Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions

Allan, R.N.; daSilva, A. M. Leite; Burchett, R. C.

doi:10.1109/tpas.1981.316721

Cited by 338 publications

(142 citation statements)

References 8 publications

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“…Given the system structure A, the parameters p and the generation load conditions u, the state x can be exactly determined by circuit law and power conservative constraints in (1). Based on states x, all other system states in y such as line flow can be exactly determined by (2). Both (1) and (2) can be nonlinear equations in AC power flow model.…”

Section: A Probabilistic Load Flowmentioning

confidence: 99%

“…The PLF models the uncertainties as input random variables (RV) with probabilistic density functions (PDF) or cumulative density functions (CDF). Based on load flow equations, it computes the output states as random variables with PDFs or CDFs [1] [2]. Recently, the PLF methods have been extensively used to analyze the distribution network operation and planning under uncertainties and to evaluate the impact of renewable energy resources and large stochastic loads.…”

Section: Introductionmentioning

confidence: 99%

“…The solution methods generally fall into two categories: the analytical methods and Monte Carlo simulation (MCS) based methods [6]. Most analytical methods are trying to compute the output RVs by simplifying power system models or probabilistic models [2] [6]. Due to the simplification, analytical methods may not be able to handle uncertainties with large variance or systems with large nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

“…In [2] and [8], a linearization and multilinearization model is used for MCS solutions. In [9], a deterministic sampling method is used to speed up the transmission stochastic load flow.…”

Section: Introductionmentioning

confidence: 99%

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A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow

Cui

Franchetti

2013

2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT)

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Abstract-Monte Carlo simulation (MCS) is a numerical method to solve the probabilistic load flow (PLF) problem. Comparing to analytical methods, MCS for PLF has advantages such as flexibility, general purpose, able to deal with large nonlinearity and large variances, and embarrassingly parallelizable. However, MCS also suffers from low convergence speed and high computational burden, especially for problems with multiple random variables. In this paper, we proposed a QuasiMonte Carlo (QMC) based method to solve the PLF for radial distribution network. QMC uses samples from low-discrepancy sequence intended to cover the high dimension random sample space as uniformly as possible. The QMC method is particularly suitable for the high dimension problems with low effective dimensions, and has been successfully used to solve large scale problems in econometrics and statistical circuit design. In this paper, we showed that the PLF for radial distribution system has the similar properties and can be a good candidate for QMC method. The proposed method possesses the advantage of MCS method and significantly increases the convergence rate and overall speed. Numerical experiment results on IEEE test feeders have shown the effectiveness of the proposed method.

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Section: A Probabilistic Load Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [2] and [8], a linearization and multilinearization model is used for MCS solutions. In [9], a deterministic sampling method is used to speed up the transmission stochastic load flow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow

Cui

Franchetti

2013

2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT)

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show abstract

“…One of the alternatives is the convolution of the PDF of the random variables involved, when they are independent of each other, and linearly related. Although this reduces the computational burden, it is costly to obtain the PDF of a line when several random power injections are considered even if Fast Fourier Transform (FFT) [5] techniques are used. Convolution techniques and FFT were also used in [6] for distribution networks with wind energy, where a simplified estimate of the PDF for short term wind power prediction was made.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic load flow in systems with wind generation

Usaola

2009

IET Gener. Transm. Distrib.

148

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Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Laowanitwattana

Uatrongjit

2020

Int Trans Electr Energ Syst

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Summary An increasing penetration of renewable energy sources, such as solar farms and wind farms, necessitates a usage of statistical analysis and modeling for efficient operation and planning of the power systems. The probabilistic power flow (PPF) analysis based on the generalized polynomial chaos expansion (gPCE) technique has been applied to investigate the effects of random parameters in the power system network. Nevertheless, the gPCE‐based methods can be applied to the systems whose random parameters belong to specific probability distributions. If there exists a correlation among random parameters, then a decorrelation technique, for example, a copula function, is required. In this paper, a new approach for PPF analysis based on the arbitrary polynomial chaos expansion (aPCE) has been proposed. A set of basic polynomial functions used in this method is constructed using the recorded dataset of random parameters. The dependency of these uncertain parameters is decoupled by the whitening transformation. Instead of applying the aPCE to the required power system responses such as active power flow, current magnitude, etc, the proposed method uses the aPCE to construct a surrogate model of each bus voltage phasor. The bus voltage phasor model can then be employed to compute other power system responses without performing power flow analysis of the original power system. The proposed technique has been implemented and demonstrated in a MATLAB environment. On the basis of the numerical experiments with the modified IEEE 14‐bus and 118‐bus systems, the results indicate that the proposed method can achieve better accuracy and use less computation time than the techniques based on the gPCE with Gaussian copula function.

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Evaluation Methods and Accuracy in Probabilistic Load Flow Solutions

Cited by 338 publications

References 8 publications

A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow

A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow

Probabilistic load flow in systems with wind generation

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

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