An analysis of delay-constrained consensus-based optimal algorithms in virtual power plants.

In virtual power plants (VPPs), consensus-based distributed optimal dispatch algorithms aim to collectively minimize the operating cost. As ubiquitous latency on communication networks may lead to divergence, convergence to a nonoptimal solution, or a longer convergence time, mitigating the impacts of arbitrarily large but bounded time-varying delays is significant both in theory and in practice. To modify a typical consensus-based optimal dispatch algorithm under time-varying delays, this paper designs new update rules and introduces a reduction approach to evaluate the performance of the algorithm. The results reveal that the modified algorithm can always converge to the optimal solution with a tactical initial setup in a distributed manner if the undirected interaction topology is connected and the gain parameter is sufficiently small. The analytical expression of the gain is also given. Furthermore, we show that the convergence time is determined by the maximum time delays, the number of generators, and the convergence accuracy. Several numerical simulation studies validate our theory.

Model-Driven Architecture of Extreme Learning Machine to Extract Power Flow Features.

Probabilistic power flow (PPF) calculation is an important power system analysis tool considering the increasing uncertainties. However, existing calculation methods cannot simultaneously achieve high precision and fast calculation, which limits the practical application of the PPF. This article designs a specific architecture of the extreme learning machine (ELM) in a model-driven pattern to extract the power flow features and therefore accelerate the calculation of PPF. ELM is selected because of the unique characteristics of fast training and less intervention. The key challenge is that the learning capability of the ELM for extracting complex features is limited compared with deep neural networks. In this article, we use the physical properties of the power flow model to assist the learning process. To reduce the learning complexity of the power flow features, the feature decomposition and nonlinearity reduction method is proposed to extract the features of the power flow model. An enhanced ELM network architecture is designed. An optimization model for the hidden node parameters is established to improve the learning performance. Based on the proposed model-driven ELM architecture, a fast and accurate PPF calculation method is proposed. The simulations on the IEEE 57-bus and Polish 2383-bus systems demonstrate the effectiveness of the proposed method.