发电机组的随机故障停运对电力系统潮流计算产生影响,应用传统半不变量法计算概率潮流(probabilistic power flow,PPF)将产生较大误差。提出一种考虑离散分布输入变量的半不变量法PPF计算方法。针对服从离散分布的发电机注入功率采用多...发电机组的随机故障停运对电力系统潮流计算产生影响,应用传统半不变量法计算概率潮流(probabilistic power flow,PPF)将产生较大误差。提出一种考虑离散分布输入变量的半不变量法PPF计算方法。针对服从离散分布的发电机注入功率采用多点线性化方法,减小潮流方程线性化误差。同时,引入阈值分析策略,提高计算效率。最后,综合运用A型Gram-Charlier级数和C型Gram-Charlier级数拟合状态变量的概率分布。对IEEE-RTS 24节点系统进行仿真,验证了算法的准确性和实用性。结果表明:所提PPF计算方法具有较高的精度,并保持一定的计算效率。展开更多
A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the proba...A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.展开更多
Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribut...Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980). It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and mote terms are included. Therefore the negative values will have no evident effect on the form of the whole surface elevation distribution when the series is truncated at higher orders. Furthermore, a simple recurrence formula is obtained to calculate the coefficients of the Gram-Charlier series in order to extend the Gram-Charlier series to high orders conveniently.展开更多
Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration...Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.展开更多
文摘发电机组的随机故障停运对电力系统潮流计算产生影响,应用传统半不变量法计算概率潮流(probabilistic power flow,PPF)将产生较大误差。提出一种考虑离散分布输入变量的半不变量法PPF计算方法。针对服从离散分布的发电机注入功率采用多点线性化方法,减小潮流方程线性化误差。同时,引入阈值分析策略,提高计算效率。最后,综合运用A型Gram-Charlier级数和C型Gram-Charlier级数拟合状态变量的概率分布。对IEEE-RTS 24节点系统进行仿真,验证了算法的准确性和实用性。结果表明:所提PPF计算方法具有较高的精度,并保持一定的计算效率。
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the University Network of Excellence in Nuclear Engineering (UNENE) through an Industrial Research Chair program,"Risk-Based Life Cycle Management of Engineering Systems",at the University of Waterloo
文摘A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.
基金This project was financially supported by the National Nature Science Foundation of China(Grant No.49876012,49976003)
文摘Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980). It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and mote terms are included. Therefore the negative values will have no evident effect on the form of the whole surface elevation distribution when the series is truncated at higher orders. Furthermore, a simple recurrence formula is obtained to calculate the coefficients of the Gram-Charlier series in order to extend the Gram-Charlier series to high orders conveniently.
文摘Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.
