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An autonomous distributed control method based on tie‐set graph theory in future grid

In future power grids where electricity flows bidirectionally, the essential problem is to maximize the total efficiency of distributed energy resources. In complicated and large‐scale systems such as modern power distribution networks, maximizing the efficiency of the entire system as a whole is extremely difficult. To solve the global optimization problem of such a complex network, this paper proposes an efficient distributed control method for future grid on the basis of tie‐set graph theory, where a tie‐set is a set of all the edges in a loop of a graph. On the basis of tie‐set graph theory, global optimization of an entire network can be realized as a result of local optimization in μ‐dimensional liner vector space, where μ is the nullity of the underlying graph of a power network. Although each tie‐set has its limited local information, an entire network is gradually optimized in an orderly manner because of the theoretical basis of a tie‐set graph. Simulation results of several thousand‐node networks demonstrate balanced allocation of dispersed energy resources and thus effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.