Dynamic Average Consensus Research Articles

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.

Combining ADMM and tracking over networks for distributed constraint-coupled optimization

In this paper, we propose a novel distributed algorithm to address constraint-coupled optimization problems in which agents in a network aim at cooperatively minimizing the sum of local objective functions subject to individual constraints and a common, linear coupling constraint. Our optimization scheme embeds a dynamic average consensus protocol in the (parallel) Alternating Direction Method of Multipliers (ADMM) to design a fully distributed algorithm. More precisely, the dual variable update step of the master node in ADMM is now performed locally by the agent, which update their own copy of the dual variable in a consensus-based scheme using a dynamic average mechanism to track the coupling constraint violation. Under convexity, we show convergence of the primal solution estimates to an optimal solution of the constraint-coupled target problem. A numerical example supports the theoretical results.

Inverter-Based Voltage Control of Distribution Networks: A Three-Level Coordinated Method and Power Hardware-in-the-Loop Validation

The reactive power of the photovoltaic (PV) inverters has great potential for voltage regulation of distribution networks. In this paper, a new three-level coordinated control method for PV inverters is proposed to address network voltage fluctuation and violation issues. In Level I, a ramp-rate control is designed to smooth the network voltage fluctuations, while in Level II, a droop control is designed to alleviate the network voltage deviations. If the local compensation provided by Level I and II is not enough to regulate the network voltages within the required limits, the Level III control based on dynamic average consensus can respond and share the reactive power requirement among other inverters in a distributed way. The proposed control method can smooth the voltage profiles, restrain the voltage rise/drop problem, and coordinate all PV inverters in real-time when there is no feasible local solution. The stability analysis of the proposed three-level coordinated control for network voltage regulation is provided. The power hardware-in-the-loop (PHIL) experiment has been conducted for validating the proposed control method under various scenarios.

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.

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.

Distributed Neuro-Dynamic Algorithm for Price-Based Game in Energy Consumption System

In this paper, a plug-in hybrid electric vehicles energy consumption system is studied. In order to protect each player’s privacy, the information exchange is going on the neighboring players, and a connected undirected graph is used to pattern the information flow between the players. Hence, it is impossible for each player to access the aggregate electricity consumption directly, which determines the electricity price. Under the noncooperative game frame, a distributed neuro-dynamic algorithm is proposed to optimize the benefit of each individual player base on the pricing strategies. A dynamic average consensus is applied to estimate the aggregate consumption and a projection neural network is employed to seek the Nash equilibrium point. The convergence of the proposed distributed algorithm is analyzed through the Lyapunov stability analysis. Finally, the effectiveness of the distributed neuro-dynamic algorithm is manifested in the simulation.

Distributed State-of-Charge Balance Control With Event-Triggered Signal Transmissions for Multiple Energy Storage Systems in Smart Grid

Modern power grid is increasingly integrated with battery energy storage systems (BESSs). This paper deals with the problem of state-of-charge (SoC) balance control for multiple distributed BESSs in smart grid. The BESSs are expected to work cooperatively to not only fulfil the overall power requirement but also meet the constraints of the same relative SoC variation rate. To achieve this objective, a distributed SoC balance control approach is presented with event-triggered signal transmissions. It is designed with the dynamic average consensus (DAC) mechanism for parameter estimations. The DAC enables distributed control of each BESS through communicating with its neighboring BESSs. Different from traditional periodic signal transmission, the event-triggered signal transmission embedded in our approach allows each BESS to transmit signal to its neighboring BESSs only when needed, thus reducing the communication traffic. Theoretical lower bounds are established for consecutive interevent intervals such that the Zeno behavior is excluded. Case studies are conducted to demonstrate the effectiveness of the presented approach.

Dynamic Average Consensus [About This Issue

Presents the introductory editorial for this issue of the publication.

Dynamic average consensus with topology balancing under a directed graph

SummaryIn this paper, the distributed average tracking problem is studied on the premise of a strongly connected directed graph. To this end, we propose a weight balance strategy that could potentially make the adjacency matrix doubly stochastic for any strongly connected directed graph. The proposed scheme is fully distributive with finite time convergence and we again prove that network connectivity (described by the first left eigenvector) is instrumental in networked control systems. Then, a discrete‐time average tracking observer is introduced to ensure that all networked systems can track the average of the reference signals with bounded error. Simulation results verify the effectiveness of the proposed methods.

Optimal Dynamic Average Consensus of Multi-Agent Systems

This paper studies the average tracking problem on the premise of networked systems where each node is only allowed to interact with its neighbours. To this end, new dynamic average consensus protocols for both continuous-time and discrete time systems are proposed, and the corresponding analysis provides the rules on the optimal settings of the proposed algorithm with respect to convergence rate and steady-state performance. Numerical simulations validate the theoretical contributions of this work.

Gesture based Human-Swarm Interactions for Formation Control using interpreters

Abstract We propose a novel Human-Swarm Interaction (HSI) framework which enables the user to control a swarm’s shape and formation. The user commands the swarm utilizing just arm gestures and motions which are recorded by an off-the-shelf wearable armband. We propose a novel interpreter system, which acts as an intermediary between the user and the swarm to simplify the user’s role in the interaction. The interpreter takes high level input drawn using gestures by the user, and translates it into low level swarm control commands. This interpreter employs machine learning, Kalman filtering and optimal control techniques to translate the user input into swarm control parameters. A notion of Human Interpretable dynamics is introduced, which is used by the interpreter for planning as well as to provide feedback to the user. The dynamics of the swarm are controlled using a novel decentralized formation controller based on distributed linear iterations and dynamic average consensus. The framework is demonstrated theoretically as well as experimentally in a 2D environment, with a human controlling a swarm of simulated robots in real time.

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.

Distributed dynamic average consensus for nonlinear multi-agent systems in the presence of external disturbances over a directed graph

This paper investigates distributed dynamic average consensus problems for a class of nonlinear multi-agent systems in the presence of local disturbances over a directed graph, where local disturbances are generated by an external system. In order to solve such problems, we establish a distributed consensus protocol based on the internal model (IM) principle such that states of the first-order nonlinear system converge to the average of multiple time-varying inputs and local disturbances are rejected. By means of Lyapunov stability theory and graph theory, a two-step mechanism is established to certify that the proposed algorithm is exponentially convergent. Furthermore, a neoteric distributed consensus algorithm is proposed to solve a dynamic average consensus problem of the second-order nonlinear multi-agent system. The proposed algorithm can guarantee that positions and velocities of the second-order nonlinear multi-agent system converge exponentially to the average of multiple time-varying inputs and their derivative and local disturbances are rejected, respectively. Finally, three numerical examples are provided to demonstrate the effectiveness of the obtained results.

Multi-stage discrete time and randomized dynamic average consensus

In this paper we propose a novel local interaction protocol which solves the discrete time dynamic average consensus problem, i.e., the consensus problem on the average value of a set of time-varying input signals in an undirected graph. The proposed interaction protocol is based on a multi-stage cascade of dynamic consensus filters which tracks the average value of the inputs with small and bounded error. We characterize its convergence properties for time-varying discrete-time inputs with bounded variations. The main novelty of the proposed algorithm is that, with respect to other dynamic average consensus protocols, we obtain the next unique set of advantages: i) The protocol, inspired by proportional dynamic consensus, does not exploit integral control actions or input derivatives, thus exhibits robustness to re-initialization errors, changes in the network size and noise in the input signals; ii) The proposed design allows to trade-off the quantity of information locally exchanged by the agents, i.e., the number of stages, with steady-state error, tracking error and convergence time; iii) The protocol can be implemented with randomized and asynchronous local state updates and keep in expectation the performance of the discrete-time version. Numerical examples are given to corroborate the theoretical findings, including the case where a new agent joins and leaves the network during the algorithm execution to show robustness to re-initialization errors during runtime.

New Internal Model Average Consensus Estimators with Light Communication Load

The dynamic average consensus problem for a group of agents is considered. Each agent in the group is supposed to estimate the average of inputs applied to all agents and the estimation should be done in a distributed way. By reinterpreting the proportional integral type estimator, a new structure for the average estimator which can embed the internal model of inputs is proposed and conditions which result in the zero estimation error in the steady state are derived. We present constructive design procedures for the cases of constant inputs and time-varying inputs employing the root locus for the former and LQR-based design for the latter. The theory is validated through numerical simulations.

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.

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent’s estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

Distributed Generalized Nash Equilibrium Seeking Algorithm Design for Aggregative Games Over Weight-Balanced Digraphs.

In this paper, two aggregative games over weight-balanced digraphs are studied, where the cost functions of all players depend on not only their own decisions but also the aggregate of all decisions. In the first problem, the cost functions of players are differentiable with Lipschitz gradients, and the decisions of all players are coupled by linear coupling constraints. In the second problem, the cost functions are nonsmooth, and the decisions of all players are constrained by local feasibility constraints as well as linear coupling constraints. In order to seek the variational generalized Nash equilibrium (GNE) of the differentiable aggregative games, a continuous-time distributed algorithm is developed via gradient descent and dynamic average consensus, and its exponential convergence to the variational GNE is proven with the help of Lyapunov stability theory. Then, another continuous-time distributed projection-based algorithm is proposed for the nonsmooth aggregative games based on differential inclusions and differentiated projection operations. Moreover, the convergence of the algorithm to the variational GNE is analyzed by utilizing singular perturbation analysis. Finally, simulation examples are presented to illustrate the effectiveness of our methods.

On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents’ reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of SCWB digraphs. We also show that for delays in the admissible bound, for static signals, the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results.

Nash equilibrium seeking for [formula omitted]-coalition noncooperative games

An N-coalition noncooperative game is formulated in this paper. In the formulated game, there are N interacting coalitions and each of them includes a set of agents. Each coalition acts as a virtual player that aims to minimize its own objective function. This objective function is defined as the sum of the agents’ local objective functions in the coalition and is a function of all the engaged agents’ actions in the game. However, the actual decision-makers are not the coalitions but the agents therein. That is, the agents within each coalition collaboratively minimize the coalition’s objective function while constituting an entity that serves as a self-interested player (i.e., the coalition) in the game among the interacting coalitions. A seeking strategy is designed for the agents to find the Nash equilibrium of the N-coalition noncooperative game. The equilibrium seeking strategy is based on an adaptation of a dynamic average consensus protocol and the gradient play. The dynamic average consensus protocol is leveraged to estimate the averaged gradients of the coalitions’ objective functions. The gradient play is then implemented by utilizing the estimated information to achieve the Nash equilibrium seeking. Convergence results are established by utilizing Lyapunov stability analysis. Numerical examples are given in supportive of the theoretical results.