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Discrete convolution (DC) is a generally accepted approach for the probabilistic analysis such as reliability assessment and probabilistic load flow. However, it has a strong precondition that the stochastic variables being convolved must be independent, which may not be fully satisfied in all cases. Using copula functions, this letter derives the formulation of DC for dependent variables. The performance of the proposed dependent discrete convolution (DDC) is illustrated using reliability assessment involving wind power. The result shows that the DDC inherits the efficient and reliable performance of DC, indicating a promising potential for practical applications. [ABSTRACT FROM PUBLISHER]

Composite power system reliability evaluation is computationally time-consuming because the optimal power flow (OPF) with the least load curtailment is calculated for a large number of samples. Most current studies of probabilistic simulation methods focus on sampling techniques to improve the sampling efficiency and decrease the calculations of the OPF. This paper proposes a fast reliability evaluation method that accelerates the calculation of the OPF using multi-parametric linear programming (MPLP). In this paper, the sampled transmission line statuses are considered by the transmission line status dictionary (TLSD). We match the line status of each sample with the scenarios in the TLSD. For matching samples, the generation status and the sampled load are treated as MPLP parameters of the DC-OPF evaluation model. A dynamic learning algorithm is applied to solve the MPLP problem. Case studies are conducted on both IEEE Reliability Test Systems and a provincial power system in China. The results show that the proposed method improves the evaluation efficiency by 23–30 times compared with the normal DC-OPF-based model. [ABSTRACT FROM AUTHOR]

The integration of high penetration of renewable energy brings greater uncertainties for the operation of future power systems due to its intermittency and lack of predictability. The uncertainties brought by wide scale renewables might have dependencies with each other because their outputs are mainly influenced by weather. However, an analysis of such uncertainties with complex dependencies faces the “curse of dimensionality”. This challenges the power system uncertainty analysis in probabilistic forecasting, power system operation optimization, and power system planning. This paper proposes an efficient approach that is able to handle high-dimensional dependencies. The approach uses the high-dimensional Copula theory and discrete convolution method to conduct a high-dimensional dependent discrete convolution (DDC) calculation. A recursive algorithm is proposed to decompose the computation of DDC into multiple convolutions between each pair of stochastic variables so that the “curse of dimensionality” is solved. The computational complexity of the proposed method is linear with respect to the number of dimensions and guarantees computational efficiency. Finally, illustrative examples of power system reserve requirement evaluation and wind power capacity credit assessment analysis are used to verify the effectiveness and superiority of the proposed approach. [ABSTRACT FROM PUBLISHER]