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The global environmental concern has promoted the installed capacity of renewable energy to explode. The uncertainty of the growing renewable energy poses a risk of incorrect forecasting of clearing prices and misled strategies to participants in the deregulated power markets. However, the transmission loss and the correlation among integrated wind power outputs are ignored in the existing research. To improve the forecasting accuracy, this paper presents a Markov Chain Monte Carlo method for stochastic LMP considering the correlation among wind power outputs and transmission loss. The expectation of an LMP with a given precision can be obtained from the proposed method. The case study verifies the validity of the proposed method, demonstrating that the squared Euclidean distance of the selected Archimedean Copula function is limited to 9.3143. Additionally, given the same convergence criteria, the sampling times are reduced by an order of magnitude compared to the Acceptance-Rejection sampling method.

Reliability evaluation of a hybrid AC/DC grid (HADG) with renewable energy is critical because of prevailing uncertainties and complex operations of voltage source converter-based high voltage direct current (DC) transmission. We propose an interval reliability evaluation model to accelerate the speed of HADG reliability evaluation with uncertainties. First, the general nonconvex optimal load shedding (OLS) model is linearized. Second, the linearized OLS model is converted into an interval model, which is decomposed into two bi-level sub-models to quantify the impact of renewable energy uncertainties at HADG. Third, an Average and Scattered Sampling-Adaptive Importance Sampling (AS-AIS) algorithm is proposed to accelerate the convergence of the reliability evaluation. Simulation results for several test systems show the effectiveness and computational tractability of the proposed interval reliability model.

This brief develops a novel interval power flow model in the presence of both uncertain network reactance and power injections. To reduce the interval growth of the interval operators, the traditional DC power flow equations are lifted into a higher dimensional space, where the admittance matrix is split into three parts and interval linear equations are with a higher dimension. Furthermore, an iteration method is designed to solve the proposed model and the convergence is strictly proved and guaranteed. Numerical studies on several test systems show the effectiveness of the proposed model.

A network inference problem focuses on discovering the structure of a diffusion network from observed cascades. This problem is significantly more challenging in several settings in which this type of an inference is desirable or necessary because of heterogeneity in the diffusion process. The heterogeneity of the diffusion process in different life stages results in the inaccuracy of a common assumption of constant influence strength. In this study, a Life Stage Heuristic (LSH) method is proposed to model life stage heterogeneity by decoupling the popularity level of an item under propagation from a true strength of social ties to improve inference accuracy. The proposed LSH is incorporated into almost all existing state-of-the-art network inference algorithms to improve estimation accuracy with only minimal changes in the implementation and maintaining the same running time. Additionally, NetRate, NetInf, and ConNIe are used as three examples to demonstrate the power of the proposed method. Furthermore, clustering of cascades prior to the LSH is proposed to eliminate noise, and the optimized method is termed as Clustered Life Stage Heuristic (CLSH). Extensive experiments on synthetic and real world datasets indicate that both LSH and CLSH methods significantly improve the accuracy of network inference.