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In this paper, a consensus based fully distributed optimization algorithm is proposed for solving economic dispatch problem (EDP) in smart grid. Since the incremental cost of all buses reach consensus when the optimal solution is achieved, it is selected as a consensus variable. An additional variable at each bus, called "surplus" is added to record the local power mismatch, which is used as a feedback variable to purse the balance between power supply and demand. Different from most of the existing distributed methods which require the communication network to be balanced, the algorithm uses a row random matrix and a column random matrix to precisely steer all the agents to asymptotically converge to a global optimal solution over a time‐varying directed communication network. Due to the use of a fixed step size, the proposed algorithm also outperforms other algorithms in terms of convergence speed. The graph and eigenvalue perturbation theories are employed for the algorithm convergence analysis, and the upper bound of the parameters required for convergence is given theoretically. Finally, the performance and scalability of the proposed distributed algorithm are verified by several case studies conducted on the IEEE 14‐bus power system and a 200‐node test system. [ABSTRACT FROM AUTHOR]

Alternating direction method of multipliers (ADMM) has been widely used for solving the distributed optimisation problems. This paper proposes a novel distributed ADMM algorithm to solve the distributed optimisation problems consisting of convex cost functions under an undirected connected graph. The proposed algorithm adopts the concepts of predecessors and successors in the distributed sequential ADMM algorithm, but changes the sequential updating manner to a parallel one, which allows the agents to update their local states and dual variables in a completely distributed and parallel manner. This brings some benefits when solving large‐scale optimisation problems. Variational inequality is applied to analyse the convergence of agents' states. It is proved that the states of all the agents converge to the optimal point, and the global cost function converge to the optimal value at a rate of O(1/k)$O(1/k)$. Numerical experiments are given to show the effectiveness and suitability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A distributed cooperative control paradigm is proposed to handle the load sharing and transmission power loss optimisation‐based optimal power flow (OPF) problems in DC microgrids, which is based on a distributed finite‐time average consensus algorithm and a linear variable weighted summation algorithm. Firstly, an OPF problem is formulated to minimise the global transmission power loss, which is then solved by a novel distributed OPF regulator in secondary control. Furthermore, a distributed OPF considering load sharing controller is proposed in secondary control, which aims to guarantee that the load sharing deviation is limited to the assigned permissible range and the global transmission power loss is reduced to a minimum simultaneously. Compared to existing methods, these two control algorithms are developed in a completely distributed fashion, and the load distribution matrix and conductance matrix of DC microgrids are not needed. The effectiveness of the proposed control methods is verified by simulation results. [ABSTRACT FROM AUTHOR]