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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. [ABSTRACT FROM AUTHOR]

Distributed generators are integrated into microgrids or geographically distributed subsystems in active distribution networks and may belong to various entities. Centralized solutions cannot meet future requirements such as high resilience and privacy protection. Therefore, fully distributed economic dispatch (ED) methods are needed and most existing algorithms exhibit linear or sublinear convergence. This paper introduces an efficient fully distributed dynamic ED solution for minimizing photovoltaic power curtailment, based on a parallel primal-dual interior-point algorithm with a quasi-Newton technique. In this method, each area optimizes its own problem with limited information exchanged with its neighbors, and no central coordinator is needed. Based on a peer-to-peer communication paradigm, this method can achieve a global optimum while the privacy of each area is obliquely protected. Numerical tests demonstrated that the algorithm outperforms gradient-based methods such as ADMM and maintains stability under a partial communication failure. [ABSTRACT FROM AUTHOR]

Although there are vast potential locations to install FACTS devices in a power system, the actual installation number is very limited due to economical consideration. Therefore the allocation strategy exhibits strong sparsity. This paper formulates FACTS device allocation problem as a general sparsity-constrained OPF problem and employs Lq(0< q\leq 1) norms to enforce sparsity on FACTS devices setting values to achieve solutions with desirable device numbers and sites. An algorithm based on alternating direction method of multipliers is proposed to solve the sparsity-constrained OPF problem. The algorithm exploits the separability structure and decomposes the original problem into an NLP subproblem, an Lq regularization subproblem, and a simple dual variable update step. The NLP subproblem is solved by the interior point method. The Lq regularization subproblem has a closed-form solution expressed by shrinkage-threholding operators. The convergence of the proposed method is theoretically analyzed and discussed. The proposed method is successfully tested on allocation of SVC, TCSC, and TCPS on IEEE 30-, 118-, and 300-bus systems. Case studies are presented and discussed for both single-type and multiple-type FACTS devices allocation problems, which demonstrates the effectiveness and efficiency of the proposed formulation and algorithm. [ABSTRACT FROM PUBLISHER]