Advanced probabilistic power flow methodology for power systems with renewable resources

Le, Duong; Nguyen, Nhi Thi Ai; Ngo, Van Duong; Berizzi, Alberto

doi:10.3906/elk-1511-302

Cited by 2 publications

(2 citation statements)

References 20 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The KTPE series with normal kernel in Table 3 is similar to Gram‐Charlier series 38 :

F ((), X) = c_{0} normalΦ ((), \frac{X - μ_{x}}{σ_{x}}) - ϕ ((), \frac{X - μ_{x}}{σ_{x}}) \sum_{k = 1}^{m} c_{k} H_{k - 1} ((), \frac{X - μ_{x}}{σ_{x}}),

where μ x and σ x are the mean and SD of X respectively, Φ(·) and ϕ (·) are the CDF and PDF of the standard normal variable, respectively. The coefficients c k ( k = 0, 1, 2, …) in Equation (12) can be determined by:

\begin{matrix} centertrue \\ c_{0} = 1, c_{1} = 1, c_{k} = \frac{μ_{k}}{k!} - {false\sum}_{s = 1}^{(⌊⌋, m / 2)} \frac{c_{k - 2 s}}{s! 2^{s}}, (k \geq 2), \\ μ_{k} = E [{(\frac{X - μ_{x}}{σ_{x}})}^{k}] . \end{matrix}

…”

Section: Kernel Tuned Polynomial Expansionmentioning

confidence: 99%

Probabilistic optimal power flow analysis incorporating correlated wind sources

Xiao

Zhou

Xiao

2020

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

Summary In this article, the Latin hypercube sampling (LHS) based probabilistic optimal power flow (P‐OPF) technique is employed to assess the performance of power systems under large wind power penetration. In the case where only wind speed samples are available, the kernel tuned polynomial expansion series are developed to recover marginal distributions of wind speeds. Because the dependence among wind speeds has a considerable impact on P‐OPF solutions, 13 Archimedean copulae are derived to represent the dependence structure of correlated wind speeds at multiple sites. The rejection sampling method and Metropolis‐Hastings algorithm are deployed to generate samples of copula models, and a midpoint LHS technique is proposed to produce correlated low discrepancy sequences for P‐OPF computation. Finally, a case study is performed on an IEEE 118‐bus system to illustrate the proposed methods.

show abstract

“…The KTPE series with normal kernel in Table 3 is similar to Gram‐Charlier series 38 :

F ((), X) = c_{0} normalΦ ((), \frac{X - μ_{x}}{σ_{x}}) - ϕ ((), \frac{X - μ_{x}}{σ_{x}}) \sum_{k = 1}^{m} c_{k} H_{k - 1} ((), \frac{X - μ_{x}}{σ_{x}}),

\begin{matrix} centertrue \\ c_{0} = 1, c_{1} = 1, c_{k} = \frac{μ_{k}}{k!} - {false\sum}_{s = 1}^{(⌊⌋, m / 2)} \frac{c_{k - 2 s}}{s! 2^{s}}, (k \geq 2), \\ μ_{k} = E [{(\frac{X - μ_{x}}{σ_{x}})}^{k}] . \end{matrix}

…”

Section: Kernel Tuned Polynomial Expansionmentioning

confidence: 99%

Probabilistic optimal power flow analysis incorporating correlated wind sources

Xiao

Zhou

Xiao

2020

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

show abstract

“…Hitherto, several statistical models have been suggested for fitting wind speed samples, such as: Weibull distribution [6, 7], Burr distribution [8], Kappa distribution [9], generalized lambda distribution (GLD) [10], Johnson system [11], Cornish–Fisher expansion [12], polynomial transformation model (PTM) [13, 14], Gram–Charlier series [15], kernel tuned polynomial expansion (KTPE) series [16], kernel density estimate method [17, 18], and Gaussian mixture model (GMM) [19, 20]. These models are summarized in Table 1, which are classified into two types: type‐I and type‐II.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic optimal power flow computation for power grid including correlated wind sources

Xiao,

Tan,

2024

IET Generation Trans & Dist

View full text Add to dashboard Cite

This paper sets out to develop an efficient probabilistic optimal power flow (POPF) algorithm to assess the influence of wind power on power grid. Given a set of wind data at multiple sites, their marginal distributions are fitted by a newly developed generalized Johnson system, whose parameters are specified by a percentile matching method. The correlation of wind speeds is characterized by a flexible Liouville copula, which allows to model the asymmetric dependence structure. In order to improve the efficiency for solving POPF problem, a lattice sampling method is developed to generate wind samples at multiple sites, and a logistic mixture model is proposed to fit distributions of POPF outputs. Finally, case studies are performed, the generalized Johnson system is compared with Weibull distribution and the original Johnson system for fitting wind samples, Liouville copula is compared against Archimedean copula for modelling correlated wind samples, and lattice sampling method is compared with Sobol sequence and Latin hypercube sampling for solving POPF problem on IEEE 118‐bus system, the results indicate the higher accuracy of the proposed methods for recovering the joint cumulative distribution function of correlated wind samples, as well as the higher efficiency for calculating statistical information of POPF outputs.

show abstract

Advanced probabilistic power flow methodology for power systems with renewable resources

Cited by 2 publications

References 20 publications

Probabilistic optimal power flow analysis incorporating correlated wind sources

Probabilistic optimal power flow analysis incorporating correlated wind sources

Probabilistic optimal power flow computation for power grid including correlated wind sources

Contact Info

Product

Resources

About