This paper proposes two second-order continuous-time algorithms to solve the economic power dispatch problem in smart grids. The collective aim is to minimize a sum of generation cost function subject to the power demand and individual generator constraints. First, in the framework of nonsmooth analysis and algebraic graph theory, one distributed second-order algorithm is developed and guaranteed to find an optimal solution. As a result, the power demand constraints can be kept all the time under appropriate initial condition. The second algorithm is under a centralized framework, and the optimal solution is robust in the sense that different initial power conditions do not change the convergence of the optimal solution. Finally, simulation results based on five-unit system, IEEE 30-bus system, and IEEE 300-bus system show the effectiveness and performance of the proposed continuous-time algorithms. The examples also show that the convergence rate of second-order algorithm is faster than that of first-order distributed algorithm.

This article proposes a novel distributed approach to solve a new dynamic economic dispatch problem (DEDP) in which environmental cost function and ramp rate constraints are taken into consideration in islanded microgrid. In our proposed optimization model, the environmental cost function with E-exponential term and ramp rate constraints are considered to make the optimization problem more practical. Then a novel fully distributed algorithm is proposed to address the DEDP based on the alternating direction method of multipliers (ADMM) and distributed consensus theory of the multi-agents system.A Lambert $W$ function is employed to tackle the E-exponential term in the environmental cost function which is different from most existing papers which discuss the DEDP only with quadratic cost functions; A parallel projection method on account of ADMM is used to deal with the ramp rate constraints in this paper. In addition, the power balance can be guaranteed at every time when the sum of initial powder output is equal to the total demand. Therefore, the proposed algorithm can deal with the supply-demand constraints, capacity limit constraints and ramp rate constraints. Finally, simulations on IEEE14-bus is introduced to further illustrate the effectiveness of the proposed algorithm.

Based on the multiagent networks, this paper introduces a continuous-time algorithm to deal with distributed convex optimization. Using nonsmooth analysis and algebraic graph theory, the distributed network algorithm is modeled by the aid of a nonautonomous differential inclusion, and each agent exchanges information from the first-order and the second-order neighbors. For any initial point, the solution of the proposed network can reach consensus to the set of minimizers if the graph has a spanning tree. In contrast to the existing continuous-time algorithms for distributed optimization, the proposed model holds the least number of state variables and relaxes the strongly connected weighted-balanced topology to the weaker case. The modified form of the proposed continuous-time algorithm is also given, and it is proven that this algorithm is suitable for solving distributed problems if the undirected network is connected. Finally, two numerical examples and an optimal placement problem confirm the effectiveness of the proposed continuous-time algorithm.

In the multimicrogrids environment, this brief proposes a distributed power management strategy to minimize a sum of generation costs function subject to generator constraints, which includes the supply-demand balance constraint, the individual constraint, the capacity constraint, and the ramp-rate constraint. First, under the framework of discontinuous dynamical system, a distributed primal-dual consensus algorithm is discussed. Then, using the property of Laplacian matrix, it is proven that the algorithm is any-time, which indicates that supply-demand balance is not disturbed. Based on theory of dynamical system, the proposed algorithm is proven to be stable, and the optimization capabilities of the distributed primal-dual consensus algorithm are also discussed. Finally, case studies based on IEEE 30-bus, IEEE-57 bus, and IEEE 300-bus system show the effectiveness and performance of the proposed distributed primal-dual consensus algorithm.

In this article, a new projection neural network (PNN) for solving L₁-minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs.