Probabilistic Computational Model for Correlated Wind Farms Using Copula Theory

Li, Bin; Shahzad, Muhammad Ali; Qi, Bing; Shoukat, Muhammad Umair; Shakeel, Muhammad; Mohammedsaeed, Elshiekh K.

doi:10.1109/access.2018.2812790

Cited by 23 publications

(16 citation statements)

References 19 publications

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“…Loads in same group is dependent but independent to other groups. The correlation between first and second group are presented in (7) and (8), respectively.…”

Section: Performance Analysis Of the Box-muller Methodsmentioning

confidence: 99%

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Probabilistic Load Flow Analysis of Power System Network Considering Uncertainty with Generation and Correlated Loads

Shahzad

et al. 2019

International Journal of Simulation: Systems, Science &Amp; Technology

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Probabilistic load flow has gain attractive attention in electric power system planning, operation, and control. Probabilistic load flow is an efficient tool to access the performance of the power system considering the uncertainties of the load demand and generation. However, future operating condition and operating criteria could not be predicted without considering uncertainty. Due to integration of renewable energy sources into power system network brought uncertainty and dependence factor. Most of the uncertainties in power system are load increment, generation scheduling, and network topology in which engineers are dealing with them. In this paper, Box-Muller sampling algorithm is proposed to solve the probabilistic load flow problems considering uncertainty with generation and correlated loads. The main advantage of the proposed approach is that accurate solution can be obtain with less computation time and can address the dependence between variables. Also, it is almost unconstrained for the probability distributions of the input random variables. The proposed method is compared with correlated simple random sampling Monte Carlo simulation. For the demonstration purpose, the proposed method is investigated using IEEE 14-bus and IEEE 118-bus test systems. The simulation results indicate that Box-Muller sampling method is a promising approach in probabilistic load flow evaluation.

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“…Loads in same group is dependent but independent to other groups. The correlation between first and second group are presented in (7) and (8), respectively.…”

Section: Performance Analysis Of the Box-muller Methodsmentioning

confidence: 99%

“…Hence, the possible output results are identified by changing the parameters. DOI [4][5][6][7]. Firstly analytical approach for PLF study, in this approach power flow equations are linearized to make working with probability function.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Load Flow Analysis of Power System Network Considering Uncertainty with Generation and Correlated Loads

Shahzad

et al. 2019

International Journal of Simulation: Systems, Science &Amp; Technology

Self Cite

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“…where φ(u i ) is the PDF of the independent standard Gaussian variable u i . Note that the f X (X) in (2) has been replaced in (6) by the product of the PDFs of independent standard Gaussian variables.…”

Section: B Nataf Transformationmentioning

confidence: 99%

“…Evidently, H (U) is approximated by n(n−1)/2 bivariate functions, n univariate functions, and a constant function. Combining (6) and (10), the central moments of Y can be expressed as follows:…”

Section: B Computing Moments Of Output Random Variablesmentioning

confidence: 99%

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Probabilistic Load Flow Based on Bivariate Dimension Reduction and Johnson System

Zhang

Yin

2020

IEEE Access

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A probabilistic load flow (PLF) is an effective tool that helps describe the uncertainty of power system operation. However, when confronting random variables with non-Gaussian distributions and highly discrete characteristics, existing PLF methods have difficulty balancing efficiency and accuracy. Therefore, a novel approach based on bivariate dimension reduction (BDR) and the Johnson system is proposed herein. BDR is used to estimate the moments of output random variables (ORVs). Because BDR considers the joint effect of input random variables, it significantly reduces the estimation error for high-order moments in particular. In addition, a strategy to improve BDR efficiency is proposed. The Johnson system is used to obtain the probability distributions of ORVs as it has better adaptability and accuracy than the series expansion method. Case studies including comparisons between this approach and others found in the literature were conducted, and the results obtained showed that the proposed method has better performance than previous approaches. INDEX TERMS Bivariate dimension reduction, Johnson system, probabilistic load flow, renewable energy source.

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