Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions

By Antony Schellenberg, William D. Rosehart, J. Aguado. IEEE Transactions on Power Systems, 2005

288 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Safety, Risk, Reliability and Quality, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/38a3fc63c4ad8516288c62d93d15f5d88663a772

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Citations in the corpus

Probabilistic load flow in systems with wind generation (2009, methodology): “The use of cumulants and the approximation of a PDF by orthogonal series (Gram-Charlier A expansion series or Laguerre polynomials [14]) have also been recently proposed for the probabilistic power flow [15], with discrete distributions [16], or for the probabilistic optimal power flow [17].”
Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies (2009, methodology): “The main steps in the cumulant-based P-OPF are as follows [3], [7], [10]: 1) Solve the cost minimization problem assuming the mean value of the loads, i.”
Economic Load Dispatch Constrained by Wind Power Availability: A Here-and-Now Approach (2010, methodology): “This type of problem was commonly referred to as the probabilistic load flow problem [4] and an extension was called the probabilistic optimal power flow (P-OPF) problem [5].”
Chance Constrained Programming for Optimal Power Flow Under Uncertainty (2011, methodology): “[5] used a cumulant method to address the POPF problem.”
Probabilistic Load Flow Evaluation With Hybrid Latin Hypercube Sampling and Cholesky Decomposition (2009, methodology): “Apart from the direct discrete convolution method, there are alternative methods including as the fast Fourier transform method [5], Von Mises method [7], [8], and cumulant method combined with Gram–Charlier expansion [9], [10].”
Probabilistic Optimal Power Flow Considering Correlations of Wind Speeds Following Different Distributions (2014, methodology): “The cumulant method (CM) [7] assumes that the cumulants of power generation costs, bus voltages and branch powerflows are the approximately linear functions of the cumulants of input variables.”
Analysis of Probabilistic Optimal Power Flow Taking Account of the Variation of Load Power (2008, methodology): “The uncertainties in system load are typically modeled as probabilistic in the POPF problem [2]–[5].”
Probabilistic Optimal Power Flow in Electricity Markets Based on a Two-Point Estimate Method (2006, methodology): “Therefore, in this paper, the comparisons are made using the corresponding mean and standard deviation of the 2PEM and MCS results, respectively, as in [2], which works reasonably”
A Novel Affine Arithmetic Method to Solve Optimal Power Flow Problems With Uncertainties (2014, methodology): “Furthermore, in [11] the Cumulant method is used to solve the P-OPF problem using the logarithmic barrier Interior Point method and the results for variable load are compared using Gaussian distribution and Gamma distribution.”
A Novel Probabilistic Optimal Power Flow Model With Uncertain Wind Power Generation Described by Customized Gaussian Mixture Model (2016, unknown): “problem, and several typical approaches to compute P-OPF include two-point estimation [6], first-order second moment method [7], [8], cumulant method [9], [10], and so on.”