Probabilistic load flow computation with polynomial normal transformation and Latin hypercube sampling

• Published in: IET generation, transmission & distribution Vol. 7; no. 5; pp. 474 - 482
• Main Authors: Cai, Defu, Shi, Dongyuan, Chen, Jinfu
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.05.2013; Institution of Engineering and Technology; The Institution of Engineering & Technology
• Subjects: Applied sciences; Computer simulation; Correlation; correlation factor; correlation matrix; Distribution functions; Electrical engineering. Electrical power engineering; Electrical power engineering; Exact sciences and technology; IEEE 118‐bus test system; IEEE 14‐bus test system; IEEE standards; Latin hypercube sampling; LHS; line flow; load flow; Miscellaneous; Monte Carlo methods; Monte Carlo simulation method; node voltage; Operation. Load control. Reliability; PNT; polynomial matrices; polynomial normal transformation; Polynomials; power injection statistical moment; Power networks and lines; probabilistic load flow computation; Probabilistic methods; probability distribution model; Probability theory; random variable; sampling methods; statistical distributions; Transformations; IEEE 14-bus test system; sampling methods; node voltage; probability distribution model; random variable; correlation matrix; statistical distributions; power injection statistical moment; line flow; polynomial matrices; Monte Carlo methods; IEEE 118-bus test system; Monte Carlo simulation method; Latin hypercube sampling; correlation factor; LHS; PNT; probabilistic load flow computation; polynomial normal transformation; IEEE standards; load flow; Correlation coefficient; Performance evaluation; Monte Carlo method; Voltage dependence; Probabilistic approach; Statistical moment; Probability distribution; Load flow; Bus system; Statistical method; Electrical network; Hypercube; Probability density function; Distribution function; Numerical simulation; Sampling; Random variable
• ISSN: 1751-8687; 1751-8695; 1751-8695
• DOI: 10.1049/iet-gtd.2012.0405

A probabilistic load flow method based on polynomial normal transformation (PNT) and Latin hypercube sampling (LHS) is proposed. The correlation between input random variables has been taken into consideration. The proposed method uses the statistical moments and correlation matrix of input random variables instead of their marginal distribution functions and joint distribution functions, which are very difficult to be obtained, to establish their probability distribution models by PNT and LHS. The statistical moments and probability distribution functions of node voltage and line flow are calculated by Monte Carlo simulation method. Performance of the proposed method is investigated using IEEE 14-bus and IEEE 118-bus test systems. The impacts of correlation factor on the statistical moments of power injections and system operation are analysed. Finally, conclusions are duly drawn.