system efficiency and reliability may deteriorate because a large circulating current could be induced at the malfunction of the communication network since there is no virtual impedance injected at the bottom control layer to limit that. This paper proposes a voltage and frequency restoration method based on the dynamic average consensus algorithm and an accurate reactive power-sharing method based on a first-order consensus algorithm and virtual impedance method. A simple pseudo-unidirectional communication network with a narrow communication band is adopted for the proposed distributed control to lower the communication burden and system complexity. The operational principle is first analyzed in detail. The proposed strategy is easily implementable and features not breaking droop characteristics. Then simulations and hardware-in-the-loop (HIL) real-time experiments verify the proposed approach.

Consensus-based state of charge dynamic equilibrium strategy in isolated DC microgrid with bus voltage regulation

Due to the tremendous benefits of integrating sustainable energy, the use of DC microgrid is gradually expanding. This paper presents a novel consensus-based State of Charge (SoC) dynamic equilibrium strategy to solve the issues of unbalanced SoC, imprecise load power distribution, and unreasonable bus voltage regulation for the Battery Energy Storage System (BESS) in DC microgrids with Distributed Sustainable Energy Generation (DSEG). In the communication layer, an adjacent communication network is built, which applies the Dynamic Average Consensus Algorithm (DACA) to estimate relevant average values. In addition, the conventional droop control is applied to distribute the load power preliminarily in the main control layer. With the proposed scheme, the dynamic SoC equilibrium and accurate current distribution are realized by the consensus iteration of the designed coupling factor, and the bus voltage recovery is achieved by compensating for the average output voltage of energy storage units (ESUs) in the secondary control layer. Furthermore, the exponential function is introduced to modify DACA, thus accelerating the convergence of DACA. Finally, the simulation and experimental results show that the proposed scheme can realize the control objectives of rapid SoC equilibrium, accurate load power distribution, and reasonable bus voltage regulation.

Distributed consensus-based reactive power sharing in microgrids: A predictive virtual capacitance control technique

In microgrids, multiple modular distributed generation (DG) are required to power the system’s loads. Nonetheless, disproportionate reactive power (Q) sharing arises with unequal feeder line impedances of DGs connected to a common bus. Hence, this study proposes a novel method, based on virtual shunt and series capacitances, to regulate both accurate reactive power sharing, and at the same time restore the DG output voltages. The proposed method utilizes a dynamic average consensus algorithm for low-bandwidth communication among the neighbor DGs. The effectiveness of the control scheme is validated through stability analysis, extensive offline simulations and real-time hardware-in-the-loop tests on a microgrid system.

Privacy-preserving dynamic average consensus via state decomposition: Case study on multi-robot formation control

Dynamic average consensus is a decentralized control/estimation framework where a group of agents cooperatively track the average of local time-varying reference signals. In this paper, we develop a novel state decomposition-based privacy preservation scheme to protect the privacy of agents when sharing information with neighboring agents. Specifically, we first show that an external eavesdropper can successfully wiretap the reference signals of all agents in a conventional dynamic average consensus algorithm. To protect privacy against the eavesdropper, a state decomposition scheme is developed where the original state of each agent is decomposed into two sub-states: one succeeds the role of the original state in inter-node interactions, while the other sub-state only communicates with the first one and is invisible to other neighboring agents. Rigorous analyses are performed to show that (1) the proposed privacy scheme preserves the convergence of the average consensus; and (2) the privacy of the agents is protected such that an eavesdropper cannot discover the private reference signals with guaranteed accuracy. The developed privacy-preserving dynamic average consensus framework is then applied to the formation control of multiple non-holonomic mobile robots, in which the efficacy of the scheme is demonstrated. Numerical simulation is provided to illustrate the effectiveness of the proposed approach.

Network sensitivity function, optimization and robust performance in dynamic average consensus

AbstractIn this article, a novel sensitivity minimization approach is proposed to optimize the performance of proportional‐integral (PI) dynamic average consensus (DAC) algorithms subject to measurement noises and model uncertainties. Network sensitivity and complementary sensitivity functions are defined to characterize the effects of the reference signals and measurement noises on the tracking error, respectively. Minimization of the norms of network sensitivity and complementary sensitivity functions, describing how large the PI DAC algorithm amplifies the reference and noise signals in the worst case, are conducted to optimize the tracking performance with respect to the reference signals and measurement noises without requiring prior knowledge. Further, by studying the weighted optimization of the network sensitivity functions, necessary and sufficient conditions are provided for the PI DAC algorithm to have a good tracking performance for low‐frequency reference signals and high‐frequency measurement noises. The proposed sensitivity minimization approach is shown to be a robust approach, by considering the PI DAC algorithm in the presence of norm‐bounded additive uncertainties. The robust weighted performance specification is formulated and a sufficient condition is provided, relying on the network topology, the bound of the uncertainties, and the parameters of the DAC algorithms. A tradeoff relationship between the tracking performance and robustness is unveiled. The special case of proportional DAC algorithms is similarly discussed.

Training Deep Neural Network for Optimal Power Allocation in Islanded Microgrid Systems: A Distributed Learning-Based Approach.

Currently, numerical optimization methods are used to solve distributed optimal power allocation (OPA) problems for islanded microgrid (MG) systems. Most of them are developed based on rigorous mathematical derivation. However, the complexity of such optimization algorithms inevitably creates a gap between theoretical analysis and real-time implementation. In order to bridge such a gap, in this article we provide a new distributed learning-based framework to solve the real-time OPA problem. Specifically, inspired by the human-thinking scheme, distributed deep neural networks (DNNs) together with a dynamic average consensus algorithm are first employed to obtain an approximate OPA solution in a distributed manner. Then a distributed balance generation and demand algorithm is designed to fine-tune it to obtain the final optimal feasible solution. In addition, it is theoretically proved that the proposed DNN can well approximate one existing OPA algorithm (Guo et al. 2018), where quantitative numbers of at most how many hidden layers and neurons are provided. Several experimental case studies show that our proposed distributed learning framework can achieve similar optimal results to those obtained by using typical existing distributed numerical optimization methods while it is superior in terms of simplicity and real-time capability.

SoC-Based Dynamic Droop Control for Battery Energy Storage Systems in DC Microgrids Feeding CPLs

In this paper, a dynamic state-of-charge (SoC)-based droop control and bus voltage stabilization strategy has been proposed for battery energy storage systems (BESSs) feeding constant power loads (CPLs). Firstly, a SoC-based dynamic droop control is proposed to realize proportional distribution of power. Secondly, a dynamic average consensus (DAC) algorithm is adopted to ensure that all SoC converge to the same value simultaneously. Thirdly, a nonlinear disturbance observer (NDO) and a backstepping controller are integrated to stabilize the DC bus voltage. In this way, the rapid voltage recovery and power distribution are obtained when droop coefficient is time-varying. Simulation results verify the feasibility and effectiveness of the proposed control strategy.

A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids

In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way. Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set.

Robust Event-Triggered Dynamic Average Consensus Against Communication Link Failures With Application to Battery Control

Dynamic average consensus (DAC) has found applications in various systems. The existing event-triggered DAC algorithms have not well addressed the issue of key communication link failures that lead to the separation of the initial communication topology. This article presents a modified event-triggered DAC algorithm that is independent of its initial conditions. As a result, it is robust against key communication link failures. In this algorithm, each agent decides locally when to transmit signals to its neighbors. In this way, the communication burden among the neighboring agents is reduced. A numerical example is provided to illustrate the effectiveness of the proposed algorithm. Moreover, the proposed algorithm is applied to a state-of-charge balance control problem of batteries in energy systems, and both simulations and hardware-in-the-loop tests are provided to demonstrate the control performance.

Dynamic Active Average Consensus

We propose a continuous-time dynamic active average consensus algorithm in which the agents can alternate between active and passive modes depending on their ability to access to their reference input. The objective is to enable all the agents, both active and passive, to track the average of the reference inputs of the active agents. The algorithm is modeled as a switched linear system whose convergence properties are carefully studied considering the agents' piece-wise access to the reference signals. We also study the discrete-time implementation of this algorithm. Next, we show how a containment control problem in which a group of followers should track the convex hull of a set of observed leaders, can be cast as an active average consensus problem, and solved efficiently by our proposed dynamic active average consensus algorithm. Numerical examples demonstrate our results.

An Improved Droop Control for Balancing State of Charge of Battery Energy Storage Systems in AC Microgrid

In order to avoid overuse of a certain battery energy storage system (BESS) and prolong the cycle life of battery in AC microgrid, an improved SoC-based droop control based on multi-agent system (MAS) is proposed for achieving State of Charge (SoC) balance of multiple BESS units. A proportional-integral (PI) adjustment item using the average SoC is added to the P -f droop to regulate the charging and discharging power of BESS, then SoC changes towards in the direction of consistency and finally reaches equalization. The dynamic average consensus algorithm is utilized to obtain the average SoC. The proposed SoC-based droop method needs not to be changed in different operating mode of BESS and can achieve SoC balance regardless of whether the capacities of different batteries are the same, which improve the applicability of this method. A complete small-signal state space model including all BESS units is built and analyzed to select the appropriate control parameters of the improved droop. The impact of communication time delay on the improved droop method for balancing SoC is investigated and the effectiveness of the proposed strategy is verified through the simulation results of different case studies.

Dual-Consensus-Based Distributed Frequency Control for Multiple Energy Storage Systems

Intermittent renewable energy sources are being increasingly integrated into modern power networks. This leads to severe frequency fluctuations in the networks. Energy storage systems can be used for frequency restoration due to their capability to provide in-time active power compensations. This paper examines the frequency control problem for power systems with multiple distributed battery energy storage systems (BESSs). A dual-consensus-based approach is presented for distributed frequency control. It consists of three main components: 1) tuning of the BESS control gain; 2) design of control signals as inputs to BESSs for proportional use of the preserved energy; and 3) estimation of BESS parameters for control implementation. A static parameter and a time-varying parameter are defined, and their average values are estimated through static average consensus (SAC) and dynamic average consensus (DAC) algorithms, respectively. Case studies are conducted to demonstrate our dual-consensus control approach.

Robust Dynamic Average Consensus Algorithms

This technical note considers the dynamic average consensus problem, where a group of networked agents are required to estimate the average of their time-varying reference signals. Almost all existing solutions to this problem require a specific initialization of the estimator states, and such constraints render the algorithms vulnerable to network disruptions. Here, we present three robust algorithms that do not entail any initialization criteria. Furthermore, the proposed algorithms do not rely on the full knowledge of the dynamics generating the reference signals nor assume access to its time derivatives. Two of the proposed algorithms focus on undirected networks and make use of an adaptive scheme that removes the explicit dependence of the algorithm on any upper bounds on the reference signals or its time derivatives. The third algorithm presented here provides a robust solution to the dynamic average consensus problem on directed networks. Compared to the existing algorithms for directed networks, the proposed algorithm guarantees an arbitrarily small steady-state error bound that is independent of any bounds on the reference signals or its time derivatives. The current formulation allows each agent to select its own performance criteria, and the algorithm parameters are distributedly selected such that the most stringent requirement among them is satisfied. A performance comparison of the proposed approach to existing algorithms is presented.

Consensus-Based SOC Balancing of Battery Energy Storage Systems in Wind Farm

Multiple battery energy storage systems (BESSs) are used to compensate for the fluctuation in wind generations effectively. The stage of charge (SOC) of BESSs might be unbalanced due to the difference of wind speed, initial SOCs, line impedances and capabilities of BESSs, which have a negative impact on the operation of the wind farm. This paper proposes a distributed control of the wind energy conversion system (WECS) based on dynamic average consensus algorithm to balance the SOC of the BESSs in a wind farm. There are three controllers in the WECS with integrated BESS, including a machine-side controller (MSC), the grid-side controller (GSC) and battery-side controller (BSC). The MSC regulates the generator speed to capture maximum wind power. Since the BSC maintains the DC link voltage of the back-to-back (BTB) converter that is used in the WECS, an improved virtual synchronous generator (VSG) based on consensus algorithm is used for the GSC to control the output power of the WECS. The functionalities of the improved VSG are designed to compensate for the wind power fluctuation and imbalance of SOC among BESSs. The average value of SOCs obtained by the dynamic consensus algorithm is used to adjust the wind power output for balancing the SOC of batteries. With the proposed controller, the fluctuation in the output power of wind generation is reduced, and the SOCs of BESSs are maintained equally. The effectiveness of the proposed control strategy is validated through the simulation by using a MATLAB/Simulink environment.

Discrete-Time Distributed Extremum-Seeking Control Over Networks With Unstable Dynamics

In this paper, we propose a discrete-time version of extremum-seeking control (ESC) which can be implemented by several agents communicating over a network. We consider the problem where several agents measure a local cost and must cooperate to minimize the total cost which is the sum of the local costs. To solve this problem, we combine a dynamic average consensus algorithm with a proportional integral ESC technique in discrete time. The consensus algorithm provides each agent with an estimate of the total cost and this estimate is used by the ESC to minimize the total cost. The main contribution of this paper is to show that the distributed agents can effectively minimize the unmeasured total cost.