Leader-following Consensus Algorithm Research Articles

Decentralized Multi-Area Economic Dispatch in Power Systems Using the Consensus Algorithm

A multi-area power system requires coordination to enhance reliability and reduce operating costs. Economic dispatch in such systems is crucial because of the uncertainties associated with variable loads and the increasing penetration of renewable energy sources. This paper presents a hierarchical consensus algorithm designed to determine the economic dispatch in a multi-area power system, accounting for the uncertainties in load and renewable generation. The proposed algorithm, which utilizes distributed agents, operates across three levels. Level 1 coordinates all areas, while levels 2 and 3 form a leader–follower consensus algorithm for overall economic dispatch. Breadth-first search is employed to identify the leader agent within each area. To address the uncertainties in loads and renewable generation, Monte Carlo simulations are performed. The efficacy of the proposed method is validated using the IEEE 39-bus and 118-bus systems, as well as a realistic 1968-bus power system in Taiwan. The traditional equal lambda method is employed to verify that the proposed approach is suitable for multi-area power systems using distributed computation.

An artificial potential field approach for event-triggered cooperative control of multiple high-speed trains with free initial states

ABSTRACT In this paper, a multi-algorithm-fusion-based cooperative tracking control strategy is proposed for high-speed trains to achieve the control objectives of reference speed trajectory tracking and adjacent safety distance maintenance simultaneously. First, the multiple high-speed train (MHST) system is formulated as a multi-agent system (MAS) with a virtual leader. Second, a coordination controller that considers the dynamic tracking performance and input saturation is designed by combining the MAS leader-follower consensus algorithm and the improved artificial potential field (APF) method. In addition, within the train-to-train (T2T) communication network, an event-triggered mechanism is introduced in the continuous state transmission process to address the communication channel capacity protection limitation issue. Third, the closed-loop stability of the MHST system is ensured by the comprehensive analysis of a novel log-type Lyapunov function. Finally, the effectiveness of the proposed event-triggered cooperative tracking control strategy is verified through a numerical example of the MHST system on a typical line.

Distributed hierarchical economic optimization approach of microgrid based on multi-agent leader-following consensus

Considering the higher generation operation cost of distributed generations (DGs) and power purchase cost in microgrid, the discrete-time mean consensus protocol (DMCP) is improved by bringing in the power offset elimination term in this paper. Then an improved multi-agent leader-following consensus algorithm (IMLCA) is proposed. The total power balance can be realized by the algorithm, which make the incremental cost (IC) of DGs converge to the consensus value quickly. Besides, the active power output objective of DGs is optimized and the overall generation operation cost of the AC microgrid is lessened. Afterwards, the distributed hierarchical economic optimization approach of microgrid based on multi-agent leader-following consensus is studied. In this approach, a distributed hierarchical framework is constructed. The economic optimization management level emits the optimal active power output objective of DGs to the droop control level. Meantime, the optimal active power output objective computed by IMLCA is carried out by using the droop control level. Thus, the active power output of DGs is apportioned reasonably. Finally, the simulation model of five-DG operation is constructed for research. The simulation results suggest that the approach can achieve the economic cost optimization goal of the grid-connected microgrid and the IMLCA possesses the better transient response performance and steady-state computation accuracy.

Leader-following consensus of multi-agent systems with connectivity-mixed attacks and actuator/sensor faults

This study investigates the leader-following consensus issue of multi-agent systems subject to simultaneous connectivity-mixed attacks, actuator/sensor faults and disturbances. Connectivity-mixed attacks are remodeled into connectivity-maintained and connectivity-paralyzed topologies in a switched version, and actuator/sensor faults are established with unified incipient-type and abrupt-type characteristics. Then, unknown input observer-based decoupling and estimation are incorporated to achieve unknown state and fault observations with the normalized technique, and the leader-following consensus-based compensation to faults, resilience to attacks and robustness to disturbances are also realized with the neighboring output information and sensor fault estimation through the distributed framework. Criteria of achieving exponential leader-following consensus of multi-agent systems under cyber-physical threats are derived with dual attack frequency and activation rate indicators. Simulation example is conducted to exemplify the validation and merits of the proposed leader-following consensus algorithm.

Cooperative control of EVs participating in demand response based on improved discrete-time leader-following consensus

As an increasing number of electric vehicles (EVs) participate in the demand response (DR) planning and control in the distribution network, the grid power imbalance is aggravated, which affects the stabilization of voltage at charging side (VCS) of EV charging stations (EVCSs). Therefore, in this paper, the cost model of EV DR and incremental cost rate (ICR) model of load response are established at first for solving the problems. Then, the ICR update criteria of agents are designed. Based on the criteria, an improved discrete-time leader-following consensus (IDTLFC) algorithm based on ICR is proposed. Also, the cooperative control method of EVs participating in DR based on the algorithm was presented. By employing the proposed algorithm, the method can calculate the ICR and response load value of agents. Likewise, the quick reduction of total system power offset and the completion of response load indicator can be achieved by utilizing the EV response layer to execute the response instructions. In the simulation experiments, the simulation model of multi-agent system based on EVs is established. The two system working modes of ”peak shaving and valley filling” (PSVF), plug-and-play characteristic of agents and so on are simulated. The results have shown that, when EV are linked to the grid and generate the power fluctuation, the total power balance and the stabilization of VCS could be kept with the method. The PSVF, minimum response cost and reasonable power distribution are realized simultaneously. The system has superior dynamic and steady-state performance, too.

A two-layer frequency control method for large-scale distributed energy storage clusters

A large number of small-capacity distributed energy storages (ESs) are expected to play an important role in grid frequency regulation. However, without suitable control scheme, it may lead to heavy computational burden and low utilizing efficiency. In this paper, a two-layer frequency control framework is proposed for large-scale distributed ESs that can be separated into several ES clusters. On the upper layer, the frequency regulation is achieved through distributed model predictive control (DMPC) among different ES clusters. The parallel computing of the distributed controllers reduces the optimization problem dimension brought by a large number of ES clusters. In addition, both the frequency deviation and rate of change of frequency are considered to achieve better frequency regulation. On the lower layer, state-of-charge (SoC) balance is considered within each cluster by the leader–follower consensus algorithm in a distributed mode, and it only requires communication between neighboring ESs in a cluster to aggregate for the upper layer. Unlike the conventional SoC balancing strategy, circulating currents are prevented to reduce the transmission losses. Moreover, a detailed small-signal model is established to show the impact of the proposed control strategy on the system stability. The effectiveness of the entire control scheme and the small-signal analysis are validated under a variety of scenarios by simulations.© 2017 Elsevier Inc. All rights reserved.

Adaptive Coalition Formation-Based Coordinated Voltage Regulation in Distribution Networks

High penetrations of photovoltaic (PV) systems can cause severe voltage quality problems in distribution networks. This paper proposes a distributed control strategy based on the dynamic formation of coalitions to coordinate a large number of PV inverters for voltage regulation. In this strategy, a rule-based coalition formation scheme deals with the zonal voltage difference caused by the uneven integration of PV capacity. Under this scheme, PV inverters form into separate voltage regulation coalitions autonomously according to local, neighbor as well as coalition voltage magnitude and regulation capacity information. To coordinate control within each coalition, we develop a feedback-based leader-follower consensus algorithm which eliminates the voltage violations caused by the fast fluctuations of load and PV generation. This algorithm allocates the required reactive power contribution among the PV inverters according to their maximum available capacity to promote an effective and fair use of the overall voltage regulation capacity. Case studies based on realistic distribution networks and field-recorded data validate the effectiveness of the proposed control strategy. Moreover, comparison with a centralized network decomposition-based scheme shows the flexibility of coalition formation in organizing the distributed PV inverters. The robustness and generalizability of the proposed strategy are also demonstrated.

Coordinated active and reactive power control for distribution networks with high penetrations of photovoltaic systems

A primary concern of the large-scale application of photovoltaic (PV) power systems in distribution networks is nodal voltage fluctuations caused by active power fluctuations of PV. Therefore, this paper proposes a novel coordinated active and reactive power optimization method for distribution networks with high penetrations of PV systems, which can reduce bus voltage fluctuations, active power curtailments of PV, operating losses of distribution networks, and adjustments of conventional voltage regulation devices such as on-load tap changers (OLTCs) and capacitor banks (CBs). The proposed method coordinates the OLTC, CBs, and PV and BESS plants in two levels. The upper level establishes a mixed integer nonlinear programming (MINP) model based on the model predictive control (MPC), which can properly plan the operation of the OLTC, CBs, and PV, and a modified NSGA-II algorithm is developed to find the best solution of the MINP model. The lower level employs the leader–follower consensus algorithm (LFCA) to coordinate the charging power and reactive power of distributed battery energy storage systems (BESSs) to control real-time bus voltage fluctuations. The LFCA based control method can make BESSs fairly participate in the real-time voltage regulation of each feeder. Case studies are conducted on a modified IEEE 33-bus distribution network system, utilizing the actual active power data of a PV plant. Simulation results indicate that the proposed method can effectively control bus voltage variations of all feeders within the pre-defined range, and the distribution network can operate with higher penetrations of PV power systems, lower losses, and better economy.

Leader-Follower Multimotor Speed Coordination via Adaptive Fuzzy Multiagent Consensus Scheme

Coordinated speed of interconnected motors has vast application in the industry. Typically, the smooth operation of the system relies on the coordinated speed of the multiple motors such as the conveyer belt system. Thus, the problem to have coordinated speed in a network-connected motor is mostly dealt with wire-connected architectures such as cross coupling. The presented study suggests a unique design to deal with the said problem by proposing a network model consisting of a DC chopper drive, termed as an ith agent of a network, while a leader-follower multiagent consensus algorithm is used, in a supervisory role, to ensure coordinated speed. Moreover, a hybrid controller (Fuzzy MRAC-RST), composed of Fuzzy logic controller, pole placement controller (F-RST), along with model reference adaptive controller (MRAC), is used to control the ith agent. The proposed hybrid controller along with MAS consensus algorithm forms an adaptive tracking performance and ensure coordinated speed. The MATLAB platform is used for simulation purpose, and the obtained results validate the design concept.

Distributed Global Economical Load Sharing for a Cluster of DC Microgrids

This paper addresses a fully distributed hierarchical coordination controller, which minimizes the global total generation cost (TGC) for a cluster of DC microgrids (MGs) through handling the optimal power-sharing between MGs. It consists of local and global tertiary controllers, in which a two-layer communication network is modeled to share information with a reduced complexity as one or some distributed generators (DGs) of each MG are pinned from the local network to broadcast the information between MGs at the global network. Under this control structure, the global tertiary controllers, based on dynamic consensus technique, generate the global optimum incremental cost (IC) reference to attain the entire cluster's economic operation. Moreover, using pinning-based leader-follower consensus algorithm, the local tertiary controllers assign MG average voltage reference at which the ICs of all DGs are matched at the global reference to ensure optimal operation of the cluster with considering DGs generation boundaries. Finally, the nominal voltage set points of each DG can be determined by the secondary controller to guarantee the generation-demand power balance. The feasibility of the proposed controller is demonstrated by simulation and experiment under various test scenarios.

Leader-following consensus control of position-constrained multiple Euler-Lagrange systems with unknown control directions

This paper studies the distributed leader-following consensus control problems of position-constrained multiple Euler-Lagrange Systems (ELSs) with unknown control directions. The objective of our discussion is to develop a consensus protocol despite the existence of position constraints and unknown control directions in each agent. Most of the existing works related to state constraints are for single systems and rare results are concerned about multi-agent systems. With the help of the barrier Lyapunov function, Nussbaum gain adjusting technique, and adaptive control methodology, a novel leader-following consensus algorithm is successfully designed to make sure the convergence to zero of the consensus errors and the boundedness of the signals in the closed-loop system. Moreover, the position constraints for each agent are never violated for all time during the control process. The effectiveness of the main result is illustrated by a practical mechanical system.

Leader–Follower Consensus Control of Multiple Quadcopters Under Communication Delays

This paper develops a novel decentralized leader–follower consensus algorithm for multiple-quadcopter systems under uniform constant and asynchronous time-varying communication delays. The consensus problem is formulated as the stability analysis and static controller design problem of a delayed system by defining the consensus error dynamics. Lyapunov-based methods along with the linear matrix inequality (LMI) techniques are utilized to derive the sufficient conditions for the control gain design that ensure asymptotic consensusability in the constant delay case, and consensus with bounded errors in the time-varying delay case. Also the computational complexity of solving control gains can be significantly reduced by decomposing the sufficient conditions into a set of equivalent low-dimensional conditions under undirected communication topologies. Simulation results show that larger systems are generally more susceptible to communication delays, and systems are more robust to delays when more followers are directly connected to the leader.

Granular load‐side frequency control with electric spring aggregators and leader–follower consensus

To utilise load-side control for frequency regulation in transmission networks, the designed control schemes need to be granulated down to the subtransmission level as only aggregate loads are used on the transmission level. Moreover, due to a higher R/X ratio in subtransmission networks, the active power changes caused by frequency control will influence bus voltages. To achieve the required active power response and regulate bus voltages, a control scheme is proposed for subtransmission networks by adopting electric spring (ES) aggregators consisting of ESs and non-critical loads. To implement the dual goals, the ES voltage of each ES aggregator is decoupled into d and q components. A distributed leader-following consensus algorithm is adopted for ES aggregators to control its active power consumption by sharing information with neighbouring aggregators. The d component of the ES voltage is adjusted accordingly to provide the required active power cooperatively. To avoid the consequent voltage variation, decentralised proportional–integral (PI) control is adopted for ES aggregators to adjust the q component of the ES voltage accordingly. Simulation results show that ES aggregators manage to achieve the required coordinated active power response to regulate frequency and keep bus voltages within the acceptable region under the proposed control method.

A Cooperative Charging Protocol for Onboard Supercapacitors of Catenary-Free Trams

Catenary-free trams with an onboard supercapacitor have been an emerging and energy-efficient way for urban rail transportation. However, the high-power charging load from catenary-free trams brings a new challenge to the design of charging systems. The traditional single-module charging system typically suffers from a high power and thermal pressure, which reduces the reliability of the charging system. In this paper, we propose a multimodule charging system to improve the system reliability by decomposing power pressure to multiple charging modules. Specifically, a cooperative charging protocol is proposed to improve the dynamic performance of the charging system by suppressing the current imbalance and avoiding the current overshoot during the startup process. First, we mathematically model the multimodule charging system using the state-space averaging method and graph theory. Second, the cooperative charging protocol is designed using the leader–follower consensus algorithm, where the virtual leader represents the desired charging current for each module with a warm-start mechanism. Third, multiple-input multiple-output root locus technique is exploited to characterize the dynamic performance of the charging system. Both simulation and experiment results show that the proposed protocol effectively suppresses the imbalance and avoids the overshoot during the startup of the charging system.

Distributed Algorithms for Searching Generalized Nash Equilibrium of Noncooperative Games.

In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players' actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Aggregated Energy Storage for Power System Frequency Control: A Finite-Time Consensus Approach

In future power systems, widespread small-scale energy storage systems (ESSs) can be aggregated to provide ancillary services. In this context, a new load frequency control scheme which incorporates the energy storage aggregator (ESA) and its associated disturbance observer is proposed. The disturbance observer is designed to supplement the secondary frequency control for the ESA, therefore the system frequency response and recovery can be improved. Within the ESA, a finite-time leader–follower consensus algorithm is proposed to control the small-scale ESSs via sparse communication networks. This algorithm ensures that the ESA tracks the frequency control signals, while the state-of-charge among each ESS is balanced in finite-time. The external characteristics of the ESA will resemble to that of one large-scale ESS. Numerical examples demonstrate the convergence of the ESA under different communication graphs. The effectiveness of the entire scheme for power system frequency control is validated under a variety of scenarios that include contingency and normal operation.

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Sampled-data based consensus for multiple harmonic oscillators with directed switching topology

This paper investigates the distributed consensus problem for a group of harmonic oscillators under directed switching topology. First, under the assumption that the union of the directed interaction graphs has a spanning tree, a class of sampled-data based consensus protocols are designed by using motion planning approaches and Pontryagin’s principle. The proposed protocols only require that the union of communication topologies switched at the sampled instants has a spanning tree, without requiring information exchanges over the sampled interval and the connectivity of communication topology at each sampling instant. Then, the distributed consensus problem can be solved under directed switching topology by using stability principle and the properties of stochastic matrixes. Compared with the existing sampled-data based consensus algorithms, in this article, a remarkable advantage is that, for the proposed sampled-data based protocols, the sampled periods, communication topologies and control gains are decoupling and can be separately designed, which relaxes many restrictions in controller designs. Finally, as an extension of the leaderless consensus protocols, a leader-following consensus algorithm is further proposed in this paper. Some numerical examples are also given to illustrate the effectiveness of the analytical results.

Event Triggered Multi-Agent Consensus of DC Motors to Regulate Speed by LQR Scheme

In the presented paper, the leader-following consensus algorithm of a multi-agent system (MAS) is used along with the centralized event-triggering scheme to make the speed of the network-coupled multiple-motors synchronizable. In the proposed method, the updates for the controller are event-driven based on local information. Moreover, the basic consensus protocol is also revised such that the speed information of the motors is used in order to reach identical speed. The main benefit of the planned event-triggered methodology is the energy saving by avoiding the continuous control of the system. As far as stability analysis of the system is concerned, a common Lyapunov function is incorporated to validate stability. The acquired results endorse the success of the proposed methodology.

Distributed consensus of non‐linear fractional‐order multi‐agent systems with directed topologies

In this study, Mittag–Leffler stability and the fractional Lyapunov direct method are used to study fractional-order leaderless and leader-following consensus algorithms with non-linear dynamics under a directed network topology. The sufficient conditions are given to guarantee that the consensus can be achieved in the non-linear fractional-order systems with and without a virtual leader, and the adaptive feedback control protocols are also given in this study. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.