where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN, University of Cambridge Biological Physics ARTHUR F. HEBARD, University of Florida Condensed Matter Physics (Experimental) RANDALL D. KAMIEN, University of Pennsylvania Soft Condensed Matter DANIEL KLEPPNER, Massachusetts Institute of Technology Atomic, Molecular, and Optical Physics (Experimental) PAUL G. LANGACKER, Institute for Advanced Study, Princeton University Particle Physics (Theoretical) VERA LÜTH, Stanford University Particle Physics (Experimental) DAVID D. MEYERHOFER, University of Rochester Physics of Plasmas and Matter at High-Energy Density WITOLD NAZAREWICZ, University of Tennessee, Oak Ridge National Laboratory Nuclear Physics JOHN H. SCHWARZ, California Institute of Technology Mathematical Physics FRIEDRICH-KARL THIELEMANN, Universität Basel Astrophysics Senior Assistant Editor: DEBBIE BRODBAR, APS Editorial Office American Physical Society

Reviews of Modern Physics

Microgrids consist of multiple parallel-connected distributed generation (DG) units with coordinated control strategies, which are able to operate in both grid-connected and islanded modes Microgrids are attracting considerable attention since they can alleviate the stress of main transmission systems, reduce feeder losses, and improve system power quality When the islanded microgrids are concerned, it is important to maintain system stability and achieve load power sharing among the multiple parallel-connected DG units However, the poor active and reactive power sharing problems due to the influence of impedance mismatch of the DG feeders and the different ratings of the DG units are inevitable when the conventional droop control scheme is adopted Therefore, the adaptive/improved droop control, network-based control methods, and cost-based droop schemes are compared and summarized in this paper for active power sharing Moreover, nonlinear and unbalanced loads could further affect the reactive power sharing when regulating the active power, and it is difficult to share the reactive power accurately only by using the enhanced virtual impedance method Therefore, the hierarchical control strategies are utilized as supplements of the conventional droop controls and virtual impedance methods The improved hierarchical control approaches such as the algorithms based on graph theory, multi-agent system, the gain scheduling method, and predictive control have been proposed to achieve proper reactive power sharing for islanded microgrids and eliminate the effect of the communication delays on hierarchical control Finally, the future research trends on islanded microgrids are also discussed in this paper

/pdf/review-of-active-and-reactive-power-sharing-strategies-in-15l30c1smy.pdf

Review of Active and Reactive Power Sharing Strategies in Hierarchical Controlled Microgrids

Distributed coordination control is the current trend in networked systems and finds prosperous applications across a variety of fields, such as smart grids and intelligent transportation systems. One fundamental issue in coordinating and controlling a large group of distributed and networked agents is the influence of intermittent interagent interactions caused by constrained communication resources. Event-triggered communication scheduling stands out as a promising enabler to strike a balance between the desired control performance and the satisfactory resource efficiency. What distinguishes dynamic event-triggered scheduling from traditional static event-triggered scheduling is that the triggering mechanism can be dynamically adjusted over time in accordance with both available system information and additional dynamic variables. This article provides an up-to-date overview of dynamic event-triggered distributed coordination control. The motivation of dynamic event-triggered scheduling is first introduced in the context of distributed coordination control. Then some techniques of dynamic event-triggered distributed coordination control are discussed in detail. Implementation and design issues are well addressed. Furthermore, this article exemplifies two applications of dynamic event-triggered distributed coordination control in the fields of microgrids and automated vehicles. Several challenges are suggested to direct the future research.

Dynamic Event-Triggered Distributed Coordination Control and its Applications: A Survey of Trends and Techniques

In this paper, an agent-based decentralized control model for islanded microgrids (MGs) is proposed, which consists of a two-layer control structure. The bottom layer is the electrical distribution MG, while the top layer is the communication network composed of agents. An agent is regarded as a local control processor together with communication devices, so agents can collect present states of distributed generators (DGs) and loads when communication lines are added between two layers. Moreover, each agent can also exchange information with its neighboring agents of the network. After information is processed according to control laws, agents adjust the production of DGs to which they connect. Further, a systematic method is presented, which can be used to derive a set of control laws for agents from any given communication network, after the rules to establish the communication network are given. Furthermore, it has been seen that the output power supplied by DGs satisfies the load demand in the MG when agents use the proposed control laws. Finally, the simulation results show that frequency and voltage fluctuations are small and meet the requirements.

/pdf/agent-based-decentralized-control-method-for-islanded-3st2pb2raq.pdf

Agent-Based Decentralized Control Method for Islanded Microgrids

In this paper, cost-based droop schemes are proposed, to minimize the total active power generation cost in an islanded microgrid (MG), while the simplicity and decentralized nature of the droop control are retained. In cost-based droop schemes, the incremental costs of distributed generators (DGs) are embedded into the droop schemes, where the incremental cost is a derivative of the DG cost function with respect to output power. In the steady state, DGs share a single common frequency, and cost-based droop schemes equate incremental costs of DGs, thus minimizing the total active power generation cost, in terms of the equal incremental cost principle. Finally, simulation results in an islanded MG with high a penetration of intermittent renewable energy sources are presented, to demonstrate the effectiveness, as well as plug and play capability of the cost-based droop schemes.

/pdf/cost-based-droop-schemes-for-economic-dispatch-in-islanded-wgzzu80bzz.pdf

Cost-Based Droop Schemes for Economic Dispatch in Islanded Microgrids

Optimization modeling for dynamic price based demand response in microgrids

In this paper, a two-layer network and distributed control method is proposed, where there is a top-layer communication network over a bottom-layer microgrid. The communication network consists of two subgraphs, in which the first is composed of all agents, while the second is only composed of controllable agents. The distributed control laws derived from the first subgraph guarantee the supply–demand balance, while further control laws from the second subgraph reassign the outputs of controllable distributed generators, which ensure active and reactive power are dispatched optimally. However, for reducing the number of edges in the second subgraph, generally a simpler graph instead of a fully connected graph is adopted. In this case, a near-optimal dispatch of active and reactive power can be obtained gradually, only if controllable agents on the second subgraph calculate set points iteratively according to our proposition. Finally, the method is evaluated over seven cases via simulation. The results show that the system performs as desired, even if environmental conditions and load demand fluctuate significantly. In summary, the method can rapidly respond to fluctuations resulting in optimal power sharing.

/pdf/networked-and-distributed-control-method-with-optimal-power-46jwmap5wr.pdf

Networked and Distributed Control Method With Optimal Power Dispatch for Islanded Microgrids

In islanded microgrids (MGs), the reactive power cannot be shared proportionally among distributed generators (DGs) with conventional droop control, due to the mismatch in feeder impedances. For the purpose of proportional reactive power sharing, a multiagent system (MAS)-based distributed control model for droop-controlled MGs is proposed. The proposed control model consists of two layers, where the bottom layer is the electrical distribution MG, while the top layer is a communication network composed of agents. Moreover, agents on the communication network exchange the information acquired from DGs with neighbors, and calculate set points for DGs they connect to, according to the control laws. Furthermore, a theorem is demonstrated, which yields a systematic method to derive the control laws from a given communication network. Finally, three cases are carried out to test the performance of the control model, in which the uncertainty of intermittent DGs, variations in load demands, as well as impacts of time delays are considered. The simulation results demonstrate the effectiveness of the control model in proportional reactive power sharing, and the plug and play capability of the control model is also verified.

/pdf/multiagent-based-reactive-power-sharing-and-control-model-31ejac3qfs.pdf

Minyou Chen

Papers

Agent-Based Decentralized Control Method for Islanded Microgrids

Cost-Based Droop Schemes for Economic Dispatch in Islanded Microgrids

Optimization modeling for dynamic price based demand response in microgrids

Networked and Distributed Control Method With Optimal Power Dispatch for Islanded Microgrids

Multiagent-Based Reactive Power Sharing and Control Model for Islanded Microgrids