This paper presents a fully distributed reactive power optimization algorithm that can obtain the global optimum solution of nonconvex problems for distribution networks (DNs) without requiring a central coordinator. Second-order conic relaxation is used to achieve exact convexification. A fully distributed second-order cone programming solver (D-SOCP) is formulated corresponding to the given division of areas based on the alternating direction method of multipliers (ADMM) algorithm, which is greatly simplified by exploiting the structure of active DNs. The problem is solved for each area with very little interchange of boundary information between neighboring areas. D-SOCP is extended by using a varying penalty parameter to improve convergence. A proof of its convergence is also given. The effectiveness of the method is demonstrated via numerical simulations using the IEEE 69-bus, 123-bus DNs, and a real 1066-bus distribution system.

The growing interconnections of regional power systems and the large-scale integration of wind energy bring about the critical need to coordinate multiarea generation unit and tie-line scheduling (MAUTS). It is recognized that because of the limitations on private data exchange and model management, it is suitable to address the multiarea power scheduling problem in a decentralized way. In this paper, the MAUTS problem is formulated using the adaptive robust optimization (RO) scheme to account for uncertain wind energy. Our model is decomposed into regional subproblems by augmented Lagrangian decomposition (ALD), which enables a fully distributed computation within an alternating direction multiplier method framework. To address the nonconvexity issue, a tractable alternating optimization procedure (AOP) is developed to obtain high-quality solutions with finite convergence for the nonconvex mixed-integer problem. Simulations on different test systems are conducted to show the computational performance, the solution quality, and scalability of the proposed method.

With the integration of distributed generation systems, distribution networks and transmission networks have become more coupled, especially, with respect to voltage problems. This paper presents a decentralized reactive power optimization method for integrated transmission networks and distribution networks based on the generalized Benders decomposition (GBD). The second-order conic programming relaxation technique is used to make the subproblem (distribution network model) convex, which can guarantee that the GBD process converges. An improved GBD iteration procedure is proposed by exploiting the special structure of the problem, which does not need to generate optimal cut. Moreover, a revised feasible cut generating approach is also developed to improve the efficiency. Theoretical analysis and numerical tests show that the convergence of this decentralized method is guaranteed and the coordinated optimization scheme outperforms conventional separated methods by eliminating overvoltage and reducing network loss in the active distribution network.

As large scale distributed energy resources are integrated into distribution networks, coordinated dynamic economic dispatch (DED) for integrated transmission and distribution networks is becoming essential. In this paper, we describe a transmission and distribution network coordinated DED model and propose an efficient decentralized method to solve this problem using multi-parametric quadratic programming. In the proposed method, only boundary variables are exchanged between transmission and distribution networks so that the privacy between different operators can be guaranteed. A revised procedure is developed based on the characteristics of the distribution network problem, which can significantly accelerate the iteration. An effective method for dealing with degeneracy in multi-parametric programming is also proposed. Numerical tests demonstrate that the proposed method can achieve a global optimal solution and that the coordinated DED method can provide additional economic benefits compared with the isolated economic dispatch method. Furthermore, the computational performance of the proposed method is far superior to some popular decentralized methods in terms of both iteration number and computation time.

Distributed generator (DG) volatility has a great impact on system operation, which should be considered beforehand due to the slow time scale of distribution network reconfiguration (DNR). However, it is difficult to derive accurate probability distributions (PDs) for DG outputs and loads analytically. To remove the assumptions on accurate PD knowledge, a deep neural network is first devised to learn the reference joint PD from historical data in an adaptive way. The reference PD along with the forecast errors are enveloped by a distributional ambiguity set using Kullback-Leibler divergence. Then a distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set. The result inherits the advantages of stochastic optimization and robust optimization. Finally, a modified column-and-constraint generation method with efficient scenario decomposition is investigated to solve this model. Numerical tests are carried out using an IEEE unbalanced benchmark and a practical-scale system in Shandong, China. Comparison with the deterministic, stochastic and robust DNR methods validates the effectiveness of the proposed method.

The rapid growth of renewables and dynamic loads has highlighted the short-term voltage stability (STVS) issue in distribution network operation. With the advances in metering, communication and control technologies, deep learning-based distribution network reconfiguration (DNR) becomes available to maintain secure and economic system operation. However, STVS is traditionally evaluated for a specific network topology using time-domain simulations, which cannot be expressed explicitly as a function for optimization, making it intractable to consider STVS in DNR. In this paper, an efficient deep learning-based method is proposed to address this issue. An STVS evaluation network is customized from deep convolution neural networks (CNNs) and trained to learn the relationship between network topology and STVS performance from historical data. To find the optimal topology, a well-trained evaluation network is applied in DNR, where STVS with various network topologies is evaluated without resorting to time-domain simulations. Then, the number of candidate topologies is significantly reduced by a threshold of STVS performance, which enables the direct solution of the DNR for STVS enhancement. The application of the proposed method in large-scale systems is also discussed via integration with heuristic algorithms. Case studies of a modified 69-bus distribution system and a real large-scale distribution system validate the necessity of considering STVS enhancement in DNR and the effectiveness of the proposed solution method.