A theory of tie‐set graph and its application to information network management

SUMMARYIn this paper, a novel decentralized algorithm is proposed to minimize power flow loss in a large-scale future grid connecting with many real-time-distributed generation systems by which power flows bi-directionally. The DC-power loss at each link is defined as the product of resistance and the square of current that can be considered as a quadratic flow cost. We employ the notion of tie-sets that reduces the complexity of the power flow loss problem by dividing a power network into a set of loops that forms a linear vector space on which the power loss problem can be formulated as a convex optimization problem. As finding a solution in each tie-set enables global optimization, we realize parallel computing within a system of independent tiesets by integrating autonomous agents. Simulation results demonstrate the minimization of the power loss on every link by iteratively optimized power flows and show the superiority against the traditional centralized optimization scheme.

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“…Tie-set graph theory is proposed in [12,28] and used in many applications such as [29,30]; we provide its brief review.…”

Section: Tie-set Graph Theorymentioning

confidence: 99%

Distributed power flow loss minimization control for future grid

Nakayama

Zhao

Bic

et al. 2014

Circuit Theory & Apps

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“…The CGF optimization problem is now to find the value of g * i (t) that minimizes ψ(g i (t), t) at each node i ∈ V λ subject to the above constraints (11) and (12). We take a derivative of ψ(g i (t), t) at i ∈ V λ at time t. ∂ψ ∂g i (t) (g i (t), t) = 0…”

Section: )) (13)mentioning

confidence: 99%

Distributed Real-Time Power Flow control with renewable integration

Nakayama

Zhao

Bic

et al. 2013

2013 IEEE International Conference on Smart Grid Communications (SmartGridComm)

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Abstract-We formulate an Optimal Real-Time Power Flow (ORPF) problem that integrates renwable energy generation and energy storage. In the ORPF problem, we seek to minimize the costs of energy storage and of power generation from fossil fuel that are required to balance the loads and generation from renewable sources. We present a novel decentralized algorithm for this problem, using tie-set graph theory. Tie-set graph theory significantly reduces the complexity of the ORPF problem by dividing a power network into a set of independent loops referred to as "tie-sets." Simulation results demonstrate real-time power production responses and flow controls that lead to reliable use of battery systems and reduce the cost of using fossil fuel.

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“…There have been previous works that focus on tie-sets in bi-connected graph [22], [23]. Those studies show graph theoretical nature of underlying loops in a network, and indicates possibilities of conducting optimal local network management based on tie-sets.…”

Section: Introductionmentioning

confidence: 98%

An Autonomous Distributed Control Method for Link Failure Based on Tie-Set Graph Theory

Nakayama

Shinomiya

Watanabe

2012

IEEE Trans. Circuits Syst. I

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This study proposes an autonomous distributed control method for single link failure based on loops in a network. This method focuses on the concept of tie-sets defined by graph theory in order to divide a network into a string of logical loops. A tie-set denotes a set of links that constitutes a loop. Based on theoretical rationale of graph theory, a string of tie-sets that cover all the nodes and links can be created by using a tree, even in an intricately-intertwined mesh network. If tie-sets are used as local management units, high-speed and stable fail-over can be realized by taking full advantage of ring-based restoration. This paper first introduces the notion of tie-sets, and then describes the distributed algorithms for link failure. Experiments are conducted against Rapid Spanning Tree Protocol (RSTP), which is generally used for fault recovery in mesh topological networks. Experimental results comparing the proposed method with RSTP suggest that our method alleviates the adverse effects of link failure with a modest increase in state information of a node.

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A theory of tie‐set graph and its application to information network management

Cited by 19 publications

References 4 publications

Distributed power flow loss minimization control for future grid

Distributed power flow loss minimization control for future grid

Distributed Real-Time Power Flow control with renewable integration

An Autonomous Distributed Control Method for Link Failure Based on Tie-Set Graph Theory

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